Improving the accuracy of streamflow predictions in ungauged basins (PUB) has long been a significant challenge in hydrological research. This study hypothesizes that deep learning-based PUB can be enhanced for historical streamflow reconstruction by integrating local climate data from ungauged or partially gauged basins (the target site) with streamflow measurements from nearby gauged basins (donor sites). The rationale is that streamflow records from donor sites offer valuable information for predicting streamflow at the target site. However, in some instances, local weather data may be more readily available, while available donors might be poorly correlated with the target. Therefore, prediction accuracy can be improved by weighting both sources effectively. To test this hypothesis, we conducted a case study using over 200 streamflow gauges in the Great Lakes region. We developed a multi-layer perceptron to estimate Spearman rank correlations of streamflow between basins, aiding in the selection of donor sites. These estimated correlations were fed into a Long Short-Term Memory (LSTM) network, along with streamflow data from donor sites and weather data from target sites. We compared this model against two other LSTMs, one trained only on climate data and the other solely on streamflow data from donor sites, as well as the average prediction from those two models. Our findings indicate that the integrated approach outperforms the alternatives, particularly for partially gauged sites and natural ungauged sites. Lastly, we demonstrate the value of the approach for improving lake-wide runoff estimates and underscore its implications for quantifying the Great Lakes water balance.

Stochastic Watershed Models (SWMs) are emerging tools in hydrologic modeling used to propagate uncertainty into model predictions by adding samples of model error to deterministic simulations. One of the most promising uses of SWMs is uncertainty propagation for hydrologic simulations under climate change. However, a core challenge with this approach is that the predictive uncertainty inferred from hydrologic model errors in the historical record may not correctly characterize the error distribution under future climate. For example, the frequency of physical processes (e.g., snow accumulation and melt, droughts and hydrologic recessions) may change under climate change, and so too may the frequency of errors associated with those processes. In this work, we explore for the first time non-stationarity in hydrologic model errors under climate change in an idealized experimental design. We fit one hydrologic model to historical observations, and then fit a second model to the simulations of the first, treating the first model as the true hydrologic system. We then force both models with climate change impacted meteorology and investigate changes to the error distribution between the models in historical and future periods. We develop a hybrid machine learning method that maps model input and state variables to predictive errors, allowing for non-stationary error distributions based on changes in the frequency of internal state variables. We find that this procedure provides an internally consistent methodology to overcome stationarity assumptions in error modeling and offers an important path forward in developing stochastic hydrologic simulations under climate change.