An Observational Streamfunction in the Gulf Stream

Contours of the main thermocline (12°C isotherm depth: Z12) topography objectively generated from Inverted Echo Sounder observations in the Gulf Stream may be treated as a baroclinic, geostrophic streamfunction ψ. As preliminary steps, the authors developed techniques to estimate geostrophic velocity Vψ = k×(g*/f)∇Z12 and geostrophic vorticity ζψ =(g*/f)∇2Z12. In doing this the authors also determined a reduced gravity g* = 1.53 cm s−2 by least-squares fitting the estimated Vψ to observed Vbc, velocities (i.e., fine-tuned for the ψ at 400 m relative to 3000 m). Accuracy of the objective maps of ψ is investigated by comparing Vψ, against Vbc directly measured from tall current meter moorings and ζψ against vorticity ζp separately estimated using a “rigid-stream” velocity section and path curvature. The Vψ, values, with speeds up to 100 cm s−1, are correlated with Vbc at the 99% confidence level, and the two measurements differ by only 10 cm s−1 rms error. Vorticity estimates, ranging between −0.44f and +0.64f, also show excellent agreement between ζψ and ζp within 0.77 × 10−5 s−1 (or 0.09f) rms difference. This study carefully documents the objective error-estimation techniques for these fields that, bemuse they are derivatives of the measured ψ field, are sensitive to noise. The objective estimates of error in Vψ and ζψ agree in each case with the rms differences from observations. The authors also illustrate the consequent utility of the objective ψ maps by applying quasigeostrophic calculations to diagnose ageostrophic motions Va, in strong events in the Gulf Stream. The authors found Va/Vψ to have peak values of 0.2–0.6. Roughly equal contributions to Va came in events of large curvature or with high temporal rate of exchange. Vertical stretching ∂w/∂z at the 400-m level was estimated using the quasigeostrophic vorticity equation, finding downwelling as large as −4 mm s−1 downstream of meander crests, and upwelling as large as 3 mm s−1 downstream of meander troughs