A framework for multivariate analysis of compound extremes based on correlated hydrologic time series

While hydrologic design has primarily relied on use of annual maxima values, many events of hydrologic interest such as active and break spells in monsoonal rains, heat waves, flash flooding from snowmelt, etc. manifest at time scales of days to weeks, and require daily (or finer resolution) data for proper characterization. Often combinations of several hydrologic variables herald highly impactful events and are labelled as compound extremes. Using a time-varying interval-censored estimation method of copula models, a novel multivariate approach for dealing with compound extremes under temporal dependence amongst variables and when data contain significant ties is developed here to enable the determination of design magnitudes and associated risk. The efficacy of this method is demonstrated over the Godavari River Basin, India, using daily precipitation and temperature data from a recent period (1977 to 2020) during the monsoon season. A conservative approach is proposed for estimating the design magnitudes of hydrologic variables in multivariate settings. The significance of ties and temporal dependence amongst precipitation and temperature data in estimation of design magnitudes of cold-wet compound extremes at specified probabilities of exceedance is explored at various spatial scales. Ties and temporal dependence are both shown to have a profound influence on design estimates. Since ties and temporal variation in dependence amongst hydrologic variables are ubiquitous features of most hydrologic data, this framework would be applicable for characterization of other compound extremes in hydrology.