Simulation of Hydrodynamics, Temperature, 

and Dissolved Oxygen in Table Rock Lake, 

Missouri, 1996–1997

Water-Resources Investigations Report 03–4237

Prepared in cooperation with the

Missouri Department of Conservation

U.S. Department of the Interior

U.S. Geological Survey
Cover Photograph: Table Rock Lake Dam, June 1987. Photograph by Wayne R. Berkas, U.S. Geological 

Survey.
U.S. Department of the Interior

U.S. Geological Survey

Simulation of Hydrodynamics, Temperature, 

and Dissolved Oxygen in Table Rock Lake, 

Missouri, 1996–1997

By W. Reed Green, Joel M. Galloway, Joseph M. Richards, and Edwin A. Wesolowski

Water-Resources Investigations Report 03–4237

Prepared in cooperation with the

Missouri Department of Conservation

Rolla, Missouri

2003
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: Copies of this report can be purchased from:

District Chief U.S. Geological Survey

U.S. Geological Survey, WRD Information Services

1400 Independence Road Box 25286, Building 810

Mail Stop 100 Denver Federal Center 

Rolla, Missouri 65401 Denver, CO 80225-0286
Contents iii

CONTENTS

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

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

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

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

Acknowledgments .................................................................................................................................................. 4

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

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

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

Boundary and Initial Conditions................................................................................................................... 4

Hydraulic and Thermal Boundary Conditions.................................................................................... 8

Chemical Boundary Conditions.......................................................................................................... 11

Initial Conditions ................................................................................................................................ 11

Model Parameters ......................................................................................................................................... 11

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

Model Calibration................................................................................................................................................... 14

Hydrodynamics and Temperature................................................................................................................. 14

Dissolved Oxygen......................................................................................................................................... 16

Sensitivity Analysis ...................................................................................................................................... 21

Model Applications ................................................................................................................................................ 27

Summary........................................................................................................................................................................... 33

References ........................................................................................................................................................................ 34
iv 

FIGURES

1. Map showing location of Table Rock Lake Basin in Missouri and Arkansas.................................................. 2

2. Plot showing idealized model segment, layers, and branches for the CE-QUAL-W2 reservoir model........... 5

3. Plot showing side view (A), top view (B), and face view from the dam (C) of the computational grid of

Table Rock Lake used in CE-QUAL-W2......................................................................................................... 6

4.–24. Graphs showing:

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

area in Table Rock Lake ...................................................................................................................... 7

5. Annual mean streamflow for the James River upstream from Table Rock Lake, 1958 through 

1997 ..................................................................................................................................................... 9

6. Daily inflow and hourly outflow for the Table Rock Lake Dam, Missouri, January 1996 through 

December 1997.................................................................................................................................... 10

7. Simulated and measured water-surface elevations near the Table Rock Lake Dam, January 1996 

through December 1997 ...................................................................................................................... 15

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

Table Rock Lake Dam, January through November 1996................................................................... 17

9. Relation of difference between simulated and measured water temperatures near the Table Rock

Lake Dam to (A) measured water temperature, (B) sampling date, and (C) water depth, 

January through November 1996 ........................................................................................................ 18

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

Table Rock Lake Dam, March through November 1997..................................................................... 19

11. Relation of difference between simulated and measured water temperatures near the Table Rock 

Lake Dam to (A) measured water temperature, (B) sampling date, and (C) water depth, March 

through November 1997...................................................................................................................... 20

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

near the Table Rock Lake Dam, January through November 1996..................................................... 22

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

the Table Rock Lake Dam to (A) measured dissolved-oxygen concentrations, (B) sampling date, 

and (C) water depth, January through November 1996....................................................................... 23

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

near the Table Rock Lake Dam, March through November 1997....................................................... 24

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

Table Rock Lake Dam to (A) measured dissolved-oxygen concentrations, (B) sampling date, 

and (C) water depth, March through November 1997......................................................................... 25

16. Vertical temperature distributions near the Table Rock Lake Dam on October 16, 1996 (top), 

and March 6, 1997 (bottom), showing calibrated model profiles and profiles as a result of 

differing model parameters.................................................................................................................. 26

17. Vertical dissolved-oxygen concentration distributions near the Table Rock Lake Dam on 

October 16, 1996 (top), and March 6, 1997 (bottom), showing calibrated model profiles 

and profiles as a result of differing model parameters ........................................................................ 28

18. Simulated outflow, measured tailwater, and estimated outflow temperatures..................................... 29

19. Simulated water temperature difference between the increased minimum flow scenario and the

calibrated model .................................................................................................................................. 29

20. Simulated and estimated outflow dissolved-oxygen concentration..................................................... 30

21. Simulated dissolved-oxygen concentrations between the increased minimum flow scenario and 

the calibrated model ............................................................................................................................ 30

22. Simulated pool elevation for the existing operational plan and the potential operational plan 

that would include increased minimum flow....................................................................................... 31

23. Simulated water temperature for Table Rock Lake Dam outflow using the existing operational

plan and the potential operational plan of increased stage and minimum flow .................................. 32

24. Simulated dissolved-oxygen concentrations for Table Rock Lake Dam outflow using the existing 

operational plan and the potential operational plan of increased conservation pool and minimum 

flow...................................................................................................................................................... 33
Contents v

TABLES

1. Streamflow-gaging station and water-quality sampling site locations in and around Table Rock Lake.......... 3

2. Hydraulic and thermal input parameters specified for Table Rock Lake model.............................................. 8

3. Rate coefficients used in water-chemistry and biological simulations and other parameters specified as 

input in the Table Rock Lake model ................................................................................................................ 12

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)

Vertical coordinate information is referenced to the National Geodetic Vertical Datum of 1929 (NGVD 29). Altitude, as used 

in this report, refers to distance above or below NGVD 29. NGVD 29 can be converted to the North American Vertical 

Datum of 1988 (NAVD 88) by using the National Geodetic Survey conversion utility available at URL 

http://www.ngs.noaa.gov/TOOLS/Vertcon/vertcon.html.

