Surface-water quality and flow Modeling Interest Group

Dynamic Modeling of Water-Supply Reservoir Physical and Chemical Processes

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

This version of the article has all of the figures converted to thumbnails with links to the larger images. A version with all of the figures inline is also available; the download time will be longer, but the inline figures may be more convenient for viewing and printing.

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
Introduction

Physical and Chemical Characteristics

Rhodhiss Lake Model Description

Study Objectives
Model Description
Boundary Conditions
Model Parameters

Dynamic Modeling of Physical and Chemical Processes

Hydrodynamics and Heat Transport
Conservative Material Transport
Chemical Transport

Summary
References

Abstract

Introduction

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

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

Model Description

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

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

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

Hydrodynamics and Heat Transport

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.

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

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.

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

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.

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

Summary

References

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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