atms 4320 / 7320 – lab 7 the thermal wind: forecasting problems and the analysis of fronts

Atms 4320 / 7320 – Lab 7Atms 4320 / 7320 – Lab 7

The Thermal Wind: The Thermal Wind: Forecasting Problems and Forecasting Problems and

the Analysis of Frontsthe Analysis of Fronts

The Thermal Wind: Forecasting Problems The Thermal Wind: Forecasting Problems and the Analysis of Frontsand the Analysis of Fronts

Thermal wind: Bluestein p 181 - 187, and Thermal wind: Bluestein p 181 - 187, and Holton p 68 - 71.Holton p 68 - 71.

The “thermal” wind: The thermal wind links The “thermal” wind: The thermal wind links the temperature field to the wind field via the temperature field to the wind field via hydrostatic balance.hydrostatic balance.

gz

p

dz

dp


We know that in a geostrophically balanced We know that in a geostrophically balanced world we can link the wind field with the mass world we can link the wind field with the mass field (pressure or height).field (pressure or height).

Thus, in order to talk about thermal wind balance Thus, in order to talk about thermal wind balance we must specify two balance conditions to exist we must specify two balance conditions to exist simultaneously. Thus, thermal wind balance is simultaneously. Thus, thermal wind balance is considered a “higher order” balance state.considered a “higher order” balance state.

gzfk

pfk

V hg ,ˆˆ


The Thermal wind is simply the vertical The Thermal wind is simply the vertical wind shear vector:wind shear vector:

VT = VVT = Vgeogeo (upper level) - V (upper level) - Vgeogeo (lower (lower

level)level)

Thus if we substitute in for Vgeo we get:Thus if we substitute in for Vgeo we get:

luhggT fk

fk

VVVlu

ˆˆ


Carrying out the subtraction,Carrying out the subtraction,

put into differential form,put into differential form,

pf

kfk

p

VV plup

gT

ˆˆ

pfk

p

VV p

gT

ˆ


Then using the equation of state:Then using the equation of state:

TfpkR

p

VV p

gT

ˆ


In component form:In component form:

thicknessp

where

xT

fpR

pxfp

vv

yT

fpR

pyfp

uu

gT

gT

1

1


Note that the thermal wind is simply a Note that the thermal wind is simply a measure of the vertical wind shear.measure of the vertical wind shear.

Vertical wind shear: BaroclinicityVertical wind shear: Baroclinicity

zV

pV


Recall that in a barotropic atmosphere, Recall that in a barotropic atmosphere, there is no vertical wind shear. The there is no vertical wind shear. The definition of a baroclinic atmosphere is that definition of a baroclinic atmosphere is that there is speed and or directional shear in there is speed and or directional shear in the vertical.the vertical.

Thus we can regard the strength of Thus we can regard the strength of Thermal Wind as a measure of Thermal Wind as a measure of baroclinicity.baroclinicity.


The thermal wind “blows” parallel to the The thermal wind “blows” parallel to the isotherms, or the thickness lines with isotherms, or the thickness lines with warm air on the right and cold air on the warm air on the right and cold air on the left. Thus, the thermal wind “blows” left. Thus, the thermal wind “blows” perpendicular to both gradient quantities.perpendicular to both gradient quantities.

)(,,|| TVTV TT


The map (Thanks OU)The map (Thanks OU)


Thus, the thickness lines can also be used Thus, the thickness lines can also be used to deduce areas of warm and cold air to deduce areas of warm and cold air advections, and locate fronts in the advections, and locate fronts in the atmosphere. atmosphere.


Another view (Dr. Brad Muller)Another view (Dr. Brad Muller)


Cold advection (winds back with height):Cold advection (winds back with height):

In the Northern Hemisphere, cold In the Northern Hemisphere, cold advection will be associated with thermal advection will be associated with thermal wind with a southerly component.wind with a southerly component.

Geostrophic Wind Shear and Thermal Geostrophic Wind Shear and Thermal AdvectionAdvection

cold

warm TV

1gV

2gV

Case 2: Geostrophic wind backs (i.e., turns counterclockwise) with height.

Lower level wind is from N.Upper level wind is from NW.

Since colder air must lie to the left of the thermal wind, the layer average wind blows from cold to warm, which implies cold advection.


Warm advection (winds veer with height). Warm advection (winds veer with height). (thanks to Dr. Broccoli, Rutgers)(thanks to Dr. Broccoli, Rutgers)

In the northern hemisphere, warm air In the northern hemisphere, warm air advection will tend to be associated with a advection will tend to be associated with a thermal wind with a westerly component.thermal wind with a westerly component.

Geostrophic Wind Shear and Thermal Geostrophic Wind Shear and Thermal AdvectionAdvection

cold

warm

TV

1gV

2gV

Case 1: Geostrophic wind veers (i.e., turns clockwise) with height.

Lower level wind is from SW.Upper level wind is from W.

Since colder air must lie to the left of the thermal wind, the layer average wind blows from warm to cold, which implies warm advection.


Areas of low pressure will tend propagate Areas of low pressure will tend propagate along with the thermal wind where it is along with the thermal wind where it is strong (along packed thickness or height strong (along packed thickness or height contours), and at the speed of the thermal contours), and at the speed of the thermal wind.wind.


Also, we can deduce fronts from the Also, we can deduce fronts from the thickness field. The warm front is located thickness field. The warm front is located on the equatorward edge of a zonal on the equatorward edge of a zonal thickness gradient as we move poleward thickness gradient as we move poleward (or perpendicular to the thermal wind (or perpendicular to the thermal wind moving over it from right to left):moving over it from right to left):


The cold front is located on the The cold front is located on the downstream edge of a meridional downstream edge of a meridional thickness gradient as we move from west thickness gradient as we move from west to east (zonally) (or perpendicular to the to east (zonally) (or perpendicular to the thermal wind moving over it from right to thermal wind moving over it from right to left)left)


In the Southern Hemisphere, the thermal In the Southern Hemisphere, the thermal wind blows with warm air to the left and wind blows with warm air to the left and cold air to the right. Why? cold air to the right. Why?

Coriolis Force is negative! We must “flip” Coriolis Force is negative! We must “flip” all the arguments made above.all the arguments made above.

TfpkR

p

VV p

gT

ˆ


Example (SH):Example (SH):

A backing wind represents represents A backing wind represents represents Warm air advectionWarm air advection

A veering wind represents cold air A veering wind represents cold air advectionadvection


The End!The End!

atms 4320 / 7320 – lab 7 the thermal wind: forecasting problems and the analysis of fronts

Documents

thermal wind balance

strength of thermal

wind field

geostrophic wind shear

upper level wind

lower level wind

forecasting problems

layer average wind