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The optimization method

A cost function, J, measures the misfits between the model and the observations over the whole period of integration. Iterative minimization of J is carried out by the so-called adjoint method of least-squares, which uses Lagrange multipliers to enforce the model as constraints and to provide numerical estimates of the descent directions.

**Figure 3:**
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As with any estimation method, adequate specification of the weight matrices is a central problem and requires much attention. As examples, the estimated error variances of the geoid and for the atmospheric heat flux are shown below.

**Figure 4:**
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The adjoint model is built in a quasi-automatic way by the Tangent linear and Adjoint Model Compiler (TAMC, Giering and Kaminsky, 1998). The control variables are the initial T and S fields, atmospheric forcing components every 10 days and the prescribed fields at the open boundaries, as illustrated below.

**Figure 5:**
$\begin{figure} \setlength{\unitlength}{1cm} \begin{picture} (20,10)(1,-0) \e... ...file=adjoint.eps, height=380pt, width=400pt, angle=-0}\end{picture} \end{figure}$

Detlef Stammer
1999-06-22