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)
Contents iii

CONTENTS

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

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

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

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

Acknowledgments .................................................................................................................................................. 4

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

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

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

Boundary and Initial Conditions................................................................................................................... 4

Hydraulic and Thermal Boundary Conditions.................................................................................... 8

Chemical Boundary Conditions.......................................................................................................... 11

Initial Conditions ................................................................................................................................ 11

Model Parameters ......................................................................................................................................... 11

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

Model Calibration................................................................................................................................................... 14

Hydrodynamics and Temperature................................................................................................................. 14

Dissolved Oxygen......................................................................................................................................... 16

Sensitivity Analysis ...................................................................................................................................... 21

Model Applications ................................................................................................................................................ 27

Summary........................................................................................................................................................................... 33

References ........................................................................................................................................................................ 34
iv 

FIGURES

1. Map showing location of Table Rock Lake Basin in Missouri and Arkansas.................................................. 2

2. Plot showing idealized model segment, layers, and branches for the CE-QUAL-W2 reservoir model........... 5

3. Plot showing side view (A), top view (B), and face view from the dam (C) of the computational grid of

Table Rock Lake used in CE-QUAL-W2......................................................................................................... 6

4.–24. Graphs showing:

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

area in Table Rock Lake ...................................................................................................................... 7

5. Annual mean streamflow for the James River upstream from Table Rock Lake, 1958 through 

1997 ..................................................................................................................................................... 9

6. Daily inflow and hourly outflow for the Table Rock Lake Dam, Missouri, January 1996 through 

December 1997.................................................................................................................................... 10

7. Simulated and measured water-surface elevations near the Table Rock Lake Dam, January 1996 

through December 1997 ...................................................................................................................... 15

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

Table Rock Lake Dam, January through November 1996................................................................... 17

9. Relation of difference between simulated and measured water temperatures near the Table Rock

Lake Dam to (A) measured water temperature, (B) sampling date, and (C) water depth, 

January through November 1996 ........................................................................................................ 18

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

Table Rock Lake Dam, March through November 1997..................................................................... 19

11. Relation of difference between simulated and measured water temperatures near the Table Rock 

Lake Dam to (A) measured water temperature, (B) sampling date, and (C) water depth, March 

through November 1997...................................................................................................................... 20

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

near the Table Rock Lake Dam, January through November 1996..................................................... 22

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

the Table Rock Lake Dam to (A) measured dissolved-oxygen concentrations, (B) sampling date, 

and (C) water depth, January through November 1996....................................................................... 23

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

near the Table Rock Lake Dam, March through November 1997....................................................... 24

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

Table Rock Lake Dam to (A) measured dissolved-oxygen concentrations, (B) sampling date, 

and (C) water depth, March through November 1997......................................................................... 25

16. Vertical temperature distributions near the Table Rock Lake Dam on October 16, 1996 (top), 

and March 6, 1997 (bottom), showing calibrated model profiles and profiles as a result of 

differing model parameters.................................................................................................................. 26

17. Vertical dissolved-oxygen concentration distributions near the Table Rock Lake Dam on 

October 16, 1996 (top), and March 6, 1997 (bottom), showing calibrated model profiles 

and profiles as a result of differing model parameters ........................................................................ 28

18. Simulated outflow, measured tailwater, and estimated outflow temperatures..................................... 29

19. Simulated water temperature difference between the increased minimum flow scenario and the

calibrated model .................................................................................................................................. 29

20. Simulated and estimated outflow dissolved-oxygen concentration..................................................... 30

21. Simulated dissolved-oxygen concentrations between the increased minimum flow scenario and 

the calibrated model ............................................................................................................................ 30

22. Simulated pool elevation for the existing operational plan and the potential operational plan 

that would include increased minimum flow....................................................................................... 31

23. Simulated water temperature for Table Rock Lake Dam outflow using the existing operational

plan and the potential operational plan of increased stage and minimum flow .................................. 32

24. Simulated dissolved-oxygen concentrations for Table Rock Lake Dam outflow using the existing 

operational plan and the potential operational plan of increased conservation pool and minimum 

flow...................................................................................................................................................... 33
Contents v

TABLES

1. Streamflow-gaging station and water-quality sampling site locations in and around Table Rock Lake.......... 3

2. Hydraulic and thermal input parameters specified for Table Rock Lake model.............................................. 8

3. Rate coefficients used in water-chemistry and biological simulations and other parameters specified as 

input in the Table Rock Lake model ................................................................................................................ 12

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)

Vertical coordinate information is referenced to the National Geodetic Vertical Datum of 1929 (NGVD 29). Altitude, as used 

in this report, refers to distance above or below NGVD 29. NGVD 29 can be converted to the North American Vertical 

Datum of 1988 (NAVD 88) by using the National Geodetic Survey conversion utility available at URL 

http://www.ngs.noaa.gov/TOOLS/Vertcon/vertcon.html.

