ALPINE BIOGEOCHEMICAL MODELING: CASE STUDIES, IMPROVENOENTS, AND PARAMETER ESTIMATION by Thomas Meixner

ALPINE BIOGEOCHEMICAL MODELING: CASE STUDIES, IMPROVENOENTS,  AND PARAMETER ESTIMATION by Thomas Meixner

ALPINE BIOGEOCHEMICAL MODELING:

CASE STUDIES, IMPROVENOENTS, AND PARAMETER ESTIMATION by

Thomas Meixner

A Dissertation Submitted to the Faculty of

HYDROLOGY AND WATER RESOURCES

In Partial Fulfillment of the Requirements

For the Degree of

DOCTORATE OF PHILOSOPHY

WITH A MAJOR IN HYDROLOGY

In the Graduate College

THE UNIVERSITY OF ARIZONA

1999

2

THE UNIVERSITY OF ARIZONA 8

GRADUATE COLLEGE

As members of the Final Examination Committee, we certify that we have read the dissertation prepared by

Thomas

Meixner entitled Alpine Biogeochemical Modeling:

Case Studies, Model Improvements, and Parameter

Estimation and recommend that it be accepted as fulfilling the dissertation requirement for the Degree of

Doctor of Philosophy

Date

.476%

Date

9-1/1

Date

(7 2_

3

-

1

/

Date

r

D t

Dr. Eric Betterton

Final approval and acceptance of this dissertation is contingent upon the candidate's submission of the final copy of the dissertation to the

Graduate College.

I hereby certify that I have read this dissertation prepared under my direction and recommend that it be accepted as fulfilling the dissertation requirement.

Dissertation Director

Date

This dissertation has been submitted in partial fulfillment of requirements for an advanced degree at the University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the library.

Brief quotations from this dissertation are allowable without special pennission, provided that accurate acknowledgement is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his or her judgment the proposed use of the material is in the interests of scholarship. In all other instances, however peiiiiission must be obtained from the author.

3

SIGNED:

4

ACKNOWLEDGEMENTS

This work would not have been possible without the aid and support of a large number of fellow researchers including: James

Sickman,

John

Melack,

Al

Leydecker,

Walter Rosenthal, Ben Balk, Francisco Rojas, Mark Williams, Jill Baron, Don Campbell,

Don Cline, David Clow, Kelly Elder, Paul Brooks,

Soroosh Sorooshian, Hoshin

Gupta, and Luis

Bastidas.

I also wish to thank the calibration research group at the University of

Arizona for the camaraderie and creativity they inspired. Most importantly I wish to thank my adviser Roger Bales whose encouragement of independence of thought enabled me to pursue cutting edge research for my dissertation. Ray Brice is to be thanked for his assistance in manuscript preparation and general computer guru status. This work would also not have been possible without the financial support of Canon USA through the

Canon National Park Science Scholarship program. The National Park Service, National

Park Foundation and the American Association for the Advancement of Science are all to be thanked for their participation in the Canon National Park Science Scholars program.

Gary

Machlis

and Michael Soukup are also to be thanked for their creativity and support for the Canon Scholars program through its early years. The National Park Service is to be thanked for its years of support for research on alpine watersheds in the western

United States; without data from that research this dissertation would not have been possible. My dissertation work was also supported by the National Science Foundation through a Graduate Research Fellowship and an

EGB

grant

(#

EAR-9523886

)

and by

NASA through its

EOS-IDS

program

(NAGW-2602 ).

I also wish to thank my sisters and my parents for their many visits to Tucson. I owe a large debt of gratitude also to my wife Kathleen without whose love and support the completion of this dissertation would have been difficult. I also owe a large debt of gratitude to

Dr.

Michael Stewart,

Dr.

Richard Rosenberg, and the capable staff of Tucson Medical Center without whose medical skill and care I would not have been around to complete this dissertation.

To my

parents,

who, at

an

early

age,

instilled

in me a love of

knowledge

and the

persistence to pursue

it.

5

TABLE OF CONTENTS

LIST OF FIGURES

LIST OF TABLES

ABSTRACT

I. INTRODUCTION

1.1 Alpine Hydrochemic

al Model

Description

1.2 Dissertation Format

1.3

Transporting AI-1M to Other Watersheds

13

14

2

1.4

Nitrogen Cycling

in Alpine

Catchments

1.5

Multi-Criteria Parameter

PRESENT STUDY

Estimation

18

20

2.1

Summary

of

Paper

#1: Importance of Biogeochemical

Processes

in

Modeling

Stream

Chemistry

in

Two Watersheds

in the Sierra Nevada,

California

2.2

Summary

of

Paper

#2: Stream

Chemistry Modeling

of

Two Watersheds

in the

20

15

16

17

9

11

12

Front Range, Colorado

2.3

Summary

of

Paper

#3 A

Nitrogen Dynamics Model

for Alpine Basins

23

26

2.4

Summary

of

Paper

#4:

Sensitivity Analysis Using

Mass Flux and Concentration

28

2.5

Summary

of

Paper

#5:

Multi-Criteria Parameter

Estimation for Hydrochemical

Models

31

3 CONCLUSIONS 34

APPENDIX

A - IMPORTANCE OF BIOGEOCHENMICAL

PROCESSES

IN

MODELING

STREAM

CHEMISTRY

IN

TWO WATERSHEDS

IN THE SIERRA

NEVADA,

CALIFORNIA

42

A.1 Introduction

45

46

A.2

Methods

A.2.1

Site

A.2.2

Sample

Collection

A.2.3

Model

46

46

47

A.2.4

Model Calibration

and

Evaluation

47

A.3

Results

A.3.1

Water

Balance

48

48

A.3.2

Precipitation Chemistry

49

A.3.3

A.3.4

Solute

Concentrations and

Nitrogen

Mass Balance

Ionic

Pulse

49

50

A.3.5

Watershed

1

Calibration

and

Evaluation

51

A.3.6

Watershed

A.3.7 Sensitvity

2

Calibration

and

Evaluation

51

52

6

TABLE OF CONTENTS - CONTINUED

A.4 Discussion

A.4.1 Water Balance

A.4.2 Base Cation and ANC Production

52

52

53

A.4.3 Nitrogen Cycling

A.4.4 Sensitivity to Changes in Loading

A.4.5 AHM Model Structure and Parameters

54

55

55

A.5 Conclusions

56

APPENDIX B - STREAM CHEMISTRY MODELING OF TWO WATERSHEDS IN

THE FRONT RANGE, COLORADO

B.1 Introduction

B.2 Methods

B.2.1 Site

B.2.2 Model Structure

B.2.3 Model Inputs

B.2.4 Parameter Estimation and Initial Conditions

B.2.5 Calibration

58

62

64

64

65

66

68

69

70 B.3 Results

B.3.1 Green Lakes Valley

B.3.2 Andrews Creek

B.4 Discussion

70

72

B.4.1 Model Performance

B.4.2 Base Stauration and pH

73

73

76

B.4.3 Nitrogen Dynamics

B.4.4 Flow Routing

B.4.5 Sensitivity to Deposition

B.5 Conclusions

77

78

79

81

APPENDIX C -A NITROGEN DYNAMICS MODEL FOR ALPINE BASINS .... 106

C.1 Introduction

C.2 Model Description

D.2.1 Soil Carbon Model

109

111

112

D.2.2 Soil Nitrogen Model

D.2.3 Plant Growth Model

C.3 Case Study

C.4 Results

C.5 Discussion

C.6 Conclusions

APPENDIX D - SENSITIVITY ANALYSIS USING MASS FLUX AND

CONCENTRATION

115

115

117

119

121

124

138

7

TABLE OF CONTENTS

- CONTINUED

D.1 Introduction

D.2 Methods

D.2.1 Site

D.2.2 Model

D.2.3 Monte-Carlo Simulation

D.2.4 MOGSA

D.3 Results

D.4 Discussion

D.4.1 Reasons for Different Information Content

D.4.2 Information About Natural Processes

D.5 Conclusions

APPENDIX

E - MULTI-CRITERIA PARAMETER ESTIMATION FOR

HYDROCHEMICAL MODELS

El Introduction

E.2 Methods

E.2.1 Multi-Criteria Parameter Estimation Methodology

E.2.2 MOCOM-UA

E.2.3 Site Description

E.2.4 Model

E.2.5 Applying MOCOM-UA to ARM

E.3 Results

E.4 Discussion

E.5 Conclusions

APPENDIX

F SOURCE CODE FOR A NITROGEN MODEL FOR ALPINE

WATERSHEDS (ANIMAL)

REFERENCES

178

179

180

182

185

188

170

173

176

178

178

142

143

143

143

145

146

148

149

150

152

153

208

239

8

9

LIST OF FIGURES

Figure

1.1,

Schematic of

AHM

Model of Emerald Lake

Figure

Figure

A.1,

Map of both watersheds.

A.2,

Modeled watershed compartments:

15

46

47

Figure

A.3,

Seasonal precipitation chemistry and hydrologic mass balance for

1992

and

1993 48

Figure

A.4,

Watershed

1

results

49

Figure

A.5,

Watershed

2

results

50

Figure

A.6,

Ratio of stream concentrations to bulk snow concentrations for each watershed with fraction of flow as independent variable for

1992

Figure

A.7,

Comparison of modeled and measured soil chemistry for Watershed

1

Figure

A.8,

Comparison of modeled and measured soil chemistry for Watershed

2

Figure

A.9,

results for doubling wet deposition using

1992

data and calibration for both watersheds

53

50

52

53

Figure

B.1,

Land cover map for Green Lakes Valley watershed

Figure

B.2,

Land cover map for Andrews Creek watershed

97

98

99

Figure

B.3,

Modeled watershed compartments

Figure

B.4,

Annual average volume weighted mean precipitation chemistry for

GLV4

and Andrews for

1994

and

1996

Figure

B.5,

Modeled

GLV4

inflow and measured stream chemical concentrations

Figure

B.6,

Observed and modeled stream chemical concentrations for the Andrews

100

101

Creek

Figure

B.7,

Nitrogen reactions and effects for models of both watersheds.

Figure

B.8,

Sensitivity of Green Lake

4

model to doubled wet deposition

Figure

B.9,

Sensitivity of Andrews Creek watershed model to doubled wet deposition

102

103

104

chemistry

Figure

C.1,

Carbon box diagram

105

133

Figure

Figure

C.2, N

soil organic matter flows

C.3,

Grass growth model diagram.

134

135

Figure

C.4,

Modeled and measured

30

day mean air temperature for Emerald

Lake 136

Figure

C.5,

Modeled and observed

NO3

-

concentrations for the Emerald Lake watershed.

137

Figure

Figure

D.1,

Elevation map of

ELW

D.2,

Soils map of

ELW

164

165

Figure

D.3, AHM

representation of the Emerald Lake watershed broken down into rock, talus, soil, stream and lake subunits.

166

Figure

D.4,

Measured and modeled concentration results for

Wolford

parameters

[from

Wolford et

al.,

1996],

for

1986

and

1987

water years.

167

10

LIST OF FIGURES

-

CONTINUED

Figure

D.5,

Measured and modeled mass flux results for

Wolford

parameters [from

Wolford et al.,

1996],

for

1986

and

1987

water years.

168

Figure

D.6,

Number of simulations versus number of sensitive parameters for ANC and

Na

for

50% quantile,

cc of

0.05

and

50

bootstraps.

169

Figure

E.1,

Simple demonstration of Pareto set in a two parameter three criteria situation

196

Figure

E.2,

Schematic of

AHM

model of Emerald Lake.

197

Figure

E.3,

Improvement in

RMSE

and simulations with search population size with discharge,

Ca

2+

, SO4

2-

,

and

Cl

-

as criteria.

198

Figure

E.4,

Parameter space and criteria space results for

MOCOM-UA

runs for Emerald

Lake using discharge,

H

+

, Ca

2+

, SO4

2-

,

Si and

NO3

-

as criteria.

199

Figure

E.5,

Parameter and criteria space results for

6

criteria using a mix of mass flux and concentration as the criteria (noted in red box)

200

Figure

E.6, 6

Parameter and Criteria space results for

MOCOM-UA

runs using

4

criteria as noted with red boxes on bottom

x

axis.

Figure

E.7,

Parameter and criteria space results for

MOCOM-UA

search with

4

criteria

201

using a mix of mass and concentration criteria as noted on bottom

x

axis by boxes in red.

202

Figure

E.8,

Parameter and Criteria space results from pushing

250

sets of random parameter values within the feasible parameter set through the

AHM 203

Figure

E.9,

Time series results for discharge, calcium, chloride and sulfate using Pareto solutions with six previously identified concentration criteria (Figure

4) 204

Figure

E.10,

Time series results for discharge, ANC, silica and nitrate with the same

Pareto solutions used as in Figure

Figure

7.

9. 205

Figure

E.11,

Time series results for driving

AHM

with

250

Pareto results as depicted in

206

Figure

E.12,

Time series results for driving

AHM

with

250

Pareto solutions as shown in

Figure

7.

Discharge, ANC, silica and nitrate shown.

207

11

LIST OF TABLES

Table

A.1,

Watershed Characteristics

Table

A.2,

Dissolved Inorganic Nitrogen

Budgets

Table

A.3,

Target Runoff

Concentrations

Table

A.4,

Final

Parameter

Values

Table

B.1,

Soil Physical Properties

Table

B.2,

Mineral Weathering

Rates

Table

B.3,

Soil Chemical Properties

Table

B.4,

Fitted Parameter

Values

Table

B.5,

Nash-Sutcliffe

values for Green

Lakes

Valley

4

47

50

51

51

87

88

89

90

92

Table

B.6,

Nash-Sutcliffe

values for Andrews

Creek watershed

Table

B.7,

Concentration Changes

with Doubling

of

N

Deposition

93

94

Table

C.1,

Ecosystem Components

as

Modeled

for

Emerald

Lake

Table

C.2,

Ecosystem Processes

as

Modeled

for

Emerald

Lake

131

132

Table

D.1,

Parameters Varied

and Range Relative

to

Values

by

Wolford

et al.

[1996] 159

Table

D.2,

Parameter Sensitivity

for Concentrations

at

2000

Simulations

161

Table

D.3,

Parameter Sensitivity

for Mass

at

2000

Simulations

162

Table

E.1,

Parameters Varied

and Range Relative

to

Values

by

Wolford

et al.

[1996] 194

ABSTRACT

The geochemical, biogeochemical, and hydrologic controls on the stream chemical composition of alpine watersheds were investigated using the Alpine Hydrochemical

Model (AHM). This model was successfully applied to the Emerald Lake watershed and two nearby watersheds as well as two watersheds in the Rocky Mountains, Andrews

Creek and the Green Lakes Valley. The results reveal that snowmelt in alpine watersheds must come into contact with either soil, sub-talus, or reactive bedrock surfaces to explain the geochemistry observed in alpine lakes and streams. These materials do not differ geochemically but they do differ in their influence on the amount of mineral nitrogen observed in alpine lakes and streams. Improvements to the carbon-nitrogen dynamics portion of the ARM indicate that the Emerald Lake watershed is nearing nitrogen saturation. A robust multi-criteria sensitivity analysis technique was used to determine what processes were important for simulating the observed stream chemical composition.

This sensitivity analysis revealed that concentration and mass flux representations of stream chemical composition contain different information about the watershed. The sensitivity analysis results were used to guide a multi-criteria parameter estimation algorithm. The results showed that stream chemical data is useful in discerning the importance of different processes and the role they play in determining stream chemical composition.

12

1.

INTRODUCTION

The thin soils, limited vegetation, and snow-dominated hydrology of alpine catchments limit their ability to buffer against changes in climate and atmospheric deposition [Melack and Stoddard,

1991].

In the Sierra Nevada of California or the Front

Range of Colorado, predictions about the response of alpine watersheds have implications for air quality, emissions standards and the health of aquatic resources.

Changes in emissions standards or the degradation of lakes and streams will have important implications for the industries affected by these policy decisions

[Takemoto et al.,

1995].

A method for improving our understanding of how alpine watersheds will respond to perturbations is to simulate that response using an integrated watershed model.

Simulating alpine watershed response to perturbations in climatic and

biogeochemical

inputs has three parts:

i)

the model used must have the proper structure,

ii)

a precise and accurate estimation of the parameters used in the model must be made,

iii)

changes in inputs to the model must be realistic.

Many stream chemical models exist for predicting stream chemical composition.

These models have been developed over the last several decades with particular interest in the problems of catchment acidification

(

e.g. [Cosby

et al.,

1985;

Wolford et al.,

1996])

and nutrient dynamics

(

e.g.

PNET

[Aber and Federer,

1992]

and CENTURY

[Parton et al.,

1987]).

13

The Alpine Hydrochemical Model (AHM) was developed specifically for the study of alpine watersheds[Wo/ford et al., 1996]. Current simulations using the AHM have problems in each of the areas outlined above: i) the structure of the nitrogen model

14 is too simple to extend simulations beyond current conditions, ii) existing parameter estimation techniques for the ARM do not take advantage of all the information available in the data, and iii) simulations of perturbed conditions have not been of realistic length and perturbations of precipitation have not been realistic. This dissertation developed and executed methods that will improve our ability to simulate alpine stream chemistry under perturbed conditions by improving our understanding of the natural processes that determine watershed response to changes in hydrologic and biogeochemical conditions.

1.1

Alpine

Hydrochemical

Model Description

The ARM

[Wolford

et al., 1996] is a daily time-step lumped/distributed model designed specifically for the hydrology and biogeochemistry of alpine watersheds. The model consists of multiple subunits representing different land classifications (rock, soil, talus, stream, lake.) Each subunit contains different compartments representing the snowpack, surface runoff, interception by trees and litter, soil horizons, surface runoff, streamflow, ice, epilimnion and hypolimnion (Figure 1.1). The model produces daily time step output of cations, anions, acid neutralizing capacity (ANC), pH, silica, and volumetric discharge.

15

Figure 1.1 Schematic of AHM Model of Emerald Lake Watershed. A) Precipitation inputs and output of evapotranspiration from subunits. B) Snowmelt runoff from the rock subunit is distributed equally to the soil and talus subunits. C) Surface runoff and subsurface drainage from the soil and talus subunit is routed to the stream.

D)

The stream flows into the lake. E)

Lake outflow is the discharge from the basin.

1.2

Dissertation Format

This dissertation contains several publications as part of its format. Five papers are included in the appendix with a description of each paper included in Chapter 2.

Each of these papers contributes to at least one of the four questions identified below:

1) How transportable is the ARM outside of the Emerald Lake watershed?

2) How sensitive is the Emerald Lake watershed to nitrogen saturation?

3) What is the temporal and quantitative importance of mineral weathering and cation exchange as the source of alkalinity for the Emerald Lake Watershed?

4) What information do the various calibration criteria contain and how should these criteria be chosen in conducting parameter estimation using a stream chemical model?

16

1.3 Transporting AHM to Other Watersheds

Prior to this research the ARM had only been applied to the Emerald Lake watershed. Applying the model to other watersheds should enable us to investigate how robust the model is at representing the processes controlling alpine stream chemistry. For this research the

AHM

was applied to two small watersheds (less than

0.5

ha) approximately

3

km from the Emerald Lake watershed

[Meixner et al.,

1998]

(Appendix

A). The

AHM

was also applied to the Green Lakes and Andrews Creek watersheds in the Rocky Mountains, Colorado

[Meixner et al.,

1999a]

(Appendix

B).

These applications of the ARM were used to investigate the ability of ARM to describe the

biogeochemical

processes and to investigate which processes control stream chemical composition in these catchments.

1.4

Nitrogen Cycling

in Alpine

Catchments

Many processes control nitrogen cycling in alpine watersheds. Nitrogen is an essential nutrient for biomass; hence biological processes transform nitrogen into different states, storing it and making it available for biota. These processes include mineralization, immobilization, nitrification, denitrification, and uptake [Parton

et al.,

1987;

Aber,

1992; Parton

et

al., 1993]. These transformations also affect the acid-base status of natural waters [Schindler

et

al., 1985; Henriksen

and

Brakke, 1988]. Currently

AHM can eliminate or create ammonium and nitrate in natural waters without regard to nutrient demand or excess present in the basin [Wolford

et

al., 1996]. This structure does not permit the modeling of chronic processes involving the nitrogen cycle like nitrogen saturation

[Aber et

al., 1989;

Aber et

al., 1998], the process where nitrogen accumulates in an ecosystem converting it from a nitrogen sink to a nitrogen source. This change can weaken an ecosystem and increase the acidity of its waters [Henriksen

and Brakke,

1988]. The current structure is in contrast to the process oriented structure of the

CENTURY model [Parton

et

al., 1987] or the BIOME-BGC model [Running

and

Gower, 1991], which allows modeling of chronic processes. A robust carbon-nitrogen cycling model was built that used AHM hydrologic output to investigate the effect on carbon-nitrogen dynamics of various scenarios of nitrogen deposition and representations of alpine hydroclimatology (Appendix C).

17

1.5 Multi-Criteria Parameter Estimation

Available parameter estimation techniques for watershed models are subjective.

They use a weighting scheme or the modelers judgment to equate the goodness of fit for different species with each other. An objective parameter estimation technique for the

ARM is necessary. Past parameter estimation attempts using the

AHM

at Emerald Lake have had two problems. One is the technique used to estimate the parameters, while the other is the time scale over which parameters were estimated. Some applications of ARM have used manual techniques to estimate model parameters [Wolford et al.,

1996].

Ohte and Bales

[1995]

also applied the ARM to the Emerald Lake watershed

(ELW)

using an automatic technique based on Chang and Delleur

[1992].

Both of these techniques ignore the multi-criteria nature of parameter estimation of

hydrochemical

models. Fitting

AHM

output to measured stream chemistry is fundamentally a multi-criteria problem, with each species representing an objective function. Weighting removes each species as a target and instead lumps all objectives into one, thus ignoring the differences between chemical species.

Current estimation techniques ignore the importance of long-term processes such as nitrogen transformations and base cation depletion on parameter values. Nitrogen cycling in a watershed is subject to a process known as nitrogen saturation, which is controlled by biological processes in a watershed and may take years to decades to exert a significant influence on stream chemistry [Stoddard,

1994].

Cation depletion is the

18

process where the removal of cations from the cation exchange complex occurs more quickly then they are replaced by mineral weathering. This process is gradual and takes years to manifest its effect on stream chemistry [Likens

et al.,

1996].

Since, both of these

19

processes require long time series of data to properly estimate model parameters a data record longer than one year should be used.

Two papers have grown out of the use of multi-criteria parameter estimation methods in conjunction with the

AHM.

The first of these, "Mass Flux and Concentration

Sensitivity Analysis", [Meixner

et al.,

1999b]

(Appendix D) dealt with applying sensitivity analysis techniques developed by [Spear

and

Homberger,

1980]

as extended by [Bastidas,

1998]

to the

AHM

model of Emerald Lake [WoIford

et al.,

1996].

Hydrological Processes has accepted this paper. The sensitivity analysis results revealed the importance of several natural processes in controlling stream chemical composition in alpine watersheds.

The second of these papers, "Multi-Criteria Parameter Estimation for

Hydrochemical

Models", involved applying the

MOCOM-UA

algorithm [Yapo,

1996]

to the

AHM

model of the Emerald Lake watershed. The particular questions being asked pertained to the proper selection of criteria for calibration of

hydrochemical

models. The results indicate that the minimum number of criteria should be selected and that the results of the sensitivity analysis may provide some useful information about which criteria to select. This remains an area of ongoing research.

20

2 PRESENT STUDY

The methods, results, and conclusions of my research are presented in five appendices attached to this dissertation. The following is a summary of the most important findings of these papers.

2.1 Summary of Paper #1: Importance of Biogeochemical Processes in Modeling

Stream Chemistry in Two Watersheds in the Sierra Nevada, California

This paper was part of a larger project to describe the biogeochemical and hydrologic processes that control stream chemistry in alpine basins. In particular the importance of areas of soil and bare rock on the geochemistry of alpine watersheds was investigated. The study centered around a two year field campaign in 1992 and 1993 that involved weekly measurements of snow depth, density and chemical composition, monitoring of soil water chemistry, meteorology, and stream chemical composition and discharge. Two watersheds were monitored that differed significantly in the fraction of each watershed that was covered by soil. Watershed 1 was 26% soil covered, while watershed 2 was 10% soil covered. These watersheds were located approximately 3 km from the Emerald Lake watershed in Sequoia National Park, California (36

°

36' 30" N

118

°

39' 55" W, elevation 2960 m). The initial measurements for 1992 were used to

systematically calibrate the ARM to each watershed. The calibrated models were then evaluated with the 1993 field data. The calibrated models were also compared to reveal

21 the differences in process between the two watersheds. The major findings of this study follow.

(1) The

AHM is

transportable.

This paper was the first application of the AHM outside the Emerald Lake watershed.

The calibration and evaluation showed the ARM to be able to represent the biogeochemical processes controlling stream chemical composition in these two watersheds. This result confirms that the conceptual structure chosen for the AHM is robust enough to be applied to other watersheds.

(2) Developed manual calibration methodology

for

AHM.

A four step general methodology for calibrating the ARM in particular and stream chemistry models in general to different watersheds was outlined as:

1) Snowmelt optimization

2 Chemical calibration a) Set soil pore water chemistry based on low flow conditions at end of melt season.

b) Adjust soil base saturation to match soil pH to late season observed stream pH.

c) Adjust exchange coefficients for each cation to match soil concentrations d) Adjust snowpack elution parameters to match observed ionic pulse for CL

3) e) Adjust sulfate adsorption parameters to match expected soil concentrations and observed stream concentrations f) Calibrate nitrogen parameters to match observed nitrate and ammonium concentrations

Adjustment of hydrologic parameters

4) Changes in model structure

22

(3) Flow

routing

in alpine

catchments

Despite the very small soil coverage on watershed 2 it was still necessary to route snowmelt through a soil subunit in order to have the model simulate the observed stream chemistry of the rock dominated watershed. This along with similar results at Emerald

Lake

[Wolford

et al., 1996] points in the direction that snowmelt must come in contact with soil or soil like material in alpine watersheds.

(4) Exposed bedrock

surfaces are

reactive.

Due to the lack of soil on watershed 2 the results also indicate that areas of exposed bedrock in alpine watersheds are capable of contributing to the buffering capacity of alpine watersheds to changes in acid deposition. This result supports the conclusions of other researchers

[Rueslatten

and Jorgensen, 1978;

Abrahamsen

et al., 1979; Dahl et al.,

1979; Allan et al., 1993; Clow and Mast, 1995].

(5)

Areas of exposed rock were a larger sink for nitrogen than areas of soil.

Areas mapped as exposed rock appear to be nitrate (as well as nitrogen) sinks in alpine watersheds. There was more nitrate export from watershed 1 than watershed 2 indicating that during snowmelt areas of soil and vegetation are possibly sources of nitrate export.

Areas of exposed bedrock, possibly due to litter fall from the previous growing season gathering in hydrologically important cracks and crevices providing a carbon source for microbes, act as a nitrate sink as evidence by the smaller nitrate export on watershed 2 as opposed to watershed 1.

23

2.2

Summary of Paper

#2:

Stream Chemistry Modeling of Two Watersheds in the

Front Range, Colorado

We extended the use of the AHM to the Andrews Creek and Green Lakes Valley watersheds in the Front Range of the Rocky Mountains, Colorado. The two watersheds differed dramatically in the spatial distribution of soil and talus area. In Andrews Creek talus fields dominated the valley bottom, while in the Green Lakes Valley soil dominated the valley bottom. Both watersheds have comprehensive data sets describing their geology, soils, vegetation, meteorology, water quality and hydrology. Good snow covered area time series existed for both 1994 and 1996 for both watersheds. The 1994 data for each watershed were used for model calibration and the 1996 data were used to

evaluate that calibration procedure. The calibration followed the procedure as outlined in

[Meixner

et al.,

1998].

A summary of the major findings of this paper follows.

24

(1) The

AHM is

applicable

outside

of the Sierra Nevada.

The calibration of the each of these watersheds resulted in very good modeling of the stream chemical composition of each of these watersheds. These two watersheds with significantly different climate and geology from the Sierra Nevada represented a difficult test for the

AHM

to pass. This result indicates that the structure chosen for the

AHM

is robust and easily applicable in locations well beyond the Sierra Nevada.

(2) Further

validation of

our methodology

of

using

spatial data and

then limited calibration to estimate model parameters.

The calibration and evaluation procedure we used resulted in good simulations of stream chemistry in each of these watersheds with only a minimum number of parameters adjusted. Now that

4

watersheds have been modeled with this procedure it should be used in applying the ARM to other watersheds.

(3)

Soil

base saturation

measurements

in the Green

Lakes

Valley are

higher than indicated by observed stream chemistry.

In calibrating the

AHM

model of the Green Lakes Valley the partial pressure of carbon dioxide in the stream was raised from the atmospheric value of

10

-3.4

to 103 1 atm this

change indicates that the modeled soil base saturation was too high. The measurements

25 we relied on for the Green lakes Valley were taken during 1985. The lower percent base saturation indicated by these results means either the original measurements were not accurate or that the Green Lakes Valley has undergone cation depletion due to acid deposition over the last 15 years

[Caine

and

Thurman,

1990;

Williams et

al.,

1996].

(4) Snowmelt

in alpine basins contacts soil or talus sufficiently long to undergo

geochemical

transformation.

Despite the dominance of exposed bedrock and little true soil in alpine basins, stream chemical composition in these catchments indicates that snowmelt must be contacting soil or soil like material in the sub-talus and reacting with it. For species that are not biotically important (i.e. Ca

2+

, Na, etc.) it does not make a difference if the snowmelt contacts soil or talus.

(5) Nitrogen dynamics are significantly different between areas of soil and areas of talus.

Andrews Creek where talus was dominant had significantly more nitrate export, especially during spring snowmelt, than the Green Lakes Valley. Independent parameterization of flow routing in alpine watersheds is necessary because of the differences in nitrate export for areas of soil and talus.

2.3 Summary of Paper #3 A Nitrogen Dynamics Model for Alpine Basins

Increased atmospheric deposition of nitrogen to alpine and remote wilderness watersheds may have deleterious effects on terrestrial and aquatic ecosystem health

[Fenn et al.,

1998].

The complexities of terrestrial carbon nitrogen dynamics prevent the

26

use of simple cause and effect relationships for the increase in atmospheric deposition of nitrogen and changes in terrestrial carbon and nitrogen pools as well as the increased export of mineral nitrogen from a catchment. To aid in the investigation of carbon nitrogen dynamics in alpine catchments the CENTURY algorithm, developed by [Parton

et al.,

1987;

Parton et al.,

1988;

Parton et al.,

1993]

for simulating carbon-nitrogen dynamics in alpine watersheds, was adapted for use in alpine watersheds. This improvement, eventually designed to be incorporated into the

AHM

model, will replace the currently inadequate nitrogen dynamics structure as can be seen by the results of the previous applications of the

AHM

[Wolford et al.,

1996;

Meixner et al.,

1998;

Meixner et al.,

1999a].

Several improvements and adaptations were made to the CENTURY model since it does not currently incorporate the full effects of soil warming that occurs under deep

snowpacks

as observed by

[Brooks et al.,

1996]

as well as other processes that are important to simulating carbon-nitrogen dynamics in alpine watersheds. The CENTURY algorithm was adapted to be linked to the

AHM

model in an

offline

mode using

AHM

output as input to the adjusted algorithm.

The adapted algorithm was applied to the Emerald Lake watershed as a test of the robustness of the model. Several different methods of estimating soil temperature were

used as well as three levels of atmospheric

N

deposition (low observed, high observed and double the current high deposition observation). The major findings of this paper follow.

27

(1) The

adapted CENTURY algorithm adequately simulated

the

carbon

and

nitrogen dynamics

of the

Emerald

Lake

watershed.

The adaptation of the CENTURY model was successful in giving adequate simulations of the carbon and nitrogen pools and fluxes in the terrestrial landscape. The simulations did underestimate the amount of soil organic carbon as well as annual biomass production when compared to the data of [Rundel

et

]

There were several other difficulties with the simulations including over or

underprediction

of

N

mineralization rates and the total flux out of mineral nitrogen out of

the

soil.

(2) Snow cover properties

and

their effect

on

soil temperatures were

important in

properly simulating soil-carbon nitrogen dynamics

in alpine

watersheds.

Simulations that were done incorporating snow cover information were better than those that did not in simulating the carbon-nitrogen dynamics of the Emerald Lake watershed.

(

3

)

The

model captured some

Emerald

Lake

watershed.

of the

variability

in

mineral

N

export

for the

During the late

1980's

and early

1990's

a gradual decline in the stream concentration of

28

NO,

-

was observed for the Emerald Lake watershed. The model managed to capture much of this decline but simulated concentrations rose before the real concentrations.

The simulated mineral

N

flux was two to three times that of the stream chemical observations and the peak mineral

N

flux predated the observed peak by

30

days. This may be due to hydrologic differences between the model and the real watershed.

(4)

Changes in

N deposition appear likely to increase NO3" export

in the

Emerald

Lake

watershed.

Simulated nitrogen export increased dramatically with increases in deposition. This indicates that Sierra Nevada watersheds may be very sensitive to increases in atmospheric deposition. This result should be confirmed in a field experiment.

2.4 Summary

of

Paper #4: Sensitivity Analysis Using

Mass Flux and Concentration

A robust multi-criteria sensitivity analysis was applied to the

AHM

model of the

Emerald Lake watershed for the

1986

and

1987

water years for

24

model parameters and

21

different criteria. The

24

model parameters govern the major chemical and hydrologic processes described within the

AHM.

The

21

criteria were discharge and the concentration and mass flux criteria for

10

chemical species. It was hoped that three questions would be answered by applying sensitivity analysis techniques to the

AHM

29 model of the Emerald Lake watershed. First, is parameter sensitivity different for mass flux and chemical concentration measures of model error? Second, do the results indicate that mass flux and concentration objective functions contain different information about catchment and model behavior? Third, what information can the sensitivity analysis provide about the biogeochemical and hydrologic processes that control stream chemical composition? The major findings of this paper follow.

(1) There were systematic differences in parameter sensitivity for chemical concentration and chemical mass flux criteria.

Mass flux criteria were not affected by evapotranspiration (ET) and mineral weathering parameters, while concentration criteria were. Cation exchange parameters were important for the model's ability to simulate observed mass flux, while these parameters were less important for simulating observed stream concentrations.

(2) Mass flux criteria contain more information about processes that are important during periods of peak spring snowmelt, the most sensitive period for alpine watersheds to acid deposition.

The parameter sensitivity results indicate that processes with a quick response time (i.e.

cation exchange) were more important for improving model simulations of mass flux observations. However those parameters that represent gradual or long-term processes

(i.e. evapotranspiration and mineral weathering parameters) had more of an effect on the model's ability to simulate observed stream chemical concentrations.

30

(3) In

contrast to earlier results,

cation

exchange is

an important

process

in

controlling

the

stream chemical

composition of the

Emerald

Lake

watershed.

