Abstract
Comparisons are made between second-order and fourth-order finite differencing using three grid resolutions in order to analyze the truncation errors in geostrophic wind and relative vorticity estimates. Horizontal wave dimensions are also varied to study sensitivity to different scales of motion. Exact calculations derived from analytic equations describing geostrophic wind and relative vorticity provide the standard against which the finite-difference estimates are compared.
Both wind speed and relative vorticity truncation errors maximized in regions where speed and vorticity values were greatest. These errors were, in general, smaller for longer wavelengths, finer grid resolution and fourth-order differencing. Although second-order differencing produced fields that were numerically less than observed and yielded errors which decreased with reduced grid interval, fourth-order differencing departed from this anticipated behavior. Rather, when the grid interval was reduced to the point that the wavelength was ten times or more greater than the grid interval, wind speeds and vorticities estimated by the fourth-order scheme were overestimated and were accompanied by increased truncation errors at finer grids.
