USGS -- SMIG --
Surface-water quality and flow Modeling Interest Group

Dynamic Modeling of Water-Supply Reservoir Physical and Chemical Processes

by Jerad D. Bales and Mary J. Giorgino

USGS, Water Resources Division
3916 Sunset Ridge Road
Raleigh, NC 27607
Internet: jdbales@usgs.gov, giorgino@usgs.gov
Phone: (919) 571-4048, (919) 571-4087
FAX: (919) 571-4041

Editor's note:
This paper was written for the First Federal Interagency Hydrologic Modeling Conference, held in Las Vegas on April 19-23, 1998.

This version of the article has all of the figures inline; therefore, it may take a noticeable amount of time to download and view. A version of this article with all of the figures converted to thumbnails is also available.

Citation:
Bales, J.D. and Giorgino, M.J., 1998, Dynamic modeling of water-supply reservoir physical and chemical processes, in Proceedings of the First Federal Interagency Hydrologic Modeling Conference, April 19-23, 1998, Las Vegas, NV: Subcommittee on Hydrology of the Interagency Advisory Committee on Water Data, p. 2-61 to 2-67.

Contents

Abstract

A spatially detailed hydrodynamic and chemical transport model was applied to Rhodhiss Lake, North Carolina. Rhodhiss Lake is about 22 kilometers long, has a maximum depth of 16 meters, is generally less than 700 meters wide, and has a theoretical mean retention time of 21 days. Monitoring data indicate that the reservoir is eutrophic. Data collected during a 15-month period in 1993-94 were used to calibrate and apply the model. The root mean square difference between measured and simulated water levels was 0.085 meter, and the mean difference between measured and simulated water temperatures was -0.24 degree Celsius. There was essentially no difference between the frequency of occurrence of measured and simulated dissolved-oxygen concentrations less than 5 milligrams per liter. The model was applied to demonstrate the transport of a neutrally buoyant, conservative tracer released into the headwaters of the reservoir during both stratified and unstratified conditions. During stratified conditions, about 40 days were required for the maximum concentration of the tracer at the dam to become less than one percent of the initial maximum concentration, whereas only 17 days were needed to reach the same condition during unstratified conditions.

Introduction

Rhodhiss Lake is an impoundment of the Catawba River in North Carolina (fig. 1) constructed in 1925. Information on hydraulic circulation and constituent transport in the reservoir is needed to more effectively manage the reservoir and its watershed, and to predict water-quality responses to changes in constituent loadings or hydrologic regime. Such changes could result from recently adopted State water-supply watershed regulations, proposed wastewater-treatment plant expansions in the watershed, and a new basinwide approach used by State regulators to permit point-source discharges.

(fig. 1)

Figure 1. Location of Rhodhiss lake in the upper Catawba River Basin of North Carolina.

The U.S. Geological Survey (USGS), in cooperation with the Western Piedmont Council of Governments, conducted a 2-year investigation of water-quality conditions in Rhodhiss Lake. The investigation included intensive data collection during 15 months in 1993-94 to (1) quantify existing water-quality conditions and (2) provide data required for calibration and application of a dynamic water-quality model of the reservoir. The purpose of this paper is to describe the development and application of the dynamic water-quality model used to simulate physical and chemical processes in Rhodhiss Lake.

Physical and Chemical Characteristics

Rhodhiss Lake is about 22 km (kilometers) long and is less than about 700 m (meters) wide throughout the length of the reservoir. The surface area of the reservoir is 10.4 km2 (square kilometers); the mean depth is 8.0 m; and the maximum depth is 16 m. The major inflow to the reservoir is the Catawba River, which has a drainage area of 2,650 km2 at the reservoir headwaters. The drainage area of the reservoir increases only slightly to 2,830 km2 at Rhodhiss Dam. Lake James, a mainstem reservoir on the Catawba River having a drainage area of 984 km2, is located about 20 km upstream from Rhodhiss Lake. Streamflow into Rhodhiss Lake is somewhat regulated by releases from Lake James and typically varies between about 10 and 1,000 m3/s (cubic meters per second). The theoretical mean retention time of the reservoir is 21 days.

Three water-supply withdrawals are located in the reservoir. The total average withdrawal rate for 1993 was 0.67 m3/s. One permitted wastewater-treatment facility discharged an average of 0.21 m3/s directly to the reservoir in 1993.

