Developing Short Term Drought Severity-Duration-Frequency Curves for Kerala Meteorological Subdivision, India Using Bivariate Copulas

Abstract

Severity-duration-frequency (S-D-F) curve is a useful hydrological tool for drought mitigation. This paper presents a bivariate copula approach for developing SDF relationships for Kerala meteorological subdivision, India based on the three month standardized precipitation index (SPI-3). First the univariate models were developed considering Gamma and Weibull distributions to represent the probability of severity and duration of SPI-3 series of the subdivision prepared from the area weighted precipitation data. The joint association of these drought variables is modeled by three Archimedean copulas namely Clayton, Frank and Gumbel- Hougaard (GH). The results showed that the difference between the joint SDF relations with the type of copulas is marginal upto return period 100 (~) whereas the conditional dependency of drought variables showed distinct differences. The conditional SDF relationships between severity and return period showed larger differences for longer duration and the behaviour is identical in the relationships between duration and return period for conditional severity values. Further, to outline the spatial variability of short term drought, a detailed examination on SDF relations of different districts in Kerala is made by considering representative fine resolution gridded rainfall (0.25o × 0.25o) datasets. SDF relationships of different locations in Kerala showed a shorter duration drought of less severity magnitude is prominent in districts like Wayanad, Kottayam and Pathanamthitta. The highest value of equilibrium severity for longer drought duration for all return periods is noticed for Palakkad while lowest value is observed for the district of Wayanad, which are the two low rainfall regions of the subdivision.