In cooperation with the North Dakota State Water Commission

Simulation of Streamflow and Wetland Storage,

Starkweather Coulee Subbasin, North Dakota,

Water Years 1981-98

Water-Resources Investigations Report 02-4113

U.S. Department of the Interior

U.S. Geological Survey

Cavanough

Lake

Dry

Lake

STARKWEATHER

COULEE

SUBBASIN

Starkweather

Coulee

Webster

BISMARCK

RED

RIVER

OF

THE

NORTH

MISSOURI

RIVER

SOUTH DAKOTA

M

O

N

T

A

N

A

MINNE

S

O

TA

SASKATCHEWAN MANITOBA

NORTH DAKOTA
U.S. Department of the Interior

U.S. Geological Survey

Simulation of Streamflow and Wetland Storage,

Starkweather Coulee Subbasin, North Dakota,

Water Years 1981-98

By Kevin C. Vining

Water-Resources Investigations Report 02-4113

In cooperation with the North Dakota State Water Commission

Bismarck, North Dakota

2002
U.S. DEPARTMENT OF THE INTERIOR

GALE A. NORTON, Secretary

U.S. GEOLOGICAL SURVEY

CHARLES G. GROAT, Director

Any use of trade, product, or firm names 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

Water Resources Division

821 East Interstate Avenue

Bismarck, ND 58503

Copies of this report can be purchased from:

U.S. Geological Survey

Information Services

Box 25286

Denver, CO 80225-0286
iii

CONTENTS

Abstract ....................................................................................................................................................................................

Introduction ..............................................................................................................................................................................

Study area.................................................................................................................................................................................

Climate data acquisition ...........................................................................................................................................................

Digital elevation model and estimation of wetlands area and volume.....................................................................................

Hydrologic model.....................................................................................................................................................................

Model parameterization ....................................................................................................................................................

Model calibration ..............................................................................................................................................................

Simulation of streamflow and wetland storage ........................................................................................................................

Model limitations and considerations ......................................................................................................................................

Summary ..................................................................................................................................................................................

References ................................................................................................................................................................................

Appendix-The Devils Lake Basin wetlands model, by George H. Leavesley.........................................................................

Introduction.......................................................................................................................................................................

Watershed characterization and parameterization.............................................................................................................

Model conceptualization ...................................................................................................................................................

References.........................................................................................................................................................................

Table A1. Original PRMS modules ..................................................................................................................................

Table A2. Prairie-pothole PRMS modules........................................................................................................................

FIGURES

1. Map showing major subbasins within the Devils Lake Basin and locations of study area, gaging station, and

weather stations.................................................................................................................................................................

2. Graph showing monthly precipitation for the study area, Starkweather Coulee subbasin, North Dakota,

water years 1981-98 ..........................................................................................................................................................

3. Map showing streamflow network of the study area as determined by GIS Weasel, and location of gaging station,

Starkweather Coulee subbasin, North Dakota ..................................................................................................................

4. Map showing simulated wetlands from the digital elevation model of the study area, Starkweather Coulee

subbasin, North Dakota.....................................................................................................................................................

5. Map showing locations of wetlands in the study area, Starkweather Coulee subbasin, North Dakota ............................

6. Map showing simulated hydrologic response units of the study area using GIS Weasel, Starkweather Coulee

subbasin, North Dakota.....................................................................................................................................................

7. Graph showing Precipitation-Runoff Modeling System simulated and observed daily streamflows,

Starkweather Coulee subbasin, North Dakota, water years 1981-98................................................................................

8. Graph showing Precipitation-Runoff Modeling System simulated daily wetlands areas, Starkweather Coulee

subbasin, North Dakota, water years 1981-98 ..................................................................................................................

9. Graph showing Precipitation-Runoff Modeling System simulated daily water volumes in open and closed

wetlands, Starkweather Coulee subbasin, North Dakota, water years 1981-98................................................................

10. Graph showing Precipitation-Runoff Modeling System simulated annual water volumes in wetlands and in

the study area, Starkweather Coulee subbasin, North Dakota, water years 1981-98........................................................

11. Graph showing Precipitation-Runoff Modeling System simulated daily wetlands areas for open-wetlands spillage

thresholds of 0.2 and 1.0, Starkweather Coulee subbasin, North Dakota, water years 1981-98 ......................................

12. Graph showing changes in Precipitation-Runoff Modeling System simulated wetlands area for an increase in openwetlands spillage thresholds from 0.2 to 1.0, Starkweather Coulee subbasin, North Dakota, water years 1981-98........

13. Graph showing Precipitation-Runoff Modeling System simulated open-wetlands water volumes at spillage

thresholds of 0.2 to 1.0, Starkweather Coulee subbasin, North Dakota, water years 1981-98.........................................
iv

TABLES

1. Hydrologic response unit parameters used in the hydrologic model, Starkweather Coulee subbasin, North Dakota,

water years 1981-98 ..........................................................................................................................................................

2. Annual water balance components and cumulative water balance from calibration of the hydrologic model,

Starkweather Coulee subbasin, North Dakota, water years 1981-98................................................................................

3. Observed and simulated annual streamflows and simulated streamflow as a percentage of observed streamflow,

Starkweather Coulee subbasin, North Dakota, water years 1981-98................................................................................

4. Simulated annual streamflow and total-period streamflow for various open-wetlands spillage thresholds,

Starkweather Coulee subbasin, North Dakota, water years 1981-98................................................................................
1

Simulation of Streamflow and Wetland Storage, Starkweathe

Coulee Subbasin, North Dakota, Water Years 1981-98

By Kevin C. Vining

Abstract

A study was conducted to simulate streamflow and wetland storage within a part of the Starkweath

subbasin. Information on streamflow and wetland storage in Starkweather Coulee subbasin may help 

management of water issues in the Devils Lake Basin. Information from a digital elevation model an

geographic-information-system analyses of the study area was used to develop the Devils Lake Basin 

model. Digital elevation model data and other climatic and topographic data were used as inputs to th

Within the study area, the average wetland depth was about 2.21 feet, the total maximum wetland area 

30,890 acres at the overflow elevation, and the total maximum wetland volume was about 68,270 acre

Model runs were made for water years 1981-98 to calibrate the model to observed streamflows th

obtained from the Starkweather Coulee gaging station. Observed annual peak streamflows were grea

simulated annual peak streamflows for all water years except 1983. The differences probably were ca

mostly by the lack of a subroutine in the model to account for frozen soil. The largest amount of simu

wetlands area occurred in April 1997 when about 40,500 acres of the study area was covered with wa

during April 1997, the simulated daily water volume in the open and closed wetlands combined attain

maximum of about 116,000 acre-feet. By increasing the spillage thresholds from 0.2 to 1.0, simulated

streamflow was reduced by 8.77 inches (from about 17.88 to 9.11 inches; 49 percent) for the 18-year 

During water years 1994-98, simulated annual streamflows for open-wetland spillage thresholds of 1.0 

less than for thresholds of 0.2 even though the open wetlands probably were near maximum volume. T

increased size of the closed wetlands during water years 1994-98 probably allowed for increased wate

and decreased simulated streamflow from the study area.

INTRODUCTION

Since the summer of 1993, the region around the Devils Lake Basin in northeastern North Dakota (fig. 1) 

intermittent flooding conditions. Copious amounts of rainfall have inundated roads, croplands, and properties. 

the low-relief topography and the lack of a prominent outlet from Devils Lake, precipitation and runoff remain 

basin, and water levels in Devils Lake increased from about 1,422 feet above sea level1 in October 1992 to mo

1,447 feet above sea level in August 1999. Millions of dollars have been spent to protect property from the ris

waters and to maintain the transportation network around Devils Lake. Many local, State, and Federal agencie

concerned about the current flooding problem and have a long-term interest in devising means for managing wa

the Devils Lake Basin. Some alternatives suggested to help stabilize Devils Lake water levels are to create dra

channel water from Devils Lake to adjacent-basin rivers and lakes and to re-establish and expand wetlands area

from Devils Lake.

The extent to which water can be retained in the Devils Lake Basin was revealed when greater-than-averag

precipitation in the 1990’s filled many of the wetlands in the basin. However, to evaluate the wetland storage a

the basin and to evaluate wetland storage changes on streamflow, accurate knowledge of surface topography wa

Therefore, a study was initiated by the U.S. Geological Survey (USGS) in cooperation with the North Dakota S

1In this report, "sea level" refers to the National Geodetic Vertical Datum of 1929 (NGVD of 1929)--a geodetic datum derived from 

adjustment of the first-order level nets of both the United States and Canada, formerly called Sea Level Datum of 1929.
2

Channel

Devils

 Lake

East Bay

East Bay

West Bay Main Bay

Sixmile Bay

DEVILS

LAKE

 East

 Devils

 Lake Stump

 Lake

Creel Bay

Lake

Irvine

Lake

Alice Chain

 Lake

Mikes

 Lake

Morrison

 Lake

Cavanough

 Lake

Sweetwater

 Lake

 Dry

Lake

Pelican

 Lake

Silver

Lake

Ibsen

Lake

Hurricane

 Lake

LITTLE

COULEE

SUBBASIN

MAUVAIS COULEE

SUBBASIN

CALIO COULEE

SUBBASIN

STARKWEATHER

COULEE

SUBBASIN

EDMORE

COULEE

SUBBASIN

STUMP

LAKE

SUBBASIN

DEVILS LAKE

SUBBASIN

DEVILS LAKE (NORTH SLOPE) SUBBASIN

(SOUTH SLOPE)

COMSTOCK

SUBBASIN

48 ̊30' 4

48 ̊ 

99 ̊

98 ̊30'

98 ̊30'

99 ̊

CAVALIER CO. RAMSEY CO. NELSON CO.

