Use of a Precipitation-Runoff Model to Simulate 

Natural Streamflow Conditions in the Methow River 

Basin, Washington 

By D. Matthew Ely and John C. Risley 

U.S. GEOLOGICAL SURVEY


Water-Resources Investigations Report 01-4198


Prepared in cooperation with 

OKANOGAN COUNTY 

Tacoma, Washington 

2001 
District Chief 

U.S. DEPARTMENT OF THE INTERIOR 

GALE A. NORTON, Secretary 

U.S. GEOLOGICAL SURVEY 

Charles G. Groat, Director 

CONTRIBUTING U.S. GEOLOGICAL SURVEY STAFF 

Geographic Information System Support


R. Viger, Physical Scientist


T.D. Olsen, Geographer


D.M. Ely, Hydrologist


Editorial, Graphics, and Text Preparation Team


L.S. Rogers, Technical Editor


C.J. Dean, Illustrator


S.L. Wahlstrom, Editor


Computer Applications Support 

T.T. Le, Computer Specialist 

Any use of trade, product, or firm names in this publication is for descriptive purposes only and does not imply 

endorsement by the U.S. Government. 

For additional information write to:


District Chief


U.S. Geological Survey


1201 Pacific Avenue – Suite 600


Tacoma, Washington 98402


http://wa.water.usgs.gov


Copies of this report can be purchased


from:


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Box 25286, Federal Center


Denver, CO 80225-0286

CONTENTS 

Abstract ................................................................................................................................................................ 1


Introduction .......................................................................................................................................................... 1


Purpose and Scope ...................................................................................................................................... 3


Description of Study Area........................................................................................................................... 4


Acknowledgments....................................................................................................................................... 5


Precipitation-Runoff Model ................................................................................................................................. 5


Description of Simulation Model................................................................................................................ 5


Time-Series Data......................................................................................................................................... 8


Precipitation ....................................................................................................................................... 8


Air Temperature................................................................................................................................. 10


Discharge ........................................................................................................................................... 10


Delineation of Basin Physical Characteristics ............................................................................................ 10


Parameterization of Basin Physical Characteristics.................................................................................... 16


Calibration of Simulation Model ................................................................................................................ 16


Long-Term Model Simulation .................................................................................................................... 27


Analysis of Errors in the Simulation........................................................................................................... 27


Data Error.................................................................................................................................................... 27


Model Error................................................................................................................................................. 28


Parameter Error ........................................................................................................................................... 28


Planned Work and Future Studies........................................................................................................................ 33


Summary and Conclusions................................................................................................................................... 33


References Cited .................................................................................................................................................. 35


Contents III 
FIGURES 

Figure 1. Map showing location of the Methow River Basin, Washington...................................................... 2


Figure 2. Schematic diagram of the Precipitation-Runoff-Modeling System................................................... 6


Figure 3. Map showing location of data-collection network in the Methow River Basin, Washington........... 9


Figure 4. Map showing drainage network defined for the Methow River Basin, Washington, 


with a minimum flow accumulation area of 3.5 square miles using GIS Weasel ............................. 12


Figure 5. Map showing generalized slope of the Methow River Basin, Washington, 


delineated using GIS Weasel ............................................................................................................. 13


Figure 6. Map showing generalized aspect of the Methow River Basin, Washington, 


delineated using GIS Weasel ............................................................................................................. 14


Figure 7. Map showing location of Modeling Response Units in the Methow River Basin, Washington, 


delineated using GIS Weasel ............................................................................................................. 15


Figure 8. Map showing simplified soil grid of the Methow River Basin, Washington,


generated from the State Soil Geographic Database and the GIS Weasel......................................... 17


Figure 9. Map showing land use and vegetation in the Methow River Basin, Washington,


delineated using the GIS Weasel ....................................................................................................... 18


Figure 10. Graphs showing simulated and measured daily mean streamflow for 


selected streamflow-gaging stations, Methow River Basin, Washington, water years 1992-99....... 20


Figure 11. Map showing location of major subbasins in the Methow River Basin, Washington, 


delineated using GIS Weasel ............................................................................................................. 22


Figure 12.	 Graphs showing simulated and measured mean monthly streamflow for 


selected streamflow-gaging stations, Methow River Basin, Washington, 


water years 1992-99........................................................................................................................... 24


Figure 13.	 Graph showing simulated and measured mean daily streamflow for selected


streamflow-gaging stations, Methow River Basin, Washington,


calendar years 1992 and 1995............................................................................................................ 26


Contents IV 
TABLES 

Table 1. Climate stations used in model simulations....................................................................................... 10


Table 2. Description of streamflow-gaging stations, Methow River Basin, Washington ............................... 11


Table 3. Simulated minimum, maximum, and mean monthly streamflows and standard deviations 


for the Methow River Basin, Washington, water years 1959–99...................................................... 29


Table 4. Simulated and measured mean annual streamflows, simulated streamflow as a


percentage of measured, and bias for water years 1992–99 .............................................................. 31


Contents V 
CONVERSION FACTORS AND VERTICAL DATUM 

CONVERSION FACTORS 

Multiply By To obtain 

acre 4,047 square meter 

0.4047 hectare 

0.4047 square hectometer 

0.004047 square kilometer 

acre-foot (acre-ft) 1,233 cubic meter 

0.001233 cubic hectometer 

cubic foot (ft

3) 28.32 cubic decimeter 

0.02832 cubic meter 

cubic foot per second (ft3/s) 0.02832 cubic meter per second 

foot (ft) 0.3048 meter 

inch (in.) 2.54 centimeter 

25.4 millimeter 

inch per year 25.4 millimeter per year 

mile (mi) 1.609k kilometer 

square miles 12.590 square kilometers 

Temperature in degrees Fahrenheit (°F) can be converted to degrees Celsius (°C) as follows: 

°C = 5/9 × (°F - 32). 

VERTICAL DATUM 

Sea level: In this report, “sea level” refers to the National Geodetic Vertical Datum of 1929 (NGVD 

of 1929)—a geodetic datum derived from a general adjustment of the first-order level nets of both the 

United States and Canada, formerly called Sea Level Datum of 1929. 

Altitude, as used in this report, refers to distance above or below sea level. 

Conversion Factors VI 
Use of a Precipitation-Runoff Model to Simulate Natural 

Streamflow Conditions in the Methow River Basin, 

Washington 

By D. Matthew Ely and John C. Risley 

ABSTRACT 

Management of the water resources of the 

Methow River Basin is changing in response to the 

listing of three species of fish under the Endangered 

Species Act and the Washington State-legislated 

watershed-planning process. Management options 

must be considered that minimize adverse effects on 

people but meet instream flow needs for fish. This 

report describes the construction and calibration of the 

Methow River Basin watershed model and evaluates 

the accuracy of the model as a predictive tool for 

assessing the natural instream flow conditions. The 

term “natural” instream flow is stressed because 

surface water within the Basin is used for agricultural 

irrigation through an extensive system of diversions. 

The USGS Modular Modeling System was used 

for the watershed modeling component of the Methow 

River Basin study. The Geographic Information System 

Weasel characterized the physical properties of the 

basin, and the Precipitation-Runoff Modeling System 

simulated the natural streamflow. Natural streamflow 

conditions in the Basin were difficult to calibrate 

because six of the seven streamflow gaging stations are 

located below irrigation diversions and few streamflow 

measurements exist for the study area before the 

diversions were present. Therefore, limited records of 

natural streamflow conditions were available and 

estimations concerning some physical processes could 

not be quantified. 

Streamflow was simulated for water years 1992-

99 to calibrate the model to measured streamflows. 

Simulated and measured streamflow generally showed 

close agreement, especially during spring runoff from 

snowmelt. Low-flow periods, most restrictive to fish 

habitation, were simulated reasonably well, yet 

possessed the most uncertainty. Simulations of the total 

annual runoff as a percentage of measured annual 

runoff for the 8-year calibration period at seven gaging 

stations ranged from -33.7 to +30.5 percent with 70 

percent of the simulated values within 16 percent. 

Simulation of water years 1959-99 demonstrated great 

variability in monthly streamflow statistics. The 

simulated mean monthly flows for the seven 

streamflow-gaging stations were an average of 11.5 

percent higher for the calibration period (1992-99) than 

for the entire simulation period (1959-99). 

INTRODUCTION 

The Methow River Basin, located in northcentral Washington in Okanogan County (fig. 1), is 

well-known for its natural beauty, wildlife, and outdoor 

recreation. Human activity and water appropriation, 

however, have affected streamflow and fish habitat 

throughout the Basin. At the most critical times of year, 

the amount of water necessary to preserve fish habitat 

and satisfy existing water rights could equal or exceed 

the amount of water naturally flowing in the stream 

(Washington State Department of Ecology, 1998). The 

Methow River and its tributaries are home to upper 

Columbia summer steelhead and spring Chinook 

salmon, which are both listed as endangered under the 

Endangered Species Act, and bull trout, which is listed 

as threatened. The Methow River Basin is currently one 

of many watersheds in Washington whose local 

citizens and governments have elected to coordinate 

with Tribes and State agencies to develop a watershed 

management plan, according to the guidelines outlined 

in the Watershed Management Act of 1998 

(Washington State Engrossed Substitute House Bill 

2514). 

