Prepared in cooperation with the

Arkansas Game and Fish Commission, the Arkansas Soil and Water 

Conservation Commission and the Beaver Water District

SIMULATION OF HYDRODYNAMICS, TEMPERATURE, 

AND DISSOLVED OXYGEN IN BEAVER LAKE, ARKANSAS, 

1994-1995

Water-Resources Investigations Report 02-4116

U.S. Department of the Interior

U.S. Geological Survey
SIMULATION OF HYDRODYNAMICS, TEMPERATURE, 

AND DISSOLVED OXYGEN IN BEAVER LAKE, ARKANSAS, 

1994-1995

Brian E. Haggard and W. Reed Green

U.S. GEOLOGICAL SURVEY

Water-Resources Investigations Report 02-4116

Prepared in cooperation with the

Arkansas Game and Fish Commission, the Arkansas Soil and 

Water Conservation Commission, and the Beaver Water District

Little Rock, Arkansas

2002
U.S. DEPARTMENT OF THE INTERIOR

GALE A. NORTON, Secretary

U.S. GEOLOGICAL SURVEY

Charles G. Groat, Director

For additional information Copies of this report can be

write to: purchased from:

District Chief U.S. Geological Survey

U.S. Geological Survey, WRD Branch of Information Services

401 Hardin Road Box 25286

Little Rock, Arkansas 72211 Denver Federal Center

Denver, Colorado 80225

The use of firm, trade, and brand names in this report is for identification purposes only and 

does not constitute endorsement by the U.S. Geological Survey.
Contents 4

CONTENTS

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

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

Purpose ......................................................................................................................................................................3

Description of Study Area .........................................................................................................................................3

Acknowledgments .....................................................................................................................................................3

Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Beaver Lake.......................................................4

Model Implementation ..............................................................................................................................................4

Computational Grid .........................................................................................................................................4

Boundary and Initial Conditions......................................................................................................................6

Hydraulic and Thermal Boundary Conditions.......................................................................................6

Chemical Boundary Conditions.............................................................................................................8

Initial Conditions ...................................................................................................................................8

Model Parameters ............................................................................................................................................8

Other Model Options.....................................................................................................................................11

Model Calibration....................................................................................................................................................11

Hydrodynamics and Temperature..................................................................................................................11

Dissolved Oxygen..........................................................................................................................................13

Sensitivity Analysis .......................................................................................................................................17

Model Applications .................................................................................................................................................18

Summary............................................................................................................................................................................20

References .........................................................................................................................................................................21

ILLUSTRATIONS

Figure 1. Map showing location of Beaver Lake and the White River Basin in Arkansas and

Missouri.......................................................................................................................................................2

2. Plot showing idealized model segments, layers, and branches for Beaver Lake ..............................................4

3. Plot showing side view, top view, and face view from the dam of the computational grid

of Beaver Lake used in CE-QUAL-W2.......................................................................................................5

4-23. Graphs showing:

4. Relation between depth and volume and depth and surface area in Beaver Lake ............................................5

5. Annual mean streamflow for the White River upstream from Beaver Lake, 1964-1995 .................................7

6. Daily inflow and dam release flow for Beaver Lake, Arkansas, January 1994

through December 1995 ..............................................................................................................................7

7. Measured and simulated water-surface elevation near the Beaver Lake dam,

January through December 1994 and January through December 1995...................................................11

8. Relation between measured and simulated water temperatures in the water column near

the Beaver Lake dam, January through December 1994...........................................................................12

9. Relation of difference between measured and simulated water temperatures at

Beaver Lake dam to measured water temperature, date, and water

depth, January through December 1994 ....................................................................................................13

10. Relation between measured and simulated water temperatures in the water column

near the Beaver Lake dam, January through December 1995 ...................................................................14

11. Relation of difference between measured and simulated water temperatures near Beaver

Lake dam to measured water temperature, date, and water depth, January through December 1995 ......14
5 Contents

12. Relation between measured and simulated dissolved-oxygen concentrations in the water column near

the Beaver Lake dam, January through December 1994 .......................................................................... 15

13. Relation of difference between measured and simulated dissolved-oxygen concentrations near Beaver

Lake dam to measured dissolved-oxygen concentrations, date, and water depth, January

through December 1994............................................................................................................................ 16

14. Relation between measured and simulated dissolved-oxygen concentrations in the water column near the 

Beaver Lake dam, January through December 1995 ................................................................................ 16

15. Relation of difference between measured and simulated dissolved-oxygen concentrations

near Beaver Lake dam to measured dissolved-oxygen concentrations, date, and

water depth, January through December 1995.......................................................................................... 17

16. Vertical temperature distributions near the Beaver Lake dam on August 8, 1994

and January 12, 1995, showing calibrated model profiles and profiles as a

result of differing model parameters ......................................................................................................... 18

17. Vertical dissolved-oxygen concentration distributions near the Beaver Lake dam on September 29, 1994

and September 25, 1995, showing calibrated model profiles and profiles as a result of differing model 

parameters ................................................................................................................................................. 18

18. Simulated surface elevations resulting from additional minimum flow with and without

increasing pool elevation........................................................................................................................... 19

19. Relation of difference between calibrated model pool elevation and pool elevations

predicted from minimum flow scenarios .................................................................................................. 19

20. Simulated water temperatures in Beaver Lake outflows and measured in the tailwater .............................. 19

21. Simulated water temperature differences between calibrated base condition and additional

minimum flow scenarios........................................................................................................................... 19

22. Simulated dissolved-oxygen concentrations in Beaver Lake outflows and measured in

the tailwater............................................................................................................................................... 20

23. Simulated dissolved-oxygen concentration differences between calibrated base condition

and additional minimum flow scenarios ................................................................................................... 20

TABLES

Table 1. Hydraulic and thermal input parameters specified for Beaver Lake model .................................................... 6

2. Rate coefficients used in water-chemistry and biological simulations and specified

as input in the Beaver Lake model.............................................................................................................. 9
Contents 6

Degrees Celsius (C) may be converted to degree Fahrenheit (F) by using the following equation:

F = 1.8(C) + 32

Degrees Fahrenheit (F) may be converted to degree Celsius (C) by using the following equation:

C = 0.55(F – 32)

Water Year: October 1 through September 30

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.

Constituent concentrations in water are in milligrams per liter (mg/L).

CONVERSION FACTORS AND VERTICAL DATUM

Multiply By To obtain

centimeter (cm) 0.3937 inch

millimeter (mm) 0.03937 inch

meter (m) 3.281 foot

kilometer (km) 0.6214 mile (mi)

hectare (ha) 2.471 acre

square meter (m2) 10.76 square foot

square kilometer (km2) 0.3861 square mile

liter (L) 0.2642 gallon (gal)

cubic meter (m3) 35.31 cubic foot

gram (g) 0.03527 ounce

kilogram (kg) 2.205 pound (lb)
7 Contents
Abstract 1

SIMULATION OF HYDRODYNAMICS, 

TEMPERATURE, AND DISSOLVED OXYGEN IN 

BEAVER LAKE, ARKANSAS, 1994-1995

By Brian E. Haggard and W. Reed Green

ABSTRACT

The tailwaters of Beaver Lake and other White 

River reservoirs support a cold-water trout fishery of 

significant economic yield in northwestern Arkansas. 

The Arkansas Game and Fish Commission has 

requested an increase in existing minimum flows 

through the Beaver Lake dam to increase the amount of 

fishable waters downstream. Information is needed to 

assess the impact of additional minimum flows on temperature and dissolved-oxygen qualities of reservoir 

water above the dam and the release water. 

A two-dimensional, laterally averaged hydrodynamic, thermal and dissolved-oxygen model was 

developed and calibrated for Beaver Lake, Arkansas. 

The model simulates surface-water elevation, currents, 

heat transport and dissolved-oxygen dynamics. The 

model was developed to assess the impacts of proposed 

increases in minimum flows from 1.76 cubic meters per 

second (the existing minimum flow) to 3.85 cubic 

meters per second (the additional minimum flow). 

Simulations included assessing (1) the impact of additional minimum flows on tailwater temperature and 

dissolved-oxygen quality and (2) increasing initial 

water-surface elevation 0.5 meter and assessing the 

impact of additional minimum flow on tailwater temperatures and dissolved-oxygen concentrations.

The additional minimum flow simulation (without increasing initial pool elevation) appeared to 

increase the water temperature (<0.9 degrees Celsius) 

and decrease dissolved oxygen concentration (<2.2 

milligrams per liter) in the outflow discharge. Conversely, the additional minimum flow plus initial 

increase in pool elevation (0.5 meter) simulation 

appeared to decrease outflow water temperature (0.5 

degrees Celsius) and increase dissolved oxygen concentration (<1.2 milligrams per liter) through time. 

However, results from both minimum flow scenarios 

for both water temperature and dissolved oxygen concentration were within the boundaries or similar to the 

error between measured and simulated water column 

profile values.

INTRODUCTION

Beaver Lake (fig. 1) is a large, deep-storage reservoir located in the White River Basin in northwestern 

Arkansas. This impoundment was completed in 1963 

and operated by the U.S. Army Corps of Engineers 

(USACE) for the purposes of flood control, hydroelectric power, and water supply. Today, in addition to 

aforementioned uses, the reservoir is used for fish and 

wildlife habitat, recreation, and waste assimilation. 

