User manual | AN ASSESSMENT OF SNOWPACK DEPLETION-SURFACE RUNOFF RELATIONSHIPS ON FORESTED WATERSHEDS

AN ASSESSMENT OF SNOWPACK DEPLETION-SURFACE RUNOFF
RELATIONSHIPS ON FORESTED WATERSHEDS
by
Rhey Maurice Solomon
A Thesis Submitted to the Faculty of the
DEPARTMENT OF WATERSHED MANAGEMENT
In Partial Fulfillment of the Requirements
For the Degree of
MASTER OF SCIENCE
In the Graduate College
THE UNIVERSITY OF ARIZONA
197k
STATEMENT BY AUTHOR
This thesis 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 thesis are allowable without special
permission, provided that accurate acknowledgment of source 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 judgment the proposed use of the material is in the interests of scholarship. In all other instances, however, permission must be obtained
from the author.
SIGNED:
/?
1
oy„
APPROVAL BY THESIS DIRECTOR
This thesis has been approved on the date shown below:
PET F. FFOLLIOTT
Associate Professor of
Watershed Management
7
øi2i (9T
DATE
ACKNOWLEDGMENTS
I wish to especially thank Dr. Peter F. Ffolliott for his
assistance in initiating this project and for his guidance and
suggestions in the preparation of this thesis.
Thanks are also due the USDA Forest Service for providing the
study areas. And special thanks are extended to Dr, Malchus Baker and
J. R. Thompson of the Rocky Mountain Forest and Range Experiment
Station for their help in the gathering and processing of data.
Gratitude is also extended to Dr. William Rasmussen and Robert
Beschta for their hours of consultations and suggestions. Appreciation
is also extended to Dr. David B. Thorud and Dr. Elisabeth A. Stull for
their critical review of this thesis.
This study was supported by funds provided by the U. S.
Department of Interior as authorized under the Water Resources Research
Act of 1964, PL 88-397.
TABLE OF CONTENTS
Page
LIST OF TABLES.
.........
.......
. • •
LIST OF ILLUSTRATIONS vi
vii
ABSTRACT viii
INTRODUCTION ................ ,
,
•
,
DESCRIPTION OF STUDY 1
7
Specific Objectives Study Area Beaver Creek Watersheds Heber Watersheds Thomas Creek Cambell Blue Field Procedures Sample Design Snowpack Water-Equivalent and Runoff Climatic Measurements Transmissivity Measurements Measurement and Sampling Errors ..... • Analytic Procedures
.e
.........
.....
Snowmelt Simulation
•
Estimation of Precipitation Type Energy Budget Determination Snowpack Conditions ........
•
Daily Runoff Calculations
Runoff Efficiency Calculations • • • a • .a .
Transmissivity Calculations ......
.....
RESULTS AND DISCUSSION 7
7
9
12
16
18
la
19
20
22
22
25
25
27
29
34
36
39
41
43
Estimating Daily Runoff Efficiency. ........ e .e .
Assessing Transmissivity and Cover Density,
Variablity of Program ARZMELT .
o.. ..
Changing Patterns of Efficiency Within a Season Factors Affecting Runoff Efficiencies Differences Among Watersheds Within a Season .
iv
43
44
52
54
62
62
TABLE OF CONTENTS--Continued
Page
Differences Within a Watershed Among Yoars. • .
Important Variables Among Years and Among
Watersheds
Prediction of Yearly Runoff Efficiencies .....
, .
63
, 65
67
73
CONCLUSIONS
APPENDIX A. METRIC CONVERSION TABLE
75
APPENDIX B. PROGRAM ARZMELT DERIVED FROM U. S. FOREST
SERVICE PROGRAM MELTMOD
APPENDIX C. FLOW CHART FOR SUBROUTINE SOLAR
76
98
100
APPENDIX D. FLOW CHART FOR SUBROUTINE DIFMOD APPENDIX E. STANDARDIZING EQUATIONS FOR SOLAR SENSORS
USED IN THE FOREST TRANSMISSIVITY STUDY
102
APPENDIX F. CORRELATION MATRIX OF REGRESSION VARIABLES 103
LITERATURE CITED 105
LIST OF TABLES
Table
Page
1, Number of Points and Sampling Intensities on
All Watersheds for Years of Record Used in
the Study
21
2, Values of Transmissivity, Cover Density, and
Other Watershed Characteristics Determined
From Field Measurements and Program ARZMELT
48
3, Correlation Coefficients for Daily Runoff
Efficiency With Daily Runoff, Daily Melt, and Daily Temperature
4. A Composite of Values for All Variables
Inventoried Over All Watersheds
5. Listing of Variables Appearing in Step-Wise
Regression Technique for Variable
Identification Purposes
61
64
68
6, Regression Equations and Their Step-Wise
Development
vi
70
LIST OF ILLUSTRATIONS
Figure
Page
1. The Location of Project Watersheds Within the
State of Arizona 8
2. Location and Shape of Watersheds 15 and 17 on
the Beaver Creek Pilot Watershed.
. •
.......
10
3. A Schematic of the Heber Watersheds
.......
13
......
28
4. General Flow Chart for Program ARZMELT. • ,
5
,
6.
7.
Graphical Integration Technique Used on All
Watersheds Except Thomas Creek 37
Integration Technique Used to Separate Daily Flows
on Thomas Creek 38
Field Measurements of Basal Area Plotted Against
. . .
Measured Transmissivity
.........
46
8. Plots of Transmissivity Against Cover Density
and Transmissivity Against Basal Area 30
9. Three Years of Snowmelt Synthesized From Program
ARZMELT .
10.
......o . . .e .......... e
Normalized Yearly Fluctuations in Snowpack
Ablation-Surface Runoff 55
11, A Plot of the Changing Slope Pattern of a
"Characteristic" Normalized Snowpack AblationSurface Runoff Curve 12, Daily Runoff Efficiencies, Generated Daily Melt,
and Daily Runoff for Watershed 17 in 1969 ,
vii
53
57
.....
60
ABSTRACT
A technique was developed for determining daily values of
runoff efficiencies from small watersheds by coupling a computer model
that simulated Arizona snowmelt processes with graphical techniques of
runoff hydrograph separation. The computer program was a USDA
Forest Service model modified to better simulate Arizona conditions,
A complete explanation of modifications and limitations of the model is
given, along with equations for estimating some of the model input
variables,
Seven small watersheds with a total of 14 years of record were
used in evaluating changing patterns of runoff efficiencies within a
year . Additionally, many physical, biological, and climatic variables
were correlated with seasonal runoff efficiencies not only among years
and among watersheds, but also within a watershed among years, and
among watersheds within a season, Prediction equations were also
formulated that could be of use in the identification of high water
yielding watersheds,
viii
INTRODUCTION
Water is a scarce resource in Arizona, as it is in most semiarid
regions. Therefore, interest in water supply and water allocation
within the State is intense, and much progress has been made in the development of management techniques for increasing this scarce resource
(Worely 1965, Thorud and Ffolliott 1972, Ffolliott and Thorud 1974).
However, the basic problem of water supply within a growing economy
still exists.
Snowmelt is a major source of runoff contribution to the reservoir system in central Arizona. It has been estimated that in excess
of 68 percent of the runoff to the reservoir system may originate as
snowmelt during the spring runoff period (Warskow 1971). As snow contributes such a large proportion of the surface water supplies in the
State, it is subject to investigation and management.
Snow research efforts have been conducted to more fully understand the processes involved in snow accumulation, melt, and its
resultant runoff (Ffolliott and Hansen 1968, Garn 1969, Ffolliott and
Thorud 1972a). However, previous research efforts have been primarily
concerned with the synthesis of inventory-prediction relationships for
predicting snowpack water-equivalent (i.e., the linear measure of
liquid water contained in a snowpack and potentially yielded by the
snowpack when it melts) on-site, or changes in on-site snowpack waterequivalent resulting from the implementation of a land management
system (Thorud and Ffolliott 1972). It is therefore important that a
1
2
greater understanding of snowpack depletion-surface runoff be obtained
and coupled with previous research to prescribe land management systems
that will maximize opportunities for effective and efficient water
yield improvement practices.
Recognition of management practices for increasing water
yield through vegetation management (Barr 1956) inspired an increase in
water yield research in Arizona, The inception of the Beaver Creek
Pilot Watershed Program was one of the first steps in establishing a
direction for initial water yield research in Arizona (Brown 1971).
Interest in water yield improvement from snowpacks subsequently became
an area of investigation for the Department of Watershed Management at
The University of Arizona, Initial research at the University consisted of a physiographic, climatic, and vegetative survey of the
State, enabling the identification of snow research study areas, Three
areas of investigation were identified: (1) reduction of forest densities, (2) reduction of forest overstories, and (3) physiographic and
climatic factors affecting snowmelt runoff. Studies investigating reduction of forest densities (Ffolliott 1970, Ffolliott and Thorud
1972a) and reduction of forest overstories (Ffolliott and Thorud 1972b,
Gopen 1974) have been completed. The third area of investigation
(physiographic and climatic factors affecting snow accumulation and
snowmelt runoff) has been the focus of continuing investigation.
Conceptually, snowpack water yield is dependant on two factors:
(1) the snowpack accumulation on-site, and (2) the inherent runoff
efficiency, which defines the portion of the snowpack that is converted into recoverable water, Continuing research efforts have been
3
primarily directed towards the understanding of the first factor, However, to prescribe and implement management systems as water yield
improvement practices, it is essential that research efforts furnish
knowledge on the second factor. Such knowledge may allow for the identification of comparative hydrologic potentials (Anderson 1967), and
assure implementation of land management systems not only for greater
water yield, but also for greater efficiencies. It was therefore the
aim of this study to investigate this area of water yield efficiencies
from snowpacks.
The concept of relating snowmelt to its subsequent water yield
is not a new subject of investigation, having been explored extensively
(U. S. Army Corps of Engineers 1956, Garstka, Love, Goodell and Bertle
1958, Leaf 1971), but the snowmelt process has been separated and analyzed apart from the runoff process in most research. Although each
process has been explained and examined in depth, the relationships between snowmelt and runoff have not been fully explored.
Snowmelt is a dynamic process involving many different systems
of energy transfer, and as such, must be assessed with changes in time.
As a consequence, the rigorous determination of snowmelt is complex
and involves the identification of many variables which themselves are
continually changing. Primary energy variables important in snowmelt
include, but are not inclusive of, the following,
1. Absorbed shortwave radiation. Shortwave radiation incident
upon the forest canopy can be affected by percent transmittance
of insolation through the forest overstory, albedo of the snowpack, snowpack density and depth, slope, and aspect.
4
2. Longwave radiation. The snowpack can both emit and absorb
longwave radiation, the relative amounts being dependant on
snowpack temperature, atmosphere temperature, soil temperature,
vegetative temperature, cloud cover, and atmospheric moisture.
3, Convective heat transfer from the air, Unlike radiative heat
transfer, convective transfer is not easily measured, but can
be estimated indirectly. Principal variables affecting convective heat exchange are the temperature gradient of the
atmosphere above the snow surface, the corresponding wind
speed, and atmospheric density.
4. Latent heat of vaporization. Energy released from condensation
is called heat of vaporization (evaporation being the negative
of condensation) and is affected by the vapor pressure of the
atmosphere and snow surface, and wind speed.
5, Conduction of heat from underlying ground. This flux is
usually upward to the snowpack and is controlled by the thermal
conductivity of the snow and soil, the temperature gradient
between the snow and soil, and the air interface between the
snow and soil.
6. Heat content of rain water. The amount of energy given up to
the snowpack by rainwater is directly proportional to the temperature and quantity of rainwater. If the rainwater freezes,
an additional 80 calories per gram (latent heat of fusion) is
also released to the snowpack.
5
From the above list of energy sources, one can appreciate the
difficulty in attempting to quantify and account for all the interactions
occuring between and among the variables. Therefore, in attempting to
quantify a day's snowmelt, only components easily measured or indexed
can be used with a degree of confidence.
By using shortwave radiation and temperature as the only indexes
of energy inputs, a simplified model can be constructed, but even though
the model may be economical and easily used, it must be realized that
inadequacies may be present (U. S. Army Corps of Engineers 1960, Leaf
and Brink 1973).
Once melt has been generated, a determination of the amount of
runoff yielded by the melting snow is required. Methods of segregating
a given day's snowmelt contributing to runoff were recognized long ago,
since without such segregation, correlation of snowmelt runoff with
snow pack ablation was practically unattainable. Surface water flow gen-
erated from a watershed can be classified into the following three
categories.
1, Overland runoff. That portion of runoff that flows through the
snowpack or over the ground surface and into the drainage
channels.
2. Subsurface runoff. That portion of the snowmelt that infiltrates
into the soil and moves laterally through the upper soil layers
until it enters a stream channel.
3. Groundwater flow. That portion of the snowmelt that infiltrates
.
into the soil and becomes part of the groundwater, eventually
discharging into the stream as groundwater flow (base flow).
6
Relationships between snowmelt and runoff are subject to constant change, depending on the effects of controlling variables. Some
important factors affecting snowpack depletion-surface runoff relationships are as follows,
1, Soil Moisture, Moisture content of the soil prior to the runoff season will affect the proportion of snowmelt retained by
the soil and the residual snowmelt resulting in runoff.
2, Vegetation overstory, Every tree species is unique in its
plant-water relations, having different rates of transpiration,
rooting depth, and foliage surface areas.
3, Soils, All soils are unique in their water holding capacities,
infiltration rates, and water conductivities.
4. Topography. Slope, aspect, and elevation all contribute to
alterations of melt rates and timing of runoff.
5, Climate. Precipitation inputs and temperature fluctuations
have marked influences on the quantity and timing of snowmelt
and runoff.
With the basic techniques and variables outlined above, it was
anticipated that relationships between changes in snowpack volume and
generated runoff could be analyzed along with the effects, if any, of
physical, climatic, and biological characteristics on water yielding
properties of watersheds. Furthermore, runoff efficiencies, defined as
that portion of the snowpack that is converted into recoverable water
during some arbitrary time period, could be used as a descriptor of
snowpack depletion-surface runoff relationships.
DESCRIPTION OF STUDY
Emsific Ob ectives
The principal objective of this study was to continue the
hydrologic knowledge necessary for the understanding and prediction
of runoff efficiencies from watersheds contributing snowmelt to the
reservoir systems. This primary objective was further divided into
four divisions of investigation,
1. Establish a technique for estimating daily runoff efficiencies.
2. Characterize patterns of changing efficiencies within a snowmelt-runoff season,
3, Identify factors affecting runoff efficiencies both within a
season and between season.
4. Predict runoff efficiencies from year-to-year,
EIaalista
The study area consisted of seven small watersheds stretching
across central Arizona and one solar transmissivity study site
(Figure 1). The large distance between watersheds was necessary in
obtaining an array of varying physical and biological characteristics.
The watersheds graduate from 20 to 444 acres, with elevations from 6735
feet to 9150 feet above sea level. Since there are elevational differences among watersheds, vegetation overstories range from
predominantly ponderosa pine (Pinus ponderosa Laws.) to predominantly
Douglas-fir (Pseudotsuga menziesii (Mirb,) Franco) and white fir
7
8
Flagstaff 0
Beaver Creek Watersheds
Heber Watersheds
Springervi I le
0
Cambel I Blue A
Thomas Creek 0
Phoenix 0
amemiammnseann•nnn•
Figure 1. The Location of Project Watersheds Within the State of
Arizona,
9
(Abbe concolor (Cord. and Glen.) Hoopes), Soils encompass basalt,
sandstone, and alluvial parent materials, The watersheds will be
described separately, because each is unique,
Beaver Creek Watersheds
Two watersheds, 15 and 17 (Figure 2) were selected from the
Beaver Creek Pilot Watershed (Worley 1965), These watersheds are within
two miles from one another and can be considered within the same general
climatic zone, having an annual precipitation averaging 25 inches, half
of which comes during the period November through April. An outline of
characteristics for Watersheds 15 and 17 follows,
1. Watershed 15,
Location and size: a 159 acre watershed located approximately
20 miles south of Flagstaff, Arizona, and two miles east of
Schnebly Hill turnoff on Interstate 17,
Vegetation: overstory is predominantly ponderosa pine and
Gambol oak (uercus gambelii Nutt.) with an intermixing of
alligator juniper
(22Eimals
Deppeana Steud,). This watershed
is stocked to an average basal area of
96 square feet per acre
with ponderosa pine and Gambel oak accounting for
59 and 30
square feet per acre, respectively (Ffolliott 1966), The watershed is uneven-aged and varies from natural openings to "dog
hair thickets".
Physiography:
Slope and aspect--average slope is 15 percent directed
towards the south and southwest, Steeper slopes up to 50
10
TO
FLAGSTAFF
FLUME
TO
PHOENIX
PAVED ROAD
- DIRT ROAD
STREAM CHANNEL
0
II
I
MILES
2
J
Figure 2, Location and Shape of Watersheds 15 and 17 on the Beaver
Creek Pilot Watershed,
1 1
percent face to the east and north.
Drainage--major channels drain to the southeast, the main
channel separating into two channels about one-third of the
way up the watershed
Elevation--6735 feet to 7160 feet.
Soils: Brolliar soil series weathered from basalt parent
material. These Brolliar soils have "moderate" to "rapid"
infiltration rates and a "wide" range of water-storage capacities
(Williams and Anderson 1967).
Unusual characteristics: a dirt access road separating the
steep northeast slopes from the moderate southwest slopes, runs
the length of the watershed paralleling the main drainage.
Also a geological fault exists beneath the surface soils.
2. Wateshed 17.
Location and size: a 283 acre watershed located approximately
20 miles south of Flagstaff, Arizona, and four miles east of
the Schnebly Hill turnoff on Interstate 17.
Vegetation: Watershed 17 was logged in 1970, but the year of
record (1969) was prior to harvesting; therefore, the vegetation
description is applicable to pretreatment conditions. Ponderosa pine comprises almost 90 percent of the overstory with
Gambel oak and alligator juniper intermixed. Ponderosa pine
accounts for 88 percent of an average basal area of 120 square
feet per acre for all overstory species, while Gambel oak and
alligator juniper accounts for only 11 and one percent,
12
respectively. The watershed is uneven aged with some trees
exceeding 30 inches in diameter.
Physiography:
Slope and aspect--average slope is less than 10 percent
with over 90 percent of the watershed having less than 20
percent slopes. Predominant orientation of the slopes is
south to southwest.
Drainage--the principal drainage is towards the southwest.
From the flum, the main channel runs back up the watershed
in an easterly direction approximately 16 chains, where the
main channel traverses in a northeast direction (Figure 2).
Elevation--6830 feet to 7200 feet.
Soils: primarily of the Brolliar soil series.
Unusual charcteristics: several roads traverse across or onto
the watershed, but none appear to affect drainage patterns.
Heber Watersheds
Four of the study watersheds are located at what is known
as
the "Heber study area" on the Apache-Sitgreaves National Forest
(Figure 3). These four watersheds are the smallest of the series,
ranging from 20 acres to 61.3 acres. Annual precipitation is less than
that for the Beaver Creek Watersheds, averaging about 22 inches, but
seasonal precipitation patterns are the same. An outline of characteristics for the Heber Watersheds follows.
1. Watershed HE-1.
Location and size: a 20 acre watershed located about 13 miles
13
A
APPROXIMATE SCALE
1:62500
FLUME
C::3
I
1
WATERSHED
PRINCIPAL ROAD
— STREAM CHANNEL
Figure 3. A Schematic of the Heber Watersheds.
14
southeast of Heber, Arizona, just off the Rim Road (Figure 3).
Vegetation: predominantly ponderosa pine with an intermixing
of Gambol oak, white fir, and Douglas-fir. This watershed is
stocked to an average basal area of 77 square feet per acre
of which ponderosa pine accounts for almost 90 percent. Tree
diameters range from under two to 28 inches (Department of
Watershed Management 1974).
Physiography:
Slope and aspect--steep southwest and east facing slopes
define the major stream channel. Slopes near the stream
channel average 40 percent, gradually decreasing to five
percent towards the watershed boundaries.
Drainage--one well defined channel drains the length of
the watershed from north to south.
Elevation--7400 feet to 7700 feet.
Soils: dived from alluvial parent materials.
Unusual characteristics: north and west boundaries are defined
by dirt roads.
2. Watershed HE-2.
Location and size: a 28.1 acre watershed approximately onequarter of a mile east of Watershed HE-I.
Vegetation: predominantly ponderosa pine with an intermixing
of Gambel oak, alligator juniper, white fir, and Douglas-fir.
Ponderosa pine accounts for over 90 percent of a total basal
area of 7 1. square feet per acre. Distribution of size classes
is similar to Watershed HE-1.
15
Physiography:
Slope and aspect--steep slopes of 30 to 40 percent near the
stream channel decreasing to five percent near the watershed
boundaries. Watershed HE-1 and HE-2 are similar in slope
and aspect characteristics.
Drainage--one well defined channel traverses the watershed
flowing from north to south.
Elevation--7400 feet to 7700 feet.
Soils: derived from alluvial parent materials.
Unusual characteristics: a road crosses the upper most section
of the watershed, but drainage pipes allow water to flow under
the road and into the stream channel.
3. Watershed HE-3.
Location and size: a 60,3 acre watershed located about six
miles south of Heber, Arizona (Figure 3).
