Development of wavelet-based Kalman Online Sequential Extreme Learning Machine optimized with Boruta-Random Forest for drought index forecasting

Abstract

Drought is a stochastic and recurring hydrological natural hazard that occurs due to a shortage of precipitation over a period of time. Drought forecasting in water resources systems has an important role in reducing devastating ecological and social impacts. However, due to the fluctuating nature of drought indicator time series, their forecasting on a short time scale without advanced pre-processing is extremely challenging, and little research has been presented in this field. In this study, a new complementary machine learning (ML) approach, Kalman filter regression-based Online Sequential Extreme Learning Machine and (KOSELM) coupled with the Boundary Corrected Maximal Overlap Discrete Wavelet Transform (BC-MODWT-KOSELM), was implemented for forecasting one-month/three-month ahead Standardized Precipitation Evapotranspiration Index (i.e., SPEI 12 and SPEI 24). Here, the Kalman filter regression was employed to optimize the hyper-parameters of the Online Sequential Extreme Learning Machine (OSELM). Precipitation and potential evapotranspiration data from Bandar Abbas (warm semi-humid climate) and Rasmar (humid climate) synoptic stations, Iran were used in the analysis for a period of (1987–2019). In order to validate the BC-MODWT-KOSELM model, it was compared with two other well-known ML approaches, classical Extreme Learning Machine (ELM) and Generalized Regression Neural Network (GRNN) in both standalone and BC-MODWT-based complementary frameworks (i.e., BC-MODWT-ELM and BC-MODWT-GRNN). First, the original time series of the benchmark drought index was decomposed into the wavelet and scaling coefficients based on three mother wavelets and different decomposition levels. Afterward, the most significant lags were extracted using the Boruta-random forest (B-RF) feature selection. The BC-MODWT-KOSELM was identified as the superior forecasting model for SPEI 12 (t ＋ 1) with R = 0.9511 and RMSE = 0.3318; for SPEI 12 (t ＋ 3) with R = 0.8171 and RMSE = 0.6168; for SPEI 24 (t ＋ 1) with R = 0.9710 and RMSE = 0.2156; for SPEI 24 (t ＋ 3) with R = 0.9014 and RMSE = 0.3937 in the Bandar Abbas station. Besides, the BC-MODWT-KOSELM outperformed the comparative counterpart model for SPEI 12 (t ＋ 1 with R = 0.9401 and RMSE = 0.3371; SPEI 12 (t ＋ 3) with R = 0.8266 and RMSE = 0.5723; for SPEI 24 (t ＋ 1) with R = 0.9640 and RMSE = 0.2974; for SPEI 24 (t ＋ 3) with R = 0.9063 and RMSE = 0.4874 in the Ramsar station.