TOWNER CO.

BENSON CO.

ROLETTE CO.

PIERCE CO.

Figure 1. Major subbasins within the Devils Lake Basin and locations of study area, gaging station, and weather stations. (Modified fro

Devils Lake Basin Advisory Committee, 1976.)

A

EXPLANATION

Red River of the No

Devils Lake Basin

Starkweather Coule

Sheyenne River Ba

Approximate bound

study area

Basin boundary

Subbasin boundary

Gaging station and 

Weather station

SOUTH DAKOTA

MONTANA

MINNESOTA

SASKATCHEWAN MANITOBA 103 ̊ 101 ̊ 99 ̊

47 ̊

BISMARCK

49 ̊

Sheyenne

River

James

River

RED

RIVER

OF THE

NORTH

MISSOURI

RIVER

Souris

River

0 20 40 MILES

Starkweather

Coulee

Webster Coulee

Big

Comstock

Coulee

Mauvais

Coulee

Edmore

Coulee

Little

Coulee

Coulee

Calio

Mauvais

Coulee

Tributary No. 3

Tributary

Coulee

Edmore

Coulee

Webster

Leeds

Belcourt

0 5 10 MILES

05056239

05056239

Langdon

Edmore

Devils

Lake

Edmore

Levee

Levee
3

Commission to simulate streamflow and wetland storage within a part of the Starkweather Coulee subbasin of 

Lake Basin. This subbasin was selected for the study because of the availability of streamflow data from a gag

located on Starkweather Coulee. The study utilized digital elevation data, geographic-information-system (GIS

the Devils Lake Basin wetlands model, which is a modified version of the USGS Precipitation-Runoff Modelin

(PRMS; Leavesley and others, 1983) (see appendix), to define flow networks, to estimate wetland storage, and 

streamflow and storage within the low-relief landscape of the study area. Information from the study may be u

water managers, researchers, and others associated with the water issues that have arisen because of the rising w

of Devils Lake. This report describes the results of the study.

In a demonstration of the capability to accurately define surface topography within the Devils Lake Basin, 

resolution digital elevation model (DEM) of a portion of the Calio Coulee subbasin, a subbasin of the Devils L

was provided by the Earth Resources Observation Systems (EROS) facility of the USGS. The high-resolution 

created by using contour and other information from standard, USGS 1:24,000-scale topographic maps. Gener

wetland information derived from the high-resolution DEM was consistent with the U.S. Fish and Wildlife Ser

National Wetlands Inventory and the results of a study conducted by the U.S. Fish and Wildlife Service and th

Dakota State Water Commission to measure the total storage capacity of wetlands within many quarter-section 

(Ludden and others, 1983). The demonstration indicated that high-resolution DEM information is sufficient to 

surface hydrologic parameters, such as basin areas and boundaries, surface-flow networks, and the areas and v

wetlands, that could be used in hydrologic models of a basin.

Many hydrologic models exist that could be used to investigate watershed hydrology, hydraulics, channel r

water quality, but not all hydrologic models have incorporated a snowmelt routine that is needed for some wate

hydrology studies. Parekh (1977) used a version of the Stanford Watershed Model to continuously model the h

conditions within the Mauvais Coulee subbasin, the Edmore Coulee subbasin, and the Devils Lake Basin. How

extensive calibration of the model algorithms was needed to produce adequate results, and difficulties in model

from inadequate simulation of snow accumulation and snowmelt and from a lack of information related to surf

storage features other than soil moisture indices. Because during any year in North Dakota, snowmelt typically 

the largest amount of runoff during rapid snowmelt and overland flow across a frozen landscape, the Devils La

wetlands model, which contains a snowmelt routine, was used to develop the streamflow data for the Devils La

The Devils Lake Basin wetlands model and the PRMS are modular systems for constructing distributed-param

that use physics-based mathematical relations to represent the hydrology of an area. The systems utilize partiti

watershed into hydrologic response units (HRUs) on the basis of characteristics such as slope, aspect, elevation

and vegetation type so that each unit has a homogeneous response to physical, meteorologic, and hydrologic in

components of the Devils Lake Basin wetlands model and the PRMS currently are contained within the Modula

System (MMS) (Leavesley and others, 1996). The MMS uses a graphical interface that allows the user to sele

appropriate algorithms necessary to create the model needed for the desired application.

The PRMS has been applied to many watersheds and river basins to estimate runoff into reservoirs (Nakam

Jeton, 2000), to simulate the effects of land use on runoff and streamflow (Risley, 1993), and to provide estima

tributary inflows to use in streamflow-routing models (Laenen and Risley, 1995). Emerson (1988) used the PR

investigate the snowmelt-dominated hydrologic systems of two small watersheds, Hay Creek watershed in Mo

West Branch Antelope Creek watershed in North Dakota. Although model calibration for snowmelt runoff was 

accurate, the greatest model errors occurred because of the difficulty in defining the quantity and distribution o

cover. The PRMS also has been applied to ungaged basins to estimate streamflows (Norris, 1986; Jeton, 1999

investigations generally indicate that results from the modeling efforts were accurate. The investigations also s

the PRMS could be modified sufficiently to incorporate the influence of various topographic features on the hyd

streamflows of small watersheds in the Devils Lake Basin.

The author acknowledges the assistance and contributions made by George Leavesley, Roland Viger, and G

of the USGS. Leavesley incorporated a wetland hydrology subroutine into the PRMS, Viger provided initial P

parameterization with GIS Weasel, and Kelly provided DEM analyses of the Starkweather Coulee subbasin.
4

STUDY AREA

The Starkweather Coulee subbasin is a major subbasin within the Devils Lake Basin (fig. 1). The Starkwea

subbasin covers an area of about 310 square miles, of which about 210 square miles reportedly contributes to s

(Harkness and others, 1998). However, abnormally wet conditions since the summer of 1993 may have increa

amount of area that contributes to streamflow. A USGS gaging station is located on Starkweather Coulee abou

northwest of Webster. The study area is located upstream from the Starkweather Coulee gaging station and cov

of about 262 square miles (fig. 1). The study area topography generally is level to slightly rolling in the south, 

more rolling in the center, and generally level in the north. The soils are predominately loams to silty clays (B

Liudahl, 1986; Simmons and Moos, 1990). Thousands of wetlands exist on the surface. Some of the original w

were drained years ago and currently are being farmed. Most of the land in the study area is owned privately a

for agriculture. Some land areas are used for pasture or are enrolled in the U.S. Department of Agriculture’s C

Reserve Program.

Generally, the climate of the area consists of short, warm summers and long, cold winters. Average month

temperatures range from -15.6 degrees Celsius in January to 20.6 degrees Celsius in July (Owenby and Ezell, 1

Average annual precipitation is about 17.3 inches, of which about 75 percent occurs during April through Sept

(Owenby and Ezell, 1992). During 1991-97, however, average annual precipitation within the study area incre

about 21.7 inches. The increase contributed to the intermittent flooding conditions and the rising water levels o

Lake. Average seasonal snowfall is about 37 inches (Jensen, 1972), which contributes about 3.5 inches of wat

precipitation on the study area. Windy conditions often redistribute the snow into large drifts, leaving some lan

bare.

CLIMATE DATA ACQUISITION

Climate data requirements for the PRMS are daily total precipitation and daily maximum and minimum tem

For water years2

 1981-98, climate data were obtained from stations located at Devils Lake, near Edmore, and a

Langdon Agricultural Experiment Station near Langdon (see index map in fig. 1). For the summers of 1981-98

daily precipitation data were obtained from the precipitation reporting network of the North Dakota Atmospher

Board (ARB). Data from nine ARB stations were used in this study. The ARB stations are located within the b

Starkweather Coulee subbasin. For water years 1990-98, daily radiation data were obtained from the North Da

Agricultural Weather Network station at Langdon. Missing values of radiation were derived from empirical eq

contained in the PRMS. Snow water equivalent information was obtained from the National Weather Service’

Operational Hydrologic Remote Sensing Center in Chanhassen, Minn. Data on the physiography, vegetation, 

hydrologic characteristics of the study area were derived from field visits, topographic maps, digital data sets, a

Cavalier and Ramsey Counties soil survey publications (Bigler and Liudahl, 1986; Simmons and Moos, 1990). 

years 1981-98, daily streamflow data for Starkweather Coulee during ice-free months (generally April through 

were obtained from records at the Starkweather Coulee gaging station.

