Copula-based joint distribution modelling of precipitation, temperature and humidity events in the assessments of agricultural risks, with a case study in Morocco

The agriculture sector is profoundly impacted by the abiotic stresses in arid or semi-arid regions that experience extreme weather patterns related to temperature (T), precipitation (P), humidity (H), and other factors. This study adopts a flexible approach that incorporates the D-vine copula density to analyze trivariate (and bivariate) joint and conditional hazard risk. The methodology was applied to a case study in the Ait Ben Yacoub region of Morocco. Monthly series for T, H, and P were modeled using the Weibull-2P and Weibull-3P models, selected based on fitness statistics. The survival BB8 copula was best described as joint dependence for pair T–P, rotated BB8 270 degrees copula for T–H, while rotated Joe 270 degrees copula for P–H. The analysis of joint probability stress focused on both primary joint scenarios (for OR and AND-hazard conditions) and conditional return periods (RPs) for trivariate and bivariate case. Lower univariate RPs resulted in higher marginal quantiles for T and lower for H and P events. Lower trivariate (and bivariate) AND-joint RPs (or higher concurrence probabilities) were associated with higher T with lower P and H quantiles. The occurrence of trivariate (and bivariate) events was less frequent in the AND-joint case compared to the OR-joint case. The conditional joint RP of T (or T with P, or T with H) was significantly affected by different P (at 10th and 25th percentile) and H (at 5th and 25th percentile) (or P, or H) conditions. Lower conditional RPs of T (or T with H, or T with P) had resulted at given low P and H (or low P, or low H levels). In conclusion, the estimated risk statistics are vital for the study region, highlighting the need for effective adaptation and resilience planning in agriculture crop management.