Data assimilation techniques are important for combining observations with numerical models. Here, we approximate the adjoint of viscous-plastic dynamics (adjoint-VP) to replace the adjoint of free-drift dynamics (adjoint-FD) for developing an advanced Arctic Ocean and sea ice modeling and adjoint-based assimilation system. We find that adjoint-VP provides a better ocean and sea ice estimation than adjoint-FD, considering the residual errors and adjustments of the atmospheric states.