SO254 – relative and planetary vorticity

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? Vorticity is a measure of spin, and charts of relative vorticitiy help quickly identify areas with greatest spin (troughs and ridges) Vorticity advection is directly related to rising and sinking motion Vertical motions are directly tied to clouds (rising motion  clouds; sinking motion  clear skies) In the charts at right, the contours show relative vorticity Yellow and orange (top) and red (bottom) is cyclonic vorticity Blue (bottom) shows anticyclonic vorticity Do the areas of cyclonic vorticity tend to show up in troughs, or ridges? 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”

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, and the axis of the spin points in the vertical direction Advantage of relative vorticity: 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

More on 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 The calculation of is the same for both curvature and shear North East Positive vorticity Negative vorticity These signs (+ / -) of the vorticity will not change between hemispheres. But, the type (cyclonic / anticyclonic) does change: in the N. Hem., cyclonic vorticity is positive. In the S. Hem., cyclonic vorticity is negative.

Planetary vorticity: spin arising from rotation of the Earth 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?) Adapted from http://apollo.lsc.vsc.edu/classes/met130/notes/chapter12/planetary_vort.html

Absolute vorticity: sum of relative and planetary 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: Above the surface, where friction is small, air flow is nearly geostrophic Can re-name relative vorticity as “geostrophic relative vorticity” Also can re-name absolute vorticity as “geostrophic absolute vorticity”

Importance of vorticity We will see later that the horizontal advection of vorticity, combined with horizontal divergence and convergence, has major implications for the development of surface pressure systems, of fronts, of precipitation features We will learn more about advection in the next lesson Source: http://www.meted.ucar.edu/radar/tropical_cases/media/graphics/midlatitude_cyclone_concept.jpg Source: https://cavu.nrlmry.navy.mil/COAMPSOS/pascal.nrlmry.navy.mil/coamps-os/cgi-bin/COAMPSOS_vis_help_wrapper.tcl%3Fname=def-500mb-rvor-wind-z0