SO441 Synoptic Meteorology
Vorticity and vorticity advection
What is vorticity?
• Many meteorological web
sites include some form of
vorticity contours on the
500-mb charts
– Why? How does having
contours of vorticity help a
meteorologist understand
the atmosphere?
http://mag.ncep.noaa.gov
http://www.wxmaps.org/pix/nam.fcst.html
What is vorticity?
• Vorticity is a measure of spin
– First, some math:
iˆ

  u 
x
u
ˆj

y
v
kˆ
 w v 

 iˆ 
 
z
 y z 
w
ˆj  u  w   kˆ  v  u 
 z x 
 x y 
• On a weather chart (like the 500 mb chart), want
to measure spin about a vertical axis
– Like if you stuck a pencil or a pinwheel on the 500 mb
chart, would it spin? And in what way?
 v
u 

:  


x

y


• So isolate the “vertical vorticity”
• This quantity is also often called “relative
vorticity”
Relative (vertical) vorticity
• Relative (vertical) vorticity is not a measure of “vertical spin”,
but rather a measure of horizontal spin
– The word “vertical” comes from the fact that it’s the k̂ component of
the vorticity vector
• Advantage: in one variable, both u and v wind components are
used
• Example: calculate the relative vorticity  for these two cases:
50 nm
50 nm
50 nm
50 nm
Relative vorticity 
• Measure of local spin
• Sign convention:
– Positive spin, or positive
vorticity, is in the same sense as
the counter-clockwise rotation
of the Earth (the earth would
spin counter-clockwise if you
looked down on it from above
the north pole)
– Negative vorticity: clockwise
spin
• Two types of vorticity:
curvature and shear
Positive
vorticity
Negative
vorticity
Earth’s vorticity
• The Earth is a rotating sphere.
– It imparts vorticity to fluid parcels
– Earth vorticity along the vertical axis is called
Coriolis: f  2 sin  , where f is Coriolis, Ω is the
angular speed of earth’s rotation, and θ is latitude
– In Southern Hemisphere, Earth’s vorticity is
negative (why?)
Adapted from http://apollo.lsc.vsc.edu/classes/met130/notes/chapter12/planetary_vort.html
Geostrophic absolute vorticity
• To examine the actual spin of an air parcel,
need to look at vorticity contributions from
both the Earth and the parcels themselves:
– Absolute vorticity:
a   f
• At 500 mb, flow is nearly geostrophic
– So re-name relative vorticity as “geostrophic
relative vorticity”  g
– Also re-name absolute vorticity as “geostrophic
absolute vorticity”  ga   g  f
Importance of vorticity
• Remember from Lesson 5 (Extratropical
cyclones), vorticity is the quantity that “spins
up” (or down) during the development of an
extratropical cyclone
Figure adapted from http://www.aos.wisc.edu/~aalopez/aos101/wk14.html
Identify relative and absolute vorticity
on a weather map
Relative & absolute vorticity in higher
latitudes (Canada)
Note color scale differences
Relationship between relative vorticity
and geopotential height
• Use the fact that the 500 mb level is nearly
geostrophic to derive another equation for
vorticity:
– (Derivation)
Summary of relative vorticity
• Geostrophic relative vorticity: average difference
in geopotential height around a central point
– If average height is higher across the region than at
the center point, geostrophic vorticity is positive (i.e.
cyclonic)
• i.e., point is lower than its surroundings, such as in a trough
– If average height is lower than at center point,
geostrophic vorticity is negative (i.e., anticyclonic)
• i.e., point is higher than its surroundings, such as in a ridge
Summary of vorticity advection
• Greatest advection of absolute vorticity occurs
between ridges and troughs
– Why?
vorticity advection =   u    g  f 
http://www.aos.wisc.edu/~aalopez/aos101/wk14/vortAdv.jpg
Advection of absolute vorticity
Physical relationship between vorticity
advection and rising motion
•
•
•
Cyclonic vorticity advection produces
height falls, proportional to the magnitude
of the vorticity advection.
Cyclonic vorticity is associated with low
heights, so if vorticity advection increases
with height (i.e., more vorticity advection
at 250 mb than at 850 mb), heights will
fall more aloft than at the surface
Thus the depth of the atmosphere
between the surface and upper levels is
decreasing
–
•
The depth of a column of air is
proportional to its mean temperature, so a
less-deep column means a colder column
If no temperature advection (or any other
change) occurs – i.e., the only thing taking
place is vorticity advection – then the only
way to cool the column of air is for rising
motion to take place
This method is adapted from from C. Doswell and K. Crawford, Univ.
Oklahoma School of Meteorology. http://www.cimms.ou.edu/~doswell/PVAdisc/PVA.html
Vorticity advection
occurs at various
upper-level heights.
More vorticity
advection occurs
higher in the
atmosphere.
Deeper trough in
upper levels causes a
smaller column of air
in the trough.
Smaller column of air
must be associated
with cooler
temperatures, and the
way to cool the air is
to lift it
Vorticity advection at different levels
Composite radar reflectivity