Archimedean copulas

Precipitation as a major water cycle variable influences the occurrences and distribution of terrestrial water storage change (TWSC), evapotranspiration (ET), and river discharge (Q) of a large river basin. However, its relationship with the other water cycle variables using probabilistic dependence structure concept has not been addressed much. Furthermore, precipitation derived from gauge record is plagued by bias due to orography and under-catch. To fill these gaps, bivariate copula and precipitation derived from reanalysis and satellite data were used. In the present study, the basin-wide averages of the precipitation products APHRODITE, ERA5, and IMERG were used as predictors, whereas the areal mean of MOD16 evapotranspiration, GRACE TWSC, and gauge discharge were used as dependent variables (predictants) for the Brahmaputra basin. The bivariate Archimedean copulas were applied to all the pairs of precipitation-TWSC, precipitation-ET and precipitation-Q based on the optimal marginal distributions obtained. Using the best copula for each pair of the variables, the conditional probability was constructed to predict the predictants for different precipitation amounts (5 th , 25 th , 50 th , 75 th , and 95 th percentiles). The focus of the analysis was on two scenarios of the predictants (i.e.,≤ 5 th and ≥ 95 th percentiles). The non-exceedance conditional distribution of TWSC, ET, and Q (all predictants ≤ 5 th percentile) decreases with precipitation increase. However, the exceedance probability of the predictants (≥ 95 th percentile) increases gradually with an increase in precipitation. The results revealed that both ERA5 and IMERG precipitation data could be used to derive probabilistic measures of the water cycle variables in the absence of gauge-based precipitation.