Daily precipitation at the ARB stations was recorded only during April through September, and several sta

not in continuous operation during water years 1981-98. Therefore, the stations were split into a north group w

stations and a south group with four stations, and the recorded daily precipitation data were averaged for each g

form two time series of data. Supplemental winter precipitation data for each group also were averaged from d

at Langdon and Edmore (north group) and at Devils Lake and Edmore (south group). The north half of the stud

the precipitation data from the north group and the south half of the study area used the precipitation data from 

group. Monthly precipitation for the study area, calculated as the average of the north and south groups, is sho

figure 2. Daily maximum and minimum temperature data for the study area were obtained by averaging the da

from Devils Lake, Edmore, and Langdon.

2In U.S. Geological Survey reports, water year is the 12-month period, October 1 through September 30. The water year is design

calendar year in which it ends; thus, the water year ending September 30, 1998, is called "water year 1998."
 5

DIGITAL ELEVATION MODEL AND ESTIMATION OF WETLANDS AREA AND VOLUME

High-resolution DEMs provided the topographic information needed for application of the PRMS hydrolo

USGS personnel created 20 initial DEMs using 20 USGS 7.5-minute topographic maps with contour intervals 

Elevation data from the topographic maps were sampled horizontally every 33 feet (10 meters) and interpolatio

were used to create a digital representation of the map. During construction of the final DEM for the study are

matching was used on the initial DEMs to guarantee that elevation contour lines were continuous between adja

Some of the initial DEMs that were created for the western side of the study area had elevations reported to 0.1

increments, which were considered sufficient for this study. Midway through the study, the USGS initiated a n

change in all DEM formats. The change resulted in elevations being reported to only 1.0-foot increments for t

DEMs for the eastern side of the study area. Thus, the final DEM contained a combination of formats with ele

reported to 1.0 foot. GIS Weasel (Viger and others, 1998) was used to determine the final DEM streamflow ne

within the study area. A shaded-relief version of the assembled final DEM was used for field verification of hy

and topographic features within the study area, and a few minor modifications were made.

The final DEM for the study area had hydrologic and topographic features similar to those observed durin

reconnaissance. The streamflow network determined by GIS Weasel (fig. 3) closely resembles the actual hydr

the basin. However, two potential problems evident from field reconnaissance and from the DEM-generated s

network are possible flow outlets on the southeast and south-central boundaries of the study area (fig. 3). USG

have observed flow from the south-central outlet of the study area into Webster Coulee during very high flows

some flow bypasses the Starkweather Coulee gaging station. No measurements or estimates have been made o

1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 199

0

11

1

2

3

4

5

6

7

8

9

10

MONTHLY PRECIPITATION, IN INCHES

WATER YEAR

Figure 2. Monthly precipitation for the study area, Starkweather Coulee subbasin, North Dakota, water years 1981-98.
6

0 1 2 3 4 5 MILES

CAVALIER CO.

RAMSEY CO.

48 ̊45'

98 ̊52'30"

98 ̊45'

48 ̊37'30"

48 ̊30'

48 ̊22'30"

48 ̊22'30"

48 ̊30'

98 ̊37'30"

98 ̊37'30"

98 ̊45' 98 ̊52'30"

48 ̊45'

48 ̊37'30"

Base from U.S. Geological Survey

1:24,000 quandrangles, Digital Elevation Model

Figure 3. Streamflow network of the study area as determined by GIS Weasel, and location of gaging

station, Starkweather Coulee subbasin, North Dakota.

05056239

05056239

 EXPLANATION

 Gaging station and number
7

basin flows, but the potential exists for overestimating some observed flows because the Devils Lake Basin wetl

assumes that all simulated flows from within the study area move past the Starkweather Coulee gaging station.

Incorporation of additional flow outlets is not feasible because the model does not support more than one flow 

each modeled basin. Also, even if subbasins for the other flow outlets are modeled, no data are available to ve

performance.

GIS tools were used to compute the surface areas and volumes to the spill elevations of the wetlands in the 

(fig. 4). The distribution of simulated wetlands corresponds generally to the National Wetlands Inventory loca

wetlands in the study area (fig. 5). The potential wetland storage in all basins to the spill elevations of the basi

calculated, and the depths and areas of individual wetlands were determined for every 10-meter grid cell from 

difference between the filled DEM elevation and the final DEM elevation. The average depth and total maxim

area computed in this manner within each HRU then was determined. Within the study area, the average wetla

was about 2.21 feet, the total maximum wetland area was about 30,890 acres at the overflow elevation, and the 

maximum wetland volume was about 68,270 acre-feet. The total maximum wetland volume represents the con

wetlands being totally full, but this condition may not be attainable from precipitation or runoff because of insu

catchment areas for all wetlands.

HYDROLOGIC MODEL

Information from the final DEM and the GIS analyses was used to develop the Devils Lake Basin wetland

the study area. Data sets from the GIS analyses, climatology, and geomorphology were incorporated into the m

simulate precipitation accumulation, snowmelt, evapotranspiration, soil infiltration, seepage to ground water, s

runoff, and streamflow (see appendix). Because snow catch by precipitation gages can underestimate the actua

snowfall on a basin from 20 percent to as much as 90 percent (Yang and others, 1995), the amount of precipita

snowfall was multiplied by an adjustment factor of 1.5 to account for the undercatch. Also, because the Devils 

wetlands model does not have a continuous streamflow-routing mechanism for daily time-step calculations, all 

that is generated by the model during the daily time step is designed to leave the modeled study area by the nex

Observations on Starkweather Coulee have indicated that the time lag for surface-water routing may be 3 to 5 d

model does not have a routine for handling frozen soil conditions that occur during spring snowmelt events but 

parameter to limit soil infiltration during periods when snow exists on the surface.

The study area was divided into 50 HRUs on the basis of elevation, slope, aspect, flow planes, soil types, a

vegetation, using GIS Weasel (fig. 6). Each HRU produced a water balance and an energy balance that then w

quantified to represent the combined effect for the study area (see appendix).

Individual wetland areas and volumes within the study area were determined from the DEM and GIS analy

However, because of model constraints and the complexities of including thousands of individual basins, only o

per HRU was simulated. Therefore, 50 wetlands were modeled within the study area, and each wetland repres

combined area and volume of all DEM wetlands within the respective HRU. This large-scale simplification m

inaccuracies about the interactions of multiple wetland catchment areas and spill elevations with hydrologic pr

was deemed satisfactory for introducing the concept of wetlands into the PRMS. Each HRU wetland had an av

and maximum area as determined by the DEM. The maximum wetland volume for each HRU was calculated 

average wetland depth multiplied by the maximum wetland area. The area-to-volume equation for each wetlan

defined as

where

is the decimal fraction of the maximum wetland area,

is the area-to-volume coefficient, and

is the decimal fraction of the maximum wetland volume.

The area-to-volume coefficient was estimated to equal 0.5 on the basis of surveying information obtained by th

1996 at several wetlands near Berthold, N. Dak. (unpublished data on file at the USGS office, Bismarck, N. Da

Amax e

c V max ( ) ln =

Amax

c

V max
8

0 1 2 3 4 5 MILES

Base from U.S. Geological Survey

1:24,000 quandrangles, Digital Elevation Model

Figure 4. Simulated wetlands from the digital elevation model of the study area, Starkweather

Coulee subbasin, North Dakota.

CAVALIER CO.

RAMSEY CO.

48 ̊45'

98 ̊52'30"

98¡45'

48 ̊37'30"

48 ̊30'

48 ̊22'30"

48 ̊22'30"

48 ̊30'

98 ̊37'30"

98 ̊37'30"

98 ̊45' 98 ̊52'30"

48 ̊45'

48 ̊37'30"
9

0 1 2 3 4 5 MILES

CAVALIER CO.

RAMSEY CO.

48 ̊45'

98 ̊52'30"

98 ̊45'

48 ̊37'30"

48 ̊30'

48 ̊22'30"

48 ̊22'30"

48 ̊30'

98 ̊37'30"

98 ̊37'30"

98 ̊45' 98 ̊52'30"

48 ̊45'

48 ̊37'30"

Base from U.S. Geological Survey

1:24,000 quandrangles, Digital Elevation Model

Figure 5. Locations of wetlands in the study area, Starkweather Coulee subbasin, North Dakota.

(Based on data from U.S. Fish and Wildlife Service National Wetlands Inventory.) 
10

0 1 2 3 4 5 MILES

CAVALIER CO.

RAMSEY CO.

48 ̊45'

98 ̊52'30"

98 ̊45'

48 ̊37'30"

48 ̊30'

48 ̊22'30"

48 ̊22'30"

48 ̊30'

98 ̊37'30"

98 ̊37'30"

98 ̊45' 98 ̊52'30"

48 ̊45'

48 ̊37'30"

Base from U.S. Geological Survey

1:24,000 quandrangles, Digital Elevation Model

Figure 6. Simulated hydrologic response units of the study area using GIS Weasel, Starkweather

Coulee subbasin, North Dakota. (Numbers indicate the individual hydrologic response units.)

