[1] Also affiliated with NOAA/OAR National Severe Storms Laboratory, Norman, Oklahoma

[2] Strictly speaking, with the triangle method a grid is completely unnecessary. We put the results onto a grid simply for ease of display, given that most display software assumes that the data to be displayed are on a grid. It is possible to do contouring even when data are not on a uniform grid, however (Watson 1992; pp. 53 ff.).

[3] This statement assumes that the analysis is done with a globally uniform weighting function. That is, the unnormalized weight function is homogeneous. Inhomogeneous, anisotropic weight function shape parameters (as in Askelson et al. 2000) might provide a qualitative change in the characteristics of the traditional scheme with respect to derivative estimation, but are not in common use and have a number of issues associated with them (see Trapp and Doswell 2000).

[4] In some cases, a digital filtering is done to the analyzed fields (i.e., on the analysis grid) prior to estimating the derivatives. We have not considered this case, since it would be roughly equivalent to choosing a larger shape parameter for the initial mapping/smoothing operation.

[5] We emphasize that the results shown thus far are for error-free, analytic observations. For a treatment of the impact of observation errors on the results, see Appendix B.

[6] Current affiliation: Cooperative Institute for Mesoscale Meteorological Studies, Norman, OK