A. Bergamasco et al., THE SEASONAL STEADY CIRCULATION OF THE EASTERN MEDITERRANEAN DETERMINED WITH THE ADJOINT METHOD, Deep-sea research. Part 2. Topical studies in oceanography, 40(6), 1993, pp. 1269-1298
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.