A Generalized Deep Learning-Based Ensemble Smoother for Data
Assimilation of Hydrological Systems
Abstract
To reduce simulation uncertainty and improve process understanding of
hydrological systems, integrating models with observations through data
assimilation techniques is paramount. Among these, the ensemble smoother
(ES) stands out for its ease of implementation and high computational
efficiency. When tackling problems involving non-linear processes and
non-Gaussian distributions, leveraging deep learning (DL) within ES,
termed the ES(DL) method, proves superior to the Kalman-based
counterpart. However, the original ES(DL) method is constrained by the
traditional paradigm that builds a mapping from the innovation vector
(i.e., the difference between observations and model predictions) to the
update vector (i.e., the difference between posterior and prior
state/parameters). In this study, we introduce a generalized form of
ES(DL), where the traditional ES(DL) approach becomes its special case.
We explore the optimal implementation of ES(DL) through surface and
subsurface scenarios, spanning various dimensions (low to high) and
parameter distributions (Gaussian to non-Gaussian). Notably, certain
implementations of ES(DL), which diverge significantly from the
traditional approach, can yield similar or even better outcomes,
especially under the non-Gaussian condition. While this study’s focus
lies on the smoothing approach for parameter estimation, the proposed
formulation can be extended to filtering problems, facilitating model
state updates.