A procedure for constructing a digital elevation model (DEM) of the northern part of the Volga-Akhtuba inter uve is described. The basis of our DEM is the elevation matrix of Shuttle Radar Topography Mission (SRTM) for which we carried out the re nement 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 oodplain (VAF) can be the results of observations of the coastlines dynamics of small reservoirs (lakes, eriks, small channels) arising in the process of spring ooding and disappearing during lowow periods. A set of digitized coastlines at di erent times of ooding can signi cantly 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 ooding based on the shallow water model.
A high-resolution 3D topographic model for the large areas is essential to solving a variety
of applied problems in the geosciences that are associated with modeling and monitoring
the environment. The progress of computer technology and numerical methods gives us new
opportunities for modeling uid dynamics in certain territories. Such problems include storm
surges, spring oods in river valleys, ooding due to heavy rainfall [
One important research area is the creation of decision support systems (DSS) for solving
various hydrological problems, and the e ectiveness of these DSS is determined by the quality
of the applied digital elevation models (DEM) [
A quality DEM is a critical component for all these tasks [
In this paper, we describe the key stages of creating a DEM for river systems based on the synthesis of various spatial data using the example of the northern part of the Volga-Akhtuba oodplain (VAF). The Volga Hydroelectric Station controls the ow of water downstream of the Volga River and the moisture reserves for the entire oodplain. The volume ow of water through the dam is called discharge Q(t) (m3 sec 1) and it varies between Q(t) ' 4000 30000 m3 sec 1 during the year.
Important components of our methodology are the use of observational data on the dynamics of the coastlines of numerous small reservoirs in the inter uve during the spring ood and the veri cation of DTM using hydrodynamic modeling. Observations of the coastlines motions for a large number of reservoirs during the spring ooding are a source of very accurate local topography data. These water reservoirs are the results of the passage of spring water and they usually disappear in early summer. Thus, the water surface area in the territory of VAF varies strongly during a few weeks from 2-5% before ooding (low water) up to a maximum value of 20-40%, which depends on the speci c conditions in each year. In late summer, the water basin area is smaller than in the early spring period before the ood, that connected with high summer temperature and lack of rain. The coastline coincides with the contour line (isoline) of the heights' distribution with very high accuracy at each time point. Thus, the local DEM may be the result of processing the monitoring data of the coastlines dynamics for a large number of small reservoirs during the spring ood. These local DEMs are high-resolution data for the most critical areas in terms of hydrology as a part of global DEM for the northern territory of the Volga-Akhtuba oodplain (Fig. 1).
2.1. Main stages of creating DEM Figure 2 shows the general scheme for constructing a digital elevation model and highlights the most signi cant steps which we will discuss below. Our DEM is based on the height matrix bij = b(xi; yj ) for nodes of the Pulkovo 95 coordinate system with step x = y: xi = x0 + i x, [SRT M] yj = y0 + j y (i = 1; 2; :::; Nx, j = 1; 2; :::; Ny). We take the SRTM3 SRTMGL1 data bij as the initial height matrix. The professional GIS \Panorama" tools allow us to recalculate the matrix by a smaller step ( x = 15 m, 10 m, 5 m) using the weighted average interpolation in 16 directions. Such matrix b[i0j] will be called the basic digital elevation model.
The main stages of the transformation matrix b[i0j] are discussed below.
1) To clarify the model of the bottom of the Volga River and the Akhtuba River, we use
model of the Volga River and the Akhtuba River, we use Sailing Directions (shipping charts) and reservoir depth maps, and then we obtain the matrix b[i1j] after digitizing and embedding this data into the basic DEM b[i0j].
2) A unique feature of the VAF is a complex system of small channels in the inter uve (the so-called eriks), which form a hierarchical system of channels between River Akhtuba and River Volga (Fig. 3). We use the satellite images of the \RESURS-P" series and UK-DMC 2, the DigitalGlobe's satellite constellation (Google Earth services) to vectorize the linear objects of this channel system for subsequent introduction into the DEM matrix of b[i1j]. UAV images and geodesic data are an important source for clarifying the location of small channels (Fig. 5). As a result, we have the matrix b[i2j], which contains the system of small channels.
3) To update the Volga River bottom model, we use the data of the last depth measurements ranging from the Volga hydroelectric power station to the Svetly Yar settlement. These data are very sparse and after approximation to all our grid nodes we have the matrix b[i3j] with the height data of the river bed.
4) We use data on dynamics of coastlines of transient reservoirs, which are lled with water at the stage of inter uve ooding (April { May) and dry out in the summer (Figure 4). These measurements provide an additional set of lines with a constant level of relief with very high accuracy. The re ned matrix b[i3j] is the result of binding these isolines to heights. Our studies have shown the e ectiveness of the UAVs use to obtain data on the boundaries of water bodies (Fig. 5). UAVs provide a more detailed sequence of isolines at the initial stage of ooding rise, which is almost unattainable for satellite data. However, this approach is local and does not allow to cover large areas.
Figure 4 shows vertical pro les along the AB and CD segments for the b[i2j] matrix, indicating the positions of the corresponding intersections of coastlines with these segments. The points for the same coastline on opposite slopes of the reservoir have di erent elevation levels, which indicates the need to update the matrix b[i2j]. For example, the height di erence is b = 0:5 m for a pair of points (1a, 1b) in the gure 4 b and b = 1 m for (2a, 2d) in the gure 4 c.
