# Determining the AMSR-E SST Footprint from Co-Located MODIS SSTs
## 5 Discussion  
The reference footprint, obtained by averaging the retrievals across all cell positions, is close to the shape and size of the 6.93 GHz pixel, this despite the inclusion of data from other spectral bands and additional processing. This came as somewhat of a surprise to us because we had understood that the SST values retrieved from the re-gridded brightness temperatures were averaged over five AMSR-E pixels in the across-scan direction, hence we expected that the SST footprint would be approximately 20 km larger in the direction normal to the scan line. This does not appear to be the case.  
The average footprint obtained in this study is robust through time as well as a function of latitude, suggesting that it is a good first choice for the SST footprint where the shape and size of the footprint is relevant.  
In order to demonstrate the importance of properly representing the AMSR-E SST footprint, we compare the AMSR-E SST field of 0155 UCT, 2009-10-31 minus the coincident MODIS SST field, assuming a \(56\times 56\) km\({}^{2}\) AMSR-E footprint, with the same difference, assuming the footprint represented by Figure 10. The criteria used to select the field was that it be largely cloud free and that there be some structure in it--the shape of the footprint is irrelevant when comparing retrievals from different sensors for a uniform field. To difference the fields, it is necessary to map them to the same grid. In this case, the MODIS data were mapped to the AMSR-E field. Specifically, for each AMSR-E pixel, all L2 MODIS SST values falling within the \"footprint\" of the AMSR-E pixel were averaged. The AMSR-E field is shown in Figure 15a. The MODIS field, averaged to the AMSR-E field using the \(56\times 56\) km square footprint, is shown in Figure 15b and the MODIS field, averaged to the AMSR-E field using the footprint of Figure 10 is shown in Figure 15c. The difference field for the \(56\times 56\) km footprint is shown in Figure 15d and that for the footprint of Figure 10 is shown in Figure 15e. The difference field associated with the \(56\) km footprint shows structure not in that associated with the footprint of Figure 10.  
Finally, although we obtained the AMSR-E SST footprint through use of the very nearly simultaneous MODIS SST product, we do not believe that the simultaneity of the observations is critical. One could use SST products from other high resolution infrared sensors as long as the time separating the observations is less than six hours. The important consideration here is to avoid times when the surface temperature is changing rapidly, specifically during daylight hours hence the six hour constraint. There must, of course, also be a large number of matchups with whatever sensor is being used to obtain the footprint.  
Figure 14: The \(\sigma_{1}/\sigma_{2}\) aspect ratio of the fitted ellipse to the 0.002 contour-line of the (**a**) across-track footprints shown in Figure 9, (**b**) year-by-year shown in Figure 12 and (**c**) those calculated as a function of latitude in Figure 11. The mean aspect ratio value corresponding to the ellipse fitted to the footprint shown in Figure 10 is plotted in red. The theoretical value corresponding to the 6.93 GHz channel aspect ratio is plotted in yellow (\(\approx\)1.74).