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 ugug ugug 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 =0
Slide 2
Lets 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)
Slide 3
Around 30-45 N, temperature drops northward, therefore westerly
winds increase in strength with height.
Slide 4
The meridional temperature gradient is large between 30-50N and
1000-300 hPa thermal wind Therefore the zonal wind increases
rapidly from 1000 hPa up to 300 hPa.
Slide 5
Question: Why, if it is colder at higher latitude, doesnt the
wind continue to get stronger with altitude ?
Slide 6
There is definitively a jet...
Slide 7
Answer: above 300 hPa, it is no longer colder at higher
latitudes... tropopause
Slide 8
Slide 9
Z 500
Slide 10
Z 500 -Z 1000
Slide 11
Slide 12
baroclinicity The atmosphere is baroclinic if a horizontal
temperature gradient is present The atmosphere is barotropic if NO
horizontal temperature gradient exists the mid-latitude belt
typically is baroclinic, the tropical belt barotropic The
atmosphere is equivalent barotropic if the temperature gradient is
aligned with the pressure (height Z) gradient in 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
levels
Slide 13
1.4.2 Geostrophic T advection: cold air advection (CAA) &
warm air advection (WAA)
Slide 14
highlight areas of cold air advection (CAA) & warm air
advection (WAA) CAA WAA
Slide 15
WAA & CAA
Slide 16
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 advection
Slide 17
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: Thermal wind and geostrophic temperature advection where is the
average wind speed perpendicular to the thermal wind. local T
change T advection The sign of + - VTVT VTVT warm coldwarm
cold
Slide 18
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. + - VTVT VTVT WARM COLD WAACAA Thermal wind and
temperature advection
Slide 19
Procedure to estimate the temperature advection in a layer:
1.On the hodograph showing the upper- and low-level wind, draw the
thermal wind vector. 2.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
advection
Slide 20
example x y WARM COLD n veering wind warm air advection between
1000-850 hPa 10C 5C s
Slide 21
friction-induced near-surface convergence into lows/trofs
Slide 22
1.5 vorticity shear and curvature vorticity
Slide 23
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Slide 25
Slide 26
Slide 27
Slide 28
Slide 29
Hovmoller diagrams (Fig. 1.20)
Slide 30
Slide 31
time scales of atmospheric variability Lovejoy 2013, EOS
Slide 32
time scales of atmospheric variability
Slide 33
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 10010 1000 wavelength [km] (1) Scales of atmospheric
motion inertial subrange
Slide 34
FA=free atmos. BL=bound. layer L = long waves WC = wave
cyclones TC=tropical cyclones cb=cumulonimbus cu=cumulus CAT=clear
air turbulence From Ludlam (1973) Energy cascade synoptic scale Big
whirls have little whirls that feed on their velocity; and little
whirls have lesser whirls, and so on to viscosity. -Lewis Fry
Richardson
Slide 35
Markowski & Richardson 2010, Fig. 1.1 Scales of atmospheric
motion
Slide 36
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 anomalies size such that planetary vort adv >
relative vort adv hydrostatic balance applies synoptic scale:
cyclonic storms and planetary-wave features: baroclinic instability
(~3000 km) deep stratiform clouds smaller features, whose relative
vort adv > planetary vort adv size controlled by =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
clouds time scale between 2 /N and 2 /f hydrostatic balance usually
applies microscale: cumuli, thermals, K-H billows, turbulence:
static instability (1-5 km) convective clouds Size controlled by
entrainment and perturbation pressures no hydrostatic balance 2 /N
~ 2 /10 -2 ~ 10 minutes 2 /f = 12 hours/sin(latitude) = 12 hrs at
90, 24 hrs at 30