Spatiotemporal transformer imputation of gauge-rainfall records under sensor-network attrition: a climate-analytics evaluation of flood-threshold exceedance error propagation

Gauge networks in data-scarce regions lose stations continuously, and the imputation methods used to fill the resulting gaps are evaluated almost exclusively on point-prediction accuracy. Such evaluation is misaligned with the downstream use of imputed rainfall: flood-threshold exceedance, a binary and highly nonlinear functional of the rainfall field. A spatiotemporal transformer imputation framework is formalised, and an analytical error-propagation model is derived that maps imputation error moments onto the probability of threshold misclassification. The model yields a closed-form bound on exceedance-probability error in terms of the imputation residual variance and the local rainfall density near the threshold, and it shows that variance reduction and bias reduction have asymmetric consequences for exceedance error. The framework is applied to a reanalysis-derived temperature record for Kampala, Uganda (2000–2023, 312 monthly observations), used here as a stand-in for a sparse gauge series to demonstrate the propagation calculation. The record has a mean of 22.443 °C and a linear trend of −0.1564 °C per decade, and the propagation model indicates that a plausible imputation residual variance translates into a materially larger exceedance-probability error than the same variance would produce in mean-squared-error terms. The paper concludes that imputation for flood-threshold applications should be tuned and reported against exceedance error rather than against point accuracy, and it specifies the reporting quantities that would make such tuning auditable.