Comparison of methods of estimating mean synoptic current structure in “stream coordinates” reference frames with an example from the Antarctic Circumpolar Current

Abstract

Stream coordinates techniques, that is, methods of deriving the mean ''synoptic'' structures of narrow meandering ocean currents from Eulerian measurements, have been in use for nearly two decades and have resulted in improvements in our understanding of the dynamics and transports of such currents. A 2-year experiment in the SubAntarctic Front (SAF) southwest of Tasmania, involving overlapping arrays of inverted echo sounders and horizontal electric field recorders, has provided an opportunity to test various stream coordinates methods. The methods differ significantly in how well, or even if, they can reveal divergence or convergence of the meandering current, and whether they accurately reproduce the current's horizontal structure and transport. Cross-stream distance was determined either via a frozen-field assumption or as the distance to an optimally interpolated (OI) origin contour; downstream direction was determined either as the local direction which maximized the vertical shear of horizontal velocity or as the tangent line to the OI mapped core contour. All combinations of these distance and direction definitions were tested. The use of a frozen field assumption in determining cross-stream distance yields overly smooth along-stream velocity cross-sections and overestimated transports. The vertical shear definition of downstream direction results in a false rotation of crossstream flows into along-stream flows near the flanks of the current. The preferred methods define the horizontal location of the front with 2-D arrays of instruments (e.g., inverted echo sounders or moored current meters). Methods employing the assumptions of a meandering ''frozen-field'' baroclinic structure or the use of the local vertical shear of the horizontal velocity to determine the downstream direction should be avoided, if possible, particularly in the SAF. r

Temporal Sampling: How Many Sections Are Needed to Quantify the Mean Transport and Structure of a Meandering Current?

“…The calculations presented herein are based on the 16 IES moorings within the main array plus one pseudo-IES that fills a spatial gap in the eastern line. The latter was created using three temperature-pressure sensor pairs (from 300 to 1000 m) on the easternmost mooring following the methods presented in Meinen and Watts (2000).…”

“…The IESs used in SAFDE transmit a 10-kHz sound pulse and measure the time () for the pulse to travel to the ocean surface and back (Watts and Rossby 1977;Chaplin and Watts 1984). Using either hydrography gathered during the IES deployment period or historical hydrography, both from the region of study, characteristic relationships between and other oceanic variables (e.g., temperature T, salinity S, specific volume anomaly ␦) can be developed and combined with the IES-measured to estimate full water column profiles of these variables (Meinen and Watts 2000;Watts et al 2001). These empirical relationships are referred to as the gravest empirical modes (GEMs); and there are separate GEM representations for T, S, and ␦.…”

“…The GEM fields used herein were derived following the methods presented in Meinen and Watts (2000). The IES-measured values were mapped onto a 10-km grid using optimal interpolation (OI) via the standard methods (Bretherton et al 1976).…”

“…The other strong branch of the ACC, the Polar Front (PF), does not enter the SAFDE region during most of the study period (K. Tracey 2003, personal communication). The moored data collected during SAFDE, along with hydrographic data collected during and prior to the experiment, have been used to provide the most complete descriptions of the structure of the SAF current and the transport along and across the front to date (Watts et al 2001;Meinen et al 2002;Sun and Watts 2002;Meinen and Luther 2003;Meinen et al 2003;Chave et al 2004). While the structure and transport of the SAF at this location have now been fairly well determined, albeit for this 2-yr period only, the time series of observations provide the opportunity for improving the design of further studies of the SAF at this and other locations along its path, and more generally for the designing of studies of strong ocean currents globally.…”

“…The small spatial extent of the SAFDE array (350 km) limits the applicability of the Eulerian results as compared to basin-crossing hydrographic sections, so the transports and velocities are also calculated in "stream coordinates" and the results are contrasted with the Eulerian results. Stream coordinates refers to a coordinate system fixed to some unique characteristic of a moving current rather than to a point on the earth, and they represent a commonly used technique for averaging observations of a meandering current so that the meandering effects can be removed from the observations prior to averaging (e.g., Halkin and Rossby, 1985;Meinen and Luther, 2003). Surprisingly, it will be shown that the number of sections that would be required to accurately describe the mean temperature and baroclinic velocity structure of the SAF may be prohibitively expensive regardless of whether Eulerian or stream coordinate averaging is applied due to the high observed variability.…”