Integration of the Non-linear Time Series GARCH Model with Fuzzy Model Optimized with Water Cycle Algorithm for River Streamflow Forecasting

For managing water resources and operating reservoirs in dynamic contexts, accurate hydrological forecasting is essential. However, it is difficult to track complex hydrological time series with highly non-linear and non-stationary characteristics. The intricacy of the issue is further increased by the risk and uncertainty that are brought about by the dependence of several factors on the hydrological system's output. To hydrologically model river outflows, a hybrid GARCH time series model technique has been applied in this study. To improve the precision of the proposed model estimation, this hybrid model employs a controllable fuzzy logic system to explore the impact of various input variables and an Archimedean detail function to account for the uncertainty in the dependence of the variables. The prediction error in this model is minimized by utilizing weighting factors and problem analysis parameters that are calculated using the water cycle algorithm. It was found that the minimum root-mean-square error values for the training and testing modeling stages are RMSE = 1.89 m and 1.92 m, respectively, by looking at the hydrological modeling results for a watershed of the Karaj dam. For extended lead (i.e., a 6-month rainfall lag), the weakest forecasting capacity was found. The modeling of the copula function using a higher percentage of answers in the confidence band and a smaller bandwidth resulted in less uncertainty for the estimation of the suggested model, according to the uncertainty analysis.