Stream-flow forecasting using extreme learning machines: A case study in a semi-arid region in Iraq

Monthly stream-flow forecasting can yield important information for hydrological applications including sustainable design of rural and urban water management systems, optimization of water resource allocations, water use, pricing and water quality assessment, and agriculture and irrigation operations. The motivation for exploring and developing expert predictive models is an ongoing endeavor for hydrological applications. In this study, the potential of a relatively new data-driven method, namely the extreme learning machine (ELM) method, was explored for forecasting monthly stream-flow discharge rates in the Tigris River, Iraq. The ELM algorithm is a single-layer feedforward neural network (SLFNs) which randomly selects the input weights, hidden layer biases and analytically determines the output weights of the SLFNs. Based on the partial autocorrelation functions of historical stream-flow data, a set of five input combinations with lagged stream-flow values are employed to establish the best forecasting model. A comparative investigation is conducted to evaluate the performance of the ELM compared to other data-driven models: support vector regression (SVR) and generalized regression neural network (GRNN). The forecasting metrics defined as the correlation coefficient (r), Nash-Sutcliffe efficiency (E_NS), Willmott's Index (WI), root-mean-square error (RMSE) and mean absolute error (MAE) computed between the observed and forecasted stream-flow data are employed to assess the ELM model's effectiveness. The results revealed that the ELM model outperformed the SVR and the GRNN models across a number of statistical measures. In quantitative terms, superiority of ELM over SVR and GRNN models was exhibited by E_NS = 0.578, 0.378 and 0.144, r = 0.799, 0.761 and 0.468 and WI = 0.853, 0.802 and 0.689, respectively and the ELM model attained lower RMSE value by approximately 21.3% (relative to SVR) and by approximately 44.7% (relative to GRNN). Based on the findings of this study, several recommendations were suggested for further exploration of the ELM model in hydrological forecasting problems.