Extreme flooding of the floodplains of large lowland rivers poses a danger to the population due to the vastness of the flooded areas. This requires the organization of safe evacuation in conditions of a shortage of temporary and transport resources due to significant differences in the moments of flooding of different spatial parts. We consider the case of a shortage of evacuation vehicles, in which the safe evacuation of the entire population to permanent evacuation points is impossible. Therefore, the evacuation is divided into two stages with the organization of temporary evacuation points on evacuation routes. Our goal is to develop a method for analyzing the minimum resource requirement for the safe evacuation of the population of floodplain territories based on a mathematical model of flood dynamics and minimizing the number of vehicles on a set of safe evacuation schedules. The core of the approach is a numerical hydrodynamic model in shallow water approximation. Modeling the hydrological regime of a real water body requires a multi-layer geoinformation model of the territory with layers of relief, channel structure, and social infrastructure. High-performance computing is performed on GPUs using CUDA. The optimization problem is a variant of the resource investment problem of scheduling theory with deadlines for completing work and is solved on the basis of a heuristic algorithm. We use the results of numerical simulation of floods for the Northern part of the Volga-Akhtuba floodplain to plot the dependence of the minimum number of vehicles that ensure the safe evacuation of the population. The minimum transport resources depend on the water discharge in the Volga river, the start of the evacuation, and the localization of temporary evacuation points. The developed algorithm constructs a set of safe evacuation schedules for the minimum allowable number of vehicles in various flood scenarios. The population evacuation schedules constructed for the Volga-Akhtuba floodplain can be used in practice for various vast river valleys.

A procedure for constructing a digital elevation model (DEM) of the northern part of the Volga-Akhtuba interfluve is described. The basis of our DEM is the elevation matrix of Shuttle Radar Topography Mission (SRTM) for which we carried out the refinement and updating of spatial data using satellite imagery, GPS data, depth measurements of the River Volga and River Akhtuba stream beds. The most important source of high-altitude data for the Volga-Akhtuba floodplain (VAF) can be the results of observations of the coastlines dynamics of small reservoirs (lakes, eriks, small channels) arising in the process of spring flooding and disappearing during lowflow periods. A set of digitized coastlines at different times of flooding can significantly improve the quality of the DEM. The method of constructing a digital elevation model includes an iterative procedure that uses the results of morphostructural analysis of the DEM and the numerical hydrodynamic simulations of the VAF flooding based on the shallow water model.

A mathematical model of the joint dynamics of shallow waters, entrained and suspended sediments is constructed, which takes into account nonlinear fluid dynamics and bottom deformations. The dynamics of shallow waters is described by the Saint-Venant equations taking into account the spatially inhomogeneous distribution of the terrain. The transport of entrained sediments is described by the Exner equation generalized to the case of an inhomogeneous distribution of the parameters of the underlying surface. The dynamics of suspended sediments is described by the transport equation, which includes convective transport by water flow and the process of diffusion of the suspension in the liquid layer. For numerical integration of the Saint-Venant, Exner equations and suspended sediment dynamics, a stable and well-tested CSPH-TVD method of the second order of accuracy is used, the parallel CUDA algorithm of which is implemented in the form of a software package «EcoGIS-Simulation» for highperformance computing on supercomputers with graphics coprocessors (GPU). The conditions for the development of a quarry of non-metallic building materials (NSM) located at the mouth of the Partridge Volozhka of the Volga-Akhtuba floodplain on the 2549–2550 km section of the Volga River are considered. To study the safety of navigation from the lower reaches of the Volga hydroelectric dam to the entrance to the VDSK, numerical hydrodynamic modeling of the dynamics of channel processes in this section of the Volga River was carried out. Based on the results of mathematical modeling of the joint dynamics of surface waters, entrained and suspended sediments in the riverbed of the Volga River, it is concluded that the development of the NSM quarry considered in the work does not significantly affect the safety of navigation both along the main ship course «The lower reaches of the Volga hydroelectric dam — VDSK» and on additional — «Volgograd zaton» and «Volozhka Partridge».

The study aims to develop effective tools for solving inverse problems of river hydrology through the joint use of hydrodynamic river flow modeling and intelligent computing based on artificial neural networks. The hydrological regime of any river system is determined by the hydraulic resistance to flow, which depends on a large number of physical factors. We have built a set of models with different hydraulic resistance input parameters. The results of hydrodynamic simulations are fitted with a series of measurements of water levels at gauging stations in the Volga River. The use of neural network with the Long Short-Term Memory architecture made it possible to calculate the optimal values of the free parameters that provide the best agreement between the observational data and the results of direct numerical simulation. Our analysis showed that the efficiency of parallelization on \(4\times\textrm{GPUs}\) is in the range of 40–50 percent when simulating flooding of river valleys, when the computational domain is approximately 20–50 percent covered with water layer.