Stochastic forecasting of drought indices

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 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 chapter is to provide two methodologies for the seasonal forecasting of SPI. In the first methodology, the transition probabilities from a current drought condition to another in the future, and from a single value of current SPI to a drought class are derived as functions of the statistics of the underlying monthly precipitation process. The proposed analytical approach appears particularly valuable from a practical stand point in light of the difficulties of applying a frequency approach or a Markov chain approach, due to the limited number of transitions generally observed even on relatively long SPI records. In the second methodology, SPI forecasts at a generic time horizon M are analytically determined, in terms of conditional expectation, as a function of a finite number of past values of monthly precipitation. Forecasting accuracy is estimated through an expression of the Mean Square Error, which enables to derive confidence intervals of prediction. Validation of the derived expressions is carried out by comparing theoretical forecasts and observed SPI values. The methodologies have been applied to the series of SPI, based on monthly precipitation observed in Sicily over 40 rain gauges in the period 1921-2003. Results seem to confirm the reliability of the proposed methodologies, which therefore can find useful application within a drought monitoring system.