On Definable Scale Reduction by Simultaneous Observations

Abstract

A two-dimensional extension of the Sampling Theorem with the inclusion of derivative samples is presented. It is shown that simultaneous sampling of geopotential and horizontal wind components on a mesh with elements ?x, ?y permits definition of waves of length ?x, and ?y along mesh lines under the geostrophic assumption. Additional independent estimates of either of the horizontal shear elements, ?u/?y or ?v/?y, permits the exact reconstruction of band-limited fields whose spectral decomposition includes waves of length ?x and ?y, or longer.