Machine learning (ML) models, and Long Short-Term Memory (LSTM) networks in particular, have demonstrated remarkable performance in streamflow prediction and are increasingly being used by the hydrological research community. However, most of these applications do not include uncertainty quantification (UQ). ML models are data driven and may suffer from large extrapolation errors when applied to changing climate/environmental conditions. UQ is required to ensure model trustworthiness, improve understanding of data limits and model deficiencies, and avoid overconfident predictions in extrapolation. Here, we propose a novel UQ method, called PI3NN, to quantify prediction uncertainty of ML models and integrate the method with LSTM networks for streamflow prediction. PI3NN calculates Prediction Intervals by training 3 Neural Networks and uses root-finding methods to determine the interval precisely. Additionally, PI3NN can identify out-of-distribution (OOD) data in a nonstationary condition to avoid overconfident prediction. We apply the proposed PI3NN-LSTM method in both the snow-dominant East River Watershed in the western US and the rain-driven Walker Branch Watershed in the southeastern US. Results indicate that for the prediction data (which have similar features as the training data), PI3NN precisely quantifies the prediction uncertainty with the desired confidence level; and for the OOD data where the LSTM network fails to make accurate predictions, PI3NN produces a reasonably large uncertainty bound indicating the untrustworthy result to avoid overconfidence. PI3NN is computationally efficient, reliable in training, and generalizable to various network structures and data with no distributional assumptions. It can be broadly applied in ML-based hydrological simulations for credible prediction.

Multimodel ensembling has been widely used to improve climate model predictions, and the improvement strongly depends on the ensembling scheme. In this work, we propose a Bayesian neural network (BNN) ensembling method, which combines climate models within a Bayesian model averaging framework, to improve the predictive capability of model ensembles. Our proposed BNN approach calculates spatiotemporally varying model weights and biases by leveraging individual models’ simulation skill, calibrates the ensemble prediction against observations by considering observation data uncertainty, and quantifies epistemic uncertainty when extrapolating to new conditions. More importantly, the BNN method provides interpretability about which climate model contributes more to the ensemble prediction at which locations and times. Thus, beyond its predictive capability, the method also brings insights and understanding of the models to guide further model and data development. In this study, we apply the BNN weighting scheme to an ensemble of CMIP6 climate models for monthly precipitation prediction over the conterminous United States. In both synthetic and real case studies, we demonstrate that BNN produces predictions of monthly precipitation with higher accuracy than three baseline ensembling methods. BNN can correctly assign a larger weight to the regions and seasons where the individual model fits the observation better. Moreover, its offered interpretability is consistent with our understanding of localized climate model performance. Additionally, BNN shows an increasing uncertainty when the prediction is farther away from the period with constrained data, which appropriately reflects our predictive confidence and trustworthiness of the models in the changing climate.