Unlike other natural disasters, drought events evolve slowly in time and their impacts generally span a long period of time. Such features do make possible a more effective drought mitigation of the most adverse effects, provided a timely monitoring of an incoming drought is available. Among the several proposed drought monitoring indices, the Standardized Precipitation Index (SPI) has found widespread application for describing and comparing droughts among different time periods and regions with different climatic conditions. However, limited efforts have been made to analyze the role of the SPI for drought forecasting. The aim of the paper is to provide two methodologies for the seasonal forecasting of SPI, under the hypothesis of uncorrelated and normally distributed monthly precipitation aggregated at various time scales k. In the first methodology, the auto-covariance matrix of SPI values is analytically derived, as a function of the statistics of the underlying monthly precipitation process, in order to compute the transition probabilities from a current drought condition to another in the future. The proposed analytical approach appears particularly valuable from a practical stand point in light of the difficulties of applying a frequency approach due to the limited number of transitions generally observed even on relatively long SPI records. Also, an analysis of the applicability of a Markov chain model has revealed the inadequacy of such an approach, since it leads to significant errors in the transition probability as shown in the paper. In the second methodology, SPI forecasts at a generic time horizon M are analytically determined, in terms of conditional expectation, as a function of past values of monthly precipitation. Forecasting accuracy is estimated through an expression of the Mean Square Error, which allows one to derive confidence intervals of prediction. Validation of the derived expressions is carried out by comparing theoretical forecasts and observed SPI values by means of a moving window technique. Results seem to confirm the reliability of the proposed methodologies, which therefore can find useful application within a drought monitoring system.
