Hybrid covariance super-resolution data assimilation

Abstract The super-resolution data assimilation (SRDA) enhances a low-resolution (LR) model with a Neural Network (NN) having learned the differences between high and low-resolution models offline and performs data assimilation in high-resolution (HR). The method enhances the accuracy of the EnKF-LR system for a minor computational overhead. However, performance quickly saturates when increasing the ensemble size due to the error introduced by the NN. We therefore combine the SRDA with the mixed-resolution data assimilation method (MRDA), into a method called ''Hybrid covariance super-resolution data assimilation" (Hybrid SRDA). The forecast step runs an ensemble at two resolutions (high and low). The assimilation is done in the HR space by performing super-resolution on the LR members with the NN. The assimilation uses the hybrid covariance that combines the emulated and dynamical HR members. The scheme is extensively tested with a quasi-geostrophic model in twin experiments, with the LR grid being twice coarser than the HR. The Hybrid SRDA outperforms the SRDA, the MRDA, and the EnKF-HR at a given computational cost. The benefit is the largest compared to the EnKF-HR for small ensembles but even with larger computational resources it is worth using a mix of high and low resolution members. Besides, the Hybrid SRDA, the EnKF-HR, and the SRDA, unlike the MRDA, prevent the smoothing of dynamical structures of the background error covariance matrix. The Hybrid SRDA method is an attractive solution because it is customizable to available resources.