Analyzing Compound Extremes in Hydrology: A Multivariate Approach Using Correlated Time Series

Traditional hydrologic design has focused on using annual maximum values. However, numerous significant hydrologic events such as active and break spells during monsoons, heat waves, and flash floods from snowmelt occur over days to weeks. These events require daily or even finer resolution data for accurate characterization. Often, impactful events result from multiple hydrologic variables exhibiting extreme behaviour concurrently - known as compound extremes - leading to different occurrence probabilities and impacts than  those extreme events identified through univariate analyses. Characterizing these extreme events is challenging due to the need for the joint consideration of multiple variables. This study introduces a novel multivariate approach using a time-varying interval-censored estimation method for copula models. This method enables the determination of design magnitudes and associated risks with compound extremes when hydrologic data exhibit (i) strong dependence, and (ii) significant ties. The method's effectiveness is demonstrated in the Godavari River Basin, India, using daily precipitation and temperature data over the monsoon seasons between 1977 and 2020. A conservative approach is recommended for estimating design magnitudes in multivariate contexts. The study examines the importance of ties and temporal dependence between precipitation and temperature data in estimating the design magnitudes of cold-wet compound extremes at specified exceedance probabilities across various spatial scales. The results show that ties and temporal dependence significantly affect design estimates. Since these characteristics are common in hydrologic data, this framework is broadly applicable for characterizing other compound extremes in hydrology.