Drought modeling using classic time series and hybrid wavelet-gene expression programming models

•SPEI droughts at three time scales were modeled at six stations located in the Ankara, Turkey.•The linear AR and non-linear BL were used as the time series-based models.•The hybrid W-GEP models were proposed using five different mother wavelets.•The non-linear BL slightly presented better performance than the linear AR.•The hybrid W-GEP models showed superiority over the standalone GEP ones. The standardized precipitation evapotranspiration index (SPEI) at three different time scales (i.e., SPEI-3, SPEI-6, and SPEI-12) from six meteorology stations located in Turkey are modeled in this study. To this end, two types of classic time series models, namely linear autoregressive (AR) and non-linear bi-linear (BL) are used. Furthermore, the hybrid models are proposed by coupling the wavelet (W) and gene expression programming (GEP). Five various mother wavelets (i.e., Haar, db4, Symlet, Meyer, and Coifflet), for the first time, are employed and compared for implementing the hybrid W-GEP approach in drought modeling. The modeling results of SPEI droughts via the time series models illustrated that the non-linear BL performs slightly better than the linear AR. Moreover, all the hybrid W-GEP models developed in the study region provide superior performances compared to the standalone GEP. In general, db4 in SPEI-3 modeling and Symlet for modeling the SPEI-6 and SPEI-12 of the studied locations are the optimal wavelets to develop the W-GEP. Finally, the SPEI series at each target station is modeled through applying the SPEI data of the five neighboring stations. It is found that the SPEI data of neighboring stations are appropriate for modeling the SPEI series of the target station when the SPEI data of the target station is not at hand. For this case, the performance of standalone GEP for modeling the SPEI-3 and SPEI-6 of the stations is generally better than the case of utilizing the original SPEI data at each target station.