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)
Introduction 1

Simulation of Hydrodynamics, Temperature, and 

Dissolved Oxygen in Table Rock Lake, Missouri, 

1996–1997

By W. Reed Green, Joel M. Galloway, Joseph M. Richards, and Edwin A. Wesolowski

Abstract

Outflow from Table Rock Lake and other 

White River reservoirs support a cold-water trout 

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

Missouri Department of Conservation has 

requested an increase in existing minimum flows 

through the Table Rock Lake Dam from the U.S. 

Army Corps of Engineers to increase the quality of 

fishable waters downstream in Lake Taneycomo. 

Information is needed to assess the effect of 

increased minimum flows on temperature and dissolved-oxygen concentrations of reservoir water 

and the outflow.

A two-dimensional, laterally averaged, 

hydrodynamic, temperature, and dissolved-oxygen model, CE-QUAL-W2, was developed and 

calibrated for Table Rock Lake, located in Missouri, north of the Arkansas-Missouri State line. 

The model simulates water-surface elevation, heat 

transport, and dissolved-oxygen dynamics. The 

model was developed to assess the effects of proposed increases in minimum flow from about 4.4 

cubic meters per second (the existing minimum 

flow) to 11.3 cubic meters per second (the 

increased minimum flow). Simulations included 

assessing the effect of (1) increased minimum 

flows and (2) increased minimum flows with 

increased water-surface elevations in Table Rock 

Lake, on outflow temperatures and dissolved-oxygen concentrations.

In both minimum flow scenarios, water temperature appeared to stay the same or increase 

slightly (less than 0.37 °C) and dissolved oxygen 

appeared to decrease slightly (less than 0.78 mg/L) 

in the outflow during the thermal stratification season. However, differences between the minimum 

flow scenarios for water temperature and dissolved-oxygen concentration and the calibrated 

model were similar to the differences between 

measured and simulated water-column profile values.

INTRODUCTION

Table Rock Lake (fig. 1) is a large, deep-storage 

reservoir located on the White River in Missouri north 

of the border of Arkansas and Missouri. Table Rock 

Lake Dam was completed in 1958 and is operated by 

the U.S. Army Corps of Engineers (USACE) for the 

purposes of flood control and hydroelectric power. 

Table Rock Lake is downstream from Beaver Lake. 

Downstream from Table Rock Lake are Lake Taneycomo and Bull Shoals Lake (fig. 1). The U.S. Geological Survey (USGS) monitors streamflow and water 

quality at various sites in and around Table Rock Lake 

(table 1). Today, in addition to aforementioned uses, the 

reservoir is used for fish and wildlife habitat, recreation, and water supply. The outflows from Table Rock 

Lake, and other White River reservoirs, also support a 

cold-water trout fishery of substantial economic yield 

in south-central Missouri and north-central Arkansas. 

The Missouri Department of Conservation (MDC) has 

requested an increase in minimum flows through Table 

Rock Lake Dam to increase the quality of fishable 

waters downstream in Lake Taneycomo. Proposed
2 Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Table Rock Lake, Missouri, 1996–1997

BARRY

STONE

CARROLL

TANEY

BOONE

CHRISTIAN

BARRY

TANEY OZARK

NEWTON

BOONE

DOUGLAS

SEARCY

MARION

STONE

BAXTER

GREENE WRIGHT

STONE

LAWRENCE

CHRISTIAN

BENTON

WEBSTER JASPER

NEWTON

TEXAS

DADE

MCDONALD

JOHNSON VAN BUREN

IZARD

CRAWFORD FRANKLIN POPE

FULTON

CARROLL

WASHINGTON

MADISON
Introduction 3

Table 1. Streamflow-gaging station and water-quality sampling site locations in and around Table Rock Lake

[Temp and DO, water temperature and dissolved-oxygen concentration monitor; Q, discharge recording station; QW, water-quality 

sampling station]

USGS

 station 

number

(fig. 1) Name Type Latitude Longitude

07049691 White River at Beaver Dam near Eureka Springs, Arkansas Temp and DO 362515 935050

07050500 Kings River near Berryville, Arkansas Q and QW 362536 933715

07053207 Long Creek at Denver, Arkansas Q only 362323 931901

07053250 Yocum Creek near Oak Grove, Arkansas Q and QW 362717 932121

07053400 Table Rock Lake near Branson, Missouri (Table Rock Lake Dam) Temp and DO 363546 931835

07052500 James River at Galena, Missouri Q only 364819 932741

07053450 White River below Table Rock Dam near Branson, Missouri Temp and DO 363542 931832

07053500 White River near Branson, Missouri Q only 363551 931742

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 Table Rock Lake. 

Increases in water temperature and decreases in dissolved oxygen could have potential negative effects on 

the cold-water trout fisheries in the downstream outflow. Comprehensive information is needed to address 

temperature and dissolved-oxygen dynamics of Table 

Rock Lake and the effects of increased minimum flow.

In July 1999, a study was initiated by the USGS 

in cooperation with the MDC to characterize the hydrodynamics, temperature, and dissolved-oxygen concentration in Table Rock Lake, and to simulate the effect of 

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

hydrodynamic model of Table Rock Lake was developed using the 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 effects of 

reservoir operations on temperature and dissolved-oxygen concentration in Beaver, Norfork, and Bull Shoals 

Lakes (Galloway and Green, 2002; 2003; and Haggard 

and Green, 2002). 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 and system 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. 

Effects of upstream reservoir management on downstream reservoirs also could be tested.

