1 / 68

680 likes | 974 Views

AOSS 401, Fall 2007 Lecture 22 November 02 , 2007. Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu 734-936-0502. Class News November 02 , 2007. Homework 5 (Due Monday) Posted to web

Download Presentation
## AOSS 401, Fall 2007 Lecture 22 November 02 , 2007

**An Image/Link below is provided (as is) to download presentation**
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.
Content is provided to you AS IS for your information and personal use only.
Download presentation by click this link.
While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

**AOSS 401, Fall 2007Lecture 22November 02, 2007**Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu 734-936-0502**Class News November 02, 2007**• Homework 5 (Due Monday) • Posted to web • Computing assignment posted to ctools under the Homework section of Resources • Next Test: November 16**Seminars Today**• Professor Cecilia Bitz is giving the Dept. of Geological Sciences’ Smith Lecture on Friday (tomorrow, Nov. 2) from 4-5pm. The lecture is held in room 1528 in C.C. Little and is followed by a reception. Cecilia is an expert in high-latitude climate, climate change and variability. The title of her lecture will be: • “Future thermohaline collapse and its impact are unlike the past”**Seminars Today**• Dr. Guy Brasseur - Professor and Associate Director, National Center for Atmospheric Research and Director of the Earth and Sun Systems Laboratory will visit U of M on Thursday/Friday. • Impact of solar variability and anthropogenic forcing on the whole atmosphere: Simulations with the HAMMONIA Model • Friday, November 2, 3:30 pm -- refreshments at 3 pm North Campus AOSS Auditorium, Room #2246**Weather**• National Weather Service • http://www.nws.noaa.gov/ • Model forecasts: http://www.hpc.ncep.noaa.gov/basicwx/day0-7loop.html • Weather Underground • http://www.wunderground.com/cgi-bin/findweather/getForecast?query=ann+arbor • Model forecasts: http://www.wunderground.com/modelmaps/maps.asp?model=NAM&domain=US**Material from Chapter 6**• Quasi-geostrophic theory • Quasi-geostrophic vorticity • Relation between vorticity and geopotential**Mathematics**• Remember the idea that mathematics is a language to use to help us explore a complex system. • Verb: equal, • Qualification: not equal, greater than, less than, approximately • We own the equations and can do to them what we want, as long as we remember equal and not equal.**Tangential coordinate system**Place a coordinate system on the surface. x = east – west (longitude) y = north – south (latitude) z = local vertical or p = local vertical Ω R=acos(f) R a Φ Earth**Tangential coordinate system**Relation between latitude, longitude and x and y dx = acos(f)dl l is longitude dy = adf f is latitude dz = dr r is distance from center of a “spherical earth” f=2Ωsin(f) Ω b=2Ωcos(f)/a R a Φ Earth**Equations of motion in pressure coordinates(using Holton’s**notation)**Scaled equations of motion in pressure coordinates**Definition of geostrophic wind Momentum equation Continuity equation ThermodynamicEnergy equation**Approximate horizontal momentum equation**• This equation states that the time rate of change of the geostrophic wind is related to • the coriolis force due to the ageostrophic wind and • the part of the coriolis force due to the variability of the coriolis force with latitude and the geostrophic wind. • Both of these terms are smaller than the geostrophic wind itself.