[1] The radius r has been nondimensionalized for our calculations. The value of 190.5 km used for the nondimensionalization is an artifact of the algorithm we have used to convert latitude-longitude locations to x-y coordinates on a map projection. That algorithm is based the Limited-area, Fine-mesh Model (LFM) grid spacing of 190.5 km at the standard latitude used in the polar stereographic projection, expressing coordinates in grid units.

[2] As used in B94, the uniformity ratio is not quite the same as that defined by Smith et al. B94 uses the average of the six nearest neighbors, rather than the single nearest neighbor, when calculating M . This should provide a somewhat smoother result than that of Smith et al.

[3] Note that D is scaled to the grid spacing (D) of the initially uniform array of sampling sites to be perturbed, so that, for example, a D value of 5.0 corresponds to D = 5D.

[4] What Barnes calls the "offset" is the same as our "scatter distance," or D . It does appear in Barnes's Fig. 10 that "saturation" occurred at an offset of 2, whereas our results suggest that saturation occurs around D = 1. When we run a test comparing the methods with identical station distributions, they both "saturate" around D = 1. Thus, whatever the source of the discrepancy, they appear to be giving similar results for a given station distribution.

[5] The surface network that we use includes all of the possible reporting stations. Generally, not all of the sites report at any given time, so the actual station density of real data sites will be slightly less than this density used here. When we test the actual reporting sites on several different days, the change in m is less than 10%.