Abstract 1 
Figure 1. Location of the Methow River Basin, Washington 

2 Use of a Precipitation-Runoff Model to Simulate Natural Streamflow Conditions in the Methow River Basin, Washington 
Naturally producing salmonid fish are important 

to Washington, both culturally and economically and 

their survival depends on the quality and quantity of 

fish habitat. In some years, water availability is limited 

by climatic conditions and instream flows become 

severely reduced, resulting in extensive dewatered 

reaches, winter icing, and high summertime water 

temperatures (Washington Conservation Commission, 

2000). If conditions are severe enough, expansion of 

dewatered reaches will reduce habitat area, restrict 

access to the habitat by adult fish, dewater redds (nests 

where females deposit eggs), and strand juvenile fish. 

Furthermore, road building, conversion of riparian 

habitat to agriculture and residential development, 

diking, and water diversions could “further exacerbate 

the naturally limiting conditions in some portions of 

the Methow River Basin” (Washington Conservation 

Commission, 2000). 

Streamflow in the Methow River and its 

tributaries has been diverted for irrigation since the late 

1800s. This practice predates any formal system of 

water measurements and, as a result, natural 

streamflow conditions of the present or past are 

unknown. Currently, a system of canals, ranging from 

unlined to completely piped, diverts water from about 

mid-April to October. The net effect of this system on 

instream flows is unknown. The net effect may be a 

combination of the rates of diversion and return, the 

rate of water loss to the ground-water system from 

leaking canals, the degree of ground-water and 

streamflow interaction, and other factors. 

The Washington State Department of Ecology is 

required to establish baseflows to protect and, where 

possible, enhance instream beneficial uses, including 

the protection of fish and wildlife habitat, recreation, 

and irrigation (Washington Conservation Commission, 

2000). The development of instream-flow requirements 

considers many factors, including the hydrology of a 

stream and its natural variations in streamflow and 

baseflow over the course of time and the need for fish 

habitat (Washington State Department of Ecology, 

1998). To protect habitat for naturally producing 

salmonids, the National Marine Fisheries Service 

(NMFS) sets minimum instream flow requirements. 

Currently, the NMFS has set minimum instream-flow 

requirements for three tributaries to the Methow River 

(the Chewuch River, Early Winters Creek, and Wolf 

Creek; National Marine Fisheries Service, 2000a, b, c) 

which have resulted in the reduction or termination of 

diversions in those tributaries before the end of the 

regular irrigation season. 

The U.S. Geological Survey (USGS) in 

cooperation with Okanogan County, Washington, 

began two studies in October 2000 to evaluate the net 

effect of the irrigation system of the Methow River 

Basin on streamflows. The first study focuses on 

understanding the unconsolidated ground-water system 

of the Basin and the interaction between ground water, 

leaking canals, and instream flows. The second study 

focuses on understanding the natural and modified 

streamflows for the Methow River and its main 

tributaries. This study is conducted in two phases. In 

Phase One (documented in this report), a basin-wide 

watershed model was constructed and calibrated to 

simulate daily natural streamflows at selected locations 

throughout the basin. In Phase Two, the model of 

Phase One will be improved to allow for the simulation 

of more complex hydrologic features such as 

streamflow diversions and returns. Findings from the 

ground-water study also will be considered. The model 

of Phase Two will be a tool that can be used to simulate 

the impact of different management options prior to 

their implementation. 

Purpose and Scope 

This report documents the development of a 

basin-wide watershed model and the ability of the 

model to accurately simulate natural streamflow 

conditions in the Methow River Basin (Phase One of 

the second study). The term "natural streamflow” 

refers to streamflow conditions that would exist if no 

surface water was diverted. The report discusses 

simulated daily streamflow for water years 1959-99, 

and focuses on simulated streamflow during low-flow 

periods, particularly late-summer and early-autumn 

months. 

This report discusses the limitations of 

accurately simulating natural streamflow, considering 

that most streamflow-gaging stations are located below 

diversions and therefore do not measure natural 

streamflow with which to calibrate the model. The 

report also documents the assumptions made about 

interactions between ground- and surface-water and the 

uncertainties that result in simulated natural 

streamflow. 

Introduction 3 
Description of Study Area 

The Methow River Basin occupies most of the 

western one-third of Okanogan County in north-central 

Washington State and covers an area of about 1,800 

square miles (fig. 1). The Basin is bordered on the west 

by the Cascade Range, on the east by the Okanogan 

River Basin, on the north by the Canadian border, and 

on the south by the Columbia River down to latitude 

48° 00’ N. The Methow River originates in the Cascade 

Range and flows southeasterly for about 60 miles to the 

confluence with the Columbia River near Pateros. The 

Methow River is formed by the confluence of the West 

Fork Methow River and Robinson Creek and is joined a 

short distance downstream by Lost River. Principal 

tributaries are the Chewuch and Twisp Rivers. The 

Chewuch River originates near the Canadian border 

and flows south for about 36 miles, joining the Methow 

River near Winthrop. The Twisp River originates high 

in the Cascade Range and flows easterly for about 27 

miles to its confluence with the Methow River near the 

city of Twisp. 

The population of the Methow River Basin is 

concentrated on the valley floor between Mazama and 

Pateros. U.S. Census data reported the permanent 

population at about 5,000 (U.S. Census Bureau, 2001). 

Additional seasonal population is about 1,200. 

Topography in the Methow River Basin ranges 

from peaks reaching 8,950 feet above sea level along 

the Cascade crest down to 775 feet at the confluence 

with the Columbia River near Pateros. Ridges rising to 

altitudes of 7,000 feet above sea level and steep Ushaped canyons carved by glacial erosion dominate 

much of the study area. In some areas, such as between 

Mazama and Carlton, the Methow River flows through 

broad valley bottoms with gentle relief. 

The geology of the Methow River Basin is 

described in many reports, including Pitard (1958), 

Waitt (1972), Walters and Nassar (1974), and 

Barksdale (1975). Bedrock, comprised primarily of 

granite, is exposed or thinly covered throughout the 

Basin except beneath or immediately adjacent to the 

valley floor. Major topographic features of the Basin 

were formed during the Pleistocene Epoch as glacial 

ice scoured and rounded upland areas. Thick deposits 

of clay, sand, and gravel cover the lower slopes and 

valley bottoms. These deposits form broad 

glaciofluvial terraces that account for most groundwater storage and flow in the Basin. 

The Basin also is an area of diverse climate with 

wide variations in temperature and precipitation. The 

high mountainous regions generally receive the coldest 

temperatures and greatest precipitation. More than 80 

inches of precipitation fall each year near the crest of 

the Cascade Range, which accumulates as snow from 

late autumn to early spring. At low altitudes, climate 

becomes semi-arid. The valley floor near Pateros 

receives about 10 inches of precipitation a year. The 

east side of the Basin receives considerably less annual 

precipitation than equal altitudes on the west side. 

Spring runoff from snowmelt originates near the 

Cascade crest. Average annual precipitation for the 

entire Basin is about 32 inches per year (Walters and 

Nassar, 1974) and temperatures range from about 100°

F to -20° F. Temperatures generally are highest in July 

and lowest in January. 

Only small glaciers exist in this part of the North 

Cascades Range. Post and others (1971) report that the 

Methow River Basin contains 15 glaciers, ranging in 

size from 0.03 to 0.07 square mile. The total surface 

area of the glaciers equals about 0.54 square mile, or 

about 0.03 percent of the total drainage basin. 

About 75 percent of the Basin is forested and the 

remainder is covered by grasslands, shrubs, irrigated 

crops, and bare rock. Intermediate altitudes are covered 

by Douglas fir, spruce, and lodgepole pine. Ponderosa 

pine inhabits low altitudes. Vegetation is sparser at high 

altitudes — smaller trees, shrubs, and grasses. Most 

agricultural production occurs in the valley bottom and 

is limited to alfalfa and small orchards. 

Numerous studies were conducted to investigate 

the hydrology of the Methow River Basin. A summary 

of the general water resources is given in Walters and 

Nassar (1974). Sorlie (1975), Milhouse and others 

(1976), and Golder Associates (written commun., 

2001) discuss water use, irrigation, surfacewater/ground-water interaction, and the Methow River 

Basin water budget. Average monthly streamflows 

under natural conditions are estimated in Richardson 

(1976). Artim (1975) discusses ground water in the 

broad valley bottom from Mazama to Winthrop. 

Individual watershed analyses were conducted for the 

Chewuch River (U.S. Forest Service, 1994b), Twisp 

River (U.S. Forest Service, 1995), Upper Methow 

River (U.S. Forest Service, 1998), and Lower Methow 

River (U.S. Forest Service, 1999). 

4 Use of a Precipitation-Runoff Model to Simulate Natural Streamflow Conditions in the Methow River Basin, Washington 
Acknowledgments 

The authors thank the members of the Methow 

River Basin Planning Unit for contributing information 

about current and historical conditions in the Basin. We 

also thank Greg H. Knott and Jennifer A. Molesworth 

of the U.S. Forest Service for their technical guidance. 