During the data-collection period, median total phosphorus concentrations in the reservoir decreased from 0.053 mg/L (milligrams per liter) in the headwaters, to 0.044 mg/L at mid-reservoir and 0.034 mg/L in the forebay. Inorganic nutrients--nitrate, ammonia, and orthophosphate--were generally depleted from the epilimnion during the summer, probably by algal uptake. Concentrations of ammonia, and to a lesser extent total phosphorus, increased in the hypolimnion during summer anoxic conditions. However, nuisance levels of phytoplankton were rarely observed in the reservoir during the data-collection period, possibly because short residence time and mixing patterns suppressed algal growth. Mean chlorophyll a concentration at the mid-reservoir site during May-September 1993 was 10 µg/L (micrograms per liter), and the maximum concentration of 52 µg/L occurred during a late fall bloom.

Rhodhiss Lake Model Description

Study Objectives

Objectives of the reservoir modeling were to develop the capability to simulate (1) movement and mixing of spills or releases in the reservoir and (2) reservoir nutrient, algal, and DO (dissolved-oxygen) concentrations in response to possible changes in external loadings and flows. Because reservoir water-quality degradation often is first evident in coves, the capability for simulation of hydrodynamics and water-quality processes in coves and embayments, including exchange with the mainstem was needed. Rhodhiss Lake is relatively narrow, and temperature and DO data indicated that a laterally averaged formulation is appropriate for the reservoir. These functional requirements were considered when selecting the model CE-QUAL-W2 for application to Rhodhiss Lake.

Model Description

The model CE-QUAL-W2 has been under continuous development since at least 1975 (Edinger and Buchak, 1975). Complete details on model theory and structure, and an extensive bibliography for theoretical development and application are given in Cole and Buchak (1995).

Finite-difference forms of the complete laterally averaged equations of conservation of mass, conservation of momentum, and transport (one equation for each constituent) are solved using an efficient and accurate numerical scheme. The computational time step is variable throughout the simulation to ensure numerical stability, but typically is about 5 minutes for the Rhodhiss application. The modeled system is divided into a series of longitudinal segments, each of which may have a unique length. Each segment is further subdivided into layers. All layers within a segment must have the same length, but each layer can have a unique width and thickness.

The Rhodhiss Lake model extends along the mainstem of the reservoir for a distance of 18.5 km. There are 37 computational segments along the mainstem. The model domain encompasses five embayments, and each embayment is represented by three segments. All segments are 500 m long. Each layer is 1 m thick. Distances from the spillway crest to the bottom of the channel ranged from 3 to 16 m.

Boundary Conditions

Upstream boundary conditions included estimated hourly streamflow, measured hourly water temperature, and estimated daily nutrient concentrations. Streamflow was measured from 70 percent of the basin upstream from Rhodhiss Lake, and inflows to the reservoir were estimated from these data. Monthly to semi-monthly measurements of nutrient concentrations were used with streamflow data to determine a relation between streamflow and nutrient levels. Daily streamflow was then used to estimate daily nutrient concentrations at the headwaters of the reservoir.

Local inflows from the 180 km2 draining directly to the reservoir were estimated using measured streamflow data from a nearby gage. Recorded hourly releases from Rhodhiss Dam were used as the downstream boundary condition. No downstream thermal or chemical boundary conditions were required. Other boundary data included measured hourly meteorological conditions (wind speed and direction, air temperature, dewpoint temperature, and cloud cover), discharge to the reservoir (including temperature and nutrient concentrations), and withdrawals from the reservoir.

Model Parameters

Parameters are used to describe physical and chemical processes that are not explicitly modeled and to provide chemical kinetic rate information. Many parameters cannot be measured directly and are often adjusted during the model calibration process until simulated results agree with observations.

Most of the key hydrodynamic and thermal processes are modeled in CE-QUAL-W2, so there are relatively few adjustable hydraulic and thermal model parameters. Simulation results were generally insensitive to changes in the hydraulic and thermal model parameters, with the exception of the wind-sheltering coefficient, primarily because the detailed computational grid resolves small-scale physical processes. The dimensionless wind-sheltering coefficient, which is temporally variable, reduces the effects of wind on the reservoir because of topographic or vegetation sheltering of the water surface.

There are 57 chemical kinetic rate coefficients required for the Rhodhiss Lake application of CE-QUAL-W2 (Giorgino and Bales, 1997). Selection of most of the parameters was based on published information. All of the kinetic coefficients are temporally and spatially invariant.

Dynamic Modeling of Physical and Chemical Processes

Model calibration was achieved through adjustment of model parameters and estimated input data for the period April 1, 1993, through March 30, 1994. The model also was applied using boundary data from this period.