Previous sensitivity analysis with the

AHM

model of Emerald Lake

[Ohte et al.,

1993]

indicated that cation exchange was not an important process in improving

AHM

simulations of stream chemical conditions. Our results indicate that cation exchange is important especially for improving simulations of mass flux.

(4)

The volume of talus and the rate of flow

through soil

are the

two most

important

hydrologic processes

in

controlling stream chemical

composition of the

Emerald

Lake

watershed.

The sensitivity results indicated that of

42

possible sensitive-parameter-criteria combinations for the reactive volume of talus

76%

were sensitive, while for flow rate through talus

(21

possible combinations)

43%

were sensitive. For soil the results were opposite with

80%

of the flow rate parameter-criteria combinations sensitive and

57%

of soil volume parameter criteria combinations sensitive.

2.5

Summary of Paper

#5:

Multi-Criteria Parameter Estimation for

Hydrochemical

Models

The use of multiple response data to calibrate hydrochemical models has been shown to be an effective methodology for calibrating hydrochemical models and for investigating the structure of conceptual models of watershed chemistry

[Mroczkowski

et

al., 1997;

Grosbois et

al., 1988; Hooper

et

al., 1988]. The work to date has not investigated how criteria should be selected and how to weigh the information content of different criteria. In this work we applied the MOCOM-UA algorithm

[Yapo,

1996] to the AHM model of the Emerald Lake watershed

[Wolford

et

al., 1996]. The purpose of the research was to learn four things. Is it best to use more or fewer criteria when calibrating hydrochemical models? What is the best methodology for selecting the criteria to be used in multi-criteria parameter estimation? What can we learn about the natural processes controlling stream chemical composition in the Emerald Lake watershed from the automatic calibration of the AHM model? What can we learn about the structure of the AHM model of Emerald Lake from this exercise? A summary of the major findings of this paper follows.

31

(

1

)

The minimum number of criteria necessary should be used to conduct a multi-criteria calibration of a

hydrochemical

model.

The calibration results from using six criteria were markedly inferior to those when using only 4 criteria for calibrating the AHM model. This result may be due to particulars of the AHM model and the Emerald Lake watershed. They are also due to the simple mathematics of multi-criteria theory that adding criteria can only increase the size of the Pareto set results.

32

(2) Sensitivity analysis should be used to select the criteria that are to be used in multi-criteria parameter estimation.

The sensitivity analysis results of

Meixner et

al. [1999b] were used to select three of the four sets of criteria. The remaining set was chosen using a correlation analysis of the observed chemical composition from the Emerald Lake outflow. The selection of criteria using the sensitivity results proved successful in improving the parameter estimation results for criteria used in the calibration as well as those not used in the calibration.

(3) The current mineral weathering rate in the AHM model of the Emerald Lake watershed is too low.

The parameter estimation results for two of the 4 criteria cases investigated indicate that the current mineral-weathering rate is too low within the AHM. The results also indicate that the elution parameter is set too high.

(4) The model has difficulty simultaneously modeling both hydrologic discharge and stream chemical composition due to structural problems with the

AHM model of Emerald Lake.

The two four-criteria calibration runs resulted in contrasting values for the hydraulic conductivity of the soil subunit. Calibration with concentration criteria indicated that a lower value of hydraulic conductivity was necessary to simulate stream chemical composition, while the case using mass flux indicated that a higher value was needed.

This indicates that in order to simulate spring stream concentrations (as represented in the mass flux measure of model error) a higher value was needed while to simulate summer and winter stream concentrations a lower value was needed. The contrast indicates that the behavior of the model depends on the criteria that we seek to minimize. This conflict indicates an inadequacy in the current model structure. Possible solutions to the conflict include: making exposed rock reactive, including preferential flow through soil, or increasing the number of horizons in the soil.

33

34

3

CONCLUSIONS

The thread that weaves this dissertation together is the goal of describing the

geochemical, biogeochemical,

and hydrologic processes that interact to create the aqueous chemistry that is observed in alpine lakes and streams. Toward this end we have used the

AHM

as a tool to investigate several hypotheses on what controls the stream chemical composition of alpine lakes, streams, and soils. The five papers included in the appendices can be categorized into one of three groups: extending

AHM,

improving

AHM,

and testing

AHM.

The first two papers extended the application of the

AHM

beyond the Emerald Lake watershed. "The Importance of

Biogeochemical

Processes in

Modeling Stream Chemistry in Two Watersheds in the Sierra Nevada, California" and

"Stream Chemistry Modeling of Two Watersheds in the Front Range Colorado" showed the usefulness of the

AHM

as a modeling tool that can be used to investigate the processes that control stream chemical composition in alpine watersheds.

These two papers together with the original papers on

AHM

[Wolford and

Bales,

1996;

Wolford et al.,

1996]

provide us with three insights into some of the overarching hydrologic and

biogeochemical

controls on stream chemical composition in alpine watersheds. First,

snowmelt

is interacting with a

geochemical

substrate (i.e. soil, talus, or reactive bare rock surfaces) for a long enough period of time for

snowmelt

to take on the

geochemical

characteristics of the substrate. The original hypothesis guiding acid

deposition research in alpine watersheds was that these watersheds would be among the

35 most sensitive to increases in acid deposition due to their thin soils and difficult-toweather bedrock [Melack and Stoddard, 19911. The results thus far in simulating stream chemistry in alpine catchments do not indicate that this hypothesis was correct. If this hypothesis were true we should see some snowmelt reaching the stream that did not show the effects of interacting with a geochemical substrate. Instead the opposite is observed at Emerald, the Pear Lake watersheds and the two Rocky Mountain watersheds simulated as part of this dissertation, it was necessary to alter model structure or model parameter values to ensure that all snowmelt came into contact with either soil or talus

[Wolford et

al., 1996;

Meixner

et al., 1998;

Meixner

et al., 1999a]. Now that this result has been observed at four catchments that are quite diverse in size (0.2 ha up to 220 ha), exposed bedrock (30% to 90%) and geography (Sierra Nevada and Rocky Mountains) it is possible to state that snowmelt in alpine watersheds invariably contacts a geochemical substrate that the snowmelt interacts with, even in watersheds with extensive areas of exposed bedrock.

Second, while snowmelt definitely comes in contact with geochemical material which material it comes in contact with is important. At the two small Sierra watersheds, areas mapped as exposed bedrock were a larger nitrogen sink than areas mapped as soil covered. At the two Rocky Mountain watersheds areas of talus exported more NO3

-

than areas mapped as soil. Combined, these results indicate that the spatial composition of alpine watersheds is important in determining the relative ability of these watersheds to

behave as

NO3"

sinks or sources. It is therefore important to simulate areas of soil, rock

36

and talus separately not so much because of the variable geochemistry of each of these areas but because of their variable

biogeochemistry.

Third, the results from the two papers indicate that the general structure adopted for the

AHM

model of Emerald Lake is suitable for simulating alpine stream chemical composition. This conclusion builds from the multiple applications of the

AHM

[Wolford and

Bales,

1996;

Wolford et al.,

1996;

Meixner et al.,

1998;

Meixner et al.,

19994

The same general structure was used each time the

AHM

was applied to a new watershed. All five applications of the

AHM

have been successful at describing the fundamental processes describing stream chemical composition.

The third paper, "A Nitrogen Dynamics Model for Alpine Basins", stands by itself as an attempt to improve the

AHM

representation of carbon-nitrogen dynamics.

The original version of

AHM

included an inadequate model of nitrogen cycling. The results from incorporating the CENTURY algorithm into the

AHM

in

offline

mode indicate that the improvements once fully incorporated into

AHM

should be successful.

This incorporation of a robust carbon-nitrogen cycling model will enable the simulation of the multiple effects of increases in atmospheric deposition of nitrogen as well as the effects of climatic events like soil thawing and drought. The results with the carbonnitrogen model also reinforce the robustness of the soil organic matter and plant growth dynamics of the CENTURY model.

The carbon-nitrogen dynamics modeling also gives us information about the processes controlling nitrogen dynamics in the Emerald Lake watershed. First, multiyear drought appears to be of central importance in controlling carbon-nitrogen cycling.

The drought of the late 1980's and 1990's had a profound impact on the mineral N export

37 of the modeled watershed. Second, the length of snow cover had an effect on the total N export with longer snow cover leading to more N export. Finally, under the current N deposition rates, the Emerald Lake watershed is approaching N saturation. These results need to be confirmed with further field research

The last two papers, "Sensitivity Analysis Using Mass Flux and Concentration" and "Multi-Criteria Parameter Estimation for Hydrochemical Models", involved the rigorous testing of the AHM model of the Emerald Lake watershed with multi-criteria parameter sensitivity and parameter estimation algorithms developed at the University of

Arizona [Yapo, 1996; Bastidas, 1998; Bastidas

et

al., 1999;

Gupta et

al., 1999]. Both of these papers provided valuable insight into how multi-criteria methods can be used to discern the importance of different hydrologic and biogeochemical processes. These papers also shed some light on some possible mechanisms that can be used to solve the continuing problem of model calibration and evaluation. This problem has prevented the use of watershed chemical models as scientific and predictive tools for future conditions due to the low reliability of the calibrated parameters

[Grosbois et

al., 1988; Hooper

et

al., 1988; Christophersen

et

al., 1993;

Kirchner et

al., 1996; Bassett, 1997].

Progress on the problem of calibrating hydrochemical models was made in two ways. First, automatic techniques were developed to discern the importance of hydrologic and geochemical processes and their importance in controlling stream chemical composition. This progress was mostly made in the paper implementing sensitivity analysis to the AHM model of the Emerald Lake watershed

[Meixner et

al.,

I

99913]. The results showed that the stream chemical time series give us information about processes internal to the watershed. These results indicate that, with the calibration

38 and sensitivity algorithms used in this dissertation, stream chemical models can be used on more than a comparative basis. In fact they indicate that stream chemical models, when supported by the proper amount of data, can be used to more fully understand the processes controlling stream chemical composition. This was demonstrated in the sensitivity analysis with the result that cation exchange was a more important process during spring snowmelt than mineral weathering. Moreover, the results show that stream chemical models can be used to guide the development of field data collection efforts.

The parameter estimation work supports the results of the sensitivity analysis paper in showing that stream chemical data can be used to determine the relative importance of different hydrologic and geochemical processes. Progress in using multicriteria methods to calibrate hydrochemical models was made in this work but some problems still present themselves. The use of the sensitivity results in determining which and how many criteria for multi-criteria parameter estimation was successful but more

work is needed. Also the multi-criteria parameter estimation results showed promise at discerning problems with model structure.

39

As important as the direct conclusions that can be drawn from this dissertation are the further research questions that we can draw from their results. The three groups of papers, extending, improving, and evaluating, each lead us to different sets of questions.

Extending the

AHM

to the two small Sierra Nevada watersheds and the two Rocky

Mountain watersheds leads to questions related to the incorporation of spatial information into the ARM. Current practice with

AHM

overlays maps of snow-covered area on top of established land cover maps that break the watershed down into soil, talus, and rock subunits. Water is then routed between these based on landscape relationships between the subunits. Two counter-intuitive results beg whether this is the best methodology to follow. The results for watershed

2,

of the paired Sierra Nevada watersheds, indicate that exposed bedrock may be reactive; a process not currently incorporated into

AHM.

The result for Green Lakes valley that talus was not important for determining stream chemical composition disagrees with field results. Combined, these results lead to three questions. First, how important are the

geochemical

and

biogeoochemical

processes that occur on exposed bedrock? Second, can more robust flow routing determination using

TOPMODEL

[Beven and Kirby,

1979]

or other distributed hydrologic models be useful in improving the simulated stream chemistry of the

AHM.

Third, can isotopic and

geochemical

tracers be used to inform the flow routing used in

AHM?

Obviously the

results for these last two methodologies should be compared for consistency and for evaluating the results of each.

The positive evaluation of the carbon-nitrogen dynamics modeling for the

Emerald Lake watershed opens up a suite of questions and a good deal of technical follow up work. First, the modeling results need to be confirmed by field hydrologic and fertilization experiments. Second, the algorithm needs to be incorporated directly into

AHM as opposed to being run in an offline mode as was done in this dissertation. Third

40 the algorithm needs to be extended to incorporate vegetation dynamics representative of trees and of talus. Talus represents a special case since it contains little vegetation but does receive organic material from uphill source areas and dryfall.

Some of the most interesting questions from this research develop out of the application of multi-criteria methods to hydrochemical models. First, can a more quantitative approach to determining which criteria to select produce better results than those thus far? Second, can the multi-criteria methods be used to discern between superior and inferior model structures? One test case would be to simplify the AHM representation of Emerald Lake down to just a rock and a soil subunit. The soil subunit would simply lump the soil and talus properties together. The multi-criteria methodology would then be applied to see if the simulation results improved or deteriorated. A smaller parameter space, objective space results closer to zero, and time series results bracketing the observations tightly would all be indicative of a model improvement. Also, many other combinations of criteria remain to be tested. The most likely mode for calibrating

watershed chemistry models will be to calibrate watershed hydrology with a limited set of criteria. Next these calibration results using one group of criteria will be used to determine the feasible parameter space for the calibration of the remaining criteria. The final result would be a parameter set that could be evaluated with the nearly 20 years of

41 data now collected at the Emerald Lake watershed [Melack

et

al., 1998]. The final results could also be used to simulate stream chemical composition under perturbed conditions.

The multiple parameter sets would result in giving a high and low bound of watershed response to perturbations. Such a result should be useful to policy makers in setting critical loads thresholds for alpine watersheds.

APPENDIX A - IMPORTANCE OF BIOGEOCHENMICAL PROCESSES IN

MODELING STREAM CHEMISTRY IN TWO WATERSHEDS IN THE SIERRA

NEVADA, CALIFORNIA

42

WATER

RESOURCES

RESEARCH

43

VOLUME 34 NOVEMBER 1998 NUMBER 11

PUBLISHED BY AMERICAN GEOPHYSICAL

UNION

American Geophysical Union

2000

Florida Avonue. NW

Washirgion. DC 2009

Tel

-

41-202-462-690^ l-

ax *1-202-328-0556

44

August 4, 1999

Mr. Tom Mcixner

Department of Hydrology and Water Resources

Room 203B, Building 411

PO I3ox 210011

University of Arizona

Tucson, AZ 85721-0011

Dear Mr. Meixncr:

We are pleased to grant permission for the use of the material requested for inclusion in your thesis, including microfilm editions thereof. Permission is restricted to the use stipulated. The original publication must be appropriately cited. The credit line should read: "authors, journal or book title, volume number, page numbers, year," and the phrase "Copyright by the American

Geophysical Union." Substitute the last phrase with "Published by the American Geophysical

Union" if the paper is not subject to U.S. copyright -- see the copyright line on the first page of the published paper for such classification.

Please feel free to contact me again if you need further assistance. Thank you.

Sincerely,

Caik4-0/vv

Pamela Calliham

Publications Administration

Coordinator

Tne Amencan Guooilyscai Limon enc,npasse: Ina Eat ant: space

Geodesy. So.trno n dy. Ai nnosphorrzSclences, Geomaritildrn

and

Paleornagnevsm

Oce2n Sc n on,ot I iydron ogy Vo:cano nogy. Geocnern.clry and Potrolny

Tect000ynyst=

Planalology.

Space Pnyscs and Awonarny

WATER RESOURCES RESEARCH. VOL. 34. NO. It. PAGES 3121-3133, NOVEMBER 1998

Importance of biogeochemical

processes

in

modeling stream chemistry

in

two watersheds

in the Sierra Nevada,

California

Thomas Meixner

Department of Hydrology and Water Resources, University of Arizona. Tucson

Aaron

Brown'

Marine Sciences Institute, University of California. Santa Barbara

Roger C. Bales

Department of Hydrology and Water Resources, University of Arizona, Tucson

Abstract. Two small

(0.22 and

0.48 ha) alpine watersheds in the Sierra Nevada of

California were studied during the

1992 and

1993 snowmelt seasons to evaluate the importance of soil properties and processes on chemical concentrations in the discharges from each watershed. Watershed watershed

1 was surveyed as having 26% soil cover, whereas

2 was 10% soil covered. Watershed 2 had greater PV

-

and nitrogen consumption than watershed 1 but similar cation and sulfate concentrations despite having one fourth the surveyed soil volume per unit area as watershed

1.

Daily stream concentrations simulated with the Alpine

Hydrochemical

Model (AHM) matched the data well, after a systematic model calibration with a subset of the data. We found that the structure of the AHM and the hydrologic parameters developed for the nearby 1.2 km

2

Emerald Lake watershed could be applied to these watersheds with only small adjustments; chemical parameters required considerably more adjustment, reflecting a greater degree of chemical versus physical heterogeneity at this scale. Calibration for watershed

2 gave a higher percent base saturation

(19 versus 4%) and lower stream P op

,

(10

-3.

' versus

10

2 6

atm) than for watershed 1 and three times the soil reactivity

(expected) of a field survey. Areas mapped as exposed bedrock in the catchments apparently contributed cations and alkalinity to stream water to a greater extent than did neighboring areas of soil. Areas of exposed bedrock were a larger nitrogen sink than the adjoining areas of soil. The pH and acid-neutralizing capacity of surface runoff in both catchments were less sensitive to changes in atmospheric deposition than at the nearby

Emerald Lake watershed. This decreased sensitivity was due to (1) a less pronounced ionic pulse, (2) less retention of sulfate in the soil, and (3) greater nitrate retention.

1. Introduction

Biogeochemical processes, including mineral weathering, cation exchange, and nitrogen (N) cycling, are major determinants of the chemical composition of alpine lakes and streams

[Williams and Melack, 1991 ]. Determining the magnitudes and locations of these processes is critical to understanding the controls on stream chemistry and how stream chemistry may be affected by changes in atmospheric deposition. Areas of exposed granite represent a large fraction of land cover in alpine watersheds of the Sierra Nevada; for example, 54% of the area of the Emerald Lake watershed (ELW) in Sequoia National

Park is covered by exposed granite [Tonnessen, 1991]. Biogeochemical modeling of alpine watersheds has treated areas of exposed granite as unreactive and as having no influence on stream chemistry [e.g., Wolford et al., 1996]. Some studies, however, have found processes generally considered to occur

'Now at Chemistry Department, Ventura Community College, Ventura, California.

Copyright 1998 by the American Geophysical Union.

Paper number 98WR02172.

0043-1397/98/98WR-02172509.00

3121 in soil occurring on areas of exposed granite, such as ion exchange, mineral weathering, and N reactions [Rueslatten and

Jorgensen, 1978; Dahl et al., 1979; Abrahamsen et al., 1979;

Allan et al., 1993; Clow and Mast, 1995].

The sources and sinks of N in alpine regions are of particular concern because of the thin soils and limited vegetation present in alpine ecosystems. Considerable work has been done in the Rocky Mountains investigating the N cycle and the adverse effects of N saturation [Williams et al., 1996a]. This work has suggested that the NO pulse observed in early spring snowmelt is due to a release of NO from soil [Williams

et al., 1995; Kendall et al., 1995]. Other work has indicated that soil microbes in areas covered by snowpack for long periods are able to retain much of the NO and NH released during the ionic pulse from seasonal snowpacks [Brooks et al., 1996].

The results of Clow and Mast [1995] indicate that bedrock may play a role as an N sink in alpine watersheds.

In this study, two small watersheds in the Tokopah Valley of

Sequoia National Park were selected as paired watersheds that differed in soil coverage. It was our hypothesis that this difference would result in higher concentrations of soil-derived chemical species in the runoff from the watershed that had more surveyed soil area and that areas of exposed rock were

45

312.2

MEIXNER

ET AL BIOGEOCHEMICAL

PROCESSES. SIERRA NEVADA

Watershed

2

%-°3625" N

Met

Meteorological station

2

Soil lysimeters sz Soil area

N

Watershed

1

Flume

, z4

46

50

0 so

100m

Figure

1.

Map of both watersheds. Elevations are in meters, with 2 m contour intervals. Gray area was mapped as soil in a field survey. Watershed boundaries were determined with a level. They are more accurate than the contour lines, which are the result of a more limited field survey. Note that Watershed 1 drains to the north, while Watershed 2 drains to the southwest. There were two suction lysimeters at location 1, one at a 100 mm depth and one at a depth of 300 mm. The other lysimeter locations all had one suction lysimeter at 100 mm.

relatively unreactive with snowmelt runoff. Further, we expected

N export to be greater on the rock watershed since there was little soil or vegetation to immobilize atmospheric inputs of dissolved inorganic nitrogen. These watersheds were also used to evaluate the varying importance of cation exchange, mineral weathering, sulfate adsorption, and N transformations on the chemical composition of snowmelt runoff of Sierra Nevada watersheds.

Previous analyses done at the ELW show that soil has a dominant effect on stream chemistry, with essentially all of the snowmelt contacting soil during runoff; however, estimated soil depth differed significantly from those estimated in a field survey [Wolford

et

al., 1996]. Three issues addressed in this paper are (1) the relative importance of biogeochemical processes on areas mapped as soil versus rock in catchments dominated by granitic rocks, (2) how well soil processes buffer daily to weekly changes in stream chemistry when acid deposition to the catchments changes, and (3) how well model structure and parameters developed for the F.T.W describe the stream discharge and chemistry of other nearby alpine catchments.

2.

Methods

2.1. Site

The watersheds studied were adjacent catchments in the

Tokopah Valley of California's Sierra Nevada (36°3630"N,

118°39'55'W, elevation 2960 m). These watersheds were located at a distance of 3 km from the previously studied ELW

[Tonnessen, 1991]. Streamflow on both watersheds is ephemeral, flowing only during snowmelt runoff. The glaciated bedrock of the watersheds is granodiorite with mafic inclusions up to 200 mm in diameter. Fracturing and incipient exfoliation of some granitic surfaces lies on a SW-NE axis and is more pronounced in watershed 2 (WS2). Watershed boundaries were determined using a rod and a builder's level. Areas were mapped as being soil if they had continuous fine material on the surface, aside from fine material in rock fractures and small crevices. Watershed 1 (WS1) (0.22 ha) is 26% soil covered, has a 13% slope and a northern aspect, and includes 15 locieepole pine (Pinus contona) trees with heights between 3 and 7 m.

WS2 (0.48 ha) is 10% soil covered (Figure 1), has a 17% slope and a southwestern aspect, and has only 2 lodgepole pine trees, both with a height <2 m. Aside from the lodgepole pines, the vegetation on both watersheds is limited to perennial grasses, wildflowers, and lichens. WS1 has more soil volume per unit area and a more highly developed soil, as indicated by a higher fraction of organic C and organic N, than WS2 (Table 1).

2.2.

Sample Collection

Both watersheds had outlet flumes (H-type) located on bedrock equipped with pressure transducers (Stevens' Model SDT

ME1XNER ET

AL.: B1OGEOCHEMICAL PROCESSES. SIERRA NEVADA 3123

H) and thermistors that permitted the recording of discharge from each watershed continuously. Each outlet was also equipped with an autosampler (ISCO Model 3500) that was used to collect stream water at intervals varying from 2 hours to 5 min between samples. Each of these samples was analyzed for major ions. The multiple measurements of stream chemistry taken each day were flow averaged to allow comparison between the data and model predictions. Soil water samples were collected daily (if possible) with suction lysimeters at two points in WS2 and at a three points in and near WS1 (Figure 1).

Chemical analyses of NO;, SOC, and C1 were done using ion chromatography (Dionex, AS4A column). Each of these samples was also analyzed for Ca

2

", Mg

2.

, K', and Na using flame atomic absorption spectrophotometry. Thep H was measured using glass electrodes maintained for low ionic strength waters. Acid-neutralizing capacity (ANC) was determined by

Gran titration. The field and laboratory techniques used are described by Melack

et

al. [1998] and

Brown et

al. [1990]. A snow survey was conducted at the time of peak accumulation and weekly thereafter to measure snow water equivalence

(SWE) and snow-covered area (SCA). Spatial distribution of snow depth and SCA was measured in a grid. Snow density was measured in duplicate profiles in two snow pits per watershed.

Chemical deposition to the watersheds was measured using a combination of snowpack chemistry samples and measurements of storm event quantity and quality after the snow survey. Storm events were sampled using a tipping bucket gauge

(Sierra Misco) for quantity and two rain buckets (DI-rinsed polyethylene) to collect samples for measurement of precipitation quality. All monitoring was conducted during the 1992 and 1993 melt seasons.

23. Model

The University of Arizona Alpine Hydrochemical Model

(AHM)

[Wolford

et al., 1996] was used to integrate the data and evaluate catchment biogeochemical processes. The AHM, a lumped conceptual model, was developed at the ELW, also in the Tokopah Valley, for evaluating watershed hydrology and hydrochemistry and investigating the sensitivity of alpine catchments to changes in atmospheric deposition and climate forcing. In this application, the first of the AHM beyond the

ELW catchment, each watershed was represented by three subunits: soil, rock, and stream. Each terrestrial subunit contains different compartments representing the snowpack, snowpack free water, snowmelt, surface runoff, interception by trees and litter, and zero, one, or multiple soil horizons. Stream subunits consist of different compartments representing the snowpack, snowpack free water, snowmelt, stream ice and streamflow (Figure 2). Model subunits may be selected for use according to the complexity of the watershed. Hydrologic processes are modeled separately from geochemical processes.

Table I.

Watershed Characteristics

Characteristic

Area, km'

Average Slope,

%

Percent soil cover

Soil volume, n

-

1

3

Soil pH

Soil organic C, %

Soil organic

N, %

Soil

C:N

Watershed

1

0.0022

13

20

57

4.4

2.0

0.12

16

Watershed

2

0.0048

17

10

24

4.2

1.2

0.09

13 a.

b.

Figure 2. Modeled watershed compartments: (Figure la)

Soil subunits have compartments including (1) rainfall litter interception, (2) snowfall canopy interception, (3) rainfall canopy interception, (4) snowpack, (5) snowpack free (liquid) water, (6) snowpack drainage, (7) surface runoff leaving the subunit, (8) soil drainage leaving the subunit, (9) contributed soil drainage, (10) contributed surface runoff, (11) litter storage beneath the snowpack, and (12) one soil horizon. Rock subunits (not shown) do not include compartments 2, 3, 8, and

12. Stream subunits (Figure lb) have compartments including the (a) snowpack, (b) snowpack free water, (c) snowpack drainage, and (d) streamflow; stream ice is not tracked other than present or absent.

Routing between the subunits is handled separately from the structure of the individual subunits.

AHM operates on a daily time step. At each time step, AHM adjusts snow-covered area, computes interception, adjusts snowpack for precipitation and melt, calculates influxes of materials to each soil and rock subunit, drains surface runoff, computes evapotranspiration and sublimation, calculates kinetic reactions, calculates chemical equilibria in soil compartments, drains water from the soil horizon, calculates chemical equilibria in streams, and produces output. Output can include detailed descriptions of all chemical calculations, tracking of both chemical and hydrologic storages and changes in storage within the watershed, soil chemical concentrations, and stream concentrations. Chemical speciation is handled using equations adapted from MINEQL

[Westall

et al., 1976]. The strength of the model is its flexibility and precise mass balance for both chemical species and hydrologic calculations

[Wolford et

al., 1996].

In the current structure, runoff from the rock subunit was routed to the soil subunit before draining to the stream for

WS1, on the basis of the physical location of soil and rock

(Figure 1). For WS2 we evaluated overland flow from rock contributing directly to streamflow; however, this structure was discarded because of poor simulations. Thus routing for WS2 also had overland flow intersecting soil area during its travel through the watershed.

2.4. Model Calibration

2,3 stream subunits and Evaluation

2,3

As a starting point for parameter estimation, parameters describing chemical processes and soil physical processes were set equal to

Wolford

et al. [1996] values for the F.LW. Model

47

3124

MEIXNER

ET AL BIOGEOCHEMICAL PROCESSES.

SIERRA

NEVADA

Figure 3. Seasonal precipitation chemistry and hydrologic mass balance for both watersheds for 1992 and 1993. Note that scales are different for each graph: (a) winter snow, (b) spring precipitation, and (c) water balance.

soil were altered to improve the fit to stream NO and NH

-

: concentrations.

After chemical calibration, improving model predictions required further adjustments to the hydrologic parameters. On both watersheds the hydraulic conductivity and surface runoffsoil water mixing ratio were adjusted to allow more mixing between surface runoff and soil water. The surface runoff-soil water mixing ratio controls the fraction of soil water in the top horizon that mixes with surface runoff before the surface runoff leaves the soil subunit. Next, the equilibrium partial pressure of CO,

(Po,)

in the stream was optimized. Further changes to model structure were required on WS2 to obtain a good fi t, as described below.

Our evaluation of model performance follows a method outlined by

Kirchner et al.

[1996] of establishing performance criteria and a benchmark for comparison. The performance criteria are outlined below. The benchmark was the initial model on each watershed using Emerald Lake parameters.

Finally, we report how well the model matched data not used for model calibration.

Calibration was done manually; however, we used a measure of model error for the purposes of comparing the initial and calibrated models. The measure used was the sum of absolute differences, the numerical value of which has the same units as the measurements: parameters for extensive properties, such as watershed area, soil area, and depth, were determined for each catchment model from field measurements. The soil subunit on both watersheds was represented by one horizon because of the shallow nature of the soils on these watersheds.

Parameter estimation for each watershed was done using the data for 1992. The model calibration involved four steps: (1) snowmelt optimization, (2) chemical calibration, (3) adjustment of hydrologic parameters, and (4) changes in model structure. Detailed snow surveys, precipitation records, watershed discharge, and an estimate of water losses to the atmosphere were used for snowmelt optimization. Evapotranspiration and sublimation rates were set at estimates for evaporation from the F,LW of 2.0 mm c1

-1

and 0.5 mm respectively

[Melack et al.,

1998]. Since snowmelt optimization requires water balance on a modeled watershed, snowpack and precipitation inputs must be equal to runoff and evaporation.

We therefore adjusted SWE to match the sum of runoff and evaporation. Within the model the remaining water is lost to an undefined hydrologic sink, for example, groundwater [Wol-

ford et al.,

1996].

Chemical calibration of the model for each watershed followed a stepwise process of adjusting model parameters to match model output to the observed values (see Table 4 for functionality of model parameters). First, cations, anions,

ANC, and pH during low flows late in the melt season were assumed to originate from the soil. Concentrations of these species were used as targets for modeling the soil chemistry.

Second, soil pH was fixed to this late season value, by adjusting the percent base saturation of the soil. Third, cation concentrations were matched by adjusting the apparent exchange coefficients for each cation until modeled soil concentrations were close to the target values. Fourth, parameters describing the intensity of the ionic pulse were adjusted to improve the fit to stream CI - concentration. Fifth, SO.

2

,

-

adsorption parameters were changed to increase or decrease SO

.

i

-

concentrations in the soil and stream waters of each catchment. Finally, the N parameters governing the dynamics of N consumption in the

F,=

E — cz'ddl (1) where F is the objective function, C is the concentration, and

k is the chemical species. The sum of absolute differences does not increase the weight of larger differences relative to smaller ones, as a least squares sum does. Since the objective function

Fk

has different values for different chemical objectives, we normalized each

Fk

by its initial value to facilitate comparison between objectives and assess the success or failure of the calibration:

Fk

Pk— r

F

(2)

The closer

Pk

is to zero, the better the fitting procedure improved the match between modeled and measured values; the closer

Pk

is to one, the less improvement provided by the model calibration.

3. Results

3.1.

Water

Balance

We used the snowmelt optimization feature of the AHM, which accounts for evaporative processes, to determine the water balance or lack thereof. Precipitation was consistently greater than runoff (Figure 3c). For WS1, precipitation of 600 mm and 1740 mm was observed for 1992 and 1993, respectively, and runoff of 480 mm and 1110 mm was observed for

1992 and 1993, respectively. For WS2, precipitation of 460 mm and 1280 mm was observed for 1992 and 1993, respectively, and runoff of 240 mm and 1020 mm was observed in 1992 and

1993, respectively. Total modeled evaporation for both watersheds was 42 mm in 1992 and 96 mm in 1993. Since the difference between precipitation and runoff is greater than evaporation, some of the snowpack as surveyed must have been lost to an unidentified hydrologic sink. For WS1, 70 mm

48

MEIXNER ET

AL.: BIOGEOCHEMICAL

PROCESSES. SIERRA

NEVADA

3125 of the surveyed 590 mm of SWE was unaccounted for in 1992, and 550 min of the 1700 mm surveyed amount was unacsnowmeit optimization, modeled and measured values of dis-

30

A ril .

Ma

,.. ,..

May

1993

450 mm, and 190 mm of that was assumed lost to an unknown sink. In 1993, 1240 mm of SWE was measured in the survey, and 200 mm was assumed lost to an unknown sink. Following

120

_

Lc,

90

60

1992

0

..

. .

charge were nearly identical for both years (Figures 4 and 5).

.......•

,

I .

T f ------

7

30

3.2. Precipitation Chemistry

Solute concentrations in snow and rain (Figure 3) were very g

20 dilute, similar to those observed at nearby Emerald Lake [Wol-

ford et al.,

19961 , typical of precipitation in the Sierra Nevada.

10 o

0

• r,

June

Jul

... r:

- '

•__

L-

-

_

The higher concentrations in rain as opposed to snow are

I I i ilijilit apparent by comparing the spring 1992 rain event with the

. spring 1993 snow event (Figure 3b). The rainfall of 4.6 mm in

1992 had concentrations for NH, NW, and a

-

of 23.1, 18.8,

6.5

.....

and 2.5 I.LeqL

-1

, respectively. The snowfall of 41.2 mm SWE in

1993 had concentrations of 5.2, 4.5, and 3.3 p.eqL

-1

, respecm

6.0

5.5

0 oo

?

::" .

••;',;i, t 51 -5Vrt ô -

, r

tively. Average snowpack concentrations for NH:, NOV, and

Cl

-

were 4.5, 2.1, and 1.5 preqL

-1

, respectively, in 1992 and 1.2,

1111

1

1i1

1.5, and 1.8 p.eqL

-1

, respectively, in 1993. The generally higher

- 25

_ concentrations in 1992 as opposed to 1993 coincide with the smaller amount of precipitation and runoff in 1992 (Figure 3c).

a)

15

_

--• , -14:-,..

1..

;

•.'.

33. Solute Concentrations and Ionic Pulse

co

Solute concentrations in outflow from both watersheds were dilute, with levels in WS2 generally being slightly more dilute than those in WS1 (Figures 4 and 5). For example, average eq c5 o

1

I

I III illi o

Observations

ELW parameters -

_

ANC values were 8.1 and 7.5 J.LeqL for WS1 and WS2, respectively, with corresponding average Ca

2

' concentrations of

8.4 and 7.7 1./eqL

-1

. The two watersheds also differed significantly in their export of H. While both watersheds received the same concentration of H

+

in wet deposition, the discharge from WS2 had a high pH and thus exported significantly less Fr than did WS1.