The tailwaters of Beaver Lake, and other White River 

reservoirs, also support a cold-water trout fishery of 

significant economic yield in northwestern Arkansas. 

Proposed changes in reservoir operations such as 

increased minimum flows through the dam and 

increased water storage have produced concerns about 

the sustainability of cold water temperature and dissolved oxygen in the bottom water (hypolimnion) 

above the Beaver Lake dam. Increases in water temperature and decreases in dissolved oxygen could have 

potential impacts on the cold-water trout fisheries in 

the downstream tailwater. Comprehensive information 

is needed to address thermal and dissolved-oxygen 

dynamics of this reservoir and the effect of increasing 

minimum flow.

Beaver Lake is the most upstream and youngest 

in a chain of major reservoirs on the White River mainstem. Downstream from Beaver Lake are Table Rock 

Lake, Lake Taneycomo, and Bull Shoals Lake, and 

Norfork Lake is located on the North Fork River, a tributary to the White River (fig. 1). In January 2000, a 

study was undertaken by the U.S. Geological Survey 
2 Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Beaver Lake, Arkansas, 1994-1995

Figure 1. Location of Beaver Lake and the White River Basin in Arkansas and Missouri.
Introduction 3

(USGS) in cooperation with the Arkansas Game and 

Fish Commission, the Arkansas Soil and Water Conservation Commission, and the Beaver Water District, 

to characterize the hydrodynamics, and thermal and 

dissolved-oxygen dynamics in Beaver Lake and to simulate the effect of reservoir operations on temperature 

and dissolved-oxygen qualities in the reservoir and 

release water. A hydrodynamic model of Beaver Lake 

was developed using the U.S. Army Corp of Engineers 

(USACE) CE-QUAL-W2 software program (Cole and 

Buchak, 1995) to simulate the expected minimum flow 

scenarios. This study was conducted in conjunction 

with other studies evaluating the impacts of reservoir 

operations on temperature and dissolved-oxygen 

releases in Table Rock, Bull Shoals, and Norfork 

Lakes. These studies will provide a better understanding of the hydro- and water-quality dynamics within 

each reservoir system. In addition, these models will 

provide the basis and framework for future water-quality modeling.

Purpose

The purpose of this report is to describe a model 

of hydrodynamics, temperature, and dissolved oxygen 

in Beaver Lake, Arkansas, for the simulation period 

1994 through 1995. Water temperature and dissolved 

oxygen concentration results from model applications 

simulating two proposed minimum flow scenarios are 

presented and compared to a calibrated, base condition.

Description of Study Area

Beaver Lake was impounded in 1963 on the 

White River, northeast of the city of Fayetteville, 

Arkansas, and in 1968 the reservoir reached conservation-water supply capacity. The primary inflows into 

Beaver Lake are Richland Creek, War Eagle Creek and 

the White River; several smaller tributaries also flow 

into the reservoir (fig. 1). The watershed has a drainage 

area of 3,087 km2 at the Beaver Lake dam. Beaver 

Lake contains 2,040 million m3

 of water at the top of 

the current conservation pool (341.4 m above sea level) 

and the surface area is 114 km2. The length of the reservoir is 80 km from the White River at the Highway 

45 bridge to the Beaver Lake dam. The depth of the 

reservoir at the dam at conservation pool elevation is 

about 60 m, and the average depth through the reservoir 

is 18 m. On average, the hydraulic retention time of 

Beaver Lake is about 1.5 years. 

In addition to the purposes of flood-control and 

hydroelectric generation, Beaver Lake contains water 

allocated for drinking-water supply. Beaver Water District, the largest of four utilities withdrawing water, 

supplies an average 144,000 cubic meters (38 million 

gallons) of water daily.

Beaver Lake is impacted both by point and nonpoint sources of contamination. The city of Fayetteville 

discharges about one-half of its sewage effluent into 

the White River immediately upstream from backwater 

of the reservoir (Highway 45). Nutrients, sediment, 

pathogenic bacteria, and other constituents enter Beaver Lake through its tributaries and around its shoreline. Agriculture is a major land use in the Beaver Lake 

watershed. As a result of all the impacts, there is much 

concern about the current and future water quality in 

Beaver Lake.

Eutrophication and water-quality trends, that 

were assessed for the period 1974 to 1994 at the Beaver 

Lake dam, suggest that eutrophication may be decreasing in the reservoir (Green, 1996; Green, 1998). 

Whereas temporal fluctuations in water quality and 

trophic condition may not be as pronounced near the 

dam, the trophic conditions of the lotic or upper end of 

Beaver Lake were eutrophic, and the level of eutrophy 

in this area of the reservoir may have increased in the 

last 10 years (Haggard and others, 1999). The trophic 

conditions of the lacustrine zone can be considered 

mesotrophic (Green, 1998; Haggard and others, 1999); 

however, increases in nutrient loading, both externally 

and internally, may alter the trophic condition from 

mesotrophic to eutrophic conditions in the lacustrine 

zone of Beaver Lake.

Acknowledgments

Edward Buchak and Rajeev Jain of J.E. Edinger 

Associates, Inc., Jerad Bales of the USGS, and Tom 

Cole of the USACE provided valuable guidance on 

model development and applications. John Kielczewski of the USACE provided much of the inflow and 

outflow and reservoir elevation data used to develop 

and calibrate the model. 
4 Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Beaver Lake, Arkansas, 1994-1995

SIMULATION OF HYDRODYNAMICS, TEMPERATURE, AND DISSOLVED OXYGEN IN 

BEAVER LAKE

A two-dimensional, laterally averaged, hydrodynamic, temperature, and dissolved-oxygen model using 

CE-QUAL-W2 Version 2.11 was developed for Beaver 

Lake and calibrated based on hydrologic records and 

vertical profiles of temperature and dissolved oxygen 

measured near the Beaver Lake dam in 1994 and 1995. 

The CE-QUAL-W2 model simulates vertical and longitudinal gradients in water-quality constituents and 

includes routines for temperature, dissolved oxygen, 

and more than 20 other parameters, including algae, 

carbon dioxide, coliform bacteria, detritus, inorganic 

carbon, iron labile and refractory dissolved organic 

matter, nitrate plus nitrite nitrogen, pH, phosphorus, 

sediment, suspended solids, total dissolved solids, and 

a conservative tracer (Cole and Buchak, 1995). Calibration and simulation of other water-quality constituents besides water temperature and dissolved oxygen, 

such as nitrogen, phosphorus, algal production. and 

organic matter are beyond the scope of this investigation. However, the Beaver Lake model presented in this 

report could be modified in the future to calibrate nutrient and algal dynamics if the appropriate data become 

available to do so.

Model Implementation

Implementation of the Beaver Lake model 

included development of the computational grid, specification of boundary and initial conditions, and preliminary selection of model parameter values. Model 

development and associated assumptions in the selection of boundary and initial conditions are summarized, 

and specific values of model parameters given.

Computational Grid

The computational grid is the geometric scheme 

(fig. 2) that numerically represents the space and volume of the reservoir. The model extends 80 km, from 

the Highway 45 bridge on the White River to the 

Figure 2. Idealized model segments, layers, and branches for Beaver Lake.
Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Beaver Lake 5

Beaver Lake dam. The grid geometry was developed 

using pre-impoundment elevation contours of the land 

surface or reservoir bottom (fig. 3). Thirty-five computational segments exist along the mainstem of the 

White River in Beaver Lake whereas 12 computational 

segments are in War Eagle Creek. In addition, four 

other embayments (branches) farther down-reservoir 

are modeled with three computational segments each. 

Volumes of the smaller embayments not included in 

the computational grid were simply added to associated 

mainstem segments so that reservoir volume was preserved.

Segment geometry varied along the upstreamdownstream gradient (fig. 3). Segment length was 

based in part on segment width. Segments ranged in 

length from 710 to 5,060 m, and orientation of the longitudinal axis relative to north was determined for each 

segment. Segment widths at the surface ranged from 

243 m in the headwaters to more than 5,000 m. Each 

segment was divided vertically into 1-m layers. Depth 

from the elevation of the top of the flood control pool 

to the reservoir bottom ranged from 10 m at the 

upstream end to 60 m near the reservoir dam. Depthand-volume and depth-and- surface area relations in 

the Beaver Lake model grid were similar to USACE 

preimpoundment data (fig. 4).

Figure 4. Relation between depth and volume and depth 

and surface area in Beaver Lake.

SURFACE AREA, IN MILLION SQUARE METERS

0 20 40 60 80 100 120 140 160

ELEVATION, IN METERS ABOVE SEA LEVEL

260

280

300

320

340

360

USACE DATA

MODEL BATHYMETRY

VOLUME, IN MILLION CUBIC METERS

0 500 1000 1500 2000 2500 3000

260

280

300

320

340

360

USACE DATA

MODEL BATHYMETRY

Figure 3. Side view (A), top view (B), and face view from the dam (C) of the computational grid of Beaver Lake used in

CE-QUAL-W2.