**Derived a vorticity equation**• Provides a “suitable” prognostic equation because need to include div(ageostrophic wind) in the prognostics. • Remember the importance of divergence in vorticity equations.**One interesting way to rewrite this equation**Expand material derivative**One interesting way to rewrite this equation**Equation of continuity Understand how this is equivalent**One interesting way to rewrite this equation**Advection of vorticity**One interesting way to rewrite this equation**Advection of vorticity Advection of relative vorticity Advection of planetary vorticity**Geopotential Map (Northern Hemisphere)**Where is geostrophic approximation valid? What other force balance is important? What is the sign of the geostrophic wind? ٠ ΔΦ > 0 B Φ0 - ΔΦ L L H Φ0 ٠ ٠ y, north Φ0 + ΔΦ A C x, east**Geostrophic wind**٠ ΔΦ > 0 vg < 0 vg > 0 B Φ0 - ΔΦ L L H Φ0 ٠ ٠ y, north Φ0 + ΔΦ A C x, east**Geopotential Map (Northern Hemisphere)**What is the sign of planetary vorticity? What is the sign of the relative vorticity? ٠ ΔΦ > 0 B Φ0 - ΔΦ L L H Φ0 ٠ ٠ y, north Φ0 + ΔΦ A C x, east**Vorticity**ζ < 0; anticyclonic ٠ ΔΦ > 0 β > 0 β > 0 B Φ0 - ΔΦ L L H Φ0 ٠ ٠ y, north Φ0 + ΔΦ A C x, east ζ > 0; cyclonic ζ > 0; cyclonic**Advection of planetary vorticity**ζ < 0; anticyclonic ٠ ΔΦ > 0 vg < 0 ; β > 0 vg > 0 ; β > 0 B Φ0 - ΔΦ L L H Φ0 ٠ ٠ y, north Φ0 + ΔΦ A C x, east ζ > 0; cyclonic ζ > 0; cyclonic**Advection of planetary vorticity**ζ < 0; anticyclonic ٠ ΔΦ > 0 -vgβ > 0 -vgβ < 0 B Φ0 - ΔΦ L L H Φ0 ٠ ٠ y, north Φ0 + ΔΦ A C x, east ζ > 0; cyclonic ζ > 0; cyclonic**Advection of relative vorticity**ζ < 0; anticyclonic ٠ ζ from >0 to <0 vg > 0; ug > 0 ΔΦ > 0 ζ from <0 to >0 vg < 0; ug > 0 B Φ0 - ΔΦ L L H Φ0 ٠ ٠ y, north Φ0 + ΔΦ A C x, east ζ > 0; cyclonic ζ > 0; cyclonic**Advection of relative vorticity**ζ < 0; anticyclonic ٠ Advection of ζ > 0 ΔΦ > 0 Advection of ζ < 0 B Φ0 - ΔΦ L L H Φ0 ٠ ٠ y, north Φ0 + ΔΦ A C x, east ζ > 0; cyclonic ζ > 0; cyclonic**Advection of vorticity**ζ < 0; anticyclonic Advection of ζ > 0 Advection of f < 0 Advection of ζ < 0 Advection of f > 0 ٠ ΔΦ > 0 B Φ0 - ΔΦ L L H Φ0 ٠ ٠ y, north Φ0 + ΔΦ A C x, east ζ > 0; cyclonic ζ > 0; cyclonic**Summary: Vorticity Advection in Wave**• Planetary and relative vorticity advection in a wave oppose each other. • This is consistent with the balance that we intuitively derived from the conservation of absolute vorticity over the mountain.**Summary: Vorticity Advection in Wave**• What does this do to the wave.**Advection of vorticity**ζ < 0; anticyclonic Advection of ζ tries to propagate the wave this way ٠ ΔΦ > 0 B Φ0 - ΔΦ L L H Φ0 Advection of f tries to propagate the wave this way ٠ ٠ y, north Φ0 + ΔΦ A C x, east ζ > 0; cyclonic ζ > 0; cyclonic**Wave like solutions**Dispersion relation. Relates frequency and wave number to flow. Must be true for waves.**Stationary wave**Wind must be positive, from the west, for a wave.**Advection of vorticity**ζ < 0; anticyclonic Advection of ζ tries to propagate the wave this way ٠ ΔΦ > 0 B Φ0 - ΔΦ L L H Φ0 Advection of f tries to propagate the wave this way ٠ ٠ y, north Φ0 + ΔΦ A C x, east ζ > 0; cyclonic ζ > 0; cyclonic**Compare advection of planetary and relative vorticity** Short waves, advection of relative vorticity is larger Long waves, advection of planetary vorticity is larger **Advection of vorticity**ζ < 0; anticyclonic Short waves ٠ ΔΦ > 0 B Φ0 - ΔΦ L L H Φ0 • Long waves ٠ ٠ y, north Φ0 + ΔΦ A C x, east ζ > 0; cyclonic ζ > 0; cyclonic

More Related