science for a changing world

Prepared in cooperation with the

Arkansas Game and Fish Commission

SIMULATION OF HYDRODYNAMICS, TEMPERATURE, 

AND DISSOLVED OXYGEN IN NORFORK LAKE, 

ARKANSAS, 1994-1995

Water-Resources Investigations Report 02-4250

U.S. Department of the Interior 

U.S. Geological Survey
Front Cover:

Photograph of Norfork Dam by Alan P. Hall, U.S. Geological Survey.
SIMULATION OF HYDRODYNAMICS, TEMPERATURE, 

AND DISSOLVED OXYGEN IN NORFORK LAKE, 

ARKANSAS, 1994-1995

By Joel M. Galloway and W. Reed Green

U.S. GEOLOGICAL SURVEY

Water-Resources Investigations Report 02-4250

Prepared in cooperation with the 

Arkansas Game and Fish Commission

Little Rock, Arkansas 

2002
U.S. DEPARTMENT OF THE INTERIOR 

GALE A. NORTON, Secretary

U.S. GEOLOGICAL SURVEY 

Charles G. Groat, Director

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.

For additional information 

write to:

District Chief

U.S. Geological Survey, WRD

401 Hardin Road

Little Rock, Arkansas 72211

Copies of this report can be 

purchased from:

U.S. Geological Survey 

Branch of Information Services 

Box 25286

Denver Federal Center 

Denver, Colorado 80225
CONTENTS

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

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

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

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

Aclmowledgments...................................................................................._^

Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Norfork Lake.................................... 3

Model Implementation..................................................

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

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

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

Chemical Boundary Conditions.............................................................................................. 9

Initial Conditions.................................................................................................................... 9

Model Parameters............................................................................................................................ 9

Other Model Options.......................................................................................................................9

Model Calibration................................................................................................................................... 12

Hydrodynamics and Temperature.................................................................................................. 12

Dissolved Oxygen.......................................................................................................................... 14

Sensitivity Analysis........................................................................................................................ 18

Model Applications................................................................................................................................. 20

Summary.........................................................................................................................................................^

References........................................................................................................................................................23

ILLUSTRATIONS

Figure 1. Map showing location of Norfork Lake and the North Fork River Basin in Arkansas and

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

2. Plot showing idealized model segments, layers, and branches for the CE-QUAL-W2

reservoir model............................................................................................................................. 4

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

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

4-23. Graphs showing:

4. Relation between water-surface elevation and volume and water-surface elevation and

surface area in Norfork Lake........................................................................................................ 6

5. Annual mean streamflow for the North Fork River upstream from Norfork Lake, 

1945-1995.............................................._

6. Daily inflow and hourly dam outflow for Norfork Lake, Arkansas, January 1994

through December 1995............................................................................................................... 8

7. Simulated and measured water-surface elevations near the Norfork Lake dam,

January through December 1994 and January through December 1995.................................... 12

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

the Norfork Lake dam, January through December 1994.......................................................... 13

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

Lake dam to measured water temperature, sampling date, and water depth, January through 

December 1994.......................................................................................................................... 14

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

near the Norfork Lake dam, January through December 1995.................................................. 15

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

Lake dam to measured water temperature, sampling date, and water depth, January through 

December 1995.................................................................................... j..................................... 15

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

the Norfork Lake dam, January through December 1994.......................................................... 16

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

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

January through December 1994.........................................................J..................................... 17

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

near the Norfork Lake dam, January through December 1995............J..................................... 17

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

near Norfork Lake dam to measured dissolved-oxygen concentration^, sampling date, and 

water depth, January through December 1995 .......................................................................... 18

16. Vertical temperature distributions near the Norfork Lake dam on July 7, 1994 and 

January 18, 1995, showing calibrated model profiles and profiles as a 

result of differing model parameters.......................................................................................... 19

17. Vertical dissolved-oxygen concentration distributions near the Norfork Lake dam on 

July 7, 1994 and January 18, 1995, showing calibrated model profiles and profiles as a 

result of differing model parameters....................................................]..................................... 19

18. Simulated water-surface elevations resulting from increased minimum flow scenarios.............. 20

19. Relation of difference between water-surface elevations predicted from increased

minimum flow scenarios and calibrated model water-surface elevation with time................... 20

20. Simulated water temperature differences between increased minimum tlow scenarios

and the calibrated model............................................................................................................ 21

21. Simulated and estimated water temperatures in Norfork Lake outflow and measured

temperatures downstream from Norfork Lake dam................................................................... 21

22. Simulated dissolved-oxygen concentration differences between increased minimum

flow scenarios and calibrated model.................................................... j..................................... 22

23. Simulated and estimated dissolved-oxygen concentrations in Norfork I^ake outflows and measured 

dissolved-oxygen concentrations downstream from Norfork Lake darja................................... 22

TABLES

Table 1. Hydraulic and thermal input parameters specified for Norfork Lake model.................................... 7

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

specified as input in the Norfork Lake model............................................................................ 10

IV Contents
CONVERSION FACTORS AND VERTICAL DATUM

Multiply

centimeter (cm)

millimeter (mm)

meter (m)

kilometer (km)

hectare (ha)

square meter (m2)

square kilometer (km2)

liter (L)

cubic meter (m3)

gram (g)

kilogram (kg)

By

0.3937

0.03937

3.281

0.6214

2.471

10.76

0.3861

0.2642

35.31

0.03527

2.205

To obtain

inch

inch

foot

mile (mi)

acre

square foot

square mile

gallon (gal)

cubic foot

ounce

pound (Ib)

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)

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).

Contents
SIMULATION OF HYDRODYNAMICS, TEMPERATURE, AND 

DISSOLVED OXYGEN IN NORFORK LAKE, ARKANSAS, 

1994-1995

By Joel M. Galloway and W. Reed Green

ABSTRACT

Outflow from Norfork Lake and other 

White River reservoirs support a cold-water trout 

fishery of significant economic yield in north-central Arkansas and south-central Missouri. The 

Arkansas Game and Fish Commission has 

requested an increase in existing minimum flows 

through the Norfork Lake dam to increase the 

amount of fishable waters downstream. Information is needed to assess the impact of increased 

minimum flows on temperature and dissolvedoxygen concentrations of reservoir water and the 

outflow.

A two-dimensional, laterally averaged, 

hydrodynamic, temperature, and dissolved-oxygen model was developed and calibrated for Norfork Lake, located on the Arkansas-Missouri State 

line. The model simulates water-surface elevation, 

heat transport, and dissolved-oxygen dynamics. 

The model was developed to assess the impacts of 

proposed increases in minimum flow from 1.6 

cubic meter per second (the existing minimum 

flow) to 8.5 cubic meters per second (the increased 

minimum flow). Simulations included assessing 

the impact of (1) increased minimum flows and (2) 

increased minimum flows with increased watersurface elevation of 1.1 meter in Norfork Lake on 

outflow temperatures and dissolved-oxygen concentrations.

