A Novel Approach for High-Performance Estimation of SPI Data in Drought Prediction

Drought, as a natural disaster, has significant negative consequences and directly impacts living organisms. Drought forecasting commonly relies on various drought indices, with the Standardized Precipitation Index (SPI) being widely used. In this study, we propose a novel approach to estimate SPI values at 3- and 6-month lead times with high accuracy. This novel method introduces a phase transfer entropy (pTE) technique that analyzes time-shifted data matrices and the connectivity of SPI-3 and SPI-6 data. By maximizing the information flow between these data points, the most suitable time index (t − n) for input data in forecasting models is determined. This approach, not previously explored in the literature, forms the basis for predicting SPI values effectively. Machine learning algorithms, in combination with the Tunable Q Factor Wavelet Transform (TQWT) optimized by the Grey Wolf Optimization (GWO) algorithm, are employed to predict SPI values using the identified input data. The TQWT method generates subband signals, which are then estimated using Artificial Neural Networks (ANN), Support Vector Regression (SVR), and the Gaussian Process Regression Model (GPR). To evaluate the performance of the proposed GWO-TQWT-ML models, the subband data derived from the SPI is also estimated using ANN, GPR, and SVR models with the Empirical Mode Decomposition and Variational Mode Decomposition methods. Additionally, non-preprocessed SPI data is estimated independently using ANN, GPR, and SVR models. The results demonstrate the superior performance of the pTE-GWO-TQWT-ML models over other methods. Among these models, the pTE-GWO-TQWT-GPR model stands out with the best prediction performance, surpassing both the pTE-GWO-TQWT-ANN and pTE-GWO-TQWT-SVR models. The pTE-GWO-TQWT-GPR model yielded determination coefficient (R 2 ) values for SPI-6 data as follows: 0.8039 for one-input, 0.9987 for two-input, and 0.9998 for three-input one ahead prediction, respectively; 0.9907 for two-input two ahead prediction; and 0.9722 for two-input three ahead prediction. For SPI-3 data, using the pTE-GWO-TQWT-GPR model, the R 2 values were as follows: 0.6805 for one-input, 0.9982 for two-input, 0.9996 for three-input one ahead prediction, 0.9843 for two-input two ahead prediction, 0.9535 for two-input three ahead prediction, 0.9963 for three-input two ahead prediction, and 0.9826 for three-input three ahead prediction. Overall, this study presents a robust method, the pTE-GWO-TOWT-GPR model, for the time series estimation of SPI data, enabling high-performance drought prediction.