Optimized River Stream-Flow Forecasting Model Utilizing High-Order Response Surface Method

摘要

Accurate and reliable stream-flow forecasting has a key role in water resources planning and management. Most recently, soft computing approaches have become progressively prevalent in modelling hydrological variables and most specifically stream-flows. This is due to their ability to capture the non-linearity and non-stationarity characteristics of the hydrological variables with minimum information requirements. Despite this, they present several challenges in the modelling architecture, as there is a need to establish a suitable pre-processing method for the stream-flow data and an appropriate optimization model has to be integrated in order re-adjust the weights and biases associated with the model structure. On top of that, artificial intelligent models require "trial and error" procedures in order to be properly tuned (number of hidden layers, number of neurons within the hidden layers and the type of the transfer function). However, soft computing approach experienced several problems while calibration such as over-fitting. In this research, the Response Surface Method (RSM) is improved based on high-order polynomial functions for forecasting the river stream-flow namely; High-Order Response Surface (HORS) method. Several higher orders have been examined, second, third, fourth and fifth polynomial functions in order to figure out the best fit that able to mimic the pattern of stream-flow. In order to demonstrate the effectiveness of the proposed model, monthly stream-flow time series data located in Aswan High Dam (AHD) has been examined. A detailed analysis of the overall statistical indicators revealed that the proposed method showed outstanding performance for monthly stream-flow forecasting at AHD. It could be concluded that the fifth order polynomial function outperforms the other orders of the polynomial functions especially with May model who achieved minimum MAE 0.12, NRMSE 0.07, MSE 0.03 and maximum SF and R-2 (0.97, 0.99) respectively.