Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Bull Shoals Lake, Arkansas, 1994-1995

Prepared in cooperation with the Arkansas Game and Fish Commission

SIMULATION OF HYDRODYNAMICS, TEMPERATURE, AND DISSOLVED OXYGEN IN BULL SHOALS LAKE, ARKANSAS, 1994-1995

Water-Resources Investigations Report 03-4077

U.S. Department of the Interior U.S. Geological Survey SIMULATION OF HYDRODYNAMICS, TEMPERATURE, AND DISSOLVED OXYGEN IN BULL SHOALS LAKE, ARKANSAS, 1994-1995

By Joel M. Galloway and W. Reed Green U.S. GEOLOGICAL SURVEY Water-Resources Investigations Report 03-4077

Prepared in cooperation with the Arkansas Game and Fish Commission

Little Rock, Arkansas 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 Copies of this report can be write to: purchased from:

District Chief U.S. Geological Survey U.S. Geological Survey, WRD Branch of Information Services 401 Hardin Road Box 25286 Little Rock, Arkansas 72211 Denver Federal Center Denver, Colorado 80225 CONTENTS

Abstract ...... 1 Introduction...... 1 Purpose...... 3 Description of Study Area...... 3 Acknowledgments...... 3 Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Bull Shoals Lake ...... 3 Model Implementation...... 3 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...... 19 Summary ...... 23 References...... 24

ILLUSTRATIONS

Figure 1. Map showing location of Bull Shoals Lake and the White 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 Bull Shoals 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 Bull Shoals Lake ...... 6 5. Annual mean streamflow for the White River near Branson, Missouri, upstream from Bull Shoals Lake, 1952-1995 ...... 7 6. Daily inflow and hourly dam outflow for Bull Shoals Lake, January 1994 through December 1995 ...... 8 7. Simulated and measured water-surface elevations near the Bull Shoals 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 Bull Shoals Lake dam, January through December 1994 ...... 13

Contents III 9. Relation of difference between simulated and measured water temperatures near the Bull Shoals Lake dam to measured water temperature, sampling date, and water depth, January through December 1994 ...... 14 10. Relation between simulated and measured water temperatures in the water column near the Bull Shoals Lake dam, January through December 1995...... 15 11. Relation of difference between simulated and measured water temperatures near the Bull Shoals Lake dam to measured water temperature, sampling date, and water depth, January through December 1995 ...... 15 12. Relation between simulated and measured dissolved-oxygen concentrations in the water column near the Bull Shoals Lake dam, January through December 1994...... 16 13. Relation of difference between simulated and measured dissolved-oxygen concentrations near Bull Shoals Lake dam to measured dissolved-oxygen concentrations, sampling date, and water depth, January through December 1994 ...... 17 14. Relation between simulated and measured dissolved-oxygen concentrations in the water column near the Bull Shoals Lake dam, January through December 1995...... 17 15. Relation of difference between simulated and measured dissolved-oxygen concentrations near Bull Shoals Lake dam to measured dissolved-oxygen concentrations, sampling date, and water depth, January through December 1995 ...... 18 16. Vertical temperature distributions near the Bull Shoals Lake dam on July 7, 1994 and January 20, 1995, showing calibrated model profiles and profiles as a result of differing model parameters...... 19 17. Vertical dissolved-oxygen concentration distributions near the Bull Shoals Lake dam on July 7, 1994, and January 20, 1995, showing calibrated model profiles and profiles as a result of differing model parameters...... 20 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...... 21 20. Simulated water temperature differences between increased minimum flow scenarios and the calibrated model...... 21 21. Simulated and estimated water temperatures in Bull Shoals Lake outflow and measured temperatures downstream from Bull Shoals Lake dam...... 21 22. Simulated dissolved-oxygen concentration differences between increased minimum flow scenarios and calibrated model...... 22 23. Simulated and estimated dissolved-oxygen concentrations in Bull Shoals Lake outflows ...... 22

TABLES

Table 1. Hydraulic and thermal input parameters specified for Bull Shoals Lake model ...... 7 2. Rate coefficients used in water-chemistry and biological simulations and other parameters specified as input in the Bull Shoals Lake model...... 10

IV Contents CONVERSION FACTORS AND VERTICAL DATUM

Multiply By To obtain

centimeter (cm) 0.3937 inch (in.)

millimeter (mm) 0.03937 inch (in.)

meter (m) 3.281 foot (ft)

kilometer (km) 0.6214 mile (mi)

hectare (ha) 2.471 acre

square meter (m2) 10.76 square foot (ft2)

square kilometer (km2) 0.3861 square mile (mi2)

liter (L) 0.2642 gallon (gal)

cubic meter (m3) 35.31 cubic foot (ft3)

gram (g) 0.03527 ounce (oz)

kilogram (kg) 2.205 pound (lb)

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)

In this report vertical coordinate information is referenced to the National Geodetic Vertical datum of 1929 (NGVD of 1929). Horizontal coordinate information is referenced to North American Datum of 1983 (NAD 83).

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

Contents V SIMULATION OF HYDRODYNAMICS, TEMPERATURE, AND DISSOLVED OXYGEN IN BULL SHOALS LAKE, ARKANSAS, 1994-1995

By Joel M. Galloway and W. Reed Green

ABSTRACT INTRODUCTION

Outflow from Bull Shoals Lake and other White Bull Shoals Lake (fig. 1) is a large, deep-storage River reservoirs supports a cold-water trout fishery of reservoir located on the White River on the border of substantial economic yield in north-central Arkansas Arkansas and Missouri. Bull Shoals Lake dam was and south-central Missouri. The Arkansas Game and completed in 1951 and operated by the U.S. Army Fish Commission has requested an increase in existing Corps of Engineers (USACE) for the purposes of flood minimum flows through the Bull Shoals Lake dam to control and hydroelectric power. In addition to afore- increase the amount of fishable waters downstream. mentioned uses, the reservoir is used for fish and wild- life habitat, recreation, and water supply. The outflows Information is needed to assess the impact of increased from Bull Shoals Lake, and other White River reser- minimum flows on temperature and dissolved-oxygen voirs, also support a cold-water trout fishery of sub- concentrations of reservoir water and the outflow. stantial economic yield in north-central Arkansas and A two-dimensional, laterally averaged, hydrody- south-central Missouri. The Arkansas Game and Fish namic, temperature, and dissolved-oxygen model was Commission (AGFC) has requested an increase in min- developed and calibrated for Bull Shoals Lake, located imum flows through Bull Shoals Lake dam to increase on the Arkansas-Missouri State line. The model simu- the amount of fishable waters downstream. Proposed lates water-surface elevation, heat transport, and dis- changes in reservoir operations, such as increased min- solved-oxygen dynamics. The model was developed to imum flows through the dam and increased water stor- assess the impacts of proposed increases in minimum age, have caused concerns about the sustainability of flow from 4.6 cubic meters per second (the existing cold water temperature and dissolved oxygen in the minimum flow) to 22.6 cubic meters per second (the bottom water (hypolimnion) of Bull Shoals Lake. increased minimum flow). Simulations included Increases in water temperature and decreases in dis- assessing the impact of (1) increased minimum flows solved oxygen could have potential negative impacts and (2) increased minimum flows with increased initial on the cold-water trout fisheries in the downstream out- water-surface elevation of 1.5 meters in Bull Shoals flow. Comprehensive information is needed to address Lake on outflow temperatures and dissolved-oxygen temperature and dissolved-oxygen dynamics of Bull concentrations. Shoals Lake and the effects of increased minimum flow. The increased minimum flow simulation (with- Bull Shoals Lake is the most downstream in a out increasing initial water-surface elevation) increased chain of major reservoirs on the White River mainstem. the water temperature and dissolved-oxygen concen- Upstream from Bull Shoals are Lake Taneycomo, Table tration in the outflow. Conversely, the increased mini- Rock Lake, and Beaver Lake. Norfork Lake is located mum flow and increased initial water-surface elevation downstream on the North Fork River, a tributary to the (1.5 meters) simulation decreased outflow water tem- White River (fig. 1). A study was conducted by the U.S. perature and dissolved-oxygen concentration through Geological Survey (USGS) in cooperation with the time. However, results from both scenarios for water AGFC to characterize the hydrodynamics, temperature, temperature and dissolved-oxygen concentration were and dissolved-oxygen concentrations in Bull Shoals within the boundaries of the error between measured Lake and to simulate the effect of reservoir operations and simulated water column profile values. on temperature and dissolved-oxygen concentrations in

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Figure 1. Location of Bull Shoals Lake and the White River Basin in Arkansas and Missouri.

