Drought forecasting using the Standardized Precipitation Index

Unlike other natural disasters, drought events evolve slowly in time and theirimpacts generally span a long period of time. Such features do make possible a more effectivedrought mitigation of the most adverse effects, provided a timely monitoring of an incomingdrought is available.Among the several proposed drought monitoring indices, the Standardized PrecipitationIndex (SPI) has found widespread application for describing and comparing droughts amongdifferent time periods and regions with different climatic conditions. However, limited effortshave 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 ofSPI, under the hypothesis of uncorrelated and normally distributed monthly precipitationaggregated at various time scales k. In the first methodology, the auto-covariance matrix ofSPI values is analytically derived, as a function of the statistics of the underlying monthlyprecipitation process, in order to compute the transition probabilities from a current droughtcondition to another in the future. The proposed analytical approach appears particularlyvaluable from a practical stand point in light of the difficulties of applying a frequencyapproach due to the limited number of transitions generally observed even on relatively longSPI records. Also, an analysis of the applicability of a Markov chain model has revealed theinadequacy of such an approach, since it leads to significant errors in the transition probabilityas shown in the paper. In the second methodology, SPI forecasts at a generic time horizon Mare analytically determined, in terms of conditional expectation, as a function of past valuesof monthly precipitation. Forecasting accuracy is estimated through an expression of theMean Square Error, which allows one to derive confidence intervals of prediction. Validationof the derived expressions is carried out by comparing theoretical forecasts and observed SPIvalues by means of a moving window technique. Results seem to confirm the reliability ofthe proposed methodologies, which therefore can find useful application within a droughtmonitoring system.