AN OBJECTIVE MAPPING METHOD FOR ESTIMATING GEOSTROPHIC VELOCITY FROM HYDROGRAPHIC SECTIONS INCLUDING THE EQUATOR

Objective mapping can remove the equatorial singularity from the probl em of estimating geostrophic shear from noisy density measurements. Th e method uses the complete thermal wind relation, so it is valid unifo rmly on and off the equator. Errors in the thermal wind balance are du e to neglected terms in the momentum balance, which are treated as noi se in the inverse problem. The question of whether the geostrophic bal ance holds near the equator is restated as a need to estimate the size of the ageostrophic noise in the thermal wind equation. Objective map ping formalizes the assumptions about the magnitudes and scales of the geostrophic currents and about the magnitudes and scales of the ageos trophic terms and measurement errors. The uncertainty of the velocity estimates is calculated as part of the mapping and depends on the sign al to noise ratio (geostrophic density signal to ageostrophic ''noise' ') in the data, as well as the station spacing and the scales assumed for the geostrophic velocities. The method is used to map zonal veloci ty from a mean Hawaii-Tahiti Shuttle density section. These are compar ed with previous velocity estimates for the same dataset calculated us ing other techniques. By choosing appropriate scales, the objective ma p can duplicate previous results. New temperature data are presented f rom a repeating, high-resolution expendable bathythermograph section c rossing the equator at about 170-degrees-W with four cruises a year be tween 1987-1991. There appear to be significant differences between th is mean temperature and the shuttle mean temperature. Temperature is c onverted to density with the aid of a mean T-S relation and geostrophi c velocity maps are calculated for the 4-year mean. The mean geostroph ic undercurrent obtained from our sections is weaker than in the shutt le estimate and is centered slightly north of the equator. Enforcing s ymmetry about the equator removes the offset of the current, giving a stronger, but narrow undercurrent. The density field apparently includ es significant (O(0.5 kg M-3)) large-scale ageostrophic variability wh ich makes velocity estimates from single cruises poorly determined nea r the equator.