The increased minimum flow simulation 

(without increasing initial water-surface elevation) 

appeared to increase the water temperature and 

decrease dissolved-oxygen concentration in the 

outflow. Conversely, the increased minimum flow 

and initial increase in water-surface elevation (1.1 

meter) simulation appeared to decrease outflow

water temperature and increase dissolved-oxygen 

concentration through time. However, results from 

both scenarios for water temperature and dissolved-oxygen concentration were within the 

boundaries or similar to the error between measured and simulated water column profile values.

INTRODUCTION

Norfork Lake (fig. 1) is a large, deep-storage reservoir located on the North Fork River in the White 

River Basin on the border of Arkansas and Missouri. 

Norfork Lake dam was completed in 1944 and operated 

by the U.S. Army Corps of Engineers (USAGE) for the 

purposes of flood control and hydroelectric power. 

Today, in addition to aforementioned uses, the reservoir 

is used for fish and wildlife habitat, recreation, and 

water supply. The outflows from Norfork Lake, and 

other White River reservoirs, also support a cold-water 

trout fishery of significant economic yield in north-central Arkansas and south-central Missouri. The Arkansas Game and Fish Commission (AGFC) has requested 

an increase in minimum flows through Norfork Lake 

dam to increase the amount of fishable waters downstream. Proposed changes in reservoir operations such 

as increased minimum flows through the dam and 

increased water storage, have caused concerns about 

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

Norfork Lake. Increases in water temperature and 

decreases in dissolved oxygen could have potential 

negative impacts on the cold-water trout fisheries in the 

downstream outflow. Comprehensive information is 

needed to address temperature and dissolved-oxygen 

dynamics of Norfork Lake and the effects of increased 

minimum flow.

Abstract 1
37"-

EXPLANATION

USGSSTREAMFLOW 

' GAGING STATION

NATIONAL CLIMATIC 

' DATA CENTER 

METEOROLOGIC 

STATION

3615' 

20KLOMETERS

Figure 1. Location of Norfork Lake and the North Fork River Basin in Arkansas and Missouri.

2 Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Norfork Lake,. Arkansas,. 1994-1995
Norfork Lake is located on the North Fork River, 

a tributary to the White River. Upstream from the North 

Fork River, on the main stem of the White River, are 

Bull Shoals Lake, Lake Taneycomo, Table Rock Lake, 

and Beaver Lake (fig. 1). In July 1999, a study was conducted by the U.S. Geological Survey (USGS) in cooperation with the AGFC to characterize the hydrodynamics, temperature, and dissolved-oxygen concentration in Norfork Lake and to simulate the effect of 

reservoir operations on temperature and dissolved-oxygen concentration in the reservoir and outflow. A 

hydrodynamic model of Norfork Lake was developed 

using the USAGE 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 concentration in Bull Shoals, Table Rock, and Beaver Lakes. 

These studies will provide a better understanding of the 

hydro- and water-quality dynamics within each reservoir system. In addition, calibrated models developed 

for these studies will provide the basis and framework 

for future water-quality modeling. As more data are 

collected in both the reservoirs and tributaries, the calibrated models can be modified to assess the nutrient 

assimilative capacity of the reservoir, nutrient limitations, and the effect of increases in nutrient loading on 

reservoir trophic status.

Purpose

The purpose of this report is to describe a model 

of hydrodynamics, temperature, and dissolved oxygen 

in Norfork Lake for the simulation period of January 

1994 through December 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

Norfork Lake was impounded in 1944 on the 

North Fork River, east of the city of Mountain Home, 

Arkansas. The primary inflows into Norfork Lake are 

Pigeon Creek, Bennetts River, and the North Fork 

River; several smaller tributaries also flow into the reservoir (fig. 1). The watershed has a drainage area of

4,683 km2 at the Norfork Lake dam. Norfork Lake contains 1,540 million m3 of water at the elevation of the 

current conservation pool (169 m above sea level) and 

the surface area is 89 km2. The length of the reservoir 

is 57 km from the North Fork River at the Highway 160 

bridge to the Norfork Lake dam. The depth of the reservoir at the dam at conservation pool elevation is about 

57m, and the average depth through the reservoir is 17 

m. On average, the hydraulic retention time of Norfork 

Lake is about 0.9 year.

Acknowledgments

Edward Buchak and Rajeev Jain of J.E. Edinger 

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

Cole of the USAGE provided valuable guidance on 

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

outflow and water-surface elevation data used to 

develop and calibrate the model.

SIMULATION OF HYDRODYNAMICS, TEMPERATURE, AND DISSOLVED OXYGEN IN 

NORFORK LAKE

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

CE-QUAL-W2 was developed for Norfork Lake and 

calibrated based on hydrologic records and vertical 

profiles of temperature and dissolved oxygen measured 

near the Norfork Lake dam from January 1994 through 

December 1995. The CE-QUAL-W2 model simulates 

water-surface elevation and vertical and longitudinal 

gradients in water-quality constituents. The model 

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, nitrite plus nitrate as nitrogen, pH, phosphorus, 

sediment, suspended solids, total dissolved solids, and 

a conservative tracer (Cole and Buchak, 1995). Calibration and simulation of water-quality parameters 

other than water temperature and dissolved oxygen, 

such as nitrogen, phosphorus, algal production, and 

organic matter, are beyond the scope of this study.

Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Norfork Lake 3
Model Implementation

Implementation of the CE-QUAL-W2 model for 

Norfolk Lake 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 described, 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 57 km from 

the upstream boundary (U.S. Highway 160 bridge) to

the downstream boundary (Norfork Lake dam). The 

grid geometry was developed by digitizing preimpoundment elevation contours of the land surface or 

reservoir bottom from USGS 7.5-minute and 15- 

minute quadrangle maps (fig. 3). Twenty-five computational segments exist along the mainstem of the North 

Fork River in Norfork Lake, whereas, 9 segments are in 

the Little Creek branch and 5 segments are in the Big 

Creek branch. In addition, three other embayments 

(branches), including Pigeon Creek, Bennetts River, 

and Brushy Creek, are modeled with three computational segments each. Volumes of the smaller embayments not included in the computational grid were 

added to associated mainstem segments so that reservoir volume was preserved.

Branch 1

N 1 Segment

A model may be derived irom multiple 

segments and segments consist of 

varying layers.

Figure 2. Idealized model segments, layers, and branches for the CE-QUAL-W2 reservoir model.

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

LU

UJ GO

UJ

s

<

GO

a:

UJ hUJ

z"

o

i

UJ

180 

175 

170

165 

160 

155 

150

146 

140 

135

130 

125

116 

nn

^ H

 

Peiist.

1

!>C»

1

1

1 1

1

«

-

10 

20 

30m

73 

Z

40 i

CO

m

73

50 

60 

70

10 20 30 40 

DISTANCE FROM DAM, IN KILOMETERS

50 60

Penstock

<-V\V/ \ \Vr

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

used in CE-QUAL-W2.

Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Norfork Lake 5
Segment geometry varied along the upstreamdownstream gradient (fig. 3). Segment length was 

based in part on segment width. Segments ranged in 

length from 926 to 5,097 m, and orientation of the longitudinal axis relative to north was determined for each 

segment. Segment widths at the reservoir surface 

ranged from 265 m in the headwaters to more than 

3,300 m. Each segment was divided vertically into 1-m 

layers. Depth from the elevation of the top of the floodcontrol pool to the reservoir bottom ranged from 14m 

at the upstream boundary to 65 m near Norfork Lake 

dam. Relations between water-surface elevation and 

volume and surface area in the Norfork Lake model 

grid were similar to USAGE preimpoundment data (fig. 

