Droughts are among the most frequently observed catastrophic weather and climate phenomena, exerting profound impacts on agriculture, water resources and ecosystem services. In this study, we focus exclusively on drought assessment in Poland by developing and validating a comprehensive, multidimensional framework. We analyze two widely used single‐variable indices—the Standardized Precipitation Index (SPI) and the Standardized Precipitation Evapotranspiration Index (SPEI)—into our more general models to ensure comparability with existing approaches [1].
Stochastic models describing severity and duration
In the random‐vector modeling component, we propose a two‐dimensional model that simultaneously tracks drought severity, and duration. By leveraging the copula theorem, our framework overcomes limitations in the dependence structure of drought‐index trajectories, allowing us to capture their joint behavior more accurately. We fitted the resulting distribution to long‐term precipitation records from multiple IMGW‐PIB stations across Poland, and benchmarked its performance against classical models from the literature [2]. Difference in our approach is in the construction of dependence structure – we introduce it through Gumbel Copula. Also, instead of geometric distribution of droughts duration, we propose a 1-inflated modification, which is a mixture of a geometric distribution with additional probability of obtaining value 1. Our results show that, although still imperfect, the proposed model consistently yields a tighter fit and better reproduces extreme events than comparable literature‐based approaches.
Spatial modelling of drought phases transitions
For spatial modeling, we applied both local and spatial Markov chains [3] to clusters of meteorological stations identified via K-Means clustering on their index time series. Despite using only drought‐index values, the clustering produced geographically coherent regions of similar drought behavior. The Markov‐chain framework then quantified transition probabilities within and between these clusters, revealing spatial dependencies and propagation patterns of drought across the stations.
Further research will include more precipitation stations – we will try to achieve sort of uniform spread of them across the territory of Poland. Also, we will focus on extensions of our stochastic model, with possibilities of multi-region multidimensional modelling.
Literature
[1] Ishfaq A., Touqeer A., Shafique U. R., Ibrahim M. A., Alshahrani F. (2024), A detailed study on quantification and modeling of drought characteristics using different copula families. Heliyon, Vol. 10, https://doi.org/10.1016/j.heliyon.2024.e25422.
[2] Arendarczyk, Marek & Kozubowski, Tomasz & Panorska, Anna. (2018). The joint distribution of the sum and maximum of dependent Pareto risks. Journal of Multivariate Analysis, Vol. 167. https://doi.org/10.1016/j.jmva.2018.04.002
[3] Santos F. J., Calvo-Pulido I., Portela M. (2010), Spatial and temporal variability of droughts in Portugal. Water Resources Research, Vol. 46. https://doi.org/10.1029/2009WR008071
By Maciej Ostapiuk (Wrocław University of Science and Technology)