# Mapping of Kill Erosion of the Middle Volga (Russia) Region Using Deep Neural Network
## 4 Results and Discussion
The inverse relationship with the other indicators is not so obvious. Selyaninov's hydrothermal coefficient of wetness (GTK) is a characteristic of the level of moisture availability of the territory. It is widely used in agronomy for general climate assessment and allocation of zones with different levels of moisture availability to determine the usefulness of the cultivation of various crops. The factor is closely related to the amount of precipitation in the territory. The inverse relationship here is explained not so much by the very nature of the dependence \"the more precipitation, the less erosion\", which cannot be, as by the influence of climatic conditions in general. This is partly confirmed by a direct relationship between the total length of the rill network and such factors, such as the sum of active temperatures and the average annual maximum temperature for the year. Apparently, with increasing temperature and climate change due to global warming, the character of precipitation changes--they may fall rarely, but with great intensity [70; 71; 72; 73; 74]. Unfortunately, it is impossible to check this hypothesis directly due to the lack of data on mean annual precipitation intensity changes. However, the same conclusions are drawn by other researchers who have worked in the study area [31; 32; 75; 76]. Nevertheless, there is still no clear answer to this question. Another question is how classical methods of relationship analysis can assess the effect of a single factor on the dependent variable. Linear dependencies are rare in nature, and polynomial dependencies of high degrees are even rarer. The analysis demonstrated poor applicability of classic correlation and regression analysis for revealing the relationships between natural-anthropogenic factors and the length of the erosion network. Some examples (Figures 9-11) demonstrate that the dependencies are close to the logistic or exponential type but more complex. Therefore, it was decided to use generalized additive models (GAM) for dependence analysis [77]. These models allow estimating the dependencies  
Figure 8: Distribution of total rill erosion length (m) (**A**) and normalized distribution of total rill erosion length (**B**). in the form of spline functions, which allows one to make better approximations and comprehensively study the dependence of a factor on a variable [(24; 78)]. Figure 10: Linear relation of the total length of fill erosion to the elevation variation in the basin. Figure 9: Linear relation of the total length of fill erosion to maximum air temperatures. Modeling of generalized relationships was performed in a package for building generalized additive models in the Python language [79]. During modeling, statistically significant (\(p<0.001\)), stable, and strong relationships were found between the density of rill erosion and such natural factors as mean basin elevation (Figure 12A), mean basin slope (Figure 12B), basin elevation range (Figure 13A), basin forest cover (Figure 13B), average air temperature in January (Figure 14A), average annual long-term maximum temperature (Figure 14B), average warm-season precipitation (Figure 15A), average basin hydrothermal coefficient (Figure 15B), longitude (Figure 16A), and latitude (Figure 16B) of the basin centroid. Figure 14: Dependence of fill erosion density on temperature factors (\({}^{\circ}\)C)—mean annual temperature in January (**A**) and mean annual maximum temperature in the warm season (**B**). Figure 13: Dependence of fill erosion density on elevation range (m) (**A**) and average forest cover (%) (**B**) in the basin. Generalized models confirmed the known relationships between soil erosion and natural factors and revealed complex nonlinear relationships. It is observed that the density of the erosion network is stable with an increase in the average elevation of the basin, but up to 100 m, after which the growth of density is replaced by a decrease in the density and its stabilization (Figure 12A).