Ion concentrations at the beginning of snowmelt were generally higher than concentrations in later snowmelt, reflecting a small ionic pulse associated with some solutes being washed

Out of the snowpack with the first meltwater

[Bales et al.,

1989],

• it•-*

I n ,

..,

Optimized parameters

-

_

,..; L..t...,.

. ,

_

_

_

•.....,...! %,„ • '

f

I and subsequent dilution. This ionic pulse can be seen clearly by dividing the concentrations for 1992 in Figures 4 and 5 by C„, the average concentration of each solute in the snowpack prior to melt (Figure 3a). This calculation did not use the spring rain event in 1992. For comparison between catchments these values are plotted versus fraction of melt (cumulative discharge divided by total seasonal discharge). On both of these watersheds at the beginning of snowmelt, the C/C for a

-

, a conservative species, is a little greater than 2 (Figure 6). For WS1,

CL

has a C/C„ above 1 for the entire season. The rainfall event on May 6th is not responsible for the C/C,, value above

1 since the amount of rain, 4.6 mm, is small in comparison to the volume of snow remaining on the watershed on May 8th,

191 mm (from a late season snow survey). The most likely source of this mass balance problem is field or laboratory contamination.

Nitrate (NOD also exhibited an ionic pulse like Cl

-

, but

NO is not conservative and the NO observed in streamflow may come from within the watershed through nitrification of

NH:, either from snowpack or soil organic matter sources.

Nitrate had a C/C„ value of around 2.0 as the melt season began and rapidly dropped below 1.0, representing a net consumption of NO (Figure 6) for WS2. Nitrate CiC,„ values for

O

100 120 140

Day of Year

130 150 170 190

Day of Year

Figure 4. Watershed 1 results. Observations are flowweighted averages. Emerald Lake watershed (ELW) parameters represent the calibration starting point and are shown with a dashed line. Optimized parameter values are described in text and Table 4. The 1992 box indicates timing of a rain event.

The 1993 box indicates timing of a snow event.

WS1 were consistently higher than for WS2, indicating that

WS1 had a larger ex-port of dissolved inorganic N than WS2 had.

Sulfate and cations had little or no ionic pulse; however,

Figure 6 does show dramatic differences between precipitation and stream concentrations for these species. Sulfate had a

49

3126

MEIXNER

ET

AL: BIOGEOCHEMICAL PROCESSES. SIERRA NEVADA ru l

May

April

120

90

_ 1992

1

1993

60

o

30

...4r:

May

.7- -

---..' :

n

-: .i.,

" g -

June

%

I

:

I

30 r c ir 20

10 o

z

0

6.5

,

-

I-

_

0.

.

5.5

-•

-

Watershed 1

Watershed 2

_

14

-

7

-)

10

.

?.

-.

..: ai

• -

-

'

•-• .......• .....

o Obs rvatiorls

ELW Parameters

Optimized parameters

_

_

-

4

_

_

__ (6

,--.....

''.

•••••

'

_

-

_

.

0 0 0.2 0.4 0.6 0.8 1 0

Fraction of Melt

Figure 6. Ratio of stream concentrations to bulk snow concentrations pendent for each watershed with fraction of flow as indevariable for 1992. The arrows indicate the timing of the May 6th rain event; arrows are different because the independent variable is a fraction of flow, not time.

-

.•':,:',..

. -

' f

120 140 110 130 150 170 190

Day of Year Day of Year

Figure 5. Watershed

2 results.

Observations are flowweighted averages.

FI.W parameters represent the calibration starting point and are shown with a dashed line. Optimized parameter values are described in text and Table 4. The 1992 box indicates timing of a rain event.

The

1993 box indicates timing of a snow event.

3.4.

Nitrogen

Mass Balance

Over the entire snowmelt season there was significantly more dissolved inorganic

N being deposited on both watersheds than was exported from these watersheds in streamflow

(Table 2). There were significant differences in

N loading to the watersheds due to differences in SWE on each of the watersheds. Dissolved inorganic

N output was almost entirely in the form of NO since

NH:', concentrations were below detection limit for much of both melt seasons.

For both

1992 and 1993, WS1 had a much greater net dissolved inorganic

N yield than

WS2 had.

C/C„ of about 2.0 for both watersheds throughout the melt season, indicating significant

S0

7

4

--

export or concentration on the watershed.

Ca

2

' had large C/C„ values for the entire

1992 melt season, 4.0-6.0, reflecting net export of cations from the watersheds.

Table 2.

Dissolved Inorganic Nitrogen

Budgets

Input, mol ha'

NO

Output,

Yield,

NH: Sum mol ha

-I

%

Watershed 1, 1992

Watershed 1, 1993

Watershed 2, 1992

Watershed 2, 1993

13.3

21.7

10.8

16.4

7.3

20.7

6.1

15.7

20.6

42.4

16.9

32.1

3.4

7.0

0.6

3.32

16

16

4

10

50

MEIXNER

ET

AL.: BIOGEOCHEMICAL PROCESSES. SIERRA NEVADA

3127

3.5. Watershed 1

Calibration and Evaluation

The simulation using ELW parameters gave ANC.

p

H, and base cation values higher than observed (Figure 4). Averaging of late season stream chemical concentrations (day of the year

(DOY) 135 and 136) resulted in the target runoff concentrations in Table 3. Values for parameters adjusted during calibration are in Table 4. For 1992 the calibration improved fits for all species (Figure 4). In particular, ANC,

p

H, Ca", Mg", and K. all saw large improvements in model performance, with

P k

values of 0.21-0.33, that is, 67-79% decreases in the sum of absolute differences from initial to calibrated simulations. Fits were slightly poorer for the evaluation year than the calibration year, with

Pk

values of 0.29-0.52.

The match between modeled and observed Ca' concentrations was relatively good for both years, the main difference being the greater day-to-day variability in the data versus the model.

CI

-

showed a modest ionic pulse in both years, and thus the elution parameter (D) was only 2 for both watersheds

(Table 4). Early season pulses for S0.i

-

were reversed by subsequent higher concentration values around DOY 112 in

1992 and 132 in 1993, most likely representing a flush of S0i

rich water from the watershed; as a result, we made adjustments to K-S0,

2

,

-

(Table 4). The apparent ionic pulses for

NO; are reflected in the model output, but to capture late season low concentrations, the N reactions in the model were set to consume all NO and NHZ that carne in contact with the soil.

Modeled ANC and pH both reflected the observed average but failed to capture the day-to-day variability. In both years, there were two periods with a poor match between measured and modeled values (Figure 4). In 1992 the model missed both the magnitude and trend of the data around DOY 120, when pH and ANC exhibited opposite trends. This is apparently a problem with the ANC values being too high. Over the whole season the ion balance showed a 17% excess of cations over anions, but days 119-120 had an ion balance near zero (data not shown). The second period in 1992 was around DOY 130, whenpH dropped and ANC varied each day. At the end of the

1993 melt season, modeled ANC and pH were higher than observed. Further, the opposite trends in pH and ANC around days 150 and 170 were not captured by the model.

While measurements of soil chemical concentrations were not used for calibration, calibration significantly improved the match between modeled and measured concentrations of several species in the soil (Figure 7). Two exceptions to this general agreement were that measured ANC concentrations from lysimeter la at a depth of 0.3 m were not captured by the model, and the modeled NO concentrations of zero versus nonzero measured concentrations.

3.6. Watershed 2 Calibration and Evaluation

Averaging of late season stream chemical concentrations

(DOY 130-132) gave the target soil chemical concentrations

Table 3.

Target Runoff Concentrations

Species Watershed 1 pH

Ca

2

*, i.reqL

Me

+

,

Na,

geqL

K*, ikeqL

SOj

, irreqL

-

'

5.4

8.5

2.0

7.5

3.5

5.0

Table

4. Final Parameter Values

Parameter

ELW Watershed 1 Watershed 2

Hydraulic cond., cm day'

Water holding capacity

400

0.522

Surface runoff mixing"

0.0

Total area, ha

120

Soil area, %

Soil depth, cm

46

3534

Log

P c02

soil, atm

-2.3

Log

P co

, stream, atm

Base saturation, %

-2.9

Snowpack elution parameter .1Y

4.0

CEC, meq kg' 55

17.9

Log K-Ca'

Log K-Mg'

-5.23

-5.73

-0.85

-3.01

Log K-1C

a

Log K-Na'

Log K-50.i

-

`

Log K-Si' aNH3toONf aNO3toONf

NO-basef

17.45

27.63

0.989

0.70

8 x 10

-6

400

0.522

0.5

0.22

20.76

10b

-2.3

-2.6

2.0

55

4.2

-4.90

-5.63

-0.72

-2.91

16.85

27.63

0.9999

0.9999

10-7

ELW, Emerald Lake watershed.

'Surface runoff mixing determines the fraction of surface runoff that can mix with the soil water of the top soil horizon.

b

Values for

WS1 are from field surveys.

For

WS2, soil area was doubled and soil depth increased by 50% from original survey values.

Also, the rock portion of

WS2 was allowed to consume N.

'Represents ratio of initial solute concentration in snowmelt to snowpack average.

All other elution parameters were unchanged from

ELW.

d

Log K for exchange of cation with H+ on cation exchange site.

'Log K for adsorption of

SOi

-

and

H

2

SiO

3

. Total site concentrations from ELW optimization used here.

"These three parameters govern the two N reactions present in the

Hydrochernical Model (ARM): NH: <-+ organic N + H

+

and

Alpine

NH: + 20

2

+-> NOT + 2H

+

. The aNH3toON determines what percent of the

NH: is converted into organic

N. NOT-base determines a minimum concentration of N0'

3

-

over which a fraction of the

NOT as governed by aNO3toON is converted into organic N.

400

0.522

0.2

0.48

20'

7.55

-2.3

-3.1

2.0

18.3

17.9

-4.37

-4.88

-0.051

-3.01

16.45

27.63

0.9999

0.9999

10-7

Watershed 2

5.7

8.0

2.0

4.0

2.0

4.0

shown in Table 3. Calibration following the scheme used on

WS1 resulted in only modest improvements in model predictions. The best opportunity for improving model output was to adjust the soil volume on the watershed. A simple grid search gave the best option as doubling soil area and increasing soil depth from 5 to 7.5 cm.

After these adjustments, modeled NO; still did not match the low observed concentrations. In order to consume all of the

NO within the model, we gave the rock portion of the watershed the ability to immobilize N equivalent to a 9 cm soil depth but not the ability to exchange cations, weather minerals, or any of the other soil processes in the AHM. During the rain event of DOY 125-126 in 1992, however, modeled concentrations of NO; were lower than observed concentrations. This was probably due to overland flow that was not reflected in the calibrated model.

The calibration improved the match between modeled and measured values for all species, as shown in Figure 5 for ANC, pH, Ca", NO;, SW,

-

, and cr.

The final parameter values for all parameters that were adjusted during calibration are in

Table 4. P, values for ANC, pH, Ca', K

+

, and NO; of

0.18-0.78 indicate 22-82% improvements in simulation results. The fits for most species improved from the initial run to the final calibrated run for 1993, the evaluation year (Figure 5).

For 1993,

Pk

values were 0.37-0.92, indicating 8-63% improvements in the evaluation year results from initial to cali-

57_

I

3128

MEIXNER ET AL.:

BIOGEOCHEMICAL

PROCESSES, SIERRA NEVADA

40

7

_,

30

g 20

-

1992 i

-

_

_

"44441e

-

, I I

{ i j ,

...

- ------

0

i

\_

1993

... ..

9•0 .

.2P ...

.

.

Vi

_

-

• ` 7 111" 8P° .

, j

°

, j

I f

.

_

7

_, o

5

5

30

25

--I cr a)

20

15

, - 10

6 5

20

,

_...

..,

ô

— •

-

15 cr

10

_ al

%

4

a

.

........ 0 f

-----

-----Ii2Z_ i e'

41

0

9i g %

P f -

o o

o

0

0

\

.

g

e

°

_

-

-

11

4

---f---C

-

1 1

' 1

11 1

,

51 I

a

0

I I

,0

"opt- ag ..... 0ge

0

4 4.1

°)

1

'

-

Lysimeter la o Lyslmeter lb

0 Lyslmeter 2

ELW

Parameters

— —

Optimized parameters

-

°

- 0

i

0 o

6

-

.

_

-

0 -

0 -

•°0.

6'

...t

o e

.

° .'

-

-

g

>

t

1

• ° e

-

'9

__

...> • ..,

%

.9

.

e -

-

0.

,,„,,8

0

,

1

6,--1-11•Fir•74-7-7-7-

100 120 140 130 150 170 190

'

Day of Year

Day of Year

Figure 7. Comparison of modeled and measured soil chemistry for Watershed 1. Symbols are average observed concentrations for the soil lysimeter indicated. Lysimeter la is at a depth of 300 mm, while lysimeter lb is at a depth of 100 mm at the same location. Simulated values for ELW parameters and optimized parameters are shown. No attempt was made to fit modeled soil concentrations to observed values.

brated models. ANC and Ca

2

+ actually had more improvement from calibration in the evaluation year than in the calibration year.

The overall match of model output to measured concentrations in the watershed was good for Ca

2

*, with the exception of the period around DOY 123 in 1992 and DOY 110-130 in

1993. Calibration also improved the fit for a

-

and SOL. The model matched general trends in the data for both years but not the day-to-day variability.

-

In both years, modeled ANC and pH captured the average concentrations. Yet some of the data's variability and its trends were missed, for example, DOY 115-120 in 1992, when ANC and pH went up even though discharge went up. The model calculated an opposite trend because of dilution. Other chemical species failed to show the same trend for this period, however. The poor ion balance for this period, 30% excess of anions over cations (data not shown), suggests that measured

ANC may be too high. Late season periods were problematic in both years. The model underpredicted ANC and pH at the end of the 1992 melt season and overpredicted ANC at the end of the 1993 melt season.

As with WS1, calibration improved the match between measured and modeled soil concentrations (Figure 8), with NO and SO.i

-

concentrations notable exceptions. Modeled NOj

concentrations are at zero for the entire season, while measured concentrations exhibit a pronounced early season spike in both years with some values greater than zero well into the melt season. Concentrations of S0,

2

,

-

are steady in the soil, while the modeled soil shows a decrease in S0i

-

during the

WS2 melt season in both years.

3.7. Sensitivity

Sensitivity to inputs was greater on WS1 than WS2 (Figure

9), despite WS1 having 40% greater modeled soil volume per unit watershed area. For both watersheds, NO, a

-

, and

SCg

-

were the most sensitive to the doubling of wet deposition. a

-

was especially sensitive since it is unreactive in the watershed. Cations, ANC, and pH were not very sensitive because of buffering by cation exchange in the soil of both watersheds. ANC depression due to the doubling of deposition was 1 Aeql-

-1

for both watersheds. Depression of pH was around 0.03 units for both watersheds.

4.

Discussion

There was less net 11+ and NO consumption on WS1 as compared to WS2, suggesting that N chemistry is different between the two. Both watersheds had approximately the same relative export for base cations and SO,;

-

, indicating that both watersheds have similar processes controlling these species.

Four aspects of data analysis and model calibration show that more chemical changes are occurring on WS2 than expected by the surveyed amount of soil: (1) equivalent C/C„ values for WS1 and WS2 for cations and SOY, (2) higher percent base saturation, (3) the need to add reactive capacity equivalent to additional soil to adequately model stream concentrations, and (4) the greater N consumption.

4.1. Water Balance

The lack of water balance on these two watersheds is not due to an underestimate of evaporation. Our estimated evaporation is an overestimate of reasonable evaporation rates during the snowmelt season in alpine watersheds of the Sierra Nevada.

Melack et al.

[1998] found that only

50 mm of snow evaporated during the 1993 snowmelt

season at

FILW.

They also calculated a range of evaporation for the Sierra Nevada of

29 mm up to

166 mm per year. An evaporation estimate on the upper end of this range might explain the lack of water balance on WS1 in 1992 but cannot explain the lack of balance for WS1 in 1993 or for WS2 in either year.

The fact that cumulative discharge was less than the water volume estimated from the snow survey, even having ac-

5 2

3129

MEIXNER ET

AL: BIOGEOCHEMICAL

PROCESSES, SIERRA

NEVADA counted for evaporation, could be because of interbasin transfers through the snowpack or subsurface leakage through the cracked, exfoliated granodiorite. Snowpack structure can change effective watershed boundaries, resulting in diversion of snowmelt to basins outside the

one

monitored. As

WS1 has a total relief of

11 m and in

1993 a snowpack depth of over

5 m, one can easily envisage channeling that would reroute water away from our stream gauge. The granodiorite underlying both of these watersheds is extensively cracked. During snowmelt the ground surface of these watersheds is constantly saturated and provides ample opportunity for water to infiltrate deep

40

7

_,

30 g

.

20

_

1992 .._

........... _ .

.

_

--s

! %),

, ff 0-

1 I 1

_

••.,8.,

I II

1993

..... -

.

So

00

-

0

_1 0

CT d_

5

C.)

-

-

— e o _

0

-

_

_

_

ift

I e

• f1 r.pas1

I

.

Lysimeter

3 -

.

.

Lyslmeter

4

-

• es

8..

ELW parameters:

Optimized perame

-

.

<0

_

-

30

25

20

15

10

5

20

_

15 no iesi am i

-

t

I

• i. 0

,, t

I

•••

-

-

10

.

...........

0

-

-.....

_

5 a * 1

0

efo -

50

40

-

..............

0

-

_ ".

...............

-

.

30

_

-

20 o 0 °•--

0 o

10

.

0 f

0 1

0 _ 0°

00

-

, . c) ° ,°

I

0

100 120 140 110 130 150 170 190

Day of

Year Day of Year

Figure

8.

Comparison of modeled and measured soil chemistry for Watershed

2. Symbols are observed concentrations for the soil lysimeter indicated. Simulated values for ET

.W parameters and optimized parameters are shown. No attempt was made to fit modeled soil concentrations to observed values.

120

7

90 co

60

30

_

--

_

A ril

6.5

6.0

-

-

5.5

7

-J

25

-

_

I

.._

Ma

I I I I I

-

'

... '.... ........

t i f ill+

..

A d

Ma

Watershed

2 -

_

_

I

}

Ill

I.

'

II

+II

_

-

-

-,

-

-

-

-

-

I

1

I I I

1

I

Doubled Inputs

Calibrated Model:

-

•-- '

....,

_

-

_

-

-

---. ........... .., il if i iiiI

I t

_

j

15

_ g 10 q-

<4, 5 o

('D

O

1

I

.. ,....

,

I

.

I

.

I

' -' .....

.

,

I

,

I

)0110 120 130 140 110 120 130 14

0

Day of Year Day of Year

Figure

9.

Results for doubling wet deposition using

1992 data and calibration for both watersheds. The solid line is model output for doubled wet deposition. The dashed line is model output from final calibrated model.

into the rock outcrop to be exported from the watershed through the subsurface.

4.2.

Base Cation and ANC Production

The field survey indicated that

WS1 had 4 times the soil volume per unit area as compared to

WS2 (2.1 versus

0.5 cm).

However, the model fit suggested that the differences were only about

40% (2.1 versus

1.5 cm). Since it is unlikely that the field estimate of soil volume was off by this much, it appears

53

3130

MEIXNER ET AL.: B1OGEOCHEMICAL PROCESSES. SIERRA NEVADA that areas of exposed rock have the ability to buffer H. release cations, and take up nutrients. It is also unlikely that our estimate of total watershed area had this large of an error. The main areas of uncertainty in field verification of drainage divides were on exposed rock, so an overestimate of rock area relative to soil area could help explain the apparent underestimate of soil on WS2.

It is possible that some areas of rock in alpine regions react with precipitation in a manner equivalent to soil. Reports by others offer evidence of pH buffering and ANC production on exposed rock surfaces.

Clow and Mast

[1995] observed that the chemical composition of rainfall runoff from a 30 m

2

granite slab was much higher in cations and ANC than was the rainfall.

Comparison of Andrews Creek and Icy Brook in the Loch Vale watershed of Rocky Mountain National Park suggests that soil processes were the dominant control on stream concentrations despite the relatively low abundance of soils and their early stage of development

[Campbell et al.,

1995]. Rueslatten

and

Jorgensen

[1978] found that organic acids and weathering on exposed surfaces contributed cations and acidity to snowmelt runoff. Rock surfaces have also been found to have ion exchange capabilities

[Dahl et al.,

1979; Abrahamsen

et al.,

1979].

From studies on the Precambrian-Canadian shield,

Allan et al.

[1993] concluded that areas of bare rock exported cations to islands of soil present within the same Watershed, where the cations were then immobilized. They also observed that soil catchments had lower pH and ANC than did bare rock catchments, consistent with the higher pH and similar ANC and cation concentrations on WS2 as compared to WS1.

Three other possible sources of the cation export and ANC production on areas mapped as exposed rock are (1) soil trapped in crevices and in rubble fields, (2) lichens that cover the rock of these watersheds, and (3) dry deposition. A recent study in the Buckskin Range, Nevada

[Blank et al..

1996], reported that talus acted as a deposition zone for eolian dust, resulting in significant soil genesis. These eolian soils had a significant clay fraction, providing some ion exchange capacity; there was also evidence of past weathering. Areas of loose rocks and boulders within areas mapped as rock could serve as traps for eolian dust on WS2.

Epilithic lichens have long been known to weather exposed rock and have been shown to exchange cations with solution by using an abiotic complex

[Nash,

1996a, b;

Jones,

1988].

Through a combination of weathering substrate and holding weathered cations on an exchange complex, lichens in our watersheds might be a source of the buffering capacity and alkalinity production seen in this work. Lichens, however, do not provide all of the cations or alkalinity production. For lichens to provide all of the cation exchange capacity represented by the additional soil area on WS2. they would have to be present in quantities around 4000 g m

-2

[Nash,

1989]. No measurements were made on this watershed as to the quantity of lichens present. However, this value is far out of range from literature values on epilithic lichens, considering that arctic ecosystems with large quantities of lichens have total biomass around 1300 g

M

-2

[Nash,

1996a].

Since the only period of significant hydrologic runoff on these watersheds is spring snowmelt, the additional cation .

SOU, and alkalinity export we observed could be a result of accumulated summer/fall dry deposition. Using

82

Sr/

55

Sr ratios to identify sources of dissolved Ca in runoff.

Clow et al.

[1997] found that runoff from their microcatchment had nearly identical

82

Sr/

56

Sr to precipitation, indicating that the dissolved Ca in runoff came from wet and dry deposition to the rock surface.

Similar dry deposition processes may be at work in these two watersheds.

43. Nitrogen Cycling

Both watersheds consumed a significant fraction of the deposited N (Table 2). In addition, the C/C,, values of NO; for

WS2 were always less than for WS1 (Figure 6), meaning that less of the incoming N left this watershed. Table 2 indicates that the yield of dissolved inorganic N from WS1 was nearly twice that of WS2, because of greater consumption of the incoming dissolved inorganic N on WS2. Previous experience in alpine basins indicates that an ionic pulse should occur for

N 0

.

3 -

held in the snowpack

[Bales et al.,

1993]. Only a mild pulse was observed in either of these watersheds, and stream

NO concentrations were consistently below those in the snowpack.

These results are in contrast to findings at nearby watersheds. At ELW it was observed that the basin was a source of

N0'; in some years, while in others it was a sink

[Williams and

Melack, 1991]. However, the ELW was shown to be an N sink, receiving more NO; and NH:: in precipitation than dissolved organic and inorganic N in lake outflow

[Williams et al.,

1995].

On the other hand, two other watersheds in the Tokopah

Valley were net sources of N during the snowmelt season

[Stoddard,

1995].

Isotopic evidence suggests that soil NO rather than snowpack NO is responsible for the pulse of N seen in snowmelt runoff in the Loch Vale watershed in Colorado

[Kendall et al.,

1995]. Recent work in the Colorado Front Range has indicated that soil mineralization under snow cover, rather than the ionic pulse from the snowpack, is the source of the springtime pulse of NO; observed in spring melt waters

[Williams et al.,

1996a, b]. Two findings suggest that the same may be true in our small catchments. First, measured NO; concentrations were higher on WS1, with very few of the zero values that were present on WS2. Second, model structure had to be altered greatly on WS2 in order to remove all NO; in the stream, while no such alterations were needed on WS1. While saturated frozen soils may be the source of spring nitrate pulses in alpine streams, we are still left with the question of where the

N in the snowpack is going. This sink must be large and somehow be stronger on exposed rock surfaces than on areas of soil.

Four possible sinks for N in these catchments are soil organic matter, vegetation, litter, and lichens. All of these sinks have different temporal timescales and different storage capacities. Recent studies at Niwot Ridge, Colorado, have shown that soil microbes can be quite active under deep winter snowpacks and can mineralize significant amounts of soil organic matter and produce much greater quantities of dissolved inorganic N than are input to a watershed from the snowpack

[Brooks et al.,

1996]. The microbial population can also assimilate the N that is mineralized or received from the snowpack, depending on the carbon status of the soil and whether the microbes must compete with vegetation for the mineralized N

[Hart et al.,

1993;

Fenn et al.,

1998]. Soils can also immobilize

N abiotically, either by reaction of ammonium with cation exchange sites or by abiotic immobilization of ammonium in humus

[Johnson,

1992]. Denitrification can also cause gaseous export of N from soil

[Tisdale et al.,

1993]. These losses have been shown to be large under seasonal snowpacks

[Brooks et al.,

1997].

Vegetation is an important long-term sink for N

[Williams et al.,

1995] but less important over the short time (days to weeks)

54

MEIXNER ET AL. BIOGEOCHEMICAL PROCESSES. SIERRA NEVADA 3131 of snowmelt runoff in alpine basins. However, vegetation is the most likely long-term sink for N that is immobilized by the soil microbial pool during spring snowmelt.

Litter is found on the soil surface and in cracks between rocks where annual grasses and flowers grow. Soil microbes need both N and water to decompose vegetative litter with its relatively high C:N ratios (20-200) compared to the C:N ratios

(6-12) of soil microbes

[Swift et al.,

1979;

Parton et al.,

1987;

Tisdale et al.,

1993]. Litter in cracks and crevices would be in the flow path of snowmelt runoff, since melt is likely to travel along cracks and crevices present on bare rock. Soil microbes would thus have a high C:N organic matter source in the litter that would serve as a substrate, and the dissolved inorganic N contained in snowmelt would provide a necessary nutrient to break down the litter. The dissolved inorganic

N immobilized by the soil microbes in the litter must eventually be exported from the watershed or be incorporated into a long-term pool for N, such as vegetation or soil organic matter.

Lichens covering the exposed granite present in alpine watersheds could be consuming precipitation inputs of N. Lichen growth may be

N limited [Crittenden

et al.,

1994]. Further, lichens can absorb N species from solution and store for later use

[Rai, 1988]. Finally, Lang et

al.

[1976] have shown through a series of experiments that lichens have the ability to remove

N from solution and contribute cations to the same solution.

Thus lichens might provide some of the extra buffering capacity and

N uptake that our calibration indicates exist on WS2.

It is unlikely that soil is the primary .net sink for dissolved inorganic N in these catchments. Both of these catchments have less soil than the ELW (2.1 cm and 0.5 cm basinwide equivalent soil depth as opposed to

13.6 cm at ELW) [Tonnes-

sen,

1991;

Wolford et al.,

1996]. If soil organic matter and vegetation were the sink for

N, dissolved inorganic export on

WS2 would be greater than export on WS1 because of the greater soil volume, larger biomass, and higher C:N ratio on

WS1 (Table 1). We observed the opposite, with higher NO; concentrations on

WS1 representing greater export of dissolved inorganic

N on WS1 than WS2. Also, if soil were the ultimate sink for

N, we would expect NO concentrations, and thus dissolved inorganic N export, to be lower at ELW than these watersheds. What we see is the opposite: highest NO; concentrations at

ELW (5 geqL

-1

), intermediate levels on

WS1 (1.5 p.eqL

-1

), and lowest concentrations on WS2 (0.2

p.eqL

-

1

).

(In all of these watersheds, NH: flux is small compared to NO flux.)

Instead of a sink, the soils of these watersheds are a likely source of inorganic N. The

C:N ratios of the soils on each catchment

(16 for WS1 and 13 for WS2) are indicative of soils in which soil microbes are mineralizing organic matter to produce inorganic

N in excess of their demand for inorganic N

[Tisdale et al.,

1993 ] . Greater export of inorganic N on WS1 may be due to its relatively larger amount of soil.

4.4. Sensitivity to Changes in Loading

The sensitivity calculations (Figure 9) further illustrate the difference between these watersheds (Table 4); WS2 was actually less sensitive to increased chemical loadings than was

WS I. This is in contrast to our hypothesis, which was based on the surveyed percent of soil cover. Also striking is the relatively small sensitivity of both catchments to a doubling of chemical fluxes in wet deposition, especially as compared to ELW [Wol-

ford and

Bales,

1996]. ANC and pH depression for these watersheds was an order of magnitude smaller than at ELW. At

ELW, doubling inputs in wet and dry deposition resulted in a maximum depression of 0.3 units and 9.1 p.eqL

-1

for pH and

ANC, respectively.

Within the model, four parameters that control the effect of the spring ionic pulse on stream chemistry combined to attenuatepH and ANC depressions on these catchments, relative to

F.I.W. First, the chemical elution parameter that determines the strength of the ionic pulse was calibrated to a value of 2 on both catchments as opposed to 4 at ELW, resulting in a weaker ionic pulse. Second, the increase of the surface runoff mixing parameter on both watersheds indicates greater contact of runoff with soil on these watersheds than at ELW. The greater contact of runoff with soil may reflect less downslope flow through the snowpack and more flow along the ground surface, possibly owing to the lower slope of these catchments as compared to ELW, a mean slope of 13% for WS1, 17% for WS2, and 31% for ELW. The lower slope permits water to travel more slowly on these catchments than at ELW and permits longer interaction with soil and rock surfaces. Third, the

SO;

.-adsorption parameter of both watersheds is lower, so the

SO.i

concentrations are high. Measured and modeled SO

1

-

concentrations (5 geqL

-1

) are already more than double concentrations in deposition to the watersheds (1.5 AeqL'). Thus doubling

S0

2

,

--

deposition to the watersheds will have a lesser impact since stream

S0,

2

,

-

concentrations are already relatively high. Finally, the

N parameters on both of these watersheds were set so that almost all

N was consumed. This attenuated the effect of an increase in N deposition on stream chemistry.

More NO consumption combined with a higher percent base saturation on WS2 explains the reduced sensitivity, as compared to

WS1, to changes in wet deposition. More NO is consumed on

WS2 than on WS1, and thus the sensitivity ofpH and ANC are reduced. The higher percent base saturation of

WS2 means more cations are released from the soil when wet deposition is increased, thus buffering the response of pH and

ANC to the increases in wet deposition.

4.5. AHM Model Structure and Parameters

The ARM was originally developed using the

F.LW data.

and this is the first application of the ARM beyond that watershed. Both watersheds were modeled with the same general model structure as on ELW. A subunit of rock and a subunit of soil were capable of capturing the mean and general variability of stream chemistry on these two watersheds. The one major deviation from the ELW structure for both watersheds was that the surface runoff mixing ratio was >0; it was set to 0.5 for

WS1 and 0.2 for WS2. The model, as applied to these two watersheds, had eight hydrologic parameters; changing one to improve fit represents only a small modification.

However, the final chemical parameter values for

WS1 were significantly changed from ELW values. The main differences in the chemical parameterization are related to the pH of stream water and the low NO; and

NFIZ concentrations in the stream. Also, the parameterizations had to achieve similar

SCg

-

and cation concentrations for both watersheds despite the lower volume of soil surveyed on WS2.

The pH of stream water was significantly different between these two watersheds. The streampH of WS1 was steady at 5.5, and the stream pH of

WS2 was a steady value around 5.8. In calibrating the model, there are only two ways to affect stream pH: a djust soil base saturation, and adjust the P of the stream. For WS1 we adjusted both of these. On

WSI the percent base saturation was changed from

17.9 to

4.2%. An

55

3132

NIF_DCNER ET AL.:

BIOGEOCHEMICAL

PROCESSES. SIERRA NEVADA increase in stream

P co,

to a value greater than atmospheric was also necessary to lower the modeled stream

pH.

The

P„,

of the stream on WS2 had to be decreased to match observed pH, but it was still above atmospheric

P oe,.

Stream P oe

, was increased to lower pH On WS1; however, organic acids (unmeasured) may also be contributing to the lower pH. Coniferous vegetation, like that of WS1, can contribute organic acids to streamflow

[Likens and Bormann,

1995].

Recent work by Boyer et al.

[1995] has shown that dissolved organic carbon in alpine basins can be an important flux. The

CO

2

addition was a parameter adjustment to provide a watershed-based source of acids, given our lack of knowledge of organic acids in the catchments. It would take 1.5 kieqL

-1

of organic acids to explain the pH depression caused by the additional CO

2

that we have calibrated WS1 to have.

Differences in calibration needed to match the observed stream NO and NH:

-

were more striking. For both watersheds the N consumption parameters in the soil compartment were set to their maximum values (Table 4). This change was necessary to have the model capture the extremely low NO2

concentrations that were observed in the stream and to remove all NH:* from snowmelt since no NH: was observed in the streams. In order to remove all of the NO from runoff on

WS2, it was necessary to give soil biogeochemical properties to material mapped as rock. While these changes illuminated the differences between the two watersheds, this alteration is conceptually unappealing for two reasons. First, suction lysimeters did measure NO in the soil pore waters, which our model did not capture. Second, significant changes to model structure had to be made to account for the low NO concentrations on

WS2. The changes to soil depth and soil area highlight the need to improve the N dynamics model of the AHM. Use of N dynamics similar to those included in the CENTURY model

[Parton et al.,

1987], which has a fuller representation of N cycling, could help test hypotheses about the location and causes of NO and NHZ immobilization during snowmelt runoff at a watershed scale.

In order to have the two watersheds behave similarly with respect to S0,1

-

, cation export, and alkalinity production, it was necessary to increase the soil reactive capacity of WS2 to properly capture the concentrations and timing of ion release during the melt season of WS2. This change in soil reactive capacity was represented by the doubling of soil area and increase in soil depth for the watershed. This step was necessary to correctly match both the stream (Figure 5) and soil chemistry

(Figure 8). This adjustment in model structure should be viewed as an attempt to quantitatively represent the extent and intensity of biogeochemical processing on the watershed.

The large changes in chemical parameters on these two watersheds and the small changes in hydrologic parameters highlight the value of good soil chemical data for estimating

AHM parameters independent of calibration to stream measurements. We lacked that information for these watersheds, so soil chemistry was calibrated from stream discharge chemistry.

