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Markov chain and 3-dimensional log-linear models were attempted to model drought class transitions derived from the newly developed drought index the Standardized Precipitation Evapotranspiration Index (SPEI) at a 12 month time scale for six major drought prone areas of India. Log-linear modelling approach has been used to investigate differences relative to drought class transitions using SPEI-12 time series derived form 48 yeas monthly rainfall and temperature data. In this study, the probabilities of drought class transition, the mean residence time, the 1, 2 or 3 months ahead prediction of average transition time between drought classes and the drought severity class have been derived. Seasonality of precipitation has been derived for non-homogeneous Markov chains which could be used to explain the effect of the potential retreat of drought. Quasi-association and Quasi-symmetry log-linear models have been fitted to the drought class transitions derived from SPEI-12 time series. The estimates of odds along with their confidence intervals were obtained to explain the progression of drought and estimation of drought class transition probabilities. For initial months as the drought severity increases the calculated odds shows lower value and the odds decreases for the succeeding months. This indicates that the ratio of expected frequencies of occurrence of transition from drought class to the non-drought class decreases as compared to transition to any drought class when the drought severity of the present class increases. From 3-dimensional log-linear model it is clear that during the last 24 years the drought probability has increased for almost all the six regions. The findings from the present study will immensely help to assess the impact of drought on the gross primary production and to develop future contingent planning in similar regions worldwide.

A log-linear modelling for 3-dimensional contingency tables was used with categorical time series of SPI drought class transitions for prediction of monthly drought severity. Standardized Precipitation Index (SPI) time series in 12- and 6-month time scales were computed for 10 precipitation time series relative to GPCC datasets with 2.5° spatial resolution located over Portugal and with 112 years length (1902–2014). The aim was modelling two-month step class transitions for the wet and dry seasons of the year and then obtain probability ratios – Odds – as well as their respective confidence intervals to estimate how probable a transition is compared to another. The prediction results produced by the modelling applied to wet and dry season separately, for the 6- and the 12-month SPI time scale, were compared with the results produced by the same modelling without the split, using skill scores computed for the entire time series length. Results point to good prediction performances ranging from 70 to 80% in the percentage of corrects (PC) and 50–70% in the Heidke skill score (HSS), with the highest scores obtained when the modelling is applied to the SPI12. The adding up of the wet and dry seasons introduced in the modelling brought improvements in the predictions, of about 0.9–4% in the PC and 1.3–6.8% in the HSS, being the highest improvements obtained in the SPI6 application.

Adequately analyzing and modeling the extreme rainfall events is of great importance because of the effects that their magnitude and frequency can have on human life, agricultural productivity and economic aspects, among others. A single extreme event may affect several locations, and their spatial dependence has to be appropriately taken into account. Classical geostatistics is a well-developed field for dealing with location referenced data, but it is largely based on Gaussian processes and distributions, that are not appropriate for extremes. In this paper, an exploratory study of the annual maximum of monthly precipitation recorded in the northern area of Portugal from 1941 to 2006 at 32 locations is performed. The aim of this paper is to apply max-stable processes, a natural extension of multivariate extremes to the spatial set-up, to briefly describe the models considered and to estimate the required parameters to simulate prediction maps.