2 Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Bull Shoals Lake, Arkansas, 1994-1995 the reservoir and outflow. A hydrodynamic model of Acknowledgments Bull Shoals Lake was developed using the USACE CE- QUAL-W2 software program (Cole and Buchak, 1995) Edward Buchak and Rajeev Jain of J.E. Edinger to simulate the expected minimum flow scenarios. This Associates, Inc., Jerad Bales of the USGS, and Tom study was conducted in conjunction with other studies Cole of the USACE provided valuable guidance on evaluating the impacts of reservoir operations on tem- model development and applications. John Kielcze- perature and dissolved-oxygen concentration in Nor- wski of the USACE provided much of the inflow and fork (Galloway and Green, 2002), Table Rock, and outflow and water-surface elevation data used to Beaver Lakes (Haggard and Green, 2002). These stud- develop and calibrate the model. ies will provide a better understanding of the hydro- and water-quality dynamics within each reservoir sys- tem. In addition, calibrated models developed for these studies will provide the basis and framework for future SIMULATION OF HYDRODYNAMICS, water-quality modeling. As more data are collected in TEMPERATURE, AND DISSOLVED both the reservoirs and tributaries, the calibrated mod- OXYGEN IN BULL SHOALS LAKE els can be modified to assess the nutrient assimilative capacity of the reservoir, nutrient limitations, and the A two-dimensional, laterally averaged, hydrody- effect of increases in nutrient loading on reservoir namic, temperature, and dissolved-oxygen model using trophic status. CE-QUAL-W2 was developed for Bull Shoals Lake and calibrated based on hydrologic records and vertical profiles of temperature and dissolved oxygen measured Purpose near the Bull Shoals Lake dam from January 1994 through December 1995. The CE-QUAL-W2 model The purpose of this report is to describe a model simulates water-surface elevation and vertical and lon- of hydrodynamics, temperature, and dissolved oxygen gitudinal gradients in water-quality constituents. The in Bull Shoals Lake for the simulation period of Janu- ary 1994 through December 1995. Water temperature model includes routines for temperature, dissolved and dissolved-oxygen concentration results from oxygen, and more than 20 other parameters, including model applications simulating two proposed minimum algae, carbon dioxide, coliform bacteria, detritus, inor- flow scenarios are presented and compared to a cali- ganic carbon, iron, labile and refractory dissolved brated, base condition. organic matter, nitrite plus nitrate as nitrogen, pH, phosphorus, sediment, suspended solids, total dissolved solids, and a conservative tracer (Cole and Description of Study Area Buchak, 1995). Calibration and simulation of water- quality parameters other than water temperature and Bull Shoals Lake was impounded in 1951 on the dissolved oxygen, such as nitrogen, phosphorus, algal White River, southeast of the city of Branson, Mis- production, and organic matter, are beyond the scope of souri. The primary inflows into Bull Shoals Lake are this study. Little North Fork River, Beaver Creek, and the White River; several smaller tributaries also flow into the reservoir (fig. 1). The watershed has a drainage area of Model Implementation 15,675 km2 at the Bull Shoals Lake dam. Bull Shoals Lake contains 4,194 million m3 of water at the eleva- Implementation of the CE-QUAL-W2 model for tion of the current conservation pool (199.3 m above Bull Shoals Lake included development of the compu- NGVD of 1929) and the surface area is 184 km2. The length of the reservoir is 130 km from the Lake Taney- tational grid, specification of boundary and initial con- como dam to the Bull Shoals Lake dam. The depth of ditions, and preliminary selection of model parameter the reservoir at the dam at conservation pool elevation values. Model development and associated assump- is about 63 m, and the average depth through the reser- tions in the selection of boundary and initial conditions voir is 23 m. On average, the hydraulic retention time are described, and specific values of model parameters of Bull Shoals Lake is about 0.75 year (Green, 1996). are given in this section.

Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Bull Shoals Lake 3 Computational Grid tional segments exist along the mainstem of the White River in Bull Shoals Lake, whereas, 10 segments are in The computational grid is the geometric scheme the Little North Fork River and 4 segments are in the (fig. 2) that numerically represents the space and vol- Big Creek and Shoal Creek branches. In addition, five ume of the reservoir. The model extends 130 km from other embayments (branches), including Bear Creek, the upstream boundary (Lake Taneycomo dam) to the West Sugarloaf Creek, East Sugarloaf Creek, Spring downstream boundary (Bull Shoals Lake dam). The Creek, and Moccasin Creek, are modeled with three grid geometry was developed by digitizing pre- computational segments each. Volumes of the smaller impoundment elevation contours of the land surface or embayments not included in the computational grid reservoir bottom from USGS 7.5-minute and 15- were added to associated mainstem segments so that minute quadrangle maps (fig. 3). Sixty-two computa- reservoir volume was preserved.

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

4 Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Bull Shoals Lake, Arkansas, 1994-1995 A. 213 2 206 9 198 15

190 23 NUMBER LAYER 182 31 174 39 166 46 Penstock 158 54

150 62 142 70 ELEVATION, IN METERS ABOVE NGVD OF 1929 136 78 0 10 20 30 40 50 60 70 80 90 100 11 0 120 130 DISTANCE FROM DAM, IN KILOMETERS C.

B.B.

Penstock

Figure 3. Side view (A), top view (B), and face view from the dam (C) of the computational grid of Bull Shoals Lake used in CE-QUAL-W2.

Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Bull Shoals Lake 5 Segment geometry varied along the upstream- Boundary and Initial Conditions downstream gradient (fig. 3). Segment length was based Hydraulic, thermal, and chemical boundary con- in part on segment width. Segments ranged in length ditions are required in CE-QUAL-W2. The boundaries from 1,208 to 4,446 m, and orientation of the longitudi- of the Bull Shoals Lake model included the reservoir nal axis relative to north was determined for each seg- bottom, the shoreline, tributary streams, the upstream ment. Segment widths at the reservoir surface ranged boundary (Lake Taneycomo dam), the downstream from 264 m in the headwaters to more than 4,400 m. boundary (Bull Shoals Lake dam), and the water-surface Each segment was divided vertically into 1-m layers. elevation of the reservoir. Initial water-surface elevation Depth from the elevation of the top of the flood-control of the reservoir, water temperature, and selected water- pool to the reservoir bottom ranged from 19 m at the quality constituent concentrations also are required. upstream boundary to 76 m near Bull Shoals Lake dam. Relations between water-surface elevation and volume Hydraulic and Thermal Boundary Conditions and surface area in the Bull Shoals Lake model grid The reservoir bottom is assumed to be an immo- were similar to USACE preimpoundment data (U.S. bile and impermeable boundary. That is, the bottom sed- Army Corps of Engineers, 1960) (fig. 4). iments 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 res- 240 ervoir bottom extracts energy from water movement by causing resistance to water flow; this phenomenon var- 220 ies with the magnitude of flow. A single, empirical coefficient (Chezy resistance coefficient) is applied to the 200 reservoir bottom in all computational segments (table

180 1).

US ARMY CORPS OF Heat exchange between the reservoir bottom and ENGINEERS BATHYMETRY 160 MODEL BATHYMETRY the overlying water column is computed from (1) the sediment temperature, (2) the simulated temperature of 140 0 2000, 4000, 6000, 8000, 10000, the overlying water, and (3) bottom-water heat exchange VOLUME, IN MILLION CUBIC METERS coefficient (table 1). The sediment temperature and the exchange coefficient are assumed to be temporally and 240 spatially constant. A reasonable estimate of sediment temperature is the annual average water temperature 220 near the sediment-water interface; a value of 7.0 ° C was used in the Bull Shoals Lake model. In general, heat 200 exchange from the reservoir bottom is about two orders of magnitude less than surface heat exchange (Cole and 180 Buchak, 1995). US ARMY CORPS OF WATER-SURFACE 1929 OF METERS ELEVATION,ABOVE NGVD IN 160 The reservoir shoreline is defined as a boundary ENGINEERS BATHYMETRY MODEL BATHYMETRY across which there is no flow. The exact position of the 140 shoreline changes during model simulation because of 0 100 200 300 400 changing water-surface elevation. SURFACE AREA, IN MILLION SQUARE METERS

Figure 4. Relation between water-surface elevation and volume and water-surface elevation and surface area in Bull Shoals Lake.

