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.
From: Jiaming Qiu [view email]
[v1]
Mon, 8 Jun 2026 22:27:24 UTC (9,252 KB)
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