PRECIPITATION-RUNOFF MODEL 

The USGS Modular Modeling System (MMS), 

developed by Leavesley and others (1996), was used 

for the watershed modeling component of the Methow 

River Basin study. MMS is an integrated system of 

computer software developed to provide a framework 

for the development and application of models to 

simulate a variety of hydrologic processes. Existing 

models can be modularized and brought into MMS. 

Modularization allows the user to select appropriate 

algorithms or develop new algorithms to create an 

optimal model for the desired application. The 

Precipitation-Runoff Modeling System (PRMS) 

(Leavesley and others, 1983) was the model 

incorporated into MMS for the simulation of natural 

streamflow conditions. 

A Geographic Information Systems (GIS) 

interface, termed the GIS Weasel (Viger and others, 

1998), is part of MMS. The GIS Weasel is an interface 

for the treatment of spatial information used in 

watershed modeling and provides an accessible tool to 

delineate and characterize a watershed. The GIS 

Weasel uses standard ARC/INFO routines for 

watershed delineation and therefore develops more 

objective and reproducible results. 

Precipitation-runoff models typically simulate 

the hydrologic response of a basin at the outlet to the 

precipitation that falls over the basin surface. The 

hydrologic response at a basin outlet represents a 

composite of numerous physical processes in that 

basin. The selection of a precipitation-runoff model for 

a study is based on the specific study objectives and the 

availability of data representing the climatic, 

hydrologic, and physical characteristics of the basin. 

PRMS has been used to model watershed systems for 

Williams Draw and Bush Draw Basins, Jackson 

County, Colorado (Kuhn, 1989), the southern Yampa 

River Basin, Colorado (Parker and Norris, 1989), 11 

small drainage basins in the Oregon Coast Range 

(Risley, 1994), the Willamette River Basin, Oregon 

(Laenen and Risley, 1997), the Lake Tahoe Basin, 

California and Nevada (Jeton, 1999a), and the Truckee 

River Basin, California and Nevada (Jeton, 1999b). 

Description of Simulation Model 

The PRMS was the simulation model selected 

for this study. Major advantages of this model include 

the ability to (1) simulate the moisture balance of each 

component of the hydrologic cycle, (2) account for 

heterogeneous physical characteristics of a basin, (3) 

appropriately simulate both mountainous and flat areas, 

and (4) easily accept parameterization output from the 

GIS Weasel. 

The PRMS is schematically diagrammed in 

figure 2 to show the components used in this study. A 

basin is conceptualized as an interconnected series of 

reservoirs whose collective output produces the total 

hydrologic response. These reservoirs include 

interception storage in the vegetation canopy, storage in 

the soil zone, subsurface storage between the surface of 

a basin and the water table, and ground-water storage. 

Subsurface flow (or interflow) is considered to be the 

relatively rapid movement of water from the 

unsaturated zone to a stream channel and typically 

accounts for 60 to 80 percent of total flow. Flow to a 

ground-water reservoir comes from a soil zone and a 

subsurface reservoir. The ground-water reservoir is 

considered the source of all baseflow. The movement 

of water from one reservoir to another is computed 

throughout the simulation. The application of the 

model for this study was run on a daily time step. The 

system inputs included daily precipitation and daily 

maximum and minimum air temperature. Streamflow 

at a basin outlet is the sum of surface, subsurface, and 

ground-water flows. 

The heterogeneity of a basin is accounted for by 

Modeling Response Units (MRUs), formerly known as 

hydrologic response units, in MMS. Total flow from 

each MRU is computed and assigned to a userspecified node, which represents a stream location. A 

water balance from all MRUs contributing flow to a 

certain node is computed during each time step. Flows 

from each node are routed to the next user-specified 

node, with a time delay, to simulate surface-water flow. 

Precipitation-Runoff Model 5 
Figure 2. Precipitation-Runoff-Modeling System 

6 Use of a Precipitation-Runoff Model to Simulate Natural Streamflow Conditions in the Methow River Basin, Washington 
Surface runoff and infiltration in the daily time 

step are computed using a variable source-area 

approach (Hewlett and Hibbert, 1967). Surface runoff 

is related to a dynamic source area that expands and 

contracts to rainfall characteristics, and to the 

capability of the soil mantle to store and transmit water 

(Troendle, 1985). As conditions become wetter, the 

proportion of precipitation diverted to surface runoff 

increases, while the portion that infiltrates to the soil 

zone and subsurface reservoirs decreases. Daily 

infiltration is computed as the net precipitation minus 

surface runoff. Precipitation retained on the land 

surface is modeled as surface-retention storage. Once 

the maximum retention storage is satisfied, excess 

water becomes surface runoff. When free of snow, the 

retention storage is depleted by evaporation. 

Precipitation that falls through the crown canopy 

infiltrates the soil zone. This soil zone is 

conceptualized as a two-layer system. Moisture in the 

upper soil (or recharge) zone and in the lower soil zone 

is depleted through root uptake and seepage to lower 

zones. Evaporation also depletes the upper soil zone of 

moisture. The depths of the soil zones are defined on 

the basis of water-storage characteristics and the 

average rooting depth of the dominant vegetation. 

Potential evapotranspiration (PET) losses were 

computed as a function of solar radiation and the 

number of cloudless days (Jensen and Haise, 1963). 

When soil moisture is nonlimiting, actual 

evapotranspiration (AET) equals PET. When soil 

moisture is limiting, AET is computed from PET to 

AET relations for soil types as a function of the ratio of 

current available water in the soil profile to the 

maximum available water holding capacity of the soil 

profile (Zahner, 1967). 

In the Methow River Basin, snow accumulation 

and subsequent melting produces the vast majority of 

runoff in the spring and summer months. Accurate 

simulation of this yearly cycle is essential for proper 

agreement between modeled and measured runoff. The 

simulation model contains a snow module to simulate 

the initiation, accumulation, and depletion of a 

snowpack in each MRU. The snow routine requires 

computed daily shortwave radiation. 

Soil water in excess of field capacity first 

satisfies the ground-water reservoir based on a userspecified recharge rate. When average moisture 

exceeds this daily rate, excess soil water goes to the 

subsurface reservoir. Soil water in excess of field 

capacity drains to subsurface and ground-water 

reservoirs. Excess moisture in the subsurface reservoir 

either percolates to a ground-water reservoir or flows to 

a discharge point above the water table. Seepage to the 

ground-water reservoir is computed first from the soil 

zone, then as a function of a recharge rate coefficient 

and the volume of water in the subsurface reservoir. 

A hydrologically similar watershed model in the 

nearby Yakima River Basin produced initial results 

suggesting that some changes to the original PRMS 

modules were needed (M.C. Mastin and J.J. Vaccaro, 

U.S. Geological Survey, written commun., 2001). 

Specifically, Mastin and Vaccaro made improvements 

in the method for distributing daily weather variables to 

MRUs to better reflect large spatial variations and to 

account for missing or erroneous data. Other changes 

were made to account for runoff from glacial melt, to 

allow for minimum ground-water storage in a subbasin, 

and to add a groundmelt component to the snow 

accumulation and ablation module. All these 

modifications were made to existing PRMS modules. 

A simplified flow-accumulation and flow-routing 

module was modified from an existing module 

developed by the U.S. Bureau of Reclamation (USBR) 

(T. Ryan, U.S. Bureau of Reclamation, written 

commun., 1996). The module changes are described in 

detail below. 

The precipitation distribution module was 

changed so that data from all precipitation sites were 

used to interpolate a daily value using a simple inverse 

distance-weighting technique. This precipitation 

distribution method reduces sensitivity to missing or 

bad data. The daily precipitation at a site is first 

weighted by the inverse square of the distance between 

the site and the MRU centroid and is then further 

corrected by the ratio of the mean monthly 

precipitation of the MRU to the mean monthly 

precipitation of the site. After interpolating all daily 

values from all precipitation sites, an average value is 

calculated for the MRU. The method and computer 

code are from Bauer and Vaccaro (1987) except that 

mean monthly precipitation values are used instead of 

mean annual precipitation values. 

Precipitation-Runoff Model 7 
Daily minimum and maximum air temperatures 

were distributed to the MRUs based on the inverse 

distance-weighting method of Bauer and Vaccaro 

(1987). First, daily minimum and maximum lapse rates 

were estimated for the Yakima Basin by (1) calculating 

daily rates for the period 1952-94 using all daily 

temperature data, and (2) estimating a value after 

analyzing the lowest 5 percent and highest 5 percent of 

the values for each month (M.C. Mastin and J.J. 

Vaccaro, U.S. Geological Survey, written commun., 

2001). These same lapse rates were used in this study. 

Next, the MRU daily minimum and maximum 

temperatures were computed from an average of the 

inverse distance-weighted temperature values from 

each temperature station’s recorded value and the basin 

lapse rate. 

A simple glacier-melt function was added to the 

surface-runoff module to account for glacier-supplied 

streamflow during the warm months. For a glacier 

MRU, glacier melt is calculated when there is no snow 

cover and the average air temperature is above a userdefined base temperature (32° F in this study). Melt is 

equal to the difference between the air temperature and 

the base temperature multiplied by a glacier-melt 

coefficient. This glacier-melt is added to the surfacerunoff component. 

