THE SEASONAL STEADY CIRCULATION OF THE EASTERN MEDITERRANEAN DETERMINED WITH THE ADJOINT METHOD

In this paper we use a rather unconventional approach to determine the steady seasonal circulation of the Eastern Mediterranean. Traditional calculations rely either on prognostic models spun-up with different forcing functions or on inverse methods having rather simple dynamics. In the present applications one of the most sophisticated inverse tec hniques, the adjoint method of control theory, is used to find the mod el state that is optimally consistent with the model dynamics, with a prescribed climatology and is steady in time. The model used is the GF DL primitive equation model in its fully time-dependent non-linear ver sion forced by seasonal wind-stress fields that are kept steady for ea ch calculation. The prescribed climatology consists of the seasonal hy drographies of the temperature and salinity fields. Steadiness upon th e seasonal time scale is required as a term in the cost function of th e adjoint that penalizes the tendencies of the prognostic variables. T his use of the adjoint method reconstructs the steady seasonal wind-dr iven circulation in an ocean with a prescribed baroclinic structure. A s such, it is equivalent to a prognostic spin-up calculation with stea dy winds and the robust diagnostic applied. i.e. adding a term that re laxes the temperature and salinity fields to the seasonal climatologie s with a time constant of 3 months. To assess the ''success'' of these calculations, the success of the inversion must be quantified. The ex amination of the final data misfits and steady state residuals shows t hat steady state has indeed been reached. The steady-state residuals a re always much smaller than the data misfits and both of them are alwa ys small, well below the one standard deviation value for each field. Thus, we can assess that a meaningful solution has indeed been attaine d. To assess further if these solutions are reasonable, we have carrie d out for comparison robust diagnostic calculations with a time consta nt of 3 months. The circulations thus obtained are extremely similar t o the adjoint solutions in reproducing the overall patterns as well as the individual sub-basin scale gyres and interconnecting currents and meandering jets. The circulations obtained with the two approaches ar e also equally strong. However, both the adjoint and the robust diagno stic results produce an overall barotropic transport that is one order of magnitude bigger than that observed. They also both show anomalous ly strong vortex structures in regions of sharp topographic breaks con necting the deep interior to the shelves, for which no observational e vidence is available. These unrealistic features can be explained by t aking into account that with the short time scale of 3 months used in both approaches biased solutions may be obtained. These biases are due to inconsistencies between the rough topography used and the smooth c limatologies, that lead to a misrepresentation of the important JEBAR effect. This explanation is supported by a further robust diagnostic c alculation in which the time constant is increased in the deep layers that gives a circulation intensity much more realistic.