Mathematical model of mudflow breakthrough, taking into account the decrease in the volume of water in the reservoir

Over the past 15 years, Kazakhstan has experienced numerous devastating floods and mudflows, which have resulted in human casualties and significant economic damage. In particular, events in the Almaty region (2010), the Karaganda region (2014), and the northern and western regions (2024) highlighted the need to create effective monitoring systems for hydraulic structures. The purpose of this work is to determine the parameters of the mathematical model describing the breakthroughs of debris flows through hydraulic structures such as dams and weirs. Achieving this goal will allow us to correlate the developed model with real observations and data. This paper presents a forecasting system capable of assessing the consequences of mudflows. The developed system is based on mathematical modeling methods. Unlike analogues, the proposed model takes into account both the parameters of the reservoir and the features of the river bed. To implement the system in practice, software was created in Python. The experiments showed that the model reliably reflects real conditions and can be successfully applied in various scenarios.