USING
A MATHEMATICAL APPROACH TO DETERMINE
VORTICITY
ADVECTION (TERM B)
Obtain an image of the
500-hPa wind barb plan view and wind direction at the location diamond by
following these steps:
1)
In the “Displays” menu, check the box next to “Wind Barbs” under the section
labeled “WIND PLOTS.”
2)
Under the section titled “DRAWING TOOLS” in the “Displays” menu, check the box
next to “Geostrophic Wind Vector.”
Q9 - What two
forces are in balance in “geostrophic” flow?
Is the flow at 500 hPa approximately geostrophic? How can you tell?
Q10 - From the wind bards, what is the approximate 500-hPa
wind speed (in knots) at the location diamond?
Convert this rough estimate to m/s.
3)
Uncheck the boxes next to “Wind Barbs” under “WIND PLOTS” and “Geostrophic Wind Vector” under “DRAWING TOOLS.”
4)
Also, uncheck the box corresponding to “500 hPa Geopotential Height Contours”
in the “GEOPOTENTIAL HEIGHT PLOTS” section of the “Displays” menu. This should yield a blank map once again with
only the gray location diamond fixed in western
Obtain the following image of
the 500-hPa absolute vorticity gradient at the location diamond by following
these steps:
1) Under the main heading titled “ABSOLUTE VORTICITY PLOTS.” Check the following subcategories:
a) “500 hPa Absolute Vorticity Contours (Max)”
b) “500 hPa Colored Absolute Vorticity Max”
c) “500 hPa Absolute Vorticity Contours (Diamond)”
2)
In addition, check the boxes corresponding to “Gradient of Absolute Vorticity”
and “Range and Bearing” under the “DRAWING TOOLS” section of the “Displays”
menu.
Q11 - What is the mathematical definition of a gradient? Why is the pink vector (absolute vorticity
gradient) directed to the WNW?
Q12 - What is the value of the contour of absolute
vorticity at the left end of the range and bearing tool overlapping the pink
gradient vector? Note that the value of the
500-hPa absolute vorticity at the location diamond is 12 x 10-5 s-1. From the computed “Distance” appearing under
the “Range and Bearing” label in the “Displays” menu and the previously
interpreted values of vorticity, calculate a rough estimate of the magnitude of
the gradient of absolute vorticity at the location diamond.
3)
Uncheck the box next to “ABSOLUTE VORTICITY PLOTS” and “Range and Bearing”
under “DRAWING TOOLS.” Leave the box
corresponding to “Gradient of Absolute Vorticity” checked.
Obtain an image of the angle
between the gradient of absolute vorticity and the geostrophic wind vector by
simply checking the box next to “Geostrophic Wind Vector” under the “DRAWING
TOOLS” section of the “Displays” menu.
Q13 - What is the approximate angle between the vectors?
Remove the vectors from the
display by unchecking the box corresponding to each under the “DRAWING TOOLS”
section of the “Displays” menu.
Q14 - Recall that Term B in the Q-G height tendency equation is given by 
. Using the definition
of a dot product, Term B can be rewritten in the following form: 
. Use your estimates of 
(magnitude of the
geostrophic wind), 
(magnitude of the
absolute vorticity gradient), and 
(estimated angle
between the geostrophic wind vector and the gradient of absolute vorticity),
and an accepted value of 
to compute an
estimated total value, , of Term B.
Q15 - Ignoring Term C, note from the Q-G height tendency equation that 
. From the procedures
followed in the answer to Q14, it is clear that
this can be rewritten as 
. So, based on your
computation of 
, use the relationship between 
and 
to predict either a
height fall or a height rise.