Derivative estimation from marginally sampled vector point functions

Abstract

It is shown that one must properly account for transformations from one vector representation to another (e.g. from u and v wind components to speed and direction). A simple technique for calculating the linear kinematic properties of a vector point function (translation, curl, divergence, and deformation) is derived for any noncolinear triad of points. This technique is equivalent to a calculation done using line integrals, but is much more efficient. It is shown that estimating derivatives by mapping the vector components onto a grid and taking finite differences is not equivalent to estimating the derivatives and mapping those estimates onto a grid, whenever the original observations are taken on a discrete, irregular network. This problem, is particularly important whenever the data network is sparse relative to the wavelength of the phenomena. It is shown that conventional mapping/differencing schemes fail to use all the information in the data, as well. -from Authors