Global Sensitivity Analysis of Spatial Interpolation for Sparse, Clustered, and Censored Data: A Case Study of Groundwater Sulfate in the Paris Basin

This study presents a comprehensive sensitivity analysis framework to disentangle the drivers of predictive uncertainty in spatial interpolation and how they ultimately affect spatial predictions. Developed within a Global Sensitivity Analysis context, the proposed approach is model-independent and generic, allowing for broad application across diverse spatial interpolation workflows.

The framework is demonstrated using groundwater Sulfate concentration in the Paris Basin, a dataset characterised by sparse and highly clustered sampling across six distinct aquifers according to the French "BD LISA" hydrogeological system (https://bdlisa.eaufrance.fr/). We represent the underlying spatial process as a  Gaussian Random Field, leveraging Integrated Nested Laplace Approximations for computationally efficient Bayesian inference. This allows for a  probabilistic treatment of uncertainty even within complex spatial structures.

We systematically evaluate the impact of several key uncertainty factors related to both data and model configuration: (1) the number of monitoring stations and their spatial distribution; (2) the selection of the environmental covariates  and the functional form of their effects (linear vs. non-linear); (3) the treatment of censored data (values below detection limits); and (4) structural assumptions regarding the spatial covariance function, specifically the estimation of variogram hyperparameters such as range, sill, and nugget effects and their prior specification. By propagating these uncertainty sources through our framework, we derive domain-wide aggregated sensitivity measures. These metrics quantify how specific data topologies—including sampling density, clustering effects, and censoring rates—govern the stability and accuracy of the resulting spatial interpolations.

Finally, the results facilitate an in-depth discussion on the limitations of purely probabilistic methods in data-poor scenarios. We provide an outlook on the potential of extra-probabilistic approaches, such as imprecise or interval-based kriging, to more robustly address the wide range of epistemic uncertainties inherent in environmental monitoring.

We acknowledge financial support of the French National Research Agency within the HOUSES project (grant N°ANR-22-CE56-0006).