Vegetation: principal species include ponderosa pine and Gambol
oak with an intermixing of alligator juniper. Of an average
basal area of 67 square feet per acre, ponderosa pine accounts
for over 85 percent. Tree diameters range from two inches to
36 inches.
Physiography:
Slope and aspect--average slope is about 10 percent with
relatively few slopes over 15 percent. Principal direction is north to northwest.
Drainage--two major tributaries join together about 100
yards upstream from the flume. Both channels flow in a
general south to north direction,
Elevation--6900 feet to 7050 feet,
Soils: derived from sandstone parent materials.
4, Watershed HE-4.
Location and size: a 61.3 acre watershed located about onequarter of a mile south of Watershed 11 E-3 (Figure 3).
Vegetation: predominantly ponderosa pine with an intermixing
of Gambol oak and alligator juniper, Ponderosa pine comprises
over 85 percent of the overstory, Average basal area of overstory species is about 64 square feet per acre. Size class
distribution are the same as Watershed HE-3,
Physiography:
Slope and aspect--over 80 percent of the slopes are 1_0
percent or less with maximum slopes approaching 25 percent,
Major aspects are south to southeast and east to northeast.
Drainage--three tributaries, draining the upper two-thirds
of the watershed, join about 12 chains from the flume thereby
forming a single well defined channel that flows from southwest to northeast.
Elevation--6900 feet to 7050 feet.
Soils: derived from sandstone parent materials.
Thomas Creek
The largest of the seven watersheds, the North Fork of Thomas
Creek provided an opportunity to study runoff efficiencies in the mixed
conifer forest zone. Annual precipitation for this area is greater
17
than the other areas, averaging approximately 27 inches, The winter
precipitation (November through April) accounts for about one-third
of the annual precipitation, An outline of the North Fork of
Thomas
Creek characteristics follows,
Location and size: a 444 acre watershed located approximately
20 miles south of Alpine, Arizona, and three miles west of
Route 666 on the Apache-Sitgreaves National Forest,
Vegetation: divided into a north-facing mixed conifer stand
and a south-facing ponderosa pine stand, The mixed conifer
stand is comprised of Douglas-fir, white fir, Engelmann
spruce (Picea engelmannii Parry), qunking aspen (populus
tremuloides Michx.), corkbark fir (Abies arizonica Merriam),
and ponderosa pine, while the ponderosa pine stand is predominantly ponderosa pine and Douglas-fir with an intermixing
of Gambol oak, quaking aspen, and corkbark fir, Average basal
area values for the north-facing and south-facing slopes are
189 and 157 square feet per acre respectively. On the north-
facing slope, Douglas-fir and white fir comprise most of the
larger size classes while white fir and Engelmann spruce are
abundant species in the smaller size classes. On the southfacing slope, 63 percent of the timber volume is ponderosa
pine and 18 percent is Douglas-fir; ponderosa pine dominates
the larger size classes while Douglas-fir dominates the
smaller classes.
18
Physiography:
Slope and aspect—approximately 51 percent of the watershed
contains slopes of or above 40 percent. The principal
aspects are northwest and southeast for the north-facing
and south-facing slopes, respectively.
Drainage--one principal channel traverses down the watershed
from the southwest to northeast.
Elevation--8400 feet to 9150 feet.
Soils: derived from basalt parent material,
Cambell Blue Study Area
The Cambell Blue area is located seven miles south of Alpine,
Arizona, on the Apache-Sitgreaves National Forest. A predominantly
ponderosa pine forest, the Cambell Blue site was utilized for previous
studies (Ffolliott 1970, Tennyson 1973, Jones 1974) and supplies a
diversification of forest cover densities ranging from open parks to
dense stands. With a mean elevation of 8010 feet, this gently rolling
study area contains few slopes in excess of 15 percent, providing a
suitable site for solar radiation transmissivity studies,
Field Procedures
Throughout this thesis all units will be expressed in the
English, American engineering * or metric systems. Conversion of all
units to the metric system can be found in Appendix A.
Runoff efficiency is an index of phenomena interactions controlling snowmelt dynamics and runoff, To describe or model these
be
interactions, some "basic" physical and biological attributes must
:19
inventoried. If an energy budget model is to be employed
in synthesizing a day's snowmelt, the minimum input variables
might consist of
some index of solar radiation and daily temperature regimes, with these
inputs a simplified model could be constructed.
The continuity equation dictates that all inputs and outputs
of a system must be known if conclusions are to by hypothesized regarding the mass balance of the system. In the system of interest,
the snowpack can be viewed as a storage tank, precipitation as the
input, and runoff as the output; losses to evapotranspiration, soilmoisture recharge, or other outputs other than surface runoff are viewed
as a second path of output. Therefore, precipitation and runoff must
be measured continually, while measurements of snowpack water-equivalent
can be recorded periodically in establishing the level of storage
within the system. Losses need not be quantified as this output is
indexed through expressions of runoff efficiency.
Sample Design
To facilitate snowpack water-equivalent measurements, transect
lines running perpendicular to the main stream channel were established
on all seven watersheds. Each transect traversed a path of maximum
diversity in vegetation and topography with enough sample points to
give an adequate distribution over the entire watershed (Leaf and
Kovner 1972). Systematic sampling with multiple random starts (Shiue
1960), typified the sample design of Beaver Creek Watersheds 15, and 17,
and the North Fork of Thomas Creek. The Heber Watersheds were sampled
with a systematic sample design (Cochran 1963, PP. 206-235). Different
20
sample sizes were used because of the variability of watershed
acreages.
The number of sample points and sampling intensity on each
watershed for those years of record are displayed in Table 1.
Snowpack Water-Equivalent and Runoff
Snowpack water-equivalent measurements were taken with a Federal
• sampler (Chow 1964, sect. 10) at arbitrarily defined time intervals
throughout the accumulation and melt periods. Not every watershed was
sampled on the same dates within a snowmelt season, but rather sampled when personnel and equipment were in proximity to the watersheds.
One "core" sample was extracted at each sample point on a watershed,
and a mean water-equivalent was used to indicate the average snowpack
water-equivalent for each measurement date.
Since the watersheds consisted of different acreages, three
stream flow recording devices were used, depending on the runoff
regimes of each watershed. The Beaver Creek Watersheds were instrumented with trapezodal flumes constructed of concrete with 30 degree
sidewalls and a floor one foot wide at the control section (Price
1967). The Heber Watersheds were instrumented with three-feet Hflumes (Holtran, Minshall, and Harrold 1962). These H-flumes are
designed for flows from 0.30 to 30 cubic feet per second, which
suited the small watersheds at Heber. The gauging station at the
North Fork of Thomas Creek, a 120 degree V-notch weir (Holtran et al.
1962), is an installation that enables large and small flows to be
recorded accurately.
21
Table 1, Number of Points and Sampling Intensities on All Watersheds
for Years of Record Used in the Study,
n•n•••••n••sawympra•
Watershed
Years
No, of Points
Area
(acres)
Intensity
(acres/point)
Watershed 15
196801969,197 0
86
159
1.85
Watershed 15
1973
62
159
2.56
Watershed 15
1974
74
159
2.15
Watershed 17
1969
93
283
3.04
Watershed HE-1
1974
30
20,0
0,67
Watershed NE-2
1973,1974
30
28,1
0.94
Watershed HE-3
1973,1974
30
6 0 .5
2,02
Watershed HE 4
1974
30
61.3
2.04
Thomas Creek
1973
60
WO
7.40
Thomas Creek
1974
93
444
4.77
-
,
22
Climatic Measurements
Employing hygrothermographs, maximum and minimum tempertures
were charted within one mile from each watershed. Where on-site
records were missing, extrapolation from nearby weather stations was
employed (Camber_ 1972).
Precipitation measurements were recorded with two gauges at
each watershed, one shielded and one unshielded. The shielded gauges
were used as "primary" gauges and the unshielded gauges as back-up
units. The shielded gauges were the dual-traverse continual recording type, while the unshielded gauges were standard eight-inch
cans (Fisher and Hardy 1972, pp. 22-29).
Solar radiation measurements were only sensored at the Beaver
Creek Watersheds (1974) and the North Fork of Thomas Creek (1973 and
1974), the installations being located at Schnebly Hill highway camp
(Figure 2) and Alpine, Arizona, respectively. In lieu of solar radiation data at Heber and past years at Beaver Creek, cloud cover data
was extrapolated from the nearest weather station possessing such
information.
Transmissivity Measurements
If solar radiation measurements are to be used as an energy
source for a simplified model, some relationship between percent
transmittance (that portion of insolation incident upon the forest
canopy that is transmitted through the overstory to the snowpack)
and some forest attribute must be identified. To this end, a secondary study was initiated at the Cambell Blue study area.
23
The sample design consisted of three clusters containing five
sample points per cluster forming a one-fifth acre plot. Each cluster
was designed in the shape of a diamond, with one point at the four
corners of the diamond and the fifth point in the center 50 feet from
each corner point. Each point in a cluster constituted a different
forest condition, enabling each point to be treated as a discreet
sampling point, This produced a total of 15 different forest conditions in the sample.
Six solar pyranometers were used in the study. As only five
sensors could be employed to sample transmissivity (the sixth sensor,
located in Alpine, Arizona atop a mobile home, served as a control),
only one cluster could be sampled per day. Every day the sensors
were assigned to each point randomly, enabling rotation of sensors.
Before sunrise of a sampling day, the sensors were mounted
and leveled atop three foot wood stands located at each sampling
point, then connected to digital integrators (Thompson and Ozment
1.972) and hourly readings taken from sunrise to sunset. Only sunrise and sunset readings were recorded on days with extensive cloud
cover. A total of 16 days of data were collected during two periods
of measurement, one in March and the second in June.
Forest overstory characteristics influence the amount of
insolation transmitted through the overstory. Therefore, a measure
of forest attributes at each point might be used to index the amount
of radiation incident upon the snowpack. Basal area and stem measurements were inventoried at each sample point employing point-sampling
techniques (Avery 1967, pp. 165-182). Canopy photographs were also
taken at each point (Brown 1962).
Measurement and Sampling Errors
Establishing confidence intervals for the various field
measurements is at best difficult, but these sources of error should
be recognized and stated. There are principally two sources of error
in this study: (1) sampling errors and (2) measurement errors. One
source of error can be as substantial as the other, depending on the
type of measurement taken.
Sampling errors, resulting from an inadequate sample in
estimating a parameter of a population, can be substantial when
estimating precipitation inputs and snowpack water-equivalent. Leaf
and Kovner (1972) advanced the theory that sampling errors of snowpack water-equivalent can be minimized when samples are taken along
an established line traversing the watershed, a criterion that the
sample design on the study watersheds meet. A criterion for snowpack water-equivalent sampling intensities is more difficult since
sampling intensity is a function of watershed characteristics.
That is to say, for the same sampling precision on two watersheds,
the intensity of sampling may be different. Precipitation sampling
is another widely discussed subject. A suggestion by Holtran et al.
(1962) of a sampling intensity of approximately one gauge per 100
acre is strictly a rule of thumb, but most of the watersheds in the
study were sampled to this intensity. By no means should it be
25
assumed that, because sampling intensities meet some minimum criterion,
that sampling errors are not substantial.
Measurement errors are a problem with any sensing, recording,
or measuring instrument, These errors, the result of instrumentation
inaccuracies, can even be substantial in runoff measurements where
sampling errors are theoretically nonexistent. Freeman ( 1 965)
suggested that the Federal snow sampler overestimates by some eight
percent, and Corbett (1965) outlined errors of rain and snow gauges
giving estimates of up to 80 percent error due to wind currents.
Therefore, even if sampling errors are negligible, measurement errors
can be overwhelming, especially with precipitation measurements,
Analytic Procedures
Analytically, for daily runoff efficiencies to be calculated,
two processes must be assessed as to their contribution for a single
day: (1) snowmelt and (2) runoff. A computer model synthesized the
snowmelt process while recession techniques partitioned daily contributions to runoff,
Snowmelt Simulation
Many researchers have attempted to model the snowmelt process
with energy budget or modified energy budget approaches (Federer 7968,
Rantz 1964, Willen, Shumway, and Reid 1971, Leaf and Brink 1972, Leaf
and Brink 1973). The difficulty with this technique is maintaining
usability by the land manager without the complicated derivations and
calculations required for accurate simulation. Many of these models
Incorporate such variables as wind speed and vapor pressure gradients
26
(Federer 1968, Fohn 1973), necessitating data inputs that are not
readily available to the land manager. Therefore, it is desirable
that a model require as few input variables as possible, yet capable
of simulating the snowmelt process. For the purpose of this study, a
USDA Forest Service computer model (Leaf and Brink 1972) appeared to
meet the requirements of easily measurable inputs, a desirable degree
of simulation, and sensitivity to "key" variables.
Basically, the computer model simulates: (1) winter snow
accumulation, (2) the energy balance, (3) snowpack conditions, and
(4) resultant snowmelt, with a sensitivity to slope, aspect, forest
cover composition, temperature, shortwave radiation, and forest
density. In the process of simulation, the model consists of three
parts: (1) the determination of precipitation type (rain or snow),
(2) the energy budget (the amount of melt), and (3) snowpack conditions in terms of energy level and free water content. The model was
originally designed to simulate Colorado snowmelt characteristics;
therefore, some modifications were necessary in adapting the model
to better simulate Arizona conditions. Many of the subroutines in
the original USDA Forest Service model have not been altered, and
their flow paths will not be discussed [Leaf and Brink (1973) presented flow charts for the unaltered subroutines], but subroutines
that have been eliminated, added, or altered will be reviewed.
The modified program, ARZMELT (Appendix B), is dependent on
(2) minonly four daily input variables: (1) maximum temperature,
radiation
imum temperature, (3) precipitation, and (4) shortwave
27
or cloud cover. In addition, a number of initializing values are
required; they include: (1) initial snowpack temperature, (2) a
solar radiation transmissivity coefficient, (3) forest cover density,
(4) initial snowpack water equivalent, (5) a threshold value for use
in calculating reflectivity (subrouting GETREF), (6) the mean slope
and aspect of the watershed, (7) latitude, (8) an atmospheric absorption coefficient, and (9) a time interval for hour-angle changes in
subroutine SOLAR. A general flow pattern for ARZMELT is shown in
Figure 4 •
Estimation of Precipitation T. As mentioned previously,
the separation of precipitation into the snow and rain components is
one of the first steps in the flow of the model. The original MELTMOD
program established the daily minimum temperature as indexing precipitation segregation into snow, rain, or a mixture. If the daily
°
minimum temperature fell below 32 F. or the daily maximum temper-
o
ature was less that 35 F., a snow event occurred; this has been altered
to consider precipitation as all snow if the maximum temperature
°
drops below 40 F. and the minimum daily temperature never exceeds
°
35 F. The mixture event and rain event criterion were altered only
slightly, a rain event occurring when the minimum temperature exceeds
°
35 F. and a mixture of rain and snow when the minimum temperature falls
0
below 35 F. and the maximum temperature tops 40 F. Mixture event
partitioning was performed through the following equation:
SNOW = (PRECIP)(1
B/A)
(1)
28
START
Initialize variables I
Read o card
Precip.
Yes
Determine type of precip, and
its energy and mass contributions
Calculate the daily energy budget
Pos
budget
Determine snowpack temperature
with the diffusion model (DIFt1,40D)
Yes
Calculate effects of energy inputs
on the snowpock
Store results
More
cords
No
Print daily results (water eq., temp., etc.)
END
Figure
L.
General Flow Chart for Program ARZMELT.
29
where
°
B = the difference between the maximum temperature and 55 F,, and
A = the difference between the maximum and minimum temperatures.
Once partitioning of precipitation had been accomplished, the
next step in the program flow was the calculation of the energy budget,
Energy Budget Determination, The assumptions and equations
used in MELTMOD were accepted with only slight modifications. The
energy budget concepts utilized in the MELTMOD and ARZMELT models can
be summarized with the following set of equations:
Shortwave radiation absorbed by the snowpack:
R
an
= R (T $)(1 - a)
(2)
from sky to snow:
= b(1 - C d ) (1,t7xI0 -7 )(Tiztx )
s
from forest cover to snow:
L
L
f
= (1,17x10 - 7 )(Cd)(T 4f )
(3)
(4)
from snowpack to forest:
= (1 17x10 -7 )(C d )(T 4s )
L sf
(5)
from snowpack to sky:
4
-7
L ss = (1.17x1.0 )(1 - C d )(T s )
(6)
net energy balance:
En = Rsn + L s L f - L s - L ss
where
Rs = shortwave radiation upon the forest canopy,
T
s
= transmissivity coefficient,
a = albedo of the snowpack,
(7)
30
R
= net shortwave radiation absorbed by
sn
the snowpack,
b = a factor (I or 0.75) which accounts for
clear or cloudy skies,
C d = cover density,
T
L
T
L
T
L
a
= ambient air temperature in o K,
s = longwave energy from sky to snow,
f
= radiating temperature of foliage in o K,
f = longwave energy from forest cover to snow,
s
sf
= radiating temperature of the snowpack in o K,
=
longwave radiation from snowpack to forest,
Lss= longwave radiation from snowpack to sky, and
En = net energy input to the snowpack.
Successive solutions of the above equations yields the final energy
input to the snowpack, as shown by equation 7.
When a caloric deficit existed (a snowpack below 0 ° C.),
Ts in equations (5) and (6) was assigned a value corresponding to the
average ambient temperature or 0 ° C., whichever was less. If a caloric
deficit did not exist, the Ts in equations (5) and (6) was provided
a value corresponding to the minimum temperature or 0 ° C,, whichever
was less.
The explanation for this "flip-flopping" of the Ts value is
made clear by exmOning Colorado snowpack conditions. In Colorado,
snowpacks build-up in water content throughout an accumulation phase
with little or no melt occurring. Therefore, to keep the pack "cold"
during an accumulation phase, energy losses from the snowpack must be
restrained to a minimum; this can be enhanced by increasing the
radiating temperature of the snowpack [an examination of equations (5)
31
and (6) verifies this]. This "flip-flopping" establishes one of the
faults in applying the original model to Arizona conditions, By
using average ambient air temperature, the snowpack remained below
o
0 C. until the melt season, at which time the model was reinitialized
forceably by assigning the pack to 0 ° C. This might be satisfactory
for an area where distinct accumulation and melt seasons exist, but in
Arizona, where periods of melt and accumulation occur throughout the
winter months, this approach was inadequate. The theories and assumptions underlying equations (1) through (7) were accepted in the
modified program, but equations (5) and (6) were altered to only allow
the minimum air temperature to be used as the radiating snowpack temperature. Assigning a radiating snowpack temperature below the average
air temperature is supported, in part, by Bergen (1968).
In the energy budget equations, only the transmissivity coefficient (Ts ), shortwave radiation (R s ), cover density (C d ), and
maximum and minimum temperatures need be supplied; all other values are
calculated within the program. The transmissivity coefficient and
temperatures
cover density are discussed later, the maximum and minimum
radiation,
were taken directly from the watersheds, and the shortwave
most cases not
one of the main components in the energy budget, was in
insolation was
available. Thus, a method for synthesizing daily
needed.
SOLAR) were coupled
Calculated values of insolation (subroutine
synthesizing daily insolwith cloud cover data (subroutine CLOUD) in
potential daily insolation
ation values. Subroutine SOLAR computes the
32
for various slopes and aspects from theoretical
and emperical expressions (Reifsnyder and Lull 1965). A flow
chart for subroutine
SOLAR can be found in Appendix C. The calculated value
of potential
insolation from subroutine SOLAR agree within three percent of
those
values found in other sources (Frank and Lee 1966).
Potential insolation values are of little use unless they are
reduced by accounting for absorption by the atmosphere. This was accomplished by obtaining clear-weather insolation data from Flagstaff,
Arizona, and Alpine, Arizona, and applying different atmospheric absorption coefficients to potential values calculated from subroutine
SOLAR until the calculated and actual daily values corresponded within
three percent. Thirteen days of clear-weather produced a mean absorption coefficient of 0.13.
Once insolation values for clear days were derived, some adjustment was necessary for cloudy days (subroutine CLOUD). An equation
developed by Gates (1962), using as variables mean cloud cover and a
coefficient dependant on latitude, proved to be satisfactory:
= Qo (1 • (1 • K) C)
(8)
where
Q
o
= total energy recieved without accounting for cloud cover,
K = a parameter which is a function of latitude given a value of
o
o
0.38 at 30 0 , 0.41 at 40 , and 0.42 at 50 , and
C = average percent cloud cover.
The cloud coefficients (K) were increased slightly from those
suggested by Gates, and results proved to be satisfactory. The
equation tends to overestimate radiation for days with considerable
33
cloud cover and underestimate for days with 50 to
70 percent cloud
cover, Testing the calculated values from the
SOLAR-CLOUD subroutine
combination against three months of Flagstaff source data (January
through March, 1974) yielded an average calculated daily value of
96
percent of the actual daily insolation with a correlation coefficient
of 0,87,
The original model used a modified energy budget during periods of negative energy inputs, In the early development of MELTMOD,
it was found that, if only the energy budget was used in assessing the
snowpack temperatures, temperature profiles within the snowpack would
drop well below those encountered in Colorado, A solution was to establish snowpack temperatures with thermal diffusion equations solved
through finite differencing techniques. The overall technique involved three subroutines and contained limitations and constraints; a
complete explanation is given by Leaf and Brink (1972), After preliminary applications of MELTMOD, it was realized that these three
Subroutines (DIFMOD, LINK, and RBI:5ACR) were used to manipulate snowpack
temperatures to whatever value the programer felt reasonable. As a
result, all three subroutines were discarded and a single subroutine
(DIFMOD) was written, A complete flow chart of
DIFMOD is given in
Appendix D,
A central differencing technique (Carnahan, Luther, and Wilkes
1969, PP. 443-453) was modified and adjusted to program ARZMELT.