0 10 20 30 40 50 60 70 80

DISTANCE FROM DAM, IN KILOMETERS

ELEVATION, IN METERS ABOVE SEA LEVEL

Penstock

Water Supply Withdrawal

Inflow

Inflow

Dam

N Penstock

B. C.

A.
6 Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Beaver Lake, Arkansas, 1994-1995

Boundary and Initial Conditions

Hydraulic, thermal, and chemical boundary conditions are required in CE-QUAL-W2. The boundaries 

of the Beaver Lake model included the reservoir bottom, the shoreline, tributary streams, the upstream 

boundary, the downstream boundary (dam), and the 

water surface. Initial reservoir surface elevation, water 

temperature, and constituent concentrations also are 

required.

Hydraulic and Thermal Boundary Conditions

The reservoir bottom is assumed to be an immobile and impermeable boundary. That is, the bottom 

sediments are stationary and not resuspended by flow, 

and groundwater discharge to the reservoir or recharge 

from the reservoir is assumed to be negligible. The reservoir bottom extracts energy from water movement by 

causing resistance to water flow; this phenomenon varies with the magnitude of flow. A single, empirical 

coefficient (Chezy coefficient) is applied to the reservoir bottom in all computational segments (table 1).

Table 1. Hydraulic and thermal input parameters specified for Beaver Lake model

[m0.5/s, meter to the one-half power per second; (watts/m2)/C, watts per square meter per degree Celsius; C, degrees Celsius;

m2/s, square meter per second]

Parameter Purpose Value

Constant or

time variable

Chezy resistance

coefficient

Represents turbulent exchange of energy at the 

reservoir bottom

70 m0.5/s Constant

Sediment – water heat 

exchange coefficient

Computes heat exchange between reservoir

bottom and overlying water

7.0x10-8

(watts/m2)/C

Constant

Sediment temperature Represents the reservoir bottom (sediment)

temperature

8.0 C Constant

Wind – sheltering

coefficient 

Reduces wind speed to effective wind speed at 

water surface

0.7

(dimensionless)

Constant

Horizontal eddy viscosity Represents laterally averaged longitudinal

turbulent transport of momentum

1 m2/s Constant

Horizontal eddy

diffusivity

Represents laterally averaged longitudinal

turbulent transport of mass and heat

1 m2/s Constant
Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Beaver Lake 7

Heat exchange between the reservoir bottom and 

the overlying water column is computed from (1) the 

reservoir bottom temperature, (2) the simulated temperature of the overlying water, and (3) a coefficient of 

sediment-water heat exchange (table 1). The exchange 

coefficient and reservoir bottom temperature are 

assumed to be temporally and spatially constant. A 

reasonable estimate of reservoir bottom temperature is 

the annual average water temperature near the sediment-water interface; a value of 8.0 C was used in the 

Beaver Lake model. In general, heat exchange from 

the reservoir bottom is about two orders of magnitude 

less than surface heat exchange.

The reservoir shoreline is defined as a boundary 

across which there is no flow. The exact position of the 

shoreline changes during model simulation because of 

changing water level. 

Inflow conditions for Beaver Lake during the 

1994 and 1995 modeling time period were slightly 

above normal (fig. 5). Annual mean streamflow from 

1964 through 1995 ranged from 4.39 to 33.9 m3

/s. The 

average annual mean streamflow for this time period 

was 16.1 m3

/s. Annual mean streamflow for the 1994 

and 1995 modeling time period was 17.7 and 18.8

m3/s, respectively.

Figure 5. Annual mean streamflow for the White River 

upstream from Beaver Lake, 1964-1995.

Daily reservoir inflow was distributed on a 

drainage area basis into two major branches (White 

River and War Eagle Creek) and one tributary (Richland Creek). Approximately 91 percent of the inflow 

was distributed between Richland Creek (15 percent), 

War Eagle Creek (34 percent) and the White River (42 

percent), and the remaining portion (9 percent) was 

evenly distributed between the four smaller branches 

and the surrounding shoreline. Total mean reservoir 

inflow from January 1, 1994, through December 31, 

1995, was estimated to be 43.7 m3

/s, whereas the 

median reservoir inflow was 14.2 m3

/s. The reservoir 

inflow exceeded 100 m3/s 10 percent of the time. 

Outflows (fig. 6) from the Beaver Lake dam 

were obtained from USACE records of hourly power 

generation based on a stage-discharge relation. The 

mean and median reservoir outflow was 42.6 and 8.5 

m3/s, respectively. The reservoir outflow exceeded 

139 m3

/s 10 percent of the time. The vertical extent 

and distribution of flow in the release zone near the 

Beaver Lake dam were simulated using penstock 

(point) dam release flow, the outflow rate, and the simulated density gradient upstream in the reservoir. The 

release structure was simulated as a point release, and 

the middle of the structure was at an elevation of 302.2 

m above sea level, model layer 45 (fig. 3). 

Figure 6. Daily inflow (top) and dam release flow (bottom) 

for Beaver Lake, Arkansas, January 1994 through 

December 1995.

Other hydraulic boundary conditions included 

water withdrawal by several municipal drinking water 

supply districts (Beaver Water District, Carroll – 

Boone County Water District, and Madison County 

Water District) (fig. 3). The Beaver Water District 

1965 1970 1975 1980 1985 1990 1995

ANNUAL MEAN STREAMFLOW,

IN CUBIC METERS PER SECOND

0

10

20

30

40

AVERAGE

 0

 200

 400

 600

 800

1,000

J FMAMJ J ASOND J FMAMJ J ASOND

DISCHARGE, IN CUBIC METERS PER SECOND

 0

 200

 400

 600

 800

1,000

INFLOW

OUTFLOW

1994 1995
8 Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Beaver Lake, Arkansas, 1994-1995

withdrawal rate was approximately 1.5 m3/s during the 

study period, whereas Carroll – Boone County Water 

and Southwest Boone County Water District withdrawal rates were considerably less (0.3 and 0.003 m3/

s, respectively). Withdrawal rates for each water district were variable by month and based on reported 

1994 through 1995 monthly intakes (Terry Holland, 

U.S. Geological Survey, written commun., May 2000).

Hydraulic boundary conditions at the water surface included evaporation, wind stress, and surface 

heat exchange. All meteorological data required for 

these computations were measured at Harrison, Arkansas (station number 723446, National Climatic Data 

Center, Asheville, North Carolina), and generally were 

recorded at hourly intervals. Evaporation in the model 

was computed from a time series of water-surface temperature, dewpoint temperature, wind speed, width of 

the surface layer, and length of the segment. Wind 

stress was computed from a time series of wind speed 

and direction, the orientation of the computational segment, and a wind sheltering coefficient (table 1). The 

wind sheltering coefficient is time variable and reduces 

the effect of wind on the reservoir because of topographic or vegetative sheltering; however, in the Beaver Lake model this coefficient was held constant. 

Surface heat exchange was computed from reservoir 

latitude and longitude, and from a time series of measured air temperature, dewpoint temperature, cloud 

cover, and wind speed and direction. In the original 

meteorological data, cloud cover was recorded as clear 

(CLR), scattered (SCT), broken (BKN), and overcast 

(OVC). The model requires cloud cover to be entered 

as a number ranging from 0.0 to 10.0. In the Beaver 

Lake model, cloud cover was recorded as: CLR = 0.0, 

SCT = 1.0, BKN = 3.6, and OVC = 7.8. The simulated 

surface water temperature and loss of heat through 

evaporation were included in the heat budget.

Chemical Boundary Conditions

A time series of concentrations of selected constituents at all inflow boundaries is required for model 

operation. In addition to temperature, concentrations 

of the following constituents were simulated for Beaver Lake: algae, ammonium nitrogen, carbonaceous 

biological oxygen demand, coliform bacteria, detritus, 

dissolved oxygen, labile and refractory dissolved 

organic matter, nitrate-nitrite nitrogen, phosphate 

phosphorus, and a tracer. Boundary data in all tributaries and branches included carbonaceous biological 

oxygen demand, dissolved oxygen, ammonium nitrogen, nitrate-nitrite nitrogen, total phosphorus, and a 

tracer. Due to the limited amount of available waterquality data, annual average concentrations from Haggard (1997) were used for all inflow boundary constituents except dissolved oxygen and carbonaceous 

biological oxygen demand (CBOD). These data (Haggard, 1997) were collected at the upstream model 

boundary between August 1993 and July 1995. Dissolved-oxygen concentrations were estimated at 80 

percent saturation for the given water temperature. A 

wastewater treatment plant (WWTP) exists about 10 

km upstream. Data reported by Haggard (1997) at the 

upstream boundary include WWTP contributions. 

Exchange of dissolved oxygen occurs at the 

water surface and is affected by wind speed and direction, water temperature, reservoir elevation above sea 

level and the molecular diffusivity of oxygen gas. 

Atmospheric nutrient inputs were not included in this 

model, and constituent inputs from the reservoir bottom were generally computed within the model based 

on the value of selected parameters (table 2) and the 

constituent concentrations in the overlying waters.

Initial Conditions

Initial water level and velocity, temperature, and 

constituent concentrations for each computational segment are required prior to initiating model simulation. 

Initial water-surface elevation was set to the value measured at the Beaver Lake dam on January 1, 1994. Initial velocities were assumed to be zero. The water was 

assumed to be isothermal throughout the reservoir, and 

equal to the water temperature measured near the dam 

(9.0 C). Initial constituent concentrations also were 

assumed to be uniform throughout the reservoir and 

equal to measured values near the dam. All initial values near the dam were obtained from triennial measurements (Evans and others, 1995).

