Bivariate Modeling of Hydroclimatic Variables in Humid Tropical Coastal Region Using Archimedean Copulas

Abstract

The present study focuses on the dependence modeling of hydroclimatic variables such as the El Niño–Southern Oscillation (ENSO) index, precipitation, tidal height, and groundwater level (GWL) in humid tropical coastal region of India. The rank-based correlation coefficient was used to determine the dependence between the pairs of cumulative monsoon precipitation of June–July–August–September (P_JJAS) and the postmonsoon groundwater level (PMGWL), ENSO–P_JJAS, ENSO–PMGWL, and GWL–tidal height. The results indicated that P_JJAS–PMGWL, ENSO–PMGWL, and GWL–tidal height had significant dependence, whereas P_JJAS–ENSO had no significant dependence. The best fit distributions for P_JJAS, PMGWL, and tidal height were found to be lognormal, extreme value, and generalized extreme value distributions, respectively, whereas for the ENSO index, it was the normal kernel-density function. The Archimedean families of copulas were used for dependence modeling, and it was observed that the ENSO–PMGWL was best modeled by the Frank copula, the P_JJAS–PMGWL by the Gumbel-Hougaard copula, and the GWL–tidal height by the Frank copula. The copula-based conditional probability for the Gumbel-Hougaard and Frank copulas for GWL were obtained to understand the risk associated with other hydroclimatic variables. Thus, copula-based dependence modeling could be useful for understanding the risk among hydroclimatic variables including groundwater.