Why Partition the QG Omega?

In a pioneering paper by Sutcliffe (1939), vertical motions characteristic of development at sea-level were diagnosed by considering the vertical variation of the acceleration vector, given that the vertical cross product of that acceleration yields the ageostrophic wind vector. The two "forcing" terms in that expansion suggested (but did not demonstrate) that the vertical motion in mid-latitude weather systems is composed of a portion transverse to the vertical shear and a component distributed along the vertical shear. I refer to these two types of vertical motions as TRANSVERSE and SHEARWISE, respectively. These two portions of the total QG-omega can be separated and explicitly calculated using the Q-vector form of the forcing term in the classical omega equation. It is suggested that these two components of the vertical motion field play very different roles in the typical cyclone and that refining our understanding of these roles will lead to more comprehensive insight into the cyclone life cycle. These ideas are further explored in Martin (2006).

The Method Used

We used Successive Overrelaxation (SOR) to solve the QG Omega Equation using the 0000 and 1200 UTC daily runs of NCEP's Eta model (on the 104 grid). Step one is to bilinearly interpolate the 104 gridded output to a 1 x 1 Latitude/Longitude grid from 25N to 65 N and from 130W to 55W, covering all of North America and some adjacent waters. We used the Q-vector form of the forcing for the QG Omega equation, developed by Hoskins et al. (1978) and then partitioned the Q vectors into components along and across the isentropes similar to the method developed by Keyser et al. (1990) and employed by Kurz (1992). Since Q describes the rate of change of the potential temperature gradient vector following the geostrophic flow, this partition effectively separates the forcing for QG omega into components TRANSVERSE and SHEARWISE to the vertical shear vector (horizontal temperature gradient vector). In the panels we portray on this page, the omega at 700 hPa is illustrated with ascent in yellow and descent in green. The dotted lines on each diagram are the 500:900 hPa thickness shown in order to illustrate the magnitude and orientation of the vertical (geostrophic) shear vector. Data from the daily 0000 UTC Eta model run is available at about 10:15 PM CST while the data from the 1200 UTC run is available at about 10:15 AM CST. We also include 0000 UTC NCEP AVN data over the North Pacific, the North Atlantic and Europe, as well as Australia and New Zealand. We hope to expand the domain of the analysis in both hemispheres at some future date.


Hoskins, B. J., I. Draghici, and H. C. Davies, 1978: A new look at the omega equation. Quart. J. Roy. Meteor. Soc., 104, 31-38.

Keyser, D., B. D. Schmidt, and D. G. Duffy, 1992: Quasi-geostrophic vertical motions diagnosed from along- and across-isentrope components of the Q vector. Mon. Wea. Rev., , 120, 731-741.

Kurz, M., 1992: Synoptic diagnosis of frontogenetic and cyclogenetic processes. Meteor. Atmos. Phys., 48, 77-91.

Martin, J. E., 1999: Quasigeostrophic forcing of ascent in the occluded sector of cyclones and the trowal airstream. Mon. Wea. Rev., 126, 70-88.

Martin, J. E., 2006: The role of shearwise and transverse quasigeostrophic vertical motions in the midlatitude cyclone life cycle. Mon. Wea. Rev., 134, 1174-1193.

Sutcliffe, R. C., 1939: Cyclonic and anticyclonic development. Quart. J. Roy. Meteor. Soc., 65, 518-524.