Interdependence between temperature and precipitation: modeling using copula method toward climate protection

In this study, copula analysis was used to eventually fill the void of the negligence of interdependence of two climate variables (temperature and precipitation). Copulas are powerful tools to model the joint distribution of two or more variables simultaneously by preserving their dependence structure. The data for monthly average temperature °C and precipitation (mm) were collected. The analyzed results indicated that a weak positive 0.233 but highly significant (0.000) correlation existed between the variables. It was also found that every 1 °C increased in temperature was associated with a 0.684 mm increase in precipitation. A scattered plot indicates a non-linear dependence structure between the variables. Generalized Pareto (GP) and Exponential distributions were selected as variables distributions for temperature and precipitation, respectively. Two Elliptical (Gaussian, Student’s t) and three Archimedean (Gumbel, Clayton, and Frank) copulas were applied to evaluate the nature of interdependence between the variables. Based on different information criteria, the Gumbel copula was identified as the best-fitted copula. The selected copula showed that extreme positive temperature and precipitation had a higher correlation (right tail dependence) as compared to their lower values. Conclusively, copula was found to be a very effective tool for bivariate modeling of drought and flood risks i.e., extreme temperature and precipitation.