6 Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Bull Shoals Lake, Arkansas, 1994-1995 Table 1. Hydraulic and thermal input parameters specified for Bull Shoals 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]

Constant or Parameter Computational purpose Value time variable

Chezy resistance Represents turbulent exchange of energy at the 70 m0.5/s Constant coefficient reservoir bottom

Bottom – water heat Computes heat exchange between reservoir bot- 7.0x10-8 Constant exchange coefficient tom and overlying water (watts/m2)/° C

Sediment temperature Represents the reservoir bottom (sediment) tem- 7.0 ° C Constant perature

Wind – sheltering Reduces wind speed to effective wind speed at 0.7 Constant coefficient water surface (dimensionless)

Horizontal eddy viscosity Represents laterally averaged longitudinal turbu- 1 m2/s Constant lent exchange of momentum

Horizontal eddy Represents laterally averaged longitudinal turbu- 1 m2/s Constant diffusivity lent mixing of mass and heat

Annual streamflow recorded at the USGS streamflow-gaging station near Branson, Missouri (sta- 250 tion number 07053500; fig. 1), on the White River indicates that inflow to Bull Shoals Lake during the 1994 200 and 1995 modeling time period was above average (fig.

5). Annual mean streamflow for the White River from 150 1952 through 1995 ranged from 23.7 to 234.7 m3/s. AVERAGE The average annual mean streamflow for this time 100 period was 110.4 m3/s. Annual mean streamflow for the 1994 and 1995 modeling time period was 149.3 and 3 50 149.0 m /s, respectively (Reed and others, 1995; STREAMFLOW, MEAN ANNUAL PER SECOND METERS CUBIC IN Hauck and others, 1996, 1997). 0 1955 1960 1965 1970 1975 1980 1985 1990 1995

Figure 5. Annual mean streamflow for the White River near Branson, Missouri, upstream from Bull Shoals Lake, 1952- 1995.

Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Bull Shoals Lake 7 Daily reservoir inflows used in the model (fig. 6) The downstream boundary for the Bull Shoals were calculated by the USACE (John Kielczewski, Lake model consists of the outflow from Bull Shoals U.S. Army Corps of Engineers, written commun., Lake dam. Hourly outflow data (fig. 6) were calculated 1999) based on daily average outflows and changes in by the USACE (John Kielczewski, U.S. Army Corps of reservoir water-surface elevations. The daily inflow Engineers, written commun., 1999) using stage-dis- was distributed into one major branch (White River) charge relations and hourly power generation records. and eight minor branches according to drainage area The mean and median reservoir outflow for the model- Daily reservoir inflows used in the model (fig. 6) were ing period (January 1994 to December 1995) was 210.6 calculated by the USACE (John Kielczewski, U.S. and 126.6 m3/s, respectively. The reservoir outflow Army Corps of Engineers, written commun., 1999) exceeded 597 m3/s 10 percent of the time for the mod- based on daily average outflows and changes in reser- eling period. The vertical extent and distribution of voir water-surface elevations. The daily inflow was flow in the release zone near the Bull Shoals Lake dam distributed into one major branch (White River) and (downstream boundary) were simulated using penstock eight minor branches according to drainage area size. (point) dam release flow, the outflow rate, and the sim- Approximately 70 percent of the inflow was distributed ulated density gradient upstream from the dam in the to the White River, 23 percent was evenly distributed reservoir. The release structure was simulated as a along the reservoir shoreline, and 7 percent was distrib- point release, and the middle of the structure was at an uted among the eight smaller branches. Total mean reservoir inflow from January 1, 1994, through December elevation of 163 m above NGVD of 1929, model layer 31, 1995, was estimated to be 208.7 m3/s, whereas, the 51 (fig. 3). estimated median reservoir inflow for the same period Hydraulic input parameters at the water surface 3 was 162.4 m /s. The estimated reservoir inflow included evaporation, wind stress, and surface heat 3 exceeded 514 m /s 10 percent of the time. exchange. All meteorological data required for these computations were measured at Harrison, Arkansas

1800, (station number 723446, National Climatic Data Cen- INFLOW 1600, ter, Asheville, North Carolina; fig. 1), and generally

1400, were recorded at hourly intervals. Evaporation in the

1200, model was computed from a time series of water-surface temperatures, dewpoint temperatures, wind 1000, speeds, surface-layer widths, and length of the seg- 800 ments. Wind stress was computed from a time series of 600 wind speeds and directions, the orientation of the com- 400 putational segment, and a wind-sheltering coefficient 200 (table 1). The wind-sheltering coefficient is time vari- 0 able and reduces the effect of wind on the reservoir

1600, OUTFLOW because of topographic or vegetative sheltering; how-

1400, ever, in the Bull Shoals Lake model this coefficient was held constant. Surface heat exchange was computed in 1200, the model from reservoir latitude and longitude, and 1000, from a time series of measured air temperatures, dew- 800

DISCHARGE, IN CUBIC METERS PER SECOND point temperatures, cloud covers, and wind speeds and 600 directions. In the original meteorological dataset, cloud 400 cover was recorded as clear (CLR), scattered (SCT), 200 broken (BKN), and overcast (OVC). The model 0 requires cloud cover to be entered as a number ranging Jan Mar May July Septt Nov Jan Mar May July Sep Nov Jan 1994 1995 from 0.0 to 10.0. In the Bull Shoals Lake model, cloud cover was recorded as: CLR = 0.0, SCT = 1.0, BKN = Figure 6. Daily inflow (top) and hourly outflow (bottom) for 3.6, and OVC = 7.8. The simulated surface-water tem- Bull Shoals Lake, January 1994 through December 1995. Inflow and outflow data provided by the U.S. Army Corps of perature and loss of heat through evaporation were Engineers. included in the heat budget.

8 Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Bull Shoals Lake, Arkansas, 1994-1995 Chemical Boundary Conditions Most of the relevant hydrodynamic and thermal A time series of concentrations of selected con- processes are modeled in CE-QUAL-W2; thus, rela- stituents at all inflow boundaries is required for model tively few hydraulic and thermal parameters are adjust- operation. Boundary data for all tributaries and able. The horizontal eddy viscosity describes turbulent branches included dissolved oxygen, ammonia as exchange of momentum, and the horizontal eddy diffu- nitrogen, nitrite plus nitrate as nitrogen, total phospho- sivity describes turbulent mixing of mass and heat rus, and a conservative tracer concentrations. Because (table 1). Other parameters such as Chezy resistance, of the small amount of available water-quality data, bottom-water heat exchange, bottom temperature, and annual average concentrations were estimated based on wind-sheltering coefficients were discussed previously similar values reported from the White River by Evans (table 1). In general, reservoir models are relatively and others (1995) and Porter and others (1996, 1997) insensitive to changes in the horizontal eddy viscosity and used for all inflow boundary constituents except and diffusivity. However, the thermal processes are rel- dissolved oxygen. Dissolved-oxygen concentrations at atively sensitive to changes in bottom-heat exchange the inflow boundaries were set to the concentration for and temperature, and the wind-sheltering coefficient. 100 percent saturation for the given water temperature. Sixty-one chemical and biological rate coefficients and other parameters are required for the appli- Exchange of dissolved oxygen occurs at the cation of CE-QUAL-W2 (table 2). Most of the water surface of the reservoir and is affected by wind parameter values were based on suggestions given in speed and direction, water temperature, water-surface the CE-QUAL-W2 manual (Cole and Buchak, 1995), elevation above NGVD of 1929, and the molecular dif- and all the parameters are temporally and spatially con- fusivity of oxygen gas. Atmospheric nutrient inputs stant. Some of the parameters have suggested ranges, were not included in this model, and constituent inputs and selected parameters were adjusted, within reason- from the reservoir bottom were generally computed able limits, until simulated values agreed with mea- within the model based on the value of selected param- sured observations (calibration). eters (table 2) and the constituent concentrations in the overlying waters. Other Model Options

Initial Conditions The maximum computational time step (interval) was limited to 1 hour because the input data were Initial water-surface elevation and velocity, tem- sometimes supplied at this interval. The model- perature, and constituent concentrations for each com- selected computational interval generally was about 5 putational segment are required prior to initiating minutes. Model calculations occurred at time steps model simulation. Initial water-surface elevation was smaller than the boundary conditions that were pro- set to the value measured at the Bull Shoals Lake dam vided, and linear interpolation occurred between values on January 1, 1994. Initial velocities were assumed to for all input conditions except meteorological data. The be zero. The water was assumed to be isothermal meteorological data were assumed to remain constant throughout the reservoir and equal to the water temper- between measured values. The ‘QUICKEST’ numeri- ° ature measured near the dam (10.0 C). Initial constit- cal scheme (Leonard, 1979) was used for solving the uent concentrations also were assumed to be uniform transport equations, and a Crank – Nicholson scheme throughout the reservoir and equal to values measured (Roache, 1982) was used to solve the vertical advection near the dam on December 30, 1993 (Evans and others, equation. 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 pro- cess until simulated values agree with measured observations.

Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Bull Shoals Lake 9 Table 2. Rate coefficients used in water-chemistry and biological simulations and other parameters specified as input in the Bull Shoals Lake model 2 o [m, meters; *, dimensionless; d, day; Q10, temperature correction factor; m/d, meters per day; watts/m , 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 Amount of solar radiation absorbed in the surface layer 0.24/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 Amount of solar radiation absorbed in the surface layer 0.24* water surface 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 m/d Algal growth rate Maximum gross algal production rate, uncorrected for 1.5/d respiration, mortality, excretion or settling; temperature dependent Algal mortality rate Maximum algal mortality rate; temperature dependent 0.01/d Algal excretion rate Maximum algal photorespiration rate, which becomes labile 0.01/d dissolved organic matter 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 500 watts/m2 rate Fraction of algal biomass lost by mortality to detritus Detritus and dissolved organic matter concentrations; 0.8* remaining biomass becomes labile dissolved organic matter 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, 0.12/d ammonia, and phosphate from algal decay; temperature dependent Labile to refractory decay rate Transfer of labile to refractory dissolved organic matter 0.001/d Maximum refractory dissolved organic matter Dissolved-oxygen loss and production of inorganic carbon, 0.001/d decay rate ammonia, and phosphate from decay of refractory dissolved organic matter; temperature dependent Detritus decay rate Dissolved-oxygen loss and production of inorganic carbon, 0.06/d ammonia, and phosphate from decay of particulate organic matter, temperature dependent 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 Organic matter decay as a function of temperature 0.99* lower temperature Sediment decay rate Decay rate of organic matter in bed sediments 0.08/d

10 Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Bull Shoals Lake, Arkansas, 1994-1995 Table 2. Rate coefficients used in water-chemistry and biological simulations and other parameters specified as input in the Bull Shoals Lake model--Continued 2 o [m, meters; *, dimensionless; d, day; Q10, temperature correction factor; m/d, meters per day; watts/m , 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 Sediment oxygen demand Zero-order sediment oxygen demand for each 3.0 (g/m2)/d computational segment 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 1.047* temperature 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 0.015* sediment oxygen demand 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 0.005 mg/L is one-half the maximum uptake rate; upper concentration at which algal growth is proportional to phosphorus concentration Release rate of ammonia from bottom sediments Nitrogen balance; computed as a fraction of the sediment 0.2* oxygen demand 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 0.014 mg/L one-half the maximum uptake rate; upper concentration at which algal growth is proportional to ammonia concentration 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 Ammonia nitrification as a function of temperature 0.99* temperature 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 Denitrification as a function of temperature 0.99* temperature Iron release from bottom sediments Iron balance; computed as a fraction of sediment oxygen demand 0.5* Iron settling velocity Particulate iron settling velocity under oxic conditions 2.0 m/d Oxygen stoichiometric equivalent for ammonia Relates oxygen consumption to ammonia decay 4.57* decay Oxygen stoichiometric equivalent for organic Relates oxygen consumption to decay of organic matter 1.4* matter decay Oxygen stoichiometric equivalent for dark Relates oxygen consumption to algal dark respiration 1.4* respiration Oxygen stoichiometric equivalent for algal growth Relates oxygen production to algal growth 1.4* Stoichiometric equivalent between organic matter Relates phosphorus release to decay of organic matter 0.011* and phosphorus Stoichiometric equivalent between organic matter Relates nitrogen release to decay of organic matter 0.08* and nitrogen Stoichiometric equivalent between organic matter Relates carbon release to decay of organic matter 0.45* and carbon Dissolved-oxygen limit Dissolved-oxygen concentration below which anaerobic processes such as nitrification and sediment nutrient 0.1 mg/L releases occur

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

Successful model application requires model calibration that includes comparing model (simulated) results with observed (measured) reservoir conditions. If possi- 208 ble, 2 or more years of water-quality data should be used SIMULATED MEASURED for adequate model calibration. Bull Shoals Lake model 206 calibration was achieved by adjusting model parameters and, in some cases, estimated input data for the 2-year 204 period of January 1994 through December 1995. Two statistics were used to compare simulated and 202 measured water-surface elevation, water temperature, and dissolved-oxygen concentration. The absolute mean error 200 (AME) indicates the average difference between simulated and measured values and is computed by equation 1: 198

Σ Simulated Value– Measured Value 196 AME = ------(1) JAN FEB MAR APR MAY JUNE JULY AUG SEPT OCT NOV DEC Number of Observations 1994 ° An AME of 0.5 C means that the simulated temperatures 208 are, on average, within + 0.5 ° C of the measured temper- SIMULATED atures. The root mean square error (RMSE) indicates the 206 MEASURED spread of how far simulated values deviate from the measured values and is computed by equation 2: 204

WATER-SURFACE ELEVATION, IN METERS ABOVE NGVD OF 1929 OF WATER-SURFACE ABOVE NGVD METERS ELEVATION, IN 202 Σ()Simulated Value Measured Value 2 RMSE = ------– - (2) Number of Observations 200 An RMSE of 0.5 ° C means that the simulated temperatures are within 0.5 ° C of the measured temperatures 198 about 67 percent of the time. 196 JAN FEB MAR APR MAY JUNE JULY AUG SEPT OCT NOV DEC Hydrodynamics and Temperature 1995 Simulated water-surface elevations in Bull Shoals Figure 7. Simulated and measured water-surface elevations Lake were adjusted to the measured water surface for the near the Bull Shoals Lake dam, January through December model period January 1994 to December 1995 (fig. 7). 1994 and January through December 1995. The water-surface elevations were corrected to the measured values by adjusting the unmeasured inflow into the lake that was distributed to all the segments within a branch. Inflow was either added or subtracted so that the simulated water-surface elevation reflected the measured water-surface elevation. By correcting the distributed inflow, the thermodynamics could be calibrated without the uncertainty incurred with having differences between simulated and measured elevations.

12 Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Bull Shoals Lake, Arkansas, 1994-1995 The heat budget in the model is computed from strong thermocline existed near the Bull Shoals Lake inflow water temperature, air-water surface heat dam during June through November in 1994 and 1995. exchange (determined from air and dew-point temper- All simulated water temperatures (711) in 1994 ature, cloud cover, wind speed and direction, and were compared with corresponding measured tempera- organic and inorganic solids concentration) and bot- tures near the Bull Shoals Lake dam (Evans and others, tom-water heat exchange. Organic and inorganic solids 1995; Porter and others, 1996). Simulated water tem- indirectly affect heat distribution by reducing light pen- peratures reproduced seasonal variations observed in etration. Thus, water temperature calibration cannot be the water column near the dam (fig. 8), even for com- performed independently from water chemistry complex temperature profiles. Simulated water tempera- putations, but water temperature can still be simulated tures ranged from 5.7 to 28.0 ° C, whereas measured neglecting the effects of solids on heat distribution. water temperatures ranged from 5.9 to 28.4 ° C. Simu- Vertical distribution of water temperature affects lated water temperatures in the vertical profile gener- vertical mixing of dissolved and suspended materials ally (79 percent) were within 1° C of measured and can be used to define the general location of the temperatures. The AME and RMSE between simulated epilimnion and hypolimnion of the reservoir. During and measured water temperature were 0.67 and 0.89 the thermal stratification season (May-November) the ° C, respectively. The difference between simulated and epilimnion and hypolimnion typically are separated by measured temperature ranged from -2.2 to 4.0 ° C, and a thermocline, in which there is a relatively large the average and median differences both were -0.2 ° C. change in temperature over a small change in depth. A

