Evaluation of Six Types of Stochastic Models Skill in Modeling and Forecasting the Standardized Precipitation Index Time Series

Drought is a temporary and recurring meteorological event, which originates from the lack of precipitation relative to its long-term average. Since drought forecasting has a critical role in water resources management, in this study, six types of stochastic models (AR, MA, ARMA, non-seasonal ARIMA, seasonal ARIMA and multiplicative ARIMA) skill in modeling and forecasting the Standardized Precipitation Index (SPI) time series was evaluated. For reaching this purpose, the monthly total precipitation data related to ten synoptic stations with hyper humid to very dry climates (1973-2007) were used. At first, by transferring the optimum distribution cumulative probability of precipitation to cumulative probability distribution of standard normal, the SPI values in three time scales of 3, 6 and 12 months were calculated. Then, the development of models was done on SPI values related to period of 1973 to 2000, over a multi stage process (Identification, Parameter estimation, Diagnostic check) and the most appropriate stochastic model was determined for each time series from the candidate models. In order to validate the chosen models, at first, one to twelve lead times ahead forecasting was done for period of 2001 to 2007.Then, the values and the classes of the observed and the forecasted SPI were compared. The results of evaluating the models accuracy in forecasting the SPI values over chosen stations showed that in one month lead time ahead drought forecasting, over 3-month time scale, the stochastic model of Bushehr station (r=0.70, RMSE= 0.66) and over 6 and 12-month time scales, the stochastic model of Hamedan Nojeh station (6-month time scale: r=0.84, RMSE=0.41; 12-month time scale: r=0.93, RMSE=0.30) have the most accuracy comparing with stochastic model of other stations. Moreover, the forecasting error decreases with increasing the time scale and the forecasting accuracy decreases with increasing the lead time. The results of evaluating the models accuracy in forecasting the SPI classes based on Kappa statistic (K), showed that the maximum agreement of the observed and the forecasted classes for one lead time ahead forecasting, about 3, 6 and 12-month time scales is related to Bushehr (K=0.46), Gorgan (K=0.66) and Zahedan (K=0.81), respectively. Moreover, the agreement of the observed and the forecasted classes increases with increasing the time scale and the agreement of the observed and the forecasted classes decreases with increasing the lead time.