Purpose

The purpose of this report is to describe the simulation of hydrodynamics, temperature, and dissolved 

oxygen in Table Rock Lake and outflows for January 

1996 through December 1997. Surface-water elevation, water temperature, and dissolved-oxygen concentration results from model applications simulating 

several proposed minimum flow scenarios are presented and compared to a calibrated, base condition. 

Data collected at the sites listed in table 1 were used in 

the model calibration. Simulated water temperature 

and dissolved-oxygen concentrations were calibrated 

to measured water-column profiles of water temperature and dissolved-oxygen concentrations collected at 

07053400, Table Rock Lake near Branson, Missouri, 

hereafter referred to as near Table Rock Lake Dam.

Description of Study Area

Table Rock Lake was impounded in 1958 on the 

White River, west of the city of Branson, Missouri. The 

primary inflows into Table Rock Lake are the James 

River, Kings River, Long Creek, and White River; several smaller tributaries also flow into the reservoir (fig. 
4 Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Table Rock Lake, Missouri, 1996–1997

1, table 1). The watershed has a drainage area of 10,412 

km2

 at the Table Rock Lake Dam. Table Rock Lake 

contains 3,330 million cubic meters of water at the elevation of the current conservation pool (278.9 m above 

NGVD 29) and the surface area is 174 km2. The length 

of the reservoir is 96 km from the Beaver Lake Dam to 

the Table Rock Lake Dam. The depth of the reservoir at 

the dam at conservation pool elevation is about 62 m, 

and the average depth through the reservoir is 19 m. On 

average, the hydraulic retention time of Table Rock 

Lake is about 0.8 year. 

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 water-surface elevation data used to 

develop and calibrate the model. 

SIMULATION OF HYDRODYNAMICS, 

TEMPERATURE, AND DISSOLVED 

OXYGEN IN TABLE ROCK LAKE

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

CE-QUAL-W2 was developed for Table Rock Lake 

and calibrated based on hydrologic records and vertical 

profiles of temperature and dissolved oxygen measured 

near the Table Rock Lake Dam from January 1996 

through December 1997 (Porter and others, 1997; 

1998; 1999). 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 report. 

Model Implementation

Implementation of the CE-QUAL-W2 model for 

Table Rock 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 

are given in this section.

Computational Grid

The computational grid is the geometric scheme 

(figs. 2 and 3) that numerically represents the space and 

volume of the reservoir. The model extends 96 km from 

the upstream boundary (Beaver Lake Dam) to the 

downstream boundary (Table Rock Lake Dam). The 

grid geometry (fig. 3) was developed by digitizing preimpoundment elevation contours of the land surface or 

reservoir bottom from USGS 7.5-minute and 15-

minute quadrangle maps. Twenty-eight computational 

segments exist along the main stem of the White River 

in Table Rock Lake. Three segments are in the Kings 

River branch, 18 segments are in the James River 

branch, and 6 segments are in the Long Creek branch. 

In addition, 10 other embayments (branches) are 

included containing two or three 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.

Segment geometry varied along the upstream-downstream gradient (fig. 3). Segment length was based in 

part on segment width. Segments ranged in length from 

1,273 to 15,332 m, and orientation of the longitudinal 

axis relative to north was determined for each segment. 

Segment widths at the reservoir surface ranged from 

316 m at the upstream White River boundary to 1,730 

m further downstream. Each segment was divided vertically into 1-m layers. Depth from the elevation of the 

top of the flood-control pool (284 m) to the reservoir 

bottom ranged from 24 m at the upstream boundary to 

68 m near Table Rock Lake Dam. Relations between 

water-surface elevation and volume and surface area in 

the Table Rock Lake model grid were similar to 

USACE pre-impoundment data (fig. 4).

Boundary and Initial Conditions

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

of the Table Rock Lake model included the reservoir
Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Table Rock Lake 5
6 Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Table Rock Lake, Missouri, 1996–1997
Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Table Rock Lake 7
8 Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Table Rock Lake, Missouri, 1996–1997

bottom, the shoreline, tributary streams, the upstream 

boundary (Beaver Lake Dam), 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 ground-water 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 2).

Heat exchange between the reservoir bottom and 

the overlying water column is computed from (1) the 

sediment temperature (table 2), (2) bottom-water heat 

exchange coefficient (table 2), and (3) the simulated 

temperature of the overlying water. 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 8.0 °C was used in the Table Rock Lake model. 

In general, heat exchange from the reservoir bottom is 

about two orders of magnitude less than surface 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 as a result 

of changing water level and, therefore, cell layers. 

Table Rock Lake receives water from the White 

River, which is regulated upstream at Beaver Lake Dam, 

from the James and Kings Rivers, and from many other 

tributaries (table 1). Other than the discharge from Beaver Lake (White River), the James River contributes the 

largest discharge into Table Rock Lake of all other tributaries. Annual streamflow recorded at the USGS streamflow-gaging station on the James River at Galena, 

Missouri (station number 07052500; fig. 1) indicates 

that inflow to Table Rock Lake during the 1996 and 1997 

simulation time period was below average (fig. 5). 

Annual mean streamflow for the James River from 1958 

through 1997 ranged from 10.3 to 63.27 m3

/s. The average annual mean streamflow during this time was 28.9 

m3

/s. Annual mean streamflow for the 1996 and 1997 

simulation time period was 26.2 and 20.9, respectively 

(Hauck and others, 1997; 1998; 1999).

Total daily reservoir inflow into Table Rock Lake 

was estimated by USACE (John Kielczewski, U.S. 