Unlike the original DIFMOD subroutine, the "new" subroutine had no
limitations of snowpack depth or minimum water-equivalent content, The
34
heat flow equation solved by this subroutine is given
by:
2
"a T
bz
s
2
=
I
K
bT
v
(9)
20t
where
T s = snowpack temperature in o C.,
z = depth within the snow pack in cm.,
-
K
v
= thermal diffusivity in cm 2 /sec,, and
t = time in seconds,
All of the above variables were known except K
v, Schwerdfeger (1963)
gives a thermal diffusivity equation dependent on density:
K
y
=
2K i
(10)
(3131P s )c i
where
K = thermal conductivity of ice in cal,/ o Cdcm./sec,,
3
pi = density of the ice in grams/cm.,
p s = density of the snow in grams/cm, and
c
1
= specific heat of ice in cal./gm,/° C.
Solutions of the thermal diffusivity equation involves knowledge
of snowpack densities, which may not be readily available. Through
graphically plotting snowpack density values from snow course data
against time of year, a satisfactory linear relationship between density and time was obtained, however.
Snowpack Conditions. Charcteristically, snowpack ablation and
areal depletion are not uniform throughout a forest, leading to incomplete snow cover towards the end of the melt season (Leaf 1971), As
35
the original model did not account for
this phenomenon, synthesized
snowpack ablation rates were excessive at
the end of the melt season,
resulting in 100 percent ablation prior to
the cessation of generated
runoff (i.e., the daily quantity of snowmelt which results
as streamflow). Snowpack water-equivalent measurements taken on small watersheds
from past years were utilized in the determination of cover density as
a function of water-equivalent. For each sampling date, the
number of
sample points with no snow were ratioed to the total points surveyed
and mean snowpack water-equivalent calculated for that date. Graphical plotting of the data revealed that only water-equivalents under
three inches showed deviation from 100 percent snow cover. Through
regression analysis, 27 snowpack water-equivalent measurements were
regressed against their corresponding percent snow cover. The correlation coefficient for this regression was 0.93, with the resultant
equation:
PERCENT COVER = 31.9 (SNOWPACK W.E.)
(11)
The above equation was only used for snowpacks containing
three inches or less of water. Therefore, when snowpack waterequivalent was below three inches, the calculated melt was reduced by
the percentage of area not covered by snow (if the calculated melt
was 0.75 inches and the percent snow cover was 80 percent, the corrected melt would be 0.75 X 0.80 or 0.60 inches). This technique was
one method of modeling observations made by other researchers (Gray
and Coltharp 1967, Ffolliott and Hansen 1968, Leaf 1971).
36
Daily Runoff Calculations
On forested watersheds there may be no substantial watershedwide overland flow from snowmelt (Garstka et al. 1958). Practically'
all of the snowmelt runoff enters the channels as subsurface flow,
groundwater flow, or a combination of both. Typically, the subsurface
contribution from a day's snowmelt to runoff will extend over days or
weeks. Therefore, recession techniques were required in segregating
daily snowmelt contributions to runoff (Garstka et al. 1958).
For all watersheds assessed in this study, other than the
North Fork of Thomas Creek, standard regression techniques were not
necessary since daily flows nearly always dropped close to zero, For
these watersheds, a decay curve was best fitted to the declining
portion of the daily hydrograph curve, and the area under the hydrograph curve and between two "decay" curves was graphically integrated
to obtain a daily contribution to runoff (Figure 5).
Recession techniques for the North Fork of Thomas Creek were
not as simple and straight forward as the technique described above.
Daily recession curves for this watershed extend over weeks for the
two years investigated. A recession coefficient of 0.79 was obtained
through techniques described by Garstka et al. (1958). Area A of
Figure 6 was graphically integrated, while area B of Figure 6 was
mathematically integrated through the following steps:
AREA B =
f
(
t dt
t dtK
QK
1 r
or
(12)
- 1
(13)
go
ln K r
37
RUNOFF HYDROGRAPH
DECAY CURVES
Efll ONE DAY'S CONTRIBUTION TO RUNOFF
PRECEDING
DAY
I
DAY OF FOLLOWING
DAY
SNOWWIELT
Figure 5. Graphical Integration Technique Used on All Watersheds
Except Thomas Creek,
38
att
MATHEMATICALLY INTEGRATED
=I GRAPHICALLY INTEGRATED
\ \\ \\ \
\ \\,\\\\\,,-\
\\\-\
\\\\\\ \, E\B\
, \\ \\ .
0 0
0.
-\...\
. . .
--\ .4 n \ \
-
4. 4
,
TIME
Figure 6, Integration Technique Used to Separate Daily Flows on
Thomas Creek,
39
where
Q 0 = flow in c.f.s. at the beginning of a day's contributing flow,
Q 1 = flow in c.f.s from the recession curve of the previous day, at
the beginning of the day in question (Figure 6),
K r = runoff recession coefficient,
t = time in days, and
n = time in days (an arbitrary n value of 30 days was Selected).
Combining areas A and B from Figure 6 yields the total runoff contribution for that day. Subsequent calculations for each day produced
daily runoff values for the entire season.
Runoff Efficiency Calculations
Daily runoff efficiencies were readily obtained by adhering
to the following mass balance equation:
P Sw - L =
R
(14)
where
P = precipitation input,
S w = change in snowpack water-equivalent (a decrease is negative),
L = outputs in the system other than surface runoff, and
R = surface runoff.
This equation can be applied on a daily, weekly, or any arbitrary
chosen time span, depending on the objectives sought. Calculating
runoff efficiencies requires only slight modifications of equation (14):
PERCENT EFFICIENCY = R
(P - Sw)
X 100
(15)
k0
Whore intermittent precipitation does not occur,
equation (15) can be
expresse as surface runoff divided by the
change in snowpack waterequivalent.
Graphical techniques and regression analysis (at
an ce= 0.10)
were used in attempting to characterize runoff efficiency
patterns
in three ways: (1) within a year, (2) between years on a
watershed, and
(3) among watersheds. Important independent variables used in regression techniques were as follows:
1. Changes within a season on a watershed,
Daily generated melt: daily values predicted from program
ARZMELT,
Daily runoff: calculated values of daily contributions,
Daily temperatures: both maximum and average temperatures.
2. Changes within a watershed among years.
Antecedent moisture: indexed by the total precipitation
two months prior to the snowpack build-up.
Peak accumulation: the peak snowpack water-equivalent on
the watershed.
Total seasonal precipitation: the total precipitation from
the first snowpack accumulation to complete ablation .
Duration of runoff: the number of days with generated runoff.
3. Changes among watersheds for various years.
Antecedent moisture.
Peak accumulation.
Vegetative density: basal area and stems per acre.
Slope and aspect: the predominant watershed slope and aspect.
41
Elevation: mean watershed elevation above sea level.
Total seasonal precipitation,
Drainage density: the total stream length in
feet,
divided by the watershed area in acres,
Duration of runoff.
Transmissivity Calculations
Transmissivity and cover density are variables controlling the
amount of shortwave and longwave radiation available at the pack's
surface for melt [equations (2) through (6) control the energy budget].
These values are determined through trial and error procedures, but once
established for a watershed, they do not change. Therefore, it was
desired that some forest attribute be used to index transmissivity; in
turn, forest cover could be empirically determined from transmissivity
by employing relationships developed by Miller (1959) and the II, S.
Army Corps of Engineers (1960).
After field data were collected, calibration of the sensors
was performed to standardize all recorders. Using shading cloths of
various transparencies, each sensor was exposed to different energy
fluxes and linear regression equations were constructed so that each
sensor was correlated with one standard sensor. The standardizing
equations are in Appendix E.
Once each sensor was calibrated to a standard scale, the next
step was to transform all data to that same scale. It was assumed
that, on clear days, radiation recorded by each sensor approximated a
cosine curve, It was further assumed that this cosine curve could be
42
approximated by two linear segments, one rising and one falling;
forming a triangle, With these two basic assumptions, it was then
possible to calculate an average langley value for the entire day,
substitute this value into the corresponding regression equation, and
arrive at the total standardized langleys for that particular sensor .
This procedure was followed for all sensors on days of clear sky . For
cloudy days, the procedure was duplicated with the exception that only
that part of the day with no cleud cover was considered as contributing significant flux differences between the opening and forested
condition, Therefore, only cloudless periods were analyzed.
The standardized daily insolations were then plotted and
regressed against several of the forest attributes to establish any
significance between variables,
RESULTS AND DISCUSSION
Estimating Daily Runoff Efficiency
Program ARZMELT, coupled with results from runoff separation
techniques proved to be satisfactory, providing estimates
of daily
runoff efficiencies for seven of the 14 years of record.
A more complete assessment would have been possible had it not been for weir
and
flume recording problems and a number of watersheds with waterequivalent measured only one or two times during the year. For years
with few sampling dates, the computer program was used to estimate
intermediate points between measured water-equivalents, enabling
the synthesis of runoff efficiencies over small increments of time
(one to two weeks). Although problems were encountered in estimating
daily melt values through the implementation of program ARZMRLT, recession techniques were easily applied with the only problem being the
time consuming nature of graphical integration of runoff peaks (Figure
5
).
Two input variables used in ARZMELT, transmissivity and cover
density, were found to have a marked influence on not daily energy
budgets. An alteration of as little as one percent in transmissivity produced a change of as much as 0.2 inches of difference in
snowpack water-equivalent predictions by the end of the snowmelt
season. Values of cover density also affected melt rates, but not to
the extent of transmissivity. Rather, cover density exhibited an
43
important role in preserving a "cold" snowpack during the seasonal
accumulation phase. By increasing the cover density coefficient,
it was noted that, although daily melt rates were not altered to the
degree transmissivity affected them, the rates in the beginning of
the season were increased. Therefore, with the fluctuations caused
by manipulating transmissivity and cover density, it was important
to develop some method of estimating these two variables other than
through trial and error procedures.
The use of subroutine DIFMOD for periods of negative energy
inputs proved to be most successful, not permitting the snowpack to
fall below -5 C. for more than a one or two day period, with quick
recovery to isothermal conditions during periods of positive energy
inputs,
Another difficulty encountered was in the use of extrapolated
temperature, cloud cover, and precipitation data. Periods from one
day to several weeks existed where climatological data were extrapolated from weather stations to watersheds. During some of these
lapses, inaccurate partitioning of precipitation into the snow and
rain components was believed to have taken place.
Assessing Transmissivity and Cover Density
Results gained from the transmissivity study (to be discussed later) were joined with program ARZMETL to estimate
transmissivity and cover density from some forest attribute.
area measurements and canopy
As mentioned previously, basal
data recorded. After
photographs were taken and solar radiation
transmissivity studies were completed and the sensors rechecked for
correct calibration, one of the sensors was found to be faulty and all
data gained from that sensor discarded. Thus, with one faulty sensor
and several days of substantial cloud cover, only 15 data points of
completely clear skies were recorded from sunrise to sunset, Incorporating days of partial cloud cover enabled a total of 31 data points
to comprise the sampling regime.
One hundred and eighty degree canopy closure values, determined from an electronic colored densitometer and a dot grid of 25
dots per square inch proved to be nonsignificant, yielding correlation
coefficients of 0.34 and 0,25, respectively,
Basal area, used as an index of transmissivity, provided
significant results. Plotting basal area values against transmis-
sivity provided the distribution depict in Figure 7, It should be
noted that cloudless days yielded a regression line statistically
identical with the curve resulting from a linear regression incorporating partially cloudy days as well as cloud free days. A closer
inspection of Figure 7 might bring one to a hypothesis that a closer
least squares regression fit through the points might be obtained by
transa logarithmic transformation of transmissivity. With such a
coefficient
formation, the following equation, with a correlation
of 0,80 and a standard error of 0.165, resulted:
ln(TR ) = 3.562 - 0.0057 BA f
f
where
TR = transmissivity in the field in percent and
BA
f
= field basal area in square feet per acre,
(16)
46
90
1
H-80
o
LLJ
7Q
>5
60
a_
(7)
r)
50
(
H 40
A
DAYS WITH PARTIAL CLOUD COVER
0 CLOUD FREE DAYS
30
0
I
1
I
25
50
75
1
100
I
T
125
150
BASAL AREA (SQUARE FEET PER ACRE)
Figure 7, Field Measurements of Basal Area Plotted Against
Measured Transmissivity,
47
It should be emphasized that the range of basal
area values was narrow,
only extending from 25 square feet per acre to 125
square foot per acre,
and that extrapolation
beyond these limits might not be justified.
Based on field estimates of average basal
area on the study
watersheds, it was then possible to select
an initial transmissivity
to be in ARZMELT from Figure 7; but, transmissivity
alone is not enough,
cover density must also be estimated. To solve this dilemma,
a trial
and error method of arriving at some combination of transmissivity
and cover density was initiated. For all years of record, various
combinations of forest cover density and transmissivity were paired
until the estimated melt pattern gave the "best fit" around the observed water-equivalent points. The "best fit" values for transmissivity
and cover density along with other measurable watershed variables are
shown in Table 2.
Using Table 2 as a guide, it is interesting to note the
differences in transmissivity values among years for Beaver Creek
Watershed 15. Theoretically, once a transmissivity value has been
established for a watershed, it should not change; but, the "best fit"
transmissivity value for Watershed 15 ranged from 0.42 (1969) to
0.53 (1968). Other substantial transmissivity differences between
years on a watershed were also noted, principally Watershed HE-2 for
1973 and 19749 Various sources of error could partially explain this
observation; for example:
1. Program ARZMELT may not be as adequate a modeling tool as
might be indicated by the results, since the model does not
account for convective and conductive energy exchanges
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between the snowpack and its environment (i.e., soil and air
interfaces with the snowpack).
2, Transmissivity is affected by the time of year (U. S. Army
Corps of Engineers 1960, Reifsnyder and Lull 1965): therefore,
different periods of melt might require different transmissivity values.
3. Errors in field measurements (precipitation, temperature, and
water-equivalent) may have been compensated for by adjustments
in transmissivity values,
Surprisingly, even with these fluctuations in transmissivity, values
of cover density stayed stable for all the watersheds modeled with
ARZMELT.
Plots of "model" transmissivity versus "model" cover density
and "model" transmissivity against basal area l along with a reduced
duplication of Figure 7, appear in Figure 8. All three lines are
curved relationships, and logarithmic transformations produced the
following significant equations:
ln(TRm ) = 4.346 - 0.0059BAw
(17)
r = 0.90, s x.y = 0.125
ln(TRm ) = 5.542 - 0.0363CDm
r = 0.83, sx.y= 0.162
where
TR = transmissivity produced from ARZMELT in percent,
m
per acre, and
basal area of watersheds in square feet
BA
in percent.
CDm = cover density produced from ARZMELT
(18)
50
COVER DENSITY (PERCENT)
2030
1
10
40
50
1
I
60
o FIELD DATA POINTS
80
—
POINTS GENERATED FROM PROGRAM
ARZMELT
POINTS GENERATED FROM PROGRAM
X
ARZMELT
70
o
\o
n o
-1=2
Z 60 o \ on00
N 0
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0 N
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20
MODEL VALUE OF TRANSMIS SIVITY AND BASAL
AREA
FIELD VALUES OF TRANSMISSIVITY AND BASAL
AREA
MODEL VALUES OF TRANSMISSIVITY AND COVER
10
DENSITY
50
100
150
200
250
300
BASAL AREA (SQUARE FEET PER ACRE)
and
Figure 8. Plots of Transmissivity Against Cover Density
Area.
Basal
Transmissivity Against
51
Utilizing values from Table 2, additional regression equations were
developed as follows:
TRm = 86.70 - 7.201n(ST)
(19)
r = 0.57, s
= 9.33
x.y
CDm = 41.46
0.0148ST
(20)
r = 0.81, sx.y = 3.91
where
ST
w
= stems per acre on a watershed.
From equations (16) through (20), it would now be possible to
estimate values of transmissivity and cover density for use in program
ARZMELT with a knowledge of basal area or stems per acre.
The question now arises whether the relationship of basal area
versus "model" transmissivity is the same as the relationship between
transmissivity and basal area resulting from observed field measurements,
One method of partial determination is establishing whether the slopes
of equations (16) and (17) are statistically equivalent (Figure 8).
With the use of a t table, the slopes were not significantly different.
Therefore, the actual measured values of transmissivity as a function
of basal area appear to coincide with values of transmissivity used in
the model; but, it must be emphasized that these two curves do not extend over the same range of source data. If the model is simulating
snowmelt properly, transmissivity values calculated in the field should
coincide with values used in the modeling processes, as is the case,
Some discrepancies do exist between transmissivity and crown
closure estimates developed by Miller (1959) and the U. S. Army Corps
52
of Engineers (1960) when compared with the
relationships developed
above. For the same amount of
cover density, the results above permitted 10 to 20 percent greater solar transmissivity than did relations
developed by Miller (1959). Many "key" factors could account for
much
of this discrepancy: (1) the authors sited developed their relationShips for lodgepole pine (Pinus contorta Dougl.), while the
relationships of this study were applicable to ponderosa pine and
Douglas-fir; (2) definitions of forest cover density differ among
authors; and (3) insolation may differ due to differences in the solar
altitude, tree heights and spacing of trees (Reifsnyder and Lull 1965).
Variability of Program ARZMELT
It is extremely difficult to statistically assess the "goodness"
of any snowmelt or time series model because of serial dependancy
within the model (Chow 1964, Yevjevich 1972). Therefore, three synthesized snowmelt seasons are graphically presented: (1) a year of
"good" fit, Watershed 17 (1969); (2) a year of "average" fit, Watershed
15 (1968); and (3) a year depicting a "poor" fit, the North Fork of
Thomas Creek (1973), These three years are shown in Figure 9,
Other peculiarities of the model were also noted, On first
trials, the North Fork of Thomas Creek was modeled as one complete
watershed, but program ARZMELT failed to produce melt patterns corresponding to measured water-equivalent. Therefore, the North Fork of
Thomas Creek, because of its steep north and south facing slopes, was
divided into two contributing subwatersheds, each area being assessed as
if it were a separate watershed. Using this technique, melt regimes
53
BEAVER CREEK
•
•
WATERSHED 17
1969
At • •
4%
.
• ••••
Lu
o
BEAVER CREEK WATERSHED 15 - 1968
• MODELED WATER-EQUIVALENT
A MEASURED WATER-EQUIVALENT
•••
..•
• •
..•
461
• °
•
*.
c,
A
NORTH FORK OF THOMAS CREEK
(south slope)
'973
III!,
JlII
II,
• J • •I..
5 15 25 5 15 25 5 15 25 I 5 15 251 5 15 25
APR
MAY
MAR
FEB
JAN
Figure 9. Three Years of Snowmelt Synthesized From Program
ARZMELT.
were produced that passed "near" points of observed water-equivalent
for each slope,
Considering all sources of error inherent within the model and
among input variables, it was felt that program ARZMELT synthesized
snowmelt
patters that were satisfactory for estimating daily melt
values. It was observed that watersheds could be analyzed as one unit
provided steep slopes were not oriented in a principal north-south
direction, Watersheds containing steep slopes in the east-west
direction (Watersheds HE-1 and HE-2) were considered as one contributing unit with no modeling difficulties encountered.
Chan in Patterns of Efficienc Within a Season
One objective of investigation was to determine whether runoff
efficiency patterns of watersheds were the same, or if each watershed
was unique in its patterns. The approach used was to normalize runoff
and melt, placing all watersheds on the same time and runoff scales.
This was accomplished by plotting accumulated percent of snowpack ablation against accumulated percent of runoff. Therefore, every season
started at the origin and terminated at 100 percent runoff and 100
graph
percent ablation regardless of the total seasonal efficiency. A
illustrating various years is depict in Figure 10, To make Figure 10
more easily readable, only 4 years of data were plotted,
There does not appear to be any one distinct pattern of runoff
unique, with
efficiency throughout a season (Figure 10). Every year is
the
some years demonstrating gradual transitions from the beginning to
have sharp breaks
end of the runoff season, while other watersheds
55
10 0
50
50
ACCUMULATED
100
MELT ( PERCENT)
WATERSHED HE-3 (1973)
WATERSHED 15 (1969)
WATERSHED 15 (1968)
WATERSHED HE-2 (1973)
Figure 10, Normalized Yearly Fluctuations in Snowpack AblationSurface Runoff,
56
between the beginning, middle, and end of the runoff season. But it
does appear that all watersheds start with a greater rate of snowpack
ablation than runoff, and the rate of runoff increases more rapidly
than the rate of ablation an the season progresses, until about 70
to 80 percent of the snowpack has ablated, thon again the rate of runoff decreases.