Model Parameters

Parameters are used to describe physical and 

chemical processes that are not explicitly modeled and 

to provide chemical kinetic rate information. Many 

parameters cannot be measured directly and are often 

adjusted during the model calibration process until 

simulated values agree with measured observations.
Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Beaver Lake 9

Table 2. Rate coefficients used in water-chemistry and biological simulations and specified as input in the Beaver Lake model

[m, meters; (m3/m)/g, cubic meter per meter per gram; *, dimensionless; m/d, meters per day; d, day; watts/m2, watts per square meter; oC, degrees Celsius; 

(g/m2

)/d, grams per square meter per day; BOD, biochemical oxygen demand; g/m, grams per meter; mg/L, milligrams per liter]

Parameter Computational purpose Value

Light extinction coefficient for water Amount of solar radiation absorbed in the surface layer 0.35/m

Light extinction coefficient for organic solids Amount of solar radiation absorbed in the surface layer 0.01/m

Light extinction coefficient for inorganic solids Amount of solar radiation absorbed in the surface layer 0.01/m

Fraction of incident solar radiation absorbed at

water surface

Amount of solar radiation absorbed in the surface layer 0.32*

Coliform decay rate Decay rate for coliforms, temperature dependent 1.1/d

Coliform decay rate temperature coefficient A Q10 formulation modifies coliform decay rate 1.04*

Suspended solids settling rate Settling rates and sediment accumulation in reservoir 2 m/d

Algal growth rate Maximum gross algal production rate, uncorrected for

respiration, mortality, excretion or settling; temperature

dependent

1.5/d

Algal mortality rate Maximum algal mortality rate; temperature dependent 0.02/d

Algal excretion rate Maximum algal photorespiration rate, which becomes labile

dissolved organic matter 0.01/d

Algal dark respiration rate Maximum algal dark respiration rate 0.02/d

Algal settling rate Representative settling velocity for algal assemblages 0.15 m/d

Saturation light intensity Saturation light intensity at maximum algal photosynthesis

rate 325 watts/m2

Fraction of algal biomass lost by mortality to detritus Detritus and dissolved organic matter concentrations;

remaining biomass becomes labile dissolved organic

matter

0.8*

Lower temperature for algal growth Algal growth rate as a function of water temperature 1.0oC

Fraction of algal growth at lower temperature Algal growth rate as a function of water temperature 0.10*

Lower temperature for maximum algal growth Algal growth rate as a function of water temperature 25oC

Fraction of maximum growth at lower temperature Algal growth rate as a function of water temperature 0.99*

Upper temperature for maximum algal growth Algal growth rate as a function of water temperature 35oC

Fraction of maximum growth at upper temperature Algal growth rate as a function of water temperature 0.99*

Upper temperature for algal growth Algal growth rate as a function of water temperature 40oC

Fraction of algal growth at upper temperature Algal growth rate as a function of water temperature 0.10*

Labile dissolved organic matter decay rate Dissolved-oxygen loss and production of inorganic carbon,

ammonia, and phosphate from algal decay; temperature

dependent

0.12/d

Labile to refractory decay rate Transfer of labile to refractory dissolved organic matter 0.001/d

Maximum refractory dissolved organic matter

decay rate

Dissolved-oxygen loss and production of inorganic carbon,

ammonia, and phosphate from decay of refractory dissolved organic matter; temperature dependent0.001/d

Detritus decay rate Dissolved-oxygen loss and production of inorganic carbon,

ammonia, and phosphate from decay of particulate organic

matter, temperature dependent

0.06/d

Detritus settling velocity Loss of particulate organic matter to bottom sediment 0.35 m/d

Lower temperature for organic matter decay Organic matter decay as a function of temperature 5.0oC

Fraction of organic matter decay at lower temperature Organic matter decay as a function of temperature 0.10*

Lower temperature for maximum organic matter decay Organic matter decay as a function of temperature 30.0oC

Fraction of maximum organic matter decay at

lower temperature

Organic matter decay as a function of temperature 0.99*
10 Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Beaver Lake, Arkansas, 1994-1995

Sediment decay rate Decay rate of organic matter in bed sediments 0.08/d

Sediment oxygen demand Zero-order sediment oxygen demand for each

computational segment 0.875-5.25 (g/m2

)/d

5-day BOD decay rate Effects of BOD loading on dissolved oxygen 0.05/d

BOD temperature rate coefficient Adjusts 5-day BOD decay rate at 20oC to ambient

temperature 1.047*

Ratio of 5-day BOD to ultimate BOD Effects of BOD loading on dissolved oxygen 1.85*

Release rate of phosphorus from bottom sediments Phosphorus balance; computed as a fraction of

sediment oxygen demand 0.015*

Phosphorus partitioning coefficient Describes sorption of phosphorus on suspended solids 1.2*

Algal half-saturation constant for phosphorus The phosphorus concentration at which the uptake rate

is one-half the maximum uptake rate; upper concentration at which algal growth is proportional to phosphorus

concentration

0.005 mg/L

Release rate of ammonia from bottom sediments Nitrogen balance; computed as a fraction of the sediment

oxygen demand 0.2*

Ammonia decay rate Rate at which ammonia is oxidized to nitrate 0.12/d

Algal half-saturation constant for ammonia Nitrogen concentration at which the algal uptake rate is

one-half the maximum uptake rate; upper concentration

at which algal growth is proportional to ammonia concentration

0.014 mg/L

Lower temperature for ammonia decay Ammonia nitrification as a function of temperature 5.0oC

Fraction of nitrification at lower temperature Ammonia nitrification as a function of temperature 0.1*

Lower temperature for maximum ammonia decay Ammonia nitrification as a function of temperature 20oC

Fraction of maximum nitrification at lower

temperature

Ammonia nitrification as a function of temperature 0.99*

Nitrate decay rate Rate at which nitrate is denitrified; temperature dependent 1.0/d

Lower temperature for nitrate decay Denitrification as a function of temperature 5.0oC

Fraction of denitrification at lower temperature Denitrification as a function of temperature 0.1*

Lower temperature for maximum nitrate decay Denitrification as a function of temperature 20.0oC

Fraction of maximum denitrification at lower

temperature

Denitrification as a function of temperature 0.99*

Iron release from bottom sediments Iron balance; computed as a fraction of sediment oxygen demand 0.5*

Iron settling velocity Particulate iron settling velocity under oxic conditions 2.0 m/d

Oxygen stoichiometric equivalent for ammonia

decay

Relates oxygen consumption to ammonia decay 4.5*

Oxygen stoichiometric equivalent for organic

matter decay

Relates oxygen consumption to decay of organic matter 2.8*

Oxygen stoichiometric equivalent for dark

respiration 

Relates oxygen consumption to algal dark respiration 2.8*

Oxygen stoichiometric equivalent for algal growth Relates oxygen production to algal growth 4.0*

Stoichiometric equivalent between organic matter

and phosphorus

Relates phosphorus release to decay of organic matter 0.011*

Stoichiometric equivalent between organic matter

and nitrogen

Relates nitrogen release to decay of organic matter 0.08*

Stoichiometric equivalent between organic matter

and carbon

Relates carbon release to decay of organic matter 0.45

Dissolved-oxygen limit Dissolved-oxygen concentration below which anaerobic

processes such as nitrification and sediment nutrient

releases occur

0.05 mg/L

Table 2. Rate coefficients used in water-chemistry and biological simulations and specified as input in the Beaver Lake model

--Continued

[m, meters; (m3/m)/g, cubic meter per meter per gram; *, dimensionless; m/d, meters per day; d, day; watts/m2, watts per square meter; oC, degrees Celsius; 

(g/m2

)/d, grams per square meter per day; BOD, biochemical oxygen demand; g/m, grams per meter; mg/L, milligrams per liter]

Parameter Computational purpose Value
Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Beaver Lake 11

Most of the relevant hydrodynamic and thermal 

processes are modeled in CE-QUAL-W2; thus, there 

are relatively few adjustable hydraulic and thermal 

parameters. The horizontal eddy viscosity describes 

turbulent exchange of momentum, and the horizontal 

eddy diffusivity describes turbulent mixing of mass 

and heat. Other parameters such as resistance, bottom 

heat exchange, bottom temperature, and wind sheltering coefficients were discussed previously. In general, 

reservoir models are relatively insensitive to changes in 

the horizontal eddy viscosity and diffusivity. The Beaver Lake model was sensitive to changes in bottom 

temperature and heat exchange, and the wind-sheltering coefficient.

There exist about 60 biological and chemical rate 

coefficients required for application of CE-QUAL-W2 

(table 2). Most of the coefficients were based on suggestions given in the CE-QUAL-W2 manual (Cole and 

Buchak, 1995), and all of the coefficients are temporally and spatially constant. Some of the parameters 

have suggested ranges, and selected parameters were 

adjusted, within reasonable limits, until simulated values agreed with measured observations (calibration).

Other Model Options

The maximum computational time step was limited to 1 hour because the boundary data were sometimes supplied at this interval; the model-selected 

computational interval generally was about 5 minutes. 

