Statistical Inference Based on Distances Between Empirical Distributions with Applications to AIRS Level-3 Data
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Atmospheric Infrared Sounder (AIRS), a sensor aboard NASA’s Aqua satellite, has been collect- ing temperatures, water vapor mass-mixing ratios, cloud fractions at various atmosphere pressure levels, and other atmospheric observations. AIRS level 2 data has a 45 km ground footprint with global coverage. The AIRS level 3 Quantization (L3Q) product summarizes valid level 2 data in each 5o × 5o latitude-longitude grid box during a time period by a set of representative vectors and their associated weights, which can be treated as an empirical distribution. In this paper, we study potential statistical tools using pairwise dissimilarities that are suitable for analyzing this nontraditional type of data. Through theoretical analysis and simulations, we investigate several different dissimilarity measures and find Mallows distance is preferable over others when the locations of the representative vectors are important for the analysis. We apply MultiDimensional Scaling and clustering method to analyze AIRS data collected in December 2002. The results from these studies provide insights on how statistical methods based on Mallows distance may extract more information from the AIRS L3Q data than from the simple sample average summary in each grid box.
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