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:

• 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?• So isolate the “vertical vorticity” : • This quantity is also often called “relative vorticity”

ˆˆ ˆ

ˆˆ ˆ

i j kw v u w v uu i j k

x y z y z z x x yu v w

v ux y

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 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

k̂

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: , 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?)

2 sinf

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:

• At 500 mb, flow is nearly geostrophic– So re-name relative vorticity as “geostrophic

relative vorticity”– Also re-name absolute vorticity as “geostrophic

absolute vorticity”

a f

ga g f

g

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?

http://www.aos.wisc.edu/~aalopez/aos101/wk14/vortAdv.jpg

vorticity advection = gu f

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

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 it

Vorticity advection at different levels

Composite radar reflectivity