Causal-Mediation Inference for Computer Agriculture Irrigation-Water Allocation Under Unobserved Root-Zone Percolation: An Artificial Intelligence Interventional-Identifiability Bound

Irrigation-water allocation models in computer agriculture routinely estimate the indirect effect of allocation decisions on crop yield through root-zone moisture, but the mediator is only partially observed: percolation below the root zone is unmeasured in most field deployments, so the mediator is a coarse proxy. the present analysis derives an interventional-identifiability bound for the natural indirect effect of irrigation allocation on yield when the mediator is subject to unobserved percolation. The bound is expressed as a closed-form interval whose width depends on the fraction of mediator variance attributable to percolation and on the strength of the allocation-mediator association. A before-after-control-impact design was evaluated across 2000 replications per cell for cluster counts of 8, 16, 24, 32 and effect sizes of 3, 5 and 8 percentage points, under a declared variance structure with between-cluster SD of 6.0, residual SD of 4.5 and intraclass correlation of 0.64. The design required 52 clusters to detect a 5 percentage-point effect at 80% power. The bound is shown to be sharp when percolation is independent of allocation and to widen monotonically as the percolation share of mediator variance increases. The contribution is a formal statement of what mediation claims remain defensible when the root-zone mediator is only partially observed, together with the design conditions under which those claims can be tested.