Applications of deep learning in hydrology

The 2017-early 2020 era, marking a proof-of-capability phase for deep learning (DL) in hydrology, has witnessed a rapid expansion of DL in the field. DL is evolving from a niche tool to a method of choice for many prediction tasks, and it starts to offer the full suite of services commonly provided by traditional hydrologic models, including dynamical modeling, forecasting, information retrieval, and inverse modeling. When data are plentiful, time series deep learning methods, especially long short-term memory (LSTM) networks, have shown prowess in capturing dynamics from data. In many studies, LSTM models have been reported to outperform traditional models. They are also capable for small-data settings when trained with data from a few sites, although caution must be taken for mission-critical tasks in such settings. On the other hand, in subsurface hydrology, where observations are limited and scattered, applications of physics-informed or physics-constrained machine learning have emerged. These approaches incorporate physical equations into neural network formulations so that the models can be trained with less data. Moreover, they provide novel opportunities to solve inverse problems for parameter fields or constitutive relationships, enabling us to ask new questions. While applications of interpretive machine learning in hydrology are still few, we argue that in the future a deep integration between domain knowledge and machine learning will lead to not only improved prediction but also better understanding.