1 2

3

4

5

6

9

7

8

10

11

12

13

14

15

16

17

18

19

20

21

22

24

25

26

31 27

23

28

29

30

32

33

34

35

36

37

38 39

40

41

42

43

44

45

49 48

46 47

50
11

Each HRU wetland was partitioned into two parts, an open wetland and a closed wetland. A parameter wa

determine the part of the HRU wetland that was defined as open, and the remainder of the HRU wetland then w

as closed. The open wetland was defined as having an outlet with a spillage threshold that was equal to a fract

total volume of the open wetland without an outlet. If an open wetland had a spillage threshold of 0.5, water w

from the wetland when the volume of the open wetland reached 50 percent of its total volume without an outle

Precipitation volumes falling on an open wetland and evaporation volumes lost from an open wetland were dep

calculated open-water area. Surface runoff generated for each HRU was routed into the open wetland using a u

fraction of runoff into the wetland. The remaining runoff entered the streamflow network. Spillage volumes fro

wetland were directly proportional to the difference between the wetland volume and the wetland water volum

spillage threshold. Spillage volumes were routed into the streamflow network. Wetland ground-water-recharge 

set to vary directly with wetland water depth. The closed wetland was defined as not having an outlet. Theref

closed wetland did not spill, but did gain and lose water in the same manner as the open wetland. All closed we

allowed to increase their volume beyond their maximum to simulate the expansion of wetlands areas within the 

The hydrologic model was set to run on a daily time step and to simulate conditions for water years 1981-

initial volume of water stored in the study area at the beginning of the run was about 33,240 acre-feet. This tot

calculated from the assumed initial conditions for the wetlands and the soil portions of the study area. The wet

volume was assumed to equal 10 percent (6,827 acre-feet) of the total maximum wetland volume (68,270 acre-

was assumed to occupy 9,760 acres of the total maximum wetland area of 30,890 acres based on the area-to-vo

equation applied to each of the 50 wetlands and summed. Soil water content was assumed to be 2 inches (0.167 

the remaining study area (167,900 minus 9,760 equals 158,140 acres) for a total soil water volume of about 26

feet. The model partitioned the precipitation and snowmelt into the wetland, into the soil, or into stream chann

from impervious areas of the study area can occur, but no such areas were defined in the model. Once the soil 

conditions were satisfied, additional inputs of water were routed to ground water or as surface runoff into the w

into stream channels. Modeled surface runoff into the wetland represents 90 percent of total surface runoff gen

remaining 10 percent flowed directly to stream channels. The amount of evapotranspiration from the soil and w

was modeled using the Jensen-Haise formulation (Jensen and Haise, 1963).

Model Parameterization

Parameter values were chosen to closely approximate actual conditions in the study area. Most values asso

surface features and atmospheric conditions were determined from information derived from GIS tools, climate 

observations, and soil survey publications. Parameter values associated with physics-based processes, such as 

infiltration, and radiation transfer, were obtained from the default parameter lists of previous versions of the PR

Selected parameter values assigned to each HRU are listed in table 1.

Several assumptions about wetlands and wetland processes were made prior to parameterization. The perc

wetlands in the study area that spilled to channels (open wetlands) was estimated from DEM products to be 50 

The assumption was based on the knowledge that many, but probably not all, wetlands in the study area have h

degree of drainage. Another assumption was that the open wetlands would begin to spill when 20 percent of th

volume was reached. The storage volumes of the wetlands were determined from the difference between the fi

elevations and the final DEM elevations. Initial storage in the wetlands was assumed to be 10 percent of the m

possible storage. Wetland seepage rates were set to 0.002 of the current wetland water depth (Winter and Rose

1995), which would equal 0.1 inch per day for wetlands with water depths of 50 inches.

Model Calibration

Model runs were made for water years 1981-98 to calibrate the model to observed streamflows that were o

from the Starkweather Coulee gaging station. Model calibration was achieved by adjusting the values for max

available soil water in the soil profil6e within the root zone until the simulated streamflow from the study area 

year period nearly equaled the observed streamflow for the 18-year period. The values of maximum available s

the soil profile that were used for calibration remained within the ranges of values for the soils involved as repo

county soil surveys (Bigler and Liudahl, 1986; Simmons and Moos, 1990). Other parameter values could have 
 12

Table 1. Hydrologic response unit parameters used in the hydrologic model, Starkweather Coulee subbasin, North Dakota, water years 1981-98[HRU, hydrologic response unit]

HRU

Area

(acres)

Elevation

(feet above

sea level)

Slope

(foot per foot)

Summer canopy

fraction

Winter canopy

fraction

Fraction of HRU

area that is

wetland

Mean wetlands

water depth

(inches)

Wetlands

seepage rate

(inches per day)

Fraction of open

wetlands

Open-wetland

fractional

volume at

spillage

Fraction of

runoff that

enters wetland

Daily maximum

surface water

that enters

ground water

(inches)

1 6,182 1,610 0.002 0.9 0.5 0.081 16.7 0.002 0.5 0.2 0.9 0.12 2 6,286 1,610 0.002 0.9 0.5 0.085 16.4 0.002 0.5 0.2 0.9 0.12 3 2,020 1,600 0.002 0.9 0.5 0.145 23.9 0.002 0.5 0.2 0.9 0.12 4 3,684 1,600 0.002 0.9 0.5 0.175 23.5 0.002 0.5 0.2 0.9 0.12 5 4,936 1,580 0.002 0.9 0.5 0.212 23.9 0.002 0.5 0.2 0.9 0.12 6 5,507 1,575 0.002 0.9 0.5 0.234 25.3 0.002 0.5 0.2 0.9 0.12 7 2,591 1,575 0.002 0.9 0.5 0.219 25.3 0.002 0.5 0.2 0.9 0.12 8 2,690 1,570 0.002 0.9 0.5 0.222 24.8 0.002 0.5 0.2 0.9 0.12 9 2,627 1,570 0.002 0.9 0.5 0.210 28.5 0.002 0.5 0.2 0.9 0.12 

10 5,298 1,530 0.002 0.9 0.5 0.258 32.4 0.002 0.5 0.2 0.9 0.12 11 2,249 1,520 0.002 0.9 0.5 0.247 32.6 0.002 0.5 0.2 0.9 0.12 12 1,751 1,570 0.002 0.9 0.5 0.250 29.4 0.002 0.5 0.2 0.9 0.12 13 806 1,565 0.002 0.9 0.5 0.197 25.4 0.002 0.5 0.2 0.9 0.12 14 9,888 1,535 0.002 0.9 0.5 0.225 29.9 0.002 0.5 0.2 0.9 0.12 15 7,725 1,535 0.002 0.9 0.5 0.216 26.7 0.002 0.5 0.2 0.9 0.12 16 1,422 1,570 0.002 0.9 0.5 0.209 28.3 0.002 0.5 0.2 0.9 0.12 17 14,558 1,535 0.002 0.9 0.5 0.207 30.0 0.002 0.5 0.2 0.9 0.12 18 8,010 1,540 0.002 0.9 0.5 0.194 29.8 0.002 0.5 0.2 0.9 0.12 19 2,428 1,550 0.002 0.9 0.5 0.226 27.6 0.002 0.5 0.2 0.9 0.12 20 3,289 1,540 0.002 0.9 0.5 0.188 28.5 0.002 0.5 0.2 0.9 0.12 21 1,656 1,550 0.002 0.9 0.5 0.208 27.3 0.002 0.5 0.2 0.9 0.12 22 1,493 1,550 0.002 0.9 0.5 0.219 30.1 0.002 0.5 0.2 0.9 0.12 23 1,319 1,560 0.002 0.9 0.5 0.188 27.1 0.002 0.5 0.2 0.9 0.12 24 7,059 1,515 0.002 0.9 0.5 0.213 30.9 0.002 0.5 0.2 0.9 0.12 25 1,465 1,510 0.002 0.9 0.5 0.236 29.4 0.002 0.5 0.2 0.9 0.12 
 13

26 1,167 1,510 0.002 0.9 0.5 0.202 25.2 0.002 0.5 0.2 0.9 0.12 27 3,454 1,520 0.002 0.9 0.5 0.176 28.6 0.002 0.5 0.2 0.9 0.12 28 1,030 1,545 0.002 0.9 0.5 0.177 28.9 0.002 0.5 0.2 0.9 0.12 29 4,398 1,495 0.002 0.9 0.5 0.160 24.8 0.002 0.5 0.2 0.9 0.12 30 4,021 1,480 0.002 0.9 0.5 0.198 24.6 0.002 0.5 0.2 0.9 0.12 31 529 1,520 0.002 0.9 0.5 0.264 39.8 0.002 0.5 0.2 0.9 0.12 32 161 1,510 0.002 0.9 0.5 0.033 17.2 0.002 0.5 0.2 0.9 0.12 33 1,179 1,510 0.002 0.9 0.5 0.188 26.0 0.002 0.5 0.2 0.9 0.12 34 1,658 1,515 0.002 0.9 0.5 0.197 27.2 0.002 0.5 0.2 0.9 0.12 35 3,634 1,500 0.002 0.9 0.5 0.137 20.6 0.002 0.5 0.2 0.9 0.12 36 2,514 1,490 0.002 0.9 0.5 0.133 17.8 0.002 0.5 0.2 0.9 0.12 37 3,506 1,500 0.002 0.9 0.5 0.209 26.5 0.002 0.5 0.2 0.9 0.12 38 3,508 1,500 0.002 0.9 0.5 0.209 26.2 0.002 0.5 0.2 0.9 0.12 39 4,534 1,505 0.002 0.9 0.5 0.143 29.2 0.002 0.5 0.2 0.9 0.12 40 3,500 1,505 0.002 0.9 0.5 0.136 23.9 0.002 0.5 0.2 0.9 0.12 41 1,278 1,470 0.002 0.9 0.5 0.115 18.1 0.002 0.5 0.2 0.9 0.12 42 4,561 1,470 0.002 0.9 0.5 0.169 16.6 0.002 0.5 0.2 0.9 0.12 43 2,457 1,475 0.002 0.9 0.5 0.083 18.7 0.002 0.5 0.2 0.9 0.12 44 956 1,465 0.002 0.9 0.5 0.146 32.0 0.002 0.5 0.2 0.9 0.12 45 1,984 1,480 0.002 0.9 0.5 0.211 19.1 0.002 0.5 0.2 0.9 0.12 46 2,005 1,465 0.002 0.9 0.5 0.102 16.4 0.002 0.5 0.2 0.9 0.12 47 1,108 1,475 0.002 0.9 0.5 0.125 15.5 0.002 0.5 0.2 0.9 0.12 48 2,318 1,470 0.002 0.9 0.5 0.067 19.9 0.002 0.5 0.2 0.9 0.12 49 4,592 1,480 0.002 0.9 0.5 0.155 21.3 0.002 0.5 0.2 0.9 0.12 50 951 1,475 0.002 0.9 0.5 0.122 17.6 0.002 0.5 0.2 0.9 0.12 

