Physics-Informed Neural Network Emulation of Convective Storm Initiation over the Sahel: Calibration Bounds and Warning-Lead-Time Equity for Climate Analytics

Physics-informed neural networks (PINNs) offer a computationally tractable route to emulating convective storm initiation over the Sahel, where sparse observations and coarse numerical weather prediction limit warning lead times. The framework combines a physics-informed residual formulation of the convective initiation problem with a distributionally robust calibration bound derived from the PINN's training residual and a warning-lead-time equity functional defined over population-weighted exposure. The framework is illustrated with a reanalysis-derived temperature record for Kampala, Uganda (NASA POWER MERRA-2, 2000–2023, 312 monthly observations, mean 22.443 °C, trend −0.1564 °C per decade), which serves as a calibration anchor for the environmental-state distribution. Calibration bounds and equity bounds must be co-designed: a PINN that is accurate on average can still violate lead-time equity, and an equity-constrained PINN may require a tighter physics residual than accuracy alone would demand. The contribution is a formal bridge between physics-informed emulation and distributive climate analytics, with implications for the design of early-warning systems in data-sparse regions.