Certified Robustness Audits for Artificial Intelligence Climate Downscaling Under Adversarial Boundary Forcing: Lipschitz Bounds and Regional Forecast Reliability

Statistical downscaling models that map coarse reanalysis fields to station-scale temperature are increasingly used to support regional climate services, yet their reliability under perturbed boundary forcing remains largely unquantified. The audit treats the downscaler as a Lipschitz-continuous operator between function spaces and derives a certified radius within which output perturbations are provably bounded by the input perturbation multiplied by the Lipschitz constant. Using NASA POWER monthly MERRA-2 air temperature at 2 m for Lagos (6.52°N, 3.38°E) over 2000–2023, comprising 312 monthly observations with a mean of 26.414 °C and a standard deviation of 0.943 °C, the study estimates a warming trend of 0.1553 °C per decade. The certified radius is then compared with the empirical sensitivity of the downscaler to boundary perturbations drawn from the observed residual distribution. The Lipschitz certificate provides a conservative but actionable bound, and that regional forecast reliability degrades non-uniformly across the seasonal cycle. The contribution is a reproducible audit protocol that couples formal robustness guarantees with observational diagnostics, allowing climate-analytics practitioners to state, for a given downscaler and region, the boundary-forcing perturbation magnitude below which forecast reliability is certified.