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A variational approach is used to develop an objective analysis technique which produces monthly average 1-deg pseudostress vector fields over the Indian Ocean. A, cost functional is constructed which consists of five terms, each expressing a lack of fit to prescribed conditions. The first expresses the proximity to the input (first-guess) field. The second deals with the closeness of fit to the climatological value for that month. The third is a measure of data roughness, and the fourth and fifth are kinematic constraints on agreement of the curl and divergence of the results to the curl and divergence of the climatology. Each term also has a coefficient (weight) which determines how closely the minimization fits each lack of fit. These weights are determined by comparing the results using various weight combinations to an independent subjective analysis of the same dataset. The cost functional is minimized using the conjugate-gradient method. Results from various weight combinations are presented for the months of January and July 1984 and the results examined in terms of thee selections. Quantitative and qualitative comparisons to the subjective analysis are made to find which weight combination provides the best results. It was found that the weight on the second term balances the influence of the original (first-guess) field and climatology. The smoothing term weight determines how wide an area deviations of the first guess from climatology is affected. The weights on the kinematic terms are fine-tuning parameters.
Legler et al. (Sat,) studied this question.