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Peppler and Smith (1984) discussed truncation errors associated with second-order and fourth-order finite difference approximations used to calculate the geostrophic wind and relative vorticity. They found that these errors were, in general, smaller for longer wavelengths, finer-grid resolution, and fourth-order differencing. Second-order differencing produced fields that were numerically less than their corresponding analytic values and yielded errors which decreased with reduced grid interval. Fourth-order differencing decreased the errors when the grid interval was reduced, but only while the wavelength was ten limes or more greater than the grid interval. Results presented here indicate that the wind speed and Vorticity errors estimated by the fourth-order scheme decreased when the grid interval was decreased independent of wavelength. Comparison with Peppler and Smith's actual computations showed only one difference: in their finite-(difference equations the coefficients were truncated to th...

The effects of horizontal and vertical data resolution, data density, data location, different objective analysis algorithms, and measurement error on mesoscale-forecast accuracy are studied with observing-system simulation experiments. Domain-averaged errors are shown to generally decrease with time. It is found that the vertical distribution of error growth depends on the initial vertical distribution of the error itself. Larger gravity-inertia wave noise is produced in forecasts with coarser vertical data resolution. The use of a low vertical resolution observing system with three data levels leads to more forecast errors than moderate and high vertical resolution observing systems with 8 and 14 data levels. Also, with poor vertical resolution in soundings, the initial and forecast errors are not affected by the horizontal data resolution.