An optimization framework of spatially stratified heterogeneous sampling under sample size and cost constraints for soil pollution surveys.

Soil pollution surveys are essential for pollution assessment, remediation and environmental management and soil contamination presents complex spatial patterns. Existing approaches, including conditioned Latin hypercube sampling (cLHS), stratified sampling, gridded sampling and the Bethel algorithm, either rely heavily on auxiliary variables or subjective designs, lacking explicit quantification of the trade-offs among sample size, cost and estimation uncertainty. In this study, we propose Optimized Environmental Pollution Sampling Survey (OEPSS), a statistically interpretable stratified sampling framework for soil pollution investigations. OEPSS provides theoretically optimal sample allocations under spatially stratified heterogeneous conditions and minimizes estimation uncertainty subject to sample size and cost constraints. Synthetic and real-world case studies demonstrate that, by accounting for sample size and cost simultaneously, OEPSS consistently outperforms the Bethel algorithm, Neyman allocation, random sampling and grid-based sampling in spatially heterogeneous scenarios, achieving lower estimation variances and improved inference accuracy. OEPSS also provides an integrated-variance framework for multivariate optimization, enabling simultaneous consideration of multiple pollutants without requiring user-defined parameters. By explicitly linking sample size, cost and uncertainty, OEPSS proposes a quantitative and practical framework for efficient soil pollution surveys under diverse spatial heterogeneity and resource constraints.