Chapter 10 - Geostrophic Currents

10.5 An Example Using Hydrographic Data

Let's now consider a specific numerical calculation of geostrophic velocity using generally accepted procedures from Processing of Oceanographic Station Data (JPOTS Editorial Panel, 1991). The book has worked examples using hydrographic data collected by the R/V Endeavor in the North Atlantic. Data were collected on Cruise 88 along 71°W across the Gulf Stream south of Ca pe Cod, Massachusetts at stations 61 and 64. Station 61 is on the Sargasso Sea side of the Gulf Stream in water 4260m deep. Station 64 is north of the Gulf Stream in water 3892m deep. The measurements were made by a Conductivity-Temperature-Depth-Oxygen Profiler, Mark III CTD/02, made by Neil Brown Instruments Systems.

The CTD sampled temperature, salinity, and pressure 22 times per second, and the digital data were averaged over 2 dbar intervals as the CTD was lowered in the water. Data were tabulated at 2 dbar pressure intervals centered on odd values of pressure because the first observation is at the surface, and the first averaging interval extends to 2 dbar, and the center of the first interval is at 1 dbar. Data were further smoothed with a binomial filter and linearly interpolated to standard levels reported in the first three columns of Table 10.2 and Table 10.3. All processing was done electronically.

δ(S, t, p) in the fifth column of Table 10.2 and Table 10.3 is calculated from the values of t, S, p in the layer. <δ> is the average value of specific volume anomaly for the layer between standard pressure levels. It is the average of the values of δ(S, t, p) at the top and bottom of the layer. The last column (10^-5 ΔΦ) is the product of the average specific volume anomaly of the layer times the thickness of the layer in decibars. Therefore, the last column is the geopotential anomaly ΔΦ calculated by integrating (10.16) between P₁ at the bottom of each layer and P₂ at the top of each layer.

The distance between the stations is L = 110,935 m; the average Coriolis parameter is f = 0.88104 × 10^-4; and the denominator in (10.18) is 0.10231 s/m. This was used to calculate the geostrophic currents relative to 2000 decibars reported in Table 10.4 and plotted in Figure 10.8.

Notice that there is no indication of Ekman currents in Figure 10.8. Ekman currents are not geostrophic, and they do not contribute to the topography. They contribute only indirectly through Ekman pumping (see Figure 12.7).

Figure 10.8 Left: Relative current as a function of depth calculated from hydrographic data collected by the Endeavor cruise south of Cape Cod in August 1982. The Gulf Stream is the fast current shallower than 1000 decibars. The assumed depth of no motion is at 2000 decibars. Right: Cross section of potential density sq across the Gulf Stream along 63.66°W calculated from CTD data collected from Endeavor on 25?28 April 1986. The Gulf Stream is centered on the steeply sloping contours shallower than 1000m between 40° and 41°. Notice that the vertical scale is 425 times the horizontal scale. Data contoured by Lynn Talley, Scripps Institution of Oceanography.

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