A more vivid interpretation of the above concept is shown by
plotting the rate of change of ablation with the rate of change of runoff or the slope of a "typical" curve (Figure 11), At the beginning
of the season a watershed demonstrates a relatively low runoff efficiency and as the season progresses, the efficiency steadily rises
to some peak, after which it falls to some lower efficiency towards the
end of the season, This pattern appears to be present regardless of
the total seasonal efficiency, and is supported by other investigators
(Leaf 1971, Orr and VanderHeide 1973). On the experimental watersheds,
the transition point from low efficiencies to relatively high efficiencies does not appear to be well defined, whereas the transition
from high efficiency back to low efficiencies towards the end of the
season occurs between 70 to 80 percent of snowpack ablation, Peak
seasonal efficiency does not occur at any one point during snowpack
ablation, but rather to peak somewhere between 40 to 60 percent of
snowpack ablation .
The shallow slopes at the beginning of the season (Figure 10)
can be explained by the necessity of replenishing soil moisture deficits prior to any runoff (U. S. Army Corps of Engineers 1960), As
a greater proportion of the watershed is satisfied, a greater amount of
57
INCREASING
EFFICIENCY
AT SEASONS
BEGINNING
HIGH EFFICIENCIES
I
DECLINING
EFFICIENCIES
TOWARDS
SEASONS
END
ACCUMULATED MELT
Figure 11. A Plot of the Changing Slope Pattern of a nCharcteristic"
Normalized Snowpack Ablation-Surface Runoff Curve.
58
surface runoff is generated. Eventually, some point is reached where
the maximum contributing area to melt and peak seasonal efficiency is
found. Az the snowpack continues to ablate, bare areas appear, exposing soil surfaces and thereby creating higher rates of evaporation
losses that occur from snow surfaces (Hutchison 1962). With a smaller
proportion of the watershed contributing to runoff and higher rates of
evaporation, the runoff efficiency declines towards the latter part of
the runoff season,
The phenomenon of soil moisture recharge was made evident on the
North Fork of Thomas Creek (1974). The total rainfall was less than one
inch for a two month period prior to snowpack build-up; this would
imply a relatively "high" soil moisture deficit. As tho year progressed
and snowpack ablation began, no surface runoff was recorded. The first
runoff occured on March 3, at which time the "average" snowpack ablation
from the watershed was approximately 40 percent of the total seasonal
ablation. The south facing slope and north facing slope had 10 and 60
percent seasonal ablation at this time, respectively.
Since there appeared to be no "exact" curve describing changing
snowpack ablation-surface runoff relationships among watersheds, it was
hypothesized that perhaps there exists a unique curve for each watershed, a curve that does not change from year-to-year for that watershed.
Again, as was found for all watersheds, there was no unique pattern of
snowpack ablation-surface runoff for a season within a watershed. And,
it was observed that a "goneral" pattern of low efficiencies at the beginning and end of the season did occur.
59
Daily runoff efficiency fluctuations were exhibited throughout a snowmelt season, Even with the "general" pattern outlined above,
daily efficiencies did not graduate in a smooth pattern (Figure 12),
This observation led to the consideration of possible variables influencing this phenomenon, several variables were considered: (1)
average and maximum temperatures, (2) calculated melt (used as an index
of all enorgy inputs to the snowpack), and (3) daily generated runoff.
These four variables were correlated with daily efficiencies of watersheds where daily values were synthesized, resulting in significant
correlation coefficients shown in Table 3. Daily snowmelt was correlated with daily efficiency and, in general, it might be inferred
that days with high predicted molt rates were also days of high runoff efficiencies; conversely, days producing low melt were days of low
daily efficiencies (Table 3), This observation may be partially explained by daily soil moisture recharge requirements. Evapotranspiration losses that occur on a daily basis must be satisfied before
runoff can occur from a contributing area (Leaf and Brink 1973, Orr
and VanderHeide 1973), Also, towards the end of the snowmelt season
when areal extent of the snowpack is diminishing and melt rates (on
a watershed-wide basis) are declining, melt water from the snowpack
serves to maintain soil moisture conditions at field capacity in much
of the exposed soil surface. These exposed surfaces have higher evaporation losses then snow surfaces (Hutchison 1962); therefore, enhanced
evaporation losses towards the end of the snowmelt season occur, .Consequently, runoff efficiency at seasons end declines along with
watershed-wide melt rates,
60
0.9
90
0.8
80
0.7
(n
70
0.6
o
0.5
0.4
0.2
20
0. 1
10
L30
Figure 12. Daily Runoff Efficiencies, Generated Daily Melt,
and Daily Runoff for Watershed 17 in 1 969.
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Maximum and average daily temperatures were, in many cases,
not statistically correlated with daily efficiency. As the molt season
progresses and daily runoff efficiencies increase, daily temperatures
are also increasing, but towards the end of the season when efficiencies
decline, temperature regimes continue to increase, creating a trend of
low runoff efficiencies with relatively high temperatures. This could
be a contributing factor towards the low correlation of temperature,
both maximum and average, with daily runoff efficiencies.
Changes in runoff efficiency within a season would appear to be
affected by the soil moisture deficits prior to snowpack build-up, the
rate of energy inputs to the system, and the snowpack areal depletion
towards the end of the season. And, although each watershed was
found to be unique in its seasonal efficiency fluctuations, a general
pattern of low to high and back to low efficiencies was observed extending over the snowmelt season.
Factors Affectin
Runoff Efficiencies
Not only are patterns of changing efficiencies important to land
managers, but knowledge of seasonal runoff efficiencies could be of use
in predicting total runoff volumes from watersheds of interest, A
first step in any predicting technique is the identification of important seasonal variables.
Differences Among Watersheds Within a Season
A composite of all variables that were inventoried over all
and peak
watersheds, along with yearly values of seasonal efficiencies
accumulation to
efficiency (the runoff efficiency from peak snowpack
63
season's end) appears in Table 4, Watersheds with records for 1973 and
1974 were selected and correlation coefficients calculated for seasonal
runoff efficiencies against the many variables appearing in Table 4.
With only 4 and 5 degrees of freedom for 1973 and 1974, respectively,
no "concrete ' statements could be made of the statistical importance of
,
the various variables, but rather only relative ranking of importance
and statements of observed trends (Yevjevich 1972).
A correlation matrix indicated that the only variables to be
significant with seasonal runoff efficiency were antecedent moisture
(r = 0.70), peak snowpack accumulation (r = 0.72), and duration of
seasonal runoff (r = 0.70), for the 1974 runoff season. These same
variables were also significant for the 1973 season; in addition,
drainage density (r = 0,83) and total seasonal precipitation (r = 0.98)
were also significant.
All Significant variables were correlated positively with
seasonal and peak runoff efficiencies. This would imply that the
highest efficiency for a given year would occur on a watershed receive
substantial precipitation prior to snowpack accumulation, having a
deep snowpack at peak accumulation, and a large amount of seasonal
precipitation,
Differences Within a Watershed Among Years
more than
Beaver Creek Watershed 15 was the only watershed with
was employed in estwo years of record, For this reason, Watershed 15
important in
tablishing variables within a watershed that might be
co
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65
determining runoff efficiencies from year-to-year, Only a total of
five years of record were available,
Variables that would change from year-to-year, principally
antecedent moisture, peak snowpack accumulation, total seasonal precipitation, and duration of runoff were all used in correlations with
seasonal and peak efficiency. Again, as with previous correlations,
peak snowpack accumulation (r = 0.80), duration of runoff (r = 0.89),
and antecedent moisture (r = 0.81) were significantly correlated with
seasonal efficiency also, significant correlations of peak efficiency
with peak snowpack accumulation (r = 0.80), antecedent moisture (r =
0.84), and duration of runoff (r = 0.91) were demonstrated.
Total seasonal precipitation did not prove to be significant
in accounting for runoff efficiencies within a watershed, but did
appear significant between watersheds within a season. The possible
significance of this will be discussed in a following section, Duration
of runoff provided the highest correlation coefficient and could be
a variable that might be a "good" index of seasonal efficiency within
a watershed. It must be emphasized that the above correlation coefficients are based on only five years of data and, therefore, these
variables may only account for trends of runoff efficiencies.
Important Variables Among Years and Among Watersheds
With a total of 14 years of record from Table 4, correlation
for
coefficients among variables were calculated. A correlation matrix
the
these variables can be found in Appendix F. From this matrix,
snowpack
significant variables were again, antecedent moisture, peak
66
accumulation, and duration of runoff. Some of the other variables that
were thought to be important (basal area, stems, elevation, drainage
density, and slope) did not appear significant in the correlation
matrix.
Vegetation density measurements, elevation, and drainage
density might have been significant in accounting for runoff efficiencies, but the range of these variables in the study was relatively
limited. Therefore, any affects on seasonal efficiency might be only
minimally detectable.
Soil differences were not quantified and were not included
in the regression analysis. This does not mean that soil type was not
influential in determining seasonal efficiencies, but rather the difficulty of assigning some "representative" value for such variables
as infiltration capacities and water holding capacities (Taylor and
Ashcroft 1972, pp, 316-328).
A second method for evaluating the importance of various
variables was through step-wise regression analysis. This method
allowed the step-wise inclusion of variables most significant in terms
2
of increasing the coefficient of determination (r ). For predicting
purposes, the inclusion of more than two variables into the equation
would produce inferences that might not be necessarily true . But, by
carefull analysis of the variables being entered and the relationships among variables entered, variables consistantly appearing in
as important,
regressions through the first three steps were considered
being influential to annual
not for predicting purposes but only as
was used in
runoff efficiencies. An arbitrary F level of 1,25
67
establishing a minimum level for a variable
to be considered, This
F value may appear extremely low, but it must
be remembered that this
technique was not used for establishing prediction equations
but rather
for variable identification purposes, If the overall F value
became
statistically insignificant, the step-wise regression was terminated.
In all of these regressions, sign changes of coefficients from step to
step should not occur, for this could be an indication of curve fitting
rather than adding significant variables. If such occurrences took
place, the regression was discarded. The results of this technique
appear in Table 5,
As with simple correlation coefficients, the variables appearing
most frequently in the step-wise assessment were: (1) peak accumulation,
(2) antecedent moisture, (5) watershed slope, (4) duration of runoff,
and (5) stems per acre, Duration of runoff and some form of peak snowpack accumulation were the principal variables occurring in step I,
also appearing frequently in step II was elevation,
Having identified some variables that were important in
accounting for seasonal runoff efficiency for the years of record,
the next step was in the combining of these variables for prediction
purposes,
Prediction of Yearly Runoff Efficiencies
Step-wise regression techniques were implemented in deriving
prediction equations, For prediction purposes, the F value for entry
was established at the alpha level of 0,10, and the regression process
terminated at the step prior to any F level failure,
68
Table 5, Listing of Variables Appearing in Stop-Wise Regression
Technique for Variable Identification Purposes.
Dependant Variable
Independant Variables
Step I
Step II
Xl
X 16
X27
0• 11.0
Xl
x1 7
X27
X26
Xl
x 17
X27
X 29
Xl
X33
X23
X2
x 17
X27
xa
X33
X2
X33
x 13
X2
X 13
X17
X2
X 13
X27
x 17
X2
X 17
X27
X 29
Step III
1IM
WOO.
MD' ONO
X 1 = seasonal runoff efficiency
X23 = (stems per acre) 3
X2 = peak efficiency
X
X 13 = Ln(antecident moisture)
26 = (slope)3
X2 7 = elevation
X 16 = peak accumulation
X 29 = (elevation) 3
X 17 = Ln(peak accumulation)
X
33
WO IWO
OS MIID
= duration of runoff
69
Significant equations and
their step-wise development are displayed in Table 6. One crossproduct
variable, X36 , may not appear
rational at first glance, but a further explanation may establish
justification for the crossproduct of
antecedent moisture and elevation.
It was hypothesized that as elevation increased, temperature regimes
became cooler, decreasing convective stresses and decreasing evapotranspiration losses (Sellers 1969, pp, 156-180). Therefore, soils at
higher elevations have less of a soil moisture deficit, everything else
being equal. Of added interest was that this crossproduct
was correlated
more significantly with seasonal and peak efficiencies than any other
variable (r = 0,55).
From Table 6, it became evident that two types of equations
had been developed: (1) equations for predicting runoff efficiencies
from watersheds based on variables that could be measured prior to
peak snowpack accumulation and (2) equations designed to estimate
efficiencies after the completion of runoff. The first set of
equations could be of use by land managers interested in knowing the
proportion of the snowpack generated from a watershed as surface water
for a specific season. The second set of equations has its utility
in characterizing small watersheds as to their past efficiency history
and water yielding potentials, based on easily measured parameters.
The ' best" equations for use in predicting runoff efficiency
,
from small watersheds were as follows:
Y 1 = -109.63 + 17.31n(X 16 ) + 0.015X 27
(21)
Y3 = =-136.9
(22)
21.61n(X 16 ) + 0.017X 27
70
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where
yi
n
seasonal efficiency in percent,
Y = peak efficiency in percent,
3
X
X
16
27
= peak snowpack accumulation in inches, and
= elevation in feet from sea level.
These equations only apply to the snail test watersheds used
in the study and extrapolation to other areas may not be meaningful.
The above equations indicate that areas of highest elevation and
greatest snowpack depths are the most efficient watersheds.
Of interest is that total seasonal precipitation was not among
those variables significant in predicting runoff efficiencies, whereas
peak snowpack accumulation appears in some of the prediction equations.
From this observation, it might be hypothesized that the timing of
precipitation throughout the build-up and melt period, as well as
total seasonal precipitation, is of importance in establishing the
runoff efficiency for that year (Orr and VanderHeide 1973).
The second set of equations ("duration index" equations)
yielded the following "best" regressions:
Y = -76.9
Y
3
0.617X
-8 3
1.47x10 x 20
33 4.
= -22.4 4- 0.74 x
33
1.71100
-8 3
x
20
(23)
(24)
where
X
20
X
33
= stems per acre, and
= duration of runoff in days.
Drainage density (X
equations (23)
and
33
) was the first variable to enter in
(24) and, as such, supplied the greatest part of
72
the predicting power, Thus, the description of "duration index" equations, Of interest is the positive sign of beta for X
20' Many
researchers (Croft and Monninger 1953, U. S. Army Corps of Engineers
1960, Bethlahmy 1973) have used inverse relationships of forest density
and water yielding capacities of forested watersheds, whereas equations
(23) and (24) imply the opposite situation. One possible explanation
is that forest density is indexing some other variable, such as elevation, which is correlated positively with seasonal and peak runoff
efficiency. The reason for this hypothesis may become evident from a
close look at Table 5. With only 14 years of record, inferences from
the data could be misleading. As an example, if these watersheds are
arrayed in ascending order of elevation, a resulting trend is for stem
densities to also ascend in order. Therefore extrapolation of prediction equations outside the scope of this study should be done
with caution.
CONCLUSIONS
Program ARZMELT coupled with integration of runoff hydrographs
proved to be a viable tool in assessment of snowpack ablation-surface
runoff relationships on the small forested watersheds in this study.
Two model variables, solar transmissivity and vegetative cover density,
were quantified and estimates of these variables could be made with a
knowledge of measurable forest attributes,
Results indicated that, although runoff efficiency patterns
were unique for each watershed for each year, there did exist a
"general" runoff pattern of relatively low runoff efficiencies at the
beginning and end of the snowmelt-runoff season, with relatively high
runoff efficiencies occurring between 40 and 60 percent of seasonal
snowpack ablation. Patterns of runoff efficiencies throughout a season
did not graduate in a smooth pattern, but rather fluctuated from day to
day. These daily fluctuations were found to be positively correlated
with daily generated melt and daily runoff; the greater the melt rates
and volume of runoff, the greater the daily runoff efficiencies.
Further, significant correlations of seasonal and peak runoff
and
efficiencies with peak snowpack accumulation, antecedent moisture,
were significant
duration of runoff were found. These same variables
with seasonal runoff efficiency from year-to-Year within a watershed,
season. Statistically
and among watersheds within a snowmelt-runoff
significant equations were produced with use of the above variables,
73
74
and additionally, appearing in those prediction equations, were watershed
elevation and forest density.
Further study is needed to provide a greater understanding of
runoff efficiency fluctuations from year-to-year, An increase in the
number of years of record for a watershed, and a greater number of
watersheds, would be necessary in expanding this type of study. With
an expanded study, it might then be possible to assess the influoncy, if
any, of the many variables outlined in this study whose ranges were not
sufficient enough to contribute significant influences on seasonal
efficiencies.
Any extrapolation of results from this study should be done
with caution, since 14 years of record supplied only a limited range
of data for use in the construction of regression equations,. It must
also be remembered that the results of this study wore limited to small
Arizona watersheds,
APPENDIX A
METRIC CONVERSION TABLE
Multiply
To Obtain
Acres
0.4047
Hectares
Acre-feet
0.1235
Hectare-meters
20,1168
Chains
Meters
0.0283
Cubic meters per sec.
0.5556
Degrees C.
Feet
0.3048
Meters
Inches
2.540
Centimeters
Miles
1.6093
Kilometers
Square feet per acre
0.2296
Square meters per ha.
Cubic feet per sec.
Degrees F.
°
- 32 F.
75
APPENDIX B
PROGRAM ARZMELT DERIVED FROM U. S. FOREST SERVICE
PROGRAM MELTMOD
76
77
PROGRAM ARZMELT(INPUTOUTPUT.TAPF5=INPUTJAPE6.0LTRUT)
THIS PROGRAM IS A REWRITTEN VERSION OF MELIMOD, A SNOW ACCUMULATION
MODEL DEVELOPED BY THE U. S. FOREST SERVICE.
DICTIONARY OF BLANK COMMON
•
•
•
ABSK - THE ABSORPTION COEFFICIENT OF THE ATMOSPHER
ACTDATE - THE DATE OF THE RECORDING OF THE VALUES IN -ACTUALASPECT - THE AVERAGE ASPECT OF 11-4 E WATER S H E D FROfr NORTH
AVETEMC - THE DEGREES CENTIGRADE EQUIVALENT OF -AVETEMFAVETEMF - MEAN OR AVERAGE OF THE MAXIMUM AND MINIMUM TEMPERATURE
IN DEGREES FARENHFIT
BASTEMF - BASE TEMPERATURE DEGREES FARENFEIT, RAIN TURNS TO SNOW
CALAIR - POTENTIAL LONCWAVE CALORIC INPUT AT AIR TEMPERATURE
CALDEF - THE CALORIE DEFICIT IS THE NUMBER OF CALORIES NEEDED
TO BRING THE SNOWPACK TEMPERATURE TC ZERO DEGREES
CENTIGRADE (NOTE SHOULD BE MADE THAT IT IS A POSITIVE
QUANTITY)
CALORIE - CALORIES OF HEAT ABSORBED OR RELEASED BY THE SNOWPACK
FROM THE NET RADIATION BALANCE
•
CALSNOW - POTENTIAL LONGWAVE CALORIC LOSS AT SNOW TEMPERATURE
CLCOV - THE AVERAGE CLOUD COVER FOR THE DAY
•
•
COVDEN - THE COVER DENSITY IS THE FRACTION OF THE GROUND OR SNOW
SURFACE SHADED FROM DIRECT SUNLIGHT OR RADIATION
•
DATE - THE DATE BEING PROCESSED IN MMODYY FORMAT
•
DATES - AN ARRAY OF THE DATE BEING PROCESSED. THE FIRST WORD IS
THE MONTH, THE SECOND THE DAY, AND THE THIRD THE YEAR
•
DELH - CHANGE IN HOUR ANGLE(H), MINUTES
DEN - THE SNOWPACK DENSITY READ FROM INPUT CARDS
•
DENSITY - THE DENSITY OF THE SNOWRAOK USED IN THE DIFFUSION MODEL.
IF -DEN- IS ZERO OR BLANK, -DENSITY IS COMPUTED AS A
FUNCTION OF THE PREDICTED WATER EQUIVALENT
ENGBAL - THE TOTAL CALORIC INPUT TO OR LOSS FROM THE SNOWPACK
•
DURING AN INTERVAL. IT IS THE ALGEBRAIC SUM OF THE
ENERGY INVOLVED WITH THE PRECIPITATION AND THAT OF
THE RADIATION BALANCE, - CALORIEFOOTNOT - ARRAY OF FOOTNOTES TO BE PRINTED AT THE BOTTOM OF EACH
•
PAGE. TWO CARDS ARE READ, THE FIRST 130 CHARACTERS
FORMING ONE LINE AND THE LAST 30 CHARACTERS FORMING A
CSECOND
LINE
FREEWAT - THE FREE WATER BEING HELD BY THE SNOWPACK
•
HOLDCAP - THE FREE WATER HOLDING CAPACITY OF THE SNOWPACK
•
(ASSUMED TO BE FOUR PERCENT OF THE WATER EQUIVLAENT)
IDATE - ARRAY FOR STORING THE DATES FOP PLOTTING
•
ISNOW - A SWITCH, TURNED ON BY SUBROUTINE SNOWED WHEN THE PRECIP
•
WAS SNOW AND THEN OFF BY SUBROUTINE GETREF AFTER
COMPUTING THE REFLECTIVITY FOR THE GIVEN INTERVAL
ITABLE = 0, NO PRINTING OF TABULATED RESULTS FROI, THE SIMULATION
•
= 1, PRINT THE TABULATED RESULTS FROM THE SIMULATION
G
SOLAR IS TO
KKPP - USED AS A COUNTER TO DETERMINE WHEN SUBROLTINE
•
BE BYPASSED
372 DUE
KOUNT - COUNTER FOR THE NUMBER OF CARDS READ, MAXIMUM OF
•
TO THE DIMENSIONS OF THE VARIABLES FOR STORING THE
INFORMATION FOR PLOTTING
TO DETERMINE
LASTUSO - AN INDICATOR USED IN SUBROUTINE GETREF
•
WHICH REFLECTIVITY FUNCTION TO USE
LINES - THE LINE COUNTER FOR PAGE EJECTION
OBSWEQV - OBSERVED WATER EQUIVALENT OF THE SNOWPACK IN INCHES
•
PACKTEM - THE EFFECTIVE TEMPERATURE OF THE SNOWPACK
•
-
78
PARTICE - THE PORTION OF THE PREDICTED WATER EQUIVALENT THAT IS
•
ICE.
