A Framework for Integrating Spatial Uncertainty into Critical Zone Models: Application to Enhanced Weathering

Spatial heterogeneity introduces uncertainty when characterizing the Critical Zone, especially when sampling is sparse or requires repeated measurements at the same locations. Here, we layout a probabilistic sequential framework to systematically account for spatial uncertainty when measuring Critical Zone transformations. First, we use measurement variance propagation and distance-based sensitivity analysis to determine measurement variance criteria for meeting overall uncertainty requirements. We then stochastically simulate spatial fields and composite sampling to infer a minimally sufficient sampling plan that meets these criteria. Throughout the study, we apply this framework to solid-phase measurement of enhanced weathering, an open-system carbon dioxide removal strategy. Results indicate that field-scale variance in baseline soil concentrations must be accurately estimated before designing a sampling plan and, even then, such variance is likely too high for element-element mixing models to be effective near-term constraints on enhanced weathering. We conclude with opportunities to extend this framework to other solid-phase mixing and stock models, multi-phase measurement models, and transient Critical Zone processes.