Modeling long-term rainfall-runoff time series through wavelet-weighted regularization extreme learning machine

Abstract

As one of the most critical points of Iran, Lake Urmia has always been subjected to ecosystem changes due to severe water level drops. Many basins serve to feed the lake, e.g. the Shaharchay River basin, located west of the lake. In this paper, a new learning machine named “Weighted Regularization Extreme Learning Machine (WRELM)” is integrated with the Wavelet Transform (WT) (W-WRELM) to predict runoff-precipitation amounts of the Shaharchay River basin within an 18 year period from 2000 to 2017. Using the autocorrelation function, lags affecting runoff-precipitation time series are detected, then seven models are developed for both WRELM and W-ERELM by the mentioned lags. After that, all mother wavelets are testes and the best member of their family is identified. Also, the best models for the simulation of precipitation and runoff amounts are introduced through a sensitivity analysis. These models forecast target function values with acceptable exactness and high correlation. For example, the determination coefficient (R2) and Mean Absolute Error (MAE) for the best model of W-WRELM for the estimation of precipitation amounts are obtained to be 0.962 and 0.128, respectively. Moreover, the variance accounted for (VAF) and Scatter Index (SI) for the approximation of rainfall amounts are computed to 0.919 and 0.236, separately. Analyses showed that more than half of the precipitation amounts predicted by the W-WRELM 7 model have an error of more than 10%, but this value is about 64% for the predicted runoff. The lags (t-1), (t-2) and (t-12) are detected as the influencing lags in the simulation of the precipitation amounts of the Shaharchay River basin. Furthermore, the error and uncertainty analyses are conducted on the best models and it is concluded that the performance of W-WRELM in the prediction of precipitation amounts is underestimated, while its performance in the estimation of runoff values is overestimated.