Model calculations occurred at time steps smaller than 

the boundary conditions that were provided, and linear 

interpolation occurred between values for all input conditions except meteorological data. The meteorological data were assumed to remain constant between 

measured values. The ‘QUICKEST’ numerical 

scheme (Leonard, 1979) was used for solving the transport equations, and a Crank – Nicholson scheme 

(Roache, 1982) was used to solve the vertical advection 

equation.

Model Calibration

Successful model application requires model 

calibration that includes comparing model (simulated) 

results with observed (measured) in-pool water quality. 

If possible, two or more years of water-quality data 

should be used to confirm or verify model calibration. 

Beaver Lake model calibration was achieved by adjusting model parameters and, in some cases, estimated 

input data, for the 2-year period of January 1, 1994 

through December 31, 1995.

Two statistics were used to compare simulated 

and measured pool elevation, water temperature, and 

dissolved-oxygen concentration. The absolute mean 

error (AME) indicates how far, on average, computed 

values are from observed values and is computed 

according to the following equation:

(1)

An AME of 0.5 C means that the simulated temperatures are, on average, within + 0.5 C of the measured 

temperatures. The root mean square error (RMSE) 

indicates the spread of how far simulated values deviate from the measured data and is given by the following equation:

(2)

Hydrodynamics and Temperature

Measured and simulated surface elevations near 

the Beaver Lake dam followed similar patterns 

between January 1 and December 31, 1994 (fig. 7).

Figure 7. Measured and simulated water-surface elevation 

near the Beaver Lake dam, January through December 

1994 and January through December 1995.

AME  Simulated Measured –

Number of Observations = ------------------------------------------------------------------

RMSE   Simulated Measured –

Number of Observations

-------------------------------------------------------------------2=

JAN FEB MAR APR MAY JUNE JULY AUG SEPT OCT NOV DEC

338

339

340

341

342

343

344

345

346

MEASURED

SIMULATED

JAN FEB MAR APR MAY JUNE JULY AUG SEPT OCT NOV DEC

WATER SURFACE ELEVATION, IN METERS

338

339

340

341

342

343

344

345

346

MEASURED

SIMULATED

AME = 0.24

RMSE = 0.27

AME = 0.12

RMSE = 0.14

1994

1995
12 Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Beaver Lake, Arkansas, 1994-1995

The AME and RMSE between measured and simulated 

water levels in 1994 was 0.12 and 0.14 m, respectively. 

The difference between measured and simulated values 

ranged from –0.29 to 0.31 m. Overall, there was good 

agreement between measured and simulated values in 

1994.

Agreement between measured and simulated 

water levels in Beaver Lake in 1995 differed from 

1994, but overall the simulated values matched the pattern of observed water levels despite larger absolute 

differences between the two (fig. 7). The AME and 

RMSE between measured and simulated water levels 

in 1995 was 0.24 and 0.27 m, respectively. The difference between measured and simulated values ranged 

from -0.75 to 0.80 m. The tendency in simulated water 

levels to be less than observed water levels in the spring 

of 1995 may reflect the fact that the model neglected 

some inflow or outflow from the reservoir such as 

ground-water recharge.

The heat budget in the model is computed from 

inflow water temperature, air-water surface heat 

exchange (air and dew-point temperature, cloud cover, 

wind speed and direction, organic and inorganic solids 

concentration) and heat exchange at the sedimentwater interface. Organic and inorganic solids indirectly affect heat distribution by reducing light penetration. Thus, water temperature calibration cannot be 

performed independently from water chemistry computations, but water temperature can still be simulated 

neglecting the effects of solids on heat distribution.

Vertical distribution of water temperature affects 

vertical mixing of dissolved and suspended materials 

and can be used to define the general location of the 

epilimnion and hypolimnion of the reservoir. The epilimnion and hypolimnion typically are separated by a 

thermocline, in which there is a relatively large change 

in temperature over a small change in depth. A strong 

thermocline existed near the Beaver Lake dam during 

August through November in 1994 and 1995. The 

model simulations agreed quite closely with the 

observed thermocline, but the changes were not as distinct because the model simulates temperature (and 

water chemistry) in homogeneous 1-m-thick layers 

within each computational segment. Hence, simulated 

changes in temperature near the thermocline would be 

more gradual than observed changes.

All simulated water temperatures (553) in 1994 

were compared with corresponding measured values 

near the Beaver Lake dam (Evans and others, 1995). 

Simulated water temperatures reproduced seasonal 

variations observed in the water column near the dam 

(fig. 8), even for complex temperature profiles.

Figure 8. Relation between measured and simulated water temperatures in the water column near the Beaver Lake dam, 

January through December 1994.

03/22/94 08/09/94 09/12/94

10/13/94

0 10 20 30

10/17/94

TEMPERATURE, IN DEGREES CELSIUS

0 10 20 30

MEASURED

SIMULATED

11/02/94

0 10 20 30

01/12/94

60

50

40

30

20

10

0

09/29/94

0 10 20 30

DEPTH, IN METERS 60

50

40

30

20

10

0 12/07/94

0 10 20 30

05/03/94

AME = 0.23

RMSE = 0.29

AME = 0.67

RMSE = 0.71

AME = 0.56

RMSE = 0.68

AME = 0.74

RMSE = 0.88

AME = 0.86

RMSE = 0.96

AME = 0.82

RMSE = 0.93

AME = 0.92

RMSE = 1.03

AME = 0.71

RMSE = 0.87

AME = 0.57

RMSE = 0.72

AME = 0.46

RMSE = 0.65

EXPLANATION
Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Beaver Lake 13

Measured water temperatures ranged from 6.0 to 

28.1C whereas simulated water temperatures ranged 

from 5.4 to 28.2 C. Simulated water temperatures in 

the vertical profile were generally (74 percent) within 

1C of measured values. The AME and RMSE between 

measured and simulated water temperature were 0.65 

and 0.80 C, respectively. The difference between 

measured and simulated values ranged from -2.5 to 2.3 

C, and the average and median absolute differences 

were 0.3 and 0.6 C, respectively.

Although the calibrated model closely simulated 

water temperature near the Beaver Lake dam, with 

most simulated values within 1C of the actual value, 

the accuracy and precision of simulated temperatures 

varied with temperature, season, and depth. Simulated 

water temperatures were greater than measured temperatures more often when measured temperatures 

were less than 10 C (fig. 9). On the other hand, simulated water temperatures were less than measured temperatures when measured temperatures were greater 

than approximately 20 C. Near-bottom simulated 

temperatures tended to be greater than measured values 

whereas near-surface simulated temperatures were less 

than measured values. Error in simulated water temperatures was greater during thermal stratification.

Figure 9. Relation of difference between measured and 

simulated water temperatures at Beaver Lake dam to (A) 

measured water temperature, (B) data, and (C) water depth, 

January through December 1994.

Simulated water temperatures in 1995 were very 

similar to 1995 measured temperatures (fig. 10). All 

simulated temperatures (560) in 1995 were compared 

with corresponding measured values (Porter and others, 1996). Measured water temperatures ranged from 

7.0 to 30.7 C whereas simulated water temperatures 

ranged from 5.1 to 30.7 C. Simulated water temperatures were generally (58 percent) within 1C of measured values. The AME and RMSE between measured 

and simulated water temperature were 0.83 and 1.04 

C, respectively. The difference between measured 

and simulated values ranged from -2.6 to 3.5C, and 

the average and median absolute differences were -0.1 

and 0.6 C, respectively. 

Errors in simulated water temperatures were better distributed during 1995 when compared to 1994 

(fig. 11). Simulated water temperatures during 1995 

were generally under-predicted when measured temperatures exceeded 25 C. During January and March 

1995, simulated water temperatures were consistently 

less than measured values, and errors were evenly distributed during the stratification season suggesting no 

tendency to over- or under-predict water temperature. 

Simulated water temperatures were generally less than 

measured values near the reservoir bottom but were 

similar near the water surface. In general, the second 

(1995) year of simulation provided similar results as 

the first (1994) with most simulated values being 

within 1 C of the measured value.

Dissolved Oxygen

Simulation of the complex biochemical reactions 

affecting chemical and physical transport processes in 

the Beaver Lake model are expressed in part within the 

simulated dissolved-oxygen results. The supply of 

nitrogen, phosphorus, and light regulate algal growth 

and the production of oxygen; photosynthesis is the 

only internal source of oxygen in the water-chemistry 

computations. Other boundary sources include the dissolved-oxygen concentration in the reservoir inflows 

and oxygen exchange at the air-water interface. Several sinks of oxygen exist including nitrification (conversion of ammonium to nitrate), algal and microbial 

respiration, organic matter decay (for example, detritus, labile and refractory dissolved organic matter), and 

sediment oxygen demand. These processes interact in 

water-chemistry computations to simulate the complex 

vertical profiles of dissolved oxygen in Beaver Lake. 

DEPTH, IN METERS

0 10 20 30 40 50 60

-4

-2

0

2

4

MEASURED TEMPERATURE, IN DEGREES CELSIUS

0 5 10 15 20 25 30

-4

-2

0

2

4

1994

JAN FEB MAR APR MAY JUNE JULY AUG SEPT OCT NOV DEC

SIMULATED MINUS MEASURED TEMPERATURE, IN DEGREES CELSIUS -4

-2

0

2

4

A

C

B
14 Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Beaver Lake, Arkansas, 1994-1995

Figure 10. Relation between measured and simulated water temperatures in the water column near the Beaver Lake dam, 

January through December 1995.

