# Mapping of Kill Erosion of the Middle Volga (Russia) Region Using Deep Neural Network
## 1 Introduction  
Soil erosion became the main factor in degrading a fertile layer of agricultural lands. Intensive land use combined with natural factors creates conditions for increased development of soil erosion, including rills, erosion furrows, and ephemeral gullies. Often, these erosion forms turn into permanent gullies, completely removing the area from agricultural turnover. Therefore, it is not surprising that researchers worldwide pay special attention to the study of soil erosion and, in particular, fill erosion. Both field and mathematical methods are the main methods for studying soil erosion. The field method is very accurate in estimating the volume of erosion changes on local areas, which somewhat complicates the spatial interpretation of the results at the region or landscape levels. Such methods include the classical methods of reference sites, landmarks, microprofiling, and measuring the length and width of washouts with a tape measure. Reference sites allow estimating the direct volume of soil washed away from the territory, providing an opportunity to artificially change the conditions of the \"environment\" [1]. Based on the data from such sites, the data for creating mathematical models of soil erosion assessment, which will be discussed below, were obtained. The method of landmarks and microprofiling makes it possible to accurately estimate the depth of washout in representative sites [2]. Studies using these techniques helped find a strong correlation between the width of washout and its depth, which, in turn, estimates the volumes of soil washed away from the territory [3, 4]. At present, geodetic methods based on relief reconstruction using scanning data or photogrammetry, both ground and airborne, are being developed to assess erosion. The most accurate results can be achieved using ground-based laser scanning datausing reference points [5]. Researchers from all over the world manage to record in this way, not only gully [6] or rill [7] soil erosion but also micro-rill and sheet soil erosion [8], the changes of which are within the first millimeters. Unfortunately, it is problematic to use such technologies for direct monitoring in areas larger than 1 hectare. This problem is attempted to be solved using airborne laser scanning; however, this technology has its limitations related to the positioning of the scanning equipment for the subsequent alignment of the repeated survey. This fact immediately precludes the use of airborne scanning to evaluate the dynamics of micro-rill and sheet erosion, but it does allow for more or less automated estimation of the total length and width of rill and gully erosion. Different approaches are used for this. For example, the most common one is based on the threshold value of the number of digital elevation model (DEM) cells, from which runoff into neighboring cells is possible. Depending on the resolution of the initial DEM obtained from scanning data, this approach allows recognizing rills depths from 5 cm. However, airborne laser scanning is not widely used due to the high cost of the scanning equipment. Nowadays, more affordable scanning sensors appeared installed on manned aircraft and unmanned aerial vehicles (UAV). Nevertheless, the applicability of such devices for solving the problem of soil erosion assessment has yet to be discovered--the analysis of the existing experience has demonstrated that the most significant relevance of such devices is in forestry [9]. Despite the current trend toward cheaper scanning systems, they are still not widely available to most researchers. Combining these factors has led to the most widespread use of photosensors as payloads for UAVs [10]. UAV photogrammetry makes it possible to achieve comparable point cloud densities with scanning systems' competitive accuracy of the resulting models and allows one of the end products to be an ultra-high-resolution orthophotoplane.