Ground Flash Density as a Function of Climate: Scenario-Conditioned Lightning Hazard with Calibrated Uncertainty

Ground flash density $N_G$---the quantity used by standards for overhead-line lightning performance and risk assessment---is typically represented as a fixed historical product. However, transmission assets operate for decades under changing climatic conditions, while existing $N_G$ datasets provide no means of estimating how this quantity changes with climate. We instead treat $N_G$ as a \textbf{function of climate state}: a graph neural network maps CMIP6 monthly climatology to $N_G$, enabling the hazard layer to be evaluated under both historical and projected climates. The surrogate reconstructs held-out municipalities with an MAE of 2.15 (RMSE 2.91), compared with 5.11 for a national-mean baseline, under a deliberately conservative whole-region holdout protocol. To quantify predictive uncertainty, we combine MC dropout with conformal prediction and show that conditioning conformal calibration on extrapolation distance maintains near-nominal coverage while reducing interval widths to nearly half near the training distribution. Applying the model to three CMIP6 SSP scenarios produces scenario-conditioned $N_G$ layers indicating a spatial redistribution of lightning hazard, with most municipalities exhibiting higher projected $N_G$ under warming. Although projected $N_G$ cannot be validated directly from observations, the proposed framework enables climate projections to be translated into scenario-conditioned estimates of lightning hazard.