Uncertainty-Decomposition Evaluation for Computer Agriculture Fertilizer-Rate Recommenders Under Soil-Sampling Grid Coarsening: An Artificial Intelligence Variance-Propagation Bound for Over-Application Risk

Soil-sampling grid coarsening degrades the reliability of artificial-intelligence fertilizer-rate recommenders in computer agriculture, yet evaluation practice typically reports a single accuracy figure that conflates sampling error, model error and decision error. The bound is expressed in terms of the sampling-grid spacing, the spatial covariance of the soil nutrient field, the recommender's calibration error and a decision-threshold sensitivity coefficient. A before-after-control-impact design is characterised analytically under a declared variance structure with between-cluster standard deviation 6.0, residual standard deviation 4.5 and intraclass correlation 0.64; power was estimated across 2000 design cells for cluster counts of 8, 16, 24 and 32 and effect sizes of 3, 5 and 8 percentage points. The design attains 80 per cent power at 54 clusters for a 5-percentage-point effect. The decomposition shows that grid coarsening inflates the sampling component superlinearly once the spacing exceeds the nutrient-field correlation length, and that this component dominates the bound at coarse spacings even when the recommender is well calibrated. The contribution is a decision-relevant evaluation quantity that separates the portion of over-application risk attributable to sampling design from the portion attributable to the model, and a design rule that links grid spacing to an admissible over-application probability.