A groundmelt component (Anderson, 1976) was 

added to the snow accumulation and ablation module to 

simulate runoff after a snowmelt event. The additional 

groundmelt component supplies much of the water 

needed to support low flows during times when a basin 

is snow-covered. The groundmelt is added to the upper 

part of the MRU soil zone. 

A simple reach-routing module was added that 

allows the runoff to be accumulated at points called 

nodes. Each defined node has a user-specified MRU, 

ground-water reservoir, and subsurface reservoir 

contributing to it. These runoff components are 

accumulated at the node and then routed to the next 

downstream node using a standard Muskingham 

routing equation (Linsley and others, 1982). The 

equation requires a storage coefficient that 

approximates an average traveltime, in hours, and a 

routing weighting-factor that adjusts the attenuation of 

a flood wave. An existing USBR module (called 

FIXROUTE) contained all but the reach-routing 

feature; that module used a user-input time lag for each 

reach between an upstream and downstream node. This 

routing module allowed streamflow statistics to be 

generated at the outlet of subbasins and then 

accumulated downstream. Streamflow could be 

examined on a basin or subbasin scale without the need 

to delineate and parameterize separate models. 

Time-Series Data 

Calibration of the various subbasins within the 

Methow River Basin was accomplished using 

measured precipitation, air-temperature, and discharge 

data for water years 1992-99. The period of climate 

station record used in model simulations spanned water 

years 1959-99. Not all stations existed for the entire 

period of record. Rain and temperature modules used a 

distance-weighted average approach to estimate 

missing data and avoid problems in the simulations. 

Monthly mean precipitation ratios between climate 

stations and MRUs were calculated from the 

Parameter-estimation Regressions on Independent 

Slopes Model (PRISM) estimates (Daly and others 

1994; 1997). 

Precipitation 

Daily precipitation totals used in the model 

simulations were collected from rain gages located 

throughout the Methow River Basin and surrounding 

basins. Rain gages operated by the U.S. National 

Weather Service (NWS) and Snowpack Telemetry 

(SNOTEL) sites operated by the Natural Resources 

Conservation Service (NRCS) provided data from a 

total of 18 precipitation gages (fig. 3, table 1) with 

varying periods of record. The rain module requires 

mean monthly estimates of precipitation for each MRU 

to compute ratios between rain gage locations and the 

MRU. For this purpose, the PRISM model estimates 

(Daly and others 1994; 1997) were used. PRISM data 

are 1961-90 mean monthly precipitation from National 

Oceanic and Atmospheric Administration Cooperative 

sites, SNOTEL sites, and selected state network 

stations. Short-term stations supplemented data-sparse 

areas. 

8 Use of a Precipitation-Runoff Model to Simulate Natural Streamflow Conditions in the Methow River Basin, Washington 
Figure 3. Location of data-collection network in the Methow River Basin, Washington 

Precipitation-Runoff Model 9 
Table 1. Climate stations used in model simulations 

[NWS, National Weather Service; NRCS Natural Resources Conservation Service] 

Altitude 

Station Name Agency Latitude Longitude (feet above Period of Record 

sea level) 

Chelan NWS 47 50 00 120 02 00 1,120 July 1890 to present 

Chief Joseph Dam NWS 48 00 00 119 39 00 820 Oct. 1949 to present 

Conconully NWS 48 33 00 119 45 00 2,320 June 1948 to present 

Mazama NWS 48 37 00 120 27 00 2,170 April 1950 to present 

Mazama 6 NWS 48 32 00 120 20 00 1,960 June 1948 to Oct. 1976 

Methow 2 NWS 48 08 00 120 01 00 1,170 Aug. 1957 to June 1970 

Methow 2S NWS 48 06 00 120 01 00 1,170 July 1970 to present 

Omak NWS 48 25 00 119 32 00 851 Jan. 1931 to Dec. 1998 

Omak 4 NWS 48 28 00 119 31 00 1,301 Nov. 1980 to July 1991 

Ross Dam NWS 48 44 00 121 03 00 1,236 Sept. 1960 to present 

Stehekin 4 NW NWS 48 21 00 120 43 00 1,270 Jan. 1931 to present 

Tonasket 4 NNE NWS 48 46 00 119 25 00 960 July 1984 to present 

Winthrop 1 WSW NWS 48 28 00 120 11 00 1,755 Jan. 1931 to present 

Harts Pass NRCS 48 43 00 120 39 00 6,500 Oct. 1981 to Oct. 1982, 

Oct. 1983 to present 

Pope Ridge NRCS 47 59 00 120 34 00 3,580 Oct. 1981 to present 

Rainy Pass NRCS 48 33 00 120 43 00 4,780 Oct. 1981 to present 

Salmon Meadows NRCS 48 40 00 119 50 00 4,500 Oct. 1981 to Oct. 1982, 

Oct. 1983 to present 

Thunder Basin NRCS 48 31 00 120 59 00 4,200 Oct. 1989 to present 

Air Temperature 

Daily minimum and maximum air-temperature 

data were collected by the NWS and the NRCS. The 

location names and altitudes of the air-temperature 

stations used for the simulations are shown in figure 3 

and table 1. To account for differences in altitude 

between the stations and MRUs, MMS adjusts the 

temperature data using a user-defined calculated lapse 

rate for every 1,000-foot increase in altitude. 

Discharge 

Daily mean streamflow data were collected at 

seven gaging stations in the Methow River Basin 

(fig. 3, table 2), according to standardized techniques 

of the USGS (Rantz, 1982). Summarized records of 

streamflow are available in USGS annual data reports. 

10 Use of a Precipitation-Runoff Model to Simulate Natural Streamflow Conditions in the Methow River Basin, Washington 
Table 2. Description of streamflow-gaging stations, Methow River Basin, Washington 

[USGS Station No.: Locations are shown in figure 3. Latitude and longitude are given in degrees, minutes, seconds. USGS, U.S. Geological Survey; 

WA, Washington; mi2, square mile] 

Altitude 

Station Drainage (feet 

No. Station Name Latitude Longitude Period of Record Area above (mi2) sea level) 

12447383 Methow River above Goat Creek 

near Mazama 

48 34 32 120 23 05 April 1991 to present 373 2,040 

12447390 Andrews Creek near Mazama 48 49 23 120 08 41 June 1968 to present 22 4,300 

12448000 Chewuch River near Winthrop 48 28 38 120 11 07 Oct. 1991 to present 525 1,736 

12448500 Methow River at Winthrop 48 28 25 120 10 34 Aug. 1971 to June 1972, 1,007 1,718 

Nov. 1989 to present 

12448998 Twisp River near Twisp 48 22 12 120 08 51	 May 1975 to Sept. 1979, 

Oct. 1989 to present 

245 1,640 

12449500 Methow River at Twisp 48 21 55 120 06 54	 June 1919 to Sept. 1962 

Apr. 1991 to present 

1,301 1,580 

12449950 Methow River near Pateros 48 04 39 119 59 02 Apr. 1959 to present 1,772 900 

Delineation of Basin Physical 

Characteristics 

Subbasins and the drainage network in the 

Methow River Basin were delineated with the GIS 

Weasel (Viger and others, 1998). MRUs are delineated 

in a manner that reflects spatially distributed attributes 

such as slope, aspect, elevation, soils, and vegetation, 

and which respond similarly to hydrologic inputs such 

as precipitation. Each MRU is a smaller area of a 

subbasin in which these physical characteristics are 

assumed to be homogeneous. The GIS Weasel also 

delineates a drainage network and computes the 

connection between the MRU and possible stream 

locations. Accuracy of the characterization can depend 

on the scale and quality of the digital input data, as well 

as hydrologic judgment. 

A standard 100-foot (30-meter) USGS 7.5 

minute digital elevation model (DEM) of the Methow 

Basin, in ARC/GRID format, was used to define 

topographic surfaces and provided the initial input to 

the GIS Weasel. The 100-foot DEM contains regularly 

spaced cells, 100 feet on center with elevation reported 

to the nearest 1 foot at each cell. The extremely steep 

slopes of the Methow Basin allowed the 100-foot DEM 

to provide accurate topographic representations. 

A more detailed 30-foot (10-meter) DEM was 

available for the study area but was not used because 

the size of the Basin added additional computation time 

at that resolution without significant gain in precision 

for the purpose of basin delineation. Because of the 

relatively large area of the study, the number of grid 

cells exceeded the maximum allowed by the GIS 

Weasel’s parameterization process. To resolve this 

problem, the DEM grid was resampled to 150-foot (45-

meter) intervals with no noticeable loss of quality. 

A drainage network is extracted from the flow 

accumulation surface by selecting points on the surface 

that drain, according to the flow accumulation surface, 

an area equal to or greater than a user-specified 

threshold (Viger and others, 1998). This threshold 

represents the minimum upslope area needed to initiate 

a first-order link in the drainage network (Jenson and 

Domingue, 1988). In this study, a threshold of 4,500 

cells or 3.5 square miles was chosen. The drainage 

network of the study area is shown in figure 4. 

The GIS Weasel was used to compute initial 

MRUs based on slope and aspect (figs. 5 and 6). USGS 

gaging station locations were used as the downstream 

outlet from which the drainage area was computed. 

