Computation of Geostrophic Streamfunction, Its Derivatives, and Error Estimates from an Array of CPIES in Drake Passage

Abstract

Abstract Current and pressure-recording inverted echo sounders (CPIES) were deployed in an eddy-resolving local dynamics array (LDA) in the eddy-rich polar frontal zone (PFZ) in Drake Passage as part of the cDrake experiment. Methods are described for calculating barotropic and baroclinic geostrophic streamfunction and its first, second, and third derivatives by objective mapping of current, pressure, or geopotential height anomaly data from a two-dimensional array of CPIES like the cDrake LDA. Modifications to previous methods result in improved dimensional error estimates on velocity and higher streamfunction derivatives. Simulations are used to test the reproduction of higher derivatives of streamfunction and to verify mapping error estimates. Three-day low-pass-filtered velocity in and around the cDrake LDA can be mapped with errors of 0.04 m s−1 at 4000 dbar, increasing to 0.13 m s−1 at the sea surface; these errors are small compared to typical speeds observed at these levels, 0.2 and 0.65 m s−1, respectively. Errors on vorticity are 9 × 10−6 s−1 near the surface, decreasing with depth to 3 × 10−6 s−1 at 4000 dbar, whereas vorticities in the PFZ eddy field are 4 × 10−5 s−1 (surface) to 1.3 × 10−5 s−1 (4000 dbar). Vorticity gradient errors range from 4 × 10−10 to 2 × 10−10 m −1 s−1, just under half the size of typical PFZ vorticity gradients. Comparisons between cDrake mapped temperature and velocity fields and independent observations (moored current and temperature, lowered acoustic Doppler current profiler velocity, and satellite-derived surface currents) help validate the cDrake method and results.