A Framework for Integrating Spatial Uncertainty into Solid-Phase Measurement and Verification of Enhanced Weathering

Reliable verification of enhanced weathering as a carbon dioxide removal strategy requires accurate quantification of feedstock dissolution in amended soils. However, spatial heterogeneity introduces significant uncertainty, particularly in sampling designs that rely on sparse sampling or repeated measurements at fixed locations. Here, we develop a probabilistic framework to evaluate how spatial uncertainty in solid-phase geochemical measurements influences the precision of feedstock dissolution estimates derived from an element-element mixing model. We first quantify how variance in soil compositions affects errors in modeled feedstock dissolution and apply distance-based sensitivity analysis to identify the measurement variance thresholds required to achieve desired uncertainty levels. Next, we simulate spatially heterogeneous soil conditions and various composite sampling configurations to identify the optimal sampling strategy likely to meet specified uncertainty criteria. Our findings underscore the necessity of accurately estimating field-scale variance in baseline soil concentrations prior to developing sampling plans. Analysis of data from existing high-density soil sampling campaigns indicates that geochemical variance is likely too high for element-element mixing models to serve as effective near-term constraints on feedstock dissolution. The framework presented here can be further extended to other solid- and multi-phase measurement models for enhanced weathering verification.