Adjoint data assimilation in coupled atmosphere-ocean models: Determining initial conditions in a simple equatorial model

The general problem of retrieving the initial conditions in coupled atmosph ere-ocean models by the adjoint data assimilation method was formulated. Fo r a simple coupled equatorial model, where the atmosphere and the ocean wer e each represented by a linear shallow water model, retrieval of three ocea nic. initial conditions (the sea level height [SLH] and the two horizontal current components) was tested with identical twin experiments. Wind and SL H data, generated from a 90-day unstable local-growth simulation of a warm event, were assimilated to test the effects of (i) data type and sparsity, (ii) initial guess, and (iii) noisy data on retrieving the oceanic initial conditions. SLH data were found to be more efficient in retrieving the oceanic initial conditions than the wind data, and the initial SLH field was more accuratel y retrieved than the initial currents. The retrieval of the initial current fields was sensitive to the temporal density of data, especially with wind data, where once a day would be the minimum density needed. As the initial guess of the oceanic state could contain errors in magnitude and phase (i. e. location) of the warm event anomaly, data assimilation was found to read ily correct the error in the magnitude of the initial guess, but not the la rge phase error. Assimilation of noisy data showed that the retrieval of th e initial conditions was far more sensitive to noise in the SLH data, than in the wind data.