The Dynamics of Shannon Entropy in Climate Variability Analysis: Application of the Clayton Copula for Modeling Temperature and Precipitation Uncertainty in Poland (1901–2010)

In this study, we analyze the long-term climate dynamics in Poland (1901–2010), using Shannon entropy as a measure of uncertainty and complexity in the atmospheric system. We focus on the monthly distributions of precipitation and temperature, modeled using a bivariate Clayton copula with a normal marginal distribution for temperature and a gamma distribution for precipitation. The correctness of the selected distributions was confirmed by the Anderson-Darling test. The conducted analysis reveals distinct trends in entropy values, indicating an increase in climate instability, which may lead to a higher frequency of extreme weather events. Nonparametric tests enabled the identification of key patterns and potential critical points in the evolution of climate variables. The structure of entropy variability was described in phase space using an attractor, revealing both periodic and chaotic components in climate dynamics. The obtained results highlight the increasing complexity of the climate system and suggest that Shannon entropy can be an effective tool not only for analyzing historical trends but also for forecasting future climate variability. This study confirms that climate is a nonlinear, dynamic system susceptible to chaotic fluctuations, which has crucial implications for modeling and predicting extreme weather conditions.