01/27/94 03/23/94 05/10/94 06/08/94 07/07/94 0

50 AME = 0.33 AME = 0.31 AME = 0.58 AME = 0.93 AME = 1.05 RMSE = 0.36 RMSE = 0.37 RMSE = 0.72 RMSE = 1.16 RMSE = 1.18 60

08/17/94 09/13/94 09/27/94 10/12/94 10/18/94 0 DEPTH, IN METERS IN DEPTH,

50 AME =0.92 AME = 0.87 AME =0.79 AME =0.60 AME =0.74 RMSE = 1.22 RMSE = 1.04 RMSE =1.13 RMSE = 0.82 RMSE =0.90 60 0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30

11/01/94 11/14/94 12/06/94 0

30 EXPLANATION SIMULATED MEASURED 40 DEPTH, IN METERS IN DEPTH,

50 AME = 0.52 AME = 0.48 AME =0.58 RMSE = 0.71 RMSE = 0.58 RMSE = 0.62 60 0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30

TEMPERATURE, IN DEGREES CELSIUS Figure 8. Relation between simulated and measured water temperatures in the water column near the Bull Shoals Lake dam, January through December 1994. Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Bull Shoals Lake 13 Although the calibrated model closely simulated All simulated temperatures (654) in 1995 were water temperature near the Bull Shoals Lake dam in compared with corresponding measured temperatures 1994, with most simulated temperatures within 1° C of (Porter and others, 1996; 1997) (fig. 10). Simulated the measured temperatures, the accuracy and precision water temperatures ranged from 5.8 to 29.1 ° C, of simulated temperatures varied with temperature, sea- whereas measured water temperatures ranged from 6.7 ° son, and depth (fig. 9). Simulated water temperatures to 30.5 C. Simulated water temperatures generally (58 ° were less than measured temperatures more often when percent) were within 1 C of measured temperatures. measured temperatures were less than 17 ° C. Con- The AME and RMSE between simulated and measured ° versely, simulated water temperatures were greater than water temperature were 0.94 and 1.13 C, respectively. The difference between simulated and measured tem- measured temperatures more often when measured peratures ranged from -2.4 to 4.0 °C, and the average temperatures were greater than approximately 17 ° C. and median differences were -0.4 and -0.6 ° C, respec- Error in simulated water temperatures was greater dur- tively. ing the thermal stratification season (May through Simulated water temperatures were similar to November). Simulated temperatures generally were measured temperatures in 1995 (fig. 11). Simulated less than measured temperatures at all depths, except water temperatures during 1995 were less than mea- between depths of 46 to 54 meters where simulated sured temperatures more often when measured temper- temperatures tended to be greater than measured tem- atures were less than 18 ° C, and were greater than peratures. measured temperatures when temperatures were greater 6 ° A than 18 C. From January 1995 through the stratifica- 4 tion season (May to November), simulated water tem- 2 peratures generally were less than measured water 0 temperatures. Near the end of the stratification season, -2 simulated water temperatures were greater than mea- -4 sured water temperatures. Simulated water tempera- -6 tures generally were less than measured temperatures 0 5 10 15 20 25 30 below depths of 20 m and near the water surface. How- MEASURED TEMPERATURE, IN DEGREES CELSIUS ever, as in 1994, most (58 percent) simulated tempera-

6 tures were within 1 ° C of the measured temperature. B 4

2 Dissolved Oxygen

0 Simulation of the complex biochemical reactions -2 affecting chemical and physical transport processes in -4 the Bull Shoals Lake model are expressed in part within -6 JAN FEB MAR APR MAY JUNE JULY AUG SEPT OCT NOV DEC the simulated dissolved-oxygen results. The supply of 1994 nitrogen, phosphorus, and light regulates algal growth and the production of oxygen; photosynthesis is the 6 C only internal source of oxygen in the water-chemistry 4 computations. Boundary sources of oxygen include the 2 dissolved-oxygen concentration in the reservoir inflows

SIMULATED MINUS MEASURED TEMPERATURE, IN DEGREES CELSIUS DEGREES IN TEMPERATURE, MEASURED MINUS SIMULATED 0 and oxygen exchange at the air-water interface. Several -2 sinks of oxygen exist including nitrification (conversion -4 of ammonia to nitrate), algal and microbial respiration, -6 organic matter decay (for example, detritus, labile and 0 10 20 30 40 50 60 refractory dissolved organic matter), and sediment oxy- WATER DEPTH, IN METERS gen demand. These processes combined with the water- Figure 9. Relation of difference between simulated and chemistry computations are used to simulate the com- measured water temperatures near the Bull Shoals Lake dam to (A) measured water temperature, (B) sampling date, plex vertical profiles of dissolved oxygen in Bull Shoals and (C) water depth, January through December 1994. Lake.

14 Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Bull Shoals Lake, Arkansas, 1994-1995 01/20/95 03/22/95 05/17/95 06/14/95 07/11/95 08/16/95 0

50 AME =0.91 AME =1.12 AME =0.82 AME =1.37 AME =1.28 AME =1.39 RMSE =1.05 RMSE =1.21 RMSE =0.92 RMSE =1.37 RMSE =1.51 RMSE =1.66 60

09/14/95 09/27/95 10/11/95 10/24/95 11/07/95 12/13/95 0 DEPTH,METERS IN 10

50 AME =1.00 AME =0.97 AME =0.69 AME =0.54 AME =0.58 AME =0.50 RMSE =1.24 RMSE =1.11 RMSE =0.82 RMSE =0.67 RMSE =0.74 RMSE =0.64 60 0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30 TEMPERATURE, IN DEGREES CELSIUS

EXPLANATION SIMULATED MEASURED Figure 10. Relation between simulated and measured water temperatures in the water column near the Bull Shoals Lake dam, January through December 1995.

6 A 4

-2

-4

-6 0 5 10 15 20 25 30 35 MEASURED TEMPERATURE, IN DEGREES CELSIUS

6 B 4

-2

-4

-6 JAN FEB MAR APR MAY JUNE JULY AUG SEPT OCT NOV DEC 1995

6 C 4

2 SIMULATED MINUS MEASURED TEMPERATURE, IN CELSIUS DEGREES MEASURED MINUS SIMULATED 0

-2

-4

-6 0 10 20 30 40 50 60 WATER DEPTH, IN METERS Figure 11. Relation of difference between simulated and measured water temperatures near the Bull Shoals 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 Bull Shoals Lake 15 Simulated dissolved-oxygen concentrations near mg/L, and the average and median differences were - the Bull Shoals Lake dam exhibited the same general 0.2 and -0.1 mg/L, respectively. patterns and magnitudes as measured concentrations Differences between simulated and measured (fig. 12). All simulated dissolved-oxygen concentra- dissolved-oxygen concentrations were compared to tions (711) for 1994 were compared to corresponding corresponding measured dissolved-oxygen concentra- measured concentrations (Evans and others, 1995; Por- tions, sampling date, and the water depth (fig. 13). Sim- ter and others, 1996). Simulated dissolved-oxygen con- ulated dissolved-oxygen concentrations typically were centrations ranged from 0.0 to 11.4 mg/L, whereas, less than measured values at concentrations less than 5 measured dissolved-oxygen concentrations ranged mg/L and greater than measured values at concentra- from 0.1 to 11.1 mg/L. Simulated dissolved-oxygen concentrations in the vertical profile generally (61 per- tions greater than 5 mg/L. Errors in simulated dis- cent) were within 1 mg/L of measured concentrations. solved-oxygen concentration were greater near the end The AME and RMSE between simulated and measured of the thermal stratification season (September- dissolved-oxygen concentrations were 1.13 and 1.71 November) and during turnover (December). Simu- mg/L, respectively. The difference between simulated lated dissolved oxygen concentrations generally were and measured concentrations ranged from -8.6 to 7.6 less than measured concentrations at all depths.