Figure 11. Relation of difference between measured and simulated water temperatures near Beaver Lake dam to (a) 

measured water temperature, (B) date, and (C) water depth, January through December 1995.

03/21/95 08/17/95 09/15/95

10/10/95

0 10 20 30

10/24/95

TEMPERATURE, IN DEGREES CELSIUS

0 10 20 30

MEASURED

SIMULATED

11/08/95

0 10 20 30

01/11/95

60

50

40

30

20

10

0

09/25/95

0 10 20 30

DEPTH, IN METERS 60

50

40

30

20

10

0 12/14/95

0 10 20 30

07/12/95

EXPLANATION

AME = 1.29

RMSE = 1.32

AME = 1.43

RMSE = 1.50

AME = 0.96

RMSE = 1.03

AME = 0.90

RMSE = 1.06

AME = 0.59

RMSE = 1.09

AME = 0.87

RMSE = 1.24

AME = 0.45

RMSE = 0.63

AME = 0.67

RMSE = 0.84

AME = 0.76

RMSE = 0.84

AME = 0.36

RMSE = 0.39

DEPTH, IN METERS

0 10 20 30 40 50 60

-4

-2

0

2

4

MEASURED TEMPERATURE, IN DEGREES CELSIUS

0 5 10 15 20 25 30 35

-4

-2

0

2

4

1995

JAN FEB MAR APR MAY JUNE JULY AUG SEPT OCT NOV DEC

SIMULATED MINUS MEASURED TEMPERATURE, IN DEGREES CELSIUS -4

-2

0

2

4

A

C

B
Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Beaver Lake 15

Simulated dissolved-oxygen concentrations near the 

Beaver Lake dam exhibited the same general patterns 

and magnitudes as measured values (fig. 12). All simulated dissolved-oxygen concentrations (553) for January through December 1994 were compared to 

corresponding measured values (Evans and others, 

1995). Measured dissolved-oxygen concentrations 

ranged from 0.1 to 11.0 mg/L, whereas simulated dissolved-oxygen concentrations ranged from 0.0 to 12.4 

mg/L. Simulated dissolved-oxygen concentrations in 

the vertical profile generally (73 percent) were within 1 

mg/L of measured values. The AME and RMSE 

between measured and simulated dissolved-oxygen 

concentrations were 0.80 and 1.24 mg/L, respectively. 

The difference between measured and simulated values 

ranged from -8.8 to 2.1 mg/L, and the average and 

median absolute differences were -0.1 and 0.6 mg/L, 

respectively. 

Differences between measured and simulated 

dissolved-oxygen concentrations were compared to 

corresponding measured dissolved-oxygen concentrations, sampling date, and the measurement depth (fig. 

13). Simulated dissolved-oxygen concentrations typically were less than measured values when measured 

dissolved-oxygen concentrations were below 2 mg/L. 

Errors in simulated dissolved-oxygen concentration 

were greater during the stratification season. The 

December 7, 1994 results produced the greatest differences between measured and simulated dissolved-oxygen concentrations. Thermal destratification was 

occurring during this time and the model simulation 

lagged a little in time to what actually occurred.

Figure 12. Relation between measured and simulated dissolved-oxygen concentrations in the water column near the Beaver 

Lake dam, January through December 1994.

03/22/94 05/03/94 08/09/94 09/12/94

10/13/94

0 2 4 6 8 1012

11/02/94

0 2 4 6 8 1012

01/12/94

60

50

40

30

20

10

0

09/29/94

0 2 4 6 8 1012

DEPTH, IN METERS 60

50

40

30

20

10

0 12/07/94

0 2 4 6 8 1012

AME = 0.12

RMSE = 0.14

AME = 0.64

RMSE = 0.64

AME = 1.08

RMSE = 1.15

AME = 1.01

RMSE = 1.19

AME = 0.70

RMSE = 1.02

AME = 0.89

RMSE = 1.16

AME = 0.67

RMSE = 0.86

AME = 0.86

RMSE = 1.06

AME = 0.35

RMSE = 0.52

AME = 1.70

RMSE = 2.80

10/17/94

DISSOLVED OXYGEN, IN MILLIGRAMS PER LITER

0 2 4 6 8 1012

MEASURED

SIMULATED

EXPLANATION

AME = 0.81

RMSE = 0.99
16 Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Beaver Lake, Arkansas, 1994-1995

Figure 13. Relation of difference between measured and 

simulated dissolved-oxygen concentrations near Beaver 

Lake dam to (A) measured dissolved-oxygen 

concentrations, (B) date, and (C) water depth, January 

through December 1994

Simulated dissolved-oxygen concentrations in 

1995 were similar to 1995 measured dissolved-oxygen 

concentrations (fig. 14), but differences were somewhat greater in 1995 than in 1994. Seasonal variations 

in simulated dissolved-oxygen concentration were 

reproduced despite pronounced differences in the vertical distribution. All simulated dissolved-oxygen concentrations (560) were compared with corresponding 

measured values near the Beaver Lake dam. Measured 

dissolved-oxygen concentrations ranged from 0.1 to 

10.4 mg/L whereas simulated values ranged from 0.0 to 

13.2 mg/L. Simulated dissolved-oxygen concentrations in the vertical profile were generally (61 percent) 

within 1.0 mg/L of measured values. The AME and 

RMSE between measured and simulated dissolvedoxygen concentrations were 1.15 and 1.70, respectively. The difference between measured and simulated 

dissolved-oxygen concentrations ranged from -2.3 to 

7.0 mg/L, and the average and median differences were 

0.28 and 0.7 mg/L, respectively.

DEPTH, IN METERS

0 10 20 30 40 50 60

-10

-8

-6

-4

-2

0

2

4

MEASURED DISSOLVED OXYGEN CONCENTRATION,

IN MILLIGRAMS PER LITER

0 2 4 6 8 10 12

-10

-8

-6

-4

-2

0

2

4

1994

JAN FEB MAR APR MAY JUNE JULY AUG SEPT OCT NOV DEC

SIMULATED MINUS MEASURED DISSOLVED OXYGEN

CONCENTRATION, IN MILLIGRAMS PER LITER -10

-8

-6

-4

-2

0

2

4

A

C

B

Figure 14. Relation between measured and simulated dissolved-oxygen concentrations in the water column near the Beaver 

Lake dam, January through December 1995.

03/21/95 07/12/95 08/17/95 09/15/95

10/10/95

0 2 4 6 8 1012

10/24/95

DISSOLVED OXYGEN, IN MILLIGRAMS PER LITER

0 2 4 6 8 1012

MEASURED

SIMULATED

11/08/95

0 2 4 6 8 1012

01/11/95

60

50

40

30

20

10

0

09/25/95

0 2 4 6 8 1012

DEPTH, IN METERS 60

50

40

30

20

10

0 12/14/95

0 2 4 6 8 1012

EXPLANATION

AME = 2.44

RMSE = 3.65

AME = 2.66

RMSE = 2.67

AME = 0.83

RMSE = 0.92

AME = 0.66

RMSE = 0.81

AME = 0.58

RMSE = 0.90

AME = 0.74

RMSE = 1.07

AME = 057

RMSE = 0.80

AME = 0.77

RMSE = 1.03

AME = 1.12

RMSE = 1.27

AME = 1.12

RMSE = 1.36
Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Beaver Lake 17

Simulated dissolved-oxygen concentrations 

were generally over-predicted when compared to measured values (fig. 15); however, greater than half of the 

measured dissolved-oxygen concentrations were 

within 1 mg/L of the simulated values. Simulated dissolved-oxygen concentrations consistently were 

greater than measured values when measured dissolved-oxygen concentration was between 3 and 7

mg/L. The greatest error occurred during the end of the 

stratification period and during turnover (NovemberJanuary). Simulated dissolved-oxygen concentrations 

often were greater than measured regardless of depth. 

Despite these tendencies, simulation of dissolved-oxygen concentration in the vertical profile near the Beaver 

Lake dam followed the same general patterns as measured values.

Figure 15. Relation of difference between measured and 

simulated dissolved-oxygen concentrations near Beaver 

Lake dam to (A) measured dissolved-oxygen 

concentrations, (B) date, and (C) water depth, January 

through December 1995.

Sensitivity Analysis

Sensitivity analysis is the determination of the 

effects of small changes in calibrated model parameters 

and input data on model results. A complete sensitivity 

analysis for all model parameters in the Beaver Lake 

model was not conducted because the Beaver Lake 

model includes more than 60 parameters (tables 1 and 

2). However, many hydrodynamic, temperature, and 

dissolved-oxygen simulations were conducted as a 

component of model development and calibration. 

Results from these simulations and information from 

previous modeling studies (Bales and Giorgino, 1998; 

Giorgino and Bales, 1997; Green, 2001) in other reservoirs form the basis for the sensitivity analysis. The 

sensitivity of water temperature and dissolved-oxygen 

concentrations near the dam to changes in the windsheltering coefficient (WSC), coefficient of bottom 

heat exchange (CBHE), light extinction (), sedimentoxygen demand (SOD), and changes in inflow temperature and dissolved-oxygen concentrations was 

assessed.

