Dynamical initialization for the numerical forecasting of ocean surface circulations using a variational assimilation system

A variational data assimilation system is presented for the initialization of an ocean surface circulation forecast system. The authors' variational data assimilation system is designed to satisfy both statistical and dynamical constraints. As is usual, the statistical part of the assimilation scheme corresponds to the optimal interpolation scheme while the dynamical part works as a weak constraint for the model equations except for the time differential terms. Thus this variational data assimilation scheme can be regarded as an extended optimal interpolation capable of obtaining the analysis field that satisfies the model dynamics. Comparison with the results of assimilating altimetric data into a 1.5-layer primitive equation model by the classical optimal interpolation clearly shows the advantage of this assimilation method. For example, the analysis field is significantly improved, in particular, in the western boundary current regions and their extensions, where some assumptions inherent in the optimal interpolation, such as the Gaussian function for the error covariance matrix and the geostrophic balance for the error fields, break down because of the nonlinear nature of the currents. To show the effectiveness of this variational assimilation system for the initialization process, several numerical forecasting experiments are carried out using the analysis fields from the variational assimilation scheme and from the optimal interpolation as initial conditions. The case initialized by the optimal interpolation scheme exhibits inertia-gravity waves generated by the geostrophic initialization leading to contamination of the forecasting result. In contrast, the variational assimilation case can effectively reduce the generation of the gravity waves, thus providing the dynamically consistent analysis field. It is also shown that the accuracy of the short-range forecast with this variational data assimilation is sensitive to the initial guess of the gradient descent method. The computational cost of this assimilation system is lower than that using other sophisticated schemes such as the adjoint method and the Kalman filter, suggesting that this system is suitable for the operational forecasting of western boundary currents.