DEVELOPMENT OF AN EMPIRICAL MODEL OF A COMPLEX, TIDALLY AFFECTED RIVER USING ARTIFICIAL NEURAL NETWORKS

Water Resources of South Carolina Publication

DEVELOPMENT OF AN EMPIRICAL MODEL OF A COMPLEX, TIDALLY AFFECTED RIVER USING ARTIFICIAL NEURAL NETWORKS

By Paul A. Conrads^*, Edwin A. Roehl , and William B. Martello

^* U.S. Geological Survey, Gracern Road, Suite 129, Columbia, SC 29210

Conference Paper

From the National TMDL Science and Policy 2003 Specialty Conference

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Abstract

The Beaufort River is a complex estuarine river system that supports a variety of uses including shellfish grounds, fisheries nursery habitats, shipping access to Port Royal, receiving waters for wastewater effluent, and an 18-mile reach of the Intracoastal Waterway. The river is on the Section 303(d) list of impaired waters of South Carolina for low dissolved-oxygen concentrations. The Clean Water Act stipulates that a Total Maximum Daily Load must be determined for impaired waters.

An empirical model was developed to simulate the impact of point-source discharges and rainfall on dissolved-oxygen concentrations in the Beaufort River. The model uses of water level, specific conductance, temperature, and dissolved-oxygen concentration data collected at 15-minute intervals from seven real-time gaging stations and effluent point-source data collected on a weekly basis for a 33- month period. The empirical model utilizes data mining techniques, including artificial neural network (ANN) models, to quantify the relations between the time series of three wastewater point-source discharges and the dissolved-oxygen concentrations recorded at seven real-time gages distributed throughout the system. Data mining is a new science that extracts knowledge from large volumes of data, and uses attributes from fields such as computer science, signal processing, advanced statistics, machine learning, and chaos theory. The data mining produced a high-fidelity water-quality model that can predict the impacts that point and non-point source loads have on the dissolved-oxygen concentration throughout the river system. The analysis included environmental factors such as tides, specific conductance, water temperature, and rainfall. The model is comprised of numerous sub-models that are based on ANN models.

The data analyses and model provided unique ways to evaluate complex tidal dissolved-oxygen effects from point-source discharges and rainfall. The model executes non-iteratively, making it amenable to very long-term simulation runs of 33 months. The model also included a non-linear, constraint-based numerical optimizer to determine the maximum allowable daily effluent loading without violating the State.s water-quality standard. Insights were garnered from this technical approach that leveraged the full historical record in which assimilative capacity was found to be constantly changing. For example, critical conditions for effluent impacts on dissolved-oxygen concentrations occur during neap tides due to the streamflow characteristics and limited flushing of the system. The predictive model/optimizer allowed for a variety of wastewater treatment plant operating scenarios and regulatory options that can be quickly evaluated. Several 33-month time series of daily loadings were simulated utilizing an optimizer. Frequency distributions of the allowable loading were subsequently generated from the time series of optimal loading. Water- resource managers can use the frequency distribution to help predict the percentage of time water-quality standards may be violated. Model dissemination is facilitated by incorporating the ANN sub-models and point-source optimizers into an Excel spreadsheet application. This paper describes the data collection and analysis, model development and Excel application, pointsource load optimization, and interpretation of model results from this unconventional approach to estuary water-quality modeling and regulatory control.

Abstract
Introduction
Description of Study Area
     Permitted Discharges
     Continuous Monitoring Network
          Water-Level and Streamflow Data
          Precipitation and Water-Quality Data
Approach
     Signal Decomposition and Correlation Analysis
     Artificial Neural Networks
     Input/Output Mapping and Problem Representation
     Decorrelation of Variables
     Estimating Point-source Discharge Impacts on a Single Time Series
     Construction of the Beaufort River Model
          Training of Artificial Neural Network Models
     Spreadsheet Application
     Statistical Measures of Prediction Accuracy
Model Applications
     Critical Conditions for Dissolved Oxygen
     Impact of Precipitation on Dissolved Oxygen
     Allowable Point-source Loading Using Constraint Optimization
     Time-series Frequency Distribution of Allowable Point-Source Loading
     Alternative Point-source Loading Scenarios
Summary
Acknowledgements
References

FIGURES

Figure 1. Study Area
Figure 2. Beaufort River real-time gaging network and location of water reclamation facilities.

