Upstream Runoff Joint Distribution Critical for River Prediction Uncertainty

Quantifying the uncertainty in hydrological predictions is essential for making informed operational decisions, especially in water resource management. While recent generative machine learning methods have advanced probabilistic streamflow prediction, they have largely been confined to "lumped" models that directly predict a basin's outlet. Concurrently, deterministic LSTM runoff models are increasingly applied at finer scales (grid or catchment) and then routed through river networks to create spatially continuous, physically consistent discharge fields. This paper argues that extending probabilistic prediction from lumped to distributed models introduces a critical new requirement: the joint distribution of upstream runoff generation must be sampled cohesively, not independently. The authors demonstrate that if upstream ensemble members are randomly matched, the resulting downstream ensembles are severely under-dispersed, failing to capture the true uncertainty. Using Japan as a case study, they trained two probabilistic basin-scale runoff LSTMs and routed their runoff through a Hayami scheme. They found that a simple quantile matching strategy significantly restored the spread of the direct basin-scale reference. This underscores that the transition to distributed probabilistic hydrology necessitates explicit consideration of the spatial joint structure of runoff uncertainty to ensure accurate and reliable downstream predictions.