Department of Applied Mathematics

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Browsing Department of Applied Mathematics by Author "Briers, C. J."

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    Data-driven river flow routing using deep learning: predicting flow along the lower Orange river, Southern Africa
    (Stellenbosch : Stellenbosch University, 2019-04) Briers, C. J.; Brink, Willie; Smit, G. J. F.; Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Division Applied Mathematics.
    ENGLISH ABSTRACT : The Vanderkloof Dam, located on the Orange River, is responsible for the water supply to consumers along its 1 400 km reach up to where it flows into the Atlantic Ocean. The Vaal River, which joins the Orange River approximately 200 km downstream of the dam, contributes significant volumes of water to the flow in the Orange River. These contributions are, however, not taken into account when planning for releases from the Vanderkloof Dam. In this thesis we aimed to develop an accurate and robust flow routing model of the Orange and Vaal River system to predict the effects of releases from the Vanderkloof Dam and anticipate inflows from the Vaal River. Since the factors that impact on flow rate and volume along the river are hard to quantify over long distances, a data-driven approach is followed which uses machine learning to predict the flow rate at downstream flow gauging stations based on flow rates recorded at upstream gauging stations. We restrict the model input to data that would be readily available in an operational setting, making the model practically implementable. A variety of neural network architectures, including fully-connected networks, convolutional neural networks (CNNs) and recurrent neural networks (RNNs), were investigated. It was found that fully-connected networks produce results with accuracy comparable to a simple linear regression model, but display a superior ability to predict the timing of peaks and troughs in flow rate trends. CNNs and RNNs displayed the same ability, as well as showing improvements in accuracy. The best-performing CNN model had a mean absolute percentage error (MAPE) of 14.5 % compared to 16.9 % of a linear regression model. To anticipate contributions from the Vaal River we investigated including inflows recorded at stations on the Vaal River and two of its tributaries, the Modder and Riet Rivers. Both approaches which were investigated, i.e. incorporating these inflows as part of multi-dimensional input into a CNN, and using a parallel CNN model architecture, showed promise with a MAPE of 21.6 % and 23.5 %, respectively. Although these models did not achieve a high level of accuracy, they did display the ability to anticipate contributions from the Vaal River system. It is believed that they could, with additional refinement or using appropriate safety factors, be practically applied in an operational setting. We further investigated including seasonal data as input into our models. Including the time of the year, and including evaporation data recorded at meteorological stations in the recent past, both resulted in improved MAPE accuracy (14.4 % and 14.8 %, respectively, compared to 18.4 % for a model including no seasonal data). Observations of errors staying relatively constant over time prompted us to include errors made in the recent past as input into subsequent predictions. A model trained with this additional data achieved a MAPE of 10.2 %, a significant improvement over other applied methods