Table 1. Hydrologic response unit parameters used in the hydrologic model, Starkweather Coulee subbasin, North Dakota, water years 1981-98—Continued

[HRU, hydrologic response unit]

HRU

Area

(acres)

Elevation

(feet above

sea level)

Slope

(foot per foot)

Summer canopy

fraction

Winter canopy

fraction

Fraction of HRU

area that is

wetland

Mean wetlands

water depth

(inches)

Wetlands

seepage rate

(inches per day)

Fraction of open

wetlands

Open-wetland

fractional

volume at

spillage

Fraction of

runoff that

enters wetland

Daily maximum

surface water

that enters

ground water

(inches)
14

adjusted to achieve calibration, but the model appeared to be less sensitive to the other parameters. By adjustin

values for maximum available soil water in the soil profile, additional assumptions about changes in other param

were not required and physically-realistic values were maintained.

Annual water balances were determined for the final calibration run as the differences between the annual 

(precipitation) and the annual water losses (evapotranspiration plus change in storage plus streamflow). Gener

cumulative water balances for most years of the calibration run were less than 0.03 inch, which indicated that a

water during those years was accountable (table 2). Four water years (1981, 1983, 1991, and 1998) had cumul

balances greater than 0.03 inch, which indicated a greater amount of water gain than water loss. However, the 

water years (1982, 1984, and 1992) had cumulative water balances that were again near zero, which indicated 

water balance for the 2-year period. The result indicates that some model discrepancy was acting to simulate e

one water year but then remove the excess the next water year for a 2-year balance. The reason for this discrep

unknown.

1Annual water balance = precipitation - evapotranspiration - change in storage - simulated streamflow.

Simulated and observed daily streamflows for water years 1981-98 are shown in figure 7. The two hydrog

many similarities, especially in the timing of spring runoff from snowmelt. However, observed annual peak st

were greater than simulated annual peak streamflows for all water years except 1983. The differences probabl

caused mostly by the lack of a subroutine in the model to account for frozen soil. Generally, recessionary limb

more on the simulated hydrographs than on the observed hydrographs. The model also tended to simulate mor

streamflow during summer and autumn rainfall. Simulated streamflows were much higher than observed strea

the spring of 1997. The difference between the streamflows during that time may have occurred because some o

flowed out of the study area and into Webster Coulee (referred to as breakout flows); thus, the flow bypassed t

Starkweather Coulee gaging station. Breakout flows were observed during the spring of 1997. However, it also 

that the difference between streamflows in 1997 resulted from problems with calibration of the model to high f

Although the simulated and observed streamflows for the 18-year period were similar, simulated annual stream

individual years varied considerably from observed annual streamflow during many of the water years (table 3

the actual hydrologic processes in the study area could not be accounted for adequately by the equations and pa

that simulated soil water infiltration and storage, snowmelt, and wetlands hydrology.

Table 2. Annual water balance components and cumulative water balance from calibration of the hydrologic model, Starkweather Coule

North Dakota, water years 1981-98

Water

year

Precipitation

(inches)

Evapotranspiration

(inches)

Storage

change

(inches)

Simulated

streamflow

(inches)

Annual water

balance1

(inches)

Cum

 1981 19.025 17.027 1.635 0.228 0.135 

 1982 22.608 22.053 0.167 0.522 -0.134 

 1983 22.085 20.339 0.394 1.086 0.266 

 1984 13.395 15.650 -2.232 0.241 -0.264 

 1985 20.960 18.757 1.917 0.287 -0.001 

 1986 22.334 22.318 -0.597 0.607 0.006 

 1987 22.314 21.673 0.347 0.294 0 

 1988 12.606 14.518 -2.046 0.135 -0.001 

 1989 13.999 13.804 0.133 0.062 0 

 1990 13.842 13.488 0.297 0.061 -0.004 

 1991 22.687 19.154 2.979 0.322 0.232 

 1992 16.185 16.938 -1.105 0.577 -0.225 

 1993 30.312 23.920 4.184 2.208 0 

 1994 18.664 20.843 -3.074 0.896 -0.001 

 1995 23.954 22.502 -0.333 1.787 -0.002 

 1996 27.293 23.490 1.879 1.921 0.003 

 1997 27.989 23.189 -0.191 4.976 0.015 

 1998 23.830 24.473 -2.531 1.673 0.215 
15

Simulated daily wetlands areas for water years 1981-98 are shown in figure 8. The simulated daily wetlan

the sum of open and closed wetlands areas. The model permitted the closed wetlands to expand beyond their D

determined areas to simulate the inundation of surface area that has occurred since the recent wet period began 

year 1993. Simulated daily wetlands areas increased during large runoff events but decreased during drier peri

summertime, because of increased evapotranspiration. The largest amount of simulated daily wetlands area oc

April 1997 when about 40,500 acres (24 percent) of the study area was covered with water. Also during April 

simulated daily water volume in the open and closed wetlands combined attained a maximum of about 116,000 

(fig. 9). The open wetlands contained about 44,000 acre-feet of water, and the closed wetlands contained abou

72,000 acre-feet of water. During most of the calibration run, the simulated daily wetlands area was less than a

31,000 acres, which was about equal to the amount of wetlands area originally determined from the final DEM 

area.

Comparisons of simulated annual water volumes in the wetlands to simulated annual water volumes in the 

for water years 1981-99 are shown in figure 10. Total water storage includes water stored in wetlands, channel

ground-water reservoirs. During water years 1981-92, the percentage of study area water stored in wetlands ra

about 17 to 31 percent. During water years 1993-98, the percentage of study area water stored in wetlands had 

between 37 and 66 percent. During water year 1998, annual evapotranspiration exceeded annual precipitation 

time since water year 1994 (table 2), which resulted in a considerable reduction in the soil moisture portion of 

water storage within the study area.

1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 19

WATER YEAR

0

1,300

100

200

300

400

500

600

700

800

900

1,000

1,100

1,200

DAILY STREAMFLOW, IN CUBIC FEET PER SECOND

Simulated

Observed

Figure 7. Precipitation-Runoff Modeling System simulated and observed daily streamflows, Starkweather Coulee subbasin, No

Dakota, water years 1981-98.
 16

1

Percent error = (simulated streamflow - observed streamflow) x 100/observed streamflow.

SIMULATION OF STREAMFLOW AND WETLAND STORAGE

After calibration, the simulated streamflow response to increased open-wetlands spillage thresholds was e

The implied physical effect of increasing spillage thresholds is a filling of the spillways from open wetlands to 

wetlands to hold more water. The larger the spillage threshold, the larger the open-wetlands water volume mu

spillage can occur. Closed wetlands were not affected by the change in spillage thresholds because closed wet

defined as not spilling. In addition to the calibration spillage threshold of 0.2, spillage thresholds of 0.3, 0.4, 0

1.0 times the wetlands volumes were used in the simulations. A spillage threshold of 1.0 makes an open wetla

similarly to a closed wetland until the spillage volume of the open wetland is reached. By increasing the spilla

thresholds from 0.2 to 1.0, simulated streamflow was reduced by about 8.77 inches (from about 17.88 to 9.11 i

49 percent) for the 18-year period, and simulated annual streamflow was reduced by more than 80 percent for 

1982, 1986, and 1992 (table 4). During the drier water years of 1988-90, simulated streamflows for spillage th

1.0 were reduced by no more than about 50 percent from simulated streamflows for spillage thresholds of 0.2 b

smaller amounts of streamflow were generated and wetlands were not filled. However, by increasing the spilla

thresholds from 0.2 to 1.0, simulated annual streamflow for water year 1997 was reduced by only 20 percent (t

Water year 1997 was a large-runoff year and wetlands were filled.

