6.3 Temporal resolution of composites

You may have noticed that the Socotra Eddy was more clearly defined in the single image from the descending orbit on 20 February than in any of the composites.

Selecting an appropriate number of images for a composite means balancing the need to reduce the number of pixels with no data against the temporal resolution (the time period of the composite). For studies of dynamic features such as ocean eddies, a fairly high temporal resolution is desirable, but there is also a need for sufficient data to interpret the images reliably. In this section you will be trying out different image combinations to find one that might suit your study of eddies in the Somali Current.

Creating a 3-day composite

You will start by calculating the mean of three images from 20-23 February. This time you will not be using the mean function, but a formula that also calculates the counts of valid data points used to make up the mean.

Open the formula composite03.frm. The first few lines look like this:

#Formula to create a gridded composite ...

# Constant declarations
const COUNT=@1;
const COMPOSITE=@2;
const SCENE1=@3;
const SCENE2=@4;
const SCENE3=@5;

Lines starting with an # are comments. They are there to help the user understand what is going on. The # prevents Bilko from reading and executing the line.

The constant declarations are there for two reasons:

• to help you identify the image planes involved (in this case two blank image planes to take the COUNT and COMPOSITE images), and
• to make it easier to modify complex formulae where the same variable may appear several times. In this example, if you want to change the image plane associated with COUNT, you only need to do it once, in the constant declarations.

The calculations occur in two steps:

• first the number of valid pixels are added up at each pixel location and written to the COUNT image,
• then the sum of all the valid data at each pixel location is divided by the count to obtain the mean value;

This is the same action carried out by the Bilko mean function you used in the last section, with some important differences:

• the formula also outputs the COUNT of valid data at each location (which may sometimes be useful, particularly for composites of longer time series);
• it deals with the null values explicitly, which means you need to uncheck Null value boxes in the formula Options! (menu bar) and Redisplay stretch.

To create the 3-day composite from the middle of the period around 20 February, will use a stack of images that matches what is described in the constant declarations of the formula document.

1. Find the set of 10 resampled images, ats_nr_20040211_20040228.set.
   (If you closed it, re-open it, accepting the default extract, and remember to apply All in the Redisplay dialog).

2. From the menu bar, select Image > Connect.

3. Select the one from 20 February, and the two others closest in time (22 and 23). Add two Blanks to take the COUNT and the COMPOSITE (enter 2 in the blanks box, and remember to check the stack box.).

4. Blanks are always added to the end of a stack, but the formula demands that they are in postions @1 abd @2. Tab to the first of the blank images and type 1 on the keyboard to change its position. Tab to the next blank image, and change its position in the same way.

5. This formula handles the null values as numbers, so you must uncheck the Null value checkbox in the Redisplay dialog before applying the formula.

6. Return to the formula, and select Options! from the menu bar. Uncheck Special Handling of Nulls and click OK.

7. Apply the formula to the stack of 3 images, and watch how it adds up the counts and creates the composite.

8. Minimise the formula, and the stack of 10, and select Windows > Tile vertical from the menu bar to see the new image and the original single image from 20 February side by side to compare them.

As you can see the 3-scene composite gives a better coverage of the area than any of the contributing images individually. However, there are still large areas where no data are available. Now take a look at the image that contains the COUNT of data points. You will notice there are only a few small areas where the average is based on 3 measurements, a few more that are based on 2 measurements, a fair number on 1 measurement, and a very large number where there is still no data.

Save the 3-day composite and count with suitable names before closing the stack of 5 images. (No need to save the stack.)

Selecting a suitable time period

Increasing the number of images contributing to the composite is likely to reduce the number of pixels with missing data due to cloud. On the other hand, the images you have available cover a period of 18 day, in which the eddies you are looking for may move. It may therefore be a good idea to check this by starting with fewer images than all 10.

If you look at the dates, the 10 images could be divided into two periods, each of roughly a week, and each containing 5 images: 11-17 February and 20-28 February. Creating two composites , one for one for each of these periods, will allow you to check both if the eddies are moving in this period, and if adding a couple of images to the composite will give an improvement in image quality.

Before you continue close composite03.frm to avoid confusion. You are now ready to create the 5-scene composite.

1. Connect the five images from the period 20-28 February, so it fits with what is required by the formula (remember to check the stack box).

2. Make a last check of the image order, using the selector (figure (3K)), and change any images that are in the wrong place.

3. Open the Redisplay (right-click on the image) and make sure the Null value box is UNchecked.

4. Select the formula composite05.frm, choose Options! from the menu bar, and check the settings, these should be Output 16-bit integer, and 'Special handling of nulls' unchecked.

5. Apply the formula to the stack (Copy, Paste).

6. Find the image that contains the count and note how the number of pixels contributing to the mean has improved.

7. Find the image that contains the composite, and adjust the display:

   • Right-click on the image and select Zoom > Preserve shape.
   • Right-click to adjust the Redisplay settings to those used previously
           Linear stretch with Min.= 29700, Max.= 30200).
   • Apply the palette modjet1.pal (open it when the image is active).

When you have finished, save the composite as ats_nr_20040220_28comp5.dat and the count as ats_nr_20040220_28count5.dat. Close the set of 7.

Question 3.
How does this composite of 5 scenes compare with the one of 3 scenes?

1. Repeat the procedure to create a 5-day composite from the period 11-17 February.

2. Save the new images as ats_nr_20040211_17comp5.dat

3. Adjust the Redisplay settings of the new composites to match those of the others, and apply the same palette.

Displaying the SST in °C (optional)

The AATSR data set stores nadir SST values as intergers, with:

Value = SST (in Kelvin) * 100

Question 5.

How would you write and apply a simple formula to display the SST in °C?
(0°Celsius = 273.15 Kelvin.)

Having decided on the formula you need, you can now turn it into a formula document, which may be applied to the AATSR image, to display the SST in °C.

1. Choose File > New .. FORMULA Document, and write the formula as suggested in the answer to question 5.

2. Save the formula as SST_degC.frm.

3. In the formula Options! dialogue select 32-bit floating point as the Output Image Type, and make sure that Use special handling for Nulls is checked.

4. Copy and Paste the formula onto your SST image.

5. Finally right-click on the image to open the Redisplay dialog and change the Min and Max value in the Stretch Settings to match those of the new image data range.

Once you have finished your studies of the AATSR data, close all the images, sets and formulae, and move on to the next section, where you will look at these eddies using sea-surface height data from the RA-2 altimeter.

Next: 6.4 Calculating Sea Surface Height Anomaly (SSHA)