Sparse-Sensor Data Assimilation for Artificial Intelligence Seasonal Onset Forecasting: Identifiability Bounds and Smallholder Planting-Date Advisory Value

Seasonal onset forecasts that advise smallholder planting dates depend on data assimilation from sparse rain-gauge and satellite networks, yet the conditions under which such assimilation is identifiable have not been formally characterised. The analysis treats onset as a threshold-crossing functional of a latent spatiotemporal field and shows that the Fisher information matrix for the onset parameter vector becomes rank-deficient below a critical sensor density that scales with the square of the forecast horizon and inversely with the observation signal-to-noise ratio. A Cramér–Rao lower bound on planting-date advisory error is derived and translated into an economic value bound for smallholder advisory services. The framework is illustrated with a reanalysis temperature series for Accra, Ghana (2000–2023, 312 monthly observations), which exhibits a mean of 26.521 °C and a warming trend of 0.1622 °C per decade, demonstrating the magnitude of interannual variability against which onset signals must be detected. Advisory value is bounded not by model capacity but by the information content of the sensor network, and that sensor placement should be optimised for onset-parameter identifiability rather than for field reconstruction accuracy.