Army Corps of Engineers, written commun., 2000) 

based on measured outflow and change in reservoir 

water-surface elevations. Total mean reservoir inflow 

from January 1, 1996 through December 31, 1997, was 

estimated to be 113 m3/s; whereas, the estimated 

median reservoir inflow for the same period was 65.1 

m3/s. The estimated inflow exceeded 269 m3/s 10 percent of time.

Table 2. Hydraulic and thermal input parameters specified for Table Rock 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 Computational purpose Value

Constant or

time variable

Chezy resistance

coefficient

Represents turbulent exchange of energy at 

the reservoir bottom

70 m0.5/s Constant

Bottom–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

0.8

(dimensionless)

Constant

Horizontal eddy viscosity Represents laterally averaged longitudinal 

turbulent exchange of momentum

1 m2/s Constant

Horizontal eddy

diffusivity

Represents laterally averaged longitudinal 

turbulent mixing of mass and heat

1 m2/s Constant
Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Table Rock Lake 9

Gaged and areal-adjusted inflows used in the 

model were applied among 14 branches and 3 tributaries. Measured discharge from the White, James, and 

Kings Rivers, and Long Creek (fig. 6) made up about 

75 percent of the total estimated inflow (White River, 

35 percent; James River, 24 percent; Kings River, 12 

percent; and Long Creek, 4 percent). The remaining 25 

percent of inflow was divided up among smaller tributaries and branches and ungaged inflows were applied 

diffusely into the White River and James River 

branches as distributed inflow.

The downstream boundary for the Table Rock 

Lake model consists of the outflow from Table Rock 

Lake Dam. Outflow data (fig. 6) were produced by the 

USACE using stage-discharge relations and hourly 

power generation records. The mean and median reservoir outflow were 104 and 6.3 m3/s, respectively. The 

reservoir outflow exceeded 370 m3

/s 10 percent of the 

time. The vertical extent and distribution of flow in the 

release zone near the Table Rock 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 about 20 m 

above the bottom at an elevation of 236.2 m above 

NGVD 29 in model layer 56 (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 

(fig. 1; 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 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 2). 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 Table 

Rock 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 air temperatures, dewpoint temperatures, 

cloud covers, and wind speeds and directions measured
10 Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Table Rock Lake, Missouri, 1996–1997
Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Table Rock Lake 11

at Harrison, Arkansas. The simulated surface-water 

temperature and loss of heat through evaporation were 

included in the heat budget.

Chemical Boundary Conditions

Concentrations of selected constituents at all 

inflow boundaries are required for model operation. 

Boundary data in all tributaries and branches included 

hourly or daily concentrations of dissolved oxygen, 

ammonia as nitrogen, nitrite plus nitrate as nitrogen, 

total phosphorus, and a conservative tracer. Because of 

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

reported by Porter and others (1997; 1998; 1999) and 

Hauck and others (1997; 1998; 1999), and used for all 

inflow boundary constituents except dissolved oxygen. 

Dissolved-oxygen concentrations in the White River 

inflow were obtained from measured data at the Beaver 

Lake tailwater station 07049693 (Porter and others, 

1997; 1998; 1999). Dissolved-oxygen concentrations 

at the remaining inflow tributary boundaries were set to 

the concentration for 80 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 NGVD 29, and the molecular diffusivity of oxygen gas. Atmospheric nutrient inputs were 

not included in this model, and nutrient constituent 

inputs from the reservoir bottom generally were computed within the model based on the value of selected 

parameters (table 3) 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 before initiating model 

simulation. Initial water-surface elevation was set to 

the value measured at the Table Rock Lake Dam on 

January 1, 1996. 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, 1995 (Porter and others, 

1997).

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 

(table 2). Other parameters such as resistance, bottomheat 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 3). 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.
12 Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Table Rock Lake, Missouri, 1996–1997

Table 3. Rate coefficients used in water-chemistry and biological simulations and other parameters specified as input in 

the Table Rock Lake model

[m, meters; *, dimensionless; Q10, temperature correction factor; 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; mg/L, milligrams per liter]

Parameter/rate coefficient Computational purpose Value

Light extinction coefficient for water Amount of solar radiation absorbed in the surface layer 0.30/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 0.28*

Coliform decay rate Decay rate for coliforms, temperature dependent 1.4/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 2.0 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 0.01/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 0.14 m/d

Saturation light intensity Saturation light intensity at maximum algal photosynthesis

rate 500 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 1.0 oC

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 15.0oC

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 35.0 oC

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 40.0 oC

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 dependent

0.001/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
Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Table Rock Lake 13

Table 3. Rate coefficients used in water-chemistry and biological simulations and other parameters specified as input in 

the Table Rock Lake model—Continued

Parameter/rate coefficient Computational purpose Value

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 5.0 oC

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 30.0 oC

Fraction of maximum organic matter decay at

lower temperature

Organic matter decay as a function of temperature 0.99*

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

3.0 (g/m2)/d

5-day BOD decay rate Effects of BOD loading on dissolved oxygen 2.0/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 sedimentoxygen demand 0.02*

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 5.0 oC

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 20.0 oC

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 5.0 oC

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 20.0 oC

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
14 Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Table Rock Lake, Missouri, 1996–1997

Oxygen stoichiometric equivalent for ammonia

decay

Relates oxygen consumption to ammonia decay 4.57*

Oxygen stoichiometric equivalent for organic

matter decay

Relates oxygen consumption to decay of organic matter 1.4*

Oxygen stoichiometric equivalent for dark

respiration 

Relates oxygen consumption to algal dark respiration 1.4*

Oxygen stoichiometric equivalent for algal growth Relates oxygen production to algal growth 1.4*

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

0.5 mg/L

Table 3. Rate coefficients used in water-chemistry and biological simulations and other parameters specified as input in 

the Table Rock Lake model—Continued

Parameter/rate coefficient Computational purpose Value

Model Calibration

Successful model application requires model calibration that includes comparing model (simulated) 

results with observed (measured) reservoir conditions. 

