Lackmann, Chapter 1:
Basics of atmospheric motion

time scales of atmospheric variability
Lovejoy 2013, EOS

time scales of atmospheric variability
Lovejoy 2013, EOS

(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]
SD
 k

5
3 inertial subrange
Gage and Nastrom (1985)
1000 100 10 wavelength [km]
1

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
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)

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

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
 v g b  
 v g
  
–
– 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 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 p /N and 2 p /f hydrostatic balance usually applies 2 p /N ~ 2 p /10 -2 ~ 10 minutes
2 p /f = 12 hours/sin(latitude) = 12 hrs at 90°, 24 hrs at 30°
– microscale: cumuli, thermals, K-H billows, turbulence: static instability (1-5 km) – convective clouds
•
• Size controlled by entrainment and perturbation pressures no hydrostatic balance

( 1 ) u g
( 2 )

Z
 p
  g f
 
RT gp

Z
 y
1.4 thermal wind balance geostrophic wind hypsometric eqn u g plug (2) into (1)

 u p g  f g




RT
 y gp 



R fp

T
 y greater thickness u g u g
=0 lower thickness finite difference expression: y
 u g

R f
 p p


T y 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 .

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)

Around 30-45 ºN, temperature drops northward, therefore westerly winds increase in strength with height.

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

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

There is definitively a jet ...

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

 p
T
 p
T

Z
500 v g 500
 f g k
ˆ  
Z
500

Z
500
-Z
1000
 v g
  p



 u g
  p
,
 v g
  p



R fp




T
 y
,

T
 x



R fp

R fp k
ˆ  
T v
T 500 , 1000
 v g 500
 v g 1000
 f g k
ˆ  

Z
500

Z
1000

 g k
ˆ   
Z f

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
 v
T
 v
 g 2

 v g 1 geostrophic wind at various levels v
 g 1 v
 g 1 cold cold warm warm

Z height gradient

T temperature gradient

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

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

WAA & CAA

geostrophic temperature advection: the solenoid method geostrophic wind:
 v g
 v g

 g f g f k
ˆ  
Z

Z
 g f




Z
 y
,

Z
 x

 fatter arrow: larger T gradient 
T geo. temperature advection is:

 v g
 
T the magnitude is:
 v g
 
T
 g

Z f the smaller the box, the stronger the temp advection

T

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
∂
∂
T t

V n
∂
T
∂ n
, (note that
∂
T
∂ s

0 )
The sign of V n cold warm
V
T
V n
+
 v
T
 v
 g 2
 v
 g 1 warm cold
V
T
V n
-

Thermal wind and temperature advection
∂
T
∂ t

V n
∂
T
∂ n
, (note that
∂
T
∂ s

0 )
V
T
V
T
V n
+ V n
-
∂ T
∂ t
>
WAA
0
∂ T
∂ t
<
CAA
0
If the wind veers with height, V n
V n is positive and there is warm advection.
If the wind is back with height, is negative and there is cold advection.

thermal wind and temperature advection
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 V n
, perpendicular to the thermal wind. Note that
V n 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.

example y
 v
T v
 g 1000

 v g 850

 v g 1000 v
 g 850
V n n s x
V n

0
∂
T
∂ t
> 0 veering wind  warm air advection between 1000-850 hPa

friction-induced near-surface convergence into lows/trofs

1.5 vorticity shear and curvature vorticity

 a
   f



 or a

?

 a
 v

   a

Hovmoller diagrams (Fig. 1.20)