Vorticity and vorticity advection What is vorticity Many meteorological web sites include some form of vorticity contours on the 500mb charts Why How does having contours of vorticity ID: 700842
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Slide1
SO441 Synoptic Meteorology
Vorticity and vorticity advectionSlide2
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
Slide3
What is vorticity?
Vorticity is a measure of spinFirst, some math:
On a weather chart (like the 500
mb
chart), want to measure spin about a vertical axisLike if you stuck a pencil or a pinwheel on the 500
mb chart, would it spin? And in what way?So isolate the “vertical vorticity” : This quantity is also often called “relative
vorticity”Slide4
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 component of the
vorticity
vectorAdvantage: in one variable, both
u and v wind components are usedExample: calculate the relative
vorticity for these two cases:
50 nm
50 nm
50 nm
50 nmSlide5
Relative vorticity
Measure of local spinSign 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 spinTwo types of vorticity: curvature and shear
Positive
vorticity
Negative
vorticitySlide6
Earth’s vorticity
The Earth is a rotating sphere.It imparts vorticity to fluid parcels
Earth
vorticity
along the vertical axis is called Coriolis: , where
f is Coriolis, Ω is the angular speed of earth’s rotation, and
θ is latitudeIn Southern Hemisphere, Earth’s vorticity is negative (why?)
Adapted from
http
://
apollo.lsc.vsc.edu/classes/met130/notes/chapter12/planetary_vort.html
Slide7
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
:
At 500
mb, flow is nearly geostrophicSo re-name relative
vorticity as “geostrophic relative vorticity”Also re-name absolute vorticity
as “geostrophic absolute vorticity”Slide8
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
Slide9
Identify relative and absolute vorticity
on a weather mapSlide10
Relative & absolute vorticity
in higher latitudes (Canada)
Note
color scale
differencesSlide11
Relationship between relative vorticity
and geopotential heightUse the fact that the 500 mb level is nearly geostrophic to derive another equation for
vorticity
:
(Derivation)Slide12
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 ridgeSlide13
Summary of vorticity advection
Greatest advection of absolute vorticity occurs between ridges and troughsWhy?
http://www.aos.wisc.edu/~
aalopez/aos101/wk14/vortAdv.jpg
Slide14
Advection of absolute vorticitySlide15
Physical relationship between vorticity
advection and rising motionCyclonic 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 surfaceThus the depth of the atmosphere between the surface and upper levels is decreasingThe 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
Vorticity
advection occurs at various upper-level heights.
More
vorticity
advection occurs higher in the atmosphere.
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
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 itSlide16
Vorticity
advection at different levels
Composite radar reflectivity