Harnessing Generative Deep Learning for Enhanced Ensemble Data Assimilation

Abstract Hydrologic modeling faces challenges due to various sources of uncertainty, the inherent nonlinearity, and high dimensionality of Earth systems. Data assimilation (DA) methods are known to improve the accuracy and account for uncertainties in modeling; however, they may be limited by restrictive assumptions about error distributions and challenges associated with updating model prognostic variables, hence, representing the posterior distributions. To address these challenges, we present a new hydrologic DA method inspired by the similarities in theoretical backgrounds of DA and generative deep learning. The proposed Hydrologic Generative Ensemble Data Assimilation (HydroGEnDA) leverages deep learning‐based autoencoders, and deep generative modeling to perform DA in a unified latent space and finally a resampling method in physical space. The HydroGEnDA benefits from an autoencoder that transforms data to a latent space and a generative model that learns the underlying distribution of model states, then conditioning the sampling from this distribution to the observed data. Finally, resampling in physical space further improves the performance of the DA method. The HydroGEnDA involves an offline training stage without relying on observations, utilizing hydrologic model outputs instead to train the deep learning models. Following the training stage, the inference stage assimilates observed data to update the states. The method is tested through several synthetic experiments with varying observation noise levels with the Lorenz‐63 model, as well as real hydrologic case studies using the coupled SNOW‐17 and SAC‐SMA models across diverse watersheds. The results demonstrate that the HydroGEnDA outperforms previous DA methods in both experiments.