A Machine Learning Approach for Data Assimilation into Terrestrial Hydrology Models

The potential of Machine Learning (ML) in hydrological modeling is undeniable. However, there are still many challenges to overcome. One major challenge is ML by its nature can only be expected to perform well in situations well represented by the data, and in general obtaining complete data records is at best impractical, and at worst infeasible. Moreover, non-stationarity ( e.g. anthropogenic effects) can make historical records incompatible with the current climatology. This is particularly troublesome when modeling dynamical systems because poor predictions propagate forward in time; even the occasional bad prediction can cause lasting effects. To overcome this, we propose a theory-guided machine learning approach that learns from assimilated data only when available observation data is similar to current conditions. This is accomplished by correcting a process-based model (PBM) at each time-step using a Gaussian Process (GP) with a vanishing prior mean. This prior allows information to be assimilated into the model only when it's available, otherwise it extrapolates to zero and reverts back to the PBM. Unlike traditional assimilation ( e.g. EnKF), here the likelihood function is modeled directly using a nonlinear-parametric model that learns the model structural error through the error patterns between the PBM and observation. By learning structural error, the corrective model is able to transfer information and make spatial-temporal corrections both in- and out-of-sample. It also provides a direct representation of the structural error at the process-level to perform diagnostics on to gain insight into model deficiencies. The approach is demonstrated using in-situ measurements of soil moisture at FluxNet stations where (out-of-sample) RMSE improvements of up to ~3x and correlation coefficients ~0.98 are obtained for yearly validation periods. Incorporating remote sensing data and multivariate GPs to predict additional state variables are discussed as the next steps towards building a global hybrid terrestrial-hydrology model.