Figure 3. Biochemical oxygen demand loads (left) and ammonia loads (right) for the period January 1999 to September 2001.

Figure 4. Ultimate oxygen demand load to Beaufort River January 1999 to September 2000.

Figure 5. Beaufort River and Brickyard Creek gage heights for three stations for August 2001.

Figure 6. Beaufort River tidal ranges.

Figure 7. Beaufort River streamflows at station 2176611 for 2002 water year.

Figure 8. Stream velocities for Brickyard Creek (station 2176585) for July 15-22, 2001. Positive flow is to the Coosaw River to the north.

Figure 9. Specific conductance values and rainfall for the Beaufort River and two tributaries for December 1998 to September 2001.

Figure 10. Time series of DO concentration for Beaufort River and two tributaries and water temperature at station 2176611 for December 1998 to September 2001.

Figure 11. Cumulative percent of DOD for the gages on the Beaufort River and its tributaries for January 1999 to September 2001

Figure 12. Plots showing time series of hourly and measured values, filtered values, and 1-day time derivatives of the lowpass filtered values for station 2176603. Note y-axis for 1- day derivative time series on the right side of the plot.

Figure 13. Multi-layer perceptron artificial neural network architecture.

Figure 14. ANN sub-model execution sequence for decorrelating variables. The model has seven instances of the decorrelation sub-model sequence shown in the blue dotted box at top, one for each gage location. There are seven DOD sub-models for computing Rainfall impact on DOD, also one per gage. There are 83 DOD sub-models for computing the impacts of BOD and NH3 from the Water Reclamation Facilities at different time delays.

Figure 15. Scatter Plot of filtered dissolved oxygen (FDO) and filtered water temperature (FWT) and least-squares regression line (R2=0.88).

Figure 16. One-day change in DO deficit (EDOD6611) and BOD5 (at a 1 day time delay) at station 2172211. Linear R2 = 0.13.

Figure 17. Measured and predicted EDOD ANN used BOD5 as an input at a time delay of 1 day. R2 ANN = 0.57.

Figure 18. Measured and predicted EDOD ANN used NH3 as an input at a time delay of 3 days. R2 ANN = 0.31.

Figure 19. Elements of a GUI worksheet for the Beaufort River assimilative capacity model. Note the extensive decision support graphics and user controls in the form of check boxes, buttons, and scroll bars. The three panels at right show plan- view color-gradient renderings of DDO- and DO-related calculated variables.

Figure 20. Delta DO concentration and tidal range for the period May to October 1999. Note the inverted delta DO y-axis scale

Figure 21. Two-day average rainfall and the dissolved oxygen impact due to precipitation for four stations on the Beaufort River and two tributaries for January 1999 to September 2001. Note the range of the second y-axis has been set to 1 to offset the dissolved oxygen impact for clarity

Figure 22. Graph showing the impact of precipitation and point-source loads on dissolved oxygen at station 2176603 for January 1999 to September 2001.

Figure 23. Time series of allowable loading: Southside WRF for March 1999 to September 2001.

Figure 24. Frequency distribution for allowable loading: Southside WRF for March 1999 to September 2001. Frequency distribution is based on time series of predicted allowable loading shown in Figure 23.

TABLES

Table 1. Estimated model accuracy statistics for cases 1 (left) and 2 (right). Arrows match like statistical measures for the two cases. RMSE in units of mg/L.

Table 2. Scenario 1 . Three discharges proposed UOD allocations to the Beaufort River summer limits

Table 3. Scenario 2 . two discharges proposed UOD allocations to the Beaufort River

Table 4. Scenario 3 . one discharge proposed UOD allocations to the Beaufort River

Table 5. Preliminary model results total UOD loading

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Water Resources of South Carolina Publication