If possible, 2 or more years of water-quality data should 

be used for adequate model calibration. Table Rock 

Lake model calibration was achieved by adjusting 

model parameters and, in some cases, estimated input 

data, for the 2 years from January 1996 through December 1997.

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:

(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 values, and is computed by equation 

2:

(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 water-surface elevations in Table 

Rock Lake (fig. 7) were adjusted to the measured water 

surface for the simulation period January 1996 to 

December 1997 (John Kielczewski, written commun., 

2000). The water-surface elevations were corrected to 

the measured values by adjusting the unmeasured 

inflow into the lake that was applied to all the segments 

within a branch segment. Inflow was either added or 

subtracted so that the simulated water-surface elevation 

reflected the measured water-surface elevation. By correcting the water budget, the thermodynamics could be 

calibrated without the uncertainty incurred with having 

differences between simulated and measured elevations 

(volumes).

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 (from Harrison, Arkansas: station number 723446, National 

Climatic Data Center, Asheville, North Carolina), simAME Σ Simulated Value Measured Value –

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

RMSE Σ( ) Simulated Values Measured Values –

Number of Observations -----------------------------------------------------------------------------------------------------------2

=
Model Calibration 15

ulated organic and inorganic solids concentrations, and 

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.

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 through 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 Table 

Rock Lake Dam (USGS station 07053400) from June 

through November in 1996 and 1997. 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.

Selected simulated water temperatures in 1996 

were compared to 465 corresponding measured temperatures near the Table Rock Lake Dam (Porter and 

others, 1997; 1998) (fig. 8). Simulated water temperatures reproduced seasonal variations measured in the 

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

temperature profiles. Simulated water temperatures 

ranged from 5.4 to 28.0 °C, whereas measured water 

temperatures ranged from 6.1 to 27.8 °C. Simulated 

water temperatures in the vertical profile were within 

1°C of measured temperatures 85 percent of the time. 

The overall AME and RMSE between simulated and 

measured water temperature were 0.58 and 0.75 °C, 

respectively. The difference between simulated and 

measured water temperature ranged from -2.8 to 3.2 

°C, and the median absolute difference was 0.40 °C.

Although the calibrated model closely simulated 

water temperature near the Table Rock Lake Dam during 1996, 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 than measured temperatures more often 

when measured temperatures were between 15 and 20 

°C (fig. 9). Simulated temperatures compared well with 

measured temperature when measured temperatures 

were less than 15 °C. Near-surface simulated temperatures were variable when compared with measured 

temperatures, whereas at greater depths, simulated 

temperatures tended to compare well with measured 

temperatures. Error in simulated water temperatures 

was greater during the thermal stratification season.

Simulated water temperatures were similar to 

measured temperatures in 1997 (fig. 10). Selected simulated temperatures in 1997 were compared to 402 corresponding measured temperatures (Porter and others, 

1998; 1999). Simulated water temperatures ranged 

from 4.8 to 26.8 °C, whereas measured water temperatures ranged from 5.6 to 28.7 °C. Simulated water temperatures were within 1°C of measured temperatures 

76 percent of the time. The overall AME and RMSE 

between simulated and measured water temperature 

were 0.79 and 0.98 °C, respectively. The difference 

between simulated and measured temperatures ranged 

from -2.4 to 4.13 °C, and the median absolute difference was 0.63 °C. 

Errors in simulated water temperatures were distributed similarly during 1997 when compared to 1996 

(figs. 10 and 11). Simulated temperatures during 1997 

varied most from measured temperatures at depths and 

temperatures associated with the thermocline. Differences in water temperature associated with the thermocline are reflected in seasonal temperature 

differences.

Dissolved Oxygen

Simulation of the complex biochemical reactions 

affecting chemical and physical transport processes in 

the Table Rock 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 Table Rock Lake. 
16 Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Table Rock Lake, Missouri, 1996–1997
Model Calibration 17
18 Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Table Rock Lake, Missouri, 1996–1997
Model Calibration 19
20 Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Table Rock Lake, Missouri, 1996–1997
Model Calibration 21

Simulated dissolved-oxygen concentrations in 

1996 near the Table Rock Lake Dam exhibited the 

same general patterns and magnitudes as measured 

concentrations (fig. 12). Selected simulated dissolvedoxygen concentrations for January through December 

1996 were compared to 465 corresponding measured 

concentrations (Porter and others, 1997; 1998). Simulated dissolved-oxygen concentrations ranged from 0.0 

to 11.8 mg/L, whereas, measured dissolved-oxygen 

concentrations ranged from 0.1 to 11.6 mg/L. Simulated dissolved-oxygen concentrations in the vertical 

profile were within 1 mg/L of measured concentrations 

74 percent of the time. The overall AME and RMSE 

between simulated and measured dissolved-oxygen 

concentrations were 0.74 and 1.00 mg/L, respectively. 

The difference between simulated and measured concentrations ranged from -5.9 to 5.3 mg/L, and the 

median absolute difference was 0.42 mg/L. 

Differences between simulated and measured 

dissolved-oxygen concentrations in 1996 were compared to corresponding measured dissolved-oxygen 

concentrations, sampling date, and the water depth (fig. 

