geostrophic wind hypsometric eqn plug 2 into 1 finite difference expression this is the thermal wind an increase in wind with height due to a temperature gradient greater thickness lower thickness ID: 421965
Download Presentation The PPT/PDF document "1.4 thermal wind balance" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
Slide1
1.4 thermal wind balance
geostrophic wind
hypsometric
eqn
plug (2) into (1)
finite difference expression:
this is the
thermal wind: an increase in wind with height due to a temperature gradient
greater thickness
lower thickness
y
u
g
u
g
The
thermal wind blows ccw around cold pools
in the same way as the geostrophic wind blows ccw around lows. The thermal wind is proportional to the T gradient, while the geostrophic wind is proportional to the pressure (or height) gradient.
u
g
=0Slide2
Let’s verify qualitatively that climatological temperature and wind fields are roughly in
thermal wind balance. For instance, look at the meridional variation of temperature with height (in Jan)Slide3
Around 30-45
ºN, temperature drops northward, therefore westerly winds increase in strength with height.Slide4
The meridional temperature gradient is large between 30-50
ºN and 1000-300 hPa
thermal wind
Therefore the zonal wind increases rapidly from 1000 hPa up to 300 hPa.Slide5
Question:
Why, if it is colder at higher latitude, doesn’t the wind continue to get stronger with altitude ?Slide6
There is definitively a jet ...Slide7
Answer: above 300 hPa, it is no longer colder at higher latitudes...
tropopauseSlide8Slide9
Z
500Slide10
Z
500
-Z1000Slide11Slide12
baroclinicity
The atmosphere is baroclinic if a horizontal temperature gradient is presentThe atmosphere is barotropic if NO horizontal temperature gradient exists
the mid-latitude belt typically is baroclinic, the tropical belt barotropicThe atmosphere is equivalent barotropic if the temperature gradient is aligned with the pressure (height Z) gradientin this case, the wind increases in strength with height, but it does not change direction
equivalent barotropic
height gradient
temperature gradient
warm
cold
baroclinic
warm
cold
geostrophic wind at various levelsSlide13
1.4.2 Geostrophic T advection:
cold air advection (CAA) & warm air advection (WAA)Slide14
highlight areas of cold air advection (CAA) & warm air advection (WAA)
CAA
WAASlide15
WAA & CAASlide16
geostrophic temperature advection: the
solenoid method
lower height Z
greater Z
geostrophic wind:
warm
cold
warm
cold
lower Z
greater Z
fatter arrow: larger T gradient
geo. temperature
advection is:
the magnitude is:
the smaller the box, the stronger the temp advectionSlide17
Let us use the natural coordinate and choose the
s direction along the thermal wind
(along the isotherms) and n towards the cold air. Rotating the x-axis to the s direction, the advection equation is:
T
hermal wind and geostrophic temperature advection
where is the average wind speed perpendicular to the thermal wind.
local T change
T advection
The sign of
+
-
V
T
V
T
warm
cold
warm
coldSlide18
If the wind veers with height, is positive and there is warm advection. If the wind is back with height, is negative and there is cold advection.
+
-
V
T
V
T
WARM
WARM
COLD
COLD
WAA
CAA
T
hermal
wind and temperature advectionSlide19
Procedure to estimate the temperature advection in a layer:
On the hodograph showing the upper- and low-level wind, draw the thermal wind vector.
Apply the rule that the thermal wind blows ccw around cold pools, to determine the temperature gradient, and the unit vector n (points to cold air)
3. Plot the mean wind , perpendicular to the thermal wind. Note that is positive if it points in the same direction as n. Then the wind veers with height, and you have warm air advection. If there is warm advection in the lower layer, or cold advection in the upper layer, or both, the environment will become less stable.
thermal wind and temperature advectionSlide20
example
x
y
WARM
COLD
n
veering wind
warm air advection
between 1000-850 hPa
10°C
5°C
sSlide21
friction-induced
near-surface
convergence into lows/trofsSlide22
1.5 vorticity
shear and curvature
vorticitySlide23Slide24Slide25Slide26Slide27Slide28Slide29
Hovmoller diagrams (Fig. 1.20)Slide30Slide31
time scales of atmospheric variability
Lovejoy 2013, EOS Slide32
Lovejoy 2013, EOS
time scales of atmospheric variabilitySlide33
Gage and
Nastrom
(1985)
[shifted x10 to right]
Note two spectral extremes:(a) A maximum at about 2000 km(b) A minimum at about 500 km
1
100
10
1000
wavelength [km]
(1) Scales of atmospheric motion
inertial subrangeSlide34
FA=free atmos.
BL=bound. layer
L = long waves
WC = wave cyclonesTC=tropical cyclonescb=cumulonimbuscu=cumulusCAT=clear air turbulence
From Ludlam (1973)
Energy cascade
synoptic scale
Big whirls have little whirlsthat feed on their velocity;and little whirls have lesser whirls,and so on to viscosity.
-Lewis Fry Richardson Slide35
Markowski
& Richardson 2010, Fig
. 1.1
Scales of atmospheric motionSlide36
Scales of atmospheric motion
Air motions at all scales from planetary-scale to
microscale explain weather:
planetary scale: low-frequency (10 days – intraseasonal) e.g. blocking highs (~10,000 km) – explains low-frequency anomaliessize such that planetary vort adv > relative vort advhydrostatic balance appliessynoptic scale: cyclonic storms and planetary-wave features:
baroclinic instability (~3000 km) – deep stratiform cloudssmaller features, whose relative vort adv > planetary vort advsize controlled by b=df/dy
hydrostatic balance applies mesoscale: waves, fronts, thermal circulations, terrain interactions, mesoscale instabilities, upright convection & its mesoscale organization: various instabilities – synergies (100-500 km) – stratiform & convective cloudstime scale between 2p/N and 2p/f
hydrostatic balance usually appliesmicroscale: cumuli, thermals, K-H billows, turbulence: static instability (1-5 km) – convective cloudsSize controlled by entrainment and perturbation pressuresno hydrostatic balance
2p/N ~ 2p/10-2 ~ 10 minutes2p
/f = 12 hours/sin(latitude) = 12 hrs at 90°, 24 hrs at 30°