Consistent vertical and horizontal resolution

Simple physical relations (namely, the Rossby ratio between vertical and horizontal scales in quasi-geostrophic flow and the dispersion relation for internal gravity waves) are used to estimate the vertical resolution consistent with a given horizontal resolution. Using these relations it is found that virtually all large scale models and observing systems have inadequate vertical resolution. In models, the excess horizontal resolution can lead to increased model 'noise' rather than improved accuracy. In observing systems, the finer horizontal scales can be severely misrepresented.