13). Simulated dissolved-oxygen concentrations typically were greater than measured values at lower concentrations. Errors in simulated dissolved-oxygen 

concentration were greater later in the thermal stratification season (September through November). The 

July 10, 1996, results had the greatest error near the 

lake bottom. Simulated dissolved-oxygen concentrations generally were less than measured values near the 

water surface.

Simulated dissolved-oxygen concentrations 

were similar to measured dissolved-oxygen concentrations in 1997 (fig. 14), but differences were somewhat 

greater in 1997 than in 1996. Seasonal variations in 

simulated dissolved-oxygen concentration were reproduced despite pronounced differences in the vertical 

distribution. Selected simulated dissolved-oxygen concentrations were compared to 402 corresponding measured concentrations (Porter and others, 1998; 1999) 

near the Table Rock Lake Dam. Simulated values 

ranged from 0.0 to 11.7 mg/L, whereas measured dissolved-oxygen concentrations ranged from 0.1 to 11.6 

mg/L. Simulated dissolved-oxygen concentrations in 

the vertical profile were within 1 mg/L of measured 

concentrations 53 percent of the time. The overall 

AME and RMSE between simulated and measured dissolved-oxygen concentrations were 1.09 and 1.41, 

respectively. The difference between simulated and 

measured dissolved-oxygen concentrations ranged 

from -3.0 to 5.3 mg/L, and the median absolute difference was 0.90 mg/L. 

On average, simulated dissolved-oxygen concentrations in 1997 were slightly greater than measured 

concentrations (fig. 15). The largest differences 

between simulated and measured dissolved-oxygen 

concentrations typically occurred at concentrations less 

than 4 mg/L. Simulated dissolved-oxygen concentrations consistently were greater than measured concentrations during thermally stratified conditions within 

the thermocline. Simulated dissolved-oxygen concentrations often were greater than measured concentrations regardless of depth except near the surface. 

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

Rock Lake Dam followed the same general patterns as 

measured concentrations.

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 Table Rock 

Lake model was not conducted because the model 

includes more than 60 parameters (tables 2 and 3). 

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; Galloway 

and Green, 2002; 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), coefficient of bottom-water heat 

exchange coefficient (CBHE), light extinction coefficient (α), sediment-oxygen demand (SOD), and 

changes in inflow water temperature (ITEMP) and dissolved-oxygen concentrations was assessed.

Water temperature in the Table Rock Lake model 

was most sensitive to changes in the WSC and α (fig. 

16). Wind speed in the calibrated Table Rock Lake 

model was adjusted (WSC = 0.8) from the meteorological data recorded at Harrison, Arkansas; that is, the 

effective wind speed was 80 percent of the recorded 

wind speed at Harrison. Surface-water temperatures 

were not affected as much by changes in WSC as was 

the position of the thermocline and hypolimnetic tem-
22 Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Table Rock Lake, Missouri, 1996–1997
Model Calibration 23
24 Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Table Rock Lake, Missouri, 1996–1997
Model Calibration 25
26 Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Table Rock Lake, Missouri, 1996–1997
Model Applications 27

peratures. During thermal stratification, vertical mixing 

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

and under-predicted when the WSC was decreased 

(0.6). Changes in the α affected vertical water-temperature profiles during stratification. Increasing α

slightly elevated the thermocline and decreasing α lowered the thermocline. Changes in CBHE and inflow 

water temperature had a slight affect on vertical watertemperature profiles near the dam. The combination of 

WSC and α appear to be the driving factors in the 

model responsible for the development, duration, and 

vertical location of the thermocline in Table Rock Lake 

near the dam.

In the Table Rock Lake model, dissolved-oxygen 

concentrations were most affected by changes in the 

WSC, α, and fraction of sediment-oxygen demand 

(FSOD) (fig. 17). FSOD is the fraction of the zeroorder 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 α regulates the amount of light penetrating 

the water, indirectly affecting dissolved-oxygen concentrations by affecting algal production. During thermal stratification, changes in α had the greatest effect 

on the position and configuration of the thermocline. 

Changes in the inflow dissolved-oxygen (IDO) concentrations had little effect on the vertical distribution of 

dissolved oxygen near the dam except near the bottom.

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

however, examination of all of these parameters is 

beyond the scope of this report 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 Table Rock Lake Dam. 

Model Applications

The calibrated Table Rock Lake model was used 

to assess the effects of increased minimum flow on 

water-surface elevation and on temperature and dissolved-oxygen concentrations in the Table Rock Lake 

outflow waters. Two scenarios were simulated: an 

increase in the outflow of Table Rock Lake Dam from 

the existing minimum flow of 4.36 to 11.33 m3/s, and 

an increase in water-surface elevation of the existing 

operational plan by 0.61 m that included 11.33 

m3/s minimum flow.

When 11.33 m3/s was applied as the minimum 

amount of outflow (increased minimum flow scenario) 

during 1996 and 1997, average annual outflow 

increased from 104.6 to 108.2 m3

/s, about a 3 percent 

increase. Approximately 55 percent of the measured 

hourly outflow data required an increase to simulate 

11.33 m3

/s. Average annual outflow increased from 

3,296 to 3,411 million cubic meters, which is equivalent to 115 million cubic meters per year increase, or 

about 3.5 percent of reservoir volume at summer conservation pool elevation (279.5 m). 

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 07053450) (fig. 

