AOSS 401, Fall 2006Lecture 19

October 26, 2007

Richard B. Rood (Room 2525, SRB)rbrood@umich.edu

734-647-3530Derek Posselt (Room 2517D, SRB)

dposselt@umich.edu734-936-0502

Class NewsOctober 26, 2007

• Homework – Homework 5 posted today– Includes a programming assignment that will

be posted this afternoon/evening– Focus your attention on question 1

Today

• Bring together physical concepts and preview the rest of the course

• Material from Chapter 6 – Middle Latitude Structure– Quasi-geostrophic theory

Flow over a mountain rangeWest to East

What is happening with planetary vorticity?(In the (east-west, north-south) plane)

Dep

th,

H

Dep

th,

H +ΔH

west easts

n Dep

th,

H -ΔH

Dep

th,

H +ΔH

f is greater for deflections to north

f is less for deflections to south

f + ζ is less than earth’s vorticity and wants to turn north.

Arrives here wanting vorticity. “Overshoots”

Flow over a mountain rangeEast to West

What is happening with planetary vorticity?(In the (east-west, north-south) plane)

Dep

th,

H

Dep

th,

H +ΔH

west easts

n Dep

th,

H -ΔH

Dep

th,

H +ΔH

Flow from east planetary and relative vorticity interact together, no overshoot or undershoot.

Wind and geopotential 200 hPa

Note: Troughs associated with

mountain ranges, continents

Observations of the Atmosphere

• Vorticity– Small scale flow– Large-scale flow

• Large scale flow and the climate system– Heat transport– Jet streams– Development of mid-latitude cyclones

Vorticity on Small Scales

• From the southern California fires:

http://video.nbc11.com/player/?id=171454

• What is the cause?http://aoss-web.engin.umich.edu/class/aoss102/tools/swf/?url=class/aoss102/tools/swf/

Vorticity on Large Scales

• Remember, vorticity is caused by– Wind shear– Rotation in the flow

• Can we identify these on weather maps?

• (The following maps come from http://www.aos.wisc.edu/weather/)

300 mb Wind Speed

Where is there positive vorticity?

500 mb Vorticity

Thermal Wind

• Remember, thermal wind relates– Vertical shear of geostrophic wind– Horizontal temperature gradients

• Can we identify these on weather maps?

Where are the strongest ?T

850 mb Temperature

Convergence/Divergence

• Remember, vertical motion on large scales directly related to– Convergence/divergence of ageostrophic

wind– Curvature in the flow

• Can we identify these on weather maps?

Where are surface lows/highs?

Surface Precipitation

850 mb Temperature

Concepts

• Vorticity: shear and curvature– Why is curvature vorticity (as opposed to

shear vorticity) usually associated with developing low pressure systems?

• Divergence and convergence and location of surface high and low pressure systems

• Thermal wind—vertical shear of the horizontal wind and horizontal temperature gradients

Concepts

• Features commonly found together– Jet stream– Upper level positive vorticity– Fronts– Midlatitude cyclones (low pressure systems)

• Coincidence?

• More on this later…

Large scale flow and the climate system

Transfer of heat north and south is an important element of the climate at the Earth’s surface.

Redistribution by atmosphere, ocean, etc.

SURFACE

Top of Atmosphere / Edge of Space

ATMOSPHERECLOUD

heat is moved to poles

cool air moved towards equator cool air moved towards equator

This is a transfer. Both ocean and atmosphere are important!

Large scale weather systems transport large quantities of thermal energy from equator toward the poles

Hurricanes and heat

Hurricanes and heat

Mid-latitude cyclones

Mid-latitude cyclones & Heat

Mid-latitude Cyclones & Jet Stream

An estimate of the January mean temperature

northwinter

southsummer

tropopause

stratopause

mesosphere

stratosphere

troposphere

note where the

horizontal temperature gradients are

large

An estimate of the January mean zonal wind

northwinter

southsummer

note the jet streams

An estimate of the July mean zonal wind

northsummer

southwinter

note the jet streams

Wind and geopotential 200 hPa

Note: Variability in east-west of the wind

field.

Note: Troughs associated with

mountain ranges, continents

Note: Time variability of the wind field.

Waves in the atmosphere

• 300 mb Jet Stream Animation

Short summary

• We have strong mean zonal winds.

• We have latitudinal and time variability of the zonal winds– Quasi-stationary long waves.

• On these quasi-stationary long waves, mid-latitude cyclones form and propagate.

Mid-latitude cyclones

• What we know:– Low pressure systems– Form through spinup of low-level positive

vorticity– Divergence/convergence is key

• This is just the beginning…– Always closely associated with fronts—why?– Sometimes develop rapidly, sometimes not at

all—why?

The mid-latitude cyclone

Mid-latitude cyclones: Norwegian Cyclone Model

Fronts and Precipitation

CloudSat Radar

Norwegian Cyclone Model

Relationship between upper troposphere and surface

note tilt with height

Idealized vertical cross section

What’s at work here?

Mid-latitude cyclone development

Mid-latitude cyclones: Norwegian Cyclone Model

• http://www.srh.weather.gov/jetstream/synoptic/cyclone.htm

Cold and warm advection

cold

warm

Lifting and sinking

Increasing the pressure gradient force

Relationship between upper troposphere and surface

divergence over low enhances surface low

//increases vorticity

Relationship between upper troposphere and surface

vertical stretching //

increases vorticity

Modern education at its best.

• http://aoss.engin.umich.edu/class/aoss102/tools/swf/

Analysis Tools

• We have used many of the concepts and tools that we have introduced and explored.– Observed characteristics of the atmosphere– Conservation principles– Scale analysis: Geostrophic and hydrostatic– Thermal wind– Divergence and convergence

• These ideas are integrated into quasi-geostrophic theory (analysis and prediction)

Programming Exercise

• Gain experience writing programs to– Read data– Analyze data– Plot data

• Tools for research/analysis

Remember the vertical structure of the atmosphere

zRT

pgp

RT

p

gz

p

Hydrostatic

Eq. of State

If we assume T is constant with height (Isothermal)

zRT

g

p

p

zRT

pgp

If we assume T varies with height (Realistic)

p

p

z

p

p

z

sfc

sfc

T

z

R

gp

T

z

R

g

p

p

zRT

g

p

p

0

0

ln

If we assume T varies linearly with height (Not a bad assumption, in general)

sfc

sfc

sfc

p

p

z

sfc

sfc

sfc

T

zT

R

g

p

p

zT

z

R

g

p

p

zT

z

R

g

p

p

zTT

sfc

lnln

0 constant,

0

If we assume T varies linearly with height (Not a bad assumption, in general)

Rg

sfcsfc

Rg

sfc

sfcsfc

sfc

sfc

sfc

T

Tpp

T

zTpp

T

zT

R

g

p

p

/

/

)(

)(

lnln

Programming Exercise

• Read in data from two sounding files– Height– Potential temperature

• Compute pressure on each level– Isothermal atmosphere– Varying temperature– Constant lapse rate

• Use this information– Geostrophic wind– Temperature gradients

Programming Exercise

• Goals: programming concepts– Reading data– Arrays– Loops– Iteration

• Materials posted to ctools this afternoon/evening– Skeleton MatLAB program– Data– Instructions

Next Week

• Programming exercise in class Monday

• Start looking at quasi-geostrophic system– Scale analysis of equations in pressure

coordinates– Quantify wave movement and development