Hydrodynamics and Heat Transport

Simulated water levels were quite sensitive to inflow rates, so only relatively small adjustments were required in the original estimates of streamflow to achieve a good calibration. The root mean square difference between measured and simulated water levels for the 12-month calibration period was 0.085 m. Eighty percent of the differences between measured and simulated water levels were between 0.02 and 0.12 m. The total range in measured water level during the period was 1.32 m.

Simulated near-surface water-temperatures were generally within 1 oC (degrees Celsius) of measured values (fig. 2). Near-bottom water temperatures were underpredicted from mid-May through August, and larger differences between measured and simulated values occurred in the deeper waters. All of the water temperature data (177 observations) from the mid-reservoir site during the calibration period were compared with corresponding simulated values. The mean difference between the simulated and measured values was -0.24 oC, and 80 percent of the differences were between 1.26 and -1.80 oC. Simulated water temperatures were generally high relative to measured values when measured water temperature exceeded 20 oC. Most of the simulated temperatures underpredicted measured values when the measured water temperatures were less than 8 oC. Simulated water temperatures were equally overpredicted as underpredicted at a particular measurement depth, although simulation errors were smallest near the water surface, and greatest at about 3 m above the reservoir bottom.

(fig. 2)

Figure 2. Measured and simulated water temperatures, May 1, 1993, through March 25, 1994, at mid-reservoir and forebay locations.

Results from the water temperature simulations provide information on physical characteristics and processes in the reservoirinformation that might not be obtained from periodic measurements. For example, water temperature data from September to November suggest that the reservoir was thermally stratified during the period (fig. 2). The simulations, however, indicate that the reservoir was continually mixing and stratifying during the period, probably as a result of changes in inflow conditions. Simulation results suggest that near-bottom water temperatures in the deeper part of the reservoir vary more gradually than those in the shallower regions. Finally, the reservoir appears to thermally stratify and destratify rather quickly and often in the upstream reaches of the reservoir. Likewise, stratification and destratification appear to occur fairly often in the downstream reaches of the reservoir in the fall and late winter.

Conservative Material Transport

The calibrated Rhodhiss Lake model was used to simulate the movement of a neutrally buoyant nonreactive material (or tracer) through the reservoir. Transport of material released from the upstream end of the reservoir at two different times (summer and winter) was simulated. The temporal distribution of the release was triangular in shape, with a time base of 2 days, and a maximum concentration of 1,000 ppt (parts per thousand). The inflow rate of the tracer was equal to the inflow rate of the water, which was between 16 and 27 m3/s during the winter period and between 12 and 40 m3/s during the summer period, resulting in a slightly greater mass of tracer released in the summer.

During the summer release, the influent Catawba River water temperature was colder than the near-surface water in the reservoir. Consequently, the tracer sank fairly rapidly as the material moved into the reservoir. The concentration of the tracer near the water surface 5 km downstream from the release was less than 5 percent of the initial peak concentration. Most of the sinking occurred between 2 and 5 km downstream from the release (fig. 3). The highest concentration at the dam was about 14 percent of the initial maximum concentration, occurred near mid-depth, and arrived at the dam 13 days after the release. The mid-depth peak likely reflects both an interflow phenomenon and, to a lesser degree, the effects of the mid-depth reservoir withdrawal on flow patterns. The effects of the interflow phenomenon are evident in the distribution of measured temperature and, to a lesser extent, DO data during selected periods in the summer of 1993 (Giorgino and Bales, 1997). The mid-depth tracer concentration at the dam remained greater than 1 percent of the initial concentration for about 40 days.

(fig. 3a)
(fig. 3b)

Figure 3. Simulated tracer concentrations at Rhodhiss Lake mid-reservoir and forebay locations for (a) summer and (b) winter.

Between 0 and 5 km downstream from the release, there was less attenuation of the peak concentration following the winter release than following the summer release (fig. 3). However, at Rhodhiss Dam, the peak concentration following the winter release was about half of the highest concentration after the summer release. The difference is the result of greater vertical mixing during the winter and, hence, greater dilution in the winter when the reservoir was less thermally stratified. Only about 17 days were required in the winter for the concentration at the dam to fall below 1 percent of the initial concentration.

These examples of simulation of the transport of a conservative material demonstrate

  1. the use of the Rhodhiss Lake model in evaluating the movement of a brief or extended release of material into the reservoir;
  2. the manner in which nonconservative materials move through the reservoir, without the confounding effects of chemical transformations, regeneration, and settling;
  3. the difficulty in identifying a single residence time for the reservoir--residence times vary seasonally, as well as with depth; and
  4. the effects of density stratification and vertical mixing on transport processes.

