Copulas for hydroclimatic analysis: A practice‐oriented overview

Abstract

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. This article is categorized under: Science of Water > Hydrological Processes Science of Water > Methods

Asymmetric Dependence in Hydrological Extremes

“…In climate science, the study of compound extremes has attracted increasing attention in recent years. Also here, mostly symmetric coefficients are used for model assessment (Boulaguiem et al., 2022; Dupuis, 2007; Tootoonchi et al., 2022) or clustering methods (Vignotto et al., 2021; Zscheischler et al., 2021).…”

On the compounding of nitrate loads and discharge

“…Early applications of copulas in hydrology primarily concerned flood frequency analysis (e.g., De Michele & Salvadori, 2003; Favre et al., 2004). Since then, bivariate copulas have gone on to account for spatial correlations of extremes at neighboring sites (e.g., Bender et al., 2016), been used in stochastic design storm generators (e.g., Kim et al., 2022; Vandenberghe et al., 2010) among other applications encompassing a variety of hydroclimatic variables (Tootoonchi et al., 2022). A flurry of recent studies chose copulas to model the joint probabilities of co‐occurring high freshwater fluxes (rainfall/river discharge) and high sea levels (e.g., Wahl et al., 2015); this is motivated by impactful events such as Hurricane Sandy (2012) and Hurricane Harvey (2017), where the interaction of these drivers likely exacerbated flooding.…”

Drought hazards and stakeholder perception: Unraveling the interlinkages between drought severity, perceived impacts, preparedness and management

“…We here computed both univariate and multivariate empirical return periods for observed March-August precipitation deficits and annual summer temperature anomalies over the period 1961-2020, following the methodology described in the Supplementary Information, section S4.3). The multivariate approach using bivariate copulas (Tootoonchi et al 2022) better reflects the compound risk of warm temperatures (high evaporation) and low precipitation (Agha-Kouchak et al 2015a).…”