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Synoptic Meteorology Lab 6

Feb 25, 2010

Q-vectors

In the previous lab we examined the two QG “forcing” terms in the Omega Equation. Specifically, we looked at the vertical structure of temperature advection and geostrophic absolute vorticity advection. We did not, however, try to compute the full RHS of the Omega Equation and evaluate the accuracy of this equation (unless you attempted the extra credit question). We will do just that in this lab, by examining Q vector convergence.

Note: instead of producing black and white maps, try color (dev=psc|filename.ps). If you do not have access to a color printer, you can email the color image to me. Note that the computers in the labs on the 1st floor have Adobe Illustrator, which allows you to import postscript files, edit them (eg add some extra text, change the color or thickness of lines, etc), and then export as a jpg image. Give it a try.

This is how gempak computes the Q-vector:

QVEC Q-vector at a level ( K / m / s )

QVEC ( S, V ) = [ - ( DOT ( DVDX (V), GRAD (S) ) ), - ( DOT ( DVDY (V), GRAD (S) ) ) ]

choose V=GEO (consistent with the QG assumptions) and S= THTA.

Please generate the following maps, for 00 UTC 01 February 2002 (3 maps).

A1. Map height (thick solid contour), Q-vector (arrows), and Q-vector divergence DIV (negative should imply rising motion:use red contours; positiveshould imply sinking motion: use blue contours) at 500 mb.Note: if you prefer to produce black&white maps on paper, please substitute reddashed lines and blue solid lines

A2. Map height (thick solid contour), and vertical velocity (OMEG) (negative or rising motion: solid or red; positive or sinking motion: dashed or blue contours) at 500 mb.

A3. Map height (thick solid contour), and the Laplacian of omega LAP(OMEG) (positive should imply rising motion: solid or red; negative should imply sinking motion: dashed or blue contours) at 500 mb.

Note that the Laplacian of omega is . That is, it does not include the vertical derivative in the full Q-vector equation:. But at 500 mb the vertical derivative term is generally small compared to the (horizontal) Laplacian term.

Questions

A1.Explain why the red contours in Maps A1 and A3 are expected to correspond with rising motion? .

A2.We oftenargue in class that the spatial pattern of the Laplacian of a field (e.g. ) is close to its opposite (-), and that it emphasizes high-frequency (small-scale) variations. How true is this, near the main shortwave trough? (compare LAP(OMEG) with OMEG)

A3.Compare the Laplacian of omega to the convergence of Q. According to the Q-vector equation, they should be the same. Discuss possible causes of the discrepancies.