Analysis of Drought Severity and Duration Using Copulas in Anuradhapura, Sri Lanka

Anuradhapura district is one of the largest agricultural crop production areas in Sri Lanka. But it is often affected by droughts and droughts caused severe damage for agricultural industry. Thus it is very important to identify the drought characteristics (drought duration and drought severity) and their joint probability distribution to minimize the adverse effects of droughts. Drought characteristics were defined using 3-month standard precipitation index (SPI). It is calculated using monthly rainfall data from 1951 to 2007 in Anuradhapura. Occurrences of 46 drought events were indentified using the calculated SPI.
Since dependency nature of the drought variables, copula based joint distribution was used to calculate the joint distribution. The joint distribution could be obtained by combining the marginal distributions using copula. Five copulas were examined and compared to find the best fitted copula to represent the joint distribution. The best marginal distributions were identified as the gamma distributions for drought durations and drought severity using AIC, BIC and Kolmogorov-Smirnov test. Frank copula was identified as the best copula based on AIC, BIC and Cramer-Von Mises statistics. The joint distribution was derived combining the gamma distributions using the Frank copula. The univariate and joint returns periods of droughts were calculated.
A drought event occurred in 1974 was identified as a major drought event. Drought duration and severity in 1974 were 9 months and 10.95 respectively. Using the indentified univariate and multivariate return periods, drought risks could be minimized by pre-planning and making decision against adverse effects.