4).

US ARMY CORPS OF 

ENGINEERS BATHYMETRY 

MODEL BATHYMETRY

2000 4000 6000 8000 10000 

VOLUME, IN MILLION CUBIC METERS

 US ARMY CORPS OF

ENGINEERS BATHYMETRY 

I MODEL BATHYMETRY

0 100 200 300 400 

SURFACE AREA, IN MILLION SQUARE METERS

Figure 4. Relation between water-surface elevation and 

volume and water-surface elevation and surface area in 

Norfork Lake.

Boundary and Initial Conditions

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

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

boundary (U.S. Highway 160 bridge), the downstream 

boundary (dam), and the water-surface elevation of the 

reservoir. Initial water-surface elevation of the reservoir, water temperature, and selected 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 to ground water is 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). 

Heat exchange between the reservoir bottom and the 

overlying water column is computed from (1) the sediment temperature, (2) the simulated temperature of the 

overlying water, and (3) bottom-water heat exchange 

coefficient (table 1). The sediment temperature and the 

exchange coefficient are assumed to be temporally and 

spatially constant. A reasonable estimate of sediment 

temperature is the annual average water temperature 

near the sediment-water interface; a value of 10.0 °C 

was used in the Norfork Lake model. In general, heat 

exchange from the reservoir bottom is about two orders 

of magnitude less than siirface heat exchange (Cole and 

Buchak, 1995).

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.

6 Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen In Norfork Lake, Arkansas, 1994-1995
Table 1. Hydraulic and thermal input parameters specified for Norfork Lake model

[m°-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

Chezy resistance 

coefficient

Bottom - water heat 

exchange coefficient

Sediment temperature

Wind - sheltering 

coefficient

Horizontal eddy viscosity

Horizontal eddy 

diffusivity

Computational purpose

Represents turbulent exchange of energy at the 

reservoir bottom

Computes heat exchange between reservoir bottom and overlying water

Represents the reservoir bottom (sediment) temperature

Reduces wind speed to effective wind speed at 

water surface

Represents laterally averaged longitudinal turbulent exchange of momentum

Represents laterally averaged longitudinal turbulent mixing of mass and heat

Constant or 

Value time variable

70 m°'5/s

7.0x1 0'8 

(watts/m2)/°C

10 °C

0.7 

(dimensionless)

Im2/s

Im2/s

Constant

Constant

Constant

Constant

Constant

Constant

Annual streamflow recorded at the USGS 

streamflow-gaging station near Tecumseh, Missouri, 

(station number 07058500; fig 1) on the North Fork 

River indicates that inflow to Norfork Lake during the 

1994 and 1995 modeling time period was slightly 

above average (fig. 5). Annual mean streamflow for the 

North Fork River from 1945 through 1995 ranged from

8.70 to 43.2 m3/s. The average annual mean streamflow 

for this time period was 21.4 m3/s. Annual mean 

streamflow for the 1994 and 1995 modeling time 

period was 28.0 and 23.3 m3/s, respectively (Evans and 

others, 1995; Porter and others, 1996,1997).

1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995

Figure 5. Annual mean streamflow for the North Fork River upstream from Norfork Lake, 1945-1995.

Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Norfork Lake 7
Daily reservoir inflows used in the model (fig. 6) 

were calculated by the USAGE based on daily average 

outflows and changes in reservoir water-surface elevations. The daily inflow was distributed into one major 

branch (North Fork River) and five minor branches 

according to drainage area. Approximately 62 percent 

of the inflow was distributed to the North Fork River, 

27 percent was evenly distributed along the reservoir 

shoreline, and 11 percent was distributed among the 

five smaller branches. Total mean reservoir inflow from 

January 1,1994, through December 31,1995, was estimated to be 70.2 m3/s, whereas, the estimated median 

reservoir inflow for the same period was 44.3 m3/s. The 

estimated reservoir inflow exceeded 142 m3/s 10 percent of the time.

700

600

500

400

300

200

100

0

700

600

500

400

300

200

100

Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan

Figure 6. Daily inflow (top) and hourly dam outflow (bottom) 

for Norfork Lake, Arkansas, January 1994 through 

December 1995.

The downstream boundary for the Norfork Lake 

model consists of the outflow from Norfork Lake dam. 

Hourly outflow data (fig. 6) were produced by the 

USAGE using stage-discharge relations and hourly 

power generation records. The mean and median reservoir outflow was 70.3 and 60.5 m3/s, respectively. The 

reservoir outflow exceeded 168 m3/s 10 percent of the 

time. The vertical extent and distribution of flow in the 

release zone near the Norfork Lake dam (downstream 

boundary) were simulated using penstock (point) dam 

release flow, the outflow rate, and the simulated density 

gradient upstream from the dam in the reservoir. The 

release structure was simulated as a point release, and 

the middle of the structure was at an elevation of 136.4 

m above sea level, model layer 46 (fig. 3).

Hydraulic input parameters 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 723446J 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 temperatures, dewpoint temperatures, wind speeds, surface 

layer widths, and length of the segment. Wind stress 

was computed from a time series of wind speeds and 

directions, 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 thq reservoir because of topographic or vegetative sheltering; however, in the Norfork Lake model this coefficient was held constant. 

Surface heat exchange was computed in the model 

from reservoir latitude and longitude, and from a time 

series of measured air temperatures, dewpoint temperatures, cloud covers, and wind speeds and directions. 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 Norfork 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.

8 Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Norfork Lake, Arkansas, 1994-1995
Chemical Boundary Conditions

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

operation. Boundary data in all tributaries and branches 

included dissolved oxygen, ammonia as nitrogen, 

nitrite plus nitrate as nitrogen, total phosphorus, and a 

conservative tracer. Because of the limited amount of 

available water-quality data, annual average concentrations were estimated based on similar values reported 

by Evans and others (1995) and Porter and others 

(1996, 1997) and used for all inflow boundary constituents except dissolved oxygen. Dissolved-oxygen concentrations at the inflow boundaries were set to the 

concentration for 100 percent saturation for the given 

water temperature.

Exchange of dissolved oxygen occurs at the 

water surface of the reservoir and is affected by wind 

speed and direction, water temperature, water-surface 

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-surface elevation 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 Norfork 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 (10.0 °C). Initial constituent 

concentrations also were assumed to be uniform 

throughout the reservoir and equal to values measured 

near the dam on December 30,1993 (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 for the

model. Many parameters cannot be measured directly 

and often are adjusted during the model calibration process until simulated values agree with measured observations.

Most of the relevant hydrodynamic and thermal 

processes are modeled in CE-QUAL-W2; thus, relatively few hydraulic and thermal parameters are adjustable. 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. However, 

the thermal processes are relatively sensitive to changes 

in bottom-heat exchange and temperature, and the 

wind-sheltering coefficient.

