# Mapping of Kill Erosion of the Middle Volga (Russia) Region Using Deep Neural Network
## 1 Introduction
The use of UAVs makes it possible to provide geomorphological surveys with up-to-date information about the condition of the survey area cheaply, quickly, and accurately enough. Unfortunately, despite the overall high productivity, the use of UAVs does not allow for making a continuous survey of large regions [11; 12]; however, it will enable verification model data. Model data obtained from office studies make it possible to estimate the intensity of exogenous processes at both local and global levels. A whole range of mathematical models has been developed to assess soil and gully erosion, subdivided into empirically and physically based [13]. The most well-known and widely used soil erosion models are USLE [14], RUSLE [15], MUSLE [16], CREAMS [17], LISAEM [18], and so on. WEPP [19], RillGrow [20], GUEST [21; 22], and EUROSEM [23] models are used to estimate rill erosion. All these models have their advantages and disadvantages, and the latter does not allow using these models everywhere. The main limitations are related to the lack of publicly available large-scale remote sensing data [24], such as terrain models [25] and detailed comparable climate data [26; 27], which does not allow the mathematical simulations needed to map streamflow paths. The lack of detailed remote sensing data also limits the possibility of applying object-oriented recognition of rill erosion [28] and stochastic modeling of erosion exposure [29; 30]. The data obtained by erosion models in the form of erosion and accumulation balances often do not reflect the actual development of rill erosion processes. For example, in the catchments of the European part of Russia, it is not uncommon that the rate of accumulation in the bottoms of dry valleys tends to decrease [31; 32; 33], while the number, total length, and, accordingly, the density of rill network increases from year to year [34]. This is often due to the peculiarities of plowing with the creation of special sloughs that retain runoff from the fields, corrupting the results obtained by erosion models. Considering the existing limitations, approaches based on manual extraction of washouts from remote sensing data, namely space images [35; 36], are applied to solve the problem of rill erosion mapping. Remote sensing mapping of rill erosion was carried out using Landsat-5 (30 m) [37; 38], QuickBird (0.6 m) and SPOT (5 m) satellite imagery [39], GeoEye-1 stereo pair [40], and UAV data [41]. Sentinel-2 (10 m) images were also used to create NDVI-images during the predictive model development [42], but the mapping hasnot been carried out directly based on them before. Such solutions allow for achieving the best accuracy but are labor consuming and low productive. To solve this problem, the development of approaches based on the automation of rills washout extraction is necessary, which is the goal of this work. The source data used as a cartographic basis sets a list of possible approaches that can be applied to solve the purpose. The simplest of them is object recognition based on a thresholding approach, where the threshold defines the boundary of the reflectivity of the spectral data characteristic of the study object. Such methods are suitable for identifying different land-use types [43; 44]. However, the result will be unpredictable when recognizing rills using a similar approach on different types of soils. Machine learning methods can be used to consider the spatial variability of environmental factors, such as the highly proven Random Forest or Support Vector Machine method [45; 46]. However, such approaches only give a probability of soil erosion in a particular pixel, while not distinguishing the erosions themselves into a \"tree-like pattern\" in the landscape. In addition, the methods are very sensitive to the amount of input data--the more information used for analysis, the more consistent the results will be. On small watersheds, such approaches can be successfully applied; for large areas, their applicability is questionable.