Geostatistical active learning for expanding monitoring networks for environmental decision making

The expansion and optimisation of environmental monitoring networks requires the efficient use of limited resources to improve spatial predictions to ensure the protection of human health and ecosystems.

Network densification is a spatial sampling problem that is often addressed by pointwise-prediction uncertainty approaches, which ignore (1) the impact of a new site on its neighbourhood and (2) the binary decision task motivating the monitoring. Active learning (AL) is a machine learning technique that iteratively selects new locations based on the current maximum uncertainty in the available training data. We therefore recast network densification as an AL task and propose model-agnostic acquisition criteria, including a decision-aligned focal logit criterion that prioritises neighbourhoods whose exceedance probabilities lie near regulatory thresholds. A look-ahead criterion based on the expected reduction in prediction standard error (SE) is also examined. In a groundwater nitrate concentration case study, the focal logit criterion consistently selected more informative sites than traditional dispersion- or prediction-SE-based criteria, yielding up to 58 % greater gains in exceedance-mapping accuracy (Cohen’s κ)). Focal logit and SE criteria outperformed pointwise counterparts by ~45 % on average, while the look-ahead criterion performed well but at much higher computational cost.

The proposed framework is simple, generalisable to other environmental pollutants (such as air pollutants), and supports a transparent, decision-oriented monitoring design.