Budget-Constrained Sensor Placement for Artificial Intelligence Agriculture Frost Early Warning Under Smallholder Plot Fragmentation: A Computer Detection-Probability Evaluation

Frost early warning for smallholder agriculture is often framed as a sensor-coverage problem, but fragmented plot geometry and tight capital budgets make coverage an unreliable proxy for detection. The framework is evaluated computationally across a design grid of 8, 16, 24 and 32 sensors and frost intensities of 3, 5 and 8 percentage points of plot-area loss, with 2000 replications per cell under a declared variance structure (between-cluster SD = 6.0, residual SD = 4.5, intraclass correlation = 0.64). Power to detect a protective effect rose with sensor count and effect size, and the minimum detectable effect at 80% power fell as the sensor field densified; 54 clusters were required to resolve a 5 percentage-point effect at 80% power. The analysis indicates that detection probability, not nominal coverage, should govern placement decisions, and that fragmentation imposes a detection penalty that budget-constrained designs must price explicitly.