About 60 biological and chemical rate coefficients and other parameters are required for the application of CE-QUAL-W2 (table 2). Most of the 

parameter values were based on suggestions given in 

the CE-QUAL-W2 manual (Cole and Buchak, 1995), 

and all the parameters 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 (interval) was limited to 1 hour because the input data were 

sometimes supplied at this interval. The modelselected 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.

Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Norfork Lake 9
Table 2. Rate coefficients used in water-chemistry and biological simulations and other parameters specified as input in the 

Norfork Lake model

[m, meters; *, dimensionless; Q10, temperature correction factor; m/d, meters per day; d, day; watts/m2, watts per square meter; °C, degrees Celsius; (g/m2)/ 

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

Parameter/rate coefficient Computational purpose Value

Light extinction coefficient for water

Light extinction coefficient for organic solids

Light extinction coefficient for inorganic solids

Fraction of incident solar radiation absorbed at 

water surface

Coliform decay rate

Coliform decay rate temperature coefficient

Suspended solids settling rate

Algal growth rate

Algal mortality rate 

Algal excretion rate

Algal dark respiration rate 

Algal settling rate 

Saturation light intensity

Fraction of algal biomass lost by mortality to detritus

Lower temperature for algal growth 

Fraction of algal growth at lower temperature 

Lower temperature for maximum algal growth 

Fraction of maximum growth at lower temperature 

Upper temperature for maximum algal growth 

Fraction of maximum growth at upper temperature 

Upper temperature for algal growth 

Fraction of algal growth at upper temperature 

Labile dissolved organic matter decay rate

Labile to refractory decay rate

Maximum refractory dissolved organic matter 

decay rate

Detritus decay rate

Detritus settling velocity 

Lower temperature for organic matter decay 

Fraction of organic matter decay at lower temperature 

Lower temperature for maximum organic matter decay

Fraction of maximum organic matter decay at 

lower temperature

Sediment decay rate 

Sediment oxygen demand

Amount of solar radiation absorbed in the surface layer 0,48/m

Amount of solar radiation absorbed in the surface layer 0.01/m

Amount of solar radiation absorbed in the surface layer 0.01/m

Amount of solar radiation absorbed in the surface layer 0.42*

Decay rate for coliforms, temperature dependent 1.4/d

A Q ] o formulation modifies coliform decay rate 1.04*

Settling rates and sediment accumulation in reservoir 2 m/d

Maximum gross algal production rate, uncorrected for 1.0/d 

respiration, mortality, excretion or settling; temperature 

dependent

Maximum algal mortality rate; temperature dependent 0.01/d

Maximum algal photorespiration rate, which becomes labile 0.01/d 

dissolved organic matter

Maximum algal dark respiration rate 0.02/d 

Representative settling velocity for algal assemblages 0.14 m/d

Saturation light intensity at maximum algal photosynthesis ,QO atts/m2 

rate

Detritus and dissolved organic matter concentrations; 0.8* 

remaining biomass becomes labile dissolved organic 

matter

Algal growth rate as a function of water temperature 1.0 °C

Algal growth rate as a function of water temperature 0.10*

Algal growth rate as a function of water temperature 25.0°C

Algal growth rate as a function of water temperature 0.99*

Algal growth rate as a function of water temperature 30.0 °C

Algal growth rate as a function of water temperature 0.99*

Algal growth rate as a function of water temperature 40.0 °C

Algal growth rate as a function of water temperature 0.10*

Dissolved-oxygen loss and production of inorganic carbon, 0.12/d 

ammonia, and phosphate from algal decay; temperature 

dependent

Transfer of labile to refractory dissolved organic matter 0.001/d

Dissolved-oxygen loss and production of inorganic carbon, 0.001/d 

ammonia, and phosphate from decay of refractory dissolved organic matter; temperature dependent

Dissolved-oxygen loss and production of inorganic carbon, 0.06/d 

ammonia, and phosphate from decay of particulate organic 

matter, temperature dependent

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

Organic matter decay as a function of temperature 5.0 °C

Organic matter decay as a function of temperature 0.10*

Organic matter decay as a function of temperature 30.0 °C

Organic matter decay as a function of temperature 0.99*

Decay rate of organic matter in bed sediments 0.08/d

Zero-order sediment oxygen demand for each 3.5 (g/m )/d 

computational segment

10 Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen In Norfork Lake, Arkansas, 1994-1995
Table 2. Rate coefficients used in water-chemistry and biological simulations and other parameters specified as input in the 

Norfork Lake model-Continued

[m, meters; *, dimensionless; Q10, temperature correction factor; m/d, meters per day; d, day; watts/m2, watts per square meter; °C, degrees Celsius; (g/m2)/ 

d, grains per square meter per day; BOD, biochemical oxygen demand; mg/L, milligrams per liter]

Parameter/rate coefficient Computational purpose Value

5-day BOD decay rate

BOD temperature rate coefficient

Ratio of 5-day BOD to ultimate BOD

Release rate of phosphorus from bottom sediments

Phosphorus partitioning coefficient

Algal half-saturation constant for phosphorus

Release rate of ammonia from bottom sediments

Ammonia decay rate

Algal half-saturation constant for ammonia

Lower temperature for ammonia decay 

Fraction of nitrification at lower temperature 

Lower temperature for maximum ammonia decay

Fraction of maximum nitrification at lower 

temperature

Nitrate decay rate

Lower temperature for nitrate decay

Fraction of denitrification at lower temperature

Lower temperature for maximum nitrate decay

Fraction of maximum denitrification at lower 

temperature

Iron release from bottom sediments 

Iron settling velocity

Oxygen stoichiometric equivalent for ammonia 

decay

Oxygen stoichiometric equivalent for organic 

matter decay

Oxygen stoichiometric equivalent for dark 

respiration

Oxygen stoichiometric equivalent for algal growth

Stoichiometric equivalent between organic matter 

and phosphorus

Stoichiometric equivalent between organic matter 

and nitrogen

Stoichiometric equivalent between organic matter 

and carbon

Dissolved-oxygen limit

Effects of BOD loading on dissolved oxygen O.I id

Adjusts 5-day BOD decay rate at 20°C to ambient 1.047* 

temperature

Effects of BOD loading on dissolved oxygen 1.85*

Phosphorus balance; computed as a fraction of 0.05* 

sediment oxygen demand

Describes sorption of phosphorus on suspended solids 1.2*

The phosphorus concentration at which the uptake rate 0.005 mg/L 

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

concentration

Nitrogen balance; computed as a fraction of the sediment 0.08* 

oxygen demand

Rate at which ammonia is oxidized to nitrate 0.12/d

Nitrogen concentration at which the algal uptake rate is 0.014 mg/L 

one-half the maximum uptake rate; upper concentration 

at which algal growth is proportional to ammonia concentration

Ammonia nitrification as a function of temperature 5.0 °C

Ammonia nitrification as a function of temperature 0.1*

Ammonia nitrification as a function of temperature 20.0 °C

Ammonia nitrification as a function of temperature 0.99*

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

Denitrification as a function of temperature 5.0 °C

Denitrification as a function of temperature 0.1*

Denitrification as a function of temperature 20.0 °C

Denitrification as a function of temperature 0.99*

Iron balance; computed as a fraction of sediment oxygen demand 0.5 *

Particulate iron settling velocity under oxic conditions 2.0 m/d

Relates oxygen consumption to ammonia decay 4.57*

Relates oxygen consumption to decay of organic matter 1.4* 

Relates oxygen consumption to algal dark respiration 1.4*

Relates oxygen production to algal growth 3.0* 

Relates phosphorus release to decay of organic matter 0.011 *

Relates nitrogen release to decay of organic matter 0.08* 

Relates carbon release to decay of organic matter 0.45*

Dissolved-oxygen concentration below which anaerobic

processes such as nitrification and sediment nutrient 0 mg/L 

releases occur

Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Norfork Lake 11
Model Calibration

Successful model application requires model 

calibration that includes comparing model (simulated) 

results with observed (measured) reservoir conditions. 

