# Modeling the Territorial Structure Dynamics of the Northern Part of the Volga-Akhtuba Floodplain

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^{†}

## Abstract

**:**

## 1. Introduction

## 2. Numerical Modeling of the Hydrological Regime of the Floodplain Area

#### 2.1. Geoinformation Modeling

#### 2.2. Single-Layer Shallow Water Model

#### 2.3. Multilayer Numerical Model of the Floodplain Hydrological Regime

- Water level rise in the Volga River by 6–10 m due to ${Q}^{\left(m\right)}$ growth by 4–5 times.
- An increase in the rate of water discharge into the Akhtuba River ${Q}_{A}\left(t\right)$, which repeats the typical form of the dependence ${Q}^{\left(m\right)}\left(t\right)$ (see Figure 2).
- Outflow of water from the Akhtuba River through large main canals with subsequent filling of medium and further small channels, which ensures flooding of the interfluve plain. This way of water movement gives about 70% of the volume and area of flooding.
- The direct outlet of water to the floodplain from the left bank of the Volga River through local relief depressions and small channels is responsible for about 30% of flooding.

## 3. Modeling the Floodplain Territorial Structure: Methods, Instruments and Technology Research

## 4. Results of Modeling the Dynamics of the ESES Territorial Structure for the Northern Part of the Volga-Akhtuba Floodplain

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**The Volga-Akhtuba floodplain is located in the Lower Volga region from Volgograd City to the Caspian Sea and the length of the interfluve is about 450 km (Google Map images).

**Figure 2.**Examples of a flood discharge function (hydrograph) of the VHPS $Q\left(t\right)$ in different periods of its operation: (

**a**) 1961–1980; (

**b**) 1981–2000; (

**c**) 2001–2021, inset shows a model of so-called two-stage hydrograph ${Q}^{\left(m\right)}\left(t\right)$, typical for the last 20 years. Such a model hydrograph is determined by a set of parameters for the following stages: (1) high constant water discharge ${Q}_{1}^{\left(m\right)}$ with duration ${\mathsf{\Theta}}_{1}$ during spring flood; (2) lower level ${Q}_{2}^{\left(m\right)}$ with duration ${\mathsf{\Theta}}_{2}$ during spring flood; (3) low water level ${Q}_{low}^{\left(m\right)}$.

**Figure 4.**(

**a**) DEM of the northern part of the VAF, 50 km by 60 km. Elevations are shown in the Shaded Relief Map model. Bottom: (

**b**) DEM fragment highlighted with a yellow line on the main DEM (

**a**,

**c**) corresponding map of this zone (Google/Landsat-8 image). Long small channels are well traced in the interfluve of the Volga and Akhtuba rivers.

**Figure 5.**DEM of the northern part of the Volga-Akhtuba floodplain and its environs. The vertical scale differs from the plane-scale (the elevation level within the Volgograd city boundary is $50\xf7100$ m higher compared to the floodplain area). The blue color shows the water distribution from our numerical simulations.

**Figure 7.**Geometric scheme of a single-layer model of shallow water. The main river channel is directed along the y-coordinate. The terrain height $b(x,y)$ depends on coordinates and does not depend on time. The water level is $\xi =b+H$ (H is the depth of the liquid).

**Figure 8.**Geometric scheme of the three-layer model, including surface water, sediment and groundwater. The solid and dashed lines show the bottom profiles b for two different times ${t}_{1}$ and ${t}_{2}$. The red color indicates the position of the waterproof layer, which is the groundwater bed.

**Figure 10.**The modern $\mathcal{FN}$-structure of the VAF: 1—ecological territories, 2—economic territories, 3—social territories, 4—territories with an uncertain cadastral type.

**Figure 11.**Virtual values, density and distribution function of the first stage parameters of the flood hydrograph through the VHPS for 1962–2021. The orange line shows the linear regression of ${Q}_{1}^{\left(m\right)}\left({\theta}_{1}\right)$.

**Figure 12.**(

**a**) Dependences of the values and confidence intervals of the hydrograph parameters for the Volgograd HPP at the first stage on T for 1962–2021; (

**b**) coefficients of lognormal distributions of the normalized volume of flood waters; (

**c**) examples of frequency distributions for $T=30$.

**Figure 13.**Relative total areas of 12 types of modern territorial $\mathcal{HF}\mathcal{N}$-structure for the northern part of the VAF.

**Figure 15.**Retrospective (1991–2021) and forecast (2022–2050) dynamics of the area of stable flooded territory in the interfluve.

**Figure 16.**Retrospective (1991–2021) and forecast (2022–2050) dynamics of ESES at $\epsilon =0.1$ and ${n}_{1}=0.85$.

**Figure 17.**(

**a**) Variability of the parameters of the lognormal distribution of the values of the relative volume of the flood hydrograph through the dam for different 30-year intervals. The color indicates the range of one standard deviation. (

**b**) Limiting lognormal distributions of the actual volumes of flood hydrographs for 1962–2021.

**Figure 19.**Forecast map of stable flooding of the VAF. The blue color shows the Intersection stable area, while the red color highlights the difference between the intersection stable area and the union stable area.

**Figure 21.**The area that will lose its flooding stability in the period 2022–2050 according to our forecast.

**Table 1.**Kinds and types of the main elements of the $\mathcal{F}$-structure of the floodplain territory and characteristic functions of the criteria of state.

Kind and Type of Element of $\mathcal{F}$-Structure | Social Criterion | Environmental Criterion | Economic Criterion | |
---|---|---|---|---|

1 | Wetlands (ecological type) | ${f}_{1}\left(n\right)$ | ${f}_{1}\left(n\right)$ | ${f}_{1}\left(n\right)$ |

2 | Water meadows (economic type) | ${f}_{1}\left(n\right)$ | ${f}_{1}\left(n\right)$ | ${f}_{1}\left(n\right)$ |

3 | Forests (ecological type) | ${f}_{2}\left(n\right)$ | ${f}_{2}\left(n\right)$ | ${f}_{2}\left(n\right)$ |

4 | Recreational areas (social type) | ${f}_{2}\left(n\right)$ | 0 | 0 |

5 | Urbanized zones (social type) | ${f}_{3}\left(n\right)$ | 0 | 0 |

6 | Economic zones, including zones of irrigated agriculture (economic type) | 0 | 0 | ${f}_{4}\left(n\right)$ |

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**MDPI and ACS Style**

Isaeva, I.I.; Voronin, A.A.; Khoperskov, A.V.; Kharitonov, M.A.
Modeling the Territorial Structure Dynamics of the Northern Part of the Volga-Akhtuba Floodplain. *Computation* **2022**, *10*, 62.
https://doi.org/10.3390/computation10040062

**AMA Style**

Isaeva II, Voronin AA, Khoperskov AV, Kharitonov MA.
Modeling the Territorial Structure Dynamics of the Northern Part of the Volga-Akhtuba Floodplain. *Computation*. 2022; 10(4):62.
https://doi.org/10.3390/computation10040062

**Chicago/Turabian Style**

Isaeva, Inessa I., Alexander A. Voronin, Alexander V. Khoperskov, and Mikhail A. Kharitonov.
2022. "Modeling the Territorial Structure Dynamics of the Northern Part of the Volga-Akhtuba Floodplain" *Computation* 10, no. 4: 62.
https://doi.org/10.3390/computation10040062