Copula-based multivariate methods in hydroclimatic applications: avoiding common misconceptions and pitfalls.

For most hydroclimatic applications, precipitation and temperature are of particular interest for modeling purposes and future projections. Both variables strongly affect the water cycle, they can easily be measured and have the benefit of typically being readily available from many meteorological stations worldwide. In order to account for precipitation and temperature variability, their interdependence and their physical correlation, several multivariate analysis methods have been adopted in the hydroclimatic literature in recent years. In fact, the total number of papers published per year has nearly doubled from roughly 300 per year in 2010 to nearly 600 per year in 2018. In line with this increasing use of multivariate methods, the notion of Copula-based probability distribution has also attracted tremendous interest to deal with the complexity of compound events in the multidimensional pool. A Copula is a function that connects a multivariate distribution to its one-dimensional margins. The Copula concept is particularly advantageous, because it allows for a joint distribution of random variables with great flexibility for the marginal distribution and because it takes into account the dependence structure of these variables. However, there seems to be a lack of comprehensive understanding of the fundamental requirements of the Copula concept such as the strength and dependability of correlation between variables, autocorrelation effects and the choice of representative Copula families, which potentially compromises the accuracy of projections of future environmental processes and natural hazards.

Therefore, we bring forward a step-by-step guide on Copula-based modeling for hydroclimatic variables such as temperature and precipitation, which (1) provides end-users with an overview of necessary requirements, statistical assumptions and consequential limitations of Copulas, and (2) offers clear guidelines on how to implement Copulas. Based on a systematic literature, we also discuss common pitfalls and misconceptions using a specific hydroclimatic case study in Sweden and provide a Copula modeling framework to support researchers and decision makers in addressing climatological hazards and sustainable development.