Learning to Generate Lumped Hydrological Models

In a lumped hydrological model structure, the hydrological function of a catchment is characterized by only a few parameters. Given a set of parameter values, a numerical function useful for hydrological prediction is generated. Thus, this study assumes that the hydrological function of a catchment can be sufficiently well characterized by a small number of latent variables. By specifying the variable values, a numerical function resembling the hydrological function of a real-world catchment can be generated using a generative model. In this study, a deep learning method is used to learn both the generative model and the latent variable values of different catchments directly from their climate forcing and runoff data, without using catchment attributes. The generative models can be used similarly to a lumped model structure, i.e., by estimating the optimal parameter or latent variable values using a generic model calibration algorithm, an optimal numerical model can be derived. In this study, generative models using eight latent variables were learned from data from over 3,000 catchments worldwide, and the learned generative models were applied to model over 700 different catchments using a generic calibration algorithm. The quality of the resulting optimal models was generally comparable to or better than that obtained using 36 different types of lump model structures or using non-generative deep learning methods. In summary, this study presents a data-driven approach for representing the hydrological function of a catchment in low-dimensional space and a method for reconstructing specific hydrological functions from the representations.