# Determining the AMSR-E SST Footprint from Co-Located MODIS SSTs
## 3 Methodology  
### Matchup Dataset  
The starting point for this work was an approximately four million point AMSR-E-MODIS SST matchup dataset generated as part of this analysis as follows. A matchup was defined as a nighttime L2 AMSR-E SST pixel, meeting the quality criteria specified in Section 2.1, and a 101\(\times\)125 MODIS L2 SST pixel region, centered on the AMSR-E pixel, for which 90% of the MODIS pixels were classified as clear--quality 0. The 101 element dimension of the MODIS regions selected is defined parallel to the MODIS across-track direction. The 125 element dimension was in the along-track direction. The size of the MODIS region was selected so that it would include all pixels contributing to the radiances of all bands used to determine the AMSR-E SST. As noted in Section 2.1, the AMSR-E antenna scanned at an off-nadir angle (47.5\({}^{\circ}\) from nadir) with each scan line defining an approximately circular section (Figure 1). Samples, numbered from \(-\)121 to 121, with zero corresponding to the scan center, were taken approximately every 10 km along this circular section as shown in Figure 2.  
Important for this discussion, the semi-major axes of the footprints of the AMSR-E spectral bands (AMSR-E spectral footprints hereafter) were parallel to the vector from the nadir position of the satellite to the pixel of interest. By contrast, MODIS scanned along lines passing through nadir, lines that were approximately normal to the nadir track. This resulted in an angle, which depended on cell position, between the semi-major axis of the AMSR-E spectral footprints and the MODIS scan geometry. Figure 3 shows this angle at each cell position. The approximately 50 km offset of the cell at which the AMSR-E scan-line is parallel to the MODIS scan-line results from the Earth's rotation. The AMSR-E and MODIS scans were centered on the direction in which the satellite is flying and the across-track direction of the scans were nearly perpendicular to the orbit of the satellite. This means that lines normal to the scans at their centers made an approximately 3.5\({}^{\circ}\) angle relative to the nadir track because the Earth is rotating under the satellite's orbit. The AMSR-E scan at the Earth's surface was approximately 870 km from the satellite's nadir point so, the MODIS scan at the location at which the AMSR-E scan intersects the nadir track is made approximately 130 s after the AMSR-E scan. In that time, the Earth rotated approximately 50 km westward at the Equator. Figure 2: Example of matchup data. Note that a matchup could also have been defined with one of the axes perpendicular to the AMSR-E scan line at the pixel of interest, however, this would have entailed a more complex subsampling of the MODIS data. Furthermore, it was not known at the outset whether or not the AMSR-E SST footprint would be aligned with the AMSR-E spectral footprints. Gaps, if they exist in the MODIS patch, were filled by solving the Laplace equation with Dirichlet boundary conditions using the MATLAB routine roifill. Following this step, the full resolution MODIS data were degraded to lower resolution (for computational efficiency, as will be shown in Section 3.2) by averaging the initial fields over 4 \(\times\) 4 pixels (\(\approx\)4 km resolution at nadir). This resulted in a total of 775 (25 \(\times\) 31) MODIS SST measurements. Figure 4 shows the global distribution of the matchup data. This figure is plotted with a logarithmic scale because of the variability in the number of samples from one region to another, with coastal areas tending to be much more clear than most of the open ocean. Finally, the matchup dataset also contains additional information about the AMSR-E SST pixel: cell position, longitude coordinates and the retrieval time, allowing for stratification of the results based on these parameters. Figure 4: Number of collocations.