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 • 48 00000NKNOOPr\KNON c0 co CO coCO N. Cs- ct\ cf\ c0 c0 CO c0 CON N n-• ••• \ ko CO N •"" n13 n.0 \ e•-• •-• n-• Cs- N. 4" 01 ON ON 01 ON 11.I N. N.kr) N. Ir\ \ or. CO N te\ %.0 CO N. trN CO •••• ON e- 4 C.) 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LrN tr\ ir\ cf\ EN- AAAAAA Ti Tt Ti TI °d TS • °.• 01 o pL, 01 4-4t'L`--N. 01 o'. ON r-e-Ir •••• 0 a) 0 0 0 Tl T1 Tt Ti Ti ;- n H $4 ri $4 ri S4 ri 0 0 a) 0 (D 0 0 0 a) 0)0 0)0 CO 0 (OC) CO .0 .0 .0 .0 CO I -14 0000000 es. P4 G> Pi G> di4 '2. o a) o il a) 2 cO :t1 2 V, 2 V. V, `A El Pt Ei 11 0 4-) 4) 434-> 4-, 4-, 4-, 4.) 4-) +3 4-) 0 0 0 0 0 0 0 CS 0 0 0 CI Cd 0 0 0 Cd 0 '5-- I.-- 5-- ogco,gggcagg •-••• •-• 49 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 o 0 N o t: n Lii n 0 n a 50 n o 0N,. >0 0 e o on H \ \x \x \ ):'N -\(. x ; 0 5 75 40 0 -, .)'n x o ( x CI) . \. e .--' c.r) z 30 < x X \ X. X \ F- 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. 0 61 1:1 g In • 4.) * 0 4-1 sl 4-) n 71 N g \\ 0 fan H <1 ) = L(\ a, --.1---1- 0.) H PZ 1 0 0 A H * 44'0 44 O V t4 A PI 0 * 4- d d 0 co N * * o. riN 0 .1) * H .4. 0 tr \ t> ,-- N 0 H • eddd 0 .- 4 1›. g--1 d 0 .g 4-) na A gri te (1) ri E-1 * 0N O N 4 4.) e›, ._ 9 s.. 0 LIN N -4-tf \ ..- N CtZn 7\4-1 g ddddddd 0 g 141 4.1 0 * 0 0 ri 0 41 ri ri 44 44to W 44 44 4-)N tr% 1.71 H f., t'-. 0 d d d Z O g n0 1.11 c0 %.0 d d EN- Cor.1 Co u'.tO d d 0 .-1 4-) 0 ri H 4) g el A A 4., P4 0 44 4-t CO 43 fil O co tr's 1/40 c0 4-) 0 0 44 0. 0 k c0 c0 d ddddod M 9-1 0 ( i * •-• LC \ 141 rel t41 kr) . 4.) g 0 .ri0 -d • 44 440 44 r40 O 1 04.) O 0 J g gl 0Ii 0 0 co n.0 •-• -r11 4.)4)utI r-1eiS S-1 r-IIi Cs. crt •-• I . 1.41 II I u' Li'sn .ti 0 41 to P 0 'Ti .0 4-1 4-) H 0) a Pfl t•-• v_ON 0 .1-1 0 II 0 Cs- 141 H t c., A H teN 0 .g 0 k 0 a41g J I 0 62 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 64 • o-1 Cr. cnI • • • N N Es- tr N . • • N 4 •-• or. ON tc‘ ON N oN Co ON • • • • • • • • . • W.\ N N n-o n.0 0 N OS r. -4- \ csl 4- LO% • n-• 0 Co CoN CO tr \ \ 0 . • • • • • • • • • T.. N 0 Ri- N tt N e". * O N tr"- — Co OS us, 3 tcn N tr, g Cs- •-•• C..- 0 CosO tc. 14'. ro\ Co N Co ON Co N Co co N N ai O. • • • • • • •-• • • • • • • • Co CO Co -4- Co Co ON Co . , g p., 8 8 8 8 cy. o. 0 if\ (1-n trN 0 000 O.