01/27/94 03/23/94 05/10/94 06/08/94 07/07/94 0 AME = 0.15 AME = 0.67 AME = 0.89 RMSE = 0.20 RMSE = 0.69 RMSE = 0.96 10 AME = 0.96 RMSE = 1.22

50 AME = 1.62 RMSE = 2.11 60

08/17/94 09/13/94 09/27/94 10/12/94 10/18/94 0 DEPTH, IN METERS IN DEPTH,

50 AME =1.41 AME = 2.07 AME =1.25 AME = 1.33 AME = 0.89 RMSE = 1.84 RMSE = 3.06 RMSE = 1.62 RMSE = 1.75 RMSE = 1.05 60 024681012 024681012 024681012 024681012 024681012

11/01/94 11/14/94 12/06/94 0

EXPLANATION 20 SIMULATED MEASURED

40 DEPTH, IN METERS DEPTH,

50 AME = 1.12 AME = 0.82 AME = 1.55 RMSE = 2.15 RMSE = 0.94 RMSE = 2.49 60 024681012 024681012 024681012 DISSOLVED OXYGEN, IN MILLIGRAMS PER LITER

Figure 12. Relation between simulated and measured dissolved-oxygen concentrations in the water column near the Bull Shoals Lake dam, January through December 1994.

16 Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Bull Shoals Lake, Arkansas, 1994-1995 10 8 A 6 Simulated dissolved-oxygen concentrations were 4 2 similar to measured dissolved-oxygen concentrations in 0 -2 1995 (fig. 14), but differences were somewhat less in -4 1995 than in 1994. Seasonal variations in simulated dis- -6 -8 solved-oxygen concentration were reproduced despite -10 024681012pronounced differences in the vertical distribution. All MEASURED DISSOLVED-OXYGEN CONCENTRATION, simulated dissolved-oxygen concentrations (654) were IN MILLIGRAMS PER LITER compared with corresponding measured concentrations 10 near the Bull Shoals Lake dam (Porter and others, 1996, 8 B 6 1997). Simulated values ranged from 0.0 to 11.1 mg/L 4 2 whereas, measured dissolved-oxygen concentrations 0 ranged from 0.0 to 13.1 mg/L. Simulated dissolved- -2 -4 oxygen concentrations in the vertical profile generally -6 -8 (67 percent) were within 1 mg/L of measured concen- -10 JAN FEB MAR APR MAY JUNE JULY AUG SEPT OCT NOV DEC trations. The AME and RMSE between simulated and 1994 measured dissolved-oxygen concentrations were 0.94 and 1.37, respectively. The difference between simu- CONCENTRATION, IN MILLIGRAMS PER LITER 10 lated and measured dissolved-oxygen concentrations

SIMULATED MINUS MEASURED DISSOLVED-OXYGEN 8 C 6 ranged from -6.9 to 6.7 mg/L, and the average and 4 2 median differences were -0.2 and -0.1 mg/L, respec- 0 tively. -2 -4 -6 -8 -10 0 10 20 30 40 50 60 Figure 13. Relation of difference between simulated and measured dissolved-oxygen concentrations near Bull Shoals Lake dam to (A) measured dissolved-oxygen concentrations, (B) sampling date, and (C) water depth, January through December 1994.

01/20/95 03/22/95 05/17/95 06/14/95 07/11/95 08/16/95 0 AME =0.91 AME =1.33 AME =0.30 AME =0.52 AME =1.03 RMSE =0.95 RMSE =1.37 RMSE =0.41 RMSE =0.71 RMSE =1.19 10

50 AME =1.81 RMSE =2.46 60

09/14/95 09/27/95 10/11/95 10/24/95 11/07/95 12/13/95 0 DEPTH, IN METERS

50 AME =0.34 AME =1.09 AME =1.06 AME =0.72 AME =1.05 AME =1.18 RMSE =1.27 RMSE =1.53 RMSE =0.97 RMSE =0.76 RMSE =1.85 60 RMSE =1.71 024681012 024681012 024681012 024681012 024681012 024681012

DISSOLVED OXYGEN, IN MILLIGRAMS PER LITER

EXPLANATION SIMULATED MEASURED Figure 14. Relation between simulated and measured dissolved-oxygen concentrations in the water column near the Bull Shoals Lake dam, January through December 1995. Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Bull Shoals Lake 17 On average, simulated dissolved-oxygen con- Sensitivity Analysis centrations in 1995 were less than measured concentra- Sensitivity analysis is the determination of the tions (fig. 15). Simulated dissolved-oxygen effects of small changes in calibrated model parameters concentrations were less than measured concentrations and input data on model results. A complete sensitivity through most of the stratification season. Near the end analysis for all model parameters in the Bull Shoals of the stratification season and during turnover, simu- Lake model was not conducted because the Bull Shoals lated concentrations were typically greater than mea- Lake model includes more than 60 parameters (tables 1 sured concentrations. Simulated dissolved-oxygen and 2). However, many hydrodynamic, temperature, concentrations often were less than measured concentrations near the water surface and greater than mea- and dissolved-oxygen simulations were conducted as a sured concentrations near the lake bottom. Despite component of model development and calibration. these tendencies, simulation of dissolved-oxygen con- Results from these simulations and information from centration in the vertical profile near the Bull Shoals previous modeling studies (Bales and Giorgino, 1998; Lake dam followed the same general patterns as mea- Giorgino and Bales, 1997; Green, 2001; Haggard and sured concentrations. 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 8 6 A to changes in the wind-sheltering coefficient (WSC), 4 bottom-water heat exchange coefficient (CBHE), light 2 0 extinction (α), sediment-oxygen demand (SOD), and -2 -4 changes in inflow temperature and dissolved-oxygen -6 concentrations was assessed. -8 024681012 Water temperature in the Bull Shoals Lake MEASURED DISSOLVED-OXYGEN CONCENTRATION, IN MILLIGRAMS PER LITER model was most sensitive to changes in the WSC, α,

8 and inflow water temperature (fig. 16). Wind speed in 6 B the calibrated Bull Shoals Lake model was adjusted 4 2 (WSC = 0.7) from the meteorological data recorded at 0 Harrison, Arkansas; that is, the effective wind speed -2 -4 was 70 percent of the recorded wind speed at Harrison. -6 During thermal stratification, more vertical mixing was -8 JAN FEB MAR APR MAY JUNE JULY AUG SEPT OCT NOV DEC simulated when the WSC was increased (1.0) and less 1995 vertical mixing was simulated when the WSC was CONCENTRATION, IN MILLIGRAMS PER LITER PER MILLIGRAMS IN CONCENTRATION, 8 decreased (0.5). Changes in the α affected vertical

SIMULATED MINUS MEASURED DISSOLVED-OXYGEN MEASURED MINUS SIMULATED 6 C 4 water temperature profiles during stratification. 2 Increasing α slightly elevated the thermocline and 0 α -2 decreasing lowered the thermocline. Changes in -4 inflow water temperature also affected vertical water -6 -8 temperature profiles near the dam during stratification. 0 10 20 30 40 50 60 Surface-water temperatures were not impacted as much WATER DEPTH, IN METERS by changes in inflow water temperatures as was the position of the thermocline and hypolimnetic tempera- Figure 15. Relation of difference between simulated and tures. The combination of WSC and α appear to be the measured dissolved-oxygen concentrations near Bull Shoals driving factors in the model responsible for the devel- Lake dam to (A) measured dissolved-oxygen concentrations, (B) sampling date, and (C) water depth, January opment, duration, and vertical location of the ther- through December 1995. mocline in Bull Shoals Lake near the dam.

