1. 1.4 thermal wind balance ug plug (2) into (1) ug ug=0 y
geostrophic wind
hypsometric eqn ug
plug (2) into (1) ug
greater thickness
ug=0
lower thickness y
finite difference expression:
this is the thermal wind: an increase in wind with height due to a temperature gradient
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.

2. 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)

3. Around ºN, temperature drops northward, therefore westerly winds increase in strength with height.

4. thermal wind
The meridional temperature gradient is large between 30-50ºN and hPa
Therefore the zonal wind increases rapidly from 1000 hPa up to 300 hPa.

5. Question:
Why, if it is colder at higher latitude, doesn’t the wind continue to get stronger with altitude ?

6. There is definitively a jet ...

7. Answer: above 300 hPa, it is no longer colder at higher latitudes...
tropopause

9. Z500

10. Z500-Z1000

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
baroclinic
geostrophic wind at various levels
cold
cold
warm
warm
height gradient
temperature gradient

13. 1.4.2 Geostrophic T advection: cold air advection (CAA) & warm air advection (WAA)

14. highlight areas of cold air advection (CAA) & warm air advection (WAA)

15. WAA & CAA

16. geostrophic temperature advection: the solenoid method
geostrophic wind:
fatter arrow: larger T gradient
cold
lower height Z
greater Z
warm
geo. temperature advection is:
greater Z
the magnitude is:
lower Z
cold
warm
the smaller the box, the stronger the temp advection

17. Thermal wind and geostrophic temperature advection
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:
local T change
T advection
where is the average wind speed perpendicular to the thermal wind.
The sign of      + - VT
warm
cold

18. Thermal wind and temperature advection
WARM VT VT
COLD - +
COLD
WARM
WAA
CAA
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.

19. thermal wind and temperature advection
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.

20. example COLD WARM y 5°C n s 10°C x veering wind  warm air advection
between hPa

21. friction-induced
near-surface
convergence into lows/trofs

22. 1.5 vorticity
shear and curvature vorticity

29. Hovmoller diagrams (Fig. 1.20)

31. time scales of atmospheric variability
Lovejoy 2013, EOS “what is climate”: Dynamics and types of scaling variability: representative temperature series from
weather (space scales and timescales), macroweather, and climate scales (bottom to top,
respectively). Each sample is 720 points long and was normalized by its overall range (bottom
to top: 2.86 K, 27.8 K, K, and 7.27 K; dashed lines indicate means). The resolutions are
280 meters, 1 hour, 20 days, and 1 century, and the data are from an aircraft at 200 mbar
(north Pacific); Lander, Wyoming; the twentieth century reanalysis (20CR, 75°N, 100°W); and
Vostok (Antarctica).
Lovejoy 2013, EOS

32. time scales of atmospheric variability
Temperature standard deviations S(Δt). (top left) Grid point scale
(2° × 2°) daily fluctuations globally averaged from the 20CR. (bottom left) The same fluctuations,
but for the global average (brown line), and the average of the three in situ global surface
series (red line) as well as S(Δt) from three multiproxy Northern Hemisphere reconstructions
(green line) [see Lovejoy and Schertzer, 2012a]. (right) The European Project for Ice Coring in
Antarctica (EPICA) Antarctic series at a 50-year resolution. Also shown is the interglacial
window (rectangle) and reference slopes H = −0.4, +0.4, −0.1, and −0.5 (Gaussian white noise).
Lovejoy 2013, EOS

33. (1) Scales of atmospheric motion
Note two spectral extremes:
(a) A maximum at about 2000 km
(b) A minimum at about 500 km
[shifted x10 to right]
inertial subrange
1000
100 10 1
wavelength [km]
Gage and Nastrom (1985)

34. Energy cascade synoptic scale FA=free atmos. BL=bound. layer
Big whirls have little whirls that feed on their velocity; and little whirls have lesser whirls, and so on to viscosity.                   -Lewis Fry Richardson
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)

35. Scales of atmospheric motion
Markowski & Richardson 2010, Fig. 1.1

36. 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 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 b=df/dy
mesoscale: waves, fronts, thermal circulations, terrain interactions, mesoscale instabilities, upright convection & its mesoscale organization: various instabilities – synergies ( km) – stratiform & convective clouds
time scale between 2p/N and 2p/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
2p/N ~ 2p/10-2 ~ 10 minutes
2p/f = 12 hours/sin(latitude) = 12 hrs at 90°, 24 hrs at 30°