Producing accurate maps of the Gulf Stream thermal front using objective analysis

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Abstract
The objective analysis (OA) method is adapted in order to map the Gulf Stream thermal front, and resulting output maps are verified against independent data. This extension of the OA method involves removing the mean field and normalizing the variance prior to performing the objective analysis; both of these fields are restored afterward. In this way, the mapped field decays to an appropriate mean field far away from the measurement sites, and the statistics of the normalized perturbation field are homogeneous, as is required by the OA method. We test the sensitivity of the adapted OA method to variations in four control parameters: mean field, correlation function, standard deviation field, and input sampling interval. Of these, specification of the mean field has the most influence upon the mapped fields, whereas the correlation function has more influence upon the estimated error fields. Using a time‐averaged mean field produces the best maps of the thermal field. The space‐time correlation function is determined empirically from 5 years of inverted echo sounder data collected in the Gulf Stream. Interestingly, even in this frontal region the observed correlations do not differ significantly in the cross‐stream and downstream directions. An input sampling interval δt = 1 day (with input data only accepted within T = ±1 day) proved to be best, as power spectra confirm that all significant variance is preserved. Within a reasonable variation of the control parameters, this adapted OA method is robust, and accurate maps of the thermal field are obtained. The OA maps of the Gulf Stream thermal field are verified against nearly 500 independent measurements from expendable bathythermographs and air‐dropped expendable bathythermographs. The rms difference is determined to be 47 m, which is less than the contour interval of 50 m, and which represents less than 7% of the dynamic range (>700 m) found across the Gulf Stream. Thus the adapted OA method can be applied to frontal regions, such as the Gulf Stream, where the traditional method cannot be used.

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