Joint probability of compound hot and dry events using the concepts of copulas

Compound hot and dry events represent a major class of climate extremes with substantial impacts on ecosystems, agriculture, and water resources. Their occurrence is driven not only by individual extremes in temperature and precipitation, but also by the structural dependence between these variables. Traditional approaches often rely on univariate statistics or simple threshold analyses, which may fail to capture the joint behavior of temperature and precipitation during extreme events. In this study, we applied copula-based methods to quantify the joint probability of compound hot and dry events across multiple meteorological stations in Poland.

We analyzed long-term observational records (1966-2025) of temperature and precipitation during the warm season. Hot and dry conditions were defined using percentile-based thresholds derived from the full observational period to ensure consistent comparison across time. The dependence between temperature and precipitation was modeled using bivariate copulas, with particular attention given to tail behavior relevant for extreme conditions. Model selection was performed using information criteria and goodness-of-fit statistics, and the selected copulas were subsequently used to estimate joint probabilities and return periods of compound events. To assess potential temporal changes, the dataset was divided into two sub-periods: 1966-1995 and 1996-2025. The comparison of joint probabilities between these periods provides insight into possible shifts in the frequency of compound hot and dry events. Additionally, spatial variability across stations was examined to identify regional differences in both dependence structure and event likelihood.

Preliminary results indicate clear spatial variability in the joint probability of compound hot and dry events across Poland, with some regions exhibiting consistently higher likelihoods than others. The dependence between temperature and precipitation is predominantly negative, reflecting the tendency for high-temperature conditions to co-occur with reduced precipitation. In most locations, the dependence structure suggests stronger association in the upper tail, highlighting an increased likelihood of concurrent extreme conditions rather than independent occurrences of hot and dry events. An analysis of the two sub-periods indicates that the joint probability of hot and dry periods occurring simultaneously has increased over the last thirty years.

Acknowledgements: Funding for this research was provided by the National Science Centre, Poland under project no. 2023/51/B/ST10/01926.