Distribution-free flash-flood human-impact forecasting under temporal covariate shift

Urban flash floods are rare but high-consequence events, so warning systems greatly benefit from calibrated probabilities, distribution-free coverage guarantees, and explicit subgroup auditing, which favor their forecasting. We present an importance-weighted, Mondrian (group-conditional) conformal prediction framework with hierarchical shrinkage and validation-tuned selective abstention to address temporal covariate shift and sparse positives within groups. Using 6,137 Texas events (2005-2019) at census-tract resolution with a strict 2018-2019 holdout (prevalence 1.86%), a calibrated three-model ensemble (Brier-optimal weights {0.420, 0.540, 0.040}) attains AUROC 0.758 (95% CI: 0.545-0.931), AUPRC 0.198 (95% CI: 0.044-0.504), Brier 0.0187, and ECE 0.012. We quantify temporal covariate shift using the Population Stability Index (PSI) on predictor distributions; predictors such as mean elevation (PSI=0.248) and event-accumulated precipitation (PSI=0.194) illustrate the shift. Importance weighting corrects measurable temporal shift and reduces the false-positive rate from 0.484 (naive, unweighted thresholds) to 0.138 at comparable recall. Due to sparse positives per stratum, adaptive grouping merges density quartiles; validation selects m* = 0, and the observed worst-group Wilson lower-bound recall is 0.213. Prequential backtesting indicates moderate temporal robustness of discrimination. Power calculations suggest that roughly 50-100 additional harmful events, distributed across strata, are required to certify 80-90% worst-group recall at 95% confidence. The framework provides deployable, distribution-free uncertainty quantification for rare events with transparent equity auditing and explicit evidence thresholds for operational urban CPS.