Further subdividing was accomplished with the 

automatic two flow-plane process. With this feature, 

each side of the subbasin divided by the stream 

becomes a separate MRU. To account for the 

orographic effect of increasing precipitation, elevation 

bands were incorporated at 2,000-foot intervals to 

subdivide any MRUs that may have spanned several of 

these intervals. Finally, all MRUs smaller than 1 square 

mile were dissolved into adjacent MRUs. This process 

resulted in 607 MRUs for the entire Methow River 

Basin (fig. 7). 

Precipitation-Runoff Model 11 
Figure 4. Drainage network defined for the Methow River Basin, Washington, with a minimum flow 

accumulation area of 3.5 square miles using GIS Weasel 

12 Use of a Precipitation-Runoff Model to Simulate Natural Streamflow Conditions in the Methow River Basin, Washington 
Figure 5. Generalized slope of the Methow River Basin, Washington, delineated using GIS 

Weasel 

Precipitation-Runoff Model 13 
Figure 6. Generalized aspect of the Methow River Basin, Washington, delineated using GIS Weasel 

14 Use of a Precipitation-Runoff Model to Simulate Natural Streamflow Conditions in the Methow River Basin, Washington 
Figure 7. Location of Modeling Response Units in the Methow River Basin, Washington, 

delineated using GIS Weasel 

15 Use of a Precipitation-Runoff Model to Simulate Natural Streamflow Conditions in the Methow River Basin, Washington 
Parameterization of Basin Physical 

Characteristics 

Initial parameters for the discrete spatial features 

of the study area were generated using the GIS Weasel. 

Mathematically, parameters are defined as numerical 

constants in equations used to compute variables 

during the simulation. In addition to elevation, slope, 

and aspect, ancillary information concerning soils, land 

use and cover, and vegetation were incorporated to 

assign further characteristics to each MRU. Digital soil 

data were obtained from a modified version of the State 

Soil Geographic Database (STATSGO) general soil 

maps (U.S. Department of Agriculture, 1994), which 

were made by generalizing detailed state soil survey 

data. The GIS Weasel used the soil properties provided 

by STATSGO but further simplified the soil to two 

different soil textures (fig. 8). Parameters from the 

contiguous U.S. Forest Type Groups map and U.S. 

Forest Density map provided vegetation information 

(Powell others, 1998; Zhu and Evans, 1992). The 

USGS, the University of Nebraska-Lincoln, and the 

European Commission’s Joint Research Centre 

generated a 3,281-foot (1-kilometer) resolution global 

land cover characteristics database (Loveland and 

others, 1991; U.S. Geological Survey, 1992) for use in 

a wide range of environmental research and modeling 

applications. The land cover/land use grid (fig. 9) used 

by the GIS Weasel is a composite of this global land 

cover and the Forest Type Group data listed above. 

The parameters not initially calculated or 

estimated by the GIS Weasel were the ground-water 

recession coefficients, monthly coefficients in 

regression equations that relate the difference between 

daily maximum and minimum air temperature to cloud 

cover, the monthly precipitation values for the MRUs 

and the weather sites, the flow-routing parameters for 

the simple reach-routing module, and the monthly 

minimum and maximum air-temperature lapse rates. 

These parameters and the methods of computation are 

discussed in following sections. 

Calibration of Simulation Model 

The calibration phase of the modeling effort 

consisted of matching simulated and measured 

variables, such as streamflow and snow water 

equivalent. Calibration was accomplished using an 

ordered approach of manual trial and error. Automated 

calibration, or optimization, was used in the adjustment 

of two subsurface reservoir routing coefficients. The 

optimization of these two parameters for three basins is 

accomplished by minimizing the errors between 

simulated and measured streamflow data. All MMS 

parameters are defined and discussed in depth by 

Leavesley and others (1983) and Leavesley and others 

(1996). 

As stated previously, one basic difficulty existed 

in calibrating natural streamflow conditions in the 

Methow River Basin. All streamflow-gaging stations 

with the exception of Andrews Creek (12447390) are 

below irrigation diversions and no historical records 

exist for the study area prior to the diversions . Certain 

assumptions concerning the flow system can be made, 

however. First, diversions remove water directly from 

the stream channel, and therefore the effect is seen 

immediately in the streamflow record. At the end of the 

irrigation season, as diversions are shut down, a 

response in the system also will be evident. Second, 

ground-water flow from irrigation recharge and leaking 

irrigation canals may return to surface-water flows, but 

in a delayed fashion. Finally, some of the diverted 

water is lost to evapotranspiration above what would 

have been lost in the river, thereby decreasing available 

return flows. It is expected that the net effect of 

diversions modifies streamflows from the natural 

conditions but the difference between natural flows and 

“irrigated” flows is unknown. Assumptions can be 

made concerning the effects of diversions on the flow 

system but these cannot be quantified at this stage of 

the study. 

Streamflow was simulated for water years 1992-

99 to calibrate the model to measured streamflows at 

the seven USGS gaging stations. This 8-year period 

was selected because it was the only time when all 

USGS gaging stations had streamflow records. 

16 Use of a Precipitation-Runoff Model to Simulate Natural Streamflow Conditions in the Methow River Basin, Washington 
Figure 8. Simplified soil grid of the Methow River Basin, Washington, generated from the State 

Soil Geographic Database and the GIS Weasel 

Precipitation-Runoff Model 17

Figure 9. Land use and vegetation in the Methow River Basin, Washington, delineated using the GIS 

Weasel 

18 Use of a Precipitation-Runoff Model to Simulate Natural Streamflow Conditions in the Methow River Basin, Washington 
Values determined by the GIS Weasel, values 

calculated and set by the MMS algorithms, and 

parameter estimates used in the hydrologically similar 

Yakima River Basin watershed model all provided 

initial estimates of parameters. The model was 

calibrated by adjusting several sensitive parameters 

within the acceptable range of known values. Most 

parameter adjustments were made to precipitation 

(rain_mon and snow_mon), temperature (tmax_adj), 

minimum ground-water storage (gwstor_min), and the 

ground-water flow coefficient (gwflow_coef). These 

parameters were adjusted uniformly throughout a 

subbasin. Other parameters, including snowinfil_max, 

soil2gw_max, melt_force, melt_look, tmax_allrain, 

tmax_allsnow, ssr2gw_rate, temperature lapse rates, 

gwstor_init, transp_begin, transp_end, and 

jh_coef_hru, were altered to an acceptable estimate and 

applied throughout the entire Methow River Basin. 

Many more parameters could have been adjusted 

during calibration but there were inadequate data about 

the physical processes to justify that approach. 

Simulated and measured daily mean streamflows 

from four selected streamflow-gaging stations for 

water years 1992-99 are shown in figure 10. Locations 

of the modeled subbasins are shown in figure 11. 

Simulated and measured streamflows have many 

similarities and generally show close agreement, 

especially during spring runoff from snowmelt. 

Measured streamflow for April through June at the 

most downstream streamflow-gaging station 

(12449950) averaged 67.3 percent of the total flow. 

Simulated streamflow for that period averaged 67.8 

percent of the total flow. Due to the hydrologic 

complexities of the subbasins, the model simulations 

performed less well in capturing the magnitude and 

timing of short-term (1 to 3-day) peak flows during the 

spring and summer runoff. The model also tended to 

over-simulate (simulated discharge greater than 

measured discharge) autumn and winter peak flows for 

the most downstream gaging station (fig. 10D). The 

model did represent the baseflow periods of autumn 

and winter well. Measured streamflow for August 

through October at the most downstream gaging station 

(12449950) averaged 8.8 percent of the total flow; 

simulated streamflow averaged 6.8 percent. 

Precipitation in the Methow River Basin 

generally occurs as snowfall. To match snowfall totals 

at the high altitudes, monthly PRISM values used in the 

calculation of snowfall generally were increased, as 

much as 25 percent for the Andrews Creek subbasin. 

The location of the Andrews Creek subbasin is shown 

in figure 11. Monthly rainfall amounts and snow for 

lower elevations were decreased from those values 

determined from PRISM data. Precipitation on MRUs 

in the lower Methow River Basin was lowered by as 

much as 50 percent. Increasing or decreasing the MRU 

PRISM value appropriately adjusted the ratio between 

the precipitation gage and the MRU. This procedure 

resulted in annual precipitation totals within reported 

ranges. 

Minimum ground-water storage (gwstor_min) 

was set at 0.0 for all MRUs except those directly above 

streamflow-gaging station 12448500, Methow River 

below the Chewuch River. Initial simulated baseflow at 

this station was considerably lower than measured. By 

increasing the minimum ground-water storage 

(gwstor_min) to 0.05 inch for these MRUs, flows in the 

winter months were increased. 

The final parameter used to adjust cumulative 

streamflow totals was an evapotranspiration 

coefficient. The procedure is one developed by Jensen 

and Haise (1963). Potential evapotranspiration (PET) 

(inches/day) is computed by: 

PET = CTS(MO) * (TAVF-CTX) * RIN (1) 

where 

CTS is a coefficient for the month (MO), 

TAVF is the daily mean air temperature (°F), 

CTX is an MRU air-temperature coefficient, and 

RIN is a daily solar radiation expressed in inches 

of evaporation potential. 