THIS QUANTITY PLUS FREE WATER IS THE TOTAL
PREDICTED WATER EQUIVALENT ( - PREWEOV-)
PASTINT - NUMBER OF INTERVALS SINCE THE LAST INITIALIZATION OF THE
REFLECTIVITY FUNCTION
PLOTOBS = 0, 00 NOT PLOT THE OBSERVED WATER EQUIVALENT
1, PLOT THE OBSERVED WATER EQUIVALENT (OPERATIVE ONLY IF
-PLOT WE- IS TURNED ON)
PLOTWE = 0, DO NOT PLOT THE SIMULATION
1, PLOT THE SIMULATION, PRECIP, ETC.
PRECIP - OBSERVED PRECIPITATION IN INCHES
PREWEOV - PREDICTED WATER EQUIVALENT OF THE SNOWPACK IN INCHES
RADIN - RADIATION IN IS THE TOTAL INCIDENT SHORT HAVE RADIATION
RADLWN - NET LONG NAVE RADIATION IS THE ALGEBRAIC SUM OF THE LCNG
WAVE RADIATION FROM THE FOREST AND THE LONG WAVE
RADIATION LOST BY THE SNOWPACK TO THE CANOPY
RADSWN - THE CALORIC INPUT TO THE PACK BY THE NET SHORT WAVE
RADIATION
REFLECT - THE FRACTION OF RADIATION THAT IS REFLECTED BY THE SNOW
SLOPE - THE AVERAGE SLOPE OF THE WATERSHED
AS DERIVED BY SUBROUTINE GETREF
SNOMELT - MELT DELIVED IN INCHES FOR THE INTERVAL
SOBSEQV - ARRAY FOR STORING THE OBSERVED WATER ECUIVALENT FOR
PLOTTING
SPRECIP - ARRAY FOR STORING THE PRECIP FOR PLOTTING
SPREQV - ARRAY FOR STORING THE PREDICTED WATER EQUIVALENT FOR
SUBTITL - ONE CARD SUBTITLE, SIMILAR TO -TITLESUM4 - SOLAR RADIATION CALCULATED FROM SUBROUTINE SOLAR PRIOR TO
ADJUSTMENT FROM SUBROUTINE CLOUD
TCOEFF - THE TRANSMISIVITY COEFFICIENT USED TO ESTIMATE THE NET
SHORT WAVE RADIATION REACHING THE SNOWPACK. SEE
REIFSNYDER AND LULL, RADIANT ENERGY IN RELATICN TO
• FORESTS, USPS TECH. BUL 1344, 1R65.
TEMPMAX - THE MAXIMUM TEMPERATURE DURING THE INTERVAL IN DEGREES
•
FARENHEIT
TEMPMIN - THE MINIMUM TEMPERATURE DURING THE INTERVAL IN DEGREES
FARENHEIT
THRSHLO - THE THRESHOLD TEMPERATURE FOR DETERMINING WHETHER OR NOT
•
•
•
G
•
•
•
•
•
c
•
•
•
•
•
•
•
TO RE-INITIALIZE THE REFLECTIVITY FUNCTION WHEN
THERE IS A SNOW EVENT. IF THE MAXIMUM TEMPERATURE IS
GREATER THAN THE THRESHOLD VALUE DO NOT RE-INITIALIZE
THE FUNCTION REGARDLESS OF THE PRECIPITATION
TITLE - ONE CARD TITLE (IF THE INFORMATION IS CENTERED ON THE CARD
IT WILL BE PROPERLY CENTERED ON THE PAGE)
TOTPREC - THE ACCUMULATED TOTAL PRECIPITATION IN INCHES
USEMEAN = 0, USE MAXIMUM AND MINIMUM TEMPERATURES AS READ
= 1, REPLACE THE MAXIMUM AND MINIMUM TEMFERATURES BY THEIR
MEAN
USEPOT = 0, 00 NOT USE SUBROUTINE SOLAR TO ESTIMATE SHORT WAVE
RADIATION
= 1, USE SOLAR TO ESTIMATE SHORT WAVE RADIATION
XLAT - LATITUDE OF THE WATERSHED
XLATE - SAME AS XLAT, USED IN SUBROUTINE SOLAR
FOR
XMAX - MAXIMUM OBSERVED OR PREDICTED WATER EQUIVALENT, USED
SUBROUTINE
CLOUD
IN
USED
ZAT - LATITUDE DIVIDED BY 10,
SCALING
COMMON ACTDATE I ACTUAL(21),AVETEMC,AVETEMF , BAS T E NF, E NGBAL,HOLOCAP
COMMON CALAIR,CALDEF,CALORIE,CALSNOW,COVDEN , PA TE,DATES(3),OEN
COMMON DENSITY,IFIRST,FOOTNOT(16),FREEWAT , I 0 A T E (372),ISNOW,ITA9LF
79
COMMON KOUNT,LAsTUSO,LINES,OBSWEOV,PADIN,PAOLWN,RADSWM,REFLECT
COMMON pACKTEm,1ARTICE,PAfiTINT,RLoTO7JS,PLOTHE,PRECIP,PRFWEQV
COMMON SNOMELT,SOOSEOV(372),SPRLCIP(372),SP9EOV(72),SU3TITL(8)
COMMON TOTRREC,TITLE(8),THFJ.SHLO,TEMPMIN,TEmPHAX,TCOEFF,USEMEAN
COMMON XMAX,USEROT,SLOPE,ASRECTIXLAT,DELH,ABSK,CLGOV,ZAT,SUM4
COMMON KKPP,XLATE
INTEGER ACTDATE,DATE,DATES,FOOTNOT,PASTINT,PLOTOES,PLOTWE,SUBTITL
INTEGER TITLE,USEMEAN,USEPoT
COMMON/CONVERT/rivE9TH,THIPTY2
DATA FIVE9TH,THIRTY2/.5555555556,32.0/
INITIALIZE THE MODEL AND READ THE PARAMETER CARDS
10 CALL INITIAL
READ A DATA CARD
20 CALL READER (HNC))
A
BLANK CARD MAY BE USED TO SEPARATE SETS OF DATA
IF(IENO.NE.0.0R.DATE.LE.0) GO TO 60
SEE HOW THIS INTERVAL AFFECTS THE SIMULATION
CALL AFFECTS
IF THE TABLE IS BEING PRINTED, WRITE THIS LINE
IF(ITABLE) 40,40,30
30 CALL WRITER
IF THE PLOT IS TO BE DONE, STORE THIS INFORMATION. THEN GO ON TO
THE NEXT CARD
40 IF(PLOTWE) 20,20,50
50 CALL STORE
GO TO 20
ALL CARDS HAVE BEEN READ, SO PLOT THE SIMULATION AFTER WRITING
THE FOOTNOTES ON THE LAST PAGE
60 IF(ITABLE.NE.0) WRITE (6,910) FOOTNOT
910 FORMAT(1H013A10/1X3A10)
IF(PLOTWE.NE.0) CALL PLOTTER
IF
THE
DATA
END OF FILE HAS NOT BEEN SENSED, GO ON TO THE NEXT SET OF
IF(IEND) 70,10,70
70 STOP
END
SUBROUTINE AFFECTS
DETERMINE THE EFFECTS OF THE DATA FROM THIS CARD
COMMON 4CTOATE,ACTUAL(21),AVETEMc,AVETEMF,BASTEMF,ENGBAL,HOLDCAR
COMMON CALAIR,CALDEF,CAL0RIE,OALSN0W,C0V0EN , DATE ,0 ATES 3), DEN
COMMON DENSITY,IFIRST,FOOTN0T(16),FREEWAT,I0ATE(372),ISNOW,ITABLE
COMMON KOUNT,LASTUSD,LINES,OBSWEOV,RADIN,RADLwN,RADSWN,REFLECT
COMMON PACKTEM,PARTICE,PASTINT,PLOTOBS,PLOTWE,PRECIP,PREWFQV
COMMON SNOVELT,SOBSEDV(372),SPRECIp(372),SpREOV(372),SUBTITL(8)
COMMON TOTPREC,TITLE(8),THRSHLD,TEmFMIN,TEMPMAX,TCOEFF,USEMEAN
COMMON XMAX,USEPOT,SLOPE,AS2ECT,XLAT,0ELH,A3SK,CLCOV,ZAT,SUM4
COMMON KKPP,XLATE
INTEGER ACTOATE,DATEIDATES,FOOTNOT,PASTINT,PLOTOESIPLOTWE,SUBTITL
INTEGER TITLE,USEMEANIUSEPOT
COMMON/CONVERTIFIVE 9 TH , THIRTY 2
THE ENERGY BALANCE AN!) SNOWHELT AT ZERO FOR THIS INTERVAL,
START
BUT
ACCUMULATE THE PRECIPITATION
ISNOW =
ENGBAL = 0.0
SNOMELT = 0.0
TOTPREC + PRECIP
TOTPREC
A SNOWPACK ALREADY EXISTS, GO FIND THE EFFECT OF THIS INTERVAL
IF
ON THE SNOWPACK
••
80
IF(PREWEOV) 10,10,40
SINCE THERE IS NO SNOWPACK, CHECK TO SEE IF THIS INTERVAL HAS ANY
PRECIPITATION AND IF SO, SEE IF IT IS ALL SNOW
10 IF(PRECIP) 120,120,20
IF THE MAXIMUM TEMPERATURE IS BELOW 40 DEGREES, CONSIDER THE
C
PRECIPITATION TO BE ALL SNOW.
20 IF(1EMFMAX.LT.40.0.AND.TEMPMIN.LT.BASTENF) GO TO 60
SEE
IF THE PRECIPITATION IS ALL RAIN OR A MIXTURE ON BARE GROUND
IF(TEMPMIN
BASTEMF) 90,30,30
IT IS ALL PAIN, DO NOT START BUILDING UP THE SNOWPACK
30 SNOMELT = PRECIP
GO TO 120
A SNOWPACK EXISTS. IF THERE IS PRECIPITATION, DETERMINE THE TYPE.
BUT OTHERWISE, JUST GO ON TO COMPUTE THE REFLECTIVITY AND
RADIATION BALANCE
40 IF(PRECIP) 110,110,50
THERE IS PRECIPITATION ON AN EXISTING PACK. IF IT IS NOT ALL
SNOW, GO SEE IF ANY OF IT WAS SNOW
C
50 IF(TEMPMAX.GT.40.0.0R.TEIPMIN.GT.BASTEMF) GO TO 70
60 CALL SNOWED (AMIN1 (AVETEMC,0.0),PRECIP)
GO TO 110
SEE WHETHER THE PRECIPITATION ON AN EXISTING PACK WAS ALL RAIN OR
A MIXTURE OF RAIN AND SNOW
70 IF(TEMFMIN - BASTEMF) 90,80,80
THIS IS A RAIN ON SNOW EVENT. THE TEMPERATURE FOR COMPUTING THE
DEPLETION OF THE TOTAL CALORIE DEFICIT IS THE DIFFERENCE OF THE
AVERAGE TEMPERATURE AND FREEZING (0.0 DEGREES CENTIGRADE)
8 0 CALL RAINED (AVETEMC,PRECIP)
GO TO 100
THIS IS A MIXTURE OF RAIN AND SNOW EVENT
90 CALL MIXTURE
IF THE PACK WAS ENTIRELY MELTED, BYPASS COMPUTATION OF THE
REFLECTIVITY AND THE RADIATION BALANCE
100 IF(PREWECIV) 120,120,110
GET THE REFLECTIVITY FOR THIS INTERVAL
110 CALL GETREF
COMPUTE THE RADIATION BALANCE AND ITS EFFECT ON THE PACK
CALL RAOBAL
RETURN
THERE IS NC gNOWPACK - REDEFINE THE RADIATION BALANCE TO A
NEGATIVE VALUE TO ASSURE THE PROPER SELECTION OF THE REFLECTIVITY
FUNCTION IN SUBROUTINE GETREF WHEN THERE IS A SNOMPAOK
120 CALORIE = -1.0
RETURN
ENO
SUBROUTINE CALIN (CALORIN)
THIS SUBROUTINE COMPUTES THE EFFECTS OF THE CALORIC INPUT ON THE
SNOWPACK
COMMON ACTDATE,ACTUAL(21),AVETEMC,AVETEMF , BASTEMF ,ENGBA L ,H0LDCAP
COMMON CALAIR,CALDEF,CALORIE,CAL0N 0 W ,0 OVCEN , S AT E ,DATES(3),DEN
COMMON DENSITY,IFIRST,FOOTN0T(16),FREEWAT,IOATE(372),ISNOW,ITABLE
COMMON KOUNT,LASTUSD,LINES,OBSWEOV , RADIN , RADL WN,RADSMN,RFFLECT
ECIP,PREWEQV
COMMON PACKTEM,PARTICE,PASTINT , PLOTOBS , PLOTWE ,R R(372),SUBTITL(8)
EOV
PR
S
(372),
COMMON SNOMELT,S000EOV(372),SPRECIR
11PMAX,TC0EFF,USEMEAN
COMMON TOTPREC,TITLE(8),THRSHLD , TEMPMIN ,T E
XMAX,USEPOT,SLOPE,ASPECT,XLAT,DELH,ABSK,CLCOV,ZAT,SUM4
COMMON
COMMON KKPR,XLATE
ACTDATE,DATE,DATES,FOOTNOT,PASTINT,PLOTOBS,PLOTWE,SUBTITL
INTEGER
81
INTEGER TITLE,USEMEAN,USEPOT
ADD THESE CALORIES INTO THE ENERGY BALANCE
ENGBAL = EGBAL + CALVIN
SEE IF A CALORIE DEFICIT EXISTS IN THE PACK
COMPARE = GALOPIN
CALDEF
IF(COMPARE) 10,20,30
THERE IS A CALORIE DEFICIT, BUT THE INPUT DID NOT COMPLETELY
WIPE IT OUT. ALL OTHER CONDITIONS ARE UNCHANGED
10 CALOEF
- COMPARE
1.27 = 0.05 * 2.54
PACKTEM = COMPARE/(PREWEQV*1.27)
RETURN
THE CALORIE DEFICIT WAS WIPED OUT, BUT ALL OTHER CONDITIONS ARE
UNCHANGED
20 CALDEF = 0.0
PACKTEM = 0.0
RETURN
ANY DEFICIT WHICH DID EXIST WAS WIPED OUT. COMPUTE THE POTENTIAL
MELT FROM THE REMAINING CALORIES (CALORIES/(80.0 * 2.54))
30 POTMELT = COMPARE/203.2
IF(PREWEDV.GT.3.0) GO TO 50
IF(PREWEDV.LT.0.01) GO Td 60
PERCOV = .312'f - PREWEQV
POTMELT = PERCOV*POTMELT
50 CALDEF=0.0
PACKTEM = 0.0
IF THE INPUT WAS ENOUGH TO MELT THE WHOLE PACK, CONTRIBUTE THE
WATER EQUIVALENT TO THE SNOWMELT AND ZERO ALL CCNDITIONS
IF(POTMELT.LT.PARTICE) GO TO 40
60 SNOMELT = SNOMELT + PREWEQV
PREWEQV = 0.0
PARTICE = 0.0
FREEWAT = 0.0
HOLDCAP = 0.0
RETURN
DEPLETE THE ICE PACK BY THE AMOUNT MELTED AND CONTRIBUTE THAT
AMOUNT TO THE FREE WATER
40 PARTICE = PARTICE - POTMELT
FREEWAT = FREEWAT + POTMELT
COMPUTE THE NEW HOLDING CAPACITY OF THE PACK AND COMPARE IT WITH
THE FREE WATER TO SEE IF SNOWMELT IS PRODUCED
HOLDCAP = 0.04 * PARTICE
COMPARE = FREEWAT - HOLDCAP
IF(COMPARE.LE.0.0) RETURN
THE SNCWMELT CONTRIBUTED IS IN -COMPARE-. REDUCE THE FREE WATER
TO LEAVE A PRIMED PACK 4 ND REDUCE THE PREDICTED WATER EQUIVLAENT
PREWEQV = PREWEQV - COMPARE
SNOMELT = SNOMELT + COMPARE
FREEWAT = HOLOCAP
RETURN
END
SUBROUTINE CALOSS (CALOUT)
SUBROUTINE COMPUTES THE EFFECTS OF THE CALORIC LOSS ON THE
SNOWPACK
COMMON ACTDATE,ACTUAL(21),AVETEMC,AVETEMF , BA 5 TE MF,ENGBAL,HOLDCAP
COMMON CALAIR,CALDEF,CALORIE,CALSN0W,C 0 VDEN , DATE , D AT E S(3),OEN
COMMON OENSITY,IFIRST,FOOTNOT(16),FREEWAT,I0ATE(372),I5NOW,ITABLE
COMMON KOUNT,LASTUSD,LINES,OBSWEQV,RADIN , RADLWN ,RADSWN,REFLECT
THIS
82
COMMON PACKTEM,PARTICE,PASTINT,PLOTOBS,PLOTWE,PRFCIP,PREWECV
COMMON SN0MELT,S0BSEOV(372),PRECIP(372),SPREOV(372),5UBTITL(8)
COMMON TOTPREC,TITLE(8),THRCHLD,TEMPHIN,T0MPMAx,ICOEFF,USFMEAN
COMMON XMAX,USEPOT,SLOPE,ASPECT,XLAT,DELN,ADSK,CLCOV,ZAT,SUM4
COMMON KKPP,XLATE
INTEGER ACTOATE,DATE,DATES,FOOTNOT,PASTINT,PLOTOES,PLOTWE,SUBTITL
INTEGER TITLE,USFMEAN,USPOT
DO ALGEBRAICALLY THESE CALORIES INTO THE ENERGY BALANCE
A
ENGBAL = ENGBAL + OALOUT
SEE IF THERE IS ANY FREE WATER IN THE PACK. IF NOT, THE LOSS IS
JUST CONTRIBUTED TO THE CALORIC DEFICIT OF THE SNOWPACK.
REMEMBER THAT -CALOUT- IS NEGATIVE
IF(FREEWAT.GT.0.0) GO TO 10
CALOEF = CALDEF - CALOUT
GO TO 50
COMPUTE THE CALORIC LOSS NECESSARY TO FREEZE ALL OF THE FREE WATER
(FREE WATER * 80.0 * 2.54)
10 CALNEED = FREEWAT * 203.2
NOW COMPARE THAT NECESSARY LOSS WITH THE ACTUAL LOSS. IF THEY ARE
THE SAME, THE FREE WATER IS WIPED OUT Bur NO OTHER CONDITIONS ARE
ALTERED
COMPARE = CALOUT + CALNEED
IF(COMPARE) 20,30,40
C- THE LOSS WAS moRE THAN ENOUGH TO FREEZE IT. THE BALANCE CREATES
AN ENERGY DEFICIT IN THE PACK AND THE FREE WATER IS WIPED OUT
20 CALDEF = - COMPARE
30 PARTICE = PARTICE + FREEWAT
FREEWAT = 0.0
GO TO 50
ONLY PART OF THE FREE WATER FROZE. COMPUTE THE BALANCE REMAINING
BALANCE = EXISTING FREE WATER - AMOUNT FROZEN, WHERE
AMOUNT FROZEN = CALORIES/(80.0 * 2.54)
40 FROZEN = - CALOUT/203.2
PARTICE = PARTICE + FROZEN
FREEWAT = FREEWAT - FROZEN
RETURN
COMPUTE THE NEW PACK TEMPERATURE AND HOLD CAPACITY
50 PACKTEM = -CALDEF/(PRFWEQV*1.27)
HOLOCAP = 0.04 * PARTICE
RETURN
END
SUBROUTINE CLOUD
THIS SUBROUTINE ACCOUNTS FOR PERCENT CLOUD COVER IN CONVERTING
POTENTIAL SOLAR RADIATION TO A NET VALUE.
