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

Abstract

Abstract. The joint probability of precipitation and soil moisture is here investigated over Europe with the goal to extrapolate meaningful insights into the potential joint use of these variables for the detection of agricultural droughts within a multivariate probabilistic modeling framework. The use of copulas is explored, being the framework often used in hydrological studies for the analysis of bivariate distributions. The analysis is performed for the period 1996–2020 on the empirical frequencies derived from 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 two standardized series (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 dependence, well reproduced by the Student's t copula, whereas the rest of the domain is almost equally split between low- and high-tail dependences (both 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 standardized precipitation and soil moisture for agriculture drought characterization may be beneficial in areas with strong low-tail dependence and how this behavior should be carefully considered in multivariate drought studies.

Optimizing Drought Assessment for Soil Moisture Deficits

“…Here, we define the in situ, observed standardized soil moisture data set as the observed Soil Moisture Index (SMI obs ). This index leverages prior research focused on standardizing soil moisture data into relative measures (Cammalleri et al, 2016(Cammalleri et al, , 2024Ravelo & Decker, 1979;Sheffield et al, 2004) by applying a beta distribution (described in greater detail below). Instead of only using the day of interest (e.g., June 1st) for each year to define the distribution, we used multiple observations centered about the day of interest to define the distribution.…”

“…The beta distribution accounts for non-Gaussian data that is bound at 0 and 1; these constraints fit the theoretical constraints of volumetric soil moisture data sets (measured as m 3 m 3 ). As such beta distributions have been used extensively to model soil moisture (e.g., Cammalleri et al, 2016;Cammalleri et al, 2024;Ravelo & Decker, 1979;Sadri et al, 2020;Sheffield et al, 2004). Using these parametrically derived probability distributions, we computed the associated parametric cumulative distribution function (CDF) associated with the observations.…”