5) Then we calculate the standard set of morphostructural analysis parameters [
2 bxxby arctan qb2x + by2 ;
2 2bxybxby + byybx ppq ; @b @b @2b @2b @2b bx = @x , by = @y , bxx = @x2 , byy = @y2 , bxy = @x@y , p = b2x + by2, q = 1 + p.
We often encounter two types of artifacts: a) Strong local errors of heights on the b[i0j] matrix are strongly highlighted against the background of a rather at territory. These errors are often caused by data processing problems for small forests and small water reservoirs. b) The second di culty is related to the detection of small channels connectedness.
There are problems with the automatic selection of objects even in images for urbanized
areas, the morphology of which is simpler compared to the wooded marsh landscape of the
oodplain [
6) Hydrodynamic modeling is carried out at the nal stage (Fig. 3a, b), reproducing the
spring ooding of the inter uve territory in accordance with the procedure described in [
8 p bpn+;m1 = < bn;m +
: b(ne;xmp) ;
Such veri cation based on hydrodynamic modeling is the most resource-intensive procedure. For
hydrodynamic simulations, we use the software for the numerical solution of the shallow water
equations described in [
One essential feature of building a digital model of river bed is the source data sparseness, which include: (i) There are two coastlines with water level mark Lcoast(~r), Lcoast(~r). 1 2 (ii) There are several depth curves on topographic maps of Libed(~r) (i = 1; :::; mB). We have only mB 3 4 even for the largest rivers. (iii) Several soundings show, as a rule, only the deepest points on a topographic map. (iv) Depth measurements using echo sounders require new eld studies.
All these data form set of points P on the height matrix bij .
We used an iterative procedure to build a river bottom DEM: h p bn+1;m 2bpn;m + bpn 1;mi + h p bn;m+1
i 2bpn;m + bpn;m 1 ;
Pn;m 2= P Pn;m 2 P ; (4) where b(ne;xmp) is the depth at the points Pn;m, is the parameter that determines the convergence of the iterative procedure (4). The formula (4) is the nite-di erence analog of the di usion equation. We obtain the solution to the Poisson's equation in the case of converging iterations (4). Figure 7 shows the results of the construction of the DEM of the Volga River area, based on the approach described above.
a) b)
Fig. 3 shows a schematic diagram of the hydrological regime in the VAF. Water ows from the Volga River to the Akhtuba River in a low water period in the case Q ' 5 9 thousands m3 sec 1, but it is not enough to ll the channels and besides the moisture reserve is very small in the area between the rivers. All channels are quickly lled with the increase of Q up to 23{30 thousands m3 sec 1 and the water is poured onto the at part of VAF. The water level is maintained by the powerful moistening at the third stage with Q = 16000 20000 m3 sec 1. In late spring, there is a change to low-water and the total moisture content decreases in the territory.
There is a large number of shallow lakes on the at territory between the large and small channels in spring and early summer. The coastlines of such reservoirs are moved on considerable distances in a short time period (Fig. 8 and See Fig. 4). Measuring the position of coastline at di erent points in time can help us determine an additional set of contour lines (isolines of heights) of the terrain for critical zones.
Fig. 9 shows the results of hydrodynamic simulations in the oodplain of the small river at various stages of the DEM re nement: (i) We use the DEM after embedding the riverbed in the SRTM matrix and assignment the coastlines, the fairway line and the river slope (Fig. 9a). (ii) Panel b in the gure demonstrates the water distribution in the river channel after processing the DEM in the \Construction of horizontals by elevation matrix" service in the GIS Panorama. (iii) The next iteration involves the DEM rebuilding taking into account the geodetic transverse pro les of the river valley, which are obtained as a result of eld measurements (Fig. 9c). (iv) The nal step involves updating the digital model on a small scale at the high water stage (Fig. 9d ).
The object of our study is the valley between the River Volga and River Akhtuba, the ecosystem of which is unique on Earth due to the special hydrological regime. We propose the iterative procedure for creating the DEM for special oodplain areas with a large number of transient reservoirs. The initial data are the SRTM matrix, the space images from the \Resource-P " and UK-DMC-2 satellites, the topographic maps, the geodetic measurements of the elevation pro les, the depth measurements. The morphostructural analysis and the numerical simulations of surface water dynamics on realistic topography can be powerful tools for veri cation of the digital elevation model.
The observed dynamics of coastlines allows building elevation levels along the boundaries of water bodies, and this approach is actively used to construct the DEM. However, this method acquires special value in the case of periodically ooded areas, since the moving coastlines
Figure 9. Resultosf local DEM re nement for the small river valley using hydrodynamic simulations. By identifying the shortcomings of the DEM, we provide ooding in the model for the nearest areas in accordance with the observations. provide detailed sets of contour lines, being the basis for a very high-quality and relevant digital elevation model. Acknowledgments The work has been supported by the Ministry of Science and Higher Education (government task no. 2.852.2017/4.6). The research is carried out using the equipment of the shared research facilities of HPC computing resources at Lomonosov Moscow State University. The authors are grateful to E. Agafonnikova, S. Khrapov, A. Pisarev, K. Tertychny for their help and assistance in carrying out this project. A. Klikunova thanks for the support of the Russian Federal Property Fund and the Administration of the Volgograd region (grant 18-47-340003).