## 2 Materials and Methods
The flow in the channel is considered one-dimensional (although purely one-dimensional flows do not exist in nature). In reality, a distinction is made between flows in the channel and on the floodplain. On the floodplain, the flow is more complex than in the channel and is more difficult to describe. Most often, the role of floodplains in the propagation of a flood wave consists of the accumulation of additional volume with weak water exchange between its individual parts. Usually, rivers are modeled on a scale that allows for an enlarged, rough schematization of floodplains. If it is necessary to represent floodplain details with greater accuracy, physical modeling is used or two-dimensional modeling is used. The hydrodynamic modeling presented in this study is based on the one-dimensional Saint-Venant equations. These equations are fundamental in hydraulic engineering for simulating unsteady open-channel flows and describe the conservation of mass (continuity equation) and momentum for gradually varied flow conditions. The continuity equation ensures that the total volume of water is conserved along the river, while the momentum equation accounts for the balance of forces acting on the flow, such as gravity, pressure, and channel resistance. These physical principles allow the equations to capture how water moves and changes depth over time and distance. The Saint-Venant equations provide a reliable mathematical basis for predicting water levels, flow velocities, and flood inundation extents in riverine environments [27; 28]. In this study, the Saint-Venant equations were applied using the MIKE 11 software environment, which implements numerical solutions based on finite difference schemes. By applying the Saint-Venant equations, the aim was to provide accurate flood hazard assessments that can inform flood risk management and emergency response planning for the East Kazakhstan region. To justify the choice of simulation tools, a comparison of commonly used hydrodynamic modeling software packages was conducted (Table 2). At the initial stage of this study, both HEC-RAS 5.0.5 and MIKE 11 were considered. HEC-RAS was used for exploratory simulations to evaluate basic hydraulic behavior and boundary conditions. However, all final hydrodynamic simulations, flood mapping, and result analyses presented in this study were performed using the MIKE 11 software. The decision to proceed with MIKE \(11\) was made due to its superior flexibility, numerical stability, and integration capabilities with remote sensing and GIS data, which were essential for the complex floodplain conditions of the Kurchum River basin. MIKE was selected as the most suitable tool for this study due to its advanced capabilities for simulating complex river-floodplain systems, strong integration with GIS and remote sensing data, a user-friendly interface, and proven accuracy in similar applications. This choice ensures high precision and flexibility in modeling flood dynamics under the specific conditions of the East Kazakhstan region. The study examines an analytical module designed to calculate the degree of flooding of territories in the event of hydrodynamic disasters that occur as a result of emergency breakthroughs. Such events are characterized by rapid flooding of the area as a result of the formation of a breakthrough wave. The size and consequences of these accidents largely depend on many factors, including the parameters and condition of hydraulic structures; the nature and scale of dam failures; the volume of water in reservoirs; the characteristics of the breakthrough wave and flood; terrains; as well as time factors, such as the season and time of day [29]. The main destructive agents in catastrophic flooding are the breakthrough wave, determined by the height and speed of movement, as well as the duration of the flood. A breakthrough wave is a powerful flow of water formed by a sudden discharge of water from an upper level to a lower one, which causes its overflow and the formation of a high and fast-moving wave with destructive force.