# Determining the AMSR-E SST Footprint from Co-Located MODIS SSTs
## 4 Results
### AMSR-E Footprint Estimation  
In this section we examine the retrieved AMSR-E SST footprint (the SST footprint henceforth to distinguish it from the footprint of individual spectral bands), as a function of AMSR-E cell position, latitude and year. Because the relative angle between the local MODIS coordinate axis and the orientation of the AMSR-E spectral footprint varies with cell position (Figure 3), the orientation of the SST footprint depends on cell position; hence the decision to retrieve the SST footprint as a function of  
Figure 5: The results using simulated AMSR-E measurements. (**a**) Imposed footprint; (**b**) Algorithm 1 output with \((R,n)\) = (1; 250,000); (**c**) \((R,n)=(1;2000)\) and (**d**) \((R,n)=(2000;2000)\); (**e**) is achieved by applying a \(4\times 4\) moving average to (**d**). Figure 6: The contour-lines of the imposed footprint (Figure 5a) and the final result shown in Figure 5e. cell position. A latitudinal dependence could arise from a dependence on the target temperature or on orbital position. Finally, we examined the temporal dependence over the life of the sensor to determine whether or not the footprint changed with time. Recall that SST was determined from a combination of spectral channels and of polarizations for each channel and changes in any of the other channels and/or changes in the characteristics of the other retrieved parameters could impact the SST retrievals. Cell position dependence. Matchups were binned by cell position (relative to nadir), with each bin containing a ten position range starting with cell position \(-115\) (\(-115\) to \(-106\), \(-105\) to \(-96\), \(\ldots\), \(85\) to \(94\)). Samples near the edge of the swath were not included in the analysis as they do not meet the quality criteria specified in Section 2; hence cell position \(-115\) (as opposed to \(-122\)) was used as the starting cell position and cell position \(96\) (as opposed to \(122\)) as the ending number. The reason that the binning was not centered on cell position \(0\), which corresponds to nadir, is because the \(0^{\circ}\) angle between the MODIS and AMSR-E scans occurred at cell position \(10\), not \(0\); i.e., because the rotation axis of the antenna pointed slightly off nadir. Binning by ten cell positions provided a suitable number of matchups while adequately capturing any cross-track dependence (Figure 7). In Figure 8, we show the empirically derived footprints for each cell position bin. The algorithm characterized by Equation (7), with \(R=2000\) (number of bootstrap repetitions) and \(n=2000\) (sample size), was applied to the matchup datasets associated with each cell position bin. Only bins involving more than 40,000 matchups were considered (20 bins). The retrieved footprints all suggest a basic elliptical shape but they differed in two key ways. Firstly, the orientation of the ellipses changed with respect to the cell position. Secondly, as the distance from nadir increases, the AMSR-E footprint becomes narrower in the across-track direction with a concomitant increase in intensity--recall that the weighting function must sum to 1.0 (Equation (7)) so the increase in intensity is consistent with the narrowing of the footprint. The varying rotation of angles results from two factors. First, the non-alignment of scan lines of the two sensors shown in Figure 3. Second, the axes of the plots in Figure 8 are in MODIS pixels, not in kilometers. Because the separation of MODIS pixels in the across-track direction increases with distance from nadir, the length of the horizontal axes increase. In contrast, the separation of MODIS pixels in the along-track direction changes little with distance from nadir, so the length of the vertical axes remain approximately the same from one end of the AMSR-E scan line to the other. The net effect of this is to decrease the magnitude of the apparent angles of the ellipse. The increase in intensity with distance from nadir results from the concomitant increase in the across-track spacing and in the size of MODIS pixels.