Rainfall-induced soil erosion of a mountain area plays a significant role in supplying sediment and shaping the landscape. The related area of soil erosion, as an index of the changed landscape, is easier to calculate visually using some popular imaging tools. By image analysis, our work shows that the changing of the soil erosion area admits the structure of an S-growth curve. Therefore, we propose to establish an S-curve model, based on incremental learning, to predict the soil erosion area. In the process of incremental learning, we dynamically update the accumulative rainfall and rainfall intensity to train the parameters of our S-curve model. In order to verify our prediction model, the index of area is utilized to express the output of eroded soil in a series of experiments. The results show that the proposed S-growth curve model can be used to estimate the growth of the soil OPEN ACCESSAppl. Sci. 2015, 5 158 erosion area (average relative error 3%-9.7%) according to variable soil material and rainfall intensity. The original S-growth curve model can calculate the erosion areas of just one soil material and one rainfall condition whose average relative error is 7.5%-12.2%; compared to the simple time series analysis-moving average method (average relative error 5.7%-12.1%), our proposed S-growth curve model can reveal the physical mechanism and evolution of the research object.

Estimations of rainfall-induced soil erosion are mostly derived from the weight of sediment measured in natural runoff. The transport distance of eroded soil is important for evaluating landscape evolution but is difficult to estimate, mainly because it cannot be linked directly to the eroded sediment weight. The volume of eroded soil is easier to calculate visually using popular imaging tools, which can aid in estimating the transport distance of eroded soil through geometry relationships. In this study, we present a straightforward geometry model to predict the maximum sediment transport distance incurred by rainfall events of various intensity and duration. In order to verify our geometry prediction model, a series of experiments are reported in the form of a sediment volume. The results show that cumulative rainfall has a linear relationship with the total volume of eroded soil. The geometry model can accurately estimate the maximum transport distance of eroded soil by cumulative rainfall, with a low root-mean-square error (4.7-4.8) and a strong linear correlation (0.74-0.86).