Том 50, № 4 (2023)

The article formulates the main requirements to numerical algorithms for hydrodynamic 2D-modeling of long and very long river segments with lengths of up to several thousand kilometers. The main feature is the use of adaptive unstructured mesh along with algorithms that give correct values of water surface elevations on coarse mesh, taking into account abrupt changes of bed elevations. A hydrodynamic model of a segment of the Amur R. with a total length of >3 thous. km is presented, which is based on a numerical solution of two-dimensional shallow-water equations (Saint-Venant) by a new high-accuracy algorithm, taking into account road and protection structures in the floodplain. The stages of model construction and verification are described, and the results of calculations for an extraordinary flood in 2013 and a high flood in 2020 are given. Water levels (with estimates of their errors) and the rates of water discharge at gages are given along with flow fields and the inundation zones of floodplain areas.

The flood cycle model FCM is a lumped conceptual water-balance model designed to simulate rain runoff at a scale of a small river basin. The development of the FCM model includes the description of the dynamics of the major components of the total moisture reserves of a basin and reproduces the effect of spatial expansion of the drainage network through temporary surface and subsurface streams during extraordinary floods. The accepted conceptual assumptions of the model, which are in agreement with the rational hydrological considerations, lead to three runoff-formation regimes, referred to as intravolume, surface and breakthrough. The concept and algorithms of FCM are given in detail.

A procedure for calculating various characteristics of snow cover formation, based on the use of the land surface model SWAP, was tested on field areas of the European Russia for a historical period (1967−2019). The comparison of simulation results with observation data showed the good quality of snow water equivalent reproduction at these objects. Variations of the climatic values of snow cover formation characteristics in the historical period were analyzed, revealing trends in changes of these characteristic in field areas in the period under consideration.

The ECOMAG hydrological model was used to evaluate runoff characteristics in the basins of the major rivers in European Russia: the Volga, Don, Northern Dvina, Pechora, and Kuban. The models of runoff formation for various hydrometric gauging stations in these basins were calibrated using data of weather station observations. Next, the input data were represented by the data of an ensemble of global climate models for assessing the regional hydrometeorological regime at the realization of a scenario of global warming by 1.5 and 2°C in the XXI century relative to the preindustrial values. The reproduction of the annual and seasonal runoff by data of climatic models was evaluated by comparison with observation data. According to the results of numerical experiments at global warming by 1.5 and 2°C, the values of the relative changes in river runoff in European Russia increase from N to S and from E to W, i.e., the hydrological systems under milder climate were found to be more sensitive to changes in the meteorological characteristics. The estimation of runoff anomalies in the European Russia showed the following common features: an increase in the winter runoff in the northern rivers and in the Volga basin, a decrease in the spring snowmelt runoff in the Northern Dvina, Volga, and Don, a decrease in the summer–autumn runoff of all studied rivers with various intensity. In this case, the annual runoff of the Pechora will show a positive trend, and that of the Northern Dvina, Volga, Don, and Kuban, a negative trend.

The water resources of the North Caucasus depend mostly on the state of glaciers, which have been intensely losing their mass in the recent decades against the background of climate changes. The deglaciation leads not only to a decrease in the glacier runoff of mountain rivers, but also to changes in the annual distribution of runoff. The focus of this study is the adaptation of ECOMAG software complex to simulating river runoff in the Baksan River basin based on data on the relief and underlying surface of the drainage basin (soil, vegetation) and daily data on the surface air temperature, air saturation deficit, and precipitation. The calibration and validation of the model and the statistical estimate of calculation efficiency were based on the data on water discharges in the Baksan River over 2000–2017. The developed model of runoff formation in the Baksan River basin was used to carry out numerical experiments for assessing the sensitivity of runoff characteristics to glacier area variations. Depending on the rate of deglaciation process, the runoff of the Baksan River can drop by 10–30% because of a decrease in its glacial component, and the maximal water discharges can drop by 10–15%.

A semi-distributed physical-mathematical model ECOMAG-HM is used to simulate the genetic structure of water and chemical runoff of copper, zinc, and manganese in a large river basin of the Nizhnekamsk Reservoir. The model was tested against long-term data of hydrological and hydrochemical monitoring of water bodies. The contributions of the surface, soil, and subsoil components of the water and chemical runoff of metals are estimated for different segments of river network. It was found that, in the major portion of the catchment, river pollution by metals is mostly due to their diffuse washout from the soil layer. The effect of the genetic structure of water and chemical runoff on the year-to-year and seasonal variations of metal concentrations in the river network is demonstrated.