COMMON ACTOATE,ACTUAL(21),AVETEMC,AVETEMF,BASTEMEIENG3AL,HOLOCAP
COMMON CALAIR,CALDEF,CALORIE,CALSNOW,COVOEN,DATE,DATES(3),DEN
(372), I SN0W,ITABLE
COMMON DENSITY,IFIRST,F00TN01(16),FREFWAT , IDATE
,RADSWN,REFLECT
RADLWN
,
COMMON KOUNT,LASTUSD,LINES,OBSwECIV,RADIN
IP,PREwEQV
COMMON PACKTEM,PARTICE,PASTINT,PLoToBS , PLOTNE , PREC
REOV (372),SUBTITL(8)
P
372),
S
SNOMELT,SOBSEOV(372),SPRECIP(
COMMON
COMMON TOTRREC,TITLE(8),THRSHLD,TEMPMIN,TE1PmAX,TCOEFF,USEMEAN
,CLCOV,ZAT,SUM4
COMMON XMAX,USEPOT,SLOPE,AS 2 ECT,XLAT , OELH , ABsK
COMMON KKPP,XLATE
INTEGER ACTOATE,DATE,DATES,FOOTNOT,PASTINT,PLOTOBS,PLOTWE,SUBTITL
INTEGER TITLE,USEMEAN,USEPOT
DIMENSION COLATIT(7)
DICTIONARY
CLCOV - AVERAGE CLCUD COVER FOR THE DAY
83
CULAI - A COEFFICIENT BASED ON LATITUDE.
DATA COLATI 7 /. 3 5,.34,38,.411.42,44,.52/
40 ZAT = XLATE/10
DO 10 M=2,7
IF(ZAT.LE.M) GO 10 20
10 CONTINUE
20 N = M-1
COLAT
(COLATIT(M)-COLATIT(N))*(ZAT-N)+COLATIT(N)
30 RADIN
SUM4*(1.0-((i-COLAT)4CLCOV))
RETURN
END
•
C
•
•
C
C
•
•
SUBROUTINE DIFMOD
THIS SUBROUTINE IS USED IN SIMULATING CHANGES IN SNOWPACK TEMPERATURES DURING PERIODS WHERE A CALORIE DEFICIT EXISTS.
DICTIONARY
DEN - DENSITY OF SNOWPACK
DEPTH - DEPTH OF SNOWPACK
DIFUS - DIFFUSIVITY OF THE SNOWPACK
TAU - TIME
OTAU - TIME INTERVAL
M - NUMBER OF DEPTH INTERVALS
FF(I) - AN ARRAY USED IN SIMULATING SNOWPAOK TEMPERATURES AT OIFFERENT DEPTHS.
DX - DEPTH INTERVAL
TENK - NORMALIZED NINIMUN AIR TEMPERATURE
0 0,01 - BOUNDARY TEMPERATURES
T(I) - TEMPERATURES WITHIN THE SNOWPACKK
COMMON ACTDATE,ACTUAL(21),AVETE11C,AVETEMF,BASTEMF,ENGBAL,HOLDCAP
COMMON CALAIR,CALOEF,CALORIE,CALSNOW,COVDEN,CATE,DATES(3),DEN
COMMON DENSITY,IFIRST,FOOTNOT(161,FREEWAT,IDATE(Z72),ISNOW,ITABLE
COMMON KOUNT,LASTUSO,LINES,OBSWEOV,RADIN,RADLWN,RADSMN,REFLECT
COMMON PACKTEM,PARTICE,PASTINT,PLOTOBS,PLOTWE,PRECIP,PREWEOV
COMMON SNOMELT,SOBSEOV(372),SPRECIP(372),SPREOV(372),SUBTITL(8)
COMMON TOTPRFC,TITLE(8),THRSHLD,TEMPMIN,TEMPMAX,TCOEFF,USEHEAN
COMMON XMAX,USEPOT,SLCPC,ASPECTIXLAT,DELH,ABSK,CLCOV,ZAT,SUM4
COMMON KKPP,XLATE
INTEGER ACTDATE,DATE,DATES,FOOTNOT,PASTINT,PLOTOBS,PLOTWE,SUBTITL
INTEGER TITLE,USEMEAN,USEPOT
DIMENSION DENN(4),F(50)18ETA(50),GAMMA(50),FF(50)
DIMENSION A(50),B(50),C(50),D(50),T(50)
DATA DENN/.259.30,351.40/
CHECK TO SEE IF DIFMCD IS A CONTINUING ESTIMATE CF TEMPERATURE OF
IF IT HAS BEEN REINITIALIZED.
•
C
210 IF(IFIRST) 10,20,10
CALCULATE SNOWPACK DENSITY, BASED ON TIME OF YEAR.
20 IF(DATES(1).LT.5) GO TO 30
IF(OATES(1).GT.9) GO TO 40
DEN= .40
GO TO 50
40 DEN= .20
GO TO 50
30 DEN.DENN(DATES(1))
CALCULATE SNOWPACK DEPTH FROM DENSITY
50 DEPTH.(PREWEOV/DEN)*2.54
•
CALCULATE DIFFUSIVITY
•
DIFUS.(0.01)/((2.751-0EN)*0.48)
CALCULATE TAU AND DTAU
TAU=DIFUS*86400/DEPTH**2
84
OTAU=TAU/48
M=48
DETERMINE THE AVERAGE PACK TEMPERATURE FROM THE EXISTING CALORIE
DEFICIT
•
PACTEM1=( - CALDEF/(PREWEOV*1.27))+273
•
SET THE INITIAL TEMPERATURE ARRAY AT THE AVERAGE PACK TEMPERATURE
DO 60 1=1,50
60 FF(I)=PACTEM1
IFIRST=1
10 00=0.0
Ol=1.0
FLOATM=M
DX=1.0/FLOATM
RATIO=DTAU/(DX*DX)
DO 2 I=1,M
A(I)=-RATIO
B(I)=1.0+2.0*RATIO
2 C(I)=-RATIO
MP1=M+1
CONVERT MINIMUM AIR TEMPERATURE TO DEGREES KELVIN
TEMPK=HAVETEMF-32.0)*.55555)4-273
NORMALIZE EXISTING PACK TEMPERATURES
•
IF(TEMPK.LE.274.0.AND.TEMPK.GE.272.0) TEMPK = 272.0
3 DO 7 1=1,50
7 F(I)=(273-FF(I))/(273-TEMPK)
DO 4 I=1,MP1
4 T(I)=F(I)
TAU=0.0
PERFORM CALCULATIONS OVER SUCCESIVE TIME-STEPS
5 TAU=TAU4-9TAU
IF(TAU.GT.48 4 0TAU) GO TO 100
•
SET BOUNDARY VALUES
T(2)=0.0
T(MP1)=1.0
COMPUTE RIGHT-HAND SIDE VECTOR V
DO 15 1=2,M
•
15 0(I)=T(I)
D(2)=0(2)+RATIO*T(1)
D(M)=0(M)4-RATIOT(MP1)
COMPUTE NEW TEMPERATURES
COMPUTE INTERMEDATE ARRAYS BETA AND GAMMA
•
6
•
11
8
100
110
•
BETA(2)=8(2)
GAMMA(2)=0(2)/BETA(2)
IFP1=3
DO 6 I=IFP1IM
BETA(I)=B(I)-A(I)*C(I-1)/BETA(I - 1)
GAMMA(I)=4D(I)-A(I)GAMMA(I1))/BETA(I)
COMPUTE FINAL SOLUTION VECTOR T
T(M)=GAMMA(M)
LAST=M-2
DO 11 K=1,LAST
I=M-K
T(I)=GAMMA(I)-C(I) 4 T(I+1)/BETA(I)
DO 8 I=1,MP1
F(I)=T(I)
GO TO 5
00 110 I=10 13 1
FF(I)=-F(I)*(273-TEMPK) 4-273
TOT=0.0
ESTABLISH AN ARRAY OF FINAL PACK TEMPERATURES TO BE USED IN STARTING
85
THE CALCULATIONS OF PACK TEMPERATURES FOR THE NEXT DAY
00 80 I=1,MP1
80 TOT=T0T+FF(I) -273
DETERMINE THE CALORIE DEFICIT AND NEW AVERAGE PACK TEMPERATURE
AV=TOT/MPi
CALDEF= AV *(PREWEQV*1.27)
PACKTEM=AV
IF(CALDEF) 90,90,95
90 PACKTEM = 0.0
CALDEF= 0.0
95 RETURN
-
END
SUBROUTINE GETREF
GET THE REFLECTIVITY
DICTIONARY
REFACUM - A REFLECTIVITY FUNCTION FOR THE SNOWPACK DURING THE
ACCUMULATION PHASE OF THE SNOWPACK
REFMELT - A REFLECTIVITY FUNCTION FOR THE SNOWPACK DURING THE
MELT PHASE OF THE SNOWPACK
COMMON ACTDATE,ACTUAL(21),AVETEMC,AVETEME,BASTEMF,ENGBAL I HOLOCAP
COMMON CALAIR I OALDEF,CALORIE,CALSNOW,COVCEN,DATE,DATES(3),DEN
COMMON DENSITY,IFIRST,FOOT0OT(16),FREEWAT,IDATE(372),ISNOW,ITABLE
COMMON KOUNT,LASTUSD,LINES,OBSWEDV,RADIN,RADLWN,RADSWN,REFLECT
COMMON PACKTEN,FARTICE,PASTINT,PLOTOBS,POTME,FRECIP,PREWEOV
COMMON SNOMELT,SOBSEOV(372),SPRECIP(372),SPREOV(372),SUBTITL(8)
COMMON TOTPREC,TITLE(8),THRSHLD,TEMPMIN,TEMPMAX,TCOEFF,USEMEAN
COMMON XMAX,USEP0T,SLOPE,ASPECT,XLAT,DELH,ABSK,CLCOV,ZAT,SUM4
COMMON KKPP,XLATE
INTEGER ACTDATE,DATE,DATES,FOOTNOT,PASTINT,PLOTOBS,PLOTWE,SUBTITL
INTEGER TITLE,USEMEAN,USEPOT
DIMENSION REFACUM(15),REFMELT(15)
DATA REFACUM/.80, .77, .751 .72, .70, .89, .681 .671 .66, .65,
1 .64
1
.63, .62, .61, .60/
DATA REEMELT/.72, .65, .60, .58, .56, .54, .52, .50, .48, .46,
1 .44, .43, .42, .41, .40/
INCREASE THE INTERVAL COUNTER BY 1 AND SEE IF THERE WAS ANY SNOW
PASTINT = PASTINT + 1
IF(ISNOW) 10,10,80
USE THE SAME FUNCTION AS LAST TIME
10 IF(LASTUSO) 20,20,50
ACCUMULATION PHASE - AFTER 15 DAYS, USE THE MELT FUNCTION
STARTING AT THE FCURTH DAY
20 IF(PASTINT - 15) 30,30,40
30 REFLECT = REFACUM(PASTINT)
RETURN
40 PASTINT = 4
LASTUSD =
GO TO 70
MELT FUNCTION - AFTER 15 DAYS, USE A CONSTANT 40 PERCENT
50 IF(PASTINT - 15) 70,70,60
60 PASTINT = 15
70 REFLECT = REFMELT(PASTINT)
RETURN
THERE IS NEW SNOW - DETERMINE IF THE FUNCTION IS TO BE RE INITIALIZED
86
ao
IF(TEMPMAX
THRSHLD) 90,90,10
IT IS, SO SEE WHICH FUNCTION IS TO BE USED
90 PASTINT . 0
IF(PACKTEM) 100,110,110
100 REFLECT
0.91
LASTUSD = 0
RETURN
THE PACK IS ISOTHERMAL, BUT IF THE ENERGY BALANCE FROM
THE
PREVIOUS INTERVAL WAS NEGATIVE, USE THE ACCUMULATION PHASE
FUNCTION ANYWAY
110 IF(CALORIE) 100,120,120
120 REFLECT = 0.81
LASTUSO = 1
RETURN
ENO
SUBROUTINE INITIAL
READ THE PARAMETERS AND INITIALIZE THE MELT MODEL
COMMON ACTDATE,ACTUAL(21),AVETENC,AVETEMF,BASTEMF,ENGBAL,HOLOCAP
COMMON CALAIP,CALDEFICALORIE,CALSNOW,COVCEN,OATE,DATES(3),DEN
COMMON DENSITY,IFIRST,FOOTNOT(16),FREEWAT,IDATE(372),ISNOW,ITABLE
COMMON KOUNT,LASTUSD,LINES,OBSNEOV,RADIN,RADLWN,PADSWNIREFLECT
COMMON PACKTEM,PARTICE,PASTINT,PLOTOBS,PLOTWE,PRECIP,PREWEOV
COMMON SNOMELT,SOBSEOV(372),SPRECIP(372),SPREOV(372),SUBTITL(8)
COMMON TOTPREC,TITLE(8),TNRSHLO,TEMPMIN,TEMPMAX,TCOEFF,USEMEAN
COMMON XMAX,USEPOT,SLOPE,ASPECT,XLAT,DELH,ABSK,CLCOV,ZAT,SUM4
COMMON KKPP,XLATE
INTEGER ACTDATE,OATE,DATES,FOOTNOT,PASTINTIPLOTOBS,PLOTWE,SUBTITL
INTEGER TITLE,USEMEAN,USEPOT
ESTABLISH THE STANDARD BASE TEMPERATURE
BASTEMF
35.0
INITIALIZE THOSE VARIABLES WHICH ARE NOT READ IN OR OTHERWISE
INITIALIZED BEFORE BEING USED
FREEWAT = 0.0
HOLDCAP = 0.0
SUM = 0.0
TOTAL = 0.0
XMAX = 0.0
IFIRST = 0.0
ISNOW = 0
KOUNT = 0
LASTUSO = 0
PASTINT = 0
ZAT = 0
KKPP = 5
LINES = 999
START THE RADIATION BALAMCE WITH A NEGATIVE VALUE FOR POSSIBLE USE
BY SUEROUTINE GETREF IN DETERMINING WHICH REFLECTIVITY FUNCTION
TO USE
CALORIE = -1.0
READ THE INSTRUCTION PARAMETERS AND THE CONTROLS ON THE MODEL
READ (5,910)ITABLE,PLOTWE,PLOTOBS,USEMEAN,TCOEFF,COVOEN,PACKTEM,
1PREWEOV,THRSHLD,USEPOT
910 FORMAT(4I1,1X,5F5.2,1X,I1)
IF(USEPOT) 130,130,140
140 READ(5,930)SLOPE,ASPECTIXLAT,DELH,ABSK
930 FORMAT(5F5.2)
130 IF(E0F(5))10,10,20
READ
THE TITLE, SUBTITLE AND FOOTNOTE CARDS
87
10 READ (5,920) TITLE,SUBTITL,FOOTNOT
920 FORMAT(8A10)
INITIALIZE THE ICE CONTENT AND ACCUMULATED PRECIPITATION
PARTICE
PREWEOV
TOTPREC = FREWEQV
CALCULATE THE CALORIE DEFICIT FROM THE PACK TEMPERATURE
CALDEF
- (PACKTEM * 80) * (PREWEOV * 2.54) / 160
CALOEF = - PACKTEM * PREWEQV * 1.27
RETURN
20 STOP
ENO
SUBROUTINE MIXTURE
C----THIS SUBROUTINE CONTROLS THE COMPUTATIONS FOR A PRECIPITATION
EVENT THAT IS A MIXTURE OF SNOW AND RAIN
DICTIONARY
AMTSNOW - THE AMOUNT OF PRECIPITATION OCCURRING AS SNOW (INCHES)
TFORAIN - THE TEMPERATURE FOR COMPUTING THE DEPLETION OF THE TOTAL
CALORIE DEFICIT CAUSED BY THE RAIN (DEGREES C)
TFORSNO - THE TEMPERATURE FOR COMPUTING THE CONTRIBUTION OF THE
SNOW TO THE TOTAL CALORIE DEFICIT (DEGREES C)
COMMON ACTOATE,ACTUAL(21),AVETENC,AVETEMF,BASTFMF,ENGBAL,HOLOCAP
COMMON CALAIR,CALDEF,CALORIE,CALSNOW,COVOEN.DATE,DATES(3),DEN
COMMON DENSITY,IFIRST,FOOTNOT(16),FREEWAT,IDATE(37 2 ),ISNOW,ITABLE
COMMON KOUNT,LASTUSO,LINES,OBSWEOV,RADIN,RADLWN,FADSNN,REFLECT
COMMON PACKTEm,PARTICE,PASTINT,PLOTOOS,PLOTWE,PRECIP,PREWEOV
COMMON SNOMELT,SOBSEOV(372),SPRECIP(372),SPREOV(372),SUBTITL(8)
COMMON TOTFREC,TITLE(8),THRSHLD,TEMPNIN,TEMPNAX,TCOEFF,USEMEAN
COMMON XMAX,USEROT,SLOPE,ASPECT,XLAT,DELH,ABSK,CLCOV,ZAT,SUM4
COMMON KKPP,XLATE
INTEGER ACTOATE,DATE,DATES,FOOTNOT,PASTINT,PLOTOBS,PLOTWE,SUOTITL
INTEGER TITLE,USEMEAN,USEPOT
COMMON/CONVERT/FIVE9TH,THIRTY2
COMPUTE THE AMOUNT OF PRECIPITATION OCCURRING AS SNOW BY
AMOUNT SNOW = P * (1.0 - B/A), WHERE
P = PRECIPITATION IN INCHES
B = DAILY MAXIMUM TEMPERATURE - BASE TEMPERATURE (DEGREES F)
A
= DAILY MAXIMUM TEMPERATURE - MINIMUM TEMPERATURE (DEGREES F)
B = TEMPMAX - BASTENF
TEMPMIN
A = TEMPMAX
AMTSNOW = PRECIP * (1.0 - (B/A))
NOW COMPUTE THE AVERAGE TEMPERATURES (DEGREES C) WHICH PRODUCE
SNOW AND RAIN
TFORSNO = (((TEMFMIN + BASTEMF) * 0.5) - THIRTY2) * FIVE9TH
TFORAIN = (((TEMPMAX + BASTEMF) * 0.5) - THIRTY21 * FIVE9TH
COMPUTE THE EFFECT OF THE SNOW ON THE SNOWPACK
CALL SNOWED (TFORSNO,AMTSNOW)
COMPUTE THE EFFECT OF THAT PORTION OF THE PRECIPITATION OCCURRING
AS RAIN ON THE SNOWPACK
CALL RAINED (TFORAIN,PRECIP - ANTSNOW)
RETURN
END
SUBROUTINE PLOTTER
SUBROUTINE CONTROLS THE PLOTTING OF THE MODEL OUTPUT
THIS
•
88
COMMON ACTDATE,ACTUAL(21),AVETEMC,AVETEMF,BASTEMF,ENGaAL,HOLOCAP
COMMON CALAIR,CALDEF,CALORIE,CALSHOW9COVUN,OGTE,OATES(3),OEN
COMMON DENSITY,IFIPST,FOOTNOT(16),VREEWAT,IOATE(372),ISNOSI,ITABLE
COMMON KOUNT,LASTUS01LINES,OOSNE7OV,R!AOIN,RhOLWN,AOSWM,Pf I FL!'CT
COMMON PACKTEM,PARJICC,PASTINT,PLOTOBS,PLOTWF,PQECIP,PREWEOV
COMMON SH0)TLT,SOOSEOV(372),SPRECIP(372),SPREOV(72),SUOTITL(8)
COMMON TOTPREC,TITLE(8),THRSHLO,TEMPAIN,TEMPI , AX,TCOEFF , USEMEAN
COMMON XMAX,USEPOT,SLOPE,ASPECT,XLAT,DELN,ADSK,CLCOV,ZAT,SU114
COMMON KKPP,XLATE
INTEGER ACTOATE,DATE,OATES,FOOTNOT,PASTINT,PLOTOES,PLOTWE , SUDTITL
INTEGER TITLE,USEMEAN,USEPOT
DIMENSION LEGEND(8)
OBSERVED WATER
PREDICTED WATER EQUIVALENT, 2
DATA LEGEND/ 80Hi
1 EQUIVALENT, 3 = PRECIPITATION/
TURN OFF THE AUTOMATIC PAGE EJECT
WRITE (6,910)
910 FORMATNO*)
INITIALIZE THE PLOT ROUTINE
CALL TSPLOT (3,0,0,0,0,010,XMAX10.0,IDATE( 1) 1 7,-1)
PLOT ONE LINE FOR EACH INTERVAL
DO 10 I = 1,KOUNT
. 0,0 . 0,XMAX,
10 CALL TSPLOT (3,SPREOV(I),SOBSEQV(I),SPRECIP(I ),0 . 0,0
i 6.0,IDATE(I),7,11
WRITE THE TITLE AND OTHER IDENTIFYING INFORMATION
T
WRITE (6,920) TITLE,SUBTITL,TCOEFF,COVDEN , LEGEND , FOOTNO
=*F4.2,74X
COEFFICIENT
920 FORMAT(iH026X0A10/27X8A10/* TRANSNISIVITY
-- *8A10//1H013A10/1X
1 *COVER DENSITY =*F4,2/1110,19X*PLOT LEGEND
2 3A10)
TURN THE AUTOMATIC PAGE EJECT BACK ON
WRITE (6,930)
930 FORMAT (*R*)
RETURN
ENO
SUBROUTINE RADBAL
TRANSFERS
SUBROUTINE COMPUTES THE RADIATION BALANCE AND
IT IS NEEDED
CONTROL TO THE DIFFUSION MODEL IF
THIS
DICTIONARY
•
THE SNOW AND THE
SNOCAN - THE LONGWAVE RADIATION BALANCE BETWEEN
•
CANOPY
BALANCE BETWEEN THE SNOW AND THE
SNOSKY - THE LONG WAVE RADIATION
SKY
COMMON ACTOATE,ACTUAL(21),AVETEMC,AVETEMF,BA5TENF,ENG9AL,HOLDCAP
COMMON CALAIR,CALOEF,CALORIE,CALSNOW,COVOEN,OATE,DATES(3),DEN
DENSITY,IFIRST,F00TN0T(16),FREEWA1,IDATE(1,72),ISNOW,ITABLE
COMMON
COMMON KOUNT,LASTUSO,LI1ES,085WEOV,4A0IN,RAOLWN,PAOSWN,REFLECT
COMMON PACKTEM,PARTICE,PASTINT,PLOTOBS,PLOTWE,PRECIP,PREWEOV
SNOMELTISOBSEOV(372),SPRECIP(372),SPREON(372),SUBTITL(8)
COMMON
TOTPR"EC,TITLE(S),THRSHLO,TEMPMIN,TENPMAX,TCOEFF,USEMEAN
COMMON
COMMON XMAX,USEPOT,SL0PEIASPECT,XLAT,0ELH,ABSK,CLC0V,ZATISUM4
COMMON KKPP,XLATE
ACTOATE,DATE,OATES,FOOTNOT,PASTINT,PLOTOES,PLOTWEISUBTITL
INTEGER
TITLE,USEMEAN,USEPOT
INTEGER
COMMON/CONVERT/FIVE9TN , THIR T Y 2
NET SHORT WAVE RADIATION AS A
COMPUTE THE CALORIC INPUT FROM
FUNCTION OF THE REFLECTIVITY
IF(USEPOT) 110,110,120
••
89
120 CALL SOLAR
110 RAOSWN= RADIN*(1.0-PEFLECT)*TCOEFF
IF
THE PRECIP WAS SNOW, THE NET LONG WAVE RADIATION BALANCE IS
ASSUMED TO BE ZERO
IF(ISNOW) 20,20,10
10 RADLWN
0.0
GO TO 50
TO COMPUTE THE LONG WAVE RADIATION COMPONENTS, CCNVERT THE AIR
AND SNOW TEMPERATURES TO POTENTIAL CALORIES BY THE STEFAN BLOTZMANN FUNCTION, CALORIES . S * (T ** 4), WHERE
C
S = 1.17E-7 CAL/((CH**2)(DEGRFES KELVIN)**4), AND
T = ABSOLUTE TEMPERATURE (DEGREES KELVIN)
20 CALAIR = 1.17E-7 * ((AVETEIC + 273.16) ** 4)
)/2) - THIRTY2)* FIVE9TH
(((TEMPMIN +
32.0
USE
UNDER NO CIRCUMSTANCES MAY THE TEMPERATURE FOR COMPUTING THE BACK
RADIATION BE GREATER THAN ZERO
IF(USE.GT.0.0) USE = 0.0
1.17E-7 * ((USE + 273.16) ** 4)
CALSNOW
COMPUTE THE LONG WAVE RADIATION COMPONENTS AS A FUNCTION OF THE
FIRST, DETERMINE WHETHER THE SKIES ARE CLEAR OR CLOUDY
IF(PRECIP) 30,30,40
WITH CLEAR SKIES, THE DOWNWARD LONGWAVE RADIATION COEFFICIENT IS
.757 (RUNOFF FROM SNOWMELT, EH 1 110-2-1406, US ARMY CORPS OF
C.
