Exploring the joint probability of precipitation and soil moisture over Europe using copulas

Abstract. The joint probability of precipitation and soil moisture is here investigated over Europe with the goal to extrapolated meaningful insights on the potential joint use of these variables for the detection of agricultural droughts within a probabilistic modeling framework. The use of copulas is explored as a parametric approach often used in hydrological studies for the analysis of bivariate distributions. The analysis is performed for the period 1996–2020 on the ERA5 precipitation and LISFLOOD soil moisture datasets, both available as part of the Copernicus European Drought Observatory. The results show an overall good correlation between the empirical frequency series derived from the two datasets (Kendall’s τ = 0.42±0.1), but also clear spatial patterns in the tail-dependence derived with both non-parametric and parametric approaches. About half of the domain shows symmetric tail-dependences, well reproduced by the Student-t copula, whereas the rest of the domain is almost equally split between low and high tail-dependences (modeled with the Gumbel family of copulas). These spatial patterns are reasonably reproduced by a random forest classifier, suggesting that this outcome is not driven by chance. This study stresses how a joint use of precipitation and soil moisture for agriculture drought characterization may be more beneficial in areas with strong low tail-dependence, such as southern France, northern UK, northern Germany, and Denmark in this study, and how this behavior should be carefully considered in drought studies.