An adjoint method for the assimilation of statistical characteristics into eddy-resolving ocean models

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Koehl, Armin ; Willebrand, Jürgen (2002)

The study investigates perspectives of the parameter estimation problem with the adjoint methodin eddy-resolving models. Sensitivity to initial conditions resulting from the chaotic nature ofthis type of model limits the direct application of the adjoint method by predictability.Prolonging the period of assimilation is accompanied by the appearance of an increasing numberof secondary minima of the cost function that prevents the convergence of this method. In theframework of the Lorenz model it is shown that averaged quantities are suitable for describinginvariant properties, and that secondary minima are for this type of data transformed intostochastic deviations. An adjoint method suitable for the assimilation of statistical characteristicsof data and applicable on time scales beyond the predictability limit is presented. The approachassumes a greater predictability for averaged quantities. The adjoint to a prognostic model forstatistical moments is employed for calculating cost function gradients that ignore the finestructure resulting from secondary minima. Coarse resolution versions of eddy-resolving modelsare used for this purpose. Identical twin experiments are performed with a quasigeostrophicmodel to evaluate the performance and limitations of this approach in improving models byestimating parameters. The wind stress curl is estimated from a simulated mean stream function.A very simple parameterization scheme for the assimilation of second-order moments is shownto permit the estimation of gradients that perform efficiently in minimizing cost functions.DOI: 10.1034/j.1600-0870.2002.01294.x
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