2.1.3 Geostrophic velocities:
The Antarctic Circumpolar Current, due East around the Earth
Satellite altimetry's contribution to ocean circulation studies.
The geostrophic circulation is the ocean circulation generated by the balance between the horizontal pressure gradient forces exerted by water masses and the effect of acceleration due to the Earth's rotation.
Geostrophic velocities can be computed using the slope of the surface (available from altimetry data), and the Coriolis force.
See e.g. Surface Geostrophic Currents From Altimetry (Introduction to Physical Oceanography, Texas A&M University) for more precise information.
We will compute geostrophic velocities from Sea level anomalies.
Compute geostrophic velocities from gridded data
In this case the best is to use pre-computed multi-mission gridded data (e.g. Aviso MSLA), since the resolution will be better than if you smooth out along-track data as a grid. But you can also use a SLA map created using BRAT from GDR data.
In this case, you can compute meridional and zonal velocities both (U and V). (Note that if you compute geostrophic velocities directly from along-track data (without gridded them beforehand), the only available slope is the one along the track. Thus the geostrophic velocity computed would be "only" its component perpendicular to the track, since the geostrophic velocities is perpendicular to the slope).
We will use the "geostrophic velocities" algorithm available within the Basic Radar Altimetry Toolbox (version 3 of the software).
Define a dataset with a gridded SLA file.
For the gridded data:
In the "Operations" tab, define longitude as X, latitude as Y.
Create two expressions as "Data expression", one you can wall "U" (zonal), the other "V" (meridional). Click in the box for the first one, then click on the "insert algorithm" button. A pop-up window opens. There you will find three existing algorithm. One is for the along-track geostrophic velocity computation, the other two are, one for U, the second for V. Choose the appropriate one. A function-like expression is inserted in the Data Expression box. You have only to check that longitude and latitude match existing variables within your datasets (sometimes they can be called "lon" and "lat"), and to insert the height you want to compute geostrophic velocities from (here SLA) instead of the indication 'height' within the function variables.
Create a second operation with only longitude as X, latitude as Y and the SLA as Data expression
In the "set resolution" pop-up window, restrict your area of computation to 45-65°S.
Go to the "Views" tab, create a new View.
Take U and plot it (Execute). Take V and plot it (Note that in the View tab, choosing Plate Carree or Mercator projection, you can pre-define your zoom, which will enable you to keep it for future use).
Create again a new View, with the same projection and zoom (or erase previous choice and replace it as follow, if you don't want to keep previous view for future references).
Select the SLA height to serve as background, then the "U" AND the "V" components. Click on the selected U expression and below, click on the box "East component"; click on the selected V and below, click on the box "North component". Execute.
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Tutorial produced by CLS under contract to ESA and CNES