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 techniques, the adjoint method of control theory, is used to find the model state that is optimally consistent with the model dynamics, with a prescribed climatology and is steady in time. The model used is the GFDL primitive equation model in its fully time-dependent non-linear version forced by seasonal wind-stress fields that are kept steady for each calculation. The prescribed climatology consists of the seasonal hydrographies of the temperature and salinity fields. Steadiness upon the seasonal time scale is required as a term in the cost function of the adjoint that penalizes the tendencies of the prognostic variables. This use of the adjoint method reconstructs the steady seasonal wind-driven circulation in an ocean with a prescribed baroclinic structure. As such, it is equivalent to a prognostic spin-up calculation with steady winds and the robust diagnostic applied, i.e. adding a term that relaxes the temperature and salinity fields to the seasonal climatologies with a time constant of 3 months. To assess the "success' of these calculations, the success of the inversion must be quantified. The examination of the final data misfits and steady state residuals shows that steady state has indeed been reached. The steady-state residuals are always much smaller than the data misfits and both of them are always small, well below the one standard deviation value for each field. Thus, we can assess that a meaningful solution has indeed been attained. To assess further if these solutions are reasonable, we have carried out for comparison robust diagnostic calculations with a time constant of 3 months. The circulations thus obtained are extremely similar to 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 are also equally strong. However, both the adjoint and the robust diagnostic results produce an overall barotropic transport that is one order of magnitude bigger than that observed. They also both show anomalously strong vortex structures in regions of sharp topographic breaks connecting the deep interior to the shelves, for which no observational evidence is available. These unrealistic features can be explained by taking 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 climatologies, that lead to a misrepresentation of the important JEBAR effect. This explanation is supported by a further robust diagnostic calculation in which the time constant is increased in the deep layers that gives a circulation intensity much more realistic. Overall, this application of the adjoint method to the GFDL model shows that it can be successfully used to find meaningful optimal solutions. These solutions also prove to be reasonable when compared with analogous robust diagnostics results.