At ELW, calibration was done using measured base saturation, cation exchange capacity, and detailed data on soil chemical reactions, as well as stream chemistry data

[ho/ford et al.,

1996].

shed from apparently similar soil on a nearby watershed. Areas of exposed rock may have properties generally attributed to soil, in that they are a source of cations and ANC. Despite the larger volume of more developed soil on WS1, it has a lower percent base saturation in the soil and a lower pH and higher stream NO; than WS2. Thus WS1 produced more acidic waters than the exposed rock catchment of WS2. Further, WS2, despite its dominance by areas of exposed granodiorite, had a higher percent base saturation and greater nitrate consumption and thus was less sensitive to changes in deposition than

WS1.

Our results lead us to conclude that soils and vegetation are not responsible for the greater N retention on WS2 as compared to WS1 during snowmelt. Litter on areas of rock and lichens growing on rocks appear to be responsible for the immobilization of snowpack-dissolved inorganic N. Whatever the hypothesis is for N retention in these alpine watersheds, the sink must be larger on areas of exposed rock than it is in well-soiled and well-vegetated areas.

These watersheds are better buffered against changes in stream chemistry from possible increases in acid deposition than is ELW for three reasons. First, the ionic pulse was less pronounced. This was apparently associated with the greater mixing of surface runoff and soil water prior to entering the stream. Greater runoff contact with soil may reflect less downslope flow through the snowpack and more flow along the ground surface, possibly due to these catchments being less steep than ELW. Second, these watersheds apparently had higher stream sulfate concentrations and thus lower sulfate adsorption. Finally, nitrate consumption and ANC production are greater on these watersheds.

The AHM is generally transportable to watersheds similar to

ELW, with chemical parameters requiring considerably more adjustment than physical (hydrologic) parameters. Estimation of soil chemistry parameters by calibrating with stream discharge chemistry data was less satisfactory than for ELW, where more data were available. Soil chemical data gave us a secondary way to evaluate our model calibration. Measurement of soil exchange reactions and sulfate adsorption would further constrain our model calibration. However, the heterogeneous nature of alpine environments and the degree of lumping needed to conduct chemical modeling of these watersheds implies that calibration will still be needed, even with extensive soil data.

The modeling of organic acids and N cycling at the watershed scale are areas for future investigation. An improved understanding of sources and sinks is required before the representation of organic acids in the AHM can be improved.

Incorporating a model that more explicitly represents N cycling in alpine watersheds might improve model performance for both nitrate and ANC. Also, processes not currently in AHM could be important in accurately modeling stream chemistry.

For example, lichens, areas of soil included within exposed rock, and the influence of snow-covered area on soil microbes need to be incorporated into biogeochemical models of alpine basins.

5. Conclusions

The extent of biogeochemical processes in alpine watersheds cannot be determined by simply mapping the relative amount of soil area and inferring soil properties of the whole water-

Acknowledgments. Support for field work and analyses was provided by the California Air Resources Board

A032-116;

J.

Melack was a co-investigator. Thanks to A. Esperanza and D. Graber and the other research staff of the National Park Service and United States Geological Survey at Ash Mountain for their support and permission to conduct this research. The first author was supported by a NSF Grad-

5 6

MEIXNER ET AL: BIOGEOCHEMICAL PROCESSES, SIERRA NEVADA 3133 uate Research Fellowship and a Canon National Park Science Scholarship. A

NASA-EOS grant provided partial support for this work. N.

Ohte and R.

Wolford both helped construct the model. The authors would also like to thank R. Harrington, J. Rohrbough, J. Melack,

M. R. Williams, M. W. Williams, S. P. Anderson, K. Cotter, and an anonymous reviewer for their helpful suggestions. R. Brice helped in manuscript preparation.

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Boyer, E. W„ G. M. Hornberger, K. E.

Bencala, and D. M. McKnight,

Variations of dissolved organic carbon during snowinelt in soil and stream waters of two headwater catchments, Summit County, Colorado, in

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Brooks, P. B., M. W. Williams, and S. K. Schmidt, Microbial activity under alpine snowpacks, Niwot Ridge, Colorado,

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Brooks, P. D., S. K. Schmidt, and M. W. Williams, Winter production of CO

2

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N

2

0 from alpine tundra: Environmental controls and relationship to inter-system C and N fluxes,

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403-413,

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Brown, A. D.,

L

J. Lund, and M. A.

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2811-2821, 1995.

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Tranter,

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235-242, 1995.

Clow, D. W., M. A. Mast, T. D.

Bullen, and J. T. Turk, Strontium

87/strontium

86 as a tracer of mineral weathering reactions and calcium sources in an alpine/subalpine watershed, Loch Vale, Colorado,

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1335-1351, 1997.

Crittenden, P. D., I. Katucka, and E. Oliver, Does nitrogen supply limit the growth of lichens?,

Clyptogamic Bot., 4,

143-155, 1994.

Dahl, J. B., C. Qvenild, O. Tollan, N. Christophersen, and H. M. Seip,

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179-190, 1979.

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Johnson, A. D.

Lemly,

S. G. McNulty, D. F. Ryan, and R.

Stottlemyer, Nitrogen excess in North American ecosystems: A review of geographic extent, predisposing factors, ecosystem responses, and management strategies, Eco!.

App!., 8,

706-733, 1998.

Hart, S. C., M. K. Firestone, E. A. Paul, and J. L. Smith, Flow and fate of soil nitrogen in an annual grassland and a young mixed-conifer forest,

Soil Biot Biochem., 25,

431

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442, 1993.

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J.

Environ. Quai.,

21,

1-12, 1992.

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in CRC Handbook of Lichenology,

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Fla.,

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Kendall, C., D. H. Campbell, D. A. Burns, J. B.

Shanley, S. R. Silva, and C. C. Y. Chang, Tracing sources of nitrate in snowmelt runoff using the oxygen and nitrogen isotopic compositions of nitrate, in

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Covered Catchments,

edited by

K. A.

Tonnessen,

M. W. Williams, and M.

Tranter,

JANS Pub!., 228,

339-347, 1995.

Kirchner, J. W. , R. P. Hooper, C. Kendall, C. Neal, and G.

Leavesley,

Testing and validating environmental models,

Sci. Total Environ.,

183,

33-47, 1996.

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Heier,

Potential alteration of precipitation chemistry,

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779-241, 1976.

Likens, G. E., and F. H. Bormann,

Biogeochemistry of a Forested Ecosystem ,

2nd ed., Springer-Verlag, New York, 1995.

Melack, J. M., J. O. Sick.man, A.

Leydecker, and D.

Marrett,

Comparative analyses of high-altitude lakes and catchments in the Sierra

Nevada: Susceptibility to acidification,

Tech. Rep. CARS

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188,

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Board, Sacramento,

1998.

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Heavy Metal Tolerance in

Plants: Evolutionary Aspects,

edited by A. J. Shaw, pp. 119-131, CRC

Press, Boca Raton, Fla.,

1989.

Nash, T. H., Nutrients, elemental accumulation and mineral cycling, in

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edited by T. H. Nash, pp.

136-153,

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Press, New York,

1996a.

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Biology,

edited by T. H. Nash, pp.

88-120,

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1996b.

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Soil Sci. Soc. Am. J., 51,

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1179, 1987.

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edited by M.

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201-237,

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H. G., and P. Jorgensen, Interaction between bedrock and precipitation at temperatures close to zero degrees celsius,

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Hydro!., 9,

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6, 1978.

Stoddard, J.

L.,

Episodic acidification during snowmelt of high elevation lakes in the Sierra Nevada Mountains of California,

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Soil Pollution, 85,

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358, 1995.

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Decomposition in Terrestrial Ecosystems,

Blackwell

Sci.,

Cambridge, Mass.,

1979.

*

Tisdale, S. L., W. L. Nelson, J. D. Beaton, and J. L.

Havlin,

Soil Fertility and Fertilizers,

MacMillan, Indianapolis, Indiana, 1993.

Tonnessen,

K. A., The Emerald Lake watershed study: Introduction and site description,

Water Resour. Res., 27,

1537-1539, 1991.

Westall, J. C., J.

L

Zachary, and F. M. M. Morel,

MINEQL: A computer program for the calculation of chemical equilibrium composition of aqueous systems,

Tech. Note 18,

EPA grant R-803738,

Dep. of

Civ.

Eng., Mass. Inst. of

Technol., Cambridge, 1976.

Williams, M. W., and J. M. Melack, Solute chemistry of snowmelt and runoff in an alpine basin, Sierra Nevada,

Water Resour. Res.,

27,

1575-1588, 1991.

Williams, M. W., R. C. Bales, A. D. Brown, and J. M.

Melack,

Fluxes and transformations of nitrogen in a high-elevation catchment,

Sierra Nevada,

Biogeochemisny, 28,

1-31, 1995.

Williams, M. W., J. S. Baron, N. Caine, R.

Sommerfeld, and J. R.

Sanford, Nitrogen saturation in the Rocky Mountains, Environ.

Sci.

Technol., 30,

640-646, 1996a.

Williams, M. W., P. D. Brooks, A. Mosier, and K. A.

Tonneson,

Mineral nitrogen transformations in and under seasonal snow in a high-elevation catchment in the Rocky Mountains, United States,

Water Resour. Res., 32,

3161

-

3171, 1996b.

Wolford,

R. A., and R. C. Bales,

Hydrochemical modeling of Emerald

Lake watershed, Sierra Nevada, California: Sensitivity of stream chemistry to changes in fluxes and model parameters,

Limnot

Oceanogr., 41(5),

947

-

954, 1996.

Wolford,

R. A., R. C. Bales, and S.

Sorooshian, Development of a hydrochemical model for seasonally snow-covered alpine watersheds: Application to Emerald Lake Watershed, Sierra Nevada,

California,

Water

Retour.

Res., 32,

1061-1074, 1996.

R. C. Bales and T.

Mebcner,

Department of Hydrology and Water

Resources, University of Arizona,

Harshbarger. Building 11, Tucson,

AZ 85721.

(e-mail: [email protected]; [email protected])

A. Brown, Ventura Community College, Ventura, CA

93003.

(e-mail: [email protected])

(Received April

7, 1998; revised June 12, 1998; accepted June 23, 1998.)

57

APPENDIX B - STREAM CHEMISTRY MODELING OF TWO WATERSHEDS IN

THE FRONT RANGE, COLORADO

58

American

Geophysical

Union

2000 Fionda Avonue.

Wasnalgion. CC 20C,09

.1-202-462-6900 r'ax

• 1-202-32B-0566

59

August 4, 1999

Mr. Torn Mcix.ner

Department of Hydrology and Water Resources

Room 203B

.

, Building #11

P0 Box 210011

University of Arizona

Tucson, AZ 85721-0011

Dear Mr. Meixner:

We are pleased to grant permission for the use of the material requested for inclusion in your thesis, including microfilm editions thereof. Permission is restricted to the use stipulated. The original publication must be appropriately cited. The credit line should read: "authors, journal or book title, volume number, page numbers, year," and the phrase "Copyright by the American

Geophysical Union." Substitute the last phrase with "Published by the American Geophysical

Union" if the paper is not subject to U.S. copyright -- see the copyright line on the first page of the published paper for such classification.

Please feel free to contact me again if you need further assistance. Thank you.

Sincerely,

Cat/di/iv\

Pamela Calliham

Publications Administration

Coordinator

Trie A

, e,an Guodlsys.cei

Linon

enmendasses Vee Earth sgrus: spa:, s.e

, ses

Geodesy. Smsmology, AlmosphondSdlede<S, Georna;neliste and l'aleomag

, evem

Ocean S,,ors..,os I tyd

, ceo;)

,

voic...snolo2y. Geochernst.

y a ne POI

,

To‘lorloylir.mn

.

S;JCe Physics and As•onarry

C 4 NY

Stream chemistry modeling of two watersheds in the

Front Range, Colorado

Thomas Meixner, Roger C.

Bales,

Mark W.

Williams',

Don

H. Campbell'

and

Jill

S.

Baron'

Department

of

Hydrology

and

Water Resources,

University of Arizona, Tucson

May 5, 1999

Received

;

accepted

60

Short

title: FRONT RANGE

WATERSHEDS

'Institute

for

Arctic

& Alpine

Res.,

University of Colorado, Boulder

2

USGS-WRD, Denver, Colorado

3

USGS-BRD, Fort Collins, Colorado

61

Abstract. We investigated the hydrologic,

geochemical,

and

biogeochemical

controls on stream chemical composition on the Green Lakes Valley and Andrews

Creek watersheds using the Alpine

Hydrochemical

Model (ARM). Both sites had comparable data sets from

1994

and

1996,

including high-resolution spatial data and high frequency time series of hydrology, geochemistry and meteorology.

The model of each watershed consisted of three terrestrial subunits (soil, talus, and rock), with the routing between the subunits determined by spatial land cover data. Using

1994

data for model calibration and

1996

data for evaluation,

AHM

captured the dominant processes and successfully simulated daily stream chemical composition on both watersheds. These results confirm our procedure of using spatial, and site specific field and laboratory data to generate an initial catchment model and then calibrating the model to calculate effective parameters for unmeasured processes. A net source of nitrogen was identified in the Andrews

Creek watershed during the spring

snowmelt

period, whereas nitrogen was immobilized in the Green Lakes Valley. This difference was most likely due to the larger and more dominant area of talus in the Andrews Creek watershed. Our results also indicate that routing of

snowmelt

through either soil or talus material is sufficient for retention of

H+

and release of base cations, but that

N

retention is more important on areas mapped as soil. Due to the larger ionic pulse and larger fraction of surface runoff the Green Lakes Valley was more sensitive to a doubling of wet deposition chemistry than the Andrews Creek watershed

62

Introduction

The thin soils, limited vegetation, and snow dominated hydrology of alpine regions limit their ability to buffer against changes in climate and atmospheric deposition

[Melack

and

Stoddard, 1991].

In the Front Range of Colorado, the predicted response of alpine watersheds to changes in climatic and chemical inputs has implications for the health of aquatic resources, and the setting of emissions standards

[Williams et

al., 1996]. Due to their close proximity to urban sources of air pollution, alpine catchments in the Colorado Front Range are subjected to increased atmospheric deposition

[Williams et

al., 1996] and are already undergoing N saturation, a process where previously N limited systems begin to leak inorganic nitrogen

[Aber,

1992;

Williams et

al. 1996].

More recently it has been hypothesized that areas of talus and the material buried beneath talus are responsible for the high

NO

3

-

concentrations observed in early spring snowmelt and the high summertime concentrations observed in the streams of the Front Range

[Williams et

al., 1997;

Baron and Campbell,

1997].

Furthermore runoff flowpath exerts a large control on the stream chemistry, and on the response to chemical perturbations of a watershed

[Grosbois et

al., 1988;

Campbell

et al., 1995;

Brown,

1998].

The Alpine

Hydrochemical

Model

(AHM) was specifically designed to investigate the problem of episodic acidification in alpine watersheds. AHM differs from several other watershed acidification models such as MAGIC that were designed with longer time steps to address questions of chronic acidification

[Cosby

et

al., 1985]. The problem of episodic acidification is especially important in alpine watersheds due to the ionic pulse of chemicals in the snowpack and the fact that even changes in watershed acidity of only three days can have an impact

63 on the aquatic biota of alpine watersheds [Barmuta

et

al.,

1990]. The AHM uses a conceptual representation of watershed hydrologic and biogeochemical processes that differs from empirical approaches that have been developed for investigating regional sensitivity to episodic acidification

[Eshleman

et

al.,

1995; Leydecker

et

al.,

1999]. This conceptual structure permits the investigation of the processes and watershed properties that determine watershed sensitivity to acidification.

Areas of modeling uncertainty can be used to guide field research and improve our understanding of alpine hydrologic and biogeochemical processes.

The Alpine Hydrochemical Model (AHM) was developed in part to improve our understanding of how alpine watersheds will respond to perturbations

[Wolford et al.,

1996]. AHM was initially used to simulate the hydrochemistry of the 1.2 km' Emerald Lake watershed in the Sierra Nevada of California

[Wolford

et

al.,

1996] and has since been applied to two watersheds near

Emerald Lake [Meixner

et

al.,

1998]. Extension of the AHM to other alpine catchments will improve both our confidence in the model and our understanding of biogeochemical processes.

We applied the AHM to the Andrews Creek and Green Lakes Valley watersheds of the Rocky Mountain Front Range to address four questions. First, can the AHM describe the stream chemistry of these two watersheds using a similar description of chemical processes as was used earlier to simulate the

Emerald Lake watershed in the Sierra Nevada? Second, what differences in nitrogen dynamics exist between these two catchments, and how can the AHM be used as a tool to investigate these differences? Third, since the physical relationship between soil, exposed bedrock, and talus differs between these two watersheds, what role does flow routing have in determining the hydrochemical

64

response of alpine watersheds? Finally, how do the models of these two watersheds differ in their sensitivity to changes in atmospheric deposition?

Met hods

Site Green Lakes Valley and Andrews Creek are alpine watersheds in the Front

Range of the Rocky Mountains. Green Lakes Valley

[Caine

1995]

is part of the

Niwot

Ridge Long Term Ecological Research site

(LTER)

and Andrews Creek

[Baron and

Mast

1992]

is part of the United States Geological Survey

(USGS)

Water, Energy, and

Biogeochemical

Budgets (WEBB) program. In the Green

Lakes Valley, water quality for eight different locations along the first order stream in the valley has been monitored since

1981. GLV4,

the upper

2.2 km

2 of the

7 km

2

Green Lakes Valley, represents the alpine portion of the larger catchment.

GLV4

ranges in elevation from

3550 m

at the outflow from Green

Lake

4

to over

4000 m

at the continental divide with relatively equal areas of rock

(30%),

talus

(36%)

and soil

(30%)

(Figure

1).

The remaining

4%

of the watershed is covered by Green Lake

4

and

5.

The soil in the Green Lakes Valley is located along the valley floor and is adjacent to the stream. The areas of talus are generally located up hill from the valley and drain into the soil. The areas of exposed rock in the watershed are located most prominently along the tops of ridges

[Brown,

1998].

Andrews Creek, a catchment nested within the Loch Vale watershed, ranges in elevation from

3200

to

4000 m

and has an area of

160

ha. The watershed is dominated by rock

(57%),

and talus

(31%)

(Figure

2).

In contrast to the Green

Lakes Valley, soils

(11%)

are confined to a few areas of tundra and wetland soils on the ridge line of the watershed and at the base of the watersheds respectively

65

[Walthall, 19851. Areas of talus dominate the valley bottom and are adjacent to

Andrews Creek.

The two watersheds share a common lithology of silver plume granite and biotite gneiss

[Cole, 1977; Pearson, 1980].

The hydrology of both watersheds is dominated by a large wintertime snowpack that melts during the spring and summer and frequent summer precipitation [Caine, 1995; Baron and Mast, 1992].

Both watersheds have no deep groundwater storage, and with the small volume of soil present in the watersheds, there is little soil zone storage.

Both watersheds are drained by a single first order stream. Stream-water discharge is monitored continuously at a gauging station at the base of each watershed. Stream water samples are collected for chemical analysis at the same locations. Both watersheds are topped by glaciers;

GLV4, the 8-ha

Arikaree glacier, and Andrews, the 10-ha Andrews glacier.

Model structure The

AHM [Wolford et al., 1996] is a lumped conceptual model that was designed for simulating the hydrology and biogeochemistry of alpine watersheds. Modeling a watershed with the

AHM requires that a particular structure be chosen to describe the hydrologic and biogeochemical cycles of a watershed. The

GLV4 and Andrews Creek watersheds were broken down into three terrestrial subunits (soil, rock, and talus), with a single stream subunit.

The area and spatial relationships of soil, rock and talus were determined from digitized soils maps [Brown, 1998; Walthall , 1985] For GLV4, flow from the rock subunit was routed onto talus, and from there to the soil subunit before entering the stream. For Andrews runoff from the rock and soil subunits, was routed to talus and from there to the stream.

Each terrestrial subunit contains different compartments representing

66 the snowpack, snowpack free water, snowmelt, surface runoff, interception by trees and litter, and zero, one or multiple soil horizons. Stream subunits consist of different compartments representing the snowpack, snowpack free water, snowmelt, stream ice, and streamflow (Figure 3). In addition to the compartments described for the stream, lake subunits can be stratified with the two lake layers varying in thickness. Hydrologic processes are modeled separately from geochemical processes.

At each daily time step AHM adjusts snow covered area, computes interception, adjusts snowpack for precipitation and melt, calculates influxes of materials to each soil and rock subunit, drains surface runoff, computes evapotranspiration and sublimation, calculates kinetic reactions, calculates chemical equilibrium in soil compartments, drains water from the soil horizon, calculates chemical equilibria in streams and produces output. Chemical speciation is handled using equations adapted from MINEQL [Westall

et

al.,

1976]. One strength of the model is its precise mass and charge balance for both chemical species and hydrologic calculations [Wolford

et

al.,

1996].

Model Inputs Many model inputs for GLV4 were taken directly from data downloaded from the Niwot Ridge LTER web site

(http://culter.colorado.edu:1030/). For Andrews, data were collected and distributed as part of ongoing USGS efforts to study biogeochemical budgets in the Loch Vale watershed

[Baron and Campbell,

1997]. Inputs to the model include: potential evapotranspiration (PET), potential sublimation (PS), snow covered area (SCA), and precipitation quantity and quality.

Mean evapotranspiration from field measurements was used for both catchments. During winter PET was set to 0.66 mm day

-1

and 1.3 mm day-1

67 during the summer. PS was set to

75% of these values based on experience from modeling evaporation at Emerald Lake

[Wolford,

1992]. The model calculates actual evaporation from soil and talus surfaces based on a parameter that defines the fraction of PET that actually evaporates. (For this application evaporation from soil was equal to PET and evaporation from talus was 0.9 of PET.)

Ingersoll [1995] developed a 1994 SCA time series for Andrews. Additional

SCA maps were developed from orthorectified airphotos of the Green Lakes

Valley in

1994 and 1996 and Andrews in

1996.

For early dates (April 22, 1994 and

May 9, 1996), shaded areas were masked out during classification and classified separately. These maps were evaluated using visual inspection, and classification repeated until a good visual match resulted. SCA maps were overlayed with soils maps to determine SCA for each subunit

[Brown,

1998;

Walthall,

1985].

Glaciers were assumed to overlie talus.

For GLV4, precipitation quantity was recorded continuously at the Niwot

Ridge LTER D-1 meteorological station at the edge of the watershed (elevation

3743 m).

The gauge is shielded by a snow fence and an alter shield to improve estimates of precipitation during windy periods. Precipitation events were classified as rain if mean daily temperature was above 0°C. Precipitation chemistry is sampled weekly 2.2 km to the east of D-1 at the Niwot

Ridge

Saddle Tundra Laboratory as part of the National Atmospheric Deposition

Program/National Trends Network

[NADP/NTN,

1998; Peden, 1986] (Figure

4).

For Andrews, precipitation quantity was recorded continuously with two

Belfort rain gauges at a meteorological station in the nearby main valley of Loch

Vale watershed (elevation 3160 m). One gauge has a nipher wind shield and the other has an alter wind shield. Previous studies have shown no significant

68 difference between the two and they are used interchangeably to produce the most continuous record

[Baron and Campbell,

1997;

Bigelow et al.,

1990].

Precipitation chemistry is sampled weekly at the same location as part of the

NADP/NTN

[NADP,

1998] (Figure 4).

Two methods were used to estimate dry deposition to these watersheds.

Winter dry deposition for all species was calculated by subtracting winter wet deposition from peak accumulation snowpits. Modeled summer N dry deposition used the estimate of

Baron and Campbell

[1997] which was

1.3 kg ha

-l yr'.

All other species were left at the values used for the Emerald Lake watershed

[Wolford

1992].

Parameter Estimation and Initial Conditions Using the model structure defined by

Wolford et al.

[1996], field and laboratory measurements were used to set most parameters and initial conditions, with remaining parameters estimated by model calibration using

1994 stream chemistry data. Soil extent, depth and bulk density were based on soil surveys

[Brown,

1998;

Litaor,

1985;

Baron and

Mast,

1992]

(Table 1). Mineral weathering rates based on a mass balance of the entire Loch Vale watershed were used for both watersheds

Mast et al.

[1990]

(Table

2).

Exchange coefficients and hydraulic conductivity parameters for the soil and talus were set to the values for the Emerald Lake watershed. Depth weighted averages of exchangeable ion amounts in soil were estimated using data from

Litaor

[1985] and

Walthall

[1985].

Exchangeable cations for talus and soil in

GLV4 were assumed to be identical since no data were available for talus. For

Andrews, data for

Entisols were used for the talus and values for

Inceptisols used for the soil subunit in Table

3. Parameters controlling sulfate adsorption were based on data from Loch Vale

[Baron et al.,

1992], with a sulfate adsorption

69 capacity of

0.71 mmol kg

-1

soil. Silica adsorption properties were based on values from the Emerald Lake watershed [ Wolford

et

al., 1996]. Glaciers were assumed to have a depth of 0.1 m of snow water equivalence

(SWE) at the beginning and end of the water year to allow for carry over of

SWE from year to year and to permit the identification of ablation or accumulation of the glacier.

Calibration Model calibration involved three steps: i) snowmelt optimization, ii) chemical calibration, and iii) optimization of hydrologic parameters

[Meixner

et

al., 1998]. Snowmelt optimization estimated daily melt rates by subunit using

SCA and discharge to constrain the search for optimal snowmelt rates. As annual discharge exceeded measured precipitation less estimated evaporation, snow was added to both watersheds in both years to achieve mass balance.

Calibration proceeded as a stepwise adjustment of chemical parameters until model output matched observations (Table 4).

First, the ionic pulse parameter

(D) was adjusted to fit stream Cr. Second, cation exchange coefficients were adjusted for each cation until modeled soil concentrations matched target values.

Third, SO ,i

-

adsorption parameters were changed to increase or decrease modeled

SO

4

2-

concentrations in the soil and stream. Fourth, parameters governing N consumption in the soil were altered to improve the fit to stream NO

3

-

and

NH

-

4

I

concentrations. N parameters were set at the beginning of each calendar month and remained constant for the entire month. Finally, mineral weathering rates and silica adsorption parameters and initial conditions were adjusted to capture the observed Si concentrations. If necessary, hydrologic parameters were changed to improve simulations. Model evaluation was done using inputs and stream chemistry for

1996.

Calibration decisions and evaluation judgments were made by visually

70

comparing modeled stream time series with the available observations. For the purposes of comparison the Nash-Sutcliffe statistic (coefficient of efficiency) was calculated for the initial

(uncalibrated)

and calibrated models for both watersheds for

1994

and

1996

for all species and hydrologic discharge. The

Nash-Sutcliffe value is calculated as:

E =

1

1.0

.

0—

E r t

2

(

1

) where,

P

is the predicted value,

0

is the observed,

0

is the mean observed value and

i

is the observation number. A value of

E

less than zero indicates that the mean of the observations is a better predictor of the observed data than the model. Higher values (closer to

1)

indicate better agreement between the model and observations

[Nash and Sutcliffe,

1970; Wilcox et al., 1990; Legates and

McCabe,

1999].

Results

Green Lakes Valley Optimization of water inputs and

snowmelt

achieved a near perfect match between measured and modeled discharge except for a few large rainfall events during the summer (Figure

5).

Measured snowfall at D-1 in the

1994

water year was

1.05 m,

while the model input was

1.11

m. In

1996,

measured snowfall at D-1 was

1.00 m,

versus a model input of

1.35

m.

Little calibration was needed to improve the match between measured and modeled stream concentrations, with soil chemical parameters being most important. A total of

13

chemical parameters were adjusted from their original Emerald Lake watershed

(ELW)

values during the calibration (Table

4).

Adjusting hydrologic parameters, altering model structure, and adjusting parameters controlling talus processes did not significantly improve modeled

71 stream chemical concentrations. After calibration, the match of model output to measured stream concentrations was improved for much of both calibration and evaluation years (Figure 5 and Table

5).

Model results show day to day variability not present in the data, due in part to sampling interval and in part to comparing modeled stream to observed lake outflow.

The best matches of modeled and measured stream concentrations were for

ANC, pH and Nat. Only after water year day (WYD) 320 (August 20th) was

ANC overpredicted, with a small underprediction at the initiation of snowmelt

(around WYD 215, May 1st). Na + predictions were very good, especially when compared to the initial model run, with some overprediction after WYD 320

(August

20th).

Predictions for Ca

2

+ were not as good as for Na+. Early to mid-winter

(WYD 1-150,

October 1st to March 1st) concentrations are overpredicted by the model, while melt season (WYD 200-250, April 20th to June 10th) concentrations are underpredicted.

In general the matches between modeled and observed

SO, Me+, and K+ (not shown) were very good for the

1994 simulation and simulation difficulties were similar as those for Ca

2

+.

The monthly calibration of nitrogen parameters resulted in a very good fit between measured and modeled NO concentrations. Modeled values were somewhat higher than observed during the initial stages of snowmelt (around

WYD 215,

May 1st) for both

1994 and

1996.

This is most likely due to the high value used for snowpack elution (Table 4). The high value for the elution parameter was necessary in order to capture the high Cl

-

concentrations in

1994 and avoid overpredicting the late summer concentrations. However, the high value for the elution parameter also resulted in faster than observed Cl-

release from the

snowpack

in

1996.

We were unable to match the observed C1 concentrations in the first half of the water year using this model structure.

72

Andrews Creek The meteorological station estimate of snowfall was

0.78 m

and

0.98 m

for

1994

and

1996

respectively, versus model inputs, to meet mass balance requirements, of

1.03 m

and

1.28

m. After optimization there was a near perfect match between measured and modeled watershed discharge, except for following a few large summer rains (Figure

6).

The main improvement to the match between measured and modeled stream concentrations came from adjusting only

12

parameters (Table

4), 11

of which controlled processes in the talus subunit and the other parameter controlling stream

Pc

02

.

Though many of the parameters controlling processes in the soil subunit were adjusted, none significantly improved model performance (Figure

6

and Table

6).

Both the mean and variability of the data are simulated well by the calibrated model in both years with the partial exception of

NO

3

-

,

Si and

ANC. Despite monthly calibrated values of parameters for immobilizing NH

T

and

NO

3

-

,

the spring

snowmelt

portion of the simulation (between

WYD 220

and

275,

May

10th

to July 1st)

underpredicts NO

3

-

concentrations.

The model captured the mean ANC for the season, but not the seasonal trend of ANC. Early season predictions (before

WYD 250,

June

10th)

are too low while mid season predictions

(WYD 250-280,

June

10th

to July

10th)

are too high for both

1994

and

1996.

Despite the general agreement between model simulation and observations for Ca+, there is still disagreement between model and measured values. The results for Ca+ typify those of cations and

S0.

Early season values are slightly below measured values and late season predicted values (after

WYD 325,

August

73

20th) are below measured values (Figure

6).

Discussion

Model

Performance The models of

GLV4 and Andrews Creek were effective in capturing the mean and seasonal variability of the observed stream chemistry for both a calibration and an evaluation year. The models were effective by fitting a few parameters and using field data to set model initial conditions, model inputs, and several model parameters. Even though the model construction and calibration can be considered a success, it was a variable one, with some measurements better matched than others by the model.

Discharge was modeled successfully, due in large part to the snowmelt optimization scheme. Optimization for GLV4 resulted in

11% and

35% increases in modeled

SWE over the amount measured at D-1 for

1994 and

1996, respectively. At Andrews the increases were 25% and 24% for 1994 and 1996 respectively. The need to add additional snow may arise from i) estimates of evaporation (and sublimation) that are too high, ii) underestimates of snowfall iii) snow blown into the watersheds from over the Continental Divide or iv) ablation of the Arikaree or Andrews glaciers. The estimates of evaporation we used are, if anything, too low; the results of Hartman

et al.

[1999] indicated much higher rates of evaporation. More likely is differences in total precipitation between the two watersheds modeled and the precipitation gauges due to orographic effects.

It is also likely that snow is blown into both watersheds from over the continental divide

[Baron and

Denning,

1992].

There is no available data concerning the ablation of either the Andrews or Arikaree glaciers during the

1994 and 1996 water years.

74

There was some overprediction of discharge for several summer storms on both watersheds (Figures 5 and 6), especially the large storms around WYD

300 (July 30th) in both 1994 and 1996 on GLV4. For the Andrews Creek watershed in 1994 discharge for the storm after WYD 320 (August 16th) was also vastly overpredicted by the model. That particular storm was also greatly overpredicted by

Hartman

et al. [1999] when they simulated discharge for the whole Loch Vale watershed using the RHESSys modeling package

[Band et al.,

1993]. The overprediction of summer rainfall peak discharges may be due to insufficient soil zone storage in both models, or using incorrect precipitation measurements as input to the models. The AHM model also overpredicted flows at the beginning of snowmelt, indicating that soil moisture status was not accurately calculated during the mid-winter period. Both problems in modeling discharge indicate a need to increase infiltration rates and subsurface water storage in both watersheds.

The AHM was variably successful at predicting stream concentrations during both 1994 and 1996, suggesting that the major processes controlling stream chemical concentrations for both watersheds are captured by their respective models. Information about the model and about the calibration procedure can be garnered from investigating the Nash-Sutcliffe values for GLV4 and Andrews for the calibrated and uncalibrated watershed models as well as by comparing the results for the calibration and evaluation years. The Nash-Sutcliffe values for Ca

2

+, ANC, K+, and Mg

2

+ were closer to 1.0 for the evaluation year of

1996 than they were for the calibration year of 1994 for both watersheds. This result indicates that the calibration was not overly tuned to the observational data from 1994 (Tables 5 and 6). Therefore, we can be more confident in our

75

calibration procedure in general and the particular parameter values arrived at in this analysis.

Model predictions for Si,

N11

-

4

1

",

and

Cl

-

in particular were inferior to the observational mean as stream composition predictors (Tables

5

and

6).

Silica has an observable hysteresis in stream chemistry of Andrews Creek

[Campbell et al.,

1995

]

.

This hysteresis may be because of soil solution and talus solution flushing processes not currently incorporated into the

AHM

models of these two watersheds

[D.

W.

Cow,

personal communication]. The observed

NH

-4

4

concentrations in both watersheds would be difficult for any model to simulate due the almost random nature of the observed values. Still the

AHM

currently nitrifies or immobilizes all NH in the

snowpack

on contact with the soil or soil litter. These results indicate that an alternative scheme should be developed.

The

Cl

-

simulations were significantly worse when compared to the mean of the observations for

1996

than they were for

1994.

The deterioration of the simulations in the evaluation year of

1996

most likely represents a change in the real ionic pulse between these two watersheds. While

Cl

-

deposition was higher in both watersheds in

1996

(Figure

3),

the

overprediction

of spring

snowmelt

stream

Cl

-

concentration during

1996

indicates that there may be differences in

snowpack

maturation between the two years

[Harrington and Bales,

1998].

Unfortunately, there was no detailed

snowpit

data available to evaluate this hypothesis.

Other problems with the models are only evident by looking at the time series results. For example, late season cation concentrations for

GLV4

are

overpredicted.