ENGINEERS, 1960, PAGE 7)
30 SNOSKY
(1.0 - COVDEN) * ((0.757 * CALAIR) - CALSNOW)
THE DOWNWARD LONG WAVE RADIATION COEFFICIENT IS 1.0 BENEATH THE
FOREST CANOPY (OR BENEATH CLOUDY SKIES)
SNOCAN = COVDEN * (CALAIR - CALSNOW)
RADLWN = SNOCAN + SNOSKY
GO TO 50
WITH CLOUDY SKIES, WHEN THE DOWNWARD LONGWAVE RADIATION COEFFICIFNT IS 1.0 INSTEAD OF .757, THE ABOVE THREE EQUATIONS MAY BE
c
REDUCED ALGEBRAICALLY TO THE FOLLOWING SINGLE EQUATION
40 RAOLWN = CALAIR - CALSNOW
OF SHORT
COMPUTE THE CALORIC INPUT OR LOSS FROM THE NET EFFECT
WAVE
RADIATION
WAVE AND LONG
50 CALORIE = RADSWN + RADLWN
70 IF(CALORIE) 80,90,100
80 IF(CALDEF) 90,90,95
90 CALL CALOSS (CALORIE)
RETURN
95 CALL DIFMOD
RETURN
100 IFIRST = 0
CALL GALIN (CALORIE)
RETURN
ENO
SUBROUTINE RAINED (TFORAIN,AMTRAIN)
OF RAIN ON SNOW
THIS SUBROUTINE COMPUTES THE EFFECT
C
C
DICTIONARY
C
PRECIPITATION OCCURRING AS RAIN (INCHES)
CAMTRAIN - THE AMOUNT OF
OF
THE TOTAL CALCRIE DEFICIT BY THIS RAIN
DEPLETION
THE
C
ALRAIN
C
C
(CALORIES)
FOR COMPUTING THE DEPLETION OF THE TOTAL
THIS RAIN (DEGREES C)
CTFORAIN - THE TEMPERATURE
DEFICIT CAUSED 9Y
CCALORIE
C
COMMON ACTDATE,ACTUAL(21),AVETEMC,AVETEMF,BASTEMFIENGBAL1HOLOCAP
90
COMMON CALAIR,CALDEF,CALORIE,CALSNOW,COVDEN,DATE,DATES(3),DEN
COMMON DENSITY,IFIRST,FOOTNOT(16),FREWAT,IDATE(372),IS000,ITABLE
COMMON KOUNT,LASTUSO,LINES,OBSWEOV,RODIN,RADLWN,PADSWN,RFFLECT
COMMON PACKT[H,PARTICE,PASTINT,PLOTO3S,PLOTOF,QUCIP,PREMEOV
COMMON SNOMELT,ODSCOV(372),PRECIP(372),SPRFOV(72),SU3TITL(8)
COMMON TOTPREC,TITLE(8),THRSHLD,TEMPMIN,TEMPMAX,ICOEFF,USEMEAN
COMMON XMAY , USEPOT,SLOPE,ASPECT,XLAT,DELH,ABSK,CLCOV,ZAT,SUM4
COMMON KKPP,XLATE
INTEGER ACTDATE,DATE,DATES,FOOTNOT,PASTINT,PLOTOBS,PLOTWE,SUBTITL
INTEGER TITLE,USEMEAN,USEPOT
DD THIS AMOUNT OF PRECIPITATION TO THE PREDICTED WATER EQUIVALENT
A
PREWEOV
SEE
PREWEOV + AMTRAIN
IF THERE IS A CALORIE DEFICIT IN THE PACK
IF(CALCEF.LE.0.0) GO TO 50
COMPUTE THE AMOUNT OF RAIN AT THIS TEMPERATURE THAT IS NEEDED TO
WIPE OUT THE DEFICIT AND COMPARE IT WITH THE ACTUAL AMOUNT
AMTNEED
CALDEF/((80.0 + TFORAIN) * 2.54)
COMPARE = AMTRAIN - AMTNEED
IF(CCMPARE) 20,10,40
THERE WAS JUST ENOUGH TO WIPE OUT THE DEFICIT
10 CALDEF
0.0
PACKTEM = 0.0
GO TO 30
THERE WAS NOT ENOUGH TO WIPE IT OUT COMPLETELY. JUST DEPLETE
THE DEFICIT
20 CALDEF = CALDEF - ((80.0 + TFORAIN) * AMTRAIN * 2.54)
PACKTEM = -CALDEF/(PREWEDV*1.27)
ADD ALL THE RAIN TO THE PACK AS ICE AND GET THE NEW HOLDING
CAPACITY
C
30 PARTICE = PARTICE + AMTRAIN
HOLDCAP = 0.04 * PARTICE
RETURN
THERE WAS MORE THAN ENOUGH TO WIPE OUT THE DEFICIT. ADD THE
FROZEN PART TO THE ICE AND GET THE NEW HOLDING CAPACITY
40 CALDEF = 0.0
PACKTEM = 0.0
PARTICE = PARTICE + AMTNEED
HOLDCAP = 0.04 * PARTICE
AMOUNT OF RAIN NOT FROZEN IS FREE WATER AND CONTRIBUTES
CALORIC INPUT TO THE PACK
THE
FREEWAT = COMPARE
CALL GALIN (TFORAIN * COMPARE * 2.54)
RETURN
ALL OF THE RAIN IS ADDED TO THE FREE WATER AND CONTRIBUTES CALORIC
INPUT TO THE PACK
50 FREEWAT = FREEWAT + AMTRAIN
CALL CALIN (TFORAIN * AMTRAIN * 2.54)
RETURN
END
SUBROUTINE READER (IEND)
SUBROUTINE READS A DATA CARD AND COMPUTES THE AVERAGE
TEMPERATURES
HOLDCA P
COMMON ACTDATE0ACTUAL(21),AVETEM0,0VETE 4 F , EA 5 TEMF , ENGBAL ,
COMMON CALAIR,CALDEF,CAL0RIE,C0LSN0W , COV 0 EN , DATE , D A T ES(3),DEN
COMMON DENSITY,IFIRST,FOOTNOT(16),FREEWAT,IDATE(372),ISNOW,ITABLE
DSWN,REFLECT
COMMON KOUNT,LASTUSD,LINES.00SWEOV , RADIN , RADLWN , RA
,PRECIP,PREWEOV
COMMON PACKTEM,PARTICE,PASTINT , PLOTOBS , PLO T WE
(372),SUBTITL(8)
'COMMON SNOMELT,SOBSEQV(372),SPRECIP (372), S P REOV
THIS
•
91
COMMON TOTFREC,TITLE(0),THRSHLD,TEMPMIN,TEMPMAX,TCOFFF,DSEMEAN
COMMON XMAX,USEPOT,SLOPE,ASPECT,XLAT,DELH,ABSK,CLCOV,ZAT,SUM4
COMMON KKPP,XLATE
INTEGER ACTDATE,DATE,DAT ,7 S,FOOTNOT,PASTINT,PLOTOPS,FLOTWE,SUBTITL
INTEGER TITLE,USEMEAN,OSEPOT
COMMON/CONVERT/FIVE9TH,THIRTY?
READ
A CARD AND CHECK FOR THE END OF FILE
READ(5,900)DATES,RADIN,TEMPMAX,TEMPHIN,OBSWEGV,PRECIP,DEN,CLCOV,
1NEXTACT
900 FORMAT(3I2,F4,0,7X,2F4.1,14X,4F5.2,10X,I1)
IF(E0F(5)) 20,20,10
10 TEND
1
RETURN
20 IEND = 0
DATE . OATES(1)*10000
IF(DATE) 70,70,30
DATES(2)*100 + DATES(3)
COMPUTE THE MEAN TEMPERATURE IN FARENHEIT, THEN CONVERT IT TO
CENTIGRADE
30 AVETEMF
(TEMPMAX + TEMPMIN) * 0.5
AVETEMC = (AVETE(IF - THIRTY?) * FIVE9TH
IF(USEMEAN) 70,70,40
40 TEMPMAX = AVETEMF
TEMPMIN = AVETEMF
70 RETURN
END
SUBROUTINE SNOWED (TFORSNO,AMTSNOW)
THIS SUBROUTINE COMPUTES THE EFFECTS OF A SNOW EVENT ON THE
SNOWPACK
DICTIONARY
•
•
AMTSNOW - THE AMOUNT OF PRECIPITATION OCCURRING AS SNOW (INCHES)
CALSNOW - THE CONTRIBUTION OF THIS SNOW TO THE TOTAL. CALORIE
•
TFORSNO - THE TEMPERATURE FOR COMPUTING THE CONTRIBUTION OF THIS
SNOW TO THE TOTAL CALORIE DEFICIT (DEGREES C)
DEFICIT (CALORIES)
COMMON ACTDATE,ACTUAL(21),AVETEMC,AVETEMF,BASTEMF , ENGBAL , HOLDOAP
COMMON CALATR,CALDFF,CALORIE,CALSN0W,COV 0 EN , DATE , DATES (3), DEN
COMMON DENSITY,IFIRST,FOOTNOT(16),FREEWAT , I 0 ATEC 7 ? ), ISNOW , I TABL E
T
COMMON KOUNT,LASTUSD,LINES,OBSWEOV,RADIN,RADLWN , FADSWN , REFLEC
COMMON PACKTEM,PARTICE,PASTINT,PLOTOBS,PLOTWE , PRCIP , P R EWEOV
COMMON SNOVELT,SOBSEOV(372),SPRECIP(3 72 ),SPREOV (372), SU 3 TITL (8)
COMMON TOTPREC,TITLF(8),THRSHLD,TEMPMIN , TEMPMAX“C 0 E FF,U0 E MEAN
COMMON XMAX,USEPOT,SLOPE,ASPECT,XLAT,OELH , ABSK , CLCOV , Z A T , SUM 4
COMMON KKPP,XLATE
U BTITL
INTEGER ACTDATF,DATE,DATES,FOOTNOT,PASTINT , PLOTOBS , PLOTWE ,S
TITLE,USEMEAN,USEPOT
INTEGER
ISNOW = 1
PREDICTED WATER EQUIVALENT
ADD THIS AMOUNT OF PRECIPITATION TO THE
CAPACITY
HOLDING
NEW
AND GET THE
RREWEQV = PPEWEQV + AMTSNOW
PARTICE = PARTICE + AMTSNOW
HOLDCAP = 0.04 * PARTICE
AND 32 DEGREES
THE SNOW FALLING WHEN THE TEMPERATURE IS BEThEEN 35
DOES NOT ALTER THE CALORIC DEFICIT
IF(TFORSNO.GE.0.0) RETURN
EQUATION
COMPUTE THE CALORIE DEFICIT FOR THIS SNOW BY THE
•
92
CALORIE DEFICIT = S(I)DELTA T*P, WHERE
S(I) = SPECIFIC HEAT OF ICE (.5 CAL/CM/DEGREES C),
DELTA T = CHANGE IN TEMPERATURE WITH RESPECT TO FREEZING (0.0
DEGREES CENTIGRADE), AUD
P = PRECIPITATION IN CH (CONVERSION FACTOR = 2.54 CH/IN).
THEREFORE, CALORIE DEFICIT = 0.5 * (TFORSNO) * (AMTSNOW * 2.54)
CALL CALOSS (TFORSNO * AMTSNOW * 1.27)
RETURN
ENO
•
•
•
•
•
•
•
C
•
•
•
•
•
SUBROUTINE SOLAR
THIS SUBROUTINE IS DESIGNED TO COMPUTE THE AMOUNT OF INCOMING
SOLAR RADIATION INCIDENT ON A GIVEN SURFACE DURING CLEAR SKY.
DICTIONARY
ADSK - ABSORPTION COEFFICIENT FOR THE ATMOSPHERE
ASPECT - AZIMUTH ANGLE, DEGREES FROM NORTH
COSZ - COSINE OF ZENITH ANGLE(Z)
D - INCOMING DIFFUSE BEAM RADIATION, LYS/MIN
DELH - CHANGE IN HOUR ANGLE(H),MINUTES
DRATIO - RATIO OF DIFFUSE TO DIRECT BEAM RADIATION AS A FUNCTION
OF Z
H - HOUR ANGLE
HI - HOURS
H2 - MINUTES
OP - OPTICAL PATH
Q - INCOMING DIRECT BEAM RADIATION, LYS/MIN
OPOT - POTENTIAL DIRECT BEAM RADIATION ON A NORMAL SURFACE ABOVE
THE EARTH S ATMOSPHERE, LYS/MIN
S - SOLAR CONSTANT, 2 LYS/MIN
SLOPE - SLOPE, PERCENT
XDEC - SOLAR DECLINATION
XLAT - LATITUDE, DEGREES
Z- ZENITH ANGLE
COMMON ACTDATE,ACTUAL(21),AVETEMC,AVETEMF,BASTEMF , ENGBAL , HOLOCAP
COMMON CALAIR,CALDEF,CALORIE,CALSNOW,COVDEN,DATE,DATES (3), DEN
COMMON DENSITY,IFIRST,FOOTNOT(16),FREEWAT,IDATE( 37 2 ) ,ISNOW , ITABLE
COMMON KOUNT,LASTUSO,LINES.OBSWEOV,RADIN,RAOLWN , RADSWN , REFLECT
COMMON PACKTEM,FARTICE,RASTINT,PLOTOBS,PLOTWE,PRECIP , PREWEOV
COMMON SNOMFLT,SOBSECV(372),SPRECIP(372),SPRE0V (372), SUBTITL (8)
COMMON TOTPRFC,TITLF(8),THRSHLD,TEMPHIN,TE1PMAX,TC 0 EFF , USEMEAN
COMMON XMAX,USEROT,SLOPE,ASPECT,XLAT,DELM,ABSK , CLCOV , ZAT , SUM 4
COMMON KKPP,XLATE
INTEGER ACTDATE,DATE,DATES,FOOTNOT,PASTINT,PLOTOPS , PLOTWE , SUBTITL
INTEGER TITLE,USEMEAN,USEPOT
DIMENSION ZCLAN(12)
DATA ZCLAN/0.0,31.0,59.0,90.0,120.0,151. 0,181 . 0,212 . 0,243 . 0,
+273.0,304.0,334.0/
PI = 3.14159265
S = 2.0
IF(KKPF.NE.5) GO TO 902
DELT = DELH
K = (24.*60.)/DELH
DELH = (DELH/60.)*15./180. * PI
XLATE = XLAT
XLAT = (XLAT/180)*PI
SLOPE = ATAN(SLOPE/100)
ASPECT =-(ASPECT/180.)*PI
902 KKPP = KKPP + 1
IF(KKPP.LT.5) GO TO 103
93
KKPP = 0
H = PI
SUM1 =0.
SUM2 =0.
SUM3 =0.
IDS =0ATES(11
X = ZCLAN(TOB)
DAY = OATES(2) + X
IF(DAY.GE.355) GO TO 114
DAY = DAY + 11
GO TO 115
114 DAY = DAY - 355
115 XOEC = -.41015*(COS(DAY* 0 1/183))
X3 = SIN(SLOPE)*COS(ASPECT)*COS(XLAT)+COS(SLOPE)*SIN(XLAT)
X4 = ((1.-X3**2)**0.5)*COS(XDFC)
X5 = ATANNSIN(SLOPE)*SIN(ASPECT))/(COS(SLOPE)*COS(XLAT)-SIN(SLOPE
.)*COS(ASPECT)*SIN(XLAT)))
X6 = X3 4 SIN(XOEC)
DO 100 I=1,K
H = H-OELH
COSZ = SIN(XLAT)*SIN(XDEC)+COS(XLAT)*COS(XDEO)*COS(H)
IF(COSZ.LT.0.) GO TO 100
Z=ACOS(COSZ)*(180./PI)
QPOT=S*COSZ
IF(Z.LT.60.) GO TO 10
IF(Z.LT.70.) GO TO 11
IF(Z.LT.80.) GO TO 12
IF(Z.LT.85.) GO 10 13
OP = -567+6.8*Z
GO TO 20
10 OP = 1.+0.0167*Z
GO TO 20
11 OP = -4.+0.1*Z
GO TO 20
12 OP = -18.+0.3 4 Z
GO TO 20
13 OP =
=0P0T*(1./(2.71828**(ABSK4OP)))
20 0
IF(Z.LT.30.) GO 10 30
IF(Z.LT.50.) GO 10 31
IF(Z.LT.70.) GO 10 32
IF(Z.LT.80.) GO TO 33
DRATIO = -5.8+0.08*Z
GO TO 40
30 DRATIO = 0.12+0.000667 4 Z
GO TO 40
31 DRATIO = 0.065+0.0025*Z
GO TO 40
32 ()RATIO = -0.135+0.0065 4 Z
GO TO 40
33 DRATIO = -1.64+0.028*Z
Q4DRATIO
40 D =
IF(SLOFE.E0.0.) GO 10 50
4 ((PI-SLOPE)/PI)
= D
D
OPOT=S 4 (X4*COS(H 4 X5)+X 6 )
IF(OPOT.GT.0.) GO TO 50
OPOT = Q.
