Computing Divergence from a Surface Network: Comparison of the Triangle and Pentagon Methods

Two methods for creating gridded fields of divergence from irregularly spaced wind observations are evaluated by sampling analytic fields of cyclones and anticyclones of varying wavelengths using a surface network. For the triangle method, which requires a triangular tessellation of the station network and assumes that the wind varies linearly within each triangle, divergence estimates are obtained directly from the wind observations and are assumed valid at triangle centroids. These irregularly spaced centroid divergence estimates then are analyzed to a grid using a Barnes analysis scheme. For the pentagon method, which requires a pentagonal tessellation of the station network and assumes that the wind varies quadratically within each pentagon, divergence estimates also are obtained directly from the wind observations and are valid at the station lying within the interior of each pentagon. These irregularly spaced divergence estimates then are analyzed to a grid using the same Barnes analysis scheme. It is found that for errorless observations, the triangle method provides better analyses than the pentagon method for all wavelengths considered, despite the more restrictive assumption by the triangle method regarding the wind field. For well-sampled wavelengths, however, the preanalyzed divergence estimates at the interior stations of pentagons are found to be superior to those at triangle centroids. When random, Gaussian errors are added to the observations, all advantages of the pentagon method over the triangle method are found to disappear.