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

2026-07-03

AI Summary

This study addresses the severe under-dispersion commonly observed in ensemble predictions of downstream river discharge from distributed probabilistic hydrological models, which often arises from neglecting the spatial dependence structure among upstream runoff uncertainties. The authors develop a watershed-scale probabilistic LSTM model coupled with the Hayami routing scheme and demonstrate, for the first time, that transitioning from lumped to distributed modeling necessitates explicit representation of spatial dependencies in upstream uncertainties. To this end, they propose a joint sampling strategy based on quantile matching, which substantially restores the predictive uncertainty range at downstream locations in a Japanese basin case study. The resulting ensembles achieve dispersion levels comparable to those of a lumped reference model, effectively mitigating the under-dispersion caused by naive random pairing of upstream realizations.

Abstract

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.

Problem

• distributed hydrological modeling
• uncertainty quantification
• joint distribution
• runoff prediction
• streamflow forecasting

Innovation

• distributed hydrological modeling
• probabilistic prediction
• joint uncertainty
• runoff routing
• ensemble calibration