Resumen
Precipitation deficit can affect different natural resources such as water, soil, rivers and plants, and cause meteorological, hydrological and agricultural droughts. Multivariate drought indexes can theoretically show the severity and weakness of various drought types simultaneously. This study introduces an approach for forecasting joint deficit index (JDI) and multivariate standardized precipitation index (MSPI) by using machine?learning methods and entropy theory. JDI and MSPI were calculated for the 1?12 months? time window (JDI1?12 and MSPI1?12), using monthly precipitation data. The methods implemented for forecasting are group method of data handling (GMDH), generalized regression neural network (GRNN), least squared support vector machine (LSSVM), adaptive neuro-fuzzy inference system (ANFIS) and ANFIS optimized with three heuristic optimization algorithms, differential evolution (DE), genetic algorithm (GA) and particle swarm optimization (PSO) as meta-innovative methods (ANFIS-DE, ANFIS-GA and ANFIS-PSO). Monthly precipitation, monthly temperature and previous amounts of the index?s values were used as inputs to the models. Data from 10 synoptic stations situated in the widest climatic zone of Iran (extra arid-cold climate) were employed. Optimal model inputs were selected by gamma test and entropy theory. The evaluation results, which were given using mean absolute error (MAE), root mean squared error (RMSE) and Willmott index (WI), show that the machine learning and meta-innovative models can present acceptable forecasts of general drought?s conditions. The algorithms DE, GA and PSO, could improve the ANFIS?s performance by 39.4%, 38.7% and 22.6%, respectively. Among all the applied models, the GMDH shows the best forecasting accuracy with MAE = 0.280, RMSE = 0.374 and WI = 0.955. In addition, the models could forecast MSPI better than JDI in the majority of cases (stations). Among the two methods used to select the optimal inputs, it is difficult to select one as a better input selector, but according to the results, more attention can be paid to entropy theory in drought studies.