Forecasting threshold exceedance of atmospheric variables at a specific location

Accurate short-term forecasting of extreme weather events is important for early warning and risk mitigation. We compare two approaches for predicting site-specific threshold exceedances of weather variables: direct binary probabilistic models trained on thresholded outcomes and full-distribution parametric models trained on the continuous target. Using an analytically tractable Gaussian random-location model, in which the distribution is predictably shifted by the covariates, we quantify the consequences of the information loss induced by thresholding and derive the rare-event behavior of prediction errors and forecast skill. The analysis predicts an increasing relative advantage of the full-distribution approach as event probability decreases, because binarization progressively discards information contained in the continuous response. We then compare the two approaches to forecast wind speed and accumulated rainfall at various weather station sites over southeastern France using the same hybrid neural-network architecture. Although wind speed and rainfall depart from the toy-model assumptions, its main qualitative predictions are recovered for both variables: the relative advantage of distributional modeling increases toward rarer thresholds. This agreement further suggests that a substantial fraction of the forecastable signal associated with extreme events arises from predictable shifts in the conditional distribution. For the reasonably suitable parametric families examined, the results show limited sensitivity to the selected class of distribution. Overall, the results highlight the statistical advantage of training on continuous observations rather than on thresholded binary outcomes when forecasting rare threshold exceedances.