Ranked Right, Sized Wrong: Ensemble Spread Fails Silently at Streamflow Extremes

Uncertainty quantification of hydrological predictions is necessary to inform operational decisions. Recent generative machine-learning methods have advanced probabilistic streamflow prediction, but have remained confined to lumped models that predict a basin outlet directly. At the same time, deterministic LSTM runoff models are increasingly applied at grid or catchment scale and routed through river networks to produce spatially continuous, physically consistent discharge fields. This technical note argues that moving probabilistic prediction from lumped to distributed models introduces a specific new requirement: the joint distribution of upstream runoff generation must be sampled jointly. In lumped inference, the model predicts the outlet distribution directly and can modulate spread from basin attributes. In distributed inference, downstream discharge is obtained by routing many upstream runoff predictions, so independent local sampling averages uncertainty away. Using Japan as a case study, we train two probabilistic basin-scale runoff LSTMs and route their runoff through a Hayami routing scheme. Randomly matching upstream ensemble members produces severely under-dispersed downstream ensembles, whereas a simple quantile matching strategy restores much of the spread of the direct basin-scale reference. The shift from lumped to distributed probabilistic hydrology therefore requires explicit attention to the spatial joint structure of runoff uncertainty.

Accurate forecasting of river discharge and floods is very challenging. River dynamics are affected by storage, meteorological forcing, and flow propagation at different spatial and temporal scales. Forecasting thus requires a framework that considers the upstream-to-downstream flow through river networks across grid cells and catchments. This modeling is known in hydrology as distributed modeling and routing. Existing deep learning approaches either ignore this topology, operate on lumped catchments, or route predicted physical quantities through a separate graph or physical routing model. We instead introduce feature-space routing: a topology-aware state-space operator embedded directly in the forecasting dynamics. At every forecast step, the operator gathers latent states from upstream grid cells and causally updates the downstream state according to the known river network. This preserves the physical connectivity of the river system while allowing the propagated state itself to be learned end-to-end and allows the model to predict river discharge considering both local dynamics and neighboring upstream contributions. To address uncertainty and provide probabilistic forecasts, we minimize the fair continuous ranked probability score (fCRPS) as a training objective. Our experiments on the European Flood Awareness System (EFAS) and observational data for river discharge forecasting demonstrate that encoding the physical structure of river networks explicitly in the feature space substantially improves the forecasting skill, particularly in an ungauged setting. Our approach achieves state-of-the-art results on both reanalysis and observational data and is able to forecast maps of river discharge at 1 arcminute and 6-hourly resolution up to 10 days lead time.

Reliable wildfire spread prediction is vital for risk-aware emergency planning, yet most deep learning models lack principled uncertainty quantification (UQ). Further, for boundary-sensitive cases like wildfire spread, evaluating models with global metrics alone is often insufficient. To shift the focus of UQ evaluation toward a more operationally relevant approach, the Fire-Centered Evaluation Region (FCER) framework is introduced as a spatially conditioned protocol to characterize UQ within critical fire zones. Using FCER, an Ensemble is compared against an distilled single-pass student model on the WildfireSpreadTS dataset. The student model demonstrates comparable calibration and complementary uncertainty ranking in boundary-relevant regimes. Code is available at https://github.com/jonasvilhofunk/WildfireUQ-FCER