The increase in open-wetlands spillage thresholds from 0.2 to 1.0 resulted in an increase in simulated daily 

area throughout most of the simulation period (fig. 11). Early in the simulation period, water years 1983-88, th

area simulated for a spillage threshold of 1.0 remained greater than for a spillage threshold of 0.2. Beginning in 

1988, a 4-year dry period resulted in simulated wetlands areas that were about the same for both thresholds. H

beginning in water year 1993, the beginning of the recent wet period, simulated wetlands areas were as much as 

more for spillage thresholds of 1.0 than for spillage thresholds of 0.2. The largest simulated daily wetlands are

in 1997; the wetlands area increased from about 40,500 acres at a spillage threshold of 0.2 to about 45,000 acre

spillage threshold of 1.0.

Table 3. Observed and simulated annual streamflows and simulated streamflow as a percentage of observed streamflow, Starkweather 

subbasin, North Dakota, water years 1981-98

Year Observed streamflow

(inches)

Simulated streamflow

(inches)

Percent

error1

 1981 0.214 0.228 6

 1982 1.043 0.522 -50

 1983 0.503 1.086 116

 1984 0.194 0.241 24

 1985 0.435 0.287 -34

 1986 0.879 0.607 -31

 1987 1.267 0.294 -77

 1988 0.120 0.135 12

 1989 0.411 0.062 -85

 1990 0.026 0.061 135

 1991 0.126 0.322 156

 1992 1.316 0.577 -56

 1993 1.619 2.208 36

 1994 1.063 0.896 -16

 1995 2.186 1.787 -18

 1996 1.798 1.921 7

 1997 3.187 4.976 56

 1998 1.513 1.673 11

 Total 17.901 17.884 0
17

The changes in simulated wetlands area for an increase in open-wetlands spillage thresholds from 0.2 to 1.0 

in figure 12. From water year 1981 to the beginning of water year 1993, the annual change in total wetlands ar

than 4,000 acres. However, beginning in water year 1993, the increased spillage thresholds resulted in increase

amounts of total wetlands area and amounts of water retained. Simulated differences in wetlands areas remain

throughout water years 1994-98, and the change in wetlands area rarely fell below 4,000 acres. Also, the mode

that total wetlands (open and closed combined) area simulated at open-wetlands spillage thresholds of 1.0 remai

even in periods of water-level decline during water years 1994-98. The increased size of the open wetlands with 

of 1.0 made open wetlands respond more similarly to closed wetlands because the enlarged open wetlands cou

more water for longer periods of time.

Simulated open-wetlands water volumes at spillage thresholds of 0.2 and 1.0 (fig. 13) show a similar patte

simulated daily wetlands areas at the same thresholds (fig. 11). The simulated maximum open-wetlands water 

a spillage threshold of 1.0, about 68,000 acre-feet, occurred during water year 1997. The 68,000-acre-feet volu

increase of 24,000 acre-feet over the simulated maximum volume for a spillage threshold of 0.2, which also oc

during water year 1997. During water years 1994-98, simulated annual streamflows for open-wetlands spillage 

of 1.0 remained less than for thresholds of 0.2 even though the open wetlands probably were near maximum vo

(table 4). The greatly increased size of the closed wetlands during water years 1994-98 probably allowed for in

water storage and decreased simulated streamflow from the study area.

1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 19

WATER YEAR

0

45,000

5,000

10,000

15,000

20,000

25,000

30,000

35,000

40,000

WETLANDS AREA, IN ACRES

Figure 8. Precipitation-Runoff Modeling System simulated daily wetlands areas, Starkweather Coulee subbasin, North Dakota,

water years 1981-98.
18

MODEL LIMITATIONS AND CONSIDERATIONS

The Devils Lake Basin wetlands model applied to the study area simulated many features of the streamflo

from the Starkweather Coulee gaging station. Although the model was challenged by the relatively flat terrain 

Devils Lake Basin, the model performed well for this study because of many modifications made to the PRMS

inclusion in the PRMS of a wetlands hydrology subroutine that allowed for the addition of wetland storage in e

permitted the Devils Lake Basin wetlands model to better simulate streamflow conditions in the study area. H

lack of a frozen-soils subroutine in the model probably inhibited the accurate simulation of snowmelt-runoff am

Many of the parameters that concerned wetlands hydrology were reasonable approximations of the physical fe

without a quantitative representation of those processes in the model.

The DEM and the Devils Lake Basin wetlands model did not include information about the locations of roa

or other diversionary structures within the study area. The DEM was used to estimate the amounts of water sto

potentially stored, in the study area as defined from topographic maps with 5-foot contour intervals. Therefore

possible that the depths and areas of all wetlands that existed in the basin were not represented adequately. Ho

horizontal sampling increment of 33 feet (10 meters) permitted the identification of small wetlands that may no

evident on a standard DEM that has a horizontal sampling increment of 100 feet (30 meters).

1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 19

WATER YEAR

0

80,000

10,000

20,000

30,000

40,000

50,000

60,000

70,000

WETLANDS WATER VOLUME, IN ACRE-FEET

Open wetlands

Closed wetlands

Figure 9. Precipitation-Runoff Modeling System simulated daily water volumes in open and closed wetlands, Starkweather Cou

subbasin, North Dakota, water years 1981-98.
19

More work is important to improve the wetlands hydrology subroutine and to include a frozen-soils subrou

Methods for incorporating more than one wetland in each HRU and for better defining the hydrology of the wet

be developed and utilized in the model. A frozen-soils subroutine was developed for an earlier version of the P

(Emerson, 1991) and work will continue to incorporate the subroutine into the current modular versions of the 

addition, other data are being collected at various sites to help define the roles and functions of wetlands in sm

watersheds.

SUMMARY

A study was initiated in cooperation with the North Dakota State Water Commission to simulate streamflo

wetland storage within a part of the Starkweather Coulee subbasin. The study utilized digital elevation data, ge

information-system tools, and the U.S. Geological Survey Precipitation-Runoff Modeling System to define flow 

to estimate wetland storage capacity, and to simulate streamflow and storage within the low-relief landscape of 

area. Information from the study may be useful to water managers, researchers, and others associated with the w

that have arisen because of the rising water levels of Devils Lake.

U.S. Geological Survey personnel created a final digital elevation model of the study area by using 20 U.S. 

Survey 7.5-minute topographic maps with contour intervals of 5 feet. Elevation data from the topographic map

sampled horizontally every 33 feet (10 meters) and interpolation schemes were used to create a digital represent

1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1

WATER YEAR

0

120,000

10,000

20,000

30,000

40,000

50,000

60,000

70,000

80,000

90,000

100,000

110,000

WATER VOLUME, IN ACRE-FEET

Wetlands

Study area

Figure 10. Precipitation-Runoff Modeling System simulated annual water volumes in wetlands and in the study area, Starkwea

Coulee subbasin, North Dakota, water years 1981-98.
20

map. The final digital elevation model had elevations reported to 1.0 foot and had features similar to those obse

field reconnaissance. The streamflow network determined by GIS Weasel closely resembles the actual hydrogr

basin. Geographic-information-system tools were used to compute the surface areas and volumes to the spill e

the wetlands in the study area. Within the study area, the average wetland depth was about 2.21 feet, the total 

wetland area was about 30,890 acres at the overflow elevation, and the total maximum wetland volume was ab

68,270 acre-feet.

Information from the final digital elevation model and the geographic-information-system analyses was us

develop the Devils Lake Basin wetlands model of the study area. Data sets from the geographic-information-s

analyses, climatology, and geomorphology were incorporated into the model to simulate precipitation accumul

snowmelt, evapotranspiration, soil infiltration, seepage to ground water, surface runoff, and streamflow. The s

was divided into 50 hydrologic response units on the basis of elevation, slope, aspect, flow planes, soil types, a

vegetation. Individual wetland areas and volumes within the study area were determined from the digital eleva

and the geographic-information-system analyses. However, because of model constraints and the complexities 

including thousands of individual basins, only one wetland per hydrologic response unit was simulated. There

wetlands were modeled within the study area, and each wetland represented the combined area and volume of 

elevation model wetlands within the respective hydrologic response unit. Each wetland was partitioned into tw

open wetland and a closed wetland. The open wetland was defined as having an outlet with a spillage threshol

equal to a fraction of the total volume of the open wetland without an outlet. The closed wetland was defined as 

an outlet. Therefore, the closed wetland did not spill, but did gain and lose water in the same manner as the ope

All closed wetlands were allowed to increase their volume beyond their maximum to simulate the expansion of 

areas within the study area.

