Joint distribution of upstream runoff governs downstream river-discharge prediction uncertainty in distributed ML models

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.

Evaluating Transformer and LSTM Frameworks for Prediction in Ungauged Basins

Watershed networks exhibit convergent topologies in which multiple tributaries merge into downstream channels,integrating diverse upstream hydrological processes. In ungauged basins, the absence of direct observations increases uncertainty and limits the ability to anticipate extreme events. This study evaluates whether an encoder-only Transformer provides an advantage over an LSTM for upstream streamflow inference under limited hydrologic information, using retrospective simulations from the NOAA National Water Model (NWM). Across both upstream-only and combined configurations, the LSTM showed stronger overall performance than the Transformer model across the two configurations. Incorporating downstream information further boosted performance for all models, increasing median NNSE by more than 60%. Rather than treating this as a leaderboard-style comparison, we interpret the experiments as a test of architectural inductive bias for hydrologic sequence inference. The results indicate that recurrent memory remains better aligned with this upstream reconstruction task than an encoder-only Transformer, while downstream hydrologic context provides a strong auxiliary constraint that substantially improves prediction skill across architectures