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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.

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.

This work was partially supported by the research project PTDC/AGR-AAM/71649/2006 - Droughts Risk Management: Identification, Monitoring, Characterization, Prediction and Mitigation as well as by CMA/FCT/UNL under the project PEst-OE/MAT/UI0297/2011. Long time series (95 to 135 yr) of the 12-month time scale Standardized Precipitation Index (SPI) relative to 10 locations across Portugal were studied with the aim of investigating if drought frequency and severity are changing through time. Considering four drought severity classes, time series of drought class transitions were computed and later divided into several sub-periods according to the length of SPI time series. Drought class transitions were calculated to form a 2-dimensional contingency table for each sub-period, which refer to the number of transitions among drought severity classes. Two-dimensional log-linear models were fitted to these contingency tables and an ANOVA-like inference was then performed in order to investigate differences relative to drought class transitions among those sub-periods, which were considered as treatments of only one factor. The application of ANOVA-like inference to these data allowed to compare the sub-periods in terms of probabilities of transition between drought classes, which were used to detect a possible trend in droughts frequency and severity. Results for a number of locations show some similarity between alternate sub-periods and differences between consecutive ones regarding the persistency of severe/extreme and sometimes moderate droughts. In global terms, results do not support the assumption of a trend for progressive aggravation of drought occurrence during the last century, but rather suggest the existence of long duration cycles. publishersversion published

In this study, drought in Portugal was assessed using 74 time series of Standardized Precipitation Index (SPI) with a 12-month timescale and 66 years length. A clustering analysis on the SPI Principal Components loadings was performed in order to find regions where SPI drought characteristics are similar. A Fourier analysis was then applied to the SPI time series considering one SPI value per year relative to every month. The analysis focused on the December SPI time series grouped in each of the three identified clusters to investigate the existence of cycles that could be related to the return periods of droughts. The most frequent significant cycles in each of the three clusters were identified and analysed for December and the other months. Results for December show that drought periodicities vary among the three clusters, pointing to a 6-year cycle across the country and a 9.4-year cycle in central and southern Portugal. Both these cycles likely show the influence of the North Atlantic Oscillation (NAO) on the occurrence and severity of droughts in Portugal. Relative to other months it was observed that cycles varied according to the common occurrence of precipitation: for the rainy months – November, December and January – cycles are similar to those for December; for the dry months – May to September – where the lack of precipitation masks the occurrence of drought, the dominant cycles are of short duration and cannot be related to the NAO or other large circulation indices to explain drought variability; for the transition months – February, March, April and October – 6-year and 3-year cycles were identified, the latter being more strongly apparent in central and southern Portugal. NAO influence is again identified relative to the 6-year cycles. The short cycles are apparently associated with positive SPI, thus with wetness, not drought. Overall, results confirm the importance of the NAO as a driving force for dry and wet periods.

This study aims at predicting the Standard Precipitation Index (SPI) drought class transitions in Portugal, considering the influence of the North Atlantic Oscillation (NAO) as one of the main large-scale atmospheric drivers of precipitation and drought fields across the Western European and Mediterranean areas. Log-linear modeling of the drought class transition probabilities on three temporal steps (dimensions) was used in an SPI time series of six- and 12-month time scales (SPI6 and SPI12) obtained from Global Precipitation Climatology Centre (GPCC) precipitation datasets with 1.0 degree of spatial resolution for 10 grid points over Portugal and a length of 112 years (1902–2014). The aim was to model two monthly transitions of SPI drought classes under the influence of the NAO index in its negative and positive phase in order to obtain improvements in the predictions relative to the modeling not including the NAO index. The ratios (odds ratio) between transitional probabilities and their confidence intervals were computed in order to estimate the probability of one drought class transition over another. The prediction results produced by the model with the forcing of NAO were compared with the results produced by the same model without that forcing, using skill scores computed for the entire time series length. Overall results have shown good prediction performance, ranging from 73% to 76% in the percentage of corrects (PC) and 56%–62% in the Heidke skill score (HSS) regarding the SPI6 application and ranging from 82% to 85% in the PC and 72%–76% in the HSS for the SPI12 application. The model with the NAO forcing led to improvements in predictions of about 1%–6% (PC) and 1%–8% (HSS), when applied to SPI6, but regarding SPI12 only seven of the locations presented slight improvements of about 0.4%–1.8% (PC) and 0.7%–3% (HSS).

A total period of 67 years of standardized precipitation index (SPI) data sets were divided into three periods of 22/23 years and a loglinear modeling approach has been used to investigate differences relative to drought class transitions among these three periods. The study was applied to several locations in Alentejo region, southern Portugal, and four drought severity classes were considered. The drought class transitions were computed for the three periods to form a 3-dimensional contingency table. The application of loglinear modeling to these data allowed the comparison of the three periods in terms of probabilities of transition between drought classes in order to detect a possible trend in time evolution of droughts which could be related to climate change. Results show that the drought behavior for the first and last periods is similar, both showing worse drought events than the second. If just the second and third periods were compared one could conclude that droughts were aggravating and easily this behavior could be attributed to climate change, supporting the common assumption that a trend for progressive aggravation of drought occurrence exists. Therefore, results are more consistent with the existence of a long-term natural periodicity; however, this hypothesis should be tested using longer time series.

SFRH/BPD/99757/2014 This work was partially supported by the projects IMDROFLOOD-Improving Drought and Flood Early Warning, Forecasting and Mitigation using real-time hydroclimatic indicators (WaterJPI/0004/2014) and project UID/MAT/00297/2013 (Centro de Matematica e Aplicacoes), both funded by funded by Fundacao para a Ciencia e a Tecnologia, Portugal (FCT). Ana Russo thanks also FCT by the Post-Doc research grant SFRH/BPD/99757/2014. Drought class transitions over a sector of Eastern Europe were modeled using log-linear models. These drought class transitions were computed from time series of two widely used multiscale drought indices, the Standardized Preipitation Evapotranspiration Index (SPEI) and the Standardized Precipitation Index (SPI), with temporal scales of 6 and 12 months for 15 points selected from a grid over the Prut basin in Romania over a period of 112 years (1902-2014). The modeling also took into account the impact of North Atlantic Oscillation (NAO), exploring the potential influence of this large-scale atmospheric driver on the climate of the Prut region. To assess the probability of transition among different drought classes we computed their odds and the corresponding confidence intervals. To evaluate the predictive capabilities of the modeling, skill scores were computed and used for comparison against benchmark models, namely using persistence forecasts or modeling without the influence of the NAO index. The main results indicate that the log-linear modeling performs consistently better than the persistence forecast, and the highest improvements obtained in the skill scores with the introduction of the NAO predictor in the modeling are obtained when modeling the extended winter months of the SPEI6 and SPI12. The improvements are however not impressive, ranging between 4.7 and 6.8 for the SPEI6 and between 4.1 and 10.1 for the SPI12, in terms of the Heidke skill score. publishersversion published

SPI time series in a 12 month time scale from 6 sites in Alentejo and Algarve, in the south of Portugal, within the period from October 1896 to September 2005, were divided into three or four periods depending on the data set length and a Loglinear modeling approach has been used to investigate differences relative to drought class transitions among these periods. Four drought severity classes were considered. The drought class transitions were computed for the different periods to form a 3-dimensional contingency table. The application of Loglinear modeling to these data allowed the comparison of the periods in terms of probabilities of transition between drought classes in order to detect a possible trend in time evolution of droughts which could be related to climate change