Streamflow simulation in data-scarce basins using Bayesian and physics-informed machine learning models

Hydrologic predictions at rural watersheds are important but also challenging due to data shortage. Long Short-TermMemory (LSTM) networks are a promising machine learning approach and have demonstrated good performance in streamflow predictions. However, due to its data-hungry nature, most of LSTM applications focused on well-monitored catchments with abundant and high quality observations. In this work, we investigate predictive capabilities of LSTM in poorly monitored watersheds with short observation records. To address three main challenges of LSTM applications in data-scarce locations, i.e., overfitting, uncertainty quantification (UQ), and out-of-distribution prediction, we evaluate different regularization techniques to prevent overfitting, apply a Bayesian LSTM for UQ, and introduce a physics-informed hybrid LSTM to enhance out-of-distribution prediction. Through case studies in two diverse sets of catchments with and without snow influence, we demonstrate that: (1) when hydrologic variability in the prediction period is similar to the calibration period, LSTM models can reasonably predict daily streamflow with Nash-Sutcliffe efficiency above 0.8, even with only two years of calibration data. (2) When the hydrologic variability in the prediction and calibration periods is dramatically different, LSTM alone does not predict well, but the hybrid model can improve the out-of-distribution prediction with acceptable generalization accuracy. (3) L2 norm penalty and dropout can mitigate overfitting, and Bayesian and hybrid LSTM have no overfitting. (4) Bayesian LSTM provides useful uncertainty information to improve prediction understanding and credibility. These insights have vital implications for streamflow simulation in watersheds where data quality and availability are a critical issue.