Article Sidebar
Main Article Content
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.
Article Details
BES Media. (2025, 2 March). Ocherednoy liven zatopil ulitsy Almaty: livnevyye kanalizatsii, kak obychno, ne spravlyayutsya s potokom vody. BES.media. https://bes.media/news/ocherednoy-liven-zatopil-ulitsi-almati-livnyovki-kak-vsegda-ne-spravlyayutsya-696088/
Blom, G. (1958). Statistical estimates and transformed beta-variables. Wiley.
Burnham, K. P., & Anderson, D. R. (2002). Model selection and multimodel inference: A practical information-theoretic approach. Springer. https://doi.org/10.1007/b97636
Chegodayev, L. (1955). Raspolozheniye elementov na grafike dlya raboty po teorii veroyatnostey. Gidrometeoizdat.
Cho, H. K., Bowman, K. P., & North, G. R. (2004). A comparison of gamma and lognormal distributions for characterizing satellite rain rates from the tropical rainfall measuring mission. Journal of Applied Meteorology, 43(11), 1586–1597. https://doi.org/10.1175/JAM2165.1
Choudhary, K., & Kumar, R. (2025). An analysis of stormwater management with the Internet of Things (IoT). Nature Environment and Pollution Technology, 24(3), B4271. https://doi.org/10.46488/NEPT.2025.v24i03.B4271
Coles, S. (2001). An introduction to statistical modeling of extreme values. Springer. https://doi.org/10.1007/978-1-4471-3675-0
Cunnane, C. (1978). Unbiased plotting positions – A review. Journal of Hydrology, 37(3‒4), 205‒222. https://doi.org/10.1016/0022-1694(78)90017-3
D’iya, S. G., Gasim, M. B., Toriman, M. E., & Abdullahi, M. G. (2014). Floods in Malaysia: Historical reviews, causes, effects and mitigations approach. International Journal of Interdisciplinary Research and Innovations, 2(4), 59–65. https://www.researchpublish.com/upload/book/FLOODS%20IN%20MALAYSIA-760.pdf
Dong, X., Jiang, L., Zeng, S. H., Guo, R., & Zeng, Y. (2020). Vulnerability of urban water infrastructures to climate change at city level. Resources, Conservation and Recycling, 161, 104918. https://doi.org/10.1016/j.resconrec.2020.104918
Duskayev, K., Mussina, A., Rodrigo-Ilarri, J., Zhanabayeva, Z., Tursyngali, M., & Rodrigo-Clavero, M. E. (2023). Study of temporal changes in the hydrographic network of small mountain rivers in the Ile Alatau, Kazakhstan. Hydrology Research, 54(11), 1420‒1431. https://doi.org/10.2166/nh.2023.305
Gentilucci, M., Rossi, A., Pelagagge, N., Aringoli, D., Barbieri, M., & Pambianchi, G. (2023). GEV analysis of extreme rainfall: Comparing different time intervals to analyse model response in terms of return levels in the study area of central Italy. Sustainability, 15(15), 11656. https://doi.org/10.3390/su151511656
Hazen, A. (1914). Storage to be provided in impounding reservoirs for municipal water supply. Transactions of the American Society of Civil Engineers, 77(1), 1539–1640. https://doi.org/10.1061/taceat.0002563
Jayawardane, J. M. P. M., Rajapakse, R. L. H. L., & Siriwardana, C. S. A. (2024). Urban flood assessment targeting flood risk mitigation: A case study focusing on changing environments. In H. R. Pasindu, H. Damruwan, P. Weerasinghe, L. Fernando & C. Rajapakse (Eds.), Proceedings of Civil Engineering Research Symposium 2024 (pp. 13‒14). Department of Civil Engineering, University of Moratuwa. https://doi.org/10.31705/CERS.2024.7
Katz, R. W., Parlange, M. B., & Naveau, P. (2002). Statistics of extremes in hydrology. Advances in Water Resources, 25(8–12), 1287–1304. https://doi.org/10.1016/S0309-1708(02)00056-8
Kreienkamp, F., Philip, S. Y., Tradowsky, J. S., Kew, S. F., Lorenz, P., Arrighi, J., Belleflamme, A., Bettmann, T., Caluwaerts, S., Chan, S. C., Ciavarella, A., De Cruz, L., Demuth, N., Ferrone, A., Fischer, E. M., Fowler, H. J., Goergen, K., Heinrich, D., Henrichs, Y., … Wanders, N. (2021). Rapid attribution of heavy rainfall events leading to the severe flooding in Western Europe during July 2021. World Weather Attribution Project. https://www.worldweatherattribution.org/wp-content/uploads/Scientific-report-Western-Europe-floods-2021-attribution.pdf
Kundzewicz, Z. W., Kanae, S., Seneviratne, S. I., Handmer, J., Nicholls, N., Peduzzi, P., Mechler, R., Bouwer, L. M., Arnell, N., Mach, K., Muir-Wood, R., Brakenridge, G. R., Kron, W., Benito, G., Honda, Y., Takahashi, K., & Sherstyukov, B. (2013). Flood risk and climate change: Global and regional perspectives. Hydrological Sciences Journal, 59(1), 1–28. https://doi.org/10.1080/02626667.2013.857411
