Four-dimensional variational data assimilation with a sea-ice thickness emulator

Developing operational data assimilation systems for sea-ice models is challenging, especially using a variational approach due to the absence of adjoint models. NeXtSIM, a sea-ice model based on a brittle rheology paradigm, enables high-fidelity simulations of sea-ice dynamics at mesoscale resolution (ĝ1/410 km) but lacks an adjoint. By training a neural network as an Arctic-wide emulator for sea-ice thickness based on mesoscale simulations with neXtSIM, we gain access to an adjoint. Building on this emulator and its adjoint, we introduce a four-dimensional variational (4D-Var) data assimilation system to correct the emulator's bias and to better position the marginal ice zone (MIZ). Firstly, we perform twin experiments to demonstrate the capabilities of this 4D-Var system and to evaluate two approximations of the background covariance matrix. These twin experiments demonstrate that the assimilation improves the positioning of the MIZ and enhances the forecast quality, achieving an average reduction in sea-ice thickness root-mean-squared error of 0.8m compared to the free run. Secondly, we assimilate real CS2SMOS satellite retrievals with this system. While the assimilation of these rather smooth retrievals amplifies the loss of small-scale information in our system, it effectively corrects the forecast bias. The forecasts of our 4D-Var system achieve a similar performance as the operational sea-ice forecasting system neXtSIM-F. These results pave the way to the use of deep learning-based emulators for 4D-Var systems to improve sea-ice modeling.