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Midlatitude Weather systems
Geraint Vaughan
University of Manchester
NCAS Director of Observations
1
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Surface weather chart for 3 January 2007 (UK Met Office)
1110 km:
1° lat =
111 km
http://www.wetterzentrale.de/topkarten/tknfax.html
http://www.ncas.ac.uk
Salient features
●
Surface pressure pattern dominated by
highs and lows, on a scale ~ 103 km. We
call this the synoptic scale
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Salient features
●
●
Surface pressure pattern dominated by
highs and lows, on a scale ~ 103 km. We
call this the synoptic scale
Pressure excursions around ± 30 mb –
much smaller than the total pressure of
~1000 mb.
http://www.ncas.ac.uk
Salient features
●
●
●
Surface pressure pattern dominated by
highs and lows, on a scale ~ 103 km. We
call this the synoptic scale
Pressure excursions around ± 30 mb –
much smaller than the total pressure of
~1000 mb.
Isobars give an indication of the wind
speed by the geostrophic relation: wind
tends to flow along isobars and its
strength is proportional to pressure
gradient
http://www.ncas.ac.uk
Time scale
00 h
3/1/07
Weather system takes ~ 1 day to
pass over the UK – so synoptic
timescale is around a day (105 s)
00 h
4/1/07
http://www.ncas.ac.uk
Fronts
AVHRR IR
image 2317
2/1/07
http://www.sat.dundee.ac.uk
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Cold and warm fronts
Warm air
Cold Air
Warm
air
Cold Air
Motion of front
Cold front: narrow (~100 km), steep, can
get line convection particularly on leading
edge
www.rossway.net,
Warm front: broad (~300 km), layer
cloud due to gentle upglide.
Convection unusual.
http://www.ncas.ac.uk
Occluded front
Warm air
Cold, unstable
air
Cold, stable air
Warm-type occlusions are much more common than cold type. This is determined by the
static stability in the warm and cold frontal zones, not by the temperature difference between
the two cold air masses
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Momentum equation
The basic equation of dynamics is F=ma, Newton’s law. In the case of
the atmosphere this equation becomes (a=F/m):
dU
1
 - p - f k U
dt

On the left hand side is the acceleration of an air parcel
The p term is the pressure gradient acceleration
The fkxU term is the Coriolis acceleration; f=2Ωsin(λ) where Ω is
the Earth’s rotation rate and λ the latitude
Geostrophy is defined by balance of the pressure gradient and Coriolis
acceleration; the Geostrophic wind is then
1
Ug  k  p
f
Geostrophic wind is proportional to pressure gradient and directed
along isobars
http://www.ncas.ac.uk
Pressure coordinates
Over the synoptic scale the atmosphere is very close to
hydrostatic balance:
p
  g
z
We can use this fact to eliminate density from the momentum
equation:
This gives us a momentum equation which doesn’t include
density:
U is the horizontal wind
dU
velocity
 - gp z - f k U
k is a unit vertical vector
dt
z is the height of a pressure surface.
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Pressure surfaces: representing the flow above the surface
700 mb,
300 mb,
~ 3 km
~ 9 km
Smoother patterns than at the surface; fronts not marked on these charts
700 and 300 mb charts show a similar pattern – synoptic scale features are generally coherent
throughout the troposphere. That is, vertical scale of synoptic-scale features ~ 10 km
Winds closer to geostrophic – no surface friction
Very strong winds at 300 mb denote the jet stream. Jet stream is related to fronts, either at the
surface or in the upper troposphere.
Westerly winds increase with height: thermal wind equation
vertical wind shear  horizontal T gradient
http://www.ncas.ac.uk
Fronts and jet streams in the general circulation
Subtropical jet stream (actually the stronger of the two) is at the poleward edge of the
Hadley circulation and is associated with an upper tropospheric front (no weather!)
Polar jet stream is associated