Deep learning based coordinates transformations for improving process understanding in hydrological modeling system

Improving the understanding of processes is vital to hydrological modeling. One key challenge is how to extract interpretable information that can describe the complex hydrological system from the growing number of observation data to advance our understanding of processes and modeling. To address the problem, we propose a data-driven framework to discover coordinate transformation, which transfers original observations to a reduced-dimension system. The framework combines deep learning method with sparse regression to approximate the specific hydrological process: deep learning methods have a rich representation to promote generalization, and sparse regression can sparsely identify parsimonious models to promote interpretability. By doing so, we can identify the essential latent variables under a physically meaning-wise coordinate system where the hydrological processes are linearly and sparsity represented to capture the behavior of the system from observations. To demonstrate the framework, we focus on the evaporation process. The relationships between potential evaporation and climate variables including long/short wave radiation, air temperature, air pressure, relative humidity, and wind speed are quantified. The connection between the climate variables and coordinates components extracted are evaluated to capture the pattern of climate variables in the component space. The robustness and statistical stability of the framework is examined based on distributed observations from FluxNet towers over North America. The resulting modeling framework shows the potential of deep learning methods for improving our knowledge of the hydrological system.