Possible causes of this

overprediction

include:

i)

high soil percent base saturation in the model,

ii)

too much soil and talus in the model, or

iii)

76 not enough snowmelt routed through the soil, preventing depletion of the cation exchange complex during snowmelt. Of these three possible causes the first is the most likely, since the base saturation values for GLV4 are high for alpine watersheds. The second goes against the hydrologic results for the summer rainfall events, which were overpredicted, indicating that the model needs more not less soil. The third item is plausible since model calculations of soil drainage and surface runoff indicate only 70% of snowmelt comes in contact with soil.

While, the Nash-Sutcliffe results indicated a conflict between the magnitude of the ionic pulse between the two years, the time series results indicate an underprediction of winter stream Cl

-

at GLV4. This result indicates either a weathering source of Cl

-

not included in the model, summer dry deposition of

Cl

-

at a greater rate than those used, or a pool of evaporated water in the GLV4 that provides the wintertime source of CI

-

.

Base Saturation and pH The overprediction of late season stream cation concentrations and the need to increase the stream P

co

, (Table 4) from that of the ambient atmosphere indicate that the base saturation of soils in the model of GLV4 is too high. The GLV4 has a soil base saturation that is 50% greater than the average base saturation in Andrews Creek. Also, the cation exchange capacity of the soils of GLV4 is nearly twice that of Andrews Creek (Table 3).

One result of this high CEC and base saturation is that the pH of soil water, after degassing to atmospheric P

co

„ will be much higher at GLV4 compared to

Andrews Creek. Note the 0.3 pH difference between the calibrated (Pco, 10

-3.1

atm) versus uncalibrated (10

-3A

atm) models of GLV4 (Figure 5).

There are several possible causes for the difference between the ambient atmosphere Pco, and the calibrated Pco, of the stream. First, the real Pco, of

77 the samples may be below atmospheric

P co

, due to the grab sample methodology of sample collection. Grab sampling prevents the degassing of

CO

2

since a sample is capped immediately while stream samples taken with an autosampler

(like those at Andrews Creek) are allowed to equilibrate with the atmosphere over the days to weeks that the sample sits in the auto-sampler

[Melack et al.,

1998]. Second, during winter and early spring lake ice may prevent the degassing of CO

2

that accumulated due to respiration in the stream and lake. Third, these results may indicate that the base saturation of

GLV4 is now much lower than measured in the mid 1980's, due to either errors in measurement or a real decline in base saturation.

Cation concentrations and alkalinity have declined in the streams of Green

Lakes Valley

[Caine,

1995], a phenomenon that, if occurring more widely in the

Front Range, will have policy implications in setting critical loads for atmospheric deposition to the region. The hypothesis that base saturation has declined can be tested by modeling

GLV4 farther back in time using stream chemistry data that is available back to 1981, but proxy data would be needed to extend the time series of hydrologic information farther back.

Nitrogen Dynamics The model succeeds in matching the NO

3

-

concentrations in part because it has been calibrated to match them on a month by month basis. Few conclusions can be drawn from the ability of the model to capture the seasonal variability of

NO

3

-

; however, it is useful to see what model output looks like when all NO

3

-

is leached and all NI-It is nitrified and when the N reactions are turned completely off (Figure

7).

These different sensitivity tests were used to identify and quantify the relative importance of nitrification, mineralization and immobilization on the stream chemical composition of mineral nitrogen.

78

The

N

sensitivity results show that during the early part of the

snowmelt

season

(WYD 230

until

270)

nitrification and immobilization are necessary for the model of

GLV4

to explain the measured

NO

3

-

and NH

-

E concentrations.

This result is in contrast to Andrews Creek where

AHM

modeling indicates a significant source of

NO

3

--

from the watershed during

snowmelt.

For NH, the sensitivity results indicate that nearly all

N11,

-

I

F

is assimilated or nitrified on both watersheds. During the summer, observed stream

NO

3

-

*

concentrations indicate a significant

NO3

-

sink on both watersheds. The summertime peak of

N

consumption indicates vegetative, or soil microbial control of

NO

3

--

in the

GLV4

and Andrews Creek watersheds. There is undoubtedly stream

NO

3

-

in both watersheds from mineralization and nitrification. Our results indicate that

GLV4

has a large

N-sink

that consumes more of atmospheric

N

deposition than does

Andrews. The larger

N-sink

is most likely due to the dominance of soil in the valley bottom of

GLV4.

Soil is expected to be more biologically active than talus and thus able to retain more N.

Flow Routing The results for these two watersheds, combined with those from previous work at Emerald Lake

[

Wolford

et

al.,

1996]

and two other Sierra Nevada watersheds

[Meixner

et

al.,

1998],

indicate that most

snowmelt

contacts either soil or talus long enough to exchange hydrogen ions for cations and to undergo other

geochemical

transformations. Furthermore, the sensitivity of parameters for a particular terrestrial subunit depends on the flow routing parameters within the

AHM.

For

GLV4,

all runoff was routed through the soil before reaching the stream. At Andrews Creek, all runoff was routed through talus before reaching the stream. At Emerald, half of the stream discharge came from talus while the other half was from soil. For

GLV4,

the soil exchange parameters and hydrologic

79 parameters of the talus subunit had no effect on model output, while the soil hydrologic and chemical parameters of the soil subunit were fundamental in determining stream chemical composition. The opposite was true at Andrews.

Emerald Lake was intermediate with some talus and some soil parameters important in determining model predictions. These model results indicate that the observed stream chemistry has a similar dependence on the structure of the landscape and the land cover most hydrologically connected to the stream.

Andrews and

GLV4 also differ in the fraction of stream discharge that is surface overland flow. Our model results show that there is virtually no surface runoff on the soil and talus in Andrews, while for

GLV4 about

30% of total hydrologic flow for the soil and talus subunits occurs as surface overland flow.

These differences as well as the differences in flow routing between subunits for the two watersheds highlight the first order importance of spatial and vertical flow routing to the hydrochemical response of alpine watersheds.

Our results indicate the need for more intensive field measurements of flow routing, including tracer tests, isotopic and geochemical mixing models, soil wetness observations, and soil chemical observations, for determining the actual hydrologic routing in these watersheds. Additionally more robust watershed hydrologic models, such as

TOPMODEL [Beven and

Kirby,

1979], should be evaluated as tools to support field observations and to aid in parameterizing flow routing for the AHM.

Sensitivity to Deposition Doubling

N deposition resulted in small depressions in ANC and pH at GLV4 (Figure 8 and Table 7). The average ANC depression and II+ increase of 3.4 and 0.1 peqL

-1

, respectively, are similar to the values (3.8 and

0.1 peqL

-1

respectively) observed for the Emerald Lake

80 watershed under conditions of doubled wet

N and

S0

2

4

-

deposition

[Meixner

et

al., 1998].

The Andrews Creek watershed model exhibited less sensitivity to increases in atmospheric deposition than GLV4, with ANC depression and

H+ increase of 2.0 and 0.02 pec1L

-1

respectively (Figure 9 and Table

7) [Wolford

et

al., 1996].

The slightly lower sensitivity of Emerald despite its lower CEC and base saturation is probably due to the the very dilute nature of precipitation in the Sierra Nevada. The lower sensitivity of Andrews to increases in deposition is probably due the the significant increase in Ca

2

+ export observed under increased deposition (Table

7) due to the greater contact of deposition with talus than in

GLV4.

The maximum concentration change due to doubling wet deposition (Table

7) gives a snapshot of the two watershed's sensitivity to episodic acidification.

The results indicate that

GLV4 is more susceptible to episodic acidification than is the Andrews Creek watershed. The maximum ANC depression and H+ increase for GLV4 were 32.2 and 2.9 yeqL

-1

respectively, while for Andrews they were

7.4 and

0.97 peciL

-1

respectively. The greater sensitivity of

GLV4 to episodic acidification is due to the larger ionic pulse (D value of 10.0) as opposed to Andrews Creek (3.4). The two Rocky Mountain watersheds are more sensitive probably due to the much larger deposition currently occuring.

The result that

GLV4 is more sensitive than the Andrews Creek watershed agrees with the results of

Wolock

et

al. [1989]. They found that watersheds with less contact time and more surface runoff were more sensitive to acid deposition. In our case the model of

GLV4 had more surface runoff and thus less soil contact than the Andrews Creek watershed. A model test was done in which soil hydraulic conductivity was increased to eliminate surface runoff. Under this

81 scenario (results not shown),

GLV4 was less sensitive to increased N deposition than the Andrews Creek watershed. This sensitivity result gives further force to the need for a more robust investigation of flow routing in alpine watersheds.

Conclusions

Five lessons were learned from this application of the AHM to the upper portion of the Green Lakes Valley and the Andrews Creek watersheds. First, calibration involving specification of flow routing and measured parameters followed by fitting of soil and talus parameters that were not explicitly measured was effective in capturing the observed stream chemical composition of the catchments. This procedure should be followed in using AHM to simulate other watersheds. Second, the Andrews Creek watershed releases significantly more mineral N than

GLV4.

This is especially true during spring snowmelt when the Andrews Creek watershed was a net source of mineral N. The greater release of mineral

N is most likely related to the dominance of areas of talus in the Andrews Creek watershed. Third, snowmelt contacts either soil or talus sufficiently long to undergo geochemical transformation. Still, independently parameterized routing is necessary since nitrate retention, apparently biologically related, is more important on areas mapped as soil as opposed to areas mapped as talus. Fourth, GLV4 is more sensitive to changes in atmospheric deposition than the Emerald Lake or Andrews Creek watersheds were on an average and episodic basis. However, this result is dependent upon a confident estimate of flow routing in both of the watersheds. Finally, our results indicate that the soil base saturation estimated from measurements at GLV4 in the mid-1980's is higher than supported by the model of stream composition developed here. This

82 result suggests that the base saturation of

GLV4 soils was either not measured properly in the

1980's or that soil base saturation has decreased over the past 15 years.

Acknowledgments. The

1996

aerial photographs for both watersheds were

orthorectified

by B. Balk. The

1994

aerial photographs for Green Lakes Valley were

orthorectified

by

F. Rojas. Maps of snow covered area for Andrews Creek provided by

G. Ingersoll and M. Hartman,

orthorectified

by D. Cline. Digitized soils map of Loch

Vale was provided by

M. Hartman. Funding for the original data collection and field work that this work depends on was funded by the National Park Service, the

USGS

and the National Science Foundation

(LTER-DEB 9211776

and

EGB

EAR-9523886).

Funding for the primary author was provided by a Canon National Park Science

Scholarship. Additional support provided by the National Aeronautics and Space

Administration

(NAGW-2602).

R. Brice and K.

Meixner

assisted in manuscript preparation.

83

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This

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AGU LATEX macros v3.0.

Table 1.

Soil Physical Properties

Property GLV4

Talus

Soil

Andrews

Talus

Soil

Area,

ha

Pb, g cm

-3

Depth, m

81.3

68.0

51.21

17.82

1.1

0.25

1.3

0.30

1.1

0.26

1.3

0.30

K

sat

,

cm

day' 400 400 400 400

87

Table

2.

Mineral Weathering Rates

Value

H+ Ca

2

+ Mg

2

+

Na

+ K+

Si0

2

S0

2 4 -

Anion mol

yr

-1

7380 21310 6070 11800 3440 27050 1970 19350

mol day

-1

20.211

58.4

16.6

32.34

9.43

74.1

5.39

53 k

2

/10

-

"

a

0.586

1.69

0.481

0.91

0.274

2.15

0.156

1.53

a

k2 is model

stoichiometric

parameter and it defines the mol day' of a given species that weather when multiplied by soil volume, soil bulk density, and specific surface area.

88

89

Table

3. Soil chemical properties

Property

CEC,

meg kg

-1

PBS

b

, %

Ca

2

+ c , meg kg

-1

mg

2+c

, meg

kg-i.

K+c, meg

kg'

Na,

meg kg

-1

Andrews Talus Andrews

Soil GLV4

67

52

76

70

138

85

27.5

4.1

1.7

1.4

38

13

1.6

1.0

102

11.6

2.6

0.8

a

Cation

Exchange Capacity, expressed

in

meg

of charge per kg of

soil.

b

Percent base saturation, the percent of the total CEC

that is occupied by

base cations as

opposed to hydrogen

ion or

aluminum

ions.

c Quantity

of

exchangeable

ion,

by species,

in the

soil.

90

Table

4.

Fitted parameter

values

Parameter

Deep

K at

,

cm

day'

log Pco

2

stream

(atm)

Snowpack

elution parameter DC

Talus Log K-Ca

2

+

d

Talus Log K-Mg

2

+

d

Talus Log K-K+

d

Talus Log K-Na+

d

Soil

Log K-Ca

2

+

d

Soil

Log K-Mg

2

+

d

Soil

Log K-K

-

E

d

Soil Log

K-Na+

d

Log K-S0

2

4

-

e

Log K-Sie

Exchangeable

Si

f

aNH3toONg aNO3toONg

NC4-baseg

ah

-2.95

-5.23

-5.73

-0.85

ELW Andrewsa GreenLake4a

1.25

-2.9

10.25

-3.4

1.25

-3.1

4.0

-6.15

-6.00

-1.00

3.4

-5.63

-5.83

-1.30

8.0

-6.15

-6.00

-1.00

-2.95

-2.15

-5.23

-5.73

-0.85

-4.83

-5.03

-1.20

-3.01

17.45

27.63

95

0.989

-3.01

17.95

27.93

90

0.000

0.70

0.5

8 x 10

-6

5 x 10

-5

0.16

0.16

-2.11

17.70

27.88

70

0.200

0.5

3 x 10

-5

0.18

a

For Andrews

Creek soil parameters had

no

effect

on

model

output. For Green

Lakes

Valley talus

parameters had

no

effect

on

model

output. This

result is discussed

more

extensively

in the

text.

b

Deep

hydraulic conductivity refers to lower

horizon

hydraulic conductivity.

91

• Represents

ratio of initial

solute

concentration in

snowmelt to snowpack

average.

All other elution parameters were unchanged from ELW.

d

Log

K

for

exchange

of cation

with H+

on cation

exchange

site.

e Log

K's

for adsorption of

SO

4

2-

and

H

2

SiO

3

.

e The

model contains

a

Si exchange

complex. The

numbers

in

this row refer to

initial condition of

complex by %

saturation of

exchange

sites. Total site concentrations

from ELW optimization were used here.

g These three parameters govern

the

two N reactions present

in

AHM:

NILT OrganicN H+

NH,t + 20

2

N%

-

+ 2H+ aNH3toON determines what

percent of the

NI-1

-

4

F is converted into organic N with

the

remainder being nitrified. NO

3

-

-base determines

a minimum concentration of

NO

3

-

over which

a fraction of the

NO

3 -

as

governed by aNO3toON is converted into organic

N.

h

The

weathering

coefficients a

is

part of the

weathering equation:

Mol

=Axkx[Hl

a

where

Mol

is

moles

added to

the

subunit, A is

total

area

of the surfaces

involved

in

reactions, [H+] is hydrogen

ion concentration, and

k

and a are constants. The total surface

area is determined

as the

product

of the

soil depth, area, bulk density,

and

specific

surface

area.

Table 5.

Nash-Sutcliffe Values for Green Lakes Valley

4

1994 1996

Species

Uncal.

Cal.

Uncal.

Cal.

ANC

Ca

2

+

-7.7

-0.32

-3.32

0.49

-1.3

0.22

0.12

0.59

K+

Mg

2

+

Na

+

-0.20

-0.01

-0.02

-0.31

-1.2

-0.38

-0.74

0.16

-27.5

0.25

-13

-150 0.12

-130

0.63

0.28

N11

4 4

"

NO

H+

-0.45

-0.44

-0.88

-0.88

0.23

0.74

0.36

0.35

-1.7

0.065

-1.9

-1.3

Discharge

0.97

0.98

0.99

0.99

Si

SO

?

i -

-2.7

0.015

-0.37

-0.086

-43.1

-0.71

-12

0.53

92

Table 6.

Nash-Sutcliffe

Values for Andrews

Creek Watershed

1994 1996

Species

Uncal.

Cal.

Uncal.

Cal.

ANC

Ca

2

+

-0.36

-0.11

-0.40

0.79

-2.0

0.12

0.48

0.90

Cl

-

K+

0.18

-4.1

0.22

0.29

-5.9

-3.6

-2.0

0.34

Mg

2

+

Na+

-2.0

-50

0.31

0.66

-0.44

-55

0.86

0.045

-0.15

-0.15

-1.3

-1.32

NETt

NO

-0.56

0.06

-.14

0.52

H+ -310 -0.056

-7.5

0.14

Discharge

0.98

0.95

-.92

0.92

Si

S0

2

4

-

-12

-17

-2.5

-3.25

0.04

0.58

-18.6

0.10

93

Table

7.

Concentration changes with doubling of

N

deposition

Average Change

GLV4

Andrews

Maximum Change

GLV4

Andrews

Species

1994 1996 1994 1996 1994

1996

1994 1996

ANC,

yeciL

-1

-2.3

-4.6

-1.7

-2.4

-32.2

-28.2

-3.5

-7.4

H+, peqL

-1

0.07

0.18

0.014

0.025

0.87

2.9

0.033

0.097

Ca

2

+, peqL

-1

0.7

0.3

4.7

4.7

8.0

4.1

11.4

12.0

peqL

-1

2.6

5.5

8.7

9.7

34.5

35.2

21.3

23.6

peqL

-1

-0.45

-0.20

-0.60

-0.80

-2.9

-1.9

-3.5

-3.8

94

95

Figure 1.

Land cover map for Green Lakes Valley watershed.

Figure 2.

Land cover map for Andrews Creek watershed.

Figure 3.

Modeled watershed compartments: a) soil subunits have compartments including

1)

rainfall litter interception,

2)

snowfall canopy interception,

3)

rainfall canopy interception,

4) snowpack, 5) snowpack

free (liquid) water,

6) snowpack

drainage,

7)

surface runoff leaving the subunit,

8)

soil drainage leaving the subunit,

9)

contributed soil drainage,

10)

contributed surface runoff,

11)

litter storage beneath the

snowpack

and

12)

one or more soil horizons. Rock subunits (not shown) do not include compartments

2, 3, 8,

and

12.

Stream subunits

b)

have compartments including the a)

snowpack, b) snowpack

free water,

c) snowpack

drainage, and d)

streamfiow;

stream ice is not tracked other than present or absent.

Figure

4.

Annual average volume weighted mean precipitation chemistry for

GLV4

(a,

13)

and Andrews

(c,

d) for

1994

and

1996.

Data was collected at

NADP

sites located near each watershed.

Figure

5.

Modeled

GL4

inflow and measured stream chemical concentrations for the outflow of Green Lake

4.

Dotted line is final calibrated model, pluses are data, and dashed line is

uncalibrated

model using field and Andrews results for model parameter values. Water year day

1

is October 1st.

Figure

6.

Observed and modeled stream chemical concentrations for the Andrews

Creek. Dotted line is final calibrated model, pluses are data, and dashed line is

uncalibrated

model using field and Emerald Lake results for model parameter values.

Figure

7.

Nitrogen reactions and effects for models of both watersheds.

96

Figure 8. Sensitivity of Green Lake 4 model to doubled nitrogen deposition chemistry. Dotted line is current conditions and solid line is model output for doubled deposition.

Figure

9.

Sensitivity of Andrews watershed model to doubled nitrogen deposition chemistry. Dotted line is current conditions and solid line is for doubled deposition.

riJ

/ Soil

['Talus

O Rock

• Glacier

1 km

"'water

97

id

11,

111

soil

Talus

El

Rock

U

Water

Ii

km

98

a.

J

2,3 b.

n

-_, soil subunits stream subunits

2,3

99

25

15

45

35

Green Lakes

(Niwot)

r

-

Andrews (Loch Vale)

-

-

-

25

35

45

-

-

-

1994 1996 1994 1996

100

Oct Jan April July

_

T

4

3

- 1994 o

2

—_ 1

O

150

-

I

,,.."

Oct Jan April July

1996

-

_

_

O 50

+4+

+ ial

I I,

+

7.5

i

7.0

+ +

6.5

+ c

` 6.0

5.5

200

I

I

#i,t

.

le

iIIII

+

1

/

1

4

l _

1111

--' —

-

T1

1

4

I

„litt-

-

+ + + +

_

IIIiill

150

47) 100 rci

50

-

7

I,

1/1 tI)Il litfir

/

I

1141

Ill

Ay

-

+

150

Li ci

a)

100

50 o

,d

4

+

60

+

± +

I

7 —I

40

O

20

15

10 ow o

- 5

_

0

0

+

+

+

I

I!

tli,".'

+ + + ÷

+

+++

H-

• i th

100 200 300 0

Water year day

,

.

100 200 300

Water year day

V L

-

1

0

1

4

Oct

Jan

— —

April July

7

>,3 1994

Oct

Jan

April July

1996

'E

2

O

60

7_, 45 cr

1

1

.

30 c5 z 15

7.0

6.5

g

;

.

6.0

5.5

150

'-. ---

owo

.

;

50

150

+_,+4-

.

,_

+

1

1

...

L*.

_ _.., _±

NI'

ill+ il

+

-, — — or)

---, to

V

II

,

I

,

I

1p

II

,

1

1

K

,,,,

till

+ +

)04

.- ,.

60

- 45 am 30

+—H

-a-

15

15

L1 cr

10

5 o

0

0

II

+ kL 'i •

+

-1-

1

-

+

1

'

I

+

1

+

100 200 300 0

Water year day

1

..,,

+

+ 1

I

1 e

41 ....

100 200 300

Water year day

4

102

4

Li

100

Oct

Jan

April July Oct Jan April July

80

60

Andrews

+

Data

— —

Final Run

--: NH, nitri fi ed and NO, leached -

— No N reactions

40

20

. +

— — —

100

80

_ n

1

GLV4

1

.•::: n i

,

A

+.

, i i

-

7_1 o

60

40

20

_

-

40

1F+7

I i

4-1

_

:-

_

4----

--_

-

Fri

__

...

T.

I I I n

‘',._ -

L

I

-

30

Li

.. a

2° z

10

_______,

I

(\ j'

I

\ ikt

, n

,

OA c10

-i u )

-,-----....' n l i,4

NI

\ 4 '

1

,- I k

.

40

Andrews

-

GLV4

30

I a

10

_

o

I

I

I

1

I

, iid

4

,

1

\l,

,-- r s

100 200 300 0

Water Year Day

1 i

li

,— -- '

,/ ,

1

,

-

\ n

,..

i

ill,,A

I i

--

+ +

,+41+4,,-i.i-if

100 200 300

Water Year Day

103

L i

150

Oct Jan April July Oct Jan April July

100

-

_ o 50

-

1994

7.5

7.0

6.5

-

°- 6.0

5.5

-

200

- 150

Q)

100

-

-

-

RS

50 iiii

150

_

_

1996

-1-

_

_ i

-

-

-

I

1

I I

80

60

C.

40

,

0 20

25

20

-

_

- ,

I

,_ _1_

_._

-_

_

_

,r_.-

------

4

_

01

_

-

-

Ii4I

I

_

_

-

-

100 200 300 0

Water year day

100 200 300

Water year day

104

-

60

Oct Jan April July

• 45 at 30 o z 15

7.0

6.5

6.0

5.5

150

Oct Jan April July

0-

100 -

- 50

160

7

120 cr

Ca

80

A

cc

i

40

60

I

I

I o

5 o o

100 200 300 0 100 200 300

Water year day Water year day

105

APPENDIX

C -

A

NITROGEN DYNAMICS MODEL

FOR ALPINE BASINS

106

A Nitrogen Dynamics Model for Alpine Basins

Thomas Meixner

Dept.

of

Hydrology

and

Water Resources,

University of Arizona, Tucson, AZ

107

Abstract

Several ecosystems in the western US are already undergoing nitrogen saturation, a condition where previously N limited ecosystems become N sources. Due to the complexities of terrestrial carbon-nitrogen dynamics, modeling is required to understand the effects of increases in nitrogen deposition. Existing carbon nitrogen models do not permit easy coupling to hydrologic models. Also existing models do not contain the full effects of snow cover on carbon and nitrogen processes. For these reasons a nitrogen model for alpine ecosystems was developed to fully implement the effects of snow cover into a carbon nitrogen model. The model was also constructed to permit ease of interface with hydrologic and energy transfer models. The model was applied to the Emerald Lake watershed. The model adequately simulated major terrestrial carbon and nitrogen pools and fluxes. The model over predicted observed stream nitrate concentrations. The model duplicated the gradual decline in stream nitrate at the Emerald Lake watershed observed over the last 15 years but the model shows an increase in stream nitrate before the real watershed. The model also predicts an earlier spring peak in nitrate concentration than the real watershed. This may be due to the fact that the model is simulating soil nitrate concentration not stream concentration, or it may be due to hydrologic lag or mixing not currently represented in the model.

108

Introduction

Over the last several decades there has been increasing concern about the damage

109 that human perturbations to the nitrogen cycle may be causing

[Galloway

et

al.,

1995]. A particular focus for the forested and wildland catchments of the world has been the increase in atmospheric deposition of reactive nitrogen to remote watersheds throughout the world. The increases in atmospheric deposition appear to have caused an increase in nitrate export from forested, chaparral, subalpine and alpine catchments. Many have hypothesized that long term increases in atmospheric deposition of nitrogen have resulted in a decreased ability of terrestrial ecosystems to retain additional inputs of nitrogen

[Fenn

et

al.,

1998]

[Henriksen

and

Brakke, 1988;

Aber et

al.,

1989;

Stoddard,

1994]. In the urbanizing western U.S. the Front Range of the Rocky Mountains and the chaparral and coniferous zones around Los Angeles are currently undergoing nitrogen saturation

[Baron et

al.,

1994;

Williams et

al.,

1996;

Fenn

et

al.,

1998]. The alpine zone of the

Sierra Nevada Range could undergo nitrogen saturation with increased atmospheric deposition that could result from the ongoing urbanization of the Central Valley,

California [Jim Sickman, personal communication].

While increases in atmospheric deposition to terrestrial ecosystems have been implicated in the rise in nitrate concentrations in aquatic ecosystems, the link is difficult to prove due to the complexities of the terrestrial carbon-nitrogen cycle

[Parton

et

al.,

1993;

Baron et

al.,

1994]. Large pools of nitrogen already on the landscape prevent simple cause effect assumptions about the correlation between increased atmospheric

deposition and increases in nitrate export from terrestrial ecosystems. In fact a diverse array of causes may result in the effect of increasing nitrogen export from an ecosystem,

110

including: changes in climate, history of disturbance, fife history, soil freezing, wintertime

snowpack,

and drought

[Sickman

and Melack,

1998];

[Brooks et al.,

1996];

[Fenn et al.,

1998;

Aber et al.,

1998].

Due to the impact that increased nitrogen deposition can have on aquatic ecosystems and the complexity of the problem a unified approach incorporating modeling, monitoring, site cross comparison and experimentation is needed. Sporadic efforts in the United States and a coordinated effort in Europe have followed this model of science. This paper deals with the modeling component of this scientific venture.

Several models of watershed or plot scale nitrogen dynamics already exist including

PNET

[Aber and

Federer, 1992],

CENTURY [Parton et al.,

1987]

BIOME-

BGC

[Running and Gower,

1991],

and MAGIC-WAND [Jenkins et al.,

1997].

All of these models have tightly coupled hydrologic and

biogeochemical

components. If you wish to substitute a different representation of watershed or plot hydrology none of these models provide a simple avenue on which to proceed. None of them address the particular concerns for modeling catchment

biogeochemistry

in alpine catchments such as the effects of snow cover duration, the insulating effect of the

snowpack

or soil freezing events. These difficulties necessitate the development of A

NItrogen

Model for the

ALpine

(ANIMAL). Such a model should meet five basic goals:

1)

Incorporate state of the art knowledge of carbon nitrogen cycle modeling.

2)

3)

Incorporate the known soil microbial activity underneath the snowpack.

Incorporation of hydrologic information as a time series enabling input to be generated from any hydrologic model.

4) Incorporate soil temperature data as a time series so any suitable energy budget model or soil temperature assumption can be used

5) A simple object oriented design to allow changes to model structure and code simply and efficiently.

111

Model Description

Several models of catchment and plot scale nitrogen dynamics exist (CENTURY and PNET for example) [Parton

et

al., 1987;

Aber and

Federer,

1992], all depend on a simplified representation of the nitrogen cycle for determining the process controlling carbon and nitrogen cycling in a watershed. The CENTURY model is one of the more widely used carbon-nitrogen dynamics models currently being used in the scientific community and it has been applied to alpine ecosystems previously with some success

[Baron et

al., 1994]. The CENTURY model includes a simplified hydrologic budget model that is used to drive portions of the soil biogeochemical cycling and plant growth portions of the model. CENTURY at this time does not include the incorporation of the effect of snow cover on soil temperatures and the resultant effects on soil microbiology

and root dynamics

[Brooks et

al., 1996]. The Alpine Hydrochemical Model (AHM) has

112 a better representation of alpine hydrology than the current models and a more flexible algorithm incorporation was sought to permit the use of AHM (or any other hydrologic model) output to be used to drive a point scale biogeochemical model. For these two reasons the CENTURY carbon-nitrogen dynamics algorithms as described in [Parton

et

al., 1987; Parton

et

al., 1993] were incorporated into a computational model that takes

AHM output as well as soil temperature and nitrogen deposition as inputs into the model.

The carbon nitrogen model itself consists of three parts: a soil carbon dynamics model, a nitrogen dynamics model linked to the carbon model and a plant growth model linked to the other two components. The fundamentals for all three components were gathered from the literature on the CENTURY model [Parton

et

al., 1987; Parton

et al.,

1988; Parton

et

al., 1993]. The following three sections contain a brief overview of the

CENTURY model structure and the changes that were necessary to adapt it to apply as desired in an offline coupled mode with AHM. The complete code for the model is included in Appendix D.

Soil carbon model

The soil carbon model consists of 8 separate compartments with the flows in and out of each compartment controlled by properties of each pool as well empirically determined rate constants for soil organic matter decay [Parton

et

al., 1987]. The 8 pools

113

are: surface litter structural, soil structural material, surface litter metabolic, root litter structural and root litter metabolic, surface microbes, soil microbes, slow soil carbon and passive soil carbon. A flow chart description of the soil carbon model taken as

[Parton

et

al., 1993]

is included in Figure

1.

The decomposition rate for each of the pools is as follows:

dC,

= K

i

L

c

AC

I

I =1,2 dt dC,

= K

1

m

1

I = 3

dt dC,

—K

J

AC,

I = 4,5,6,7,8

dt

T

m

= (1— 0.75 T)

(1)

(2)

(3)

(4)

L c

.

e

(-1 L

''

)

(5)

where

CI

=

the carbon in pool; I=

1,2,3,4,5,6,7,8

which are surface and soil structural material, active SUM, surface microbes, surface and soil metabolic material, slow and passive SUM fractions respectively; 1(1 is the maximum decomposition rate (day') for each of the above pools (K1=

0.010685, 0.01315, 0.02, 0.16438, 0.40548, 0.050685,

0.000548, 0.0000123);

A is the combined effect of soil moisture and soil temperature on decomposition,

T

m

is the effect of soil texture on active SUM turnover,

T

is silt plus clay content (fraction); and L e

is the impact of

lignin

content of structural material (L s

) on

structural decomposition. The maximum decomposition rates used in this model are simply those used by Parton et al., [1993] divided by 365. The C flows to each pool and the corresponding fraction lost to respiration are included in Figure 1.

114

A number of adjustments to the CENTURY model structure were necessary to permit easy coupling with the AHM. First, the non-linear equation describing the effect of soil temperature on soil organic matter decomposition from Baron et al. [1994] had to be extended down to -5 C

°

, which is the temperature at which Brooks et al. [1993] observed no soil respiration in the alpine tundra of Niwot Ridge, Colorado. Second, the effect of soil moisture on soil organic matter decomposition had to be redefined using soil moisture status. The equation used in ANIMAL was:

M e

= (0, — O w

)/(0 —O

w

) (6) where M e

is the effect of soil moisture on organic matter decomposition, O t

is the soil water content at timestep t, O w

is the water content at which plants wilt, 0, is the saturated soil water content. M e

is equivalent to the fraction of pores filled with water in the soil.

Third the leaching parameters in the CENTURY model use monthly water leached below

30 cm in the soil profile. In this application we use daily drainage from the soil profile

(as modeled by AHM) as an input to the model. These two facts result in a need to multiply the daily drainage by 30 to produce the correct leaching fraction from the active soil organic matter pool.

Soil nitrogen model

The soil nitrogen model mirrors that of the soil carbon model (Figure 2). Organic nitrogen flows follow those of carbon at the C:N ratio of the pool receiving the flow of C and N. The C:N ratios of the eight pools are 150, 150, 3-15, 10-20, 12-20, and 7-10 respectively for surface and soil structural material, active SOM, surface microbes, slow and passive SOM fractions. The C:N ratio of surface microbes varies with the n content of plants. The C:N ratio of the three soil organic matter pools varies according to the mineral N concentration of the soil. The C:N ratio of the surface and subsurface metabolic pools depends on the C:N ratio of the incoming litter and its lignin [Parton

et

al., 1987; Parton

et

al., 1988; Parton

et

al., 1993].

Only one change was required of the nitrogen submodel as a result of decreasing the time step of modeling from monthly to daily. The fraction of mineral N lost to the atmosphere in the form of

N2 was divided by 30.

115

Plant growth model

Only a grassland plant growth submodel is currently incorporated into the

ANIMAL algorithm. This was done because grasslands are fairly simple to model and the incorporation of a grassland model permitted a quick method of validation for the model. A diagram of the grassland model is included in Figure 3. After Parton [1993] the maximum production each day was calculated as:

116

P =P TM S

p

max p P P

(7)

where P p

is potential plant production rate (g

m

-2

day

-1

),

P

rnax

is maximum potential aboveground plant production rate

(8.3

g rT1

-2

day

-1

),

T

p

is the effect of soil temperature on plant production rate,

M

p

is the effect of soil moisture on plant production rate, and

S p

is the effect of self shading on plant production rate. Root and shoot death and root to shoot ratios were treated as Parton et al.

[1993]

but for the exceptions noted below.

As with the carbon and nitrogen

submodels

changes were necessary to permit the coupling of the carbon nitrogen model with

AHM.

First, the maximum potential plant production was divided by

30

to achieve a daily value. Second, root and shoot death calculations were divided by

30

to achieve a daily value. Third, the effect of soil temperature on plant growth was assumed to be for

C3 plants due to the alpine nature of the model application. Fourth, the effect of soil moisture on plant growth was simplified to a single function as:

M

p

=

O

a

*1.24 — 0.060

(8)

where

M

p

is the effect of soil moisture on plant production rate, O a

is the fraction of soil pores filled with water, and the two constants were calculated from Figure

6a

in Parton et al.

[1993].