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

should be used for adequate model calibration. Norfork 

Lake model calibration was achieved by adjusting 

model parameters and, in some cases, estimated input 

data, for the 2-year period of January 1994 through 

December 1995.

Two statistics were used to compare simulated 

and measured water-surface elevation, water temperature, and dissolved-oxygen concentration. The absolute 

mean error (AME) indicates the average difference 

between simulated and measured values and is computed by equation 1:

and 0.24 m, respectively. The difference between individual simulated and measured water-surface elevations ranged from -0.52 to 0.25 m. 

The heat budget in the model is computed from inflow 

water temperature, air-water surface heat exchange 

(determined from air and dew-point temperature, cloud 

cover, wind speed and direction, organic and inorganic 

solids concentration) amjl bottom-water heat exchange. 

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.

AME =

Value - Measured Value\

Number of Observations

/i\

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 values and is computed by equation 

2:

RMSE =

(SimulatedValues - MeasuredValues) 

Number of Observations (2)

An RMSE of 0.5 °C means that 67 percent of the simulated temperatures are within 0.5 °C of the measured 

temperatures.

Hydrodynamics and Temperature

Simulated and measured water-surface elevations near the Norfork Lake dam followed similar patterns for January through December 1994 (fig. 7). The 

AME and RMSE between simulated and measured 

water-surface elevations was 0.34 and 0.40 m, respectively. The difference between simulated and measured 

water-surface elevations ranged from -0.47 to 0.74 m. 

Overall, there was good agreement between simulated 

and measured water-surface elevations in 1994.

Agreement between simulated and measured 

water-surface elevations in Norfork Lake improved in 

1995 compared to 1994 (fig. 7). The AME and RMSE 

between simulated and measured water-surface elevations for January through December 1995, were 0.20

180

178

176

174

172

170

168

166

164

162

160

AME=0.34 

I- RMSE=0.40

JAN FEB MAR APR MAY ^JUNE JULY AUG SEPT OCT MOV DEC 

1994

180

178

176

174

172

170

168

166

164

162

160

AME=0.20 

RMSE=0.24

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

1995

Figure 7. Simulated and measured water-surface elevations 

near the Norfork Lake dam, January through December 

1994 and January through December 1995.

12 Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Norfork Lake, Arkansas, 1994-1995
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. During 

the thermal stratification season (May-November) 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 Norfork Lake dam 

during June through November in 1994 and 1995. The 

model simulations agreed quite closely with the measured 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 measured changes.

All simulated water temperatures (664) in 1994 

were compared with corresponding measured temperatures near the Norfork Lake dam (Evans and others,

1995) (fig. 8). Simulated water temperatures reproduced seasonal variations observed in the water column 

near the dam (fig. 8), even for complex temperature 

profiles. Simulated water temperatures ranged from 5.2 

to 28.9 °C whereas measured water temperatures 

ranged from 6.2 to 29.0 °C. Simulated water temperatures in the vertical profile generally were (67 percent) 

within 1°C of measured temperatures. The AME and 

RMSE between simulated and measured water temperature were 0.82 and 0.98 °C, respectively. The difference between simulated and measured temperature 

ranged from -1.9 to 2.4 °C, and the average and median 

differences were 0.3 and 0.2 °C, respectively.

Although the calibrated model closely simulated 

water temperature near the Norfork Lake dam, with 

most simulated temperatures within 1°C of the measured temperatures, the accuracy and precision of simulated temperatures varied with temperature, season, 

and depth. Simulated water temperatures were greater

01/25/94 03/23/94 05/10/94 06/07/94 07/07/94

AME = 0.47 

RMSE = 0.48

I

1 '.

AME = 0.50 

RMSE = 0.57

1 ' f ' 

,

AME. 0.41 

RMSE. 0.49

',

(

AME = 0.45 

RMSE = 059

irAME = 065 

RMSE. 084

06/18/94 09/13/94 09/28/94 10/12/94 10/19/94

5 1015202630 0 5 1015202630 

11/01/94

0 5 1015202630 

11/14/94

0 5 1015202630

12/05/94

0 5 10 1S 20 26 30

S 30 EXPLANATION

 MEASURED

 SIMULATED

05 10 15 202630 05 10 15 202630 05 10 15 202630 

TEMPERATURE, IN DEGREES CELSIUS

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

January through December 1994.

Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Norfork Lake 13
than measured temperatures more often when measured temperatures were less than 20 °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-surface simulated temperatures were generally less than 

measured temperatures, whereas at greater depths, simulated temperatures tended to be greater than measured 

temperatures. Error in simulated water temperatures 

was greater during the thermal stratification season.

<j-0 5 10 15 20 25 

2 MEASURED TEMPERATURE, IN DEGREES CELSIUS

IS '

T7I

W JAN FEB MAR APR MAY JUNE JULY AUG SEPT OCT MOV DEC 

W 1994

0 10 20 30 40 50 60

DEPTH, IN METERS

Figure 9. Relation of difference between simulated and 

measured water temperatures at Norfork Lake dam to (A) 

measured water temperature, (B) sampling date, and (C) 

water depth, January through December 1994.

Simulated water temperatures were similar to 

measured temperatures in 1995 (fig. 10). All simulated 

temperatures (613) in 1995 were compared with corresponding measured temperatures (Porter and others, 

1996). Simulated water temperatures ranged from 5.1 

to 30.0 °C, whereas measured water temperatures 

ranged from 7.0 to 31.1 °C. Simulated water temperatures were generally (58 percent) within 1°C of measured temperatures. The AME and RMSE between 

simulated and measured water temperature were 0.98 

and 1.26 °C, respectively. The difference between simulated and measured temperatures ranged from -3.0 to

2.6 °C, and the average and median differences were - 

0.5 and -0.2 °C, respectively.

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

1994 (fig. 11). Simulated water temperatures during

1995 were generally under-predicted when measured 

temperatures were less than 10 °C or exceeded 25 °C. 

During January and March 1995, simulated water temperatures were consistently less than measured temperatures, and errors were evenly distributed during the 

thermal stratification season indicating no tendency to 

over- or under-predict water temperature. Simulated 

water temperatures were generally less than measured 

temperatures near the reservoir bottom and near the 

water surface. However, as in 1994, most (58 percent) 

simulated temperatures were within 1 °C of the measured temperature.

