Modeling extreme meteorological droughts from paleo-climatic reconstructions using a metastatistical framework

The vulnerability of large areas to drought events emphasizes the importance of a reliable probability analysis of drought events. A drought is notoriously considered as one of the most complex natural phenomenon, which, more than other natural hazards, remains difficult to quantitatively model due to the difficulty of sampling a sufficient number of events in the historical record. In fact, due to the persistence and often long interarrival times between droughts, occurring on time scales of years to decades or more, very long observational time series are necessary to study their statistical properties. It is indeed rare that such a large amount of observational information, at appropriate space-time resolutions and consistency, are available in practical applications.

One possible approach to overcome this problem relies on the use of proxy climatic data to extend the instrumental record. Additionally, since relatively few drought events occur even within records of several hundred years, techniques which optimally use available information, such as the metastatistical framework, may be highly beneficial in these analyses.

Motivated by the above considerations, this work exploits a publicly available tree-ring based Old World Drought Atlas (OWDA; Cook et., 2015), a reconstruction of the June–August self-calibrating Palmer Drought Severity Index (sc-PDSI), to model the stochastic nature of the drought characteristics. To gain a quantitative understanding of how well tree ring-based data capture drought occurrences, we compare the sc-PDSI computed with direct observations of precipitation and temperature, with those obtained from tree-ring proxies. Furthermore, we characterize drought events and their properties using the statistical “theory of runs”. We then explore the potential of the Metastatistical Extreme Value Distribution (MEVD) to estimate the probability of occurrence of drought events and compare its performance with that obtained by the use of traditional approaches. A cross-validation scheme, dividing the available data into independent calibration and test sub-sample, is used to quantify the estimation uncertainty associated with different sample sizes and estimation methods.

The analysis of extreme droughts in two case studies in Italy suggests that the MEVD-based formulations are more robust and flexible approaches with respect to traditional ones. The comparative analysis of the predictive estimation uncertainty is site-specific, but MEVD estimates outperform, in terms of bias and uncertainty, traditional GEV estimates.

The analyses also (1) confirm the usefulness of the paleoclimate reconstructions for improving the robustness of the statistical study of extreme droughts, and (2) highlight that the metastatistical formulations allow estimations of probability of intense droughts even when observational length is too short to apply traditional methods.