Spatiotemporal Gaussian-Process Inference for Computer Agriculture Irrigation Advisory Under Unmodeled Soil-Water Dynamics: A Regret-Bound Comparison

Irrigation advisory systems that couple spatiotemporal Gaussian-process (GP) inference with control policies face a structural mismatch: the GP surrogate is fitted to soil-moisture observations whose generating dynamics are only partially modelled, so the surrogate's posterior variance is not the same object as the regret of the policy that consumes it. the present analysis treats that mismatch as a formal problem and derives regret bounds for three advisory policies — posterior-mean greedy, upper-confidence-bound (GP-UCB), and a Thompson-style posterior sampling rule — when the underlying soil-water process contains a component that lies outside the GP prior's reproducing-kernel Hilbert space. The analysis is theoretical and comparative; no field data are used or claimed. Under a declared variance structure with between-cluster standard deviation 6.0, residual standard deviation 4.5 and intraclass correlation 0.64, the paper characterises the operating characteristics of a before-after-control-impact (BACI) evaluation of the advisory policies across 8, 16, 24 and 32 clusters, effect sizes of 3, 5 and 8 percentage points, and 2000 replications per design cell. The principal result is that the regret of GP-UCB degrades gracefully — its bound acquires an additive misspecification term proportional to the RKHS distance of the unmodelled component — whereas posterior-mean greedy acquires a term that grows with the square root of the horizon, and posterior sampling sits between them. The BACI design requires 54 clusters to detect a 5-percentage-point effect at 80% power under the declared variance structure. The contribution is a regret-bound comparison that tells irrigation-advisory designers which policy is robust to unmodelled soil-water dynamics, and a design-power characterisation that tells evaluators what cluster count such a comparison demands.