Statistical Comparison of Map Projection Distortions Within Irregular Areas

Abstract

We describe a statistical sampling approach to characterizing and comparing map projection distortion within irregular areas. Statistical measures of distortion, coupled with traditional distortion isoline maps, give a clear picture of map projection distortion for irregularly shaped areas, like the United States or portions of it. We calculate cumulative distribution functions and several descriptive statistics from the distortion measures. In our example, we compare two common projections, the Lambert azimuthal equal area and the Albers conic equal area, over the conterminous United States and over two subregions. In addition to scale and angle distortion, we develop a new measure of shape distortion. Our analyses show that the Lambert projection has lower mean and median shape distortion when compared over the conterminous U.S., whereas the Albers projection has a lower maximum distortion and distortion variance for all three distortion measures. The cumulative distribution functions are substantially different and show that the Lambert projection has lower distortion values for approximately 80% of the sample points. We also compare a large unrestricted random sample with a systematic random sample. The sample size is large enough that the unrestricted and systematic samples give virtually identical results.

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