Case Study

ANIMAL was applied to the Emerald Lake watershed in Sequoia National Park,

California as a test of the algorithm and its applicability to alpine watersheds. This application builds on the AHM modeling already conducted at Emerald. The Emerald

Lake watershed is a 120 ha headwater catchment located in the Sierra Nevada (36 35' N,

118 40' W), with elevation ranging from 2800 m at the lake to 3417 m at the summit of

Alta Peak. The watershed is 48% covered by exposed granite and granodiorite, 23% by soil and 23% by talus and includes a 2 ha lake

[Tonnessen,

1991;

Wolford

et

al.,

1996].

Emerald was selected for four reasons: a long time series of stream chemistry measurements

[Melack

et

al.,

1998], over a decade of data on atmospheric deposition

[Melack

et

al.,

1997], good measurements of biomass and soil properties for the watershed

[Rundel

et

al.,

1988;

Brown et

al.,

1990], and familiarity of modeling the watershed with previous applications of the AHM

[Wolford

et

al.,

1996;

Meixner

et

al.,

1999].

Estimation of four time series inputs were necessary to permit ANIMAL modeling of the Emerald Lake watershed: soil temperature, atmospheric N deposition, water draining the soil, and soil water content. Soil temperature was estimated in two ways. The first method for estimating soil temperature was to use a 30 day average of air temperature in the Emerald Lake watershed. Daily mean air temperature was reconstructed using the 52 year record of minimum and maximum recorded air

117

temperature at the Grant Grove Ranger Station in Sequoia National Park [A.

Esperanza,

personal communication]. The

?

for the regression equation used to develop the reconstructed time series of Emerald Lake mean air temperature was

0.86.

A graph of the reconstructed time series with the available Emerald Lake data from the

1980's

and

1990's

shows that the reconstructed values, while not perfect, are effective at capturing that major variability of air temperature at Emerald Lake (Figure

4).

The reconstructed air temperatures were only used when no observations were available for the Emerald

Lake watershed. The second methodology was to take the reconstructed air temperature time series and to assume that when the soil was snow covered (using data from the

47

year Emerald Lake runs) that the effective air temperature was

-0.1 C

0

.

The purpose of this second methodology was to investigate the effect that snow cover would have on the

biogeochemistry

of alpine catchments.

Three levels of atmospheric deposition were used as inputs to the model. Two of the deposition amounts were the lowest

(1

kg ha t

yr

i

)

and highest

(3.6

kg

ha:' yr

1

)

observed

N

deposition to the Emerald Lake watershed [Melack

et al.,

1997].

An additional simulation was done with twice the

N

deposition as the highest observed

N

deposition

(7.2

kg

ha

-

' yr

-1

).

This

N

deposition was assumed to occur at a constant rate throughout the year.

A

47

year

AHM

model simulation has been completed for the Emerald Lake

118

basin using reconstructed discharge data developed from stream gauging data and

California cooperative snow survey data [C. Gutmann, personal communication]. Output

from this simulation pertaining to soil drainage and soil water state was used as input to

119

ANIMAL.

The 47 year input time series of predicted soil temperature was used to simulate the plant growth and soil organic matter dynamics with ANIMAL. A total of six different simulations were conducted three with 30 day mean air temperature as the predicted soil temperature (one each for the three deposition levels) and three with the soil temperatures fixed under the snow covered area (SCA) and using the 30 day mean air temperature when snow free. For each simulation a total of 1880 years were simulated.

Only the last 47 years of each simulation were analyzed. The long runs are necessary to permit equilibration of ecosystem dynamics, including plant and soil processes [Baron et

al., 1994].

Results

The long runs permitted the equilibration as expected with only minor differences in model output noted for the final period of 47 years simulated as opposed to the preceding 47 years. Four major results can be seen looking at the modeling results for individual ecosystem components (Table 3.1.). First, increased atmospheric deposition resulted in more biomass and more soil organic matter. Second, using soil temperatures as predicted from using snow cover as a -0.1 C

°

resulted in less live biomass and smaller soil organic matter pools for carbon and nitrogen. Third, the predicted below ground

biomass for the low deposition scenario comes closest to the observed below ground biomass

[Rundel

et al.,

1988].

Fourth, neither the results using average

30

day air temperature or the

SCA

soil temperature time series come close to the observed soil organic carbon of

Rundel

et al.

[1988

]. The results for both soil temperature time series are well below the observed

17,500

g

m

2

",

the results using

30

day mean air temperature are closer but still a factor of

2

less than the observed values.

The results for the modeling of ecosystem processes (Table

3.2)

are similar to those for the ecosystem component results. Five things can be learned from looking at the results for ecosystem processes. First, using the

SCA

soil temperature time series resulted in smaller annual production and smaller

N

fluxes per year. Second, increasing

N

deposition resulted in greater biomass production and larger fluxes of

N

per year.

Third, both soil temperature time series inputs

underpredict

observed above ground biomass production. Fourth, the

SCA

soil temperature time series does a better job of simulating net

N

mineralization, coming closest to the observed value. Fifth, the

SCA

temperature series slightly

underpredicts

plant

N

uptake while the

30

day mean prediction of soil temperature

overpredicts

plant

N

uptake.

Comparing model predicted

N

fluxes and the observed

N

fluxes for the Emerald

Lake watershed reveals a number of interesting facts about the model and about the carbon and nitrogen dynamics of the watershed (Figure

5).

First, the drought years during the late

1980's

and early

1990's

resulted in large spikes of mineral nitrogen in the soils of the watershed in late summer early fall. These spikes were probably caused by

120

large-scale root death due to the severe drought conditions present in the watershed.

These large fall spikes of mineral N were not observed in the discharge time series from

121

Emerald Lake. Second, a spring peak for mineral N was observed in the model simulations. It is of larger magnitude than the spring pulse of NO

3

-

observed at Emerald

Lake. This pulse also predates the observed pulse of NO

3

-

for the Emerald Lake watershed by several months. Third, the SCA temperature scenario does a better job than

30 day mean air temperature at simulating the observed pulse of NO3

-

. Finally, doubling deposition increases modeled NO3

-

concentrations for either soil temperature scenario.

Discussion

The carbon nitrogen cycle modeling using ANIMAL and ARM output for

Emerald Lake provides us with information about the natural processes governing nitrogen dynamics in alpine watersheds as well as the model chosen to simulate these dynamics. Four things were learned with this exercise: the conversion of the CENTURY algorithm to a daily format receiving four time series inputs was successful, snow covered area improves simulations of N dynamics, current rates of deposition appear capable of inducing nitrogen saturation at Emerald Lake, and the model was capable of capturing the trends of mineral N export at Emerald Lake with some displacement.

The CENTURY model was originally built to simulate the carbon-nitrogen dynamics of the Great Plains, U.S.A

[Parton

et

al.,

1987]. Transferring this model to the

alpine meadows of the Sierra Nevada is a stretch for the CENTURY representation of terrestrial carbon-nitrogen dynamics. The results from this modeling exercise indicate that the CENTURY algorithm is able to adequately simulate carbon-nitrogen dynamics in alpine ecosystems. This result was earlier confirmed by Baron et al.

[1994].

However, their application of the CENTURY model was in the Rocky Mountains, which are

122

significantly different from the

Sierra Nevada both in climate and vegetation.

These simulations do indicate some problems with

CENTURY's

representation of carbon-nitrogen dynamics in alpine watersheds. The CENTURY algorithm was unable to adequately model total soil carbon as it was in Baron et al.

[1994].

The results

overpredicted

live subsurface biomass. The algorithm was also unable to properly predict the amount of above ground biomass production on an annual basis. The model was fairly successful in simulating

N

mineralization and plant

N

uptake. As a whole these results indicate that the current algorithm is a good starting point for further research into carbon-nitrogen dynamics in alpine watersheds.

The use of

SCA

to adjust the soil temperature predictions was successful in improving model simulations. The

SCA

time series resulted in better simulations of NO; flux, plant

N

uptake,

N

mineralization and below ground live biomass. The

30

day mean air temperature results were significantly different from the results using SCA. Almost all biomass or soil organic matter pools are nearly double or even triple those simulated with the

SCA

time series. The fluxes of NO; and mineral

N

are also much larger for the

30 day mean air temperature time series. These results indicate that snow cover

information should be incorporated into any simulation of

biogeochemistry

in alpine catchments.

Even with the low current deposition rates of mineral

N

to the Emerald Lake watershed the model indicates that relatively large fluxes of NO; should currently be observed in the Emerald Lake watershed. These large fluxes are not currently observed

123

at Emerald Lake. Still current stream chemistry observations do indicate significant NO; losses from the watershed. The simulations also indicate that with any significant increase in deposition over current levels the watershed should experience significant mineral

N

export. This simulation result should be confirmed with field fertilization experiments. This simulation result also indicates that care should be taken in setting critical loads for alpine areas in California. While, the Sierra Nevada currently receive some of the lowest atmospheric deposition in the world these results indicate that relatively small increases in loading from currently levels could cause major terrestrial and aquatic ecosystem changes.

The simulations did duplicate observed trends in NO; flux for Emerald Lake.

The gradual decline in NO; export observed in the late

1980's

early

1990's

was duplicated by the model but the simulations increased export earlier than observed in the real watershed. The simulations also had large spikes in NO export in the late summer and early fall of drought years. The model contains a so-called drought effect that does not appear to occur in the real watershed. A secondary drought effect, the decline in

124

stream NO; concentrations during the late

1980's

and early

1990's

drought, does occur in both the model and the real watershed.

The lack of a fall spike in simulated NO; and the model's simulated NO; peak which predates and is much larger than the observed spring peak may indicate a hydrologic disconnect between the soils and surface waters of the Emerald Lake watershed. The NO; concentrations in Emerald Lake soils may indeed spike in the late summer of drought years but this spike may either not reach the streams or the signal may be mixed out by more dilute waters from talus areas or from rock fractures. As for the spring peak being delayed in the real watershed as compared to the modeled catchment, this may be due to areas of talus releasing more NO; than areas of soil and talus areas melting later in the season. This asynchrony may also be due to a flushing episode that the

AHM

hydrologic input to the algorithm does not currently capture. This hypothesis put forth by Creed et al.,

[1996]

states that as soils saturate they release NO; that has been hydrologically disconnected from the stream during a seasonal or longer period drought. These results indicate that a mechanism for the delay of these NO; pulses needs to be incorporated into

AHM.

Conclusions

The incorporation of

AHM

output as input into a copied CENTURY algorithm was successful. It was a variable success, which should be improved upon through validation

of the modeling results using field experiments. The incorporation of SCA as an input to biogeochemical models for alpine watersheds appears to be necessary to achieve good

125 simulations of watershed carbon-nitrogen dynamics. These results also indicate that increases in N deposition could easily increase NO

3

export from the watershed. This result should be verified with extensive field experimentation since it could have a dramatic impact on the setting of air quality standards in California. Finally, improvements in the hydrology of ARM appear to be necessary to adequately time the pulse of NO from the Emerald Lake watershed during spring. A number of tasks remain to be done to fully apply this model to alpine watersheds. First, soil freezing and its effect on stream NO

3

export should be incorporated

[Likens

and Bormann,

1995;

Brooks et

al.,

1996]. Second, a more robust energy budget model should be used to drive the soil temperature inputs of the algorithm.

Acknowledgements

A Canon National Park Science Scholarship made this work possible to the lead author.

Additional support provided by NASA and NSF. Ray Brice and Kathleen Meixner aided in manuscript preparation. Chris Gutmann and Jim Sickman are thanked for their contributions of data, model output, and insight in to the processes occurring at Emerald

Lake.

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Nicolson,

R. S.

Semkin,

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D. S. Jeffries, Regulation of

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Poth,

J. D. Aber, J. S. Baron, B. T. Bowman, D. W. Johnson, A. D.

Lemly,

S. G. McNulty, D. F. Ryan, and R.

Stottlemyer,

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Schnoor,

Nitrogenfixation

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M.

O. Scurlock, D.

S.

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G. Gilmanov, R. J. Scholes, D.

S.

Schimel,

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Kamnalrut,

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J.

W. B. Stewart, and C. V. Cole,

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and

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T.V.

&

Berry,

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(1988). Progress Rep., Contr. A4-121-32,

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S. W. and S. T.

Gower, Forest-BGC,

a

general model

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for

regional

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Dynamic carbon

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nitrogen

budgets,

Tree Physiology,

9:147-160, 1991.

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J. O. and

J.

M. Melack, Nitrogen and sulfate export from high elevation catchments of the Sierra Nevada, California, Water

Air and Soil

Pollution,

1

05:217-226, 1998.

Stoddard,

J.

L., Long-term changes in watershed retention of nitrogen

-

its causes and aquatic consequences, in Environmental Chemistry of Lakes

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Reservoirs,

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K. A., The Emerald Lake watershed study: introduction and site description,

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J.

S. Baron, N. Caine, R. Sommerfeld, and

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Sanford, Nitrogen saturation in the Rocky Mountains, Environmental

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Technology,

30:640-646, 1996.

Wolford,

R. A., R. C. Bales, and S.

Sorooshian,

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model for seasonally snow-covered alpine watersheds: Application to Emerald Lake

Watershed, Sierra Nevada, California,

Water.

Resource. Res.,

32(4):1061-1074,

1996.

Table

3.1 Ecosystem Components

as

Modeled

for

Emerald

Lake. Values are

mean

for

last 15 years

of an

1880 year

simulation, and for observations

by Rundel

et

al. [1988]. Observed

values

multiplied by 0.45 to convert biomass to

g carbon.

Dep.

Mean

air

temperature

Low High

SCA

and

mean

air

temp.

Double

Low High

Double

Obs.

Data

Live

shoots

(g m

-2

)

Live roots (g m

-2

)

34 45

1570 2100

53

2500

9

440

21

1018

31

1584 n/a

392

Live N (g rn

-2

) 25 34 41 7 17

Total

soil C (g rn

-2

) 8300 10400 11900 3700 6000

Total

soil N (g rn

-2

) 500 610 690 280 390

Active

soil C (g m

-2

) 300

Active

soil N (g m

-2

) 20

410

27

480

32

86

6

200

13

26

8243

510

310

21 n/a

17500

1195 n/a n/a

131

132

Table

3.2 Ecosystem Processes as Modeled for Emerald Lake. Values are mean for last

15 years of an

1880 year simulation, and for observations by

Rundel et al. [1988], Brown et al. 1986.

Observed values multiplied by

0.45 to convert biomass to g carbon.

Dep.

Above ground

C production

(g rri

2

yr

-

')

Below ground C production (g m

2

yr

1

)

Mean air temperature

Low High Double

SCA

Low and mean air temp.

Obs.

High Double

Data

59 88 110 10

32 60 143.1

65 100 120 11 36 61 n/a

Net Mineralization

(g

m

-2

yr

-i

)

2 3.2

3.9

0.002

0.7

1.9

0.924

Plant uptake

cg

m

-2 yfl)

1.9

2.9

3.6

0.3

1 1.8

1.89

SURFACE LITTER ROOT LITTER

133

0.55

C

C = 003-• 009*T

UN

= Lignin:nitrogen ratio

A

=

Soil temp. and soil moisture effect

T =

Silt plus clay fraction

T s

= Sand fraction

T c

=

Clay fraction

L s

= Fraction of sturctural C as lignin

L c

= exp(-3.0*L

5

)

I-1

2

0

=

Water leached out each day times

30

F =

Metabolic fraction of litter

K

1

=

Max. deacy rate (day

-1

)

Figure

1 Carbon

box

diagram

134

N dep

I or

M

SURFACE

LITTER

STRUCTURAL

I ,,,,

LIGNIN 1 ''.

!CELLULOSE

I or M

METABOLIC

N

MINERAL

N

.05*NO

3

N

2

0,

NO

--------

--6,..02*G

N

I or M

I or M

NO

3

F

ROOT LITTER o M

: STRUCTURAL

'

.

I ,,,

I

,

1 CELLULOSE

METABOLIC

N

••••

SURFACE

MICROBE

N

ACTIVE SOM

N

I'

SLOW SOM

N

LEACHED

N

PASSIVE SOM

N

N dep

=

GN=

Atmospheric deposition

Gross N mineralization of nitrogen

I

=

Immobilization of mineral

N

M = Mineralization of organic matter

F = Fraction of mineral N leached, function of texture and water flow

Figure

2 N

soil organic matter flows.

N

flows follows those of carbon with nitrogen moving from one box to the next having the

C:N

ratio of the receiving compartment.

135

LIVE SHOOTS

STANDING DEAD

SURFACE

PLANT GROWTH

LITTER

LIVE ROOTS

ROOT LITTER

Figure

3

Grass growth model diagram. Plant growth rate depends on soil temperature, soil moisture and a

self-shading

factor. Root and shoot death depends on soil moisture function and for live shoots on plant senescence at the end of the growing season.

—10

30

20

— — - Reconstructed temperatures

— —

Observed temperatures

\I ri!

I

1 f 11,

I

1

) ,

El

,

i

I

i ,,,

r

1, ,,) , r ' r

, 1 1,.

,,, l i

, ,) ')

t i

li) el r

lilli

Io

—20

1986 1988

1990

Year

1992 1994 1996

Figure

4

Modeled

and

measured

30

day mean

air

temperature

for

Emerald

Lake

136

O 00000000010

CO

Tt OW10103'

1

1' 000417-

1-1-.-

.1- 1- 1-

_

1

ball '_

6

0N

1.--

1 ball `_ c

ON

O

u)

vl bell '_cON

0

*- 0

....

LI.

137

APPENDIX D

-

SENSITIVITY ANALYSIS USING MASS FLUX AND

CONCENTRATION

138

139

4111gt,

,

754

1

Forwarded by JoAnne Peirce/Chichester/Wiley on 07/05/99 14:51

Tom Meixner <[email protected]> on 04 105199 20:16:45

To: JoAnne Peirce/Chichester/VViley cc:

Subject: Re: Hydrological Processes

Jo.

/ mailed off my copy of the form yesterday.

I have a question for you. I am currently in the process of wrapping up my dissertation. I would like to include the paper "Sensitivity analysis using

mass

flux and concentration" as an appendix to the dissertation.

I am the first author of the paper. The dissertation will be reatined by the University of Arizona and microfilmed by University Microfilms

Incorporated (UMI). UmI may sell, on demand, single copies of the dissertation including the paper in question for scholarly purposes.

Thanks,

Tom

On Fri, 30 Apr 1999 jpeirceewiley.co.uk wrote:

> From: JoAnne PeirceeW1LEY on 04/30/99 11:22 AM

• ranziebsing.ing.unibs.it, gerry_jones(PINRS-EAU.UQuebec.CA, pratapecc.nih.ernet.in, ntutejaadlwo.nsw.aov.au, Pfisteraslf.ch, ipquiseredline.ru, gaoehwr.arizona.edu, bruendleslf.ch, tomOhwr.arizona.edu, wintherenpolar.no

> cc:

> Subject: Hydrological Processes

Perrnis&ongnmitadfortheuserequested.

Proper credit must be given to our publication.

(

3 -

Copyright& Licensing Department

JohnWiley&SonslimIted il ma:terlat apposro hi our work with credit to another souro3, autnortsation trom is source must be obtnined.

Credit must

Include the components: Title of following the work,

Editor(s) name(s).

Author(s)

Copyright and/or

John Wiley

&

Fleproduced with

Sons Limited.

permission.

I f

j

tC;,9

Sensitivity Analysis Using Mass Flux and Concentration

Thomas Meixner, Hoshin V. Gupta, Luis A. Bastidas, and Roger C.

Bales

Department of Hydrology and Water Resources, University of Arizona,

Tucson

Received

accepted

140

Short title: CONCENTRATION

VS. MASS

141

Abstract. Sensitivity analysis for hydrochemical models requires consideration of the multivariate nature of watershed response. A robust multiobjective generalized sensitivity analysis

(MOGSA) procedure, recently developed at the University of Arizona, was used to fully investigate the single objective parameter sensitivity of the Alpine Hydrochemical

Model

(AHM).

A total of 20,000 simulations for a two-year period were conducted for the Emerald

Lake watershed in Sequoia National Park, California. For each simulation

21 objective functions were evaluated: they were discharge and both concentration and mass flux for

10 chemical species. The MOGSA procedure revealed that only

2000 simulations were necessary to establish the parameters sensitive to mass flux or concentration. We found significant differences in parameter sensitivity for concentration versus mass flux objective functions. For example, a snowpack elution parameter and a number of hydrologic parameters were sensitive for

Cl

-

concentration, while only the snowpack elution parameter was sensitive for Cl

-

mass flux. By using mass flux instead of concentration fewer mineral weathering parameters and more soil exchange parameters were sensitive. Mass flux calculations emphasize the spring snowmelt and peak discharge events of the early summer. Our results indicate that using mass instead of concentration permits better identification of the model parameters that most affect stream conditions during peak springtime flows and that some combination of mass flux and concentration objectives should be used in evaluating model performance.

142

Introduction

Alpine watersheds are susceptible to changes in

biogeochemical

conditions due to their thin soils, limited vegetation, and snow dominated hydrology

[Melack et al.,

1998; Stoddard, 1995; Melack and Stoddard, 1991].

In the Sierra

Nevada of California, predictions about the response of alpine watersheds have implications for the health of aquatic resources and thus for air quality management

[Takemoto

et al.,

1995].

The Alpine

Hydrochemical

Model

(AHM)

is an integrated watershed model that was designed to improve our understanding of how alpine watersheds will respond to perturbations in climate and deposition

[Wolford

et al.,

1996].

Proper simulation of a perturbed watershed must include a precise and accurate estimation of model parameters, based on an understanding of the parameter sensitivity within

AHM.

Sensitivity analysis and model calibration of stream chemistry models depends on the formulation of one or more objective functions that will be used as criteria for goodness of fit, i.e., the error between observations and model output

[Gupta et al.,

1998;

Mroczkowski

et al.,

1997;

Ohte

and Bales,

1995;

Chang and

Delleur,

1992].

Different conceptual and mathematical formulations of objective functions for catchment

hydrochemical

models exist; e.g. the sum of squared errors, sum of absolute values of errors, likelihood methods etc.

[Hornberger

et al.,

1985;

Sorooshian

and

Dracup,

1984

applied to concentrations of various chemical species. While the mass flux of solutes is often used to gain insight into catchment

biogeochemical

processes

[Anderson et al.,

1997; Pilgrim

et

a/., 1979],

it does not appear to have been used as an objective function for parameter sensitivity analysis.

In this study, a generalized parameter sensitivity analysis

[Spear and

143

Hornberger,

1980;

Bastidas,

1998]

of the

AHM

model was conducted for the

Emerald Lake watershed

(ELW)

located in Sequoia National Park, California.

Observed and simulated values of concentration and mass flux for each of

10

chemical species, as well as discharge at the lake outflow, for the period of the

1986

and

1987

water years (a water year begins on October 1st), were used as the basis for the analysis of model parameter sensitivity.

The study was focused around the following three questions: First, is parameter sensitivity different for chemical mass flux and chemical concentration objective functions? Second, do the differences in parameter sensitivity indicate that objective functions based on mass flux and concentration emphasize different aspects of the underlying hydrologic and chemical processes controlling stream chemistry? Finally, can a sensitivity analysis of this nature provide information about how best to allocate resources for the study of alpine catchment processes?

Methods

Site This application of

AHM

builds on the original application of the model to the

ELW

during an intensive field campaign conducted from

1985

until

1987

[Tonnessen,

1991;

Wolford

et

al.,

1996]. ELW

is a

120

ha headwater catchment located in the Sierra Nevada

(36° 35' N, 118° 40' W),

with elevation ranging from

2800 m

at the lake to

3417 m

at the summit of Alta Peak (Figure

1).

The watershed is

48%

covered by exposed granite and

granodiorite, 23%

by soil and

23%

by talus and includes a

2

ha lake (Figure

2).

Model The

AHM [

Wolford

et

al.,

1996]

is a lumped conceptual model that was designed for simulating the hydrology and

biogeochemistry

of alpine watersheds.

144

It was originally applied to the ELW with the intent of investigating the sensitivity of Sierra Nevada watersheds to changes in climate and deposition.

Modeling a watershed with the AHM requires specification of the particular watershed structure in which the hydrologic and biogeochemical processes occur.

The ELW was partitioned into three terrestrial subunits (rock, talus and soil) and a stream (Figure 3). Within this structure, a set of parameters define the routing of flow from the rock subunit to the talus and soil subunits, and from there sequentially into the stream, the lake and out of the watershed.

Each terrestrial subunit is made up of different compartments (representing the snowpack, snowpack free water, snowmelt, surface runoff, interception by trees and litter) and may contain multiple soil horizons. Stream subunits are made up of different compartments representing the snowpack, snowpack free water, snowmelt, stream ice and streamflow. Lake subunits contain similar compartments to the stream subunits as well as a layered lake model which includes a hypolimnion and epilimnion. Model subunits may be selected for use according to the complexity of the watershed. Hydrologic processes are modeled separately from geochemical processes. Routing between the subunits is handled separately from the structure of the individual subunits.

AHM simulates the watershed response on a daily time step. At each time step the model adjusts snow covered area, computes interception, adjusts snowpack for precipitation and melt, calculates influxes of materials to each soil and rock subunit, drains surface runoff, computes evapotranspiration and sublimation, calculates kinetic reactions, calculates chemical equilibrium in soil compartments, drains water from the soil horizon, calculates chemical equilibria in streams and produces output. The outputs can include detailed descriptions

14.5

of

all chemical calculations, tracking

of

both chemical

and

hydrologic storages

and changes in

storage within

the

watershed, soil chemical

concentrations and

stream

concentrations.

Chemical

speciation

is handled using equations adapted from

MINEQL[

Westall

et

al., 1976] . The

"strength"

of the

model is its precise calculations

of mass and charge

balance

for

chemical species

and

hydrologic fluxes

[

Wolford

et

al., 1996].

Monte-Carlo Simulation

Instead

of

simulating

the 1986 and

1987

water years separately

as

was done

in

previous studies

[

Wolford

et

al., 1996;

Ohte

and

Bales, 1995], the

2

water years were run

as a

continuous

simulation (Figures

4 and

5).

This

continuous run was

made possible

with

data

from

the Lodgepole

Ranger

Station in

Sequoia

National

Park

(A. Esperanza,

personal

communication),

which permitted

the estimation of

winter storm

occurrences

at

ELW.

A total of 20,000 Monte-Carlo simulations of ELW

response were conducted

for the

selected two year period. Each

simulation

was conducted by uniformly selecting

values for the 24

model parameters from

the ranges

specified

in Table

1:

10 of

them

are

hydrologic parameters (five

for

each subunit),

and 14 are

chemical parameters

(4

cation exchange

coefficients on

each

of the

soil

and talus

subunits

and

6

chemical parameters that

are

constrained by model

structure

to be

the

same

for

all subunits).

For

each

simulation, 21

different

objective

functions were calculated, each being

the

sum

of

squared error

(SSE)

between

a

model simulated

output and

its associated

value

measured at

the

Emerald outflow.

For

each

of the

10

chemical species,

2 objective

functions were calculated:

i) the

SSE between

the

measured

and

modeled

concentration and ii) the

SSE between

the

measured

mass and the

modeled

mass flux. This second objective

function was

146

calculated as:

ssE k

= E

[(c r i o

4

d=1

Q

obs

)

_

(o rnod,/

nm d 1

Ni k ,d

X

‘ze

°

6

»

2 where

k

is each chemical species,

d

is day,

n

is total number of observations,

C

is concentration of chemical species, and

Q

is daily discharge. Differences

(1 )

between the concentration and mass flux objective functions can be understood on a qualitative level by looking at the distance between modeled and measured values of concentration and mass flux for

Ca

2

+,

ANC and

Cl

-

over both of the years simulated (Figures

4

and

5).

These figures show that the mass flux objective functions are heavily dependent on the chemical observations in

1986

and particularly on those observations made at the highest flows.

MOGSA

The

20,000

Monte-Carlo simulations were used as the basis for a

multiobjective

generalized sensitivity analysis

(MOGSA) [Bastidas, 1998].

MOGSA

is an extension of the methodology developed by

Spear

and Hornberger

[1980]

that has come to be called generalized sensitivity analysis (GSA). In the

GSA method, a series of Monte-Carlo simulations is conducted by randomly sampling over a feasible parameter space defined by establishing upper and lower limits for the possible values of each parameter. The samples are then classified as being behavioral

(B)

(i.e., having desired qualities) or non-behavioral

(B)

-

typically the desired quality is a low value for the objective function. The discrimination into behavioral and non-behavioral sets is entirely subjective and depends on the selection of a threshold "acceptable" value for the objective function. For each parameter

(0

k

)

the empirical cumulative distribution function is computed for both behavioral,

FA

I

B)

and non-behavioral,

FA

I

B)

outcomes. The

Komolgorov-Smirnov (K-S)

statistic is used

[Stephens, 1970]

147

to discern whether the sampling distributions belong to the same underlying population distribution or not. If not, the parameter in question is deemed to be sensitive.

MOGSA

extends the GSA methodology to multiple objectives by introducing the notion of Pareto ranking [Goldberg,

1989]

into the selection of the discriminatory threshold between behavioral and non-behavioral categories, thereby using additional information to overcome weaknesses of the original method

[Beck,

1987].

To avoid dependence of the results on the sampling procedure, bootstrapping [Efron,

1979]

has been incorporated into the algorithm, and for robustness, the median of the

K-S

statistic is used as the indicator for sensitivity at a particular significance level. When working with single objectives, the

MOGSA

code uses a

quantile

of the objective function as the threshold for discerning between behavioral and non-behavioral solutions.

The results presented in this paper use the

50% quantile

to partition the samples into behavioral and non-behavioral categories. The selection of the

50% quantile

is based on tests of

MOGSA

which have indicated that this

quantile

tends to coincide with the most stable

multiobjective

solution for sensitive parameters (results unpublished). Fifty bootstraps were conducted for each of the sample sizes of

500, 750, 1000, 2000, 3000, 5000, 10,000,

and

15,000

(selected from the

20,000

simulations with replacement) to determine the sensitivity of model parameters to the number of simulations used for sensitivity analysis. For each sample size, the

K-S

statistic was calculated and the probability of the acceptable and unacceptable distributions being the same was recorded. A significance level (a) of

0.05

was used to discriminate sensitive from insensitive parameters, i.e., a

< 0.05

means that the behavioral and non behavioral distributions of a

148

parameter are not drawn from the same population and therefore the parameter being tested is sensitive.

Results

The

MOGSA

procedure revealed that only

2000

simulations were necessary to establish parameter sensitivity for mass flux or concentration objective functions. This result is illustrated for ANC and Na

+

in Figure

6.

Similar results occurred for all of the objectives, with the sensitive parameters for some of the objective functions requiring as few as

500

simulations to be identified (data not shown).

There were more sensitive hydrologic parameters than sensitive chemical parameters for concentration objective functions (Table

2).

There were fewer sensitive hydrologic parameters for Si and

SO

42-

than for other concentration objectives. The

Pc

o2

in the subsurface, two weathering parameters, and a, and the elution parameter,

D,

were sensitive for the largest number of concentration objectives. Exchange coefficients for the cations, Si and SO

?

1 -

were important for the species they are associated with and few other species.

The sensitivity analysis for the mass flux objectives tells a different story

(Table

3).

While more sensitive ion exchange parameters were found for mass flux objective functions, there were fewer sensitive hydrologic parameters. For example, only the elution parameter

D

was sensitive for

Cl

-

mass flux, while there were several sensitive hydrologic parameters for

Cl

-

concentration. In total, there were

40

sensitive chemical parameters for the

10

mass flux objective functions, while there were

41

sensitive chemical parameters for the concentration objective functions. However, the sensitive chemical parameters for concentration

149

and mass flux were different. Fewer weathering parameters

(15

weathering parameters for concentration,

7

for mass flux) but more exchange parameters

(13

exchange parameters for concentration,

22

for mass flux) were found to be sensitive for mass flux objective functions.

For hydrologic parameters, using mass flux as opposed to concentration greatly decreased the number of sensitive parameters. There were

63

sensitive hydrologic parameters for chemical concentration as opposed to only

44

for mass flux. There were fewer sensitive hydrologic parameters for each of the chemical species except for Si, which saw no change, and

SO

4

2-

which had

6

sensitive hydrologic parameters for mass flux as opposed to

2

for concentration. The evapotranspiration parameters (ET) for both of the subunits were important parameters for concentration objective functions, with a total of

10

sensitive ET parameters either on the soil or on the talus subunit; however, when mass flux was used, only ET on the soil subunit was sensitive with respect to

Discussion

The results show systematic differences in parameter sensitivity for objective functions calculated from a chemical species concentration as opposed to mass flux of the same species, for this application of

AHM

to

ELW.

There is a high degree of confidence in these results due to the large number of simulations that were executed and the bootstrapping technique which shows the results to be repeatable and robust. Using concentration as an objective function revealed parameter sensitivities that are important all year and especially during periods of low flow. Examples are fraction of potential evapotranspiration

(ET)and

the mineral weathering parameters

(K

and a). Using mass flux as the objective

150

function revealed parameters that can have a large effect for a short period of time, and especially during higher flows. Examples are ion exchange and

snowpack

elution parameters.

Differences for hydrologic parameters other than ET are more mixed.

Hydrologic parameters that determine soil pore-water volume (O sa t and soil depth

)

and residence time in that volume (K sa t and

N)

are important year round.

These parameters determine the mixing volume of the subsurface and the rate of exchange between surface and subsurface water, respectively. These hydrologic parameters affect stream chemical composition throughout the year. We might therefore expect mixed results for parameter sensitivity using mass flux as opposed to concentration as the objective function. In general, fewer hydrologic parameters were sensitive when mass flux was used as the objective function possibly because the chemical parameters that mainly influence individual species were relatively more important when using mass flux as the objective.

Reasons for different information content Stream chemical concentrations for Emerald Lake are relatively constant and the data are representative of many stages of discharge (Figure

4);

therefore, concentration objective functions equally weight errors in model output among observations. Thus, model output for the entire year is important in determining parameter sensitivity for concentration objective functions. Mass flux objective functions weight periods of high discharge more heavily in calculating total model error (Figure

5).

Trends of stream concentration during periods of high discharge have long been used to investigate storm-water dilution, weathering and flow paths in headwater catchments

[Anderson et

al., 1997; Webb and Walling, 1996].

Particularly in alpine catchments of the Sierra Nevada, dilution

[Stoddard, 1987]

and acidification

151

[Williams and Melack, 1991]

have been identified as important processes in controlling ANC during spring

snowmelt,

the period of highest discharge for the

ELW.

Our results indicate that mass flux and concentration objective functions contain different information about watershed processes. In particular, mass flux emphasizes parameters that have a faster response within the model and possibly within the watershed. Exchange coefficients and

snowpack

elution parameters influence modeled stream chemistry over shorter periods of time, with the elution parameter in particular influencing modeled stream chemistry during peak discharge. These processes are important in determining stream chemical composition during spring

snowmelt,

the period of greatest sensitivity to acid deposition for alpine catchments

[Williams et

al.,

1993].