For all MRUs, except those at the highest 

elevations, jh_coef_hru (or CTX) was reduced by 25 

percent, thus increasing PET for the MRU and 

reducing simulated streamflow. Farnsworth and 

Thompson (1982) reported a PET value of 51.87 inches 

per year for Yakima, Washington, for the period of 

1956-70. The simulated PET value in this study for the 

Methow River Basin was 50.04 inches per year for the 

simulation period of 1958-70. 

Precipitation-Runoff Model 19 
Figure 10. Simulated and measured daily mean streamflow for selected streamflow-gaging stations, Methow River 


Basin, Washington, water years 1992-99


20 Use of a Precipitation-Runoff Model to Simulate Natural Streamflow Conditions in the Methow River Basin, Washington 
Figure 10. Simulated and measured daily mean streamflow for selected streamflow-gaging stations, Methow River 

Basin, Washington, water years 1992-99—Continued 

Precipitation-Runoff Model 21

Figure 11. Location of major subbasins in the Methow River Basin, Washington, delineated using GIS 

Weasel 

22 Use of a Precipitation-Runoff Model to Simulate Natural Streamflow Conditions in the Methow River Basin, Washington 
One of the major goals of this study was to better 

understand mean monthly flows at certain stream 

locations. After the model was adjusted to match 

measured annual streamflow totals, the timing of flows 

was matched. Simulated and measured mean monthly 

streamflow for four selected stream-gaging stations is 

shown in figure 12. Because diverted water, some of 

which is transported out of the subbasin of origin, was 

not considered in this phase of the study, some 

difference between simulated and measured mean 

monthly streamflow is expected. The general shapes of 

the graphs, which include winter baseflows and spring 

runoff from snowmelt, show good agreement. In two of 

the graphs, the Methow River above Goat Creek 

(12447383) (fig. 12A) and the Chewuch River 

(12448000) (fig. 12B), simulated streamflows for 

September and October (1992-99) are greater than 

measured streamflows. 

The possibility exists that the model does not 

adequately represent all hydrologic processes at these 

locations or that water diversion during these months 

decreases flows beyond what may return from canal 

leakage and irrigation. The streamflow records for the 

Chewuch River (calendar year 1995) and Twisp River 

(calendar year 1992) indicate that when diversions 

were shut off at the beginning of October, the measured 

mean daily flow increased by the amount that is 

generally diverted (fig. 13A and 13B). Rain increased 

later in October and November and the simulated and 

measured daily streamflow match more closely. 

The timing of the spring runoff and shape of the 

hydrograph during high flow were controlled largely 

by adjustments in precipitation rates and maximum air 

temperature. Temperature adjustments also affected the 

form of precipitation (snow versus rain) and 

evapotranspiration. The recessionary limb of the 

hydrograph was affected by precipitation and air 

temperature (as it affects snowmelt rates), but also 

subsurface and ground-water flow parameters. Flow 

algorithms in MMS move water to a ground-water 

reservoir from both a soil zone and a subsurface 

reservoir. Detailed explanations of these processes are 

given in Leavesley and others (1983). The groundwater system is conceptualized as a linear reservoir and 

is assumed to be the source of all baseflow (BAS). 

BAS expressed in acre-inches is computed by: 

BAS = GWFLOW_COEF * GW (2) 

where 

GWFLOW_COEF is the reservoir routing 

coefficient, and 

GW is the ground-water reservoir 

storage, in acre-inches 

The ground-water flow coefficient proved to be 

an important parameter to estimate because it has a 

large effect on the shape of the streamflow hydrograph 

during low-flow periods. The ground-water reservoir 

for each MRU was assigned a flow coefficient based 

on reasonable ranges and measured streamflow. MRUs 

located largely in the broader alluvial valley near the 

rivers were given higher flow coefficients within an 

acceptable range and adjusted to match the shape of the 

simulated and measured hydrographs. The higher 

coefficient resulted in more ground-water discharge 

per unit area. The values given to the ground-water 

coefficients decreased with distance from the streams. 

The rate of outflow from the subsurface reservoir 

was matched in three subbasins, Andrews Creek, 

Twisp River, and Chewuch River (fig. 11), by 

optimizing the routing coefficients, ssrcoef_sq and 

ssrcoef_lin, using the Rosenbrock process in MMS 

(Rosenbrock, 1960). The rate of movement to a 

ground-water reservoir from a subsurface reservoir was 

adjusted by a daily recharge coefficient (ssr2gw_rate). 

The model proved to be less sensitive to this parameter, 

resulting in a single value for the entire basin. 

Precipitation-Runoff Model 23 
Figure 12. Simulated and measured mean monthly streamflow for selected streamflow-gaging stations, Methow River


Basin, Washington, water years 1992-99


24 Use of a Precipitation-Runoff Model to Simulate Natural Streamflow Conditions in the Methow River Basin, Washington 
Figure 12. Simulated and measured mean monthly streamflow for selected streamflow-gaging stations, Methow River 

Basin, Washington, water years 1992-99—Continued 

Precipitation-Runoff Model 25

Figure 13.Simulated and measured mean daily streamflow for selected streamflow-gaging stations, Methow River 


Basin, Washington, calendar years 1992 and 1995


26 Use of a Precipitation-Runoff Model to Simulate Natural Streamflow Conditions in the Methow River Basin, Washington 
Long-Term Model Simulation 

The calibrated model can be used as a tool to 

simulate flows at ungaged streams or flows at gaged 

streams for periods outside the historical record. This 

ability allows the examination of the system’s 

hydrologic response to climatic conditions. For 

example, long-term mean streamflows could differ 

significantly from means computed from the shorterterm record of the stream gages. Annual, or even 

decadal, trends in streamflows would be more evident. 

To demonstrate the capability of simulating streamflow 

outside the gaging record and at ungaged streams, 

water years 1959-99 were simulated and monthly 

streamflow statistics generated for the seven gage 

locations and two biologically important ungaged 

tributaries, Early Winters Creek and Wolf Creek 

(table 3). Standard deviations for the period of 

simulation were relatively large, suggesting great 

variability in monthly flows. To demonstrate this point, 

mean monthly flows for the calibration period (1992-

99) were compared to mean monthly flows for the 

entire simulation period (1959-99). The simulated 

mean monthly flows for the seven streamflow-gaging 

stations were an average of 11.5 percent higher for the 

calibration period than for the entire simulation period. 

Analysis of Errors in the Simulation 

All modeling studies contain errors. Certain 

approximations and simplifications must be made to 

simulate the actual flow systems. Precipitation-runoff 

modeling errors typically are caused by a combination 

of inadequate input data, inadequate representation of 

the physical processes by the algorithms of the model, 

and inadequate parameter estimation during the 

calibration procedure (Troutman, 1985). Lack of 

understanding about some aspects of the natural flow 

system, coupled with only one streamflow-gaging 

station demonstrating the natural flow system (above 

irrigation diversions), accounts for much of the error. 

As a result, model-predicted values must be used with 

caution in consideration of simulation error. 

Annual runoff totals for simulated and measured 

streamflow varied considerably during many of the 

water years, yet there was no definite pattern or bias in 

the results for the entire calibration period (table 4). 

Simulations of the total annual runoff as a percentage 

of measured annual runoff for the 8-year calibration 

period at seven gaging stations ranged from –33.7 to 

+30.5 percent with 70 percent of the simulated values 

within 16 percent. For the 8-year simulation period, 

measured annual runoff totals were highest for water 

years 1995, 1996, 1997, and 1999. Water years 1996 

and 1999, with above-average measured annual flows, 

were under-simulated at all gaging stations, indicating 

that the current model is less effective at simulating 

high-flow conditions. The model performed reasonably 

well during low-flow years. These results were deemed 

acceptable because the major interest for biological 

importance is in these low-flow years. Simulated and 

measured annual runoff for the 8-year period matched 

closely for all calibration points with the exception of 

station 12448500, Methow River at Winthrop. The 

under-simulation occurred mostly in the baseflow 

period of autumn and winter. A significant amount of 

Methow River streamflow enters the ground-water 

system above Goat Creek and then returns to the river 

upstream of Winthrop (Caldwell and Catterson, 1992). 

The current model does not simulate channel losses 

and, therefore, it is not correctly representing this 

ground-water/surface-water interaction. At the next 

downstream station (12449500) on the Methow River, 

the simulated deficit is made up and simulated 

streamflows closely match the measured annual runoff. 

Data Error 

The PRMS watershed model requires measured 

rainfall, air-temperature, and streamflow time-series 

data, and physical characteristics of the basin. Rainfall 

volume is often the most important driving factor of the 

simulation and it is often the most difficult to estimate. 

Rainfall records are point measurements, whereas the 

model requires input distributed throughout the study 

area. This study used 18 precipitation sites within and 

Precipitation-Runoff Model 27 
adjacent to the study area and the measurements were 

extrapolated to estimate precipitation throughout the 

entire Basin. Precipitation in the Methow River Basin 

varies widely. The mean elevation of an MRU can 

differ significantly from that of the closest precipitation 

gage and the MRU area can span a wide range of 

average precipitation. Rainfall data indicate a large 

variation over relatively short distances. In addition to 

errors introduced by spatially distributing precipitation, 

error is also introduced regarding the type of 

precipitation (rain versus snow). Usually, precipitation 

collection devices are subject to catchment losses that 

are believed to be smaller for rain than for snow. These 

measurement and interpolation factors introduce error 

to the simulation. 

