Interpreting Deep Machine Learning for Streamflow Modeling Across Glacial, Nival, and Pluvial Regimes in Southwestern Canada

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Abstract
The interpretation of deep learning (DL) hydrological models is a key challenge in data-driven modeling of streamflow, as the DL models are often seen as “black box” models despite often outperforming process-based models in streamflow prediction. Here we explore the interpretability of a convolutional long short-term memory network (CNN-LSTM) previously trained to successfully predict streamflow at 226 stream gauge stations across southwestern Canada. To this end, we develop a set of sensitivity experiments to characterize how the CNN-LSTM model learns to map spatiotemporal fields of temperature and precipitation to streamflow across three streamflow regimes (glacial, nival, and pluvial) in the region, and we uncover key spatiotemporal patterns of model learning. The results reveal that the model has learned basic physically-consistent principles behind runoff generation for each streamflow regime, without being given any information other than temperature, precipitation, and streamflow data. In particular, during periods of dynamic streamflow, the model is more sensitive to perturbations within/nearby the basin where streamflow is being modeled, than to perturbations far away from the basins. The sensitivity of modeled streamflow to the magnitude and timing of the perturbations, as well as the sensitivity of day-to-day increases in streamflow to daily weather anomalies, are found to be specific for each streamflow regime. For example, during summer months in the glacial regime, modeled daily streamflow is increasingly generated by warm daily temperature anomalies in basins with a larger fraction of glacier coverage. This model's learning of “glacier runoff” contributions to streamflow, without any explicit information given about glacier coverage, is enabled by a set of cell states that learned to strongly map temperature to streamflow only in glacierized basins in summer. Our results demonstrate that the model's decision making, when mapping temperature and precipitation to streamflow, is consistent with a basic physical understanding of the system.

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