6.4 Calculating Sea Surface Height Anomaly (SSHA)

One of the most useful parameters for studying ocean circulation is the Sea Surface Height Anomaly (SSHA) (see 'Using SSHA to study ocean currents'). SSHA is not one of the standard RA-2 products, but can be calculated from the RA-2 data using a simple Bilko formula, ra2corrections.frm. As you see when you open this formula, the calculations start with the altitude of the satellite. A list of parameters are then subtracted to give the SSHA; all these are supplied with the RA-2 GDR data.

The method behind the basic calculation of SSHA is best demonstrated with the diagram Calculating SSHA. Consulting this diagram and the explanation that goes with it will help you understand what the correction formula is doing, and what parameters you need to extract from the long list of data-sets that make up the RA-2 file.

1. Open the file named RA2_GDR_2POF-P20040220_~.N1.bz2. The left hand side of the file structure window contains two folders Metadata and Bands.
   Note: To view the RA-2 metadata, click Metadata on the left and double click MPH (Main Product Header) on the right.

2. Click the + symbol next to Bands on the left hand side of the file structure window, and choose RA2_DATA_SET_FOR_LEVEL_2. The right hand side now displays all 130 datasets available from the RA-2 GDR product.

RA-2 data is different from the satellite data you have encountered so far. The data sets in the file are vector data - a long array of measurements, equivalent to an image that is only one pixel wide, but many pixels long. The RA-2 footprint depends on the waveheight, but is between 5 and 9 km in diameter, at wind speeds common in the open ocean. Each measurement therefore represents an area that 5-9 km wide and about 9 km long, where the length (pixel height) is determined by the distance the satellite travels during the time it takes to make a measurement.

The radar instrument is nadir-pointing - that is it 'looks' straight down. As a result the 5-9 km wide RA-2 'swath' runs down the centre of images obtained by other nadir-pointing sensors such as MERIS and AATSR. In Bilko you can take advantage of this by using MERIS or AATSR images to help you open the corresponding section of the RA-2 data.

Opening RA-2 data based on another image

There are several ways of opening and viewing RA-2 data, depending on what the data is to be used for.

• the full half orbit, on a regular grid,
• the full half orbit in polar projection, or
• based on another image, which may be either in a regular or polar projection, or, in the case of Envisat N1 data from MERIS or AATSR in the original (not resampled) satellite projection.

In this part of the lesson, we will be looking at RA-2 data from the orbit that also contained the AATSR image from the 20th February 2004, which you worked with earlier. The spatial resolution of this is 1km, so the 5-8 centre columns of the AATSR image correspond roughly to a section somewhere on the RA-2 track. The AATSR image is therefore a good choice to help you open the relevant part of the RA-2 data sets.

The data sets you need to calculate sea surface height anomaly (SSHA) are included with many other parameters in the RA2_DATA_SET_FOR_LEVEL_2 folder. You could open these by holding down the control key and selecting these one by one, but this is a tedious business which involves much scrolling, so instead we have created a Bilko set called RA2_GDR_2POF-P20040220_ssha_bz2.set to save you the hassle. Open this in a text editor (not in Bilko) to see how it is constructed. As you can see it includes the 13 data sets listed in the formula.

1. Return to Bilko and open the cloud masked image you saved earlier, ATS_NR__20040220m.dat.

2. Open the set RA2_GDR_2POF-P20040220_ssha_bz2.set (file type SETS).

   • In the Extract dialogue select the Initialise tab,
   • and in the Based On: box choose ATS_NR_20040220m from the drop-down menu.
   • Leave the Null value set to the default of 0, and
   • change the footprint size from the default of 7500 m to 10000 m
     (a bit on the large side, but it will make the data easier to see and manipulate).
   • Remember to click Apply before you start the Extract by clicking OK.

   Note: The default option, 'Self', will open the whole RA-2 track, which covers half an orbit, and map it onto a lat/long grid. For our study of eddies in the Somali Current system, only a small section of this orbit is required.

3. Accept the Redisplay default by clicking All.

4. If necessary use Zoom > Preserve shape to see the altimetry track.

Applying corrections to calculate SSHA

1. Open ([CTRL+O]) the FORMULA document ra2corrections.frm.

2. Select Options! from the menu bar ([ALT+O]) and make sure the Use special handling for nulls tick box is UNchecked,

3. Copy the formula and Paste it onto the image stack. A new image will open, containing the corrected SSHA data (surrounded by a lot of null values!).

4. Redisplay the new image, with Stretch setting from 0 to 1000.

As you can see the RA-2 data appears as a line of circles down the centre of the new image. If you apply a palette you will be able to see the data points more clearly - a good choice here is modjet1.pal.

Taking a transect to see how SSHA changes

It is still very difficult how the SSHA changes along the RA-2 track. Any changes in colour from one pixel with SSHA data to the next is hidden from the eye because of the surrounding black. However, you can see what is going on by Taking a transect to see how SSHA changes.

1. Open the Go to dialogue (select Edit > Go to from the menu bar or press [CTRL+G] on the keyboard)

   • in the Position box, enter X: 0256, Y: 0,
   • in the Selection Size box, enter DX: 1 and DY:1056,
   • make sure the Selection Type is Line Selection, and
   • accept these settings (figure (5K)) by clicking OK.

   You should now have a line selection that covers all of the RA-2 data points.

2. Open the 'New' dialogue ([CTRL+N]) or ) and choose TRANSECT Document, making sure that the Apply stretches to new documents tick box is unchecked.

Clicking on the transect with your mouse positions the cursor at that point. You can then read the position and the data values for the corresponding pixel (figure (4K)). (figure). You may have to adjust the cursor position by holding down [CTRL] and using the left or right arrow keys to find an actual data point.

This is a good point to discuss the data that is being displayed. With SSHA data, we would expect the roughly half the sea surface to be above the mean level, and half below. As you can see from the transect all the valid data point displayed here are above the mean sea surface.

The reason for this is that the mean sea surface used in the calculations is that measured by a combination of previous altimeter missions, not the RA-2 itself. There is therefore an offset in the data, which should be corrected for.

Question 2.

Based purely on the data you have looked at here, of what order would you say the offset should be?

In the next and final section you will see one of the ways in which SSHA is used in practice. By combining data from all the altimeters currently in orbit it is possible to provide maps of SSHA that resemble more familiar image formats. Before you move on, select 'Windows' from the menu bar and close everything now open.

Next: 6.5 Maps of SSHA: The DUACS dataset