Spatial Prediction of Local Soil Erosion Distribution in the Wasserstein Space

2026-06-08

AI Summary

Accurate, large-scale mapping of soil erosion distributions is challenging to achieve through field surveys alone. This study proposes a novel approach by modeling local soil erosion distributions in Wasserstein space for the first time, representing them as trajectories of square-integrable functions via basis expansion. A multivariate random field is constructed to capture spatial dependence, and distribution predictions at arbitrary locations are enabled by integrating local regression with kriging. The method overcomes limitations of traditional parametric models and Fréchet regression, offering flexible estimation of full distribution functions and their functionals—such as means and exceedance probabilities. Simulations demonstrate its superiority over misspecified parametric models and existing nonparametric alternatives. The framework is successfully applied to province-wide soil erosion prediction in Shaanxi, effectively incorporating covariates such as land use and elevation.

Abstract

Obtaining precise erosion measurements requires costly fieldwork, making it infeasible to directly survey large domains such as a province or river basin. To extend fieldwork results across such extensive domains, we propose a novel spatial prediction method that treats local erosion distributions as objects in the Wasserstein space. These distributions are mapped into square-integrable trajectories and represented via basis expansion, forming a multivariate random field that captures spatial dependence. By applying local regression and Kriging in this representation, our approach flexibly models and predicts erosion distributions at arbitrary locations. This framework improves prediction for functionals of the distribution, such as the mean and exceedance probabilities. Simulation studies demonstrate that the proposed method outperforms a misspecified parametric alternative and existing Fréchet regression approaches. We illustrate the approach with a detailed erosion analysis in Shaanxi province, China, where local measurements from surveyed watersheds are extended to predict erosion distributions across the entire province using covariates such as land use and elevation.

Problem

• soil erosion
• spatial prediction
• Wasserstein space
• distributional data
• large-domain inference

Innovation

• Wasserstein space
• spatial prediction
• distributional data
• basis expansion
• Kriging