Air-temperature data can be the source of as 

much potential error as the precipitation data. Again, 

air temperature is recorded as a point measurement and 

basin-wide distributed values must be estimated for 

each MRU. Differences of a few degrees can determine 

if precipitation is simulated as snow or rain, or if an 

accumulated snowpack melts. Precipitation, combined 

with air temperature, determines both the cumulative 

annual runoff and the basic shape of the simulated 

hydrograph. 

In general, the DEM and the GIS Weasel 

represented the physical characteristics of the Basin 

well. Even with the delineation of 607 MRUs, 

however, approximations of slope and aspect were 

necessary. Coarse coverages of forest density, land use, 

and soils introduced error in sensitive parameters such 

as evapotranspiration and soil recharge. 

Model Error 

The precipitation-runoff algorithm cannot 

completely represent all physical processes of a basin. 

Determining if a weakness in a simulation is 

attributable to input data error or model shortcomings 

is almost impossible in some cases. This issue is further 

complicated by the fact that the vast majority of the 

streamflows measured in the study area are affected by 

human activity. A more rigorous method of model 

calibration, such as automated nonlinear regression, 

might help to constrain some of the uncertainty. 

However, use of these techniques was not within the 

scope of this study. 

Ground-water flow is a dominant component of 

streamflow during late summer-autumn months. These 

low-flow periods can limit the habitat of fish and, 

therefore, are a critical period to understand and 

simulate accurately. PRMS is designed to simulate 

surface and shallow subsurface flow and simplifies 

ground-water flow much more than would a groundwater flow model. The current ground-water flow 

equations of PRMS use few parameters and are not 

physically based. Simple hydrograph separation 

indicates that one value for the rate of ground-water 

flow is insufficient. The methodology for routing water 

between ground-water reservoirs is currently nonexistent and probably accounts for some differences in 

measured and simulated flows. 

Parameter Error 

Parameter error occurs when improper values are 

chosen during the calibration process. Various 

combinations of parameter values can achieve the 

desired reduction in residual error, yet improperly 

represent the actual system. For example, an increase 

in evapotranspiration or a decrease in precipitation 

would both result in a lower simulated discharge at a 

node. With all watershed models, the most sensitive 

parameters will be those directly related to 

precipitation and air temperature. Ground-water flow 

parameters had a large effect on the shape of the 

simulated hydrograph during low-flow periods. Model 

fit was accomplished primarily with manual calibration 

and this method does not provide statistical insight into 

observation sensitivity to parameters or correlation 

between parameters. Uncertainty of parameters is 

therefore not quantified. 

28 Use of a Precipitation-Runoff Model to Simulate Natural Streamflow Conditions in the Methow River Basin, Washington 
---------------------------------

Table 3. Simulated minimum, maximum, and mean monthly streamflows and standard deviations for the Methow River Basin, Washing[Standard deviation: 

n x

2 ∑ (∑x 2 – 

n n( – 1

- - -

)

) ] 

Station MONTHLY STREAMFLOWS, IN CUBIC FEET PER SECOND 

No. OCT NOV DEC JAN FEB MAR APR MAY JUNE JUL

12447390 Minimum 1.2 1.1 1.0 0.9 0.8 0.8 1.5 32.5 4.2 1.

Maximum 31.0 7.6 3.0 2.6 2.4 2.2 76.6 251.8 427.6 133.Mean 4.1 2.9 2.0 1.8 1.7 1.6 25.5 135.5 136.4 33.Standard 4.8 1.4 0.5 0.4 0.3 20.9 48.8 92.4 38.1 14.

deviation 

12448000 Minimum 14.8 45.1 35.0 20.9 17.7 21.8 65.0 93.2 30.3 22.

Maximum 589.4 524.4 225.5 92.2 131.5 183.8 1,040.1 3,673.3 5,584.2 1,148.Mean 126.2 163.5 79.4 54.5 58.6 100.3 425.1 1,691.4 1,351.5 303.Standard 106.8 114.2 38.4 19.10 22.2 37.6 202.7 822.6 1,161.6 301.

deviation 

12448998 Minimum 32.4 38.7 33.6 32.4 28.9 39.6 148.2 279.7 116.4 52.

Maximum 245.6 300.8 148.1 74.8 112.3 285.4 794.5 2,017.8 2,522.8 739.Mean 77.7 101.7 68.1 48.0 52.5 107.4 464.4 991.8 833.7 283.Standard 35.6 59.1 27.3 11.0 17.2 47.5 152.3 385.8 470.3 182.

deviation 

12447383 Minimum 29.1 45.4 32.2 17.1 14.9 19.3 134.2 677.4 146.1 54.

Maximum 605.9 480.7 121.0 57.7 117.4 543.8 1,712.3 4,556.1 6,298.9 2,533.Mean 116.8 116.1 53.3 37.1 38.9 102.8 840.7 2,439.9 1,982.5 642.Standard 

Precipitation-Runoff Model 

97.6 85.6 18.0 8.6 19.0 103.4 409.0 796.5 1,191.5 616.

deviation 

12448500 Minimum 56.7 108.1 86.0 61.7 72.6 130.7 499.1 839.0 200.8 94.

Maximum 1,509.8 1,362.7 456.3 184.3 381.6 999.6 3,324.8 9,053.7 13,607.0 3,643.Mean 307.2 382.9 170.5 118.7 169.7 381.3 1,689.7 4,708.2 3,694.9 1,060.Standard 265.5 269.8 74.8 32.8 78.8 182.0 696.2 1,797.2 2,616.2 985.

deviation 

29 
30 Table 3. Simulated minimum, maximum, and mean monthly strea

mflows and standard deviations for the Methow River Basin, Washing

water years 1959–99 — Continued 

Use of a Precipitation-Runoff Model to Simulate Natural Streamflow Conditions in the Methow River Basin, Washington Station MONTHLY STREAMFLO

WS, IN CUBIC FEET PER SECOND 

No. OCT 

N

OV DEC JAN FEB 

MAR APR MAY JUNE JUL

12449500 Minimum 89.2 155.5 127.4 102.5 115.2 265.5 641.8 1128.3 319.6 147.

Maximum 1,833.0 1,814.5 716.3 318.7 631.1 1,325.7 4,098.8 10,830.7 16,258.7 4,434.Mean 401.5 541.6 273.9 181.6 277.6 601.4 2,196.4 5,729.4 4,571.4 1,363.Standard 316.5 367.7 125.9 52.0 121.9 241.1 823.6 2,170.5 3,090.4 1,168.

deviation 

12449950 Minimum 91.3 169.3 149.5 118.3 129.4 275.0 642.8 1,172.3 331.0 151.

Maximum 2,096.6 2,239.8 1,218.6 566.8 1,107.9 2,307.7 4,871.1 11,583.7 17,052.5 4,714.Mean 482.8 751.3 394.3 253.7 465.6 1,077.9 2,672.1 6,099.4 4,861.4 1,486.Standard 398.7 519.5 228.8 105.0 228.9 454.8 981.2 2,350.0 3,260.7 1,239.

deviation 

Early Winters 

Minimum 14.7 13.6 12.7 11.9 11.2 12.6 17.5 112.1 24.7 19.Maximum 127.9 58.1 29.5 26.3 32.0 70.7 401.2 1,020.9 1,367.6 538.

Mean 32.1 26.9 21.2 18.9 17.8 22.1 191.7 547.1 406.5 121.

Standard 17.9 8.0 3.4 2.8 3.4 14.2 98.6 178.2 266.0 133.

deviation 

Wolf Minimum 0.6 1.1 0.3 0.1 0.0 0.2 41.2 20.2 5.6 2.

Maximum 51.9 47.7 5.6 2.0 27.0 78.9 242.0 495.5 542.2 185.Mean 9.8 10.2 1.8 0.7 2.0 15.3 128.9 192.4 122.7 38.Standard 10.0 9.2 1.3 0.4 4.7 18.1 49.7 93.4 93.8 38.

deviation 
Table 4. Simulated and measured mean annual streamflows, simulated streamflow as a 

percentage of measured, and bias for water years 1992–99 

[Difference: [(SIM–OBS)/OBS] × 100. Bias: as a percentage of mean measured runoff = 100 × SUM{[(S–O)/O]/N} 

for all 0>0.0. ft

3/s, cubic foot per second] 

Station 

No. Water year 

12447383 1992


1993


1994


1995


1996


1997


1998


1999


Total ..............


12447390 1992


1993


1994


1995


1996


1997


1998


1999


Total ..............


12448000 1992


1993


1994


1995


1996


1997


1998


1999


Total ..............


12448500 1992


1993


1994


1995


1996


1997


1998


1999


Total ..............


