Gradient-Based Inverse Estimation for a Rainfall-Runoff Model

Abstract

Recent advances in deep learning for neural networks with large numbers of parameters have been enabled by automatic differentiation, an algorithmic technique for calculating gradients of measures of model fit with respect to model parameters. Estimation of high-dimensional parameter sets is an important problem within the hydrological sciences. Here, we demonstrate the effectiveness of gradient-based estimation techniques for high-dimensional inverse estimation problems using a conceptual rainfall-runoff model. In particular, we compare the effectiveness of Hamiltonian Monte Carlo and automatic differentiation variational inference against two nongradient-dependent methods, random walk Metropolis and differential evolution Metropolis. We show that the former two techniques exhibit superior performance for inverse estimation of daily rainfall values and are much more computationally efficient on larger data sets in an experiment with synthetic data. We also present a case study evaluating the effectiveness of automatic differentiation variational inference for inverse estimation over 25 years of daily precipitation conditional on streamflow observations at three catchments and show that it is scalable to very high dimensional parameter spaces. The presented results highlight the power of combining hydrological process-based models with optimization techniques from deep learning for high-dimensional estimation problems.