- hC'- Cs- .4, • P. 0 }., CS CS Ci El 0 C. C. 4-. • 0 4-> l-, 44 .....) 0 0 .-1 H P. . 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C1/4• • ,, • . • • . • • ---1- 4- 4. --I- C, - ,A 4- 46 Co • 0, • • If'. Co • ,.D N N N N N -4- -4' 4- trN u-\ •.0 ,-- )--, 4-4.r4 Et-I ..--- CO 0 0 111)4) 4.., O _ ._ — coCs O rr) -4' 0, 4- te», \ k.0 01/4 C"-• C"•-• C,- so Co Co Co Co Co Co Co .-- tc,, -1- --I-\ Cr, Co C‘- OS csnCriI-eN reN --t A A Cr!) ..si .-l4 Q 0 1:,-4 ' Cri, 14: o Ci rd 4) rd il .-0 ,c1C.$4 4).0 o 0 0 0 0 0 0 t.) C.) c.) 0 Al .0 .0 t) ,r .0 .g 41 o o o .), cil ,0 0 0 u) 0 O 0 cl C.C.t-, Si f4 FA C.14 C)o O 0 0 0 o 0 0 0 El Cl - ✓d 4-,4. Cl Ci ni CS cc: 4, 4, 4, 4, 4, 4, 4, 0 0 0 0 0 0 0 0 0 ,c1 .0 N Fec EQ ,.- ,'" N ,'" E4 CA P _D 0 4. 0 ,o ci c-, . .14. r. cd II II II .....) 0 0 il g 2, 0 0 4) il, 0 II Co Co.4 I f C r!) ✓S Lf \ ,rs LCS irs C ,., N PI 0 er, 0 g 0 0 0 C. C. a f. o o b o o b..9 ,0 0 Ci Pt g4 0 C. 0 ..! 0 El H 0 0 -1'2, C3n .' ON ON -r4 Co Co sr) Co 0 O.- .-- .- 1,- C,-- --t C.- C,-- Co Co Co C1/41 EN. C`n C1/4. 1/40 1/40 Co n.0 CO Co OS 0 .0 n-• H-5 os D._ g- ifs CoL C,-e \ 0- US 4* --1- 0 0 • • • • • • • • • • • • • • co u-‘ •-• •-• t.-\ Co EE-N -- feN C"-- te\ te1 0 te% •-• •-• •"' ' ---, E's- 0 CO CO 0- D-- ifs Li-) ,- .- CN crS UN O. N. CO CO CO Co CO — fc*\ N N .-- .- Co II H VI crl frà 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 N F.0 O3 C- kl) D- •-• • 03 • N 1 ,1 • • • 03 D.- -1. (r) •-• •-• "-• r-1 lf"\ D. co 0 \ • • N N tr, \ CO '.00 N 03k.0 n.0 Cs- • . • • • • N D.- k.0 • N. k.0 kt) F. 0 k.0 0 1,- .0 F.0 0 0 •O fi 0 $4 O 4-, 0 . C•-• • ON • %.0 D.- N Co t -t •-- N • • CO ‘..0 C•-• 14", , • F,4 V) v0 V‘l Fr \ es- C'•• • • • • • • k.D 1')•.o IA 4-C- FIl .- H ..-.1 0 El 4-, O O '0 O O O 0 N 0 0 o 0 cl f. II U co Fvl c•- cv o N ..-.. .-- ÷ g l"-• ... %...0 e", Es- TI H >4 >4 >4 .--. ..-. 4, 0 • + .--0 0 4- • • .--0 ...ni „..... .-. ..0 ,-- '7'. Cs. ' •••• 0 N N i\1 r• 3• l'- _ 14 O• c\i >4 N ?. >4 N 0 A V- o r..- 4 \ 0 re1 N >4 .- >4 co 0 >4'. I N • o 0 ._ Co 10 0 4) 4-1 ...... 14 11 0 0 PI •,-1 4-, 4-) 0 ,..0 4) co O O O H C) .--, .0 0 P.0 ...., 0) ir) g Cl -.1 ...... 0 N + + —. + '-N .- Cl $4 C- i4 ...... X >... m o ...-. >4 .-- C.