Of the hydraulic parameters (tables 1 and 2), 

water temperature in the Beaver Lake model was most 

sensitive to changes in the WSC and  (fig 16). Wind 

speed in the calibrated and verified Beaver Lake model 

was adjusted (WSC = 0.7) from the meteorological 

data recorded at Harrison, Arkansas; that is, the effective wind speed was 70 percent of the recorded wind 

speed at Harrison. Surface-water temperatures were 

not impacted as much by changes in WSC as was the 

position of the thermocline and hypolimnetic temperatures. During stratification, vertical mixing was overpredicted when WSC was increased (>0.7) and underpredicted when WSC was decreased (<0.7). Changes 

in the  affected vertical water temperature profiles 

during stratification. Increasing  elevated the thermocline and decreasing  lowered the thermocline. 

Changes in inflow water temperature had little affect 

on vertical water temperature profiles near the dam. 

The combination of WSC and  appear to be the driving factors in the model responsible for the development, duration, and vertical location of the thermocline 

in Beaver Lake near the dam.

In the Beaver Lake model, dissolved-oxygen 

concentrations appeared to be most affected by changes 

in the WSC, , and FSOD (fig. 17). FSOD is the fraction of the zero-order SOD rate and is applied to adjust 

SOD equally among all segments. Near the air-water 

interface, dissolved-oxygen concentrations were not 

impacted by changes in these coefficients. Changes in 

the WSC tended to affect dissolved-oxygen concentrations near the thermocline and throughout the hypolimnion. Both increases and decreases in FSOD affected 

dissolved-oxygen concentrations deeper than about 8 

m. The  regulates the amount of light penetrating the 

water, indirectly affecting dissolved-oxygen concentrations by influencing algal production. Inflow dissolved-oxygen concentrations had little effect on the 

vertical distribution of dissolved oxygen near the dam.

DEPTH, IN METERS

0 10 20 30 40 50 60

-4

-2

0

2

4

6

8

MEASURED DISSOLVED OXYGEN CONCENTRATION,

IN MILLIGRAMS PER LITER

0 2 4 6 8 10 12

-4

-2

0

2

4

6

8

1995

JAN FEB MAR APR MAY JUNE JULY AUG SEPT OCT NOV DEC

SIMULATED MINUS MEASURED DISSOLVED OXYGEN

CONCENTRATION, IN MILLIGRAMS PER LITER -4

-2

0

2

4

6

8

A

C

B
18 Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Beaver Lake, Arkansas, 1994-1995

Figure 16. Vertical temperature distributions near the 

Beaver Lake dam on August 9, 1994 (top) and January 11, 

1995 (bottom), showing calibrated model profiles and 

profiles as a result of differing model parameters.

Many other parameters indirectly affect dissolved-oxygen concentrations through algal dynamics; 

however, examination of all of these parameters is 

beyond the scope of this study given that so many 

assumptions were made in evaluating dissolved-oxygen concentrations near the dam. Regardless, it is 

apparent that algal dynamics play a substantial role in 

the dissolved-oxygen conditions near the Beaver Lake 

dam. 

Model Applications

The calibrated Beaver Lake model was used to 

assess the impacts of minimum flow scenarios on reservoir stage and on temperature and dissolved-oxygen 

concentrations in the dam release waters. Increased 

Figure 17. Vertical dissolved-oxygen concentration 

distributions near the Beaver Lake dam on August 9, 1994 

(top) and January 11, 1995 (bottom), showing calibrated 

model profiles and profiles as a result of differing model 

parameters.

minimum flow simulations were developed by increasing the discharges that originally were less than 3.85 

m3/s (1.76 to 3.84 m3/s) to 3.85 m3/s in the outflow discharge file. Changes in reservoir stage were evaluated 

and a second scenario was applied correcting for the 

volume displaced by additional minimum flow.

When 3.85 m3/s was applied as the minimum 

amount of discharge (minimum flow scenario), average annual outflow increased from 42.60 to 43.57

m3/s, about a 2.3 percent increase. Approximately 47 

percent of the hourly outflow data required an increase 

to 3.85 m3

/s. Average annual outflow increased from 

1,344 to 1,374 million m3, which is equivalent to about 

30 million m

 per year increase, about 1.5 percent of 

reservoir volume at conservation pool elevation. The 

difference in reservoir elevation by the end of 1994 was 

reduced 0.25 m and by the end of 1995, about 0.5 m 

Wind-Sheltering

Coefficient (WSC)

5 10 15 20 25 30

60

50

40

30

20

10

0

WSC = 0.7

(calibration value)

WSC = 0.5

WSC = 1.0

Coefficient of Bottom

Heat Exchange (CBHE)

WATER TEMPERATURE, IN DEGREES CELSIUS

5 10 15 20 25 30

CBHE = 7E-8

(calibration value)

CBHE = 7E-9

CBHE = 7E-7

Light Extinction

Coefficient (

5 10 15 20 25 30

= 0.35

(calibration value)

 = 0.18

 = 0.53

EXPLANATION

Inflow Water

Temperature (ITEMP)

5 10 15 20 25 30

1.0 x ITEMP

(calibration value)

0.75 x ITEMP

1.25 x ITEMP

0 5 10 15

DEPTH, IN METERS BELOW WATER SURFACE

60

50

40

30

20

10

0

0 5 10 15 0 5 10 15 0 5 10 15

January 11, 1995

August 9, 1994

Wind-Sheltering

Coefficient (WSC)

0 2 4 6 8 10 12

60

50

40

30

20

10

0

WSC = 0.7

(calibration value)

WSC = 0.5

WSC = 1.0

Fraction of Sediment

Oxygen Demand (FSOD)

DISSOLVED OXYGEN CONCENTRATION, IN MILLIGRAMS PER LITER

0 2 4 6 8 10 12

FSOD = 1.75

(calibration value)

FSOD = 1.0

FSOD = 2.5

Light Extinction

Coefficient (

0 2 4 6 8 10 12

= 0.35

(calibration value)

 = 0.18

 = 0.53

EXPLANATION

Inflow Dissolved

Oxygen Concentration

(IDO)

0 2 4 6 8 10 12

1.0 x IDO

(calibration value)

0.75 X IDO

1.25 X IDO

0 2 4 6 8 10 12

DEPTH, IN METERS BELOW WATER SURFACE

60

50

40

30

20

10

0

0 2 4 6 8 10 12 0 2 4 6 8 10 12 0 2 4 6 8 10 12

January 11, 1995

August 9, 1994
Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Beaver Lake 19

(figs. 18 and 19). The initial elevation on January 1, 

1994 was 342.75 m. When 0.5 m of water was applied 

to the initial elevation (minimum flow plus increased 

pool elevation scenario), the difference in elevation 

after 1 year was 0.27 m greater than the calibrated 

model and ended up after 2 years about the same elevation (340.40 m) as the calibrated model without the 

additional minimum flow.

Figure 18. Simulated surface elevations resulting from 

additional minimum flow with and without increasing pool 

elevation.

Figure 19. Relation of difference between calibrated model 

pool elevation and pool elevations predicted from minimum 

flow scenarios.

Temperature in the discharged water differed little between results from the calibrated model and the 

minimum flow scenarios (figs. 20 and 21). Absolute 

maximum difference in outflow water temperature 

between the minimum flow scenario and the calibrated 

model was 0.9 C and between the minimum flow plus 

increased pool elevation and the calibrated model was 

0.5 C. Temperature differences for both scenarios 

were within the AME and RMSE between observed 

and simulated water-column profile temperature differences reported earlier in this report. Modeled outflow 

temperatures were similar to estimated outlet values 

from water-column profiles above the dam and measured downstream (3.5 km) tailwater temperature (fig. 

20). It appears that water temperature in the dam outflow increased slightly through time with the addition 

of increased minimum flow. Conversely, with the 

increase in pool elevation plus the addition of minimum flow, it appears that water temperature in the dam 

outflow decreased slightly through time.

Figure 20. Simulated water temperatures in Beaver Lake 

outflows and measured in the tailwater.

Figure 21. Simulated water temperature difference between 

calibrated base condition and additional minimum flow 

scenarios.