=OPOT*(1./(2.71828**(A8SK*0P)))
50 0
QTOTAL = 0+0
SA = 90.-Z
94
61 sUM1 = SUM]. +
SUM2 = SUM2 +
SUM3 = SUM3 +
100 CONTINUE
101 CONTINUE
SUM 4 = SUM2 +
103 CONTINUE
OPOT*OELT
(MELT
D 4 0ELT
S0M3
CALL CLOUD
RETURN
END
SUBROUTINE STORE
STORE THE INFORMATION NEEDED FOR THE PLOT
COMMON ACTDATE,ACTUAL(21),AVETE1C,AVETE1F,BASTEmF,ENGBAL,HOLDCAP
COMMON CALAIR,CALDEF,CALORIEICALSNoW,00VOEN,DATE,DATES(3),DEN
COMMON DENSITY,IFIRST,FoOTNOT(16),FREEWAT,IOATE(372),ISNOW,ITABLE
COMMON KOUNT,LAsTUSO,LINES,OBSWEOV,RADIN,RADLWN,RADSWN,REFLECT
COMMON FACKTEM,RARTICE,PASTINT,PLOTOBS,PLOTWE,PREcIP,PREWEQV
COMMON SNOMELT,SOBSEQV(372),SPRECIP(372),SPREDV(372),SUBTITL(8)
COMMON TOTPREC,TITLE(8),THRSHLD,TEMPMIN,TEMPMAX,TCCEFF,USEMEAN
COMMON XMAX,USEPOT,SL0PE,ASPECT,XLAT,DELHIABSK,CLCOV I ZAT,SUM4
COMMON KKPP,XLATE
INTEGER ACTDATF,DATE,DATESIFOOTNOT,PASTINT,PLOTOCS,PLOTWE,SUBTITL
INTEGER TITLE,USENEAN,USEPOT
KEEP TRACK OF THE LARGEST VALUE FOR SCALING THE FLOT
XMAX = AMAX1 (XMAX,OBSWEQV,PREWEOV)
INCREASE THE COUNTER
KOUNT = KOUNT + 1
IDATE(KOUNT) = DATE
SPRECIP(KOUNT) = PRECIP
SPREOV(KOUNT) = PREWEGIV
IF(PLOTOBS) 10,10,20
BY STORING A NUMBER OUTSIDE THE LIMITS OF THE PLOT, IT WILL BE
IGNORED
10 SOBSEDV(KOUNT) = -1.0
RETURN
THE OBSERVED WATER EQUIVALENT IS TO BE PLOTTED
20 SOBSEQMOUNT) = OBSWEQV
RETURN
END
SUBROUTINE TS2LOT(MX,X1,X2,X3,X4,X5,X6,XMAX,XMIN,IT,INT,INIT)
HIS ROUTINE DOES THE ACTUAL PLOTTING
T
1 JULY, 1962
C. HWANG, A.G. HOGGATT
ARGUMENTS
C
MX=NUMBER OF VARIABLES TO RE PLOTTED, LESS THAN OR EQUAL TO 6
C X1=VALUE ATTACHED TO FIRST VARIABLE. PLOTTING SYMBOL WILL BE A 1.
C X2=VALUE ATTCHED TO SECOND VARIABLE. PLOTTING SYMBOL WILL BE A 2.
C
C
C
C
C
C
C
C
C
C
X3
.
X6 AND SO ON FOR XN
XMAX=UPPER END OF ORDINATE SCALE
XMIN=LOWER END OF ORDINATE SCALE
IT =ABCISSA VALUE. (I.E., T, FOR XI)
INT=ABCISSA LABELLING INTERVAL. (I.E., EVERY ICHTH LINE OF PLOT
WILL BE LABELLED WITH VALUE OF IDY ON HORIZONTAL AXIS)
INIT =INITIALIZING PARAMETER, USED AS FOLLOWS.
95
INIT
=1, GRAPH WILL COMPUTE AND P RUNT ORDINATE, PLOD
C AND PRINT FIRST LINE OF GRAPH. SURSEQUENT CALL WILL PLOT AND PR+NT
C A LINE OF GRAPH ONLY.
INIT =-1 USED TO READY SUBROUTINE FOR PLOTTING NEW GRAPH.
C SUBROUTINE DOES NO PLOTTING OR PRINTING WITH THIS SETTING OF INIT.
IF THE VALUE OF SCALING PARAMETERS XMIN AND/OR XMAX DIFFER FROM
THE PREVIOUSLY GIVEN ONES WITHOUT RESETTING OF INIT,IS PLOT
WILL RESET SCALE ACCORDING TO HEW XMIN AND/OR XMAX AND PRINT CUT
C
C
C
C
C
NEW ORDINATE POINT VALUES TO AGREE WITH SCALING OF PLOTTED POINTS
INTERNAL VARIABLES
CHARS CONTAINS BCD CHARACTERS USED AS PLOTTING SYMBOL.
PLOT HOLDS THE HOLLERITH IMAGE FOR ONE LINE OF FLOT.
XN. SCALAR ARGUMENTS ARE STORED IN THIS LINEAR ARRAY.
DELTA IS A SCALING PARAMETER, EQUAL TO THE RANGE DIVIDED BY 110, AND
IS RECOMPUTED WHEN NEW SCALE IS INDICATED (4HEN TWIT =1 OR WHEN
XMAX OR XMIN VALUE DIFFERING FROM PREVIOUS VALUE IS GIVEN).
PASMIN, PASMAX, ARE FCR REMEMBERING PREVIOUS VALUE OF XMIN, XMAX.
DIMENSION CHARS(8), PLOT(111), OROPT(6), XN(6)
EQUIVALENCE(OROPT(6),PLOT(6))
CHARS(1) 1 1H11, CHARS(2) 1 1H21, CHARS(3)/11 -131, CHARS(4)/1H4/,
*CHARS(5)/1H5/, CHARS(6)/1H6/, CHARS(7)/1H /, CHARS(8)/1H./
DATA NCALLS/0/,NDY/0/
IF(INIT)1000,1000,9001
DATA
CALL WAS TO INITIALIZE ONLY....
1000 NDY=0
NCALLS=0
GO TO 701
COMMENCE BY PROTECTING THE INDEX MX
9001 M=HAXO(MX11)
M=MINO(M,6)
CONJURE PLOTTING CHARACTERS
3 XN(1)=X1
XN(2)=X2
XN(3)=X3
XN(4)=X4
XN(5)=X5
XN(6)=X6
IF(NDY) 15,15,28
28 IF(PASMAX-XMAX) 45,40,45
43 IF(PASMIN-XMIN) 45,80,45
15 NDY=1
COMPUTE AND PRINT ORDINATE POINTS, SCALE.
45 AN=(XMAX-XMIN)*.2
OROPT(1)=XMIN
NCALLS = 0
DO 17 1=2,6
17 OROPT(I)=OROPT(I - 1)+AN
WRITE (6,100) (ORDFT(N),N=1,6)
00 705 N=1,2
WRITE (6,101)
705 CONTINUE
9X1H.,5(21X1H.))
101 FORMAT(
WRITE (6,800)
9X111(1H.))
800 FORMAT(
100 FORMAT(1H1,4(E10.3,12X),E 10 . 3 1 11 X , E 10.3)
DELTA=(XMAX - XMIN)/110.
CLEAR PRINTER LINE.
80 DO 99 K=2,111
PLOT(K)=CHARS(7)
99 CONTINUE
96
PLOT(1)=CHARS(8)
CAUSE X TO GE PUT ON THE INTERVAL (1,111).
20 00 34 N=1,11
LOC=1.54- (XN(N)-XMIN)/DELTA
CHECK FOR X WITHIN THE INTERVAL (XMIN,XMAX),
IF(LOC) 34,34,611
811 IF(111-L0C) 34,814,814
CHARACTERS FOR PRINTING NOW GET DROPPED INTO PLACE.
814 PLOT(LOC)=CHARS(N)
34 CONTINUE
CHOOSE OUTPUT FORMAT.
NCALLS=NCALLS4-1
IF(MOD(NCALLS,INT)) 815,2004,815
CRANK OUT ONE LINE OF PLOT.
2004 WRITE (6,700) ITI(PLOT(K),K=1,111)
GO TO 702
700
815
600
702
FORMAT(1H
I6,2H..111A1)
WRITE (6,600) (PLOT(K),K=1,111)
FORMAT(9H
111A1)
PASMAX=XMAX
PASMIN=XMIN
CODING COMPLETED.
701 RETURN
ENO
SUBROUTINE WRITER (CODE)
SUBROUTINE KEEPS TRACK OF THE PRINTING DETAILS
COMMON ACTDATE,ACTUAL(21),AVETEMC,AVETEmF,GAsTEMF,FNGBAL,HOLDCAR
COMMON CALAIR,CALDEF,CALORIE,CALSNoW,COVCEN,CATE,DATES( 3 ),DEN
COMMON DENSITY,IFIRST,FOOTNOT(15),FREEWAT,IDATE(Z;72),ISNOW,ITABLE
COMMON KOUNT,LASTuSO,LINES,OGSNEOV,RADIN,RADLNN,RADSWN , REFLECT
COMMON RACKTEm,PARTICE,PASTINT,PLOTODS,PLOTWE,PRECIP , PRFNEOV
COMMON SNONELT,SOBSEOV(372),SPRECIP(372) , SPPEOV( 372), SUBTITL (8)
COMMON TOTFREC,TITLE(8),THRSHLD,TEMPMIN,TEMPmAX,TCOEFF , USEMEAN
COMMON XMAX,USEFoT,SLOPE,ASPECT,XLAT,DELP,ABSK , CLCCV , ZAT ,5 U 14
COMMON KKPP,XLATE
INTEGER ACTDATE,DATE,DATES,FOOTNOT,PASTINT, P LOTOPS , FLOTNE , SUBTITL
INTEGER TITLE,USEMEAN,USEPOT
HECK THE LINE COUNTER
C
THIS
IF(LINES
SEE
48) 40,10,10
IF THIS IS STARTING A NEW STATION - IF SO, BYPASS THE FOOTNOTE
10 IF(LINES - 999) 20,30,30
WRITE THE FOOTNOTE
20 WRITE (6,910) FOOTNOT
910 FORMAT(1H013A10/1X3A10)
HEADINGS
30 WRITE (6,920) TITLE,SUBTITL
920 FORMAT(1H150X*SNOWMELT RUNOFF SIMULATION MODEL*/27X8A10/27X8A10)
WRITE (6,930) TCOEFF,COVDEN
=*F7.2
930 FORMAT(* TRANSMISIVITY COEFFICIENT =*F4.2,74X*COVER DENSITY
1)
WRITE (6,940)
NET RAD (CAL)
PRECIP (IN)
940 FORMAT(*O*32X*TEmPERATURE (F) ICTED/
D
SNONPACK
PRE
1ENERGY
LONG B
SHORT
DAY ACCUM
AVE
MIN
MAX
223X*0ATE
W.E. (IN)*/)
TEMP (C)
3AL (CAL)
LINES = 0
40 WRITE (6,950) DATES,TEMpMAX,TEMPmIN,AVETEMF,PRECIP,TOTPREC,RADSWN,
RAOLWN,ENGBAL,PACKTEM,PREWEQV
97
950 FORMAT(1H020XI2,2I 7i0A3F6.112F7.2,3X3E8.1.,6XF5.1,5XF6.2)
LINES = LINES + 2
RETURN
ENO
APPENDIX C
FLOW CHART FOR SUBROUTINE SOLAR
98
99
SOLAR
Initialize counters and variables
Compute the number of days since winter solstice
1
Add an increment to sun's path
----
Calculate optical path from zenith angle
L
Calculate direct beam radiation on a flat surface
Calculate ratio of insolation that is diffuse beam
Calculate direct and diffuse beam accounting for slope
Add direct and diffuse beam components
Add the insolation for this interval to the daily accumulated insolation
[Call CLOUD
APPENDIX D
FLOW CHART FOR SUBROUTINE DIFMOD
100
101
Normalize minimum air temp. and 0°C to a 0 to 1.0 scale
Calculate snowpack density
Determine an average snowpack temp.
1.
Normalize temperatures throughout the snowpack
----
Calculate new t
throughout a
s over succesive time-steps
approximations
pack temperatures to be used
Establish the array
array
and
calorie
deficit
for the next day
as the
Determine the calorie deficit and average pack temp.
(RETURN)
APPENDIX E
STANDARDIZING EQUATIONS FOR SOLAR SENSORS USED IN THE
FOREST TRANSMISSIVITY STUDY
Sensor 2,5k
sensor 49
Y = 0.18714 + 0.830X
Sensor 2 ,54ys, sensor 9.35
Y = 0.54319 + 0.820X
Sensor 2.54 vs, sensor=2
Y = 0.38158 0.818X
E212=2_04 vs. sensor /a
Y = 0.27843 4' 0.93 21
Sensor 2,54 vs. sensor 486
Y = 0.58657 + 0.814X
102
APPENDIX F
CORRELATION MATRIX OF REGRESSION VARIABLES
1 03
104
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LITERATURE CITED
Anderson, Henry W. 1967. Watershed modeling approach to evaluation
of hydrologic potential of unit areas. International
Symposium on Forest Hydrology, Proc. PP , 737-748 ,
Avery, T. Eugene. 1967. Forest measurements. McGraw-Hill Book
Company. New York. 290 p.
Barr, George W. (Editor). 1956. Recovering rainwater. Dept. of Agr.
Economics. Univ. of Arizona. 33 p.
Bergen, James D. 1968. Some observations on temperature profiles of
a mountain snow cover. USDA Forest Service Res, Note PM-lb.
7p.
Bethlahmy, Nedavia. 1973. Water yield, annual peaks and exposure in
mountainous terrain. Jour. of Hydrology. 20:155-169.
Brown, Harry E. 1962. The canopy camera. USDA Forest Service Res,
Paper RM-72, 22 p.
Brown, Harry E. 1971. Evaluating watershed management alternatives.
Jour, of Irrig, and Drain, Division ASCE. 97:93-1 0 8.
Cambell, Ralf E. 1972. Prediction of air temperature at a remote site
from official weather station records. USDA Forest Service
Res. Note RM-223. 4 p.
Carnahan, Bruce, H. A. Luther and James D. Wilkes, 1969. Applied
numerical methods. John Wiley and Sons, Inc. New York. 605 p.
Chow, Ven Te. 1964. Handbook of applied hydrology. McGraw-Hill Book
Company. New York. 1505 p.
Wiley and Sons,
Cochran, William G. 1965. Sampling techniques. John
Inc. New York. 413 p.
estimating of precipitation
Corbett, Edward S. 1965. Measurement and
Symposium on Forest
experimental
watersheds.
International
on
Hydrology, Proc. pp. 107-129.
Evapotranspiration and other
Croft, A. R. and L. V. Monninger. 1953, types in relation to water
water losses on some aspen forest
Geophys. Union. 34:
available for streamflow. Trans. Am.
563-574.
1 05
106
Department of Watershed Management, 1
974. Validation and refinement
of resource response models on sandstone
and alluvial soils in
ponderosa pine type. Annual Report. Univ. of Arizona.
60 p.
Federer, C. A. 1968. Radiation and snow melt
on a clearcut watershed.
Eastern Snow Conference, Proc. pp.
2 8-42.
-
Ffolliott, Peter F. 1966. An overstory inventory
of the ponderosa
pine watersheds on Beaver Creek, USDA Forest Service, Rocky Mtn.
For. and Range Exp. Sta. Unpublished office
report. 72 p.
Ffolliott, Peter F. 1970. Characterization of Arizona snowpack
dynamics for prediction and management purposes. Unpublished
Ph. D. dissertation. Univ. of Arizona. 171 p.
Ffolliott, Peter F. and Edward A. Hansen. 1968. Observation
of snow
accumulation, melt and runoff on a small Arizona watershed.
USDA Forest Service Res, Note RM-124. 7 p.
Ffolliott, Peter F. and David B. Thorud, 1972a. Use of forest
attributes in snowpack inventory-prediction relationships for
Arizona ponderosa pine. Jour. of Soil and Water Conservation.
27:109-111.
Ffolliott, Peter F. and David B. Thorud, 1972b. Observation of
snowpack profiles in and adjacent to forest openings.
Unpublished report. Univ. of Arizona. 9 p.
Ffolliott, Peter F. and David B. Thorud. 1974. Vegetation management
for water yield in Arizona. Univ. of Arizona Agric. Exp. Sta,
Tech, Bulletin 215. 38 p.
Fisher, William C. and Charles E. Hardy. 1972. Fire-weather observers'
handbook. USDA Forest Service. Intermountain Forest and
Range Exp. Sta, Ogden, Utah. 152 p.
Fohn, Paul M. B. 1973. Short-term snow melt and ablation derived from
heat and mass-balance measurements. Jour. of Glaciology.
12:275-289.
Frank, Ernest C. and Richard Lee. 1966. Potential solar beam
irradiation on slopes. USDA Forest Service Res, Paper RM-18.
116 p.
Freeman, T. G. 1965. Snow survey samplers and their accuracy. Eastern
Snow Conference, Proc. pp. 1-10.
Garn, Herbert Sigfried. 1969. Factors affecting snow accumulation,
melt and runoff on an Arizona watershed. Unpublished Master's
thesis. Univ. of Arizona. 155 p.
1 07
Garstka, W. U., L. D. Love, B. C. Goodell and F. A. Bertle,, 1958,
Factors affecting snowmelt and stroamflow. USDA Forest Service.
Govt. Printing Office. 189 p.
Gates, David Murry, 1962. Energy exchange in the biosphere. Harper
and Row, New York. 151 p.
Gopen, Stuart Rogers, 1974. A time-space technique to analyze
snowpacks in and adjacent to openings in the forest. Unpublished
Master's thesis. Univ. of Arizona. 77 p.
Gray, Howard L. and George B. Coltharp. 1967. Snow accumulation and
disappearance by aspect and vegetation type in the Santa Fe,
New Mexico, USDA Forest Service Res, Note RM-95„ 11 p.
Holtran, H. N., N. E, Minshall and L. L. Harrold. 1962. Field mannual
for research in agriculture hydrology. USDA Soil and Water
Conservation Res. Div, Agriculture Handbook No. 224 , 215 P.
Hutchison, Boyd A. 1962. A comparison of evaporation from snow and
soil surfaces. USGI International Assoc. Sci, Hydrology,
11:34 42.
-
Jones, Mikeal Edgar. 1974. Differencial release of water from Arizona
snowpacks. Unpublished Master's thesis. Univ. of Arizona.
53 P.
Leaf, Charles F. 1971. Areal snow cover and disposition of snowmelt
runoff in central Colorado. USDA Forest Service Res. Paper
RM 66. 16 p.
-
Leaf, Charles F. and Glen E, Brink, 1972. Computer simulation of
snowmelt within a Colorado subalpine watershed. USDA Forest
Service Res, Paper RM-99, 22 p.
simulation
Leaf, Charles F. and Glen E. Brink. 1973. Hydrologic
Service Res.
Forest
forest.
USDA
model of a Colorado subalpine
Paper RM-107. 23 p.
Sampling requirements
Leaf, Charles F. and Jacob L. Kovner. 1972.
forested subalpine
in
for areal water equivalent estimates
8:713-716.
Research.
watersheds. Water Resources
insolation through pine forests
Miller, David H. 1959. Transmission of
Schweiz. Anst, F.
canopy as it affects the melting snow,
Forstl. Versuchsw. Mitt. 35:57 79.
-
1973. Water yield characteristics
Orr, Howard K. and Tony VanderHeide.
Black Hills of South Dakota.
of three small watersheds in the
RM-100. 8 p.
USDA Forest Service Res. Paper
10 8
Price, Raymond. 1967. Possibilities of increasing streamflow from
forest and range watersheds by manipulating the vegetative
cover. International Union For. Res, Organ. XIV IufroKongress. 1:487-504.
Rantz, S. E. 1964. Snowmelt hydrology of a Sierra Nevada stream,
USGS Water-Supply Paper 1779-r , 36 P.
Reifsnyder, William E, and Howard W. Lull , 1965. Radiant energy in
relation to forests, USDA Forest Service Tech, Bulletin 1344.
111 p,
Sehwerdfeger, P. 1963. Theoretical derivation of the thermal
conductivity and diffusivity of snow. USGI Int. Assoc. Sci,
Hydrology Comm. Pub. 61. PP. 75-81.
Sellers, William D. 1969. Physical climatology. The Univ. of Chicago
Press. Chicago. 272 p.
Shiue, Cherng-Jiann. 1960. Systematic sampling with multiple random
starts. Forest Science. 6:42-50.
Taylor, Sterling A. and Gaylen L. Ashcroft. 1972, Physical edaphology.
W. H. Freeman and Company. San Francisco. 533 P.
Tennyson, Larry Charles, 1973. Snowfall interception in Arizona
forests. Unpublished Master's thesis, Univ. of Arizona. 56 p.
Thompson, J. R. and A, D. Ozment. 1972. The Rocky Mountain millivolt
integrator for use with solar radiation sensors. USDA Forest
Service Res. Note PH-225. 8 p.
of
Thorud, David B. and Peter F. Ffolliott. 1972, Development
water yield for
management guidelines for increasing snowpack
ponderosa pine forests in Arizona. National Symposium on
Watersheds in Transition, Proc. pp. 171 173.
Snow hydrology, North Pacific
U. S. Army Corps of Engineers. 1956.
Div. Portland, Oregon. 437 p.
-
Runoff from snowmelt. PM 1110U. S. Army Corps of Engineers. 1960.
2-11406. 59 P.
as a watershed management
Warskow, William L. 1971. Remote sensing ARES Symp., Proc. Tucson,
tool on the Salt-Verde watershed.
Arizona, pp, 100-108.
J. E. Reid, 1971. Simulation of daily
Willen, D. W., C. A. Shumway and
Snow Conf., Proc.
snow water equivalent and melt. Western
39:1-8.
109
Williams, John A. and Truman C. Anderson Jr. 1967. Soil survey of
Beaver Creek area, Arizona. USDA. Washington D. C. 76 p.
Worley, David P. 1965. The Beaver Creek pilot watershed for evaluating
multiple-use effects on watershed treatments. USDA Forest
Service Res. Paper PM-15. 12 p.
Yevjevich, Vujica. 1972. Probability and statistics in hydrology.
Water Resources Publication. Fort Collins, Colorado. Sec, 11.3.
PP. 242-247.

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