18 Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Bull Shoals Lake, Arkansas, 1994-1995 July 7, 1994 Wind-Sheltering Coefficient of Bottom Light Extinction Inflow Water Coefficient (WSC) Heat Exchange (CBHE) Coefficient ( Temperature (ITEMP) 0

60 5 1015202530 5 1015202530 5 1015202530 5 1015202530

January 20, 1995 0

20 DEPTH, IN METERS BELOW WATER SURFACE

60 5 1015202530 5 1015202530 5 1015202530 5 1015202530 WATER TEMPERATURE, IN DEGREES CELSIUS

EXPLANATION

WSC = 0.7 CBHE = 7E-8 α = 0.24 1.0 x ITEMP (calibrated value) (calibrated value) (calibration value) (calibration value) WSC = 0.5 CBHE = 7E-9 α = 0.38 0.75 x ITEMP WSC = 1.0 CBHE = 7E-7 1.25 x ITEMP α = 0.10

Figure 16. Vertical temperature distributions near the Bull Shoals Lake dam on July 7, 1994 (top), and January 20, 1995 (bottom), showing calibrated model profiles and profiles as a result of differing model parameters. In the Bull Shoals Lake model, dissolved-oxy- assumptions were made in evaluating dissolved-oxygen concentrations were most affected by changes in gen concentrations near the dam. Regardless, algal the WSC and FSOD (fig. 17). FSOD is the fraction of dynamics play a substantial role in the dissolved-oxy- the zero-order SOD rate and is applied to adjust SOD gen conditions near the Bull Shoals Lake dam. equally among all segments. Changes in the WSC and FSOD had the greatest effect on dissolved-oxygen concentrations near the thermocline and throughout the Model Applications hypolimnion. The α regulates the amount of light pen- The calibrated Bull Shoals Lake model was used etrating the water, indirectly affecting dissolved-oxy- to assess the impacts of increased minimum flow on gen concentrations by influencing algal production. α water-surface elevation and on temperature and dis- Changes in and inflow dissolved-oxygen concentra- solved-oxygen concentrations in the Bull Shoals Lake tions had little effect on vertical distribution of dis- outflow waters. Two scenarios were simulated, includ- solved oxygen near the dam. ing (1) an increase in the outflow of Bull Shoals Lake Many other parameters indirectly affect dis- dam from the existing minimum flow of 4.6 m3/s to solved-oxygen concentrations through algal dynamics; 22.6 m3/s, and (2) an increase in water-surface eleva- however, examination of all of these parameters is tion of Bull Shoals Lake of 1. 5 m to correct for the vol- beyond the scope of this report given that so many ume displaced by the additional minimum flow.

Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Bull Shoals Lake 19 July 7, 1994 Inflow Dissolved Wind-Sheltering Fraction of Sediment Light Extinction Oxygen Concentration Coefficient (WSC) Oxygen Demand (FSOD) Coefficient ( (IDO) 0

60 024681012 024681012 024681012 024681012

January 20, 1995 0

DEPTH, IN METERS BELOW WATER SURFACE 20

60 024681012 024681012 024681012 024681012 DISSOLVED OXYGEN CONCENTRATION, IN MILLIGRAMS PER LITER

EXPLANATION

WSC = 0.7 FSOD = 1.75 α = 0.24 1.0 X IDO (calibrated value) (calibrated value) (calibration value) (calibration value) WSC = 0.5 FSOD = 0.5 α = 0.38 0.75 X IDO WSC = 1.0 FSOD = 2.5 1.25 X IDO α = 010

Figure 17. Vertical dissolved-oxygen concentration distributions near the Bull Shoals Lake dam on July 7, 1994 (top), and January 20, 1995 (bottom), showing calibrated model profiles and profiles as a result of differing model parameters.

When 22.6 m3/s was applied as the minimum end of 1995 only 0.04 m greater than the calibrated amount of outflow (increased minimum flow scenario), model (fig. 19). mean annual outflow increased from 210.6 to 215.1 m3/ s, about a 2 percent increase. Approximately 37 percent 208 of the hourly outflow data required an increase to 22.6 206 m3/s. Average annual outflow increased from 6,641 to 204 3 3 202 6,782 million m , which is equivalent to 141 million m 200

ELEVATION, 198 per year increase, or about 3.4 percent of reservoir vol- 1929 OF NGVD ume at conservation pool elevation. The water-surface IN METERSABOVE 196 194 elevation at the end of 1994 was reduced 0.79 m and at JAN MAR MAY JULY SEPT NOV MAR MAY JULY SEPT NOV 1994 1995 the end of 1995 was reduced about 1.5 m (figs. 18 and EXPLANATION 19) from the initial elevation on January 1, 1994 Calibrated Model Increased Minimum Flow Scenario Increased Minimum Flow with Increased (168.79 m). When 1.5 m of water was applied to the ini- Water-Surface Elevation Scenario tial elevation (increased minimum flow with increased water-surface elevation scenario), the difference by the Figure 18. Simulated water-surface elevations resulting from end of 1994 was 0.77 m greater than the calibrated increased minimum flow scenarios. model without the increased minimum flow and by the

20 Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Bull Shoals Lake, Arkansas, 1994-1995 Simulated temperature in the outflow water differed little between the increased minimum flow scenarios and the calibrated model (figs. 20 and 21). MINIMUM FLOW WATER TEMPERATURE DIFFERENCE 3.5 Absolute maximum difference in outflow water tem- 3.0 perature between the increased minimum flow scenario 2.5 2.0 and the calibrated model was 3.03 ° C and between the 1.5 increased minimum flow with increased water-surface 1.0 0.5 elevation and the calibrated model was 1.03 ° C. The 0.0 IN DEGREES CELSIUS -0.5 maximum temperature differences occurred at the end JAN MAR MAY JULY SEPT NOV MAR MAY JULY SEPT NOV

SCENARIO MINUS CALIBRATED CALIBRATED MINUS SCENARIO 1994 1995 of the stratification season in November 1994 and OUTFLOW WATER TEMPERATURE, 1995. This could be attributed to the difference in the timing of turnover, when the lake goes from a stratified condition to a well-mixed condition. Turnover occurs MINIMUM FLOW WITH INCREASED WATER-SURFACE within a short time period and the timing could be ELEVATION WATER TEMPERATURE DIFFERENCE affected by the difference in flow conditions from the 1.0 calibrated model to the minimum flow scenarios. Over- 0.5 all, temperature differences for both scenarios were 0.0 within the AME and RMSE between simulated and measured water-column profile temperature differ- -0.5 IN DEGREES CELSIUS DEGREES IN ences reported in the “Model Calibration” section of -1.0 JAN MAR MAY JULY SEPT NOV MAR MAY JULY SEPT NOV this report. Simulated outflow temperatures were simi- CALIBRATED MINUS SCENARIO 1994 1995 OUTFLOW WATER TEMPERATURE, OUTFLOW WATER TEMPERATURE, lar to estimated outflow temperatures from water-column profiles measured upstream from the dam (George Figure 20. Simulated water temperature differences Robins, Southwestern Power Administration, written between increased minimum flow scenarios and the commun., 2000) and to measured downstream outflow calibrated model. temperatures (USGS station number 07054501) (fig. 21). Water temperature in the dam outflow increased slightly (less than 0.2 ° C, on average) with increased minimum flow. Conversely, with the increase in water- surface elevation plus the increased minimum flow, 20 18 water temperature in the dam outflow decreased 16 slightly (less than 0.1 ° C, on average) through time dur- 14 ing the stratification season. 12 10 8

TEMPERATURE, 6

IN DEGREES CELSIUS 4 JAN MAR MAY JULY SEPT NOV MAR MAY JULY SEPT NOV 2.0 1994 1995 1.6 1.2 0.8 0.4 EXPLANATION 0.0 Calibrated Model -0.4 Minimum Flow Scenario -0.8 Minimum Flow with Increased -1.2 Water-Surface Elevation Scenario -1.6

CALIBRATED MODEL Measured Outflow

ELEVATION,METERS IN -2.0 JAN MAR MAY JULY SEPT NOV MAR MAY JULY SEPT NOV Above Dam Water-Column Profile Estimate SCENARIO ELEVATIONSCENARIO MINUS 1994 1995

EXPLANATION Increased Minimum Flow Scenario Figure 21. Simulated and estimated water temperatures in Bull Increased Minimum Flow with Increased Shoals Lake outflow and measured temperatures downstream from Water-Surface Elevation Scenario Bull Shoals Lake dam.

Figure 19. Relation of difference between water-surface elevations predicted from increased minimum flow scenarios and calibrated model water-surface elevation with time.

Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Bull Shoals Lake 21 Simulated dissolved-oxygen concentrations in the outflow water differed little between the two increased minimum flow scenarios and the calibrated MINIMUM FLOW DISSOLVED- model (figs. 22 and 23). Absolute maximum difference OXYGEN CONCENTRATION DIFFERENCE 5 in outflow dissolved oxygen between the increased 4 minimum flow scenario and the calibrated model was 3 4.34 mg/L and between the increased minimum flow 2 with increased water-surface elevation and the cali- 1 brated model was 2.02 mg/L. The maximum dissolved- 0 IN MILLIGRAMS PER LITER -1 oxygen concentration differences occurred at the end of JAN MAR MAY JULY SEPT NOV MAR MAY JULY SEPT NOV DISSOLVED OXYGEN CONCENTRATION, the stratification season in November 1994 and 1995. OUTFLOW CALIBRATED MINUS SCENARIO 1994 1995 The differences could be attributed to the difference in timing of the turnover, caused by the changes in flow condition from the calibrated model to the minimum flow scenarios. Overall, dissolved-oxygen concentra- MINIMUM FLOW WITH INCREASED WATER-SURFACE tion differences for both scenarios generally were about ELEVATION DISSOLVED-OXYGEN CONCENTRATION DIFFERENCE the same as the AME and RMSE between simulated 2 and measured water-column profile dissolved-oxygen 1 differences reported in the “Model Calibration” section 0 of this report. Simulated outflow dissolved-oxygen concentrations were similar to estimated outflow con- -1 IN MILLIGRAMS PER LITER -2 centrations from water-column profiles measured JAN MAR MAY JULY SEPT NOV MAR MAY JULY SEPT NOV DISSOLVED OXYGEN CONCENTRATION, DISSOLVED OXYGEN upstream from the dam (George Robins, Southwestern OUTFLOW CALIBRATED MINUS SCENARIO 1994 1995 Power Administration, written commun., 2000) (fig. 23). Simulated dissolved-oxygen concentrations in the Figure 22. Simulated dissolved-oxygen concentration dam outflow increased slightly with the addition of differences between increased minimum flow scenarios and increased minimum flow (less than 0.05 mg/L, on aver- calibrated model. age). Conversely, with the increase in water-surface elevation and the increased minimum flow, simulated dissolved-oxygen concentrations in the dam outflow decreased slightly (less than -0.05 mg/L, on average) during the simulation period. 14 Small changes in water temperature and dis- 12 solved-oxygen concentration compared to the cali- 10 brated, base condition were simulated for the two 8 increased minimum flow scenarios. However, the 6 changes were similar to the error between simulated 4 2 and measured temperature and dissolved-oxygen con- CONCENTRATION, centrations determined for model calibration. DISSOLVED-OXYGEN 0 IN MILLIGRAMS PER LITER PER MILLIGRAMS IN JAN MAR MAY JULY SEPT NOV MAR MAY JULY SEPT NOV 1994 1995

EXPLANATION Calibrated Model Minimum Flow Scenario Minimum Flow with Increased Water-Surface Elevation Scenario Above Dam Water-Column Profile Estimate

Figure 23. Simulated and estimated dissolved-oxygen concentrations in Bull Shoals Lake outflows.

22 Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Bull Shoals Lake, Arkansas, 1994-1995 SUMMARY temperature and dissolved-oxygen concentrations. However, these results were within the boundaries of Outflow from Bull Shoals Lake and other White the error between simulated and measured water tem- River reservoirs support a cold-water trout fishery of perature and dissolved-oxygen concentrations for the substantial economic yield in north-central Arkansas calibrated model. and south-central Missouri. Proposed increases in min- This model provides the basis and framework for imum flows released from the dam have caused con- future water-quality modeling of Bull Shoals Lake. As cerns about the sustainability of cold-water additional data are collected in the reservoir and tribu- temperature and dissolved oxygen in the bottom water taries, the calibrated model can be modified to assess of Bull Shoals Lake. Increases in water temperature the nutrient assimilative capacity of the reservoir, nutri- and decreases in dissolved oxygen could have poten- ent limitation, and the effect of increases in nutrient tially negative impacts on the cold-water trout fisheries loading on reservoir trophic status. in the downstream outflow. The U.S. Geological Sur- vey, 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 Bull Shoals 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 Bull Shoals Lake, Arkansas. The model was calibrated using hydrologic records and vertical profiles of temperature and dissolved oxygen measured in or near Bull Shoals Lake from January 1994 through December 1995. The model simulates water-surface elevation, water temperature, and dissolved-oxygen concentration. The model simulated temperatures generally within 1 ° C of the measured temperatures. The AME and RMSE between simulated and measured water temperature for 1994 were 0.67 and 0.89, respectively, and for 1995 were 0.94 and 1.13, respectively. The model simulated dissolved-oxygen concentrations generally within 1 mg/L of the measured concentrations. The AME and RMSE between simulated and measured dissolved-oxygen concentrations for 1994 were 1.13 and 1.71, respectively, and for 1995 were 0.94 and 1.37, respectively. The Bull Shoals Lake model was developed to assess the impacts of proposed increases in minimum flows from 4.6 m3/s (the existing minimum flow) to 22.6 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 1.5 m greater than the initial water-surface elevation on outflow temperatures and dissolved-oxygen concentrations. With the increased minimum flow, water temperatures and dissolved oxygen concentrations increased in the outflow. Conversely, increased minimum flow with increased water-surface elevation decreased the outflow water

Summary 23 REFERENCES Porter, J.E., Evans, D.A., and Pugh, A.L., 1996, Water resources data, Arkansas, water year 1995: U.S. Geo- Bales, J.D., and Giorgino, M.J., 1998, Lake Hickory, North logical Survey Water-Data Report AR-95-1, 408 p. Carolina: Analysis of ambient conditions and simula- ———1997, Water resources data, Arkansas, water year tion of hydrodynamics, constituent transport, and 1996: U.S. Geological Survey Water-Data Report AR- water-quality characteristics, 1993-94: U.S. Geological 96-1, 238 p. Survey Water-Resources Investigations Report 98- Reed, H.L., Perkins, T.J., and Gray, G.L., 1995, Water 4149. 62 p. resources data, Missouri, water year 1994: U.S. Geo- Cole, T.M., and Buchak, E.M., 1995, CE-QUAL-W2—A logical Survey Water-Data Report MO-94-1, 338 p. two- dimensional, laterally averaged, hydrodynamic Roache, P.J., 1982, Computational fluid mechanics: Albu- and water quality model, version 2.0, user manual: querque, New Mexico, Hermosa Publishers, 446 p. Vicksburg, Miss., Instruction Report EL-95-1, U.S. U.S. Army Corps of Engineers, 1960, Area and capacity Army Engineer Waterways Experiment Station. tables, supplement to reservoir regulation manual for Evans, D.A., Porter, J.E., and Westerfield, P.W., 1995, Table Rock, Bull Shoals, and Norfork Reservoirs, Water resources data, Arkansas, water year 1994: U.S. Appendix III (Revised) to master manual for reservoir Geological Survey Water-Data Report AR-94-1, 466 p. regulation, White River Basin, Arkansas and Missouri: Little Rock, Arkansas, U.S. Army Engineer District, Galloway, J.M., and Green, W.R., 2002, Simulation of variously paginated. hydrodynamics, temperature, and dissolved oxygen in Norfork Lake, Arkansas, 1994-95: U.S. Geological Survey Water-Resources Investigations Report 02- 4250, 23 p. Giorgino, M.J., and Bales, J.D., 1997, Rhodhiss Lake, North Carolina: Analysis of ambient conditions and simulation of hydrodynamics, constituent transport, and water-quality characteristics, 1993-94: U.S. Geological Survey Water-Resources Investigations Report 97- 4131, 62 p. Green, W.R., 1996, Eutrophication trends inferred from hypolimnetic dissolved-oxygen dynamics within selected White River Reservoirs, northern Arkansas - southern Missouri, 1974-94: U.S. Geological Survey Water-Resources Investigations Report 96-4096, 22 p. ——— 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 Investiga- tions Report 01-4045, 60 p. Haggard, B.E., and Green, W.R., 2002, Simulation of hydrodynamics, temperature, and dissolved-oxygen in Bea- ver Lake, Arkansas, 1994-1995: U.S. Geological Survey Water-Resources Investigations Report 02- 4116, 21 p. Hauck, H.S., Huber, C.G., and Nagel, D.D., 1996, Water resources data, Missouri, water year 1995: U.S. Geo- logical Survey Water-Data Report MO-95-1, 320 p. ——— 1997, Water resources data, Missouri, water year 1996: U.S. Geological Survey Water-Data Report MO- 96-1, 292 p. Leonard, B.P., 1979, A stable and accurate convective modeling procedure based on upstream interpolation: Com- puter Methods in Applied Mechanics and Engineering, v. 19, p. 59-98.

24 Simulation of Hydrodynamics, Temperature, and Dissolved Oxygen in Bull Shoals Lake, Arkansas, 1994-1995