# Determining the AMSR-E SST Footprint from Co-Located MODIS SSTs
## 1 Introduction  
Sea surface temperature (SST), one of the ten ocean surface essential climate variables (ECVs) [1], is measured from satellite-borne sensors in both the microwave portion of the electromagnetic spectrum and the infrared portion of the spectrum. The current generation of infrared instruments provide very high-resolution, \(\mathcal{O}\left(1\,\mathrm{km}\right)\), SST fields contributing significantly to the study of small scale features at the ocean surface and their impact on large scale phenomena [2]. However, infrared radiometers only supply an SST estimate when they view the sea surface under cloud-free skies. This limitation severely reduces the coverage of the global oceans by infrared sensors, coverage that is strongly dependent on location and season, with some areas experiencing cloud free conditions less than 5% of the time for extended periods (months). By contrast, with the exception of regions of heavy rainfall, the atmosphere is relatively transparent to radiation in significant portions of the microwavespectrum; i.e., SST retrievals through clouds are possible with satellite-borne instruments measuring in the microwave. The downside of microwave SST retrievals is that to achieve a reasonable accuracy, the sensor must sample a large area--the spatial resolution of these fields is generally quite coarse, \(\mathcal{O}\left(60\,\mathrm{km}\right)\). Another important characteristic of SST fields derived from extant microwave sensors is the large overlap in pixels. As will be discussed below (Section 2.1) the sensors of interest sample approximately every \(10\,\mathrm{km}\) in both the along- and across-track directions, while the radiometer footprint is \(\mathcal{O}\left(45\times 75\,\mathrm{km}\right)\). These two characteristics of microwave SST retrievals, large pixel size and significant overlap in adjacent pixels, lead to some interesting problems/possibilities, one related to instrument-to-instrument comparisons and the other to enhanced resolution of the microwave SST field. Microwave-to-infrared SST comparisons. Of interest to the work presented herein are two sensors, the advanced microwave scanning radiometer-Earth observing satellite (EOS) (AMSR-E), a microwave instrument, and the moderate-resolution imaging spectroradiometer (MODIS), an infrared instrument, both carried on the National Aeronautics and Space Administration's (NASA's) Aqua satellite, launched in May 2002 [3]. The collocation of these two instruments on the same satellite platform offers the interesting possibility of providing passive microwave and infrared radiometer data, and SST fields retrieved from these data, very nearly simultaneously. A number of investigators have taken advantage of this to compare the performance of the two instruments, e.g., [4; 5; 6]. This has been done in the context of AMSR-E/MODIS matchup datasets, sets of high quality, simultaneous retrievals from the two instruments. However, in their analyses of these matchup datasets, the authors of these studies did not take into account the mismatch in the shape and size of the region sampled by each sensor. Specifically, one must average the higher resolution MODIS SSTs to the AMSR-E grid (the coarsest grid) at a similar spatial resolution in order to eliminate the MODIS high spatial variability. Given that the power spectral density of SST in the open ocean decreases linearly in log-log space with a slope of \(\mathcal{O}\left(-2\right)\)[7; 8], the variation of SST is a factor of 50 or more on the scale of microwave SST pixels as it is on the scale of infrared pixels. This means that SST can vary significantly from one MODIS sized region in the AMSR-E pixel to another when compared to the variation within a MODIS pixel--ignoring the shape and size of the AMSR-E SST pixel will overestimate the root-mean-square difference between the two observations. Enhanced spatial resolution.