  A lumped hydrological model structure can be considered a generative model
because, given a set of parameter values, it can generate a hydrological
modeling function that accurately predicts the behavior of a catchment under
external forcing. It is implicitly assumed that a small number of variables
(i.e., the model parameters) can sufficiently characterize variations in the
behavioral characteristics of different catchments. This study adopts this
assumption and uses a deep learning method to learn a generative model of
hydrological modeling functions directly from the forcing and runoff data of
multiple catchments. The learned generative model uses a small number of latent
variables to characterize a catchment's behavior, so that assigning values to
these latent variables produces a hydrological modeling function that resembles
a real-world catchment. The learned generative model can be used similarly to a
lumped model structure, i.e., the optimal hydrological modeling function of a
catchment can be derived by estimating optimal parameter values (or latent
variables) with a generic calibration algorithm. In this study, a generative
model was learned from data from over 3,000 catchments worldwide. The model was
then used to derive optimal modeling functions for over 700 different
catchments. The resulting modeling functions generally showed a quality that
was comparable to or better than 36 types of lumped model structures. Overall,
this study demonstrates that the hydrological behavior of a catchment can be
effectively described using a small number of latent variables, and that
well-fitting hydrologic model functions can be reconstructed from these
variables.
