The Minimum Horizontal Length Scale When Evaluating Quasi-Geostrophic Omega

The quasi-geostrophic (QG) omega equation has been frequently applied in many situations that require the diagnosis of the sources of vertical motion.  Recently though, the datasets upon which QG analysis is applied have become of such high spatial resolution that the horizontal length scale renders the geostrophic assumption invalid.  Theory dictates that length scales shorter than 1000 km are not suitable, but more information is necessary to apply this to modern numerical weather prediction model grids.  In this study, we empirically investigate the minimum horizontal length scale suitable for QG vertical motion analysis on 28 baroclinic systems from the North American Mesoscale (NAM) model.  Two methods are tested:  (1) the box method, which averages each field around a point before finite-differencing, and (2) the cross method, which increments the distance between finite-difference calculations.  We evaluate the traditional QG omega equation using both methods and find the minimum QG length scale to be 240 km based on correlations with the NAM omega field.  Additionally, the box method is found to perform marginally better than the cross method due to a larger reduction in higher order wavenumbers.