Table 4. Simulated annual streamflow and total-period streamflow for various open-wetlands spillage thresholds, Starkweather Coulee s

Dakota, water years 1981-98

Water

year

Simulated streamflow for indicated spillage threshold

(inches)

0.2 0.3 0.4 0.6 0.8

1981 0.228 0.170 0.167 0.167 0.167 

1982 0.522 0.248 0.123 0.091 0.091 

1983 1.086 0.904 0.703 0.522 0.439 

1984 0.241 0.149 0.105 0.084 0.084 

1985 0.287 0.106 0.084 0.083 0.083 

1986 0.607 0.350 0.186 0.112 0.107 

1987 0.294 0.157 0.109 0.089 0.088 

1988 0.135 0.082 0.066 0.065 0.065 

1989 0.062 0.049 0.048 0.048 0.048 

1990 0.061 0.052 0.052 0.052 0.052 

1991 0.322 0.119 0.075 0.073 0.073 

1992 0.577 0.429 0.218 0.099 0.096 

1993 2.208 1.988 1.801 1.404 1.164 

1994 0.896 0.725 0.622 0.481 0.413 

1995 1.787 1.610 1.424 1.100 0.831 

1996 1.921 1.712 1.509 1.159 0.885 

1997 4.976 4.828 4.711 4.510 4.295 

1998 1.673 1.527 1.382 1.111 0.902 

 Total 17.884 15.207 13.385 11.250 9.884 
21

Model runs were made for water years 1981-98 to calibrate the model to observed streamflows that were o

from the Starkweather Coulee gaging station. Simulated and observed daily streamflows for water years 1981

many similarities, especially in the timing of spring runoff from snowmelt. However, observed annual peak st

were greater than simulated annual peak streamflows for all water years except 1983. The differences probabl

caused mostly by the lack of a subroutine in the model to account for frozen soil. The largest amount of simul

wetlands area occurred in April 1997 when about 40,500 acres of the study area was covered with water. Also d

1997, the simulated daily water volume in the open and closed wetlands combined attained a maximum of abo

116,000 acre-feet. The open wetlands contained about 44,000 acre-feet of water, and the closed wetlands cont

72,000 acre-feet of water.

After calibration, the simulated streamflow response to increased open-wetlands spillage thresholds was ev

The implied physical effect of increasing spillage thresholds is a filling of the spillways from open wetlands to 

wetlands to hold more water. By increasing the spillage thresholds from 0.2 to 1.0, simulated streamflow was 

about 8.77 inches (from about 17.88 to 9.11 inches; 49 percent) for the 18-year period. However, by increasin

spillage thresholds from 0.2 to 1.0, simulated annual streamflow for water year 1997, which was a large-runoff 

reduced by only 20 percent. During water years 1994-98, simulated annual streamflows for open-wetlands spi

thresholds of 1.0 remained less than for thresholds of 0.2 even though the open wetlands probably were near m

volume. The greatly increased size of the closed wetlands during water years 1994-98 probably allowed for in

water storage and decreased simulated streamflow from the study area.

1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1

WATER YEAR

0

50,000

5,000

10,000

15,000

20,000

25,000

30,000

35,000

40,000

45,000

WETLANDS AREA, IN ACRES

Spillage threshold 0.2

Spillage threshold 1.0

Figure 11. Precipitation-Runoff Modeling System simulated daily wetlands areas for open-wetlands spillage thresholds of 0.2 a

1.0, Starkweather Coulee subbasin, North Dakota, water years 1981-98.
22

The Devils Lake Basin wetlands model of the Starkweather Coulee subbasin simulated many features of th

streamflow record from the Starkweather Coulee gaging station. The model performed well for this study becau

modifications made to the Precipitation-Runoff Modeling System. More work is important to improve the wet

hydrology subroutine and to include a frozen-soils subroutine. Additional data collection at various sites will h

the roles and functions of wetlands in small watersheds.

1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 19

WATER YEAR

0

8,000

1,000

2,000

3,000

4,000

5,000

6,000

7,000

CHANGE IN SIMULATED WETLANDS AREA, IN ACRES

Figure 12. Changes in Precipitation-Runoff Modeling System simulated wetlands area for an increase in open-wetlands spilla

thresholds from 0.2 to 1.0, Starkweather Coulee subbasin, North Dakota, water years 1981-98.
23

REFERENCES

Bigler, R.J., and Liudahl, K.J., 1986, Soil survey of Ramsey County, North Dakota: U. S. Department of Agriculture, Soi

Conservation Service, 169 p.

Devils Lake Basin Advisory Committee, 1976, The Devils Lake Basin study: Bismarck, North Dakota, v. 1, 235 p.

Emerson, D.G., 1988, Surface-water hydrology of Hay Creek watershed, Montana, and West Branch Antelope Creek wate

Dakota: U.S. Geological Survey Water-Resources Investigations Report 88-4038, 111 p.

———1991, Documentation of a heat and water transfer model for seasonally frozen soils with application to a precipitat

model: U.S. Geological Survey Open-File Report 91-462, 92 p.

Harkness, R.E., Berkas, W.R., Norbeck, S.W., and Robinson, S.M., 1998, Water resources data--North Dakota, Water Ye

Volume l. Surface Water: U.S. Geological Survey Water-Data Report ND-97-1, 465 p.

Jensen, M.E., and Haise, H.R, 1963, Estimating evapotranspiration from solar radiation: Journal of the Irrigation and Dra

Division, Proceedings of the American Society of Civil Engineers, v. 89 (1R4), p. 15-41.

1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1

WATER YEAR

0

70,000

10,000

20,000

30,000

40,000

50,000

60,000

OPEN-WETLANDS WATER VOLUME, IN ACRE-FEET

Spillage threshold 0.2

Spillage threshold 1.0

Figure 13. Precipitation-Runoff Modeling System simulated open-wetlands water volumes at spillage thresholds of 0.2 to 1.0,

Starkweather Coulee subbasin, North Dakota, water years 1981-98.
24

Jensen, R.E., 1972, Climate of North Dakota: National Weather Service and North Dakota State University, Fargo, North 

Jeton, A.E., 1999, Precipitation-runoff simulations for the Lake Tahoe Basin, California and Nevada: U.S. Geological Su

Resources Investigations Report 99-4110, 61 p.

———2000, Precipitation-runoff simulations for the upper part of the Truckee River Basin, California and Nevada: U.S. 

Survey Water-Resources Investigations Report 99-4282, 41 p.

Laenen, A., and Risley, J.C., 1995, Precipitation-runoff and streamflow-routing models for the Willamette River Basin, O

Geological Survey Water-Resources Investigations Report 95-4284, 197 p.

Leavesley, G.H., Lichty, R.W., Troutman, B.M., and Saindon, L.G., 1983, Precipitation-Runoff Modeling System--User’s 

U.S. Geological Survey Water-Resources Investigations Report 83-4238, 207 p.

Leavesley, G.H., Restrepo, P.J., Markstrom, S.L., Dixon, M., and Stannard, L.G., 1996, The modular modeling system (M

manual: U.S. Geological Survey Open-File Report 96-151, 200 p.

Ludden, A.P., Frink, D.L., and Johnson, D.H., 1983, Water storage capacity of natural wetland depressions in the Devils L

North Dakota: Journal of Soil and Water Conservation, v. 38, p. 45-48.

Nakama, L.Y., 1993, Application of the Precipitation-Runoff Modeling System model to simulate dry season runoff for th

watersheds in south-central Guam: U.S. Geological Survey Water-Resources Investigations Report 93-4116, 38 p.

Norris, J.M., 1986, Application of the Precipitation-Runoff Modeling System to small basins in the Parachute Creek Basin

U.S. Geological Survey Water-Resources Investigations Report 86-4115, 38 p.

Owenby, J.R., and Ezell, D.S., 1992, Monthly station normals of temperature, precipitation, and heating and cooling degr

1961-90 (by State): U.S. Department of Commerce, National Oceanic and Atmospheric Administration, National Clim

Center, Asheville, North Carolina, Climatography of the United States, no. 81, unpaginated.

Parekh, B.M., 1977, Hydrologic modeling of the Devils Lake Basin watersheds: Research Project Progress Report, North 

Water Resources Research Institute, North Dakota State University, Fargo, and University of North Dakota, Grand Fo

Risley, J.C., 1993, Use of a precipitation-runoff model for simulating effects of forest management on streamflow in 11 sm

basins, Oregon Coast Range: U.S. Geological Survey Water-Resources Investigations Report 93-4181, 61 p.

Simmons, M., and Moos, D.K., 1990, Soil survey of Cavalier County, North Dakota: U.S. Department of Agriculture, So

Conservation Service, 192 p.

Viger, R.J., Markstrom, S.L., and Leavesley, G.H., 1998, The GIS Weasel--An interface for the treatment of spatial inform

watershed modeling and water resource management: Proceedings of the First Federal Interagency Hydrologic Mode

Conference, April 19-23, 1998, Las Vegas, Nevada, v. 2, chap. 7, p. 73-80.

Winter, T.C., and Rosenberry, D.O., 1995, The interaction of ground water with prairie pothole wetlands in the Cottonwoo

east-central North Dakota, 1979-1990: Wetlands, v. 15, no. 3, p. 193-211.

Yang, D., Goodison, B.E., Metcalfe, J.R., Golubev, V.S., Bates, R., Pangburn, T., and Hanson, C.L., 1995, Accuracy of N

standard non-recording precipitation gauge--results of WMO intercomparison: Ninth Conference on Applied Climato

Texas, January 15-20, 1995, p. 29-34.
25

APPENDIX
26

APPENDIX - The Devils Lake Basin Wetlands Model

By George H. Leavesley

INTRODUCTION

The Devils Lake Basin wetlands model is a modified version of the U.S. Geological Survey’s (USGS) Pre

Runoff Modeling System (PRMS) (Leavesley and others, 1983; Leavesley and Stannard, 1995). PRMS is a di

parameter, physical process watershed model. Distributed-parameter capabilities are provided by partitioning a 

into units, using characteristics such as slope, aspect, elevation, soil type, vegetation type, and precipitation dis

Each unit is assumed to be homogeneous with respect to its hydrologic response and to the characteristics liste

Each unit is termed a hydrologic response unit (HRU). A water balance and an energy balance are computed da

HRU. The sum of the responses of all HRUs, weighted on a unit-area basis, produces the daily watershed resp

Snow is a major form of precipitation in the Devils Lake Basin and a major source of streamflow. The sno

components of PRMS simulate the accumulation and depletion of a snowpack in each HRU. A snowpack is m

and modified both as a water reservoir and as a dynamic heat reservoir. A water balance is computed daily and 

balance is computed twice each day. The energy-balance computations include estimates of net shortwave and 

radiation, the heat content of precipitation, and approximations of convection and condensation terms.

