A gene–wavelet model for long lead time drought forecasting Ali Danandeh Mehr ⇑ , Ercan Kahya 1 , Mehmet Özger 2 Istanbul Technical University, Civil Engineering Department, Hydraulics Division, 34469 Maslak, Istanbul, Turkey article info Article history: Received 3 January 2014 Received in revised form 9 April 2014 Accepted 10 June 2014 Available online 19 June 2014 This manuscript was handled by Andras Bardossy, Editor-in-Chief, with the assistance of Purna Chandra Nayak, Associate Editor Keywords: Drought forecasting Linear genetic programing Wavelet transform El Niño–Southern Oscillation Palmer’s modified drought index Hydrologic models summary Drought forecasting is an essential ingredient for drought risk and sustainable water resources manage- ment. Due to increasing water demand and looming climate change, precise drought forecasting models have recently been receiving much attention. Beginning with a brief discussion of different drought fore- casting models, this study presents a new hybrid gene–wavelet model, namely wavelet–linear genetic programing (WLGP), for long lead-time drought forecasting. The idea of WLGP is to detect and optimize the number of significant spectral bands of predictors in order to forecast the original predictand (drought index) directly. Using the observed El Niño–Southern Oscillation indicator (NINO 3.4 index) and Palmer’s modified drought index (PMDI) as predictors and future PMDI as predictand, we proposed the WLGP model to forecast drought conditions in the State of Texas with 3, 6, and 12-month lead times. We compared the efficiency of the model with those of a classic linear genetic programing model developed in this study, a neuro-wavelet (WANN), and a fuzzy-wavelet (WFL) drought forecasting models formerly presented in the relevant literature. Our results demonstrated that the classic linear genetic programing model is unable to learn the non-linearity of drought phenomenon in the lead times longer than 3 months; however, the WLGP can be effectively used to forecast drought conditions having 3, 6, and 12-month lead times. Genetic-based sensitivity analysis among the input spectral bands showed that NINO 3.4 index has strong potential effect in drought forecasting of the study area with 6–12-month lead times. Ó 2014 Elsevier B.V. All rights reserved. 1. Introduction Drought forecasting is an essential ingredient in watershed management. In recent years, its importance is being intensified owing to increasing water demand and looming climate change (Mishra and Singh, 2010). The success of drought preparedness and mitigation depends upon timely information on the drought onset and propagation in time and space (Özger et al., 2012). This information may be obtained through precise drought forecasting models, which is normally generated using drought indices. Many drought forecasting models have been developed in recent years (e.g., Rao and Padmanabhan, 1984; Sen, 1990; Bogradi et al., 1994; Lohani and Loganathan, 1997; Mishra and Desai, 2005; Cancelliere et al., 2007; Modarres, 2007; Fernandez et al., 2009; Özger et al., 2012). Mishra and Singh (2011) have provided a comprehensive review on different drought forecasting approaches. In recent years, artificial intelligence (AI) techniques such as artificial neural network (ANN), fuzzy logic (FL), and genetic programing (GP) have been pronounced as a branch of computer science to model wide range of hydro-meteorological processes (Pesti et al., 1996; Whigham and Crapper, 2001; Dolling and Varas, 2002; Morid et al., 2007; Kisi and Guven, 2010; Özger et al., 2012; Nourani et al., 2013a). Successful application of fuzzy rule-based modeling for short term regional drought forecasting using two forcing inputs, El Niño–Southern Oscillation (ENSO) and large scale atmospheric circulation patterns (CP), was described by Pongracz et al. (1999). Mishra and Desai (2006) used both recursive and direct multi-step ANNs for up to 6-month LT drought forecasting and found that the recursive multi-step model is the best suited for 1 month LT. When a LT longer than 4 months was considered, the direct multi-step model outperformed the recursive multi-step models. Morid et al. (2007) developed an ANN-based drought forecasting approach with the LTs of 1–12 months using Effective Drought Index (EDI), SPI, and different combinations of past rainfalls. The results indicated that forecasts using EDI were superior to those using SPI for all LTs. Barros and Bowden (2008) applied self-organizing maps and multivariate linear regression analysis to forecast SPI at Murray-Darling Basin in Australia up to 12 months in advance. http://dx.doi.org/10.1016/j.jhydrol.2014.06.012 0022-1694/Ó 2014 Elsevier B.V. All rights reserved. ⇑ Corresponding author. Tel.: +90 553 417 8028. E-mail addresses: danandeh@itu.edu.tr (A. Danandeh Mehr), kahyae@itu.edu.tr (E. Kahya), ozgerm@itu.edu.tr (M. Özger). 1 Tel.: +90 212 2853002. 2 Tel.: +90 212 2853717. Journal of Hydrology 517 (2014) 691–699 Contents lists available at ScienceDirect Journal of Hydrology journal homepage: www.elsevier.com/locate/jhydrol