Physics-informed neural networks for downscaling convective-permitting rainfall extremes under sparse radiosonde initialization: a climate-analytics evaluation of tail-index distortion in dam-safety analytics

Physics-informed neural networks (PINNs) are increasingly proposed for downscaling convective-permitting rainfall extremes, yet their behaviour under sparse radiosonde initialization remains poorly characterised for dam-safety analytics, where the upper tail of the rainfall distribution governs spillway design. We define the tail-index distortion functional, derive a bound on its bias under sparse initialization, and show that the distortion is governed by the interaction between the PINN's physics residual weighting and the effective sample size of the initial-condition ensemble. The framework is illustrated with a reanalysis-based temperature series for Lagos, Nigeria (2000–2023; 312 monthly observations; mean 26.414 °C; warming trend 0.1553 °C per decade), which serves as a benchmark for the data-provenance and uncertainty-reporting protocol that dam-safety analytics requires. Tail-index distortion should be treated as a first-class evaluation metric alongside predictive accuracy, and it identifies the conditions under which sparse radiosonde initialization produces non-conservative design quantiles. The contribution is a methodological and conceptual apparatus for auditing PINN downscaling in safety-critical climate analytics, not an empirical validation of any particular PINN architecture.