Abstract
Accurate selection of a best-fit probability distribution function for rainfall data is crucial in hydrological studies and plays a fundamental role in the planning and design of infrastructure for the city of Almaty. This study presents a comprehensive statistical and probabilistic assessment of extreme precipitation in the city of Almaty, Kazakhstan, based on annual maximum precipitation data from five meteorological stations for the period 2000–2023. Given the complex mountainous terrain and distinct seasonal precipitation regimes, selecting an appropriate distribution is particularly critical for modeling design rainfall and flood risks. The reliability of the rainfall data was verified through tests for independence and stationarity. Five theoretical probability distributions – exponential, generalized extreme value, normal, lognormal, and gamma – were evaluated using the maximum likelihood estimation method. The best-fit distribution was determined using the chi-square goodness-of-fit test. The results indicate that the generalized extreme value distribution provides the best fit for most stations, followed by the lognormal and gamma distributions, confirming its robustness in representing extreme precipitation in mountainous urban environments such as Almaty. Furthermore, spatial variability and increasing intensity of extreme rainfall events were observed, especially during the warm season. Design rainfall estimates were calculated for various exceedance probabilities (e.g., 1%, 2%, and 10%), corresponding to return periods of 100, 50, and 10 years, respectively. These findings are critical for flood risk assessment and the development of climate-resilient urban drainage systems, highlighting the broader applicability of this distribution-fitting methodology in regions exposed to hydrological extremes.