Using concentration as an objective function highlighted sensitivities to evapotranspiration and mineral weathering parameters, which affect model output throughout the year and influence the mean model output. Thus for investigating model error and structure with the goal of improving catchment models, it is important to include measurements of model error that incorporate both mass flux and concentration objective functions.

Mass flux objective functions place a heavier weight on chemical observations during high flows than on observations during low flows (Figure

5).

This reliance permits the extraction of information about short time scale watershed processes.

However, it also makes parameter estimation and sensitivity analysis dependent on the accuracy of a reduced number of chemical observations during periods of high flow. Our confidence in the stream chemical composition observations is high due to the extensive quality control and quality assurance protocols of

152 the laboratory that conducted the analysis of stream samples

[Melack

et

al.,

1998]. However, the measurement errors for mass flux observation are also heteroscedastic (increasing error with increasing measurement value) due to the multiplication of observed concentration with discharge. While heteroscedasticity has been well studied in the context of rainfall runoff models

[e.g.,Sorooshian

and

Dracup,

1980] little similar work has been done for hydrochemical models.

Investigations of this issue, using model output as "true data", would need to be done to further investigate the effects of using mass flux as a measure of model error prior to using mass flux objective functions in a parameter estimation context

[Kirchner et

al.,

1996].

Information about natural processes Our sensitivity analysis differed from the more limited analysis of

Ohte

and

Bales

[1995] in that similar parameters for different subunits and the exchange coefficients for each applicable chemical species were varied independent of each other. These changes allowed the identification of differing sensitivities for each exchange coefficient by objective function and subunit. Ohte and Bales found that Ca

2

+ and Me+ objective functions were unaffected by exchange coefficient parameters, while our results showed exchange coefficients to be important.

Also, our results indicate that the volume of talus and residence time of water in the soil subunit were among the most important hydrologic parameters in determining model output. Each subunit has two parameters that represent soil water holding capacity (O sa t and soil depth) and two parameters that represent rate of flow through that water holding volume (K sa t and

N

for unsaturated flow). Summing the results from Tables 2 and 3 shows that for soil, 22 flow rate parameters and 24 soil volume parameters were sensitive for

153 chemical (concentration or mass flux) objective functions. For talus, 18 flow rate parameters and 32 talus volume parameters were sensitive for chemical objective functions. These results indicate that the AHM model of

ELW is more sensitive to talus volume than it is to flow rate through the talus. These results also indicate that flow rate through soil is more important than is flow rate through talus. Campbell et al. [1995] and

Williams et al. [1997] have recently concluded that areas of talus are more important than previously thought in determining alpine stream chemistry. They also state that there is a lack of knowledge as to the total reaction volume of talus volume in a watershed. Isotopic methods have shown some promise in estimating talus volume [Mast et al., 1995]. Our results indicate that more time should be spent in the field trying to estimate the reactive volume of talus fields. Until talus volume is more accurately measured in the field it will need to be estimated using calibration techniques.

Conclusions

Testing model sensitivity with different measures can reveal more information about both the model and the natural system. Mass flux objective functions revealed greater parameter sensitivity for cation exchange and snowpack elution parameters, while mineral weathering and evapotranspiration parameters were more important for concentration objective functions. The mass flux objective function emphasized processes that are most important during periods of peak discharge while concentration emphasized more long term processes. Since peak discharge is the period when alpine ecosystems are most in danger of being impacted by acid deposition, mass flux objective functions provide information about watershed processes that are important in addressing acid

154 deposition questions in alpine watersheds. However, using mass flux objective functions introduces the problems of heteroscedasticity into the parameter estimation problem for hydrochemical models. These issues would need to be further investigated before using mass flux in a parameter estimation context.

Our results also indicate that future field efforts for alpine basins should be concentrated on talus and soil hydrologic properties. These efforts should emphasize discerning the volume of talus in a watershed and the conductivity of the soils.

Acknowledgments.

The

first author was supported by

a

NSF Graduate

Research

Fellowship

and a Canon National Park Science

Scholarship.

A NASA-EOS

grant

(IDP-88-086)

provided

partial support for

this work.

N. Ohte

helped

in initial

coding

for Monte

Carlo

simulations.

Thank you to J.

Sickman for

providing

insight and data about the

Emerald

Lake

watershed. We wish to thank

K. Meixner and B.

Matson

for

comments

on an

earlier

version of

this manuscript. We also wish to thank two anonymous reviewers whose comments improved this manuscript.

155

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AGU LATEX macros v3.0.

159

Table

1.

Parameters varied

and range relative

to

values

by

Wolford

et

al.

[1996]

Parameter' Range

ET b

0-1

Soil

— depthc 0.5-1.5

Nc 0.8-1.8

K at

El u ti on

(Dc)

K-Ca

2

+e

K_m g

2+e

K- Na+e

K-K+

K-SOr

K-Si r

Soil P,

02 a h

0.5-1.5

0.5-1.5

0.5-1.5

0.5-1.5

0.5-1.5

0.5-1.5

0.2-4

0.5-1.5

0.5-1.5

0.5-1.5

0.5-1.5

0.5-1.5

a

The

hydrologic parameters

and cation

exchange

coefficients

were varied independently

for

each subunit within

the

same mathematical

range.

b

ET

represents

the fraction of

potential evapotranspiration that is permitted to

occur; the

varied

range

is

the

possible

range.

The

parameters Soil-depth,

N, K sat

, and O

sa t

represent

total

depth

of

soil

on a

subunit,

a

drying

coefficient for

unsaturated

flow,

saturated hydraulic conductivity

and

saturated soil water

holding

capacity.

160

d

The

equation used to represent

snowpack

elution

in

AHM

is:

-=

A x

B

e(—BXX) (1 —

A)

x

D x

e(-DxX).

In the

models current form

A and

B

are

small so

D

is the

dominant

parameter

and

was thus

the

parameter used

in the

sensitivity analysis.

e

Log

K

for

exchange

of cation

with

H+

on cation

exchange

site.

f

Log

K

for adsorption of

SO

42-

and

H

2

SiO

3

.

Total site concentrations

from

ELW

optimization used here. These parameters cannot be varied independently

for the

soil

and talus

subunit.

g

The partial pressure of

carbon dioxide P

, was varied simultaneously

for

both subunits.

h

The

weathering coefficients

K

and a

were varied independently

of

each other but uniformly

for

all species

due

to

issues of charge balance.

They contribute to weathering

via the

equation:

Mol

=Axnx [H

4

1'

where

Mol

is

moles

added to

the

subunit,

A

is

total

area

of the surfaces

involved

in

reactions,

[11+]

is hydrogen

ion concentration, and

K

and a are constants. The total surface

area is determined

as the

product

of the

soil depth, area, bulk density,

and

specific

surface

area.

Table 2. Parameter Sensitivity for Concentrations at

2000

Simulations

Parameter

ET (soil)

Soil-D

(soil)

N

(soil)

Ksat

6

1 sa t (SOH)

ET (talus)

Soil-D (talus)

N

(talus)

e

K

sat

(talus)

sa t

(talus)

Elution (D)

K-Ca

2

+

(soil)

K-Mg

2

+

(soil)

K-K+

(soil)

K-

Na

+

(soil)

K-S0

2

4

-

(both)

K-Ca

2

+

(talus)

K-Mg

2

+

(talus)

K-K+

(talus)

K-

Na

+

(talus)

K-Si

(both)

K-H

2

CO

3

(both)

x

(all species) a (all species)

x x x x x x

X

ANC

x x

Objective Function

Ca

2

C1

K+ Mg

2

+

Na+ NO

H+ Q

Si

S0

2

4

-

x x x

.x

x x x x x x x x x x x x x x x x x

X X

x x x x

X

X

x x x x x x x x x x x x x x x x

X X

x x x

X

x x x x x x x

X X

x x x x x x x x x x x x x x

X

x x x x x x x x x x x x x x x x x x x x x x x x x x x x

161

Table 3. Parameter Sensitivity for Mass at

2000

Simulations

Parameter

ET

(soil)

Soil-D (soil)

N (soil)

Ksat

(soil)

O sa

(soil)

ET (talus)

Soil-D (talus)

N (talus)

'< sa,

(talus)

O sa

,

(talus)

Elution (D)

K-Ca

2

+

(soil)

K-Mg

2

+ (soil)

K-K+

(soil)

K-

Na

+ (soil)

K-S0?

1

-

(both)

K-Ca

2

+

(talus)

K-Mg

2

+

(talus)

K-K+

(talus)

K-

Na

+

(talus)

K-Si

(both)

K-H

2

CO

3

(both)

(all species) a

(all species) x

Objective Function

ANC Ca

2

+ Cl

-

K+ Mg

2

+ Na + NO H+ Si

S0

2

4

x x x x x x

X X X X X X X X x x x x x x x x x x x x x x x x x x x x x

X x x x x x x x x x x

X x x x x x x x x x x

X x x x x x x x x x x x

X x x x x x

X x x x x x x x

162

163

Figure 1.

Elevation map

of ELW.

Figure 2.

Soils map

of ELW.

Figure

3. AHM

representation

of the

Emerald

Lake

watershed broken down into

rock, talus,

soil, stream

and

lake subunits.

All

subunits include compartments that represent

the snowpack

including

the

preferential elution

of ions

during

snowmelt.

Soil

and talus

subunits include

snowpack

compartments

and

two

horizons

that incorporate

major

soil physical

and

chemical processes.

Stream

compartments include

snowpack

compartments, stream ice

and

discharge.

Lake

compartments include

snowpack

compartments, ice

cover, a hypolimnion, an epilimnion

(both

for the

lake)

and

lake

or

stream discharge.

Inputs and

outputs to each subunit

are

shown by arrows.

A) Inputs of

precipitation quantity

and

quality,

and dry

deposition to subunits. Output

of

evapotranspiration from subunits.

B) Snowmelt

runoff from

the rock

subunit is distributed equally to

the

soil

and talus

subunits.

C) Surface

runoff

and

subsurface

drainage

from

the

soil

and talus

subunit is routed to

the

stream.

D) The

stream flows into

the

lake.

E) Lake

outflow is

the

discharge from

the basin.

Figure 4.

Measured

and

modeled

concentration

results

for Wolford

parameters

[from

Wolford

et

al.,

1996], for 1986 and 1987

water years.

Figure 5.

Measured

and

modeled

mass flux

results

for Wolford

parameters

[from

Wolford

et

al.,

1996], for 1986 and 1987

water years.

Figure 6.

Number

of simulations versus

number

of sensitive

parameters

for

ANC

and Na+ for 50% quantile, a of 0.05 and 50

bootstraps.

NORTH

164

lnflowing

Streams

Contour Interval

25

Meters

165

166

7

cts

40

V

30

E 20

c.

° io

60

cr

40

(

5

20

< 45

-

I

+ +

LIII

- -H

I

I

I

H-

I

I

I

++

+ _

+

+

-1-1-

_L___

I

.

-±±_—

100 200 300 0

Water year day

tF±t

+

+-1+-

1-

1+

100 200 300

Water year day

167

-'-

-

F

1986

_ -

Modeled

-

-

±

Measured

-7 -,-

1

1987 -

100 200

Water year day

300 100 200

Water year day

300

168

2

24

465

20

co

16

°

12

F.,

8

CI)

4

0

oc = 0.05

-

Na

+

Na* mass

ANC

ANC mass

1000 3000 5000 10000

N points in sample

15000

169

APPENDIX E - MULTI-CRITERIA PARAMETER ESTIMATION FOR

HYDROCHEMICAL MODELS

170

Multi-Criteria Parameter Estimation for

Hydrochemical

Models

Thomas Meixner, Luis A. Bastidas, Hoshin V. Gupta and Roger C.

Bales

Dept.

of

Hydrology

and

Water Resources,

University of Arizona, Tucson, AZ 85721

171

Abstract

The calibration of hydrochemical models using stream chemical composition and discharge data is commonly done by manual methods. A body of literature is being developed on the automatic calibration of hydrochemical catchment models using multiple response data. These past multiple response model calibration studies have neglected to investigate which criteria should be used in a multi-criteria framework for the purposes of parameter estimation and model evaluation. We applied the MOCOM-

UA algorithm to the Alpine Hydrochemical Model of the Emerald Lake watershed. The model was calibrated in different ways by varying both the criteria used as well as the

172 total number of criteria used in the MOCOM-UA algorithm. The results indicate that fewer criteria yield improved performance for parameter estimation problems with hydrochemical models. The results also indicate that a mix of mass flux and concentration criteria should be used in calibrating hydrochemical models. The model calibration also revealed that the current weathering rate in the AHM model is too low.

The results also raise doubts about the completeness of the current description of catchment hydrology.

Introduction

During the last two decades, many stream chemistry models have been developed to address issues ranging from acidification, chemical denudation rates, non-point source pollution, climate change, and land use change [Cosby

et

al., 1985; Christophersen

et al.,

1993; Wolford

et

al., 1996]. Models of catchment hydrology and hydrochemistry suffer from two fundamental problems that have uncoupled these models from rigorous hypothesis testing: i) calibration data do not contain enough information to uniquely determine model parameters, and ii) state variables within catchment biogeochemical models are difficult to relate to field observations (e.g. model represents average field conditions while field measurements are point scale measurements). Two solutions to these problems have been proposed: i) an improvement in field observations of the processes that govern stream chemistry, and ii) investigation of hydrochemical models with synthetic data sets, as has often been done with hydrologic models [Christophersen

et

al., 1993]. The first of these solutions has been pursued by a number of different researchers

[Anderson et

al., 1997; McDonnell

et

al., 1998]. While the second has been pursued, the results are more limited

[Kirchner et

al., 1996; Mroczkowski

et

al., 1997].

Recent developments in multi-criteria analysis of hydrologic problems provide a tool that can be used to solve calibration, estimation, sensitivity and model evaluation problems in catchment hydrochemical modeling

[Gupta et

al., 1998].

173

The core issue in multi-criteria analysis of catchment hydrochemical models is the need to investigate all of the non-commensurate measures of model error simultaneously. This investigation must occur with recognition of the tradeoffs inherent in trying to predict several model fluxes simultaneously. As an example, for hydrochemical modeling of a forested watershed to be successful it is necessary for the model to match both stream discharge and observed alkalinity. The "best" set of model parameters for discharge may be a poor set for ANC or vice versa. It is important to understand that compromises must be made to account for the errors in the structure of catchment hydrochemical models. The real watershed produces the measured output that the model is trying to predict but the model must compromise in coming to a "best solution" that is less accurate than the observed stream chemistry. Therefore, multicriteria parameter estimation is a tool to investigate conceptual errors in catchment hydrochemical models.

Several applications have been made using multi-criteria model calibration methods with hydrochemical and hydrologic watershed models. In one recent example

174

Mroczkowski

et

al.

[1997] investigated using discharge, groundwater state and stream salinity for a watershed model calibration. They investigated the structure of the model and chose between two possible model structures. In this study they successfully showed that using multiple criteria can be used to improve model structure. Another example of using multiple criteria in model calibration and evaluation is the Birkenes series of papers

[Grosbois et

al.,

1988;

Hooper

et

al.,

19881, which used discharge and

18

0 isotope ratios

to calibrate the hydrologic parameters within the

Birkenes

model. Their work was successful at improving the

Birkenes

model but not without incorporating unrealistic flow paths into the model [Stone and

Seip,

1989;

Lundquist

et

al.,

1990].

Past studies that used multiple criteria for parameter estimation and model evaluation have neglected to investigate which criteria should be used. The purpose of this study was to determine: i) what subset of criteria available for

AHM

calibration at the Emerald Lake watershed

(ELW)

are necessary for parameter estimation and model evaluation, ii) iii) iv) what methodology is best suited to selecting the criteria, what do the calibration results imply about the hydrologic and

hydrochemical

processes that control stream chemical composition in the

ELW,

and what do the results imply about the model structure?

175

Methods

Multi-Criteria Parameter Estimation Methodology

A thorough discussion of the application of multi-criteria theory to calibration of conceptual physically based models can be found in [Gupta et al., 1998]. The following is a brief summary of that methodology. Consider a model with parameters

0 = {O h

....,

on)

that is to be calibrated with observations (0,) over m simulated model output variables. For each simulated response X, it is possible to define a criterionfl Co) that represents the distance between the simulated value X and the observations 0, The criterion f; may be defined with any number of measures of model error or residual. The root mean squared error (RMSE) is commonly used since its units are the same as those of the observations and its values are easy to comprehend. RMSE can be represented as

176

RMSE(q)= (O — X,(0))

2

(1) n

with 0 the set of model parameters, n the total number of observations 0, and X the simulated value at time step t. The multi-criteria model calibration problem can formally be stated as:

Minimize F(0) = { f i

(0),..., f„(0)} subject to 0 c 0 (2) where the goal is to find values for 0 within the feasible set 0 that minimize all of the criteria

(f

( e),

1.1,...,m) simultaneously.

In practice it is not possible to minimize all criteria simultaneously. Instead a set of solutions is commonly found, with the property that within the set of solutions it is

177

necessary to deteriorate performance at simulating one criteria in order to improve the performance of a second criteria. Figure I illustrates a multi-criteria problem with two parameters

(0, and

0

2

)

and three criteria

(f,, f,

and

f, ).

Figure la shows the feasible parameter space e and Figure lb is a projection of the multi-dimensional criteria space onto a

2-dimensional

plot. The points

a,

p,

and

yindicate

the three solutions which minimize each of the individual criteria. The shaded region indicates the Pareto set solution to the minimization problem. The points

8

and

E represent arbitrary points in the feasible space in and outside the Pareto set. Every point

5

is superior to every point

E,

i.e.

(S)

<4(8),

for all

j =

1,...3.

However no point within the Pareto set is superior to any other point. A particular point may be superior for one or more criterion, but it will be inferior to other points for at least one criterion. The Pareto set is sometimes called the trade-off set, non-inferior set, non-dominated set or the efficient set. The Pareto set represents the best solution available through model calibration without incorporating the subjective judgment stating that one or more of the criteria are more important than the others. The size of the Pareto set is related to errors in model structure and the calibration data set. Only when a perfect model and perfect data are available will the Pareto set be a unique solution.

MOCOM-UA

A number of different methodologies are available for solving the multi-criteria problem. Recently,

[Yapo,

1996]

presented an efficient population-based optimization strategy that provides an approximate representation of the Pareto set with a single optimization run. This algorithm, Multi-Objective Complex Evolution

(MOCOM-UA),

is based on the successful SCE-UA optimization method

[Duan et al.,

1992; Duan et al.,

1993].

The

MOCOM-UA

method begins by sampling the feasible space

(9

at a number of preset locations and then evolves that population using multi-criteria methods to drive the sample towards the Pareto set; for details see

[Yapo,

1996].

The final solution consists of a set of points that approximate the Pareto set.

178

Site Description

This application of

AHM

builds on the original application of the model to the

ELW

during an intensive field campaign conducted from

1985

until

1987 [Tonnessen,

1991; Wolford et al., 1996]. ELW

is a

120

ha headwater catchment located in the Sierra

Nevada

(36

°

35' N, 118

°

40' W),

with elevation ranging from

2800 m

at the lake to

3417 m

at the summit of Alta Peak. The watershed is

48%

covered by exposed granite and

granodiorite, 23%

by soil and

23%

by talus and includes a

2

ha lake.

Model

The ARM

[Wolford et

al., 1996]

is a lumped conceptual model that was designed for simulating the hydrology and

biogeochemistry

of alpine watersheds. It was originally applied to the

ELW

with the intent of investigating the sensitivity of Sierra Nevada watersheds to changes in climate and deposition. Modeling a watershed with the ARM requires specification of the particular watershed structure in which the hydrologic and

biogeochemical

processes occur. The

ELW

was partitioned into three terrestrial subunits

(rock, talus and soil) and a stream (Figure

2).

Within this structure, a set of parameters define the routing of flow from the rock subunit to the talus and soil subunits, and from there sequentially into the stream, the lake and out of the watershed.

Each terrestrial subunit is made up of different compartments (representing the

snowpack, snowpack

free water,

snowmelt,

surface runoff, interception by trees and litter) and may contain multiple soil horizons. Stream subunits are made up of different compartments representing the

snowpack, snowpack

free water,

snowmelt,

stream ice and

streamflow.

Lake subunits contain similar compartments to the stream subunits as well as a layered lake model that includes a

hypolimnion

and

epilimnion.

Model subunits may be selected for use according to the complexity of the watershed. At each time step, hydrologic processes are modeled separately from

geochemical

processes. Routing between the subunits is handled separately from the structure of the individual subunits.

179

AHM

simulates the watershed response on a daily time step. At each time step the model adjusts hydrologic and chemical inputs, outputs, and state variables for

13

separate compartments representing, snow, vegetation, infiltration, and soil processes.

Model output can include detailed descriptions of all chemical calculations, tracking of both chemical and hydrologic storages and changes in storage within the watershed, soil chemical concentrations and stream concentrations. Chemical

speciation

is handled using equations adapted from

MINEQL

[Westall et al.,

1976].

The "strength" of the model is its precise calculations of mass and charge balance for chemical species and hydrologic fluxes

[Wolford et al.,

1996].

180

Applying

MOCOM-UA

to

AHM

The

MOCOM-UA

algorithm was applied to the

AHM

model of

ELW

for the

1986

and

1987

water years. The parameters used and their feasible space were determined from available field data or generally accepted understandings of the variability of hydrologic parameters in the field (Table

1) [Meixner et al.,

1999].

The

AHM

model of

ELW

simulates a total of

11

fluxes that can be readily compared with available stream observations. The wealth of criteria available for model calibration provides both opportunities and difficulties in applying multi-criteria methods to this model. Since criteria containing similar information should not be used simultaneously in a multi-criteria optimization problem

[Gupta et al.,

1998],

we developed four sets of

criteria that were independent of each other. The first set chosen was on the basis of a correlation analysis of the observations of stream chemical composition at the Emerald outflow. The correlation analysis showed that the time series for discharge, H

+

, Ca

2+

,

SO4

2

, NO3

-

, and Si were not correlated with each other

(p <

0.6). The concentration criteria for these five chemical species were used.

The remaining three sets of criteria used were selected on the basis of information gained from the sensitivity analysis

[Meixner

et

al.,

1999]. Two changes to the 6 selected criteria were made for the second of the four criteria sets used. Since the current representation of nitrogen chemistry in the AHM was known to be inadequate and the sensitivity results had shown that the Cl

-

mass flux criteria was very good for estimating the ionic pulse, the NO3

-

criteria was replaced by the Cl

-

mass flux criteria. The Ca

2+ concentration criteria was replaced by the Ca

2+ mass flux criteria due to the greater parameter sensitivity shown for the mass flux criteria.

For the third and fourth of the criteria sets the number of criteria used was reduced from 6 to 4. The large number of criteria (6) could cause a very large Pareto set to be found and by reducing the number of criteria it might be possible to reduce the size of the Pareto set. For both cases discharge, Ca

2+

, SO4

2-

, and cr were used as the set of criteria. For the first case all chemical criteria were represented as concentration and for the second case Ca

2+

and CI

-

mass flux criteria were used instead of the concentration criteria.

181

For each of these sets of criteria three estimations of the Pareto set were conducted. One using a set of

20,000

Monte-Carlo simulations and two using the

MOCOM-UA

algorithm, one with a population of

100

points and one with a population of

250

points. The results were compared to the original results of

Wolford

[1992]

as well as the available stream chemical observations for

1986

and

1987.

182

Results

Increasing the search population size enabled an improved calibration of the model with smaller

RMSE

values as shown in Figure

3.

The random search gave inferior results to the

MOCOM-UA

algorithm and the search with

100

points gave results inferior to those with

250

points. Comparing the

RMSE

values for the

MOCOM-UA

parameter estimation results with the

RMSE

values from manual calibration

[Wolford,

1992]

shows that for the chemical criteria the

RMSE

results are superior while for discharge the original

Wolford

results are generally superior.

The calibration results for each of the four sets of criteria used in the

MOCOM-

UA algorithm can be viewed in four different ways: parameter space, criteria space, time series for criteria included in the calibration, and time series for criteria not included in the calibration. The results for each of these methods will be presented separately for the

250-point

search case.

The parameter space results for each of the sets of criteria show a tightening of the parameter space in the four as opposed to the six criteria space. In fact the results for

183

the parameter space for both of the

6

criteria cases cover almost the entire feasible parameter space (Figure

4

and

5).

The parameter space is much more confined for the two searches conducted with

4

criteria (Figure

6

and

7).

The parameter space results for the two cases using

4

criteria with the

MOCOM-UA

algorithm differ for soil hydraulic conductivity

(Ksat).

Using two mass flux criteria results in a higher estimated

Ksat

value. Also using mass flux criteria resulted in a higher and more precise estimate for the

ET parameter on the talus subunit. The incorporation of mass flux data also resulted in more precise estimations for cation exchange parameters

(K-Ca(soil), K-K(soil), K-

Ca(talus),

and

K-Mg(talus)

despite including more exchange parameters than in the

4

criteria case using all concentration criteria (more parameters were added as the results from the sensitivity analysis indicated

[Meixner et

al., 1999].

More precise estimates were also made for the

K-SO4

and

PCO2

parameters when mass flux criteria were incorporated into the search algorithm. Finally for both cases using just

4

criteria a higher value of the mineral weathering parameter a than used by

[Wolford and

Bales,

1996]was

indicated.

The results also show significant differences in the criteria space for each of the four sets of criteria used in the

MOCOM-UA

search. The criteria space is shown in each of the figures as the calculated

RMSE

divided by the mean observed value for the criteria

in question (Figure

4, 5, 6

and

7).

This was done to facilitate ease of interpretation of the results and to make comparisons of the results for different calibrated and noncalibrated criteria easier.

RMSE

represents the variance of the simulated values, dividing

184

by the mean gives us an order of magnitude representation as to how accurate the simulations were for each of the

250

Pareto set results from the

MOCOM-UA

algorithm.

For each of the

4

figures the criteria results for

Wolford et al.

[1996]

(shown in black) can be used as benchmarks to compare the results of each of the criteria sets used. Both cases where

6

criteria were used in the

MOCOM-UA

algorithm show dramatically inferior

Pareto set criteria space results as compared to the results using only

4

criteria. In fact the results almost represent what is produced by randomly varying the parameter values across the feasible space (Figure

8).

The results for

4

in the criteria space (Figure

6

and

7)

were much better than those using

6

criteria (Figure

4

and

5).

In some cases the

MOCOM-UA

results represent dramatic improvements over the calibration results found by

Wolford et al.

[1996].

This result is particularly true when a mix of mass flux and concentration criteria are used

(Figure

7).

One benefit of the multiple parameter sets that are a result of multi-criteria parameter estimation algorithms, such as

MOCOM-UA,

is that each set can then be used to drive the model and show the user what the time series space results for the estimated parameters look like. Good parameter estimates should bound the observations as well as provide precise simulation of those observations. This is equally true for observations

that were included in the search as well as those that were not. The time series results for the 6 criteria (just concentration) and the 4 criteria cases (using concentration and mass flux) show that the 6 criteria search results do bound the observation but only by having very wide bounds around the observations (Figure 9 and 10). This is equally true whether the criteria were included in the calibration or were not included in the

185 calibration. The 4 criteria results do a relatively good job of bounding those observations included as criteria during the search (Figure 11) but does an inferior job in terms of bounding the observations for criteria not incorporated in the search algorithm (Figure

12). The mean simulated concentration for the Pareto set simulations also show some improvement over the concentration simulations garnered by

Wolford

and Bales

[1996]

(Figure 11). This is not true for the species not used in calibration (Figure 12).

Discussion

These results indicate that fewer rather than more criteria are preferable for multicriteria calibration of hydrochemical models. There are three possible reasons for the improved performance of the calibration with fewer rather than more criteria. First, by adding criteria it is impossible to decrease the size of the Pareto set. Referring back to

Figure 2 you can see that the Pareto set in a two criteria case is a line. When a third criteria is added the Pareto set can remain the same (if the optimum point for the third criteria is on that line) or become larger as is the case in Figure 2. Second the 6 criteria

we selected may contain similar information about the hydrologic and

hydrochemical

processes in the

ELW.

If they do contain similar information then adding criteria simply

186

adds more noise and presents particular difficulties for multi-criteria methods since the criteria must contain non-commensurate information [Gupta et al.,

1998].

The results for the

6

criteria cases would appear to indicate that using a correlation analysis of stream chemical observations is not the optimal method for determining the criteria that should be used for parameter estimation of

hydrochemical

models. Finally, the observations of stream chemical composition in the

ELW

may contain distinct and non-commensurate information about the hydrologic and

hydrochemical

processes of the watershed but an inadequacy of model structure does not permit this information to be expressed in the calibration process.

The use of the sensitivity analysis results in developing both of the

4

criteria cases indicates that the results of generalized sensitivity can be used to determine what set of criteria should be used in multi-criteria parameter estimation problems. The results were superior for both of the more limited sets over the

6

criteria problems. Also the

4

criteria case which incorporated

Ca

2

+

and Ci mass flux show marked improvement over the case where only the concentration criteria were used. This result is evidenced in the superior performance of the mix of mass flux and concentration criteria in both the parameter and criteria space (Figure

6

and

7).

The choices of criteria in this work were qualitative and subjective based on an expert's view of the sensitivity analysis results for selecting the criteria that were to be used for the multi-criteria calibration. A more objective and

rigorous approach to utilizing the sensitivity results for criteria selection should be pursued.

The calibration results for the four criteria calibration also give us information about the natural processes that control stream chemical composition in the

ELW.

In his original manual calibration of the

AHM

model of the

ELW,

Wolford

[1992]

cut the weathering rate in half due to model

overpredictions

of observed ANC. The calibration results here for either of the

4

criteria cases indicate that the weathering rate chosen was too low as the calibrated values for the mineral weathering parameter a for all

250

points for either

4

criteria case are greater than the

Wolford

parameter value. The

4

criteria results also indicate that a smaller ionic pulse would best simulate the observed stream chemistry since both of the limited criteria calibrations resulted in lower estimated values of the elution parameter. Since the two

4

criteria cases gave conflicting results for the various hydrologic parameters the calibration results give us little information about the hydrologic process controlling stream chemical composition.

The lack of coherence in the hydrologic parameter results may be giving us information about the current structure of the model. The significant differences in parameter space for the two

4

criteria results indicate that simulating mass flux requires more rapid flow through soil while simulating concentration requires slower flow through soil. The conflict indicates that the hydrologic representation of the

ELW

by the

AHM

may not be complete and should be investigated to see what changes in model structure could improve the multi-criteria calibration results. Possible changes to the model that

187

could be investigated are: lumping soil and talus together as a single process, or incorporating a third soil and/or talus horizon that has even slower release of water than the second horizon currently present in both soil and talus subunits within the

AHM

model of the

ELW.

188

Conclusions

Multi-criteria parameter estimation is a promising avenue for investigating the accuracy and structure of

hydrochemical

watershed models. A number of steps must be completed before the full power of multi-criteria techniques can be realized. The preliminary results from this work indicate a need to limit the number of criteria used in multi-criteria analysis of

hydrochemical

models. The sources of difficulty with using more criteria lie in the methodology as well as the structure of

hydrochemical

models.

The results from generalized sensitivity analysis showed promise in being used to determine the proper number and which criteria should be used in multi-criteria parameter estimation problems. A more rigorous framework should be developed so that criteria selection is objective and complete. The multi-criteria parameter estimation results for the

AHM

model of the

ELW

indicated a need to increase the rate of mineral weathering and decrease the magnitude of the ionic pulse. The results also indicated a need to investigate the hydrologic structure of the model for inaccuracies and inadequacies.

Acknowledgements

This work was made possible by a Canon National Park Science Scholarship to the primary author. This work was conducted, in part, for completion of a Ph.D. by the lead author at the University of Arizona. Partial support for this work was provided by

NASA-EOS,

NSF and

NOAA

research grants. Special thanks to Jim

Sickman,

Al

Leydecker

and John

Melack

for their help in interpreting field data and to the Surface

Water Calibration Research Group at the University of Arizona for the many good conversations and quality insight into model calibration and parameter estimation.

189

References

Anderson, S. P., W. E. Dietrich, R. Torres, D. R. Montgomery, and K.

Loague,

Concentration-discharge relationships in runoff from a steep,

unchanneled catchment, Water. Resourc. Res., 33(1):211-225, 1997.

Christophersen,

N., C. P. Neal, and R. P. Hooper, Modeling the hydrochemistry of catchments: a challenge for the scientific method,

J. Hydrol., 152:1-12, 1993.

Cosby, B. J., G. M.

Hornberger, J. N.

Galloway, and B. F. Wright, Modeling the effects of acid deposition: Assessment of a lumped parameter model of

soilwater

and

streamwater

chemistry,

Water. Resourc. Res., 27:51-63, 1985.

Duan, Q., V. K. Gupta, and S.

Sorooshian,

Effective and efficient global optimization for conceptual rainfall-runoff models,

Water. Resourc. Res., 28:1015-1031, 1992.

Duan, Q., V. K. Gupta, and S.

Sorooshian,

A shuffled complex evolution approach for effective and efficient global minimization,

Journal of Optimization Theory

Applications, 76:501-521, 1993.

190

Grosbois, E. D., R. P. Hooper, and N.

Christophersen,

A

multisignal

automatic calibration methodology for

hydrochemical

models: a case study of the

Brikenes

191

Model,

Water.

Resourc.

Res.,

24:1299-1307,

1988.

Gupta, H. V., S.

Sorooshian,

and P.

0. Yapo,

Toward improved calibration of hydrologic models: multiple and

noncommensurable

measures of information,

Water.

Resourc.

Res.,

34:751-763, 1998.

Hooper, R. P., A. Stone, N.

Christophersen,

E. De Grosbois, and H. M.

Seip,

Assessing the

Birkenes

model of stream acidification, using a

multisignal

calibration methodology,

Water.

Resourc.

Res.,

24:1308-1316,

1988.

Kirchner, J. W., R. P. Hooper, C. Kendall, C. Neal, and G. Leavesley, Testing and validating environmental models,

The Science of the Total Environment,

1

83:33-

47, 1996.

Lundquist, D., N.

Christophersen,

and C. Neal, Towards developing a new short-term model for the

Birkenes

Catchment,

J. Hydra,

11

6:391-401, 1990.

McDonnell, J. J., J. Freer, R. P. Hooper, C. Kendall, D. Burns, K.

Beven,

and J. Peters,

New method developed for studying flow on

hillslopes, EOS,

Trans.

AGU,

77:465,472, 1998.

192

Meixner,

T., H. V. Gupta, L. A.

Bastidas,

and R. C. Bales, Sensitivity Analysis Using

Mass Flux and Concentration,

Hydrol.

Processes, in

press: 1999.

Mroczkowski,

M., G. P. Raper, and G.

Kuczera,

The quest for more powerful validation of conceptual catchment models,

Water.

Resourc.

Res.,

33:2325-2335, 1997.

Stone, A. and H. M.

Seip,

Mathematical models and their role in understanding water acidification: An evaluation using

Birkenes

model as an example,

Ambio,

18:192-199, 1989.

