Hierarchically Disentangled Recurrent Network for Factorizing System Dynamics of Multi-scale Systems

We present a knowledge-guided machine learning (KGML) framework for modeling multi-scale processes, and study its performance in the context of streamflow forecasting in hydrology. Specifically, we propose a novel hierarchical recurrent neural architecture that factorizes the system dynamics at multiple temporal scales and captures their interactions. This framework consists of an inverse and a forward model. The inverse model is used to empirically resolve the system's temporal modes from data (physical model simulations, observed data, or a combination of them from the past), and these states are then used in the forward model to predict streamflow. In a hydrological system, these modes can represent different processes, evolving at different temporal scales (e.g., slow: groundwater recharge and baseflow vs. fast: surface runoff due to extreme rainfall). A key advantage of our framework is that once trained, it can incorporate new observations into the model's context (internal state) without expensive optimization approaches (e.g., EnKF) that are traditionally used in physical sciences for data assimilation. Experiments with several river catchments from the NWS NCRFC region show the efficacy of this ML-based data assimilation framework compared to standard baselines, especially for basins that have a long history of observations. Even for basins that have a shorter observation history, we present two orthogonal strategies of training our FHNN framework: (a) using simulation data from imperfect simulations and (b) using observation data from multiple basins to build a global model. We show that both of these strategies (that can be used individually or together) are highly effective in mitigating the lack of training data. The improvement in forecast accuracy is particularly noteworthy for basins where local models perform poorly because of data sparsity.