Which modelling choices shape your interpolation map? An Optimal Transport sensitivity analysis for groundwater sulfate concentration
Abstract
Spatial prediction maps are crucial for environmental management yet highly sensitive to subjective modelling choices such as, e.g., covariates, spatial dependence structures, or mesh resolution. We develop a workflow that attributes the resulting map uncertainty to these choices and is applicable to any spatial model, since it operates only on an ensemble of maps produced by propagating the choices through spatial prediction. This ensemble is then filtered to retain only models with acceptable predictive performance, reduced in dimension by principal component (PC) analysis, and the sensitivity of the resulting scores to each choice is quantified by global sensitivity analysis based on optimal transport (OT) metrics. We demonstrate the framework with Bayesian geostatistics applied to the spatial mapping of sulphate concentrations in groundwater of Paris Basin (France), which is key for assessing groundwater chemical quality and establishing the natural geochemical baseline of aquifers. For this application, the covariates, mesh resolution, covariance models, and priors are combined into 18000 candidate configurations. These are filtered by cross-validated root mean square error (RMSE) and 95% coverage of the prediction interval, and the retained configurations are then inferred on a high-resolution grid and reduced to its three PCs. The OT analysis identifies covariate selection (under 95% coverage) and mesh resolution (under RMSE) as the dominant sources of uncertainty to the PCs, and a negligible one for the choice of the covariance model.
Related
- Transport-based interpolation of dyadic meshes for problems with variable conditions
- Differentiable Hybrid Modelling for Learning and Optimising Chemical Transport Processes from Experimental Data
- Graphene-Assisted Electrostatic Screening of Resonant Transport in MR-DWELL Dosimeters with Tunable Sensitivity--Radiation Tolerance Trade-off: A Reduced-Order Benchmark and Self-Consistent Perspective
- Spline interpolation on compact riemannian manifolds
- Some Notes on Neville's Algorithm of Interpolation with Applications to Trigonometric Interpolation
BibTeX
@misc{perchtold2026which,
title = {{Which modelling choices shape your interpolation map? An Optimal Transport sensitivity analysis for groundwater sulfate concentration}},
author = {Corinna Perchtold and Jérémy Rohmer and Augustin Thomas and Julie Lions},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06101},
eprint = {2610.06101},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06101},
}
RIS
TY - UNPB
TI - Which modelling choices shape your interpolation map? An Optimal Transport sensitivity analysis for groundwater sulfate concentration
AU - Corinna Perchtold
AU - Jérémy Rohmer
AU - Augustin Thomas
AU - Julie Lions
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.06101
UR - https://arxiv.org/abs/2610.06101
AB - Spatial prediction maps are crucial for environmental management yet highly sensitive to subjective modelling choices such as, e.g., covariates, spatial dependence structures, or mesh resolution. We develop a workflow that attributes the resulting map uncertainty to these choices and is applicable to any spatial model, since it operates only on an ensemble of maps produced by propagating the choices through spatial prediction. This ensemble is then filtered to retain only models with acceptable predictive performance, reduced in dimension by principal component (PC) analysis, and the sensitivity of the resulting scores to each choice is quantified by global sensitivity analysis based on optimal transport (OT) metrics. We demonstrate the framework with Bayesian geostatistics applied to the spatial mapping of sulphate concentrations in groundwater of Paris Basin (France), which is key for assessing groundwater chemical quality and establishing the natural geochemical baseline of aquifers. For this application, the covariates, mesh resolution, covariance models, and priors are combined into 18000 candidate configurations. These are filtered by cross-validated root mean square error (RMSE) and 95% coverage of the prediction interval, and the retained configurations are then inferred on a high-resolution grid and reduced to its three PCs. The OT analysis identifies covariate selection (under 95% coverage) and mesh resolution (under RMSE) as the dominant sources of uncertainty to the PCs, and a negligible one for the choice of the covariance model.
ER -