Wavelet Packet-Genetic Programming: A New Model for Meteorological Drought Hindcasting

Abstract

This study presents developing procedures and verification of a new hybrid model, namely wavelet packet-genetic programming (WPGP) for short-term meteorological drought forecast. To this end, the multi-temporal standardized precipitation evapotranspiration index (SPEI) has been used as the drought quantifying parameter at two meteorological stations at Ankara province, Turkey. The new WPGP model comprises two main steps.  In the first step, the wavelet packet, which is a generalization of the well-known wavelet transform, is used to decompose the SPEI series into deterministic and stochastic sub-signals. Then, classic genetic programming (GP) is applied to formulate the deterministic sub-signal considering its effective lags. To characterize the stochastic component, different theoretical probability distribution functions were assessed, and the best one was selected to integrate with the GP-evolved function. The efficiency of the new model was cross-validated with the first order autoregressive (AR1), GP, and random forest (RF) models developed as the benchmarks in the present study. The results showed that the WPGP is a robust model, superior to AR1 and RF, and significantly increases the predictive accuracy of the standalone GP model.