Statistical comparisons of methods for interpolating the output of a numerical air quality model

This paper compares Models-3/Community Multiscale Air Quality (CMAQ) outputs at multiple resolutions by interpolating from coarse resolution to fine resolution and analyzing the interpolation difference. Spatial variograms provide a convenient way to investigate the spatial character of interpolation differences and, importantly, to distinguish between naive (nearest neighbor) interpolation and bilinear interpolation, which takes a weighted average of four neighboring cells. For example, when the higher resolution is three times the lower, the variogram of the difference between naive interpolation of the lower resolution output and the higher resolution output shows a depression at every third lag. This phenomenon is related to the blocky nature of naive interpolation and demonstrates the inferiority of naive interpolation to bilinear interpolation in a way that pixelwise comparisons cannot. Theoretical investigations show when one can expect to observe this periodic depression in the variogram of interpolation differences. Naive interpolation is in fact used widely in a number of settings; our results suggest that it should be routinely replaced by bilinear interpolation.