Tonnessen,

K. A., The Emerald Lake watershed study: introduction and site description,

Water.

Resourc.

Res.,

27:1537-1539, 1991.

Westall,

J. C., J. L. Zachary, and F. M. M. Morel,

MINEQL

A computer program for the calculation of chemical equilibrium composition of

aqueous systems, Dept. of

Civil Engineering,

M.I.T., 1976.

Wolford, R.A. Integrated hydrogeochemical modeling of an alpine watershed: Sierra

Nevada, California. Tucson, AZ: Department of Hydrology and Water

Resources, University of Arizona. (1992). 92-040,

193

Wolford, R. A. and R. C. Bales, Hydrochemical modeling of Emerald Lake watershed,

Sierra Nevada, California: Sensitivity of stream chemistry to changes in fluxes and model parameters,

Limnol. Oceanogr.,

41(5):947-954, 1996.

Wolford, R. A., R. C. Bales, and S. Sorooshian, Development of a hydrochemical model for seasonally snow-covered alpine watersheds: Application to Emerald Lake

Watershed, Sierra Nevada, California,

Water. Resourc. Res.,

32(4):1061-1074,

1996.

Yapo, P. 0., A multiobjective global optimization algorithm with application to calibration of hydrological models, Ph.D. thesis, Department of Hydrology and

Water Resources, University of Arizona, Tucson, AZ, 1996.

194

Table 1.

Parameters varied

and range

relative to

values

by

Wolford

et al.

[1996]

Parameter'

Range

ET b

0-1

Soil

depth'

0.5-1.5

NC

0.8-1.8

I<L,t

O sat

0.2-4

0.5-1.5

Elution(D d

) 0.5-1.5

K-Ca

2

+e 0.5-1.5

K-Mg

2

+e

K- Na+e

K-S0

2

4

-f

K-Si r

Soil P

02 ah

0.5-1.5

0.5-1.5

0.5-1.5

0.5-1.5

0.5-1.5

0.5-1.5

0.5-1.5

0.5-1.5

a

The

hydrologic parameters

and cation

exchange

coefficients

were varied independently

for

each subunit within

the

same mathematical

range.

b

ET

represents

the fraction of

potential evapotranspiration that is permitted to

occur; the

varied

range

is

the possible range.

The

parameters Soil-depth,

N, K sat

, and

O sa t

represent

total

depth

of

soil

on a

subunit,

a

drying

coefficient for

unsaturated flow, saturated hydraulic conductivity

and

saturated soil water

holding

capacity.

195 d

The

equation used to represent snowpack elution

in

AHM

is: v

=AxBxe

(

(1 —

A) x

D

x e

(

In the

models current form A

ave and

B

are

small so

D

is

the dominant

parameter

and

was thus

the

parameter used

in the

sensitivity analysis.

e

Log

K

for

exchange

of cation

with H+

on cation

exchange

site.

f

Log

K

for adsorption of

SO

4

2-

and

H

2

SiO

3

.

Total site concentrations

from ELW optimization used here. These parameters cannot be varied independently

for the

soil

and talus

subunit.

g

The partial pressure of

carbon dioxide P

co

, was varied simultaneously

for

both subunits.

h

The

weathering

coefficients

bc

and a

were varied independently

of

each other but uniformly

for

all species

due

to

issues of charge

balance. They contribute to weathering

via the

equation:

Mol

= A

x

[H+r where

Mol

is

moles

added to

the

subunit, A is

total

area

of the surfaces

involved

in

reactions,

[H+]

is hydrogen

ion concentration, and and a are constants. The total surface

area is determined

as the

product

of the

soil depth, area, bulk density,

and

specific

surface

area.

a)

Parameter Space

f

2

b)Criterion

Space

f i L

Parameter

0

1

t3 f i f2

Figure

1

Simple

demonstration

of Pareto set in a

two parameter three criteria

situation.

196

Figure

2

Schematic of

AHM

Model of the Emerald Lake

Watershed. A Represents precipitation and evapotranspiration.

B

represents flow routed from rock subunit onto soil and talus subunits.

C

is surface and subsurface flow to stream from soil and talus.

D is inflow to lake.

E

is lake outflow.

197

0

RUSE

Vet

a

1.4

n

CI- RUSE

.•

Eh

at

'

• •

at

0

RUSE

I

§

§ §

'

I

' ' •

I I

'

I o

1.3

SO

4

2-

RUSE a, at

198

ri t

••

1

,

1 •I

.I.

1.

1.1

0

RUSE

§

n

§

o

SO:

-

RUSE o

01.I

7

;3 s.

M

IN"

VP:

fp

at

• --)

-I pz i-ri

Lf

,

P)rIc -.

.0, Z "Z) CI,

Crq

O do

-I

0)

00000

6•' '6

.

ci)

-

g

I

,,o

= i l

O

RMSE/Mean

Normalized

.

-4 is) ic

range

..)-Ncri

• r) o

AP .0

F .'

7.... 0

5

(.9 R

e•

Po

7j c a E, FI') a r

• tr

,..--- c c.) r--

n.

o)

P "

H

~0 pi)

-• =•• 0

0 ("D

0 h

n.

<

.-t v,

=-•

11,

ro r

) o) i—

CD P.)

..; c o -i•

Pa .r.' co

.-, rl, --, pw .

up (:). . rD ._,P co

-s

9.

= a.

'

P

0

.-i

0- qo

0

Sizoog0

.

• c < ca.,

,-. p.) v) pc,

Fb r

0. -I

(1)

Z z

..1

(0 —

CI)

0

g "°

ril ri) a a

.

4

< -,,,

sto .

'LI

0

• R o

CD

...

< v) Po

0 n

0

--;-• c) 2

0

2 0

II,

II

I z w

2

CD

liii

a)

0 2 0 5 c1/4

TP o o

CD

3 a)

CL a

;

199

rn r

-

Normalized range

00000

iV

111111111

61

200

c

o

o

c7

3

T

T

(.0

h

0

;

a

ri

a

3 cp

cn

cn

RMSE/Mean

Normalized range

00000 in en

42.

201 co

1111[1111

F•

o

CL

CD

• F .;

''Cf

5

O PV,

O CM)

O AD

O 74

CD

3

O AD

`11

CL CrQ

Crg 0

-I z 0

CD

rp 0

A)

n 5

$

.4

Ao

1-0.)

-1

.

A)

6 .

4

'f.

-

;* 0 c

+D

CD

0 F

5 c y

,

O e>

cr

0

6 a

'0)

• 0

>4

7,.

4

0-

0

cn

*I CD

O AD

P

..

• •;'"' co

,

n

RMSE/Mean ry i in - iv

o

c„ i f y

411 nn

C.)

Normalized range

00000

Cob

•-•

1 1 1 1 1 1 1 1

I

1_11111111

o

1‘) Ca

A

202

n

0

RMSE/Mean

0

61 -•

CV

Normalized range

00000 in

•--.1 im

Co — iN)

I 1111 II I

Cn

(D

-1

3

-o

1D

3

CD

(

If

Cp

(i t;

-

03

CL

-i

3

.

a-1

St

4

2

0

z o

cn

Cr

o

I I I

203

n

— n

CD trC)

Sulfate

0 —` IV

()Q

0 0 0 0 0 0 0

_. i i

--,

Chloride

N.) o o

CD CD

CD

ÇA

W

7 o fp

— 7

0

o

ce5 o

5.

CL

.

(")

$1)

CD OsCi

.r1

CfQ

C

o

re_ o n

0

CD t

)

CD ra.,

Cfp p.)

0 CD

C col n

—• •

CD

CL MI

C-

C

204

o

0 0

Nitrate

0

C)

Silica

••Z'

:

:

O

3

205

- i

0 '

71 n

-

crg

0 c n

Sulfate

0

-`

o o cn o cr a)

C-

C s.<

Cc

- o

J

0 o

C_

X

206

Nitrate

N)

0 0

Silica

0

N) -A 0) 0 no

0 0 0 no

ANC

N) 0)

0 0 0

c_ a)

1:3

C-

C

w

ri

o o

207

X

o

C.

-

13)

7

-

0

-a.

APPENDIX

F

SOURCE CODE FOR A NITROGEN MODEL FOR ALPINE

WATERSHEDS (ANIMAL)

208

Program nmodel

This program is a recreation from the published literature of the CENTURY model without the soil temperature model or the hydrology of the CENTURY model. The only portion of CENTURY incorporated into this model is its N dynamics. Some additional improvements will be made to the model once translated into fortran.

1)

2) incorporation of SOil T under snow breaking up landscape subunits to represent variable SCA of basin.

3) driving model input with AHM output

include common sets of parameters.

INCLUDE 'nparams.inc'

INCLUDE 'ndeclare.inc'

INCLUDE 'ncommon.inc'

209

C

---- Read in user defined variables form a file --subroutine reads in constants, initial condition location information and input time series

WRITE (*,*) ' Read in parameters from User defined Files'

CALL READNDAT

Calculate variables that will stay constant for the entire run.

210

WRITE (*,*) ' Caluclate constants dependent on inputs'

CALL CONSTCALC the following subroutine represents the bulk of the model it also further calls several other subroutines.

CALL NCYCLE

STOP

END

SUBROUTINE READNDAT

• This subroutine reads in user defined N parameters from the file uservar

211

include commmon sets of parameters.

INCLUDE 'nparams.inc'

INCLUDE 'ndeclare.inc'

INCLUDE

'ncommon.inc'

INTEGER i

CHARACTER*11 varname

The file name 'constants is for all parameters that should be inputed as user defined constants currently this is commented out as I have hardwired in these constants for now. TM

9/1/98

OPEN(unit=40, file='constants',status='OLD')

READ(40,*) kl,varname

READ(40,*) k2,varname

READ(40,*) k3,varname

READ(40,*) k4,varname

READ(40,*) k5,varname

READ(40,*) k6,varname

READ(40,*) k7,varname

READ(40,*) k8,varname

CLOSE(unit = 40) readin information from file name initial

OPEN(unit=41, file='initial',status='OLD')

READ(41,*) mineraln(1),varname

READ(41,*) c(1,1),varname

READ(41,*) c(2,1),varname

READ(41,*) c(3,1),varname

READ(41,*) c(4,1),varname

READ(41,*) c(5,1),varname

READ(41,*) c(6,1),varname

READ(41,*) c(7,1),varname

READ(41,*) c(8,1),varname

READ(41,*) c2n(1,1),varname

READ(41,*) c2n(2,1),varname

READ(41,*) c2n(3,1),varname

READ(41,*) c2n(4,1),varname

READ(41,*) c2n(5,1),varname

READ(41,*) c2n(6,1),varname

READ(41,*) c2n(7,1),varname

212

READ(41,*) c2n(8,1),varname

READ(41,*) liveroot(1),varname

READ(41,*) liveshoot(1),varname

READ(41,*) rootn(1),varname

READ(41,*) shootn(1),varname

READ(41,*) stddead(1),varname

READ(41,*) stddeadn(1),varname

CLOSE(unit = 41) if

( mineraln(1) .LE.

2.0) c2n(3,1) = -6.0*mineraln(1) + 15 if ( mineraln(1) .LE.

2.0) c2n(7,1) = -4.0*mineraln(1) + 20 if ( mineraln(1) .LE.

2.0) c2n(8,1) = -1.5*mineraln(1) + 10 n(1,1) = c(1,1)/c2n(1,1) n(2,1) = c(2,1)/c2n(2,1) n(3,1) = c(3,1)/c2n(3,1) n(4,1) = c(4,1)/c2n(4,1) n(5,1) = c(5,1)/c2n(5,1) n(6,1) = c(6,1)/c2n(6,1) n(7,1) = c(7,1)/c2n(7,1) n(8,1) = c(8,1)/c2n(8,1)

OPEN(unit=42, file='location',status='OLD')

WRITE(*,*) 'reading in location defined parameters'

READ(42,*) tsi,varname

READ(42,*) thetawilt,varname

213

READ(42,*) thetasat,varname

READ(42,*) depth,varname

READ(42,*) ts,varname

READ(42,*) tc,varname

READ(42,*) appt,varname

READ(42,*) pmax,varname

READ(42,*) totdays,varname

CLOSE (UNIT=42) read inputs

150

WRITE(*,*) 'Reading in time series inputs'

OPEN(unit=43, file='inputs',status='OLD')

DO 150 i = 1,totdays

READ(43,*) temp(i),dep(i),aguaout(i),theta(i)

CONTINUE

CLOSE(unit=43)

C

RETURN

END

214

SUBROUTINE CONSTCALC

This subroutine calculates parameters that depend on user defined inputs. The Parameters are then used for the remainder of the model run.

include commmon sets of parameters.

INCLUDE 'nparams.inc'

INCLUDE 'ndeclare.inc'

INCLUDE 'ncommon.inc' tm is the factor that helps control the decomposition of active SOM text = tsi + tc tm = 1 - 0.75*text ft controls the fraction of active SOM that ends up as CO2 ft = 0.85-0.68*text cap controls fraction of active som that becomes passive som tc is the fraction of the soil that is clay

215

cap = 0.003+0.032*tc csp controls the fraction of slow sent to passive csp = 0.003 - 0.009*tc csa controls amount of slow allocated to active csa = 1 - csp - 0.55

cmax and cmin determine maximum and minimum C:N ratios for biomass cmax = 44 + 0.2*appt cmin = 39 + 0.2*appt root to shoot ratio is determined by using annual precipitation to determine the ratio this equation is based on Parton et al. 1987 pamax = -40 + 7.7 *appt rmax = 100 + 7.0*appt root2shoot = rmax/pamax

216

C

C

C

C

C

1 is lignin fraction of biomass calulated using annual mean precipitation lr is for roots la is for soils

C

C

C

C N lr = 0.26 - 0.0015 * appt la = 0.02 + 0.0012 * appt fixation is also dependant on annual precipitation nfix = -0.18 + 0.014 * appt nfix = 0.0

RETURN

END

217

SUBROUTINE NCYCLE

C

C

C

C

C

C

This subroutine conatins the entire

SOM dynamics and production models.

The equations for this subroutine are culled from PArton et al. 1987 and 1993

INCLUDE 'nparams.inc'

INCLUDE 'ndeclare.inc'

INCLUDE 'ncommon.inc'

C

First I need to declare some local varaibles

INTEGER i,j,k,jj

REAL cal,fn,cas,c2nin(box),thetaabs,mp,production,tp,

& fg,navail,possc2n,nuptake,prod(days),newroot,newshoot,tpl,

& newrootn,newshootn,rd,sd,anfrac,rnfrac,12na,12nr,fma,fmr,

& fsa,fsr,lca,lcr,td,md,a,dec(box),minc(box),inc(box),

& nlossc(box),nin(box),mnrlzdextra(box),minctot(days),origprod,

& minlosston2o(days),minlosston2,minlosttoleach,norig,

& mnrlzdxtra(days),litterfall(days),rootlitter(days),

& litterfalln(days),rootlittern(days),rootlitterc2n(days),

& litterfallc2n(days),td1,abiomass(days),rbiomass(days),track,

& ninputs,noutputs,nstored,nstoredlast,deltas,nbal,deltas2,

& nprod,prelive,predead,livedead,stddeadc2n(days),shootndie(days),

218

& shootdead,liga,noliga,ligr,noligr,availh2o,

& live2dead,sp

DO

500 jj = 1,40

IF ( JJ .GT. 1 ) THEN c(1,1) = c(1,totdays) c(2,1) = c(2,totdays) c(3,1) = c(3,totdays) c(4,1) = c(4,totdays) c(5,1) = c(5,totdays) c(6,1) = c(6,totdays) c(7,1) = c(7,totdays) c(8,1) = c(8,totdays) n(1,1) = n(1,totdays) n(2,1) = n(2,totdays) n(3,1) = n(3,totdays) n(4,1) = n(4,totdays) n(5,1) = n(5,totdays) n(6,1) = n(6,totdays) n(7,1) = n(7,totdays) n(8,1) = n(8,totdays) mineraln(1) = mineraln(totdays) liveroot(1) = liveroot(totdays) liveshoot(1) = liveshoot(totdays) rootn(1) = rootn(totdays)

219

shootn(1) = shootn(totdays) rootc2n(1) = rootc2n(totdays) shootc2n(1) = shootc2n(totdays) stddead(1) = stddead(totdays) stddeadn(1) = stddeadn(totdays) stddeadc2n(1) = stddeadc2n(totdays) c2n(1,1) = c2n(1,totdays) c2n(2,1) = c2n(2,totdays) c2n(3,1) = c2n(3,totdays) c2n(4,1) = c2n(4,totdays) c2n(5,1) = c2n(5,totdays) c2n(6,1) = c2n(6,totdays) c2n(7,1) = c2n(7,totdays) c2n(8,1) = c2n(8,totdays)

ENDIF

Next I need to OPEN and afterwards close several files

OPEN(unit=44, file='carbon',status='UNKNOWN')

OPEN(unit=45, file='nitro',status='UNKNOWN')

OPEN(unit=46, file='biomass',status='UNKNOWN')

OPEN(unit=47, file='c2nratios',status='UNKNOWN')

OPEN(unit=48, file='production',status='UNKNOWN')

220

C

C DO loop covers the rest ot this subroutine

DO 200 i = 2,totdays

C

First calculate the items that are constant for this iteration

C cal is the fraction of active som leached cal = (aguaout(i)*30.0/18.0)*(0.01+0.04*ts)

C

C fn is fraction of mineral n lost to subsurface during a time step fn = (aguaout(i)/18)*(0.2+0.7*ts)

221

C

C cas is the fraction of active som that goes to the slow som compartment

C cas = 1 - cal - cap -ft track = i /1.0

if ( (track/10000) .EQ. (int(track/10000))) WRITE (*,*) track

Calculate new C/N ratios for all compartments

C

C

C

C c2nin(1) = 150.0

c2nin(2) = 150.0

c2nin(5) = c(5,i-1)/n(5,i-1) c2nin(6) = c(6,i-1)/n(6,i-1) c2nin(3) = 3 if ( mineraln(i-1) .LT.

2.0) c2nin(3) = -6.0*mineraln(i-1)+15 c2nin(7) = 12 if ( mineraln(i-1) .LT.

2.0) c2nin(7) = -4.0*mineraln(i-1)+20 c2nin(8) = 7 if ( mineraln(i-1) .LT.

2.0) c2nin(8) = -1.5*mineraln(i-1)+10 c2nin(4) = 10 if ( (anfrac*100) .LT. 2.0) c2nin(4) = -5*(anfrac*100) + 20

---- add in deposition from atmosphere mineraln(i) = mineraln(i-1) + dep(i) write(*,*)i,mineraln(i-1)+dep(i)-mineraln(i)

Temperature requirements for plant production tp = tp1(temp(i))

Water availability limits on plant production

222

C

C changed from CENTURY to use state variable as opposed to CENTURY which uses rain+stored over PET thetaabs = (theta(i)-thetawilt)/(thetasat-thetawilt) mp = (thetaabs) * 1.24 - 0.060

if (thetaabs .GT. 0.85) mp = 1.00

if (mp .LT. 0) mp = 0 write(*,*)i,mp,md

C

C Effects of shading live2dead = liveshoot(i-l)/(stddead(i-1))

IF (live2dead .GT. 2.0) THEN sp = 1.0

ELSEIF (live2dead .LT. 1.0) THEN sp = 0.4*live2dead + 0.3

ELSE sp = 0.3*live2dead + 0.5

ENDIF

C calculate possible production production = pmax * tp * mp * sp

223

C

C write(*,*)i,mp

C

C introduce nutrient limitation fg = 1.0 -(0.8 * (exp(-0.015*liveroot(i-1)*2.2))) fg = fg navail = fg * mineraln(i) nprod = navail nprod = navail + nfix incorporate nutrient limitation on production.

origprod = production norig = nprod ninputs = navail possc2n = production/nprod nuptake = 0

IF (possc2n .GE. cmax) THEN production = cmax*nprod possc2n = cmax

ENDIF

IF (possc2n .LE. cmin) THEN nuptake = production/cmin nprod = nuptake possc2n = cmin

224

C

C

C

ENDIF

IF ( nprod .LT. norig ) THEN

IF( nprod .LT. nfix) THEN navail = 0.0

ENDIF

IF( nprod .GT. nfix) THEN navail = nprod-nfix

ENDIF

IF (nprod .EQ. 0.0) navail = 0.0

ENDIF prod(i) = production mineraln(i) = mineraln(i) - navail write(*,*) i,prod(i),origprod root to shoot ratio for produced biomass is dependent on precipitation as described in Parton et al. 1987 newroot = root2shoot*(production/(root2shoot + 1)) newshoot = production/(root2shoot+1) liveroot(i) = liveroot(i-1) + newroot liveshoot(i) = liveshoot(i-1) + newshoot newrootn = root2shoot*(nprod/(root2shoot + 1)) newshootn = nprod/(root2shoot+1) rootn(i) = newrootn + rootn(i-1) shootn(i) = newshootn + shootn(i-1)

225

C

C rootc2n(i) = liveroot(i)/rootn(i) shootc2n(i) = liveshoot(i)/shootn(i) write(*,*)i,newshoot,production,root2shoot+1,

& production/(root2shoot+1)

C

C

C

On above I currently incorporate tracking for each compartment independent of each other in reality I only need to tack either c2n ratio or n stored

C

C

C Now to incorporate the death model availh2o = (theta(i)-thetawilt)*depth rd = 0.12*(exp(-5.0*availh2o))/30 sd = 0.20*(exp(-5.0*availh2o))/30 rd = 0.04/30.0

C

C sd = 0.06/30.0

write(*,*)i,rd,sd,availh2o,depth,theta(i),thetawilt

C

C litterfall and standing dead biomass prelive = shootn(i) predead = stddeadn(i-1)

IF ( temp(i) .LT. 0 .AND. temp(i-1) .GT. 0) THEN rd = 0.12*(exp(-5.0*availh2o))/30 sd = 0.95

rd = 0.04/30.0

sd = 0.96

rootlitter(i) = liveroot(i)*rd

226

liveroot(i) = liveroot(i) - rootlitter(i) rootlittern(i) = rootn(i)*rd rootn(i) = rootn(i) - rootlittern(i) rootlitterc2n(i) = rootlitter(i)/rootlittern(i) shootdead = liveshoot(i)*sd liveshoot(i) = 1iveshoot(i) - shootdead stddead(i) = shootdead + stddead(i-1) shootndie(i) = shootn(i)*sd shootn(i) = shootn(i) - shootndie(i) shootndie(i) = shootndie(i)*0.96

stddeadn(i) = stddeadn(i-1) + shootndie(i) litterfall litterfall(i) = stddead(i-1)*(0.2/30.0) litterfalln(i) = stddeadn(i-1)*(0.2/30.0) litterfallc2n(i) = litterfall(i)/litterfalln(i) stddead(i) = stddead(i) - litterfall(i) stddeadn(i) = stddeadn(i) - litterfalln(i) write(*,*) i,rootlitter(i),rd,sd,liveroot(i),availh2o

ELSE rootlitter(i) = liveroot(i)*rd liveroot(i) = liveroot(i) - rootlitter(i) rootlittern(i) = rootn(i)*rd rootn(i) = rootn(i) - rootlittern(i) rootlitterc2n(i) = rootlitter(i)/rootlittern(i) shootdead = liveshoot(i)*sd

227

liveshoot(i) = liveshoot(i) - shootdead stddead(i) = shootdead + stddead(i-1) shootndie(i) = shootn(i)*sd stddeadn(i) = stddeadn(i-1) + shootndie(i) shootn(i) = shootn(i) - shootndie(i) litterfall litterfall(i) = stddead(i-1)*(0.2/30.0) litterfalln(i) = stddeadn(i-1)*(0.2/30.0) litterfallc2n(i) = litterfall(i)/litterfalln(i) stddead(i) = stddead(i) - litterfall(i) stddeadn(i) = stddeadn(i) - litterfalln(i) write(*,*) i,rootlitter(i),rd,sd,liveroot(i),availh2o

ENDIF stddeadc2n(i) = stddead(i)/stddeadn(i) write(*,*) i,rootlitter(i),rd,sd,liveroot(i),availh2o,

& newroot nitro is Nitrogen fraction of biomass calculating fraction of n in biomass requires calculating biomass and then n fraction of that biomass for now I will multiply carbon by 2.222 to get biomass of a compartment

228

C

C

C

C

C

C

C abiomass(i) = 2.222 * litterfall(i) rbiomass(i) = 2.222 * rootlitter(i) anfrac is for above ground n fraction rnitorfrac is for below groudn n fraction anfrac = litterfalln(i)/abiomass(i) rnfrac = rootlittern(i)/rbiomass(i)

12n is the ratio of lignin to N find lignin to n ratio for incoming litter of each compartment

229

12na = la/anfrac

12nr = lr/rnfrac fm determines partioning between structural and metabolic litter pools fma = 0.85 - 0.018*12na fmr = 0.85 - 0.018*12nr flip side of above fsa = 1 -fma fsr = 1 -fmr

lc is a further correction factor for structural litter that depends on the lignin content of the particular pool of interest liga = la/fsa ligr = 1r/fsr noliga = 1 - liga noligr = 1 - ligr lca = exp(-3.0*(liga)) lcr = exp(-3.0*(ligr)) write(*,*)i,fsa,liga,fsr,ligr,lca,lcr

Decay amounts for each of the eight compartments td = td1(temp(i)) md = (theta(i)-thetawilt)/(thetasat-thetawilt) write(*,*)i,td,md,td*md a = td * md dec(1) = c(1,i-1)*kl*a*lca dec(2) = c(2,i-1)*k2*a*lcr dec(3) = c(3,i-1)*k3*a*tm dec(4) = c(4,i-1)*k4*a dec(5) = c(5,i-1)*k5*a dec(6) = c(6,i-1)*k6*a

230

dec(7) = c(7,i-1)*k7*a dec(8) = c(8,i-1)*k8*a

C

C

N lost to mineralized pool from compartment due to decay of organic matter

C mineralization

& minc(1) = (dec(1)/c2n(1,i-1))*0.3*liga +

(dec(1)/c2n(1,i-1))*0.6*noliga

& minc(2) = (dec(2)/c2n(2,i-1))*0.3*ligr +

(dec(2)/c2n(2,i-1))*0.55*noligr minc(3) = (dec(3)/c2n(3,i-1)) * ft minc(4) = (dec(4)/c2n(4,i-1)) * 0.6

minc(5) = (dec(5)/c2n(5,i-1)) * 0.6

minc(6) = (dec(6)/c2n(6,i-1)) * 0.55

minc(7) = (dec(7)/c2n(7,i-1)) * 0.55

minc(8)

=

(dec(8)/c2n(8,i-1)) * 0.55

C

C

C

Increases in each carbon compartment due to litterfall and fluxes of C due to movement of C from one box to the next.

inc(1) = fsa * litterfal1(i) inc(2) = fsr * rootlitter(i)

231

inc(3) = dec(2)*noligr*0.45 + dec(6)*0.45 +

& csa*dec(7) + dec(8)*0.45

inc(4) = (dec(1)*no1iga)*0.4 + dec(5)*0.4

inc(5) = fma * litterfall(i) inc(6) = fmr * rootlitter(i) inc(7) = dec(2)*ligr*0.7+dec(1)*liga*0.7+

& dec(4)*0.4+ cas*dec(3) inc(8) = csp*dec(7) + cap*dec(3)

C

C write(*,*)i,cas,cal,cap,ft,cas+cal+cap+ft write(*,990) i,dec(3),inc(3),dec(2)*noligr*0.45,dec(6)*0.45,

C

C990

& csa*dec(7),dec(8)*0.45,c(3,i-1)

FORMAT(I5,6F10.6,F10.2 )

C

C

&

(dec(2)*noligr)*0.45,dec(6)*0.45, csa*dec(7),dec(8)*0.45

C

C

C

C

C dec(1)*liga*0.7,

& dec(4)*0.4,cas*dec(3) n lost from each compartment and put into other compartments

& nlossc(1) = (dec(1)*noliga)*0.4/c2n(1,i-1) + dec(1)*liga*0.7/c2n(1,i-1) nlossc(2) = ((dec(2)*noligr)*0.45)/c2n(2,i-1) +

232

& dec(2)*(ligr)*0.7/c2n(2,i-1) nlossc(3) = cas*dec(3)/c2n(3,i-1) + cap*dec(3)/c2n(3,i-1)

&

+ cal*dec(3)/c2n(3,i-1) nlossc(4) = dec(4)*0.4/c2n(4,i-1) nlossc(5) = dec(5)*0.4/c2n(5,i-1) nlossc(6) = dec(6)*0.45/c2n(6,i-1) nlossc(7) = csa*dec(7)/c2n(7,i-1) + csp*dec(7)/c2n(7,i-1) nlossc(8) = dec(8)*0.45/c2n(8,i-1)

C

C

C n contributed to a compartment from other compartments through transfer of c to the compartment Nitrogen content of N that is transfered is dependent on C:N ratio of compartment

C receiving carbon

C N income into each box

233

nin(1) = fsa*litterfall(i)/150 nin(2) = fsr*root1itter(i)/150 nin(3) = (dec(2)*noligr*0.45)/c2nin(3) +

& dec(6)*0.45/c2nin(3)+csa*dec(7)/c2nin(3)+dec(8)*0.45/c2nin(3) nin(4) = (dec(1)*noliga)*0.4/c2nin(4) +

& dec(5)*0.4/c2nin(4) nin(5) = litterfalln(i) - nin(1) nin(6) = rootlittern(i) - nin(2) nin(7) = dec(2)*ligr*0.7/c2nin(7) +

& dec(1)*liga*0.7/c2nin(7) + dec(4)*0.4/c2nin(7) +

& cas*dec(3)/c2nin(7) nin(8) = csp*dec(7)/c2nin(8) + cap*dec(3)/c2nin(8)

• since nitrogen content of transfer depends on C:N ratio of receiving compartment there is a need to account for the nitrogen that leaves with the carbon from compartment A but does not arrive at compartment B. This section is done by the compartment from which the carbon left

EXTRA

N mineralization mnrlzdextra(1) = nlossc(1)-(dec(1)*noliga)*0.4/c2nin(4)-

& dec(1)*liga*0.7/c2nin(7) mnrlzdextra(2) = nlossc(2)-(dec(2)*noligr*0.45)/c2nin(3)-

& - dec(2)*ligr*0.7/c2nin(7) mnrlzdextra(3) = nlossc(3) - cas*dec(3)/c2nin(7) -

& cap*dec(3)/c2nin(8) - cal*dec(3)/c2n(3,i-1) mnrlzdextra(4) = nlossc(4) - dec(4)*0.4/c2nin(7) mnrlzdextra(5) = nlossc(5) - dec(5)*0.4/c2nin(4) mnrlzdextra(6) = nlossc(6)

- dec(6)*0.45/c2nin(3) mnrlzdextra(7) = nlossc(7)

- csa*dec(7)/c2nin(3) -

& csp*dec(7)/c2nin(8) mnrlzdextra(8) = nlossc(8) - dec(8)*0.45/c2nin(3) mnrlzdxtra(i) = mnrlzdextra(1) + mnrlzdextra(2) + mnrlzdextra(3)

& + mnrlzdextra(4) + mnrlzdextra(5) + mnrlzdextra(6) +

& mnrlzdextra(7) + mnrlzdextra(8)

234

5 % of mineral n is lost to N2 during each time step also a percentage is leached out of the water column defined above by fn which needs to be turned into a function call minlosston2 = mineraln(i)*(0.05/30) mineraln(i) = mineraln(i) - minlosston2 minlosttoleach = mineraln(i)*fn*0.1

minlosttoleach = mineraln(i)*fn

IF ( minlosttoleach .GT. mineraln(i) ) write(*,*)i,mineraln(i), minlosttoleach,fn

235

mineraln(i) = mineraln(i) - minlosttoleach

New n content before additional immobilization of each compartment

0.98 represents fraction that reaches mineral n pool minlosston2o represents the loss of n to the atmosphere during mineralization minctot(i) = 0.0

k= 0

DO 518 k=1,box

518 minctot(i)=minc(k)+minctot(i) mineraln(i) = mineraln(i) + 0.98*mnrlzdxtra(i) +

& minctot(i)*0.98

minlosston2o(i) = mnrlzdxtra(i)*(0.02) + minctot(i)*(0.02)

- New carbon and nitrogen content of each compartment

300

DO 300 j = 1,box c(j,i) = c(j,i-1) - dec(j) + inc(j) n(j,i) = n(j,i-1) - minc(j) -nlossc(j) + nin(j) c2n(j,i) = c(j,i)/n(j,i)

CONTINUE j = 0

Error checking write line ninputs = 0.0

ninputs = production noutputs = 0.0

noutputs = litterfall(i) + rootlitter(i) nstoredlast = nstored nstored = 0.0

nstored = stddead(i) + liveroot(i) + liveshoot(i) deltas = 0.0

deltas2 = 0.0

DO 402 j = 1,box noutputs = dec(j) - inc(j) + noutputs nstored = c(j,i) + nstored nstoredlast = c(j,i-1)

236

C 990

C 402 write(*,990) i,j,ninputs,noutputs,deltas,deltas2,nbal

FORMAT(I5, 5F10.6 )

CONTINUE

C990 deltas = nstored-nstoredlast deltas2 = ninputs-noutputs nbal = deltas2-deltas write(*,990) i,ninputs,noutputs,deltas,deltas2,nbal

FORMAT(I5, 5F10.2 )

IF ( ninputs .LT. noutputs) write(*,*) minlosston2o(i),minlosston2,minlosttoleach,

(cal*(dec(3)/c2n(3,i-1))),mineraln(i)

402 CONTINUE

980

WRITE(44,980) i,c(1,i),c(2,i),c(3,i),c(4,i),c(5,i),c(6,i),

& c(7,i),c(8,i)

FORMAT(I5, 8F8.1 )

WRITE(45,981) i,n(1,i),n(2,i),n(3,i),n(4,1),n(5,i),n(6,i),

&

981 n(7,i),n(8,i),mineraln(i),mnrlzdxtra(i)+minctot(i)

FOR11AT(I5, 10F8.2 )

WRITE(46,982) i,liveroot(i),liveshoot(i),rootn(i),shootn(i), rootc2n(i),shootc2n(i),stddead(i),stddeadn(i),stddeadc2n(i)

982

FORMAT(I5, 9F8.1)

WRITE(47,983) i,c2n(1,i),c2n(2,i),c2n(3,i),c2n(4,i),c2n(5,i),

237

983

984 c2n(6,i),c2n(7,i),c2n(8,i)

FORMAT(I5, 8F8.2 )

WRITE(48,984) i,prod(i),newroot,newshoot,nprod

FORMAT(I5, 4F10.5 )

200

500

CONTINUE

CLOSE(unit=44)

CLOSE(unit=45)

CLOSE(unit=46)

CLOSE(unit=47)

CLOSE(unit=48)

CONTINUE

RETURN

END

238

239

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