1994

JAN MAR MAY JULY SEPT NOV MAR MAY JULY SEPT NOV

ELEVATION, 

IN METERS ABOVE 

SEA LEVEL 338

339

340

341

342

343

344

345

346

Calibrated Model

Minimum Flow Scenario

Minimum Flow plus Increased 

 Pool Elevation Scenario

EXPLANATION

1995

1994

JAN MAR MAY JULY SEPT NOV MAR MAY JULY SEPT NOV

SCENARIO MINUS

CALIBRATION ELEVATION,

IN METERS -0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

Minimum Flow Scenario

Minimum Flow plus Increased 

 Pool Elevation Scenario

EXPLANATION

1995

1994

JAN MAR MAY JULY SEPT NOV MAR MAY JULY SEPT NOV JAN

TEMPERATURE,

IN DEGREES CELSIUS

4

6

8

10

12

14

16

18

20

Calibrated Model

Minimum Flow Scenario

Minimum Flow plus Increased Pool Elevation Scenario

Measured Tailwater Temperature

Above Dam Water-Column Profile Estimate

EXPLANATION

1995

MINIMUM FLOW WATER TEMPERATURE DIFFERENCE

1994

JAN MAR MAY JULY SEPT NOV MAR MAY JULY SEPT NOV JAN

MINIMUM FLOW MINUS CALIBRATION

OUTFLOW WATER TEMPERATURE, 

IN DEGREES CELSIUS

-1.0

-0.5

0.0

0.5

1.0

1995

MINIMUM FLOW PLUS INCREASED POOL ELEVATION 

WATER TEMPERATURE DIFFERENCE

1994

JAN MAR MAY JULY SEPT NOV MAR MAY JULY SEPT NOV JAN

MINIMUM PLUS INCREASED POOL ELEVATION 

FLOW MINUS CALIBRATION OUTFLOW WATER 

TEMPERATURE, IN DEGREES CELSIUS -1.0

-0.5

0.0

0.5

1.0

1995
20 Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Beaver Lake, Arkansas, 1994-1995

Dissolved-oxygen concentrations in the discharged water also differed little between results from 

the calibrated model and the two minimum flow scenarios (figs. 22 and 23). Absolute maximum difference 

in outflow dissolved oxygen between the minimum 

flow scenario and the calibrated model was 2.2 mg/L 

and between the minimum flow plus increased pool 

elevation and the calibrated model was 1.9 mg/L. Dissolved-oxygen concentration differences for both scenarios were about the same as the AME and RMSE 

between observed and simulated water-column profile 

dissolved-oxygen differences reported earlier in this 

report. Modeled outflow dissolved-oxygen concentrations were similar to estimated outlet values from 

water-column profiles above the dam and measured 

downstream (3.5 km) tailwater temperature (fig. 22). It 

appears the dissolved-oxygen concentrations in the 

dam outflow decreased slightly through time with the 

addition of increased minimum flow. Conversely, with 

the increase in pool elevation plus the increase minimum flow, it appears that dissolved-oxygen concentrations in the dam outflow increased slightly through 

time.

Figure 22. Simulated dissolved-oxygen concentrations in 

Beaver Lake outflows and measured in the tailwater.

Figure 23. Simulated dissolved-oxygen concentration 

differences between calibrated base condition and additional 

minimum flow scenarios.

SUMMARY

The tailwaters of Beaver Lake and other White 

River reservoirs support a cold-water trout fishery of 

significant economic yield in northwestern Arkansas. 

Proposed increases in minimum flows released from 

the dam have produced concerns about the sustainability of cold-water temperature and dissolved oxygen in 

the bottom water above the Beaver Lake Dam. There is 

concern that even slight warming of the release waters 

might decrease the length of the tailwaters thermally 

suitable for trout growth and sustainability, possibly 

adversely impacting the trout fishery. Thus, this study 

intended to assess the impact of additional minimum 

flows on the temperature and dissolved-oxygen qualities in Beaver Lake water above the dam and the 

released water.

A two-dimensional laterally averaged hydrodynamic, thermal, and dissolved-oxygen model was 

developed for Beaver Lake, Arkansas. The model was 

calibrated and verified using hydrologic, meteorological, physicochemical and other water-quality data measured in or near Beaver Lake from January 1994 

through December 1995. The model simulates surfacewater elevation, currents, heat transport, and dissolved1994

JAN MAR MAY JULY SEPT NOV MAR MAY JULY SEPT NOV JAN

DISSOLVED OXYGEN 

CONCENTRATION,

IN MILLIGRAMS PER LITER

0

2

4

6

8

10

12

14

Calibrated Model

Minimum Flow Scenario

Minimum Flow plus Increased Pool Elevation Scenario

Measured Tailwater Dissolved Oxygen Concentration

Above Dam Water-Column Profile Estimate

EXPLANATION

1995

MINIMUM FLOW DISSOLVED 

OXYGEN CONCENTRATION DIFFERENCE

1994

JAN MAR MAY JULY SEPT NOV MAR MAY JULY SEPT NOV JAN

MINIMUM FLOW MINUS CALIBRATION

OUTFLOW DISSOLVED OXYGEN

CONCENTRATION DIFFERENCE,

IN MILLIGRAMS PER LITER

-3

-2

-1

0

1

2

3

MINIMUM FLOW PLUS INCREASED POOL ELEVATION 

DISSOLVED OXYGEN CONCENTRATION DIFFERENCE

1994

JAN MAR MAY JULY SEPT NOV MAR MAY JULY SEPT NOV JAN

MINIMUM PLUS INCREASED POOL ELEVATION 

FLOW MINUS CALIBRATION OUTFLOW 

DISSOLVED OXYGEN CONCENTRATION

DIFFERENCE, IN MILLIGRAMS PER LITER -3

-2

-1

0

1

2

3

1995

1995
References 21

oxygen dynamics. The model was developed to assess 

the impacts of proposed increases in minimum flows 

from 1.76 m3

/s (the existing minimum flow) to 3.85 

m3/s (the additional minimum flow). Simulations 

included (1) the impact of additional minimum flows 

on tailwater temperature and dissolved-oxygen qualities and (2) increasing initial water-surface elevation 

0.5 m and assessing the impact of additional minimum 

flow on tailwater temperatures and dissolved-oxygen 

concentrations. With the increase in minimum flow, 

water temperatures appeared to increase (<0.9 C) and 

dissolved oxygen appeared to decrease (<2.2 mg/L) in 

the outflow discharge. Conversely, increasing minimum flow plus increasing initial pool elevation (0.5 m) 

apparently lowered the outflow water temperature 

(<0.5 C) and increased dissolved-oxygen concentrations (<1.2 mg/L). However, these results were within 

the boundaries or similar to the error between measured 

and simulated water-column profile values.

This model provides the basis and framework for 

future water-quality modeling of Beaver Lake—as 

extensive data are collected in both the reservoirs and 

tributaries the existing model can be adjusted to assess 

the nutrient assimilative capacity of the reservoir, nutrient limitation, and the effect of increases in nutrient 

loading on reservoir trophic status.

REFERENCES

Bales, J.D., and Giorgino, M.J., 1998, Lake Hickory, 

North Carolina: Analysis of ambient conditions 

and simulation of hydrodynamics, constituent 

transport, and water-quality characteristics, 1993-

94: U.S. Geological Survey Water-Resources 

Investigations Report 98-4149. 62 p.

Cole, T.M., and Buchak, E.M., 1995, CE-QUAL-W2 A 

two- dimensional, laterally averaged, hydrodynamic and water quality model, version 2.0, user 

manual: Vicksburg, Miss., Instruction Report EL95-1, U.S. Army Engineer Waterways Experiment 

Station.

Evans, D.A., Porter, J.E., and Westerfield, P.W., 1995, 

Water resources data, Arkansas, water year 1994: 

U.S. Geological Survey Water-Data Report AR94-1, 466 p.

Giorgino, M.J., and Bales, J.D., 1997, Rhodhiss Lake, 

North Carolina: Analysis of ambient conditions 

and simulation of hydrodynamics, constituent 

transport, and water-quality characteristics, 1993-

94: U.S. Geological Survey Water-Resources 

Investigations Report 97-4131, 62 p.

Green, W.R., 1996, Eutrophication trends inferred 

from hypolimnetic dissolved-oxygen-dynamics 

within selected White River reservoirs, northern 

Arkansas - southern Missouri, 1974-1994: U.S. 

Geological Survey Water-Resources Investigations Report 96-4096, 63 p.

———1998, Relations between reservoir flushing rate 

and water quality: Ph.D. Dissertation, University 

of Arkansas, Fayetteville, 227 p.

Green, W.R. 2001, Analysis of ambient conditions and 

simulation of hydrodynamics, constituent transport, and water-quality characteristics in Lake 

Maumelle, Arkansas: U.S. Geological Survey 

Water-Resources Investigations Report 01-4045, 

60 p.

Haggard, B.E., 1997, Trophic Status of Beaver Lake, 

Arkansas: M.S. Thesis, University of Arkansas, 

Fayetteville.

Haggard, B.E., Moore, Jr., P.A., Daniel, T.C., and 

Edwards, D.R., 1999, Trophic conditions and gradients in the headwater reaches of Beaver Lake, 

Arkansas: Proceedings of the Oklahoma Academy 

of Sciences, v. 79, p. 73-84.

Johnson, J.E., Allee, R.J., and Flores, K.S., 1996, Limnology and habitat available for cool-water fishes 

in four Arkansas reservoirs: Beaver, Bull Shoals, 

Norfork, and Ouachita: Arkansas Game and Fish 

Commission and the U.S. Fish and Wildlife Service. Arkansas Cooperative Fish and Wildlife 

Research Unit, University of Arkansas, Fayetteville.

Leonard, B.P., 1979, A stable and accurate convective 

modeling procedure based on upstream interpolation: Computer Methods in Applied Mechanics 

and Engineering, v. 19, p. 59-98.

Porter, J.E., Evans, D.A., and Pugh, A.L., 1996, Water 

resources data, Arkansas, water year 1995: U.S. 

Geological Survey Water-Data Report AR-95-1, 

408 p.

———1997, Water resources data, Arkansas, water 

year 1996: U.S. Geological Survey Water-Data 

Report AR-96-1, 238 p.

Roache, P.J., 1982, Computational fluid mechanics: 

Albuquerque, New Mexico, Hermosa Publishers, 

446 p.