28 Jun 2023
 | 28 Jun 2023

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

Carmelo Cammalleri, Carlo De Michele, and Andrea Toreti

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.

Carmelo Cammalleri et al.

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • CC1: 'Comment on egusphere-2023-1318', Francesco Serinaldi, 29 Jun 2023
    • AC1: 'Reply on CC1', Carmelo Cammalleri, 15 Sep 2023
  • RC1: 'Comment on egusphere-2023-1318', Anonymous Referee #1, 27 Jul 2023
    • AC2: 'Reply on RC1', Carmelo Cammalleri, 15 Sep 2023
  • RC2: 'Comment on egusphere-2023-1318', Anonymous Referee #2, 30 Jul 2023
    • AC3: 'Reply on RC2', Carmelo Cammalleri, 15 Sep 2023

Carmelo Cammalleri et al.

Carmelo Cammalleri et al.


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Short summary
Precipitation and soil moisture have the potential to be jointly used for the modelling of drought conditions. In this research, we analysed how their statistical inter-relationship varies across Europe. We found some clear spatial patterns, especially in the so-called tail dependence (which measures the strength of the relationship for the extreme values). The results suggest that the tail-dependence needs to be accounted to correctly assess the value of a joint modelling for drought.