Analysing Drought Severity and Areal Extent by 2D Archimedean Copulas

Droughts can be considered as multidimensional hazardous phenomena characterised by three attributes: severity, duration and areal extent. Conventionally, drought events are assessed for their severity, using drought indices such as SPI (Standardised Precipitation Index), RDI (Reconnaissance Drought Index), PDSI (Palmer Drought Severity Index) and many others. This approach may be extended to incorporate the modelling of an additional dimension, the duration or the areal extent. Since the marginal distributions describing these dimensions of drought are often different, no simple mixed probability distribution can be used for the bivariate frequency analysis. The copula approach seems to be sufficiently general and suitable for this type of analysis. It is the aim of this paper to analyse droughts as two-dimensional phenomena, including drought severity and areal extent. In this paper, the Gumbel-Hougaard copula from the Archimedean family is used for this two-dimensional frequency analysis. Annual data on historical droughts from Eastern Crete are analysed for their severity and areal extent, producing copula-based probability distributions, incorporating Gumbel marginal probability functions. Useful conclusions are derived for estimating the «OR» return period of drought events related to both severity and areal extent.