Dissolved Oxygen

Simulation of the complex biochemical reactions 

affecting chemical and physical transport processes in 

the Norfork Lake model are expressed in part within 

the simulated dissolved-oxygen results. The supply of 

nitrogen, phosphorus, and light, regulates algal growth 

and the production of oxygen; photosynthesis is the 

only internal source of oxygen in the water-chemistry 

computations. Boundary sources of oxygen 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 ammonia to nitrate), algal and microbial 

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

sediment oxygen demand. These processes combined 

with the water-chemistry computations are used to simulate the complex vertical profiles of dissolved oxygen 

in Norfork Lake.

14 Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen In Norfork Lake, Arkansas, 1994-1995
01/18/95 03/23/95 05/15/95 06/15/95 07/11/95

09/14/95 09/28/95 10/26/95 11/07/95

06/16/95

12/13/95

5 10 15 20 2S 20 0 6 10 15 20 2S 20 0 5 10 16 20 2S 20 061015202630 0 5 10 16 20 2S 30 06 10 16202520

TEMPERATURE, IN DEGREES CELSIUS

EXPLANATION

- - MEASURED

 SIMULATED

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

January through December 1995.

S 10 15 20 25 30 35 

MEASURED TEMPERATURE, IN DEGREES CELSIUS

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

1995

20 30

DEPTH, IN METERS

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

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

Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Norfork Lake 15
Simulated dissolved-oxygen concentrations near 

the Norfork Lake dam exhibited the same general patterns and magnitudes as measured concentrations (fig. 

12). All simulated dissolved-oxygen concentrations 

(664) for January through December 1994 were compared to corresponding measured concentrations 

(Evans and others, 1995). Simulated dissolved-oxygen 

concentrations ranged from 0.0 to 12.8 mg/L, whereas, 

measured dissolved-oxygen concentrations ranged 

from 0.1 to 11.6 mg/L. Simulated dissolved-oxygen 

concentrations in the vertical profile generally (71 percent) were within 1 mg/L of measured concentrations. 

The AME and RMSE between simulated and measured 

dissolved-oxygen concentrations were 0.87 and 1.24 

mg/L, respectively. The difference between simulated 

and measured concentrations ranged from -4.9 to 5.8 

mg/L, and the average and median absolute differences 

were 0.1 and -0.2 mg/L, respectively.

Differences between simulated and measured 

dissolved-oxygen concentrations were compared to 

corresponding measured dissolved-oxygen concentrations, sampling date, and the water depth (fig. 13). Simulated dissolved-oxygen concentrations typically were 

less than measured values at lower concentrations. 

Errors in simulated dissolved-oxygen concentration 

were greater near the enjl of the thermal stratification 

season (October-Novem|ber) and during turnover 

(December). The DecerAber 5,1994, results had the 

greatest differences between simulated and measured 

dissolved-oxygen concentrations. Thermal destratification was occurring during this time and the model simulated turnover occurring slightly earlier than it 

actually occurred. Simulated dissolved oxygen concentrations generally were under-predicted near the water 

surface and over-predicted near the lake bottom.

03/23/94 05/10/94 06/07/94 07/07/94

I

08/18/94 09/13/94 09/28/94 10/12/94

u

11/01/94 11/14/94 12/05/94

10/19/94

u

EXPLANATION

-* MEASURED

 SIMULATED

DISSOLVED OXYGEN, IN MILLIGRAMS PER LITER

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

Lake dam, January through December 1994.

16 Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Norfork Lake, Arkansas, 1994-1995
MEASURED DISSOLVED-OXYGEN CONCENTRATION, 

IN MILLIGRAMS PER LITER

. B

'III>+T

* 1 ° 1 1 o . o I

iHgi' ° si

o

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

1994

DEPTH IN METERS

Figure 13. Relation of difference between simulated and 

measured dissolved-oxygen concentrations near Norfork 

Lake dam to (A) measured dissolved-oxygen concentrations, (B) sampling date, and (C) water depth, January 

through December 1994.

Simulated dissolved-oxygen concentrations 

were similar to measured dissolved-oxygen concentrations in 1995 (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 (613) were compared with corresponding measured concentrations near the Norfork Lake dam. 

Simulated values ranged from 0.0 to 13.0 mg/L 

whereas, measured dissolved-oxygen concentrations 

ranged from 0.0 to 11.3 mg/L. Simulated dissolvedoxygen concentrations in the vertical profile generally 

were (67 percent) within 1 mg/L of measured concentrations. The AME and RMSE between simulated and 

measured dissolved-oxygen concentrations were 0.95 

and 1.41, respectively. The difference between simulated and measured dissolved-oxygen concentrations 

ranged from -6.9 to 4.3 mg/L, and the average and 

median differences were -0.13 and 0.1 mg/L, respectively.

03/23/95 05/15/95

2 »

z

r

09/14/95 09/28/95

06/15/95 07/11/95 08/16/95

10/26/95 11/07/95 12/13/95

V

M4EXUT

DISSOLVED OXYGEN, IN MILLIGRAMS PER LITER 

EXPLANATION

- -MEASURED

 SIMULATED

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

Lake dam, January through December 1995.

Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Norfork Lake 17
On average, simulated dissolved-oxygen concentrations were slightly under-predicted when compared to measured concentrations (fig. 15). The largest 

differences between simulated and measured dissolved-oxygen concentrations typically occurred at 

concentrations greater than 5 mg/L. The model consistently over-predicted dissolved-oxygen concentrations 

during isothermal conditions, and typically under-predicted concentrations during the stratification season. 

Simulated dissolved-oxygen concentrations often were 

less than measured concentrations regardless of depth. 

Despite these tendencies, simulation of dissolved-oxygen concentration in the vertical profile near the Norfork Lake dam followed the same general patterns as 

measured concentrations.

MEASURED DISSOLVED-OXYGEN CONCENTRATION. 

IN MILLIGRAMS PER LJTER

> B 

-J ' ll,'I I

i ;im i

8 I

o

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

1995

DEPTH, IN METERS

Figure 15. Relation of difference between simulated and 

measured dissolved-oxygen concentrations near Norfork 

Lake dam to (A) measured dissolved-oxygen 

concentrations, (B) sampling 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 Norfork Lake 

model was not conducted because the Norfork 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; Haggard and 

Green, 2002) in other reservoirs were used to identify 

several parameters for evaluation in the sensitivity 

analysis. The sensitivity of simulated water temperature and dissolved-oxygen concentration near the dam 

to changes in the wind-sheltering coefficient (WSC), 

bottom-water heat exchange coefficient (CBHE), light 

extinction (a), sediment-oxygen demand (SOD), and 

changes in inflow temperature and dissolved-oxygen 

concentrations was assessed.

Water temperature in the Norfork Lake model 

was most sensitive to changes in the WSC and a (fig 

16). Wind speed in the calibrated Norfork 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 thermal stratification, vertical mixing 

was over-predicted when the WSC was increased (1.0) 

and under-predicted when the WSC was decreased 

(0.5). Changes in the a affected vertical water temperature profiles during stratification. Increasing a 

slightly elevated the thermocline and decreasing a lowered the thermocline. Changes in inflow water temperature had little affect on vertical water temperature 

profiles near the dam. liie combination of WSC and a 

appear to be the driving factors in the model responsible for the development, duration, and vertical location 

of the thermocline in Norfork Lake near the dam.

