Copulas for hydroclimatic analysis: A practice-oriented overview

A warming climate is associated with increasing hydroclimatic extremes, which are often interconnected through complex processes, prompting their concurrence and/or succession, and causing compound extreme events. It is critical to analyze the risks of compound events, given their disproportionately high adverse impacts. To account for the variability in two or more hydroclimatic variables (e.g., temperature and precipitation) and their dependence, a rising number of publications focuses on multivariate analysis, among which the notion of copula-based probability distribution has attracted tremendous interest. Copula is a mathematical function that expresses the joint cumulative probability distribution of multiple variables. Our focus is to re-emphasize the fundamental requirements and limitations of applying copulas. Confusion about these requirements may lead to misconceptions and pitfalls, which can potentially compromise the robustness of risk analyses for environmental processes and natural hazards. We conducted a systematic literature review of copulas, as a prominent tool in the arsenal of multivariate methods used for compound event analysis, and underpinned them with a hydroclimatic case study in Sweden to illustrate a practical approach to copula-based modeling. Here, we (1) provide end-users with a didactic overview of necessary requirements, statistical assumptions and consequential limitations of copulas, (2) synthesize common perceptions and practices, and (3) offer a user-friendly decision support framework to employ copulas, thereby support researchers and practitioners in addressing hydroclimatic hazards, hence demystify what can be an area of confusion.