18). Temperature in the outflow water differed little 

between results from the increased minimum flow scenarios and the calibrated model (fig. 19). Absolute 

maximum difference in outflow water temperature 

between the increased minimum flow scenario and the 

calibrated model was 0.62 °C. The absolute mean and 

median differences were 0.14 and 0.10 °C, respectively. Temperature differences with and without additional minimum flow 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 dissolved-oxygen concentrations were similar to estimated outflow concentrations 

from water-column profiles measured upstream from 

the dam (George Robins, written commun., 2000) (fig. 

20). Dissolved-oxygen concentrations in the outflow 

water differed little between results from the minimum 

flow scenario and the calibrated model (fig. 21). Absolute maximum difference in outflow dissolved oxygen 

between the increased minimum flow scenario and the 

calibrated model was 1.30 mg/L. The absolute mean 

and median differences were 0.16 and 0.09 mg/L, 

respectively. Dissolved-oxygen concentration differences with and without additional minimum flow were 

about the same as the AME and RMSE between simulated and measured water-column profile dissolvedoxygen differences reported in the Model Calibration 

section of this report. 
28 Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Table Rock Lake, Missouri, 1996–1997

 
Model Applications 29
30 Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Table Rock Lake, Missouri, 1996–1997
Model Applications 31

The existing operational plan for Table Rock 

Lake is to maintain a conservation pool at an elevation 

of 278.9 m between December 1 and April 30, and 

279.50 m between May 1 and November 30. An 

increase in conservation pool of 0.6 m or 2 feet also is 

proposed along with the proposed increase in minimum 

flow. The potential water-surface elevation of the conservation pool would then be 279.5 m between December 1 and April 30, and 280.11 between May 1 and 

November 30. Two model simulations were developed 

to assess the temperature and dissolved-oxygen differences between the existing operational plan without 

increased minimum flow and the potential operational 

plan with increased pool elevation and increased minimum flow of 11.33 m3/s.

The water budget in the calibrated model was 

modified by adding or subtracting discharge in the distributed tributary file so that pool elevation in the model 

matched the pool elevation of the existing operational 

plan and the proposed minimum flow plan (fig. 22). All 

other inflow and outflow files in the model remained 

unchanged with the exception of the outflow file that 

included the increase in minimum flow in the increased 

minimum flow simulation.
32 Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Table Rock Lake, Missouri, 1996–1997

Water temperature and dissolved-oxygen concentrations in the outflow differed little between the 

existing operational plan and the simulation containing 

the potential operational plan (figs. 23 and 24). Temperature differences ranged from -0.34 to 0.37 °C and 

dissolved-oxygen concentration differences ranged 

from -0.71 to 0.78 mg/L between the two simulations. 

Both, temperature and dissolved-oxygen differences 

were similar to the error between simulated and measured temperature and dissolved-oxygen concentrations in the model calibration.
Summary 33

SUMMARY

Outflow from Table Rock Lake and other White 

River reservoirs support a cold-water trout fishery of 

substantial economic yield in south-central Missouri 

and north-central Arkansas. 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 Table Rock Lake. Increases in water temperature and 

decreases in dissolved oxygen potentially could have 

negative effects on the cold-water trout fisheries in the 

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

in cooperation with the Missouri Department of Conservation, conducted a study to assess the effects of 

additional minimum flows and increased water-surface 

elevations on the hydrodynamics, temperature, and dissolved-oxygen concentrations in Table Rock Lake and 

on temperature and dissolved-oxygen concentrations in 

the downstream outflow.

A two-dimensional, laterally averaged, hydrodynamic, temperature, and dissolved-oxygen model (CEQWAL-W2) was developed for Table Rock Lake, Missouri. The model was calibrated using hydrologic 

records and vertical profiles of temperature and dissolved oxygen measured in or near Table Rock Lake 

from January 1996 through December 1997. The 

model simulates surface-water elevation, water temperature, and dissolved-oxygen concentration. The model 

simulated temperatures generally within 1 °C of the 

measured temperatures. The AME and RMSE for 1996 

were 0.58 and 0.75, respectively, and for 1997 were 
34 Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Table Rock Lake, Missouri, 1996–1997

0.79 and 0.98, respectively. The model simulated dissolved-oxygen concentrations generally within 1 mg/L 

of the measured concentrations. The AME and RMSE 

for 1996 were 0.74 and 1.00, respectively. For 1997, the 

AME and RMSE were 1.09 and 1.41, respectively.

 The Table Rock Lake model was developed to 

assess the effects of proposed increases in minimum 

flows from 4.36 m3/s (the existing minimum flow) to 

11.33 m3/s (the increased minimum flow). Scenarios 

included assessing the effect of (1) increased minimum 

flows using the calibrated model as the basis for comparison and (2) creating a simulation of current operational plan and comparing results with a simulation 

including a potential increase in conservation pool elevation and increased minimum flow on outflow temperature and dissolved-oxygen concentrations. With 

the increased minimum flow in both scenarios, water 

temperature appeared to increase slightly (less than 

0.37 °C) and dissolved oxygen appeared to decrease in 

the outflow during the thermal stratification season. 

However, results were similar to the differences 

between measured and simulated water-column profile 

values.

Water temperature and dissolved-oxygen concentrations in the outflow differed little between the 

existing operational plan and the simulation containing 

the potential operational plan. Temperature differences 

ranged from -0.34 to 0.37 °C and dissolved-oxygen 

concentration differences ranged from -0.71 to 0.78 

mg/L between the two simulations. Both, temperature 

and dissolved-oxygen differences were similar to the 

error between simulated and measured temperature and 

dissolved-oxygen concentrations in the model calibration.

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