- Hl .....O 0 •-0i< trl 0 P• +I 1 , 0 X .- \ tr‘ -,..... , it' rl n reN e 0 H '-.' . ....• H \ >4 O i f Cl S., 0 H v0 7.' kl K1 CI 4 (76' g H ,--4 hl, CO C'Cs- N N H ?) •H ln • \ 0 I-4 0 ,..0 Dr- • Q'. u 00 • • 0, <A •D- 0 0 0 tr. ,'S W.I co 44 Ô •-• LIN _. 0 • 0 0 + , ,--. C)) It' .rN x 0 0 + • + • c.... — + + + .-+ NO' 0 D- C, • • 'C) op 1 il ii I • kl) 7 II ..0 • MI 0% • 1 t>r- C-4 f4p•-t + + c•-. 0 0 + + 1 -4. 1 I 11 H 11 11 II ) 't'it'it' fir-'4 1,4 ( t4 „i ,.-4 ,i + + • .-- ..1-• N N 1 D-I •— .— + + II 11 WI it' • 4' • V) II\ Co I-V \ • •-• -4.1 aj n H I 1 1 11 H 11 't' t34 >4 T3-4 it'it' 1,4 D4 44 FT41 44 44 o o A A if. A A A ,_ o vS 0 g I4 44 0 4, Cl o 40 g TI It - O o 11 H P4 •-• H1 1F•4 >4 4- .. 2 C.-,P °Cl ,4 2 a .2 O 4-n '4 44 'al Re 0 .c1 •••n• 9 . ÇA 0 0 0 0 n.0 4 + N 0 LA ON F.1) 0",• 0 0 • 4 • •-.0 ko '- 1.1 0 0 0 PI •0 tiS) •-• Hl Hl X : >4 71 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 a ch o Lin d. N. T-1 0 0 t-, et, to E-1 ..0 A4 -,-, ON UN .— 4 r A 0 4-) co COtiO trN t tc‘ 4I4 0 I 0 0 I cd a) H H 0 ai gs N- t os 0 0 › r-I d o ta '4 4-) CH 0 gI-i I.4 0 0 o 7131 cd 0L. -s- 0 "0 H H P4 ON 0 Eil fg 4- n04 r=1 E4 A 0 N ON N tel a0 ô ô d d e .- COt•- ON ON %.0N 4- 0 .-- o .-- o •- • ON U'S .- d d d LIN NN C-- ON 0 d CO 4- .- • I n0 CV N Le'. ko .- — '; CON1 COU'S ON , • • 0 0 1 4-N.0 fsc1 - d d t•-ON .- 0 ND co N.0 .— co .- 0 o 0 '6 d . 0 I d d I CO .-- cp. (t'. ti-N ON 00 00 N ON 71 ô ô I 1.4N e o o tCn '.0 • • 0 — ts- 1 o Pi Il .4 p., A A ri 0 0 0 4-1 0 >-I .4 4-1 ci) 0 tn 01 .4 4-1 4-0, o 51 0 14 o ri 0 a) cd 2:1 0 4. dl% 0 A Ii II 0")r.11 4 1,4".P:1 n 0 N.\ Cs-- 0 ci:3 • P-r-cd o 0 0 Pl ›. PI ?) t•- 0 0) II reN <4 1:11 cd g 0 0 0 icl -d-t•-- 4-/ E 0 N o. 4 co Cs- CO-1; .IN .- r\f0 v3 — o CO-4tfN CO 4-d N I a, N.o L.C1 CV CO1,- .- 4uN .- • Pi • 0 0 0 0 0* Oe 0* d CO4- • (N1 ‘.0 d • 0 N N g .,01 C) C7N nO O CO N GN N ô ô ô ô1 ô . C' 0 N ". K . N • . 0 0 Ô d.' I 4-.,--H u1 ON 4* r41 CO N c0 4 COv:› 00 N 0 O C''Ri .-\ 10 00 01 I.. co tr. . • . • 0 0 0 0 I I I I 0 .- 0 UN 0 .-- d' uN C' CO l.f I • I(\ C- • 0 0 o 1 . 0 o C)-,-1 • N-. 0 d a> Pi o d • 0 0 N 0 0 Cl o - Ir\ 1 4-4 E4 4:1 .g 0 P4 II cd Li Ti .0 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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