Chemical Transport

Eleven water-chemistry constituents were simulated in the Rhodhiss Lake model. These constituents included labile and refractory dissolved organic matter, volatile solids, organic bottom sediments, carbonaceous biological oxygen demand, DO, PO4 (orthophosphate), ammonium, nitrate, iron, and algae.

The calibrated model provided a reasonable simulation of DO concentrations in Rhodhiss Lake. Near-surface and near-bottom DO appears to be predicted better than DO concentrations at mid-depth, where DO was typically overpredicted. The frequency of occurrence of DO concentrations less than 5 mg/L, the concentrations of most interest to regulators, was almost the same for measured and simulated DO. Simulation of the exact timing of low DO events was within about 5 days of the actual occurrence. Simulation results indicated that near-bottom DO concentrations were less than 4 mg/L only 2 percent of the time during April 1993 through March 1994 at the headwaters of the reservoir, compared to about 40 percent of the time at the forebay. Simulated near-bottom DO was less than 1 mg/L about 6 percent of the time at mid-reservoir, but near-bottom DO concentrations of 1 mg/L or less occurred about 30 percent of the time at the forebay.

Simulated algal concentrations generally agreed with measured values at the mid-reservoir site, with a few exceptions (fig. 4). Algal concentrations were overpredicted on July 14 and September 15, when PO4 concentrations also were over-predicted. On November 17, 1993, when USGS data indicated a mid-reservoir algal concentration of 3.48 mg/L, data collected by the North Carolina Division of Environmental Management at the same location showed an algal concentration of 0.87 mg/L, which closely agrees with the simulated value. Accurate simulation of algal concentrations is very difficult for several reasons. First, algae are not uniformly distributed in the reservoir but often occur in patches. Consequently, obtaining a representative sample can be difficult, as suggested by the November 17 data. Second, phytoplankton is simulated by the Rhodhiss model as a single assemblage, so distinctions among algal types which bloom under different ambient conditions are not possible. Third, simulated algal concentrations represent the accumulated results of simulated solids concentrations, light penetration, water temperature, nutrient concentrations, and transport. Errors in simulations of each of these parameters are reflected in simulated algal concentrations. Finally, algal concentrations (biomass) are simulated, but chlorophyll a is measured as an indicator of biomass. For this application, biomass in milligrams per liter was obtained by multiplying chlorophyll a in micrograms per liter by 0.067 (American Public Health Association and others, 1992). This factor may not be appropriate for Rhodhiss Lake under all conditions.

(fig. 4)

Figure 4. Measured and simulated algal concentrations at mid-reservoir location, May 1, 1993 through March 25, 1994.

Summary

A spatially detailed hydrodynamic and chemical transport model was developed for Rhodhiss Lake, North Carolina. A laterally averaged formulation was used for the model, which consisted of 16 1-meter layers and 37 500-meter segments along the mainstem of the reservoir. The availability of comprehensive data for model calibration and testing was instrumental in obtaining good agreement between measured and simulated physical and chemical conditions. Predictions of physical conditions (water level and temperature) were better than predictions of chemical processes in the reservoir. The root mean square difference between measured and simulated water levels was 0.085 meter, and the mean difference between measured and simulated water temperatures was -0.24 degree Celsius. There was essentially no difference between the frequency of occurrence of measured and simulated DO concentrations less than 5 milligrams per liter. However, simulation of the exact timing of low DO events was only within about 5 days of the actual occurrence of such events. Reasonable simulations of algal concentrations were obtained. However, in general, highly accurate simulations of algae are difficult because of problems associated with obtaining representative samples, the accumulation of errors in the simulation of contributing physical and chemical processes, and simplifications made in the formulation of the algal simulation algorithms.

References

American Public Health Association, American Water Works Association, and Water Environment Federation, 1992, Standard methods for the examination of water and wastewater, 18th ed.: American Public Health Association, 981 p.

Cole, T.M., and Buchak, E.M., 1995, CE-QUAL-W2: A two-dimensional, laterally averaged, hydrodynamic and water-quality model, version 2.0, user's manual: Vicksburg, Mississippi, Instruction Report EL-95-1, U.S. Army Engineer Waterways Experiment Station, 57 p. + app.

Edinger, J.E., and Buchak, E.M., 1975, A hydrodynamic, two-dimensional reservoir model--The computational basis: Cincinnati, Ohio, U.S. Army Corps of Engineers, Ohio River Division.

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: U.S. Geological Survey Water-Resources Investigations Report 97-4131, 62 p.

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