Title: Spatial Prediction of Local Soil Erosion Distribution in the Wasserstein Space

Abstract: It is valuable yet difficult to measure local erosion distributions within small watersheds without costly fieldwork at the targeted locations. We propose a novel spatial prediction method for the erosion distributions as probability density objects in the Wasserstein space. Local erosion distributions are transformed into square-integrable trajectories and represented using basis expansion, which becomes a multivariate random field that encodes the spatial structure. Further application of local regression and Kriging enables flexible modeling and prediction of the spatially distributed density objects. Our method also leads to the prediction of functionals of the density/distribution, such as the mean value and exceeding probabilities. Simulation studies suggest that the proposed method substantially outperforms parametric methods if the latter are misspecified and have comparable performance even if the parametric model is well-specified. The proposed method is applied for a detailed local erosion analysis over Shaanxi province in China based on limited field survey data, where local erosion profiles are obtained conditioning on local land use type and covariates derived from a digital elevation model.