Calculating return periods and design quantiles in a multivariate environment is a difficult problem: this paper tries to make the issue clear. First, we outline a possible way to introduce a consistent theoretical framework for the calculation of the return period in a multi-dimensional environment, based on Copulas and the Kendall's measure. Secondly, we introduce several approaches for the identification of suitable design events: these latter quantities are of utmost importance in practical applications, but their calculation is yet limited, due to the lack of an adequate theoretical environment where to embed the problem. Throughout the paper, a case study involving the behavior of a dam is used to illustrate the new concepts outlined in this work.

Compound weather and climate events are combinations of climate drivers and/or hazards that contribute to societal or environmental risk. Studying compound events often requires a multidisciplinary approach combining domain knowledge of the underlying processes with, for example, statistical methods and climate model outputs. Recently, to aid the development of research on compound events, four compound event types were introduced, namely (a) preconditioned, (b) multivariate, (c) temporally compounding, and (d) spatially compounding events. However, guidelines on how to study these types of events are still lacking. Here, we consider four case studies, each associated with a specific event type and a research question, to illustrate how the key elements of compound events (e.g., analytical tools and relevant physical effects) can be identified. These case studies show that (a) impacts on crops from hot and dry summers can be exacerbated by preconditioning effects of dry and bright springs. (b) Assessing compound coastal flooding in Perth (Australia) requires considering the dynamics of a non‐stationary multivariate process. For instance, future mean sea‐level rise will lead to the emergence of concurrent coastal and fluvial extremes, enhancing compound flooding risk. (c) In Portugal, deep‐landslides are often caused by temporal clusters of moderate precipitation events. Finally, (d) crop yield failures in France and Germany are strongly correlated, threatening European food security through spatially compounding effects. These analyses allow for identifying general recommendations for studying compound events. Overall, our insights can serve as a blueprint for compound event analysis across disciplines and sectors.

Key Points: New consistent and well‐founded definition of Multivariate Return Period Easy‐to‐use formulas for performing Multivariate design and risk assessment The new approach is so general that all hydrological sciences may benefit of it