Kyrgyzbay, K., Kakimzhanov, Y., & Sagin, J. (2023). Climate data verification for assessing climate change in the Almaty region of the Republic of Kazakhstan. Climate Services, 32, 100423. https://doi.org/10.1016/j.cliser.2023.100423
Latif, M., Syed, F. S., & Hannachi, A. (2017). Rainfall trends in the South Asian summer monsoon and its related large-scale dynamics with focus over Pakistan. Climate Dynamics, 48(11), 3565‒3581. https://doi.org/10.1007/s00382-016-3284-3
Ling, Z., Jing, Y., Aqeel, M., Siddiqa, F., Yan, L., & Wenlong, M. (2025). Urban Flood Modeling and Mitigation Strategies Using Remote Sensing and GIS. Scholars Journal of Engineering and Technology, 13(7), 535‒551. https://doi.org/10.36347/sjet.2025.v13i07.007
Mirlas, V., Zhakyp, A., Auelkhan, Y., & Anker, Y. (2024). Assessment of urbanization-related groundwater flooding process via Visual MODFLOW modeling: A case study for the northern part of Almaty city, Kazakhstan. Journal of Flood Risk Management, 18(1), e13029. https://doi.org/10.1111/jfr3.13029
Montes Pajuelo, R., Rodríguez Pérez, Á. M., López, R., & Rodríguez, C. A. (2024). Analysis of probability distributions for modelling extreme rainfall events and detecting climate change: Insights from Mathematical and Statistical Methods. Mathematics, 12(7), 1093. https://doi.org/10.3390/math12071093
Muhammad Iskandar, M. F., Ibrahim, A., Mohtar, Z. A., Pakir Mohamed Latif, M. F., & EM Yahaya, N. K. (2025). Assessing rainfall trends and variability in a climate change. ESTEEM Academic Journal, 21, 91‒105. https://doi.org/10.24191/esteem.v21iMarch.4892.g3087
Nakispekova, A. (2024). Kazakhstan unites in response to flood crisis. The Astana Times. Bringing Kazakhstan to the World. https://astanatimes.com/2024/04/kazakhstan-unites-in-response-to-flood-crisis/
Pietras, B., & Pyrc, R. (2025). Extreme short-duration rainfall and urban flood hazard: Case studies of convective events in Warsaw and Zamość, Poland. Water, 17(18), 2671. https://doi.org/10.3390/w17182671
Republic State Enterprise Kazhydromet. (2025, October 2). Weather forecast. https://www.kazhydromet.kz/ru/
Rima, L., Haddad, K., & Rahman, A. (2025). Generalised Additive Model-Based Regional Flood Frequency Analysis: Parameter Regression Technique Using Generalised Extreme Value Distribution. Water, 17(2), 206. https://doi.org/10.3390/w17020206
Stedinger, J. R., Vogel, R. M., & Foufoula-Georgiou, E. (1993). Frequency analysis of extreme events. In D. R. Maidment (Ed.), Handbook of Hydrology (pp. 18.1‒18.66). McGraw-Hill.
Tukey, J. W. (1962). The future of data analysis. In Breakthroughs in Statistics: Methodology and Distribution (pp. 408‒452). Springer. https://doi.org/10.1007/978-1-4612-4380-9_31
Weibull, W. (1939). A statistical theory of the strength of materials. Generalstabens Litografiska Anstalts Förlag.
Wilks, D. S. (Ed.) (2011). Statistical methods in the atmospheric sciences. Academic Press.
World Meteorological Organization [WMO]. (1989). Calculation of Monthly and Annual 30-year Standard Normals (WMO/TD-No. 341). World Meteorological Organization. https://posmet.ufv.br/wp-content/uploads/2017/04/MET-481-WMO-341.pdf
World Meteorological Organization [WMO]. (2009). Manual on estimation of Probable Maximum Precipitation (PMP). World Meteorological Organization. https://library.wmo.int/records/item/35708-manual-on-estimation-of-probable-maximum-precipitation-pmp?offset=2
World Meteorological Organization [WMO]. (2017). WMO Guidelines on the Calculation of Climate Normals (WMO-No. 1203). World Meteorological Organization. https://www.agroorbi.pt/livroagrometeorologia/DocsProg/Temas&Exerc%C3%ADciosExtraPorCap%C3%ADtulo/Cap1_Introdu%C3%A7%C3%A3o/Docs/WMO%20Guidelines%20on%20the%20Calculation%20of%20Climate%20Normals_en.pdf
Downloads
- Wojciech Ciężkowski, Magdalena Frąk, Ignacy Kardel, Marcin Kościelny, Jarosław Chormański, Long-term water quality monitoring using Sentinel-2 data, Głuszyńskie Lake case study , Scientific Review Engineering and Environmental Sciences (SREES): Vol. 31 No. 4 (2022)
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.