PRMS uses daily inputs of solar radiation and the variables precipitation (PRCP), maximum air temperatur

and minimum air temperature (TMIN). Solar radiation is distributed to each HRU as a function of HRU slope 

Where solar radiation data are not available on a daily basis, they are computed using existing algorithms in PR

Estimates of daily shortwave radiation received on a horizontal surface are computed using air temperature, pr

and potential solar radiation.

PRMS and the Devils Lake Basin wetlands model modifications have been developed and applied using th

Modular Modeling System (MMS) (Leavesley and others, 1996; Leavesley and others, 2002). MMS is an inte

system of computer software that provides a common framework in which to focus multidisciplinary research 

operational efforts to develop, evaluate, and apply a wide range of modeling capabilities across a broad range of 

temporal scales. MMS has a master library that contains compatible modules for simulating a variety of water, 

biogeochemical processes. The library may contain several modules for a given process, each representing an 

conceptualization to simulating that process. The different conceptualizations are functions of a variety of con

include the types of data available and the spatial and temporal scales of application. A model for a specified ap

created by coupling appropriate modules from the library. If existing modules cannot provide appropriate proc

algorithms, new modules can be developed and incorporated into the library.

The process modules that compose the original version of PRMS are given in table A1. The documentatio

modules can be found on the Internet at http://wwwbrr.cr.usgs.gov/mms. The process modules that compose th

Lake Basin version of PRMS are given in table A2. Only those modules given in table A2 that contain the wo

their name have been modified from the original PRMS version. The complete documentation for these new m

also be found on the Internet at http://wwwbrr.cr.usgs.gov/mms. A general description of the modifications m

PRMS to create the Devils Lake Basin version of the model are given in the Watershed Characterization and

Parameterization section of this appendix.

WATERSHED CHARACTERIZATION AND PARAMETERIZATION

A watershed is delineated, characterized, and parameterized using the USGS GIS Weasel. GIS Weasel is a 

information system (GIS) interface for applying tools to delineate, characterize, and parameterize topographica

hydrological, and biological basin features for use in a variety of lumped- and distributed-modeling approache

composed of ARC/INFO (Environmental Systems Research Institute, 1992) GIS software, C language program

scripts. Distributed basin features, such as the HRUs of PRMS, are delineated within a watershed using spatia

distributed attributes, such as elevation, slope, aspect, soils, and vegetation. HRUs can be characterized using 

attributes.
 27

Table A1. Original PRMS modules

Module

basin_prms.f

obs_prms.f

soltab_prms.f

ddsolrad_prms.f

temp_1sta_prms.f

precip_prms.f

potet_jh_prms.f

intcp_prms.f

snowcomp_prms.f

srunoff_smidx_prms.f

smbal_prms.f

ssflow_prms.f

gwflow_prms.f

strmflow_prms.f

basin_sum_prms.f

hru_sum_prms.f

Table A2. Prairie-pothole PRMS modules

Module

basin_wet.f

obs_prms.f

soltab_prms.f

ddsolrad_prms.f

temp_1sta_prms.f

precip_prms.f

potet_jh_prms.f

intcp_wet.f

snowcomp_prms.f

srunoff_smidx_wet.f

smbal_wet.f

ssflow_wet.f

gwflow_wet.f

strmflow_prms.f

basin_sum_wet.f

hru_sum_prms.f

Parameter estimation methods are implemented using ARC Macro Language (AML) functions applied to 

digital data bases. A library of parameter estimation methods is maintained in a similar fashion to the library o

modules in MMS. For a given model, a recipe file of AML functions can be created and executed to estimate a 

of spatial parameters. This recipe file also can be modified to change the parameter estimation method associa

selected parameter, thus enabling the evaluation of alternative parameter estimation methods.

Spatially distributed parameters in PRMS are estimated using available digital data bases for the United St

including: (1) USGS 3-arc second digital elevation models (DEMs); (2) State Soils Geographic (STATSGO) 1

gridded soils data (U.S. Department of Agriculture, 1994); and (3) Forest Service 1-kilometer gridded vegetati

density data (U.S. Department of Agriculture, 1992). Spatially distributed HRU parameters estimated using th

bases include elevation, slope, aspect, topographic index, soil type, available water-holding capacity of the soil

type, vegetation cover density, solar radiation transmission coefficient, interception-storage capacity, stream top

stream reach slope and length.

Parameters that are derived from categorical data, such as vegetation type or soil type, are calculated as th

commonly occurring category for an HRU. Parameters derived from non-categorical data, such as elevation, s

aspect, are calculated as the statistical mean or median of the distribution of values for an HRU. Estimation of s

parameters required the use of two or more of the digital data bases, in combination with user estimates of an a

variable. For example, in PRMS, the available water-holding capacity of the soil zone of an HRU is a function 

average rooting depth of the dominant vegetation on that HRU. No digital data base of rooting depth exists. H

default rooting depths for each vegetation group type were estimated to create a rooting-depth data base for use 

computation of available water-holding capacity. The user can modify the defaults as needed to reflect conditi

specific basin.

MODEL CONCEPTUALIZATION

In the Devils Lake Basin version of PRMS, one additional parameter is computed for each HRU using GIS 

This parameter is an estimate of the storage volume contained in the aggregate of all wetlands contained within 
28

This volume is estimated by computing the difference between the raw DEM and a new, modified version of th

has had all the wetlands artificially filled to make a hydrologically contiguous surface. That is, a drop of water 

anywhere on this new surface could flow to the outlet of the basin and would not be captured in a wetland.

The wetland storage for each HRU is divided into wetlands that do not spill and those that are openly conn

stream channels. The flow from an open wetland is computed as a linear function of the volume in storage tha

threshold storage volume. The linear routing coefficient and the threshold storage values also are model param

flow is routed from a closed wetland.

Precipitation or snowmelt occurring on wetland areas adds to the storage volume of these wetlands. Chan

surface area of the ponded water in the wetlands change with time as a function of inflow, evaporation, seepag

water, and outflow to stream channels. Evaporation from the area covered by water is computed as a user-defi

percentage of potential evapotranspiration. Evapotranspiration from the soil areas of an HRU are computed as 

of potential evapotranspiration, soil texture, and the amount of water available in the soil profile. The dynamic 

areas of open water and soil on an HRU are accounted for at each time step to enable appropriate water-balanc

computations on each HRU.

Precipitation or snowmelt occurring on non-wetland areas of an HRU are assumed to infiltrate and/or run 

stream channel adjacent to the HRU. Surface runoff is computed as a function of antecedent soil moisture con

precipitation volume. Infiltration is computed as the difference between net precipitation (total precipitation m

precipitation stored on vegetation cover) and surface runoff. Currently, there is no frozen-soil algorithm in the 

During the period of spring snowmelt, the soil is assumed to be frozen and no infiltration from the melt is assu

occur.

The sum of the surface runoff and wetland outflow of each HRU plus the subsurface and ground-water ou

weighted on a contributing area basis, is equal to the streamflow from the basin. Using a daily time step, there 

channel routing computation.

REFERENCES

Environmental Systems Research Institute, 1992, ARC/INFO 6.1 user’s guide: Redlands, Calif.

Leavesley, G.H., Lichty, R.W., Troutman, B.M., and Saindon, L.G, 1983, Precipitation-Runoff Modeling System--User's m

Geological Survey Water-Resources Investigations Report 83-4238, 207 p.

Leavesley, G.H., Markstrom, S.L., Restrepo, P.J., and Viger, R.J., 2002, A modular approach to addressing model design

parameter estimation issues in distributed hydrological modeling: Hydrological Processes, v. 16, no. 2, p. 173-187.

Leavesley, G.H., Restrepo, P.J., Markstrom, S.L., Dixon, M., and Stannard, L.G., 1996, The modular modeling system (M

Manual: U.S. Geological Survey Open-File Report 96-151, 200 p.

Leavesley, G.H., and Stannard, L.G., 1995, The Precipitation-Runoff Modeling System--PRMS, in Singh, V.P., ed., Comp

of watershed hydrology: Water Resources Publications, Highlands Ranch, Colo., p. 281-310.

U.S. Department of Agriculture, 1992, Forest land distribution data for the United States: accessed July 2000 at URL

http://www.srsfia.usfs.msstate.edu/rpa/rpa93.htm

U.S. Department of Agriculture, 1994, State soil geographic (STATSGO) database--Data use information: Natural Resou

Conservation Service, Miscellaneous Publication No. 1492, 107 p.