Mean annual streamflow Difference between 

(ft3/s) simulated and measured Bias 

as percentage of (percent) 

Simulated Measured measured 

343.8 405.5 -15.2 

374.1 309.2 21.0 

337.6 286.4 17.9 

685.5 590.7 16.0 

655.7 690.3 -5.0 

821.5 725.4 13.2 

586.7 589.9 -0.5 

603.0 798.3 -24.5 

4,407.9 4,395.8 0.3 2.9 

19.7 22.1 -10.8 

27.1 25.3 7.1 

18.8 28.4 -33.7 

42.9 40.7 5.4 

34.2 41.4 -17.3 

50.5 43.5 15.9 

43.9 37.2 18.2 

35.7 45.0 -20.6 

272.8 283.5 -3.8 -4.5 

199.6 223.3 -10.6 

299.5 275.4 8.7 

217.3 281.6 -22.8 

622.6 527.6 18.0 

494.6 529.3 -6.6 

735.5 580.7 26.7 

565.1 511.1 10.6 

500.8 629.7 -20.5 

3,635.0 3,558.7 2.1 0.4 

659.4 869.3 -24.1 

782.7 814.5 -3.9 

651.0 758.1 -14.1 

1,559.7 1,444.1 8.0 

1,366.2 1,570.4 -13.0 

1,808.2 1,639.6 10.3 

1,361.8 1,423.6 -4.3 

1,303.9 1,728.9 -24.6 

9,492.9 10,248.5 -7.4 -8.2 

Precipitation-Runoff Model 31 
Table 4. Simulated and measured mean annual streamflows, simulated streamflow as a 

percentage of measured, and bias for water years 1992–99—Continued 

Station 

No. Water year 

12448998 1992


1993


1994


1995


1996


1997


1998


1999


Total ..............


12449500 1992


1993


1994


1995


1996


1997


1998


1999


Tota...............l


12449950 1992


1993


1994


1995


1996


1997


1998


1999


Total ..............


Mean annual streamflow Difference between 

(ft3/s) simulated and measured Bias 

as percentage of (percent) 

Simulated Measured measured 

183.7 179.8 2.2 

167.2 170.4 -1.8 

164.4 151.9 8.2 

378.4 341.4 10.9 

337.5 409.5 -17.6 

395.7 384.9 2.8 

315.3 294.9 6.9 

332.8 344.0 -3.3 

2,275.0 2,276.7 -0.1 1.0 

868.0 1,033.8 -16.0 

976.4 947.7 3.0 

832.2 901.3 -7.7 

2,008.6 1,752.4 14.6 

1,759.7 1,915.3 -8.1 

2,277.8 1,922.8 18.5 

1,718.2 1,670.9 2.8 

1,678.7 1,968.6 -14.7 

12,119.7 12,112.8 0.1 -1.0 

1,000.6 1,084.0 -7.7 

1,144.0 1,022.9 11.8 

952.3 963.0 -1.1 

2,420.4 1,854.1 30.5 

2,041.2 2,053.6 -0.6 

2,631.6 2,128.1 23.7 

1,955.6 1,914.2 2.2 

1,927.9 2,251.0 -14.4 

14,073.5 13,271.0 6.0 5.6 

32 Use of a Precipitation-Runoff Model to Simulate Natural Streamflow Conditions in the Methow River Basin, Washington 
PLANNED WORK AND FUTURE STUDIES 

The next phase of the current study will improve 

the watershed model by simulating more complex 

hydrologic features such as streamflow diversions and 

returns and by considering findings from the 

concurrent ground-water study. Inverse modeling 

using non-linear regression will be used to better 

construct and calibrate these simulations and to provide 

a more rigorous sensitivity analysis. The Phase Two 

model will be calibrated and validated to newly 

measured streamflow- and diversion-discharge 

measurements collected through the 2001 irrigation 

season and the historical record of streamflow that 

includes the effects of diversions. If additional 

streamflow and diversion data are collected in future 

years, the model calibration can be further improved. 

The Phase Two watershed model will be a userfriendly tool that can be used to simulate the impact on 

streamflow of different watershed-management options 

prior to their implementation. A special case that can 

be simulated includes summers without diversions and 

returns. Because the Phase Two model will be better 

calibrated than the current Phase One model, the 

special-case simulation would provide natural 

streamflows for the period of the climate record (1959 

to the present) with greater reliability than natural 

streamflows simulated with the current model. 

The calibrations of the Phase Two and possible 

other models will be improved if the current data sets 

continue to be expanded to include future years with 

different climatic and water-use conditions. Useful data 

to be measured include streamflow discharge, 

irrigation-canal diversion and return discharge, 

irrigation-canal leakage, rates of streamflow losses and 

gains to and from the ground-water system, 

respectively, climate variables, land- and water-use, 

and water levels in the ground-water system. 

SUMMARY AND CONCLUSIONS 

A study was conducted in cooperation with 

Okanogan County to evaluate natural streamflows for 

the Methow River and its tributaries. The need for this 

study was due in part to the listing of Upper Columbia 

River steelhead, including the Methow River run, and 

Upper Columbia River spring-run Chinook salmon, 

including the Methow River run, as “endangered” 

under the Endangered Species Act. Also, bull trout in 

the Methow River were listed under the Endangered 

Species Act as “threatened.” In an effort to focus on 

habitat conditions to sustain naturally producing 

salmonid populations, the National Marine Fisheries 

Service set instream flow requirements for three 

tributaries to the Methow River: the Chewuch River, 

Early Winters Creek, and Wolf Creek. Irrigation 

diversions from the river above existing and historical 

streamflow-gaging stations make it difficult to assess 

the natural streamflow conditions in the Basin. A 

calibrated watershed model could properly assess the 

available water resources throughout the Basin and 

provide guidance as to the natural streamflow 

conditions. 

Delineation of subbasins and the drainage 

network was accomplished with the Geographic 

Information System (GIS) Weasel. A 150-foot (45-

meter) USGS 7.5 minute digital elevation model of the 

Methow River Basin was used to define topographic 

surfaces. The GIS Weasel delineated 607 modeling 

response units (MRUs) based on slope, aspect, 

elevation, and flow planes. The parameterization 

component of the program then generated parameters 

for the MRUs incorporating ancillary information 

concerning soils, land use and land cover, and 

vegetation. 

Planned Work and Future Studies 33 
Information from the GIS Weasel was used to 

construct and calibrate a computer-simulation model of 

natural streamflow conditions for the Methow River 

Basin. The Modular Modeling System (MMS), using 

the Precipitation-Runoff Modeling System, was the 

simulation model chosen for this study. Major 

advantages of this system include the ability to (1) 

simulate the moisture balance of each component of 

the hydrologic cycle, (2) account for heterogeneous 

physical characteristics of a basin, (3) appropriately 

simulate both mountainous and flat areas, and (4) 

easily accept parameterization output from the GIS 

Weasel. Additionally, the system was recently applied 

and calibrated to a nearby, hydrologically similar 

watershed, the Yakima River Basin. Calibration of the 

various subbasins within the Methow River Basin was 

accomplished by using measured precipitation and airtemperature data as model input and by matching 

simulated and measured streamflows. Precipitation and 

air-temperature modules used a distance-weighted 

average approach to estimate missing data and avoid 

problems in the simulations. Monthly mean 

precipitation ratios between climate stations and MRUs 

were calculated from Parameter estimation Regressions 

on Independent Slopes Model (PRISM) estimates. 

Streamflow was simulated for water years 1992-

99 to calibrate the model to measured streamflows at 

the seven USGS gaging stations. Values determined by 

the GIS Weasel, values calculated and set by MMS 

algorithms, and parameter estimates used in the 

hydrologically similar Yakima River watershed basin 

model all provided initial estimates of parameters. 

Most parameter adjustments were related to 

precipitation, air temperature, minimum ground-water 

storage, and the ground-water flow coefficient. 

Difficulty existed in calibrating natural 

streamflow conditions in the Methow River Basin 

because all streamflow-gaging stations, with the 

exception of Andrews Creek (12447390), are located 

below irrigation diversions and few historical records 

exist for the study area prior to the diversions. Certain 

assumptions were made about the flow system. 

Simulated and measured streamflow generally showed 

close agreement, especially for spring runoff from 

snowmelt and low-flow conditions. The model 

simulations were less accurate capturing the magnitude 

and timing of short-term (1 to 3-day) peak flows. 

Annual water totals for simulated and measured 

streamflow varied considerably during many of the 

water years but total annual runoff for the 8-year period 

matched closely for all calibration points with the 

exception of station 12448500, Methow River at 

Winthrop. Simulated mean monthly September and 

October streamflow for two gaging stations, the 

Methow River above Goat Creek (12447383) and the 

Chewuch River (12448000), were greater than 

measured flows. 

The calibrated model can be used as a tool to 

simulate flows at ungaged streams or flows at gaged 

streams for periods outside the historical record. To 

demonstrate this ability, the period of water years 

1959-99 was simulated and monthly streamflow 

statistics generated. 

Certain approximations and simplifications must 

be made to simulate actual flow systems. Lack of 

understanding about some aspects of the natural flow 

system, coupled with only one streamflow-gaging 

station that measures natural streamflow (above 

irrigation diversions), accounts for much of the error in 

simulated results. Additional sources of error are data 

error, model error, and errors in the estimated 

parameter values. As a result, model-predicted values 

must be used with caution in consideration of 

simulation error. 

34 Use of a Precipitation-Runoff Model to Simulate Natural Streamflow Conditions in the Methow River Basin, Washington 
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36 Use of a Precipitation-Runoff Model to Simulate Natural Streamflow Conditions in the Methow River Basin, Washington