Continuous data assimilation of drifting buoy trajectory into an equatorial Pacific Ocean model

A variational adjoint method is developed to assimilate the trajectories of drifting buoys into a simple ocean model. The method is applied to the equatorial Pacific Ocean. In the variational formalism a cost function measuring the distance between the trajectories of the model simulated buoys and of the observed buoys is minimized. Adjoint equations are forced by the model-data misfit that is proportional to the difference of model simulated and observed buoy positions. A hypothetical mean upper layer thickness of the model is used as a control parameter. The optimal spatial structure giving the best fit of the model to the observations is determined, and it is used as the initial condition of the model. Model simulated data are used first in several experiments and later experiments with real observations are discussed. Assimilation periods and regional effects with relations of buoy trajectory and wave propagation on the assimilation processes are examined. Upper layer thickness in the western equatorial region is improved relatively better than in the eastern region for the assimilation period of three months, because the western equatorial region acts as a special “caustic” region in the adjoint system. This east-west inhomogeneity vanishes using a one-year period. The upper layer thickness optimized with real buoy data is compared with independently observed sea level data.