In the Norfork Lake model, dissolved-oxygen 

concentrations were most affected by changes in the 

WSC, a, and FSOD (fig. 17). FSOD is the fraction of 

the zero-order SOD rate and is applied to adjust SOD 

equally among all segments. Changes in the WSC and 

FSOD had the greatest effect on dissolved-oxygen concentrations near the thermocline and throughout the 

hypolimnion. The a regulates the amount of light penetrating the water, indirectly affecting dissolved-oxygen concentrations by influencing algal production. 

During thermal stratification, changes in a had the 

greatest affect on the position and configuration of the 

thermocline. Changes in the inflow dissolved-oxygen 

concentrations had little effect on the vertical distribution of dissolved oxygen near the dam.

18 Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Norfork Lake, Arkansas, 1994-1995
July 7,1994

Wind-Shattering Coefficient of Bottom Light Extinction inflow Water 

Coefficient (WSC) Heat Exchange (CBHE) Coefficient (a) Temperature (fTEMP)

: 5 10 15 20 25 30 35 5 10 15 20 25 30 5 10 15 20 25 30 5 10 15 20 25 30

January 18,1995

10 15 0 5 10 15 0 5 10 15 

WATER TEMPERATURE, IN DEGREES CELSIUS

EXPLANATION

 WSC = 0.7 

(calbrated value) 

WSC = 0.5

 WSC = 1.0

CBHE = 7E-8 

(calibrated value) 

CBHE = 7E-9 

CBHE = 7E-7

a = 0.48 1.0XITEMP 

(calibration value) (calibration value) 

a-024 0.75XITEMP 

a=072 USxITEMP

Figure 16. Vertical temperature distributions near the Norfork Lake dam on July 7,1994 (top), and January 18,1995 (bottom), 

showing calibrated model profiles and profiles as a result of differing model parameters.

July 7,1994

inflow Dissolved

Wind-Sheltering Fraction of Sediment Light Extinction Oxygen Concentration 

Coefficient (WSC) Oxygen Demand (FSOD) Coefficient (a) (IDO)

January 18,1995

DISSOLVED OXYGEN CONCENTRATION, IN MILLIGRAMS PER LITER 

EXPLANATION

 WSC = 0.7 

(calfcrated value) 

WSC = 0.5

FSOD =1.75 - 

(calbrated value) 

FSOD-1.0

 WSC = 1.0 FSOD = 2.5 __

 0 = 0.48

(calibration value) 

a=0.24

 1.0 X IDO 

(calibration value) 

0.75 X IDO 

 1.25 X IDO

Figure 17. Vertical dissolved-oxygen concentration distributions near the Norfork Lake dam on July 7,1994 (top), and 

January 18,1995 (bottom), showing calibrated model profiles and profiles as a result of differing model parameters.

Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen In Norfork Lake 19
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, algal 

dynamics play a substantial role in the dissolved-oxygen conditions near the Norfork Lake dam.

Model Applications

The calibrated Norfork Lake model was used to 

assess the impacts of increased minimum flow on 

water-surface elevation and on temperature and dissolved-oxygen concentrations in the Norfork Lake outflow waters. Two scenarios were simulated, including 

(1) an increase in the outflow of Norfork Lake dam 

from the existing minimum flow of 1.6 m3/s to 8.5 m3/ 

s, and (2) an increase in water-surface elevation of Norfork Lake to correct for the volume displaced by the 

additional minimum flow.

When 8.5 m3/s was applied as the minimum 

amount of outflow (increased minimum flow scenario), 

average annual outflow increased from 70.32 to 71.74 

m3/s, about a 2 percent increase. Approximately 23 

percent of the hourly outflow data required an increase 

to 8.5 m3/s. Average annual outflow increased from 

2,218 to 2,262 million m3, which is equivalent to 44 

million m3 per year increase, or about 2.8 percent of 

reservoir volume at conservation pool elevation. The 

water-surface elevation at the end of 1994 was reduced 

0.41 m and at the end of 1995 was reduced about l.lm 

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

1994 (168.79 m). When 1.1 m of water was applied to 

the initial elevation (increased minimum flow with 

increased water-surface elevation scenario), the difference by the end of 1994 was 0.68 m greater than the 

calibrated model without the increased minimum flow 

and by the end of 1995 only 0.17 m greater than the calibrated model (fig. 19).

176

174

172

170

35 168

W 166 

164

162

JAN MAR MAY JULY SEPT NOV 

1994

MAR MAY JULY SEPT NOV 

1995

EXPLANATION

 Calibrated Model

Increased Minimum Row Scenario

 Increased Minimum Flow with Increased 

Water-Surface Elevation Scenario

Figure 18. Simulated water-surface elevations resulting from increased minimum flow scenarios.

CO

Z CO 1 6

5 -I OC 

* IU UJ 1.2

O O UJ no

Sll 0.4

2l}iJ~- 0.0

UJJ^Q -0.4

Qjn£ -0.8 

<*Cu -1-2

Z ° -I

O J/i 

CO

"""" "*-« * "

'*""'"* »«.

"""": ' "' ;--'-' : ' .:... -""'~: " : '--:'. ...,- .,..

N MAR MAY JULY SEPT NOV MAR MAY JULY SEPT NOV 

1994 1995

EXPLANATION

Increased Minimum Row Scenario

 Increased Minimum Row with Increased

Water-Surface Elevation Scenario

Figure 19. Relation of difference between water-surface elevations predicted from increased minimum flow scenarios and 

calibrated model water-surface elevation with time.

20 Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen In Norfork Lake, Arkansas, 1994-1995
Temperature in the outflow water differed little 

between results from the increased minimum flow scenarios and the calibrated model (figs. 20 and 21). Absolute maximum difference in outflow water temperature 

between the increased minimum flow scenario and the 

calibrated model was 0.79 °C and between the 

increased minimum flow with increased water-surface 

elevation and the calibrated model was 1.08 °C. Temperature differences for both scenarios were within the 

AME and RMSE between simulated and measured 

water-column profile temperature differences reported 

in the Model Calibration section of this report. Simulated outflow temperatures were similar to estimated 

outflow temperatures from water-column profiles measured upstream from the dam (George Robins, Southwestern Power Administration, written commun., 

2000) and to measured downstream outflow temperatures (USGS station number 07060000) (fig. 21). Water 

temperature in the dam outflow increased slightly with 

the addition of increased minimum flow. Conversely, 

with the increase in water-surface elevation plus the 

increased minimum flow, water temperature in the dam 

outflow decreased slightly through time.

INCREASED MINIMUM FLOW 

WATER TEMPERATURE DIFFERENCE

JAN MAR MAY JULY SEPT NOV 

1994

MAR MAY JULY SEPT NOV

1995

INCREASED MINIMUM FLOW WITH INCREASED

WATER-SURFACE ELEVATION 

WATER TEMPERATURE DIFFERENCE

MAR MAY JULY SEPT NOV 

1995

Figure 20. Simulated water temperature differences 

between increased minimum flow scenarios and the 

calibrated model.

JAN MAR MAY JULY SEPT NOV 

1994

MAR MAY JULY SEPT NOV 

1995

EXPLANATION

 Calibrated Model

 Increased Minimum Row Scenario

 Increased Minimum Flow with Increased 

Water-Surface Elevation Scenario 

Measured Downstream Outflow 

 Water-Column Profile Estimate Upstream From Dam

Figure 21. Simulated and estimated water temperatures in Norfork Lake outflow and measured temperatures downstream 

from Norfork Lake dam.

Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Norfork Lake 21
Dissolved-oxygen concentrations in the outflow 

water differed little between results from the two 

increased minimum flow scenarios and the calibrated 

model (figs. 22 and 23). Absolute maximum difference 

in outflow dissolved oxygen between the increased 

minimum flow scenario and the calibrated model was 

0.81 mg/L and between the increased minimum flow 

with increased water-surface elevation and the calibrated model was 1.59 mg/L. Dissolved-oxygen concentration differences for both scenarios were about the 

same as the AME and RMSE between simulated and 

measured water-column profile dissolved-oxygen differences reported in the Model Calibration section of 

this report. Simulated outflow dissolved-oxygen concentrations were similar to estimated outflow concentrations from water-column profiles measured 

upstream from the dam (George Robins, Southwestern 

Power Administration, written commun., 2000) and to 

measured downstream outflow concentrations (USGS 

station number 07060000) (fig. 23). Dissolved-oxygen 

concentrations in the dam outflow decreased slightly 

through time with the addition of increased minimum 

flow. Conversely, with the increase in water-surface 

elevation and the increased minimum flow, dissolvedoxygen concentrations in the dam outflow increased 

slightly through time.

Small changes in water temperature and dissolved-oxygen concentration compared to the calibrated, base condition were simulated for the two

increased minimum flow scenarios. However, the 

changes were similar to the error between simulated 

and measured temperature and dissolved-oxygen concentrations determined for model calibration.

INCREASED MINIMUM FLOW DISSOLVEDOXYGEN CONCENTRATION DIFFERENCE

JAN MAR MAY JULY SEPT NOV 

1994

MAR MAY JULY SEPT NOV 

1995

INCREASED MINIMUM FLOW WITH INCREASED WATERSURFACE ELEVATION DISSOLVED-OXYGEN 

CONCENTRATION DIFFERENCE

JAN MAR MAY JULY SEPT NOV 

1994

MAR MAY JULY SEPT NOV 

1995

Figure 22. Simulated dissolved-oxygen concentration 

differences between increased minimum flow scenarios and 

calibrated model.

LU 

G

i

Q

LU 

>

^ O

co

CO

Q

LU 14 

Z~IJ 12

Orr

P LU 10 <Qrr co 8

nig

Od 

o =

6

G 4 

2

JAN MAR MAY JULY SEPT NOV 

1994

MAR MAY JULY SEPT NOV 

1995

EXPLANATION

 Calibrated Model

 Increased Minimum Flow Scenario

 Increased Minimum Flow with Increased 

Water-Surface Elevation Scenario 

Measured Downstream Outflow 

 Water-Column Profile Estimate Upstream From Dam

Figure 23. Simulated and estimated dissolved-oxygen concentrations in Norfork Lake outflows and measured dissolvedoxygen concentrations downstream from Norfork Lake dam.

Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Norfork Lake 22
SUMMARY

Outflow from Norfork Lake and other White 

River reservoirs support a cold-water trout fishery of 

significant economic yield in north-central Arkansas 

and south-central Missouri. Proposed increases in minimum flows released from the dam have caused concerns about the sustainability of cold-water 

temperature and dissolved oxygen in the bottom water 

of Norfork Lake. Increases in water temperature and 

decreases in dissolved oxygen could have potentially 

negative impacts on the cold-water trout fisheries in the 

downstream outflow. Thus, the U.S. Geological Survey 

in cooperation with the Arkansas Game and Fish Commission, conducted a study to assess the impact of additional minimum flows on the hydrodynamics, 

temperature, and dissolved-oxygen concentrations in 

Norfork Lake and on temperature and dissolved-oxygen concentrations in the downstream outflow.

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

developed for Norfork Lake, Arkansas. The model was 

calibrated using hydrologic records and vertical profiles of temperature and dissolved oxygen measured in 

or near Norfork Lake from January 1994 through 

December 1995. The model simulates surface-water 

elevation, water temperature, and dissolved-oxygen 

concentration. The model predicted temperatures generally within 1 °C of the measured temperatures. The 

AME and RMSE for 1994 were 0.82 and 0.98, respectively, and for 1995 were 0.98 and 1.26, respectively. 

The model predicted dissolved-oxygen concentrations 

generally within 1 mg/L of the measured concentrations. The AME and RMSE for 1994 were 0.87 and 

1.24, respectively. For 1995, the AME and RMSE were 

0.95 and 1.41, respectively.

The Norfork Lake model was developed to 

assess the impacts of proposed increases in minimum 

flows from 1.6 m3/s (the existing minimum flow) to 8.5 

m3/s (the increased minimum flow). Scenarios 

included assessing the impact of (1) increased minimum flows and (2) increased minimum flows with 

increased water-surface elevation of 1.1 m greater than 

the initial water-surface elevation on outflow temperatures and dissolved-oxygen concentrations. With the 

increased minimum flow, water temperatures increased 

and dissolved oxygen decreased in the outflow. Conversely, increased minimum flow with increased watersurface elevation lowered the outflow water temperature and increased dissolved-oxygen concentrations. 

However, these results were similar to the error

between simulated and measured water temperature 

and dissolved-oxygen concentrations.

This model provides the basis and framework for 

future water-quality modeling of Norfork Lake. As 

additional data are collected in the reservoir and tributaries, the calibrated model can be modified 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 twodimensional, laterally averaged, hydrodynamic and 

water quality model, version 2.0, user manual: Vicksburg, Miss., Instruction Report EL-95-1, US. Army 

Engineer Waterways Experiment Station.

Evans, D.A., Porter, I.E., and Westerfield, PW, 1995, Water 

resources data, Arkansas, water year 1994: U.S. Geological Survey Water-Data Report AR-94-1,466 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: US. Geological 

Survey Water-Resources Investigations Report 97- 

4131,62 p.

Green, WR. 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., and Green, W.R., 2002, Simulation of hydrodynamics, temperature, and dissolved-oxygen in Beaver Lake, Arkansas, 1994-1995: U.S. Geological 

Survey Water-Resources Investigations Report 02- 

4116, 21 p.

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, I.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 AR96-1, 238 p.

Roache, P.J., 1982, Computational fluid mechanics: Albuquerque, New Mexico, Hennosa Publishers, 446 p.

Summary 23

U.S. GOVERNMENT PRINTING OFFICE: 2002-555-177/30007
Galloway, J.M., and Green, W.R. SIMULATION OF HYDRODYNAMICS, TEMPERATURE, AND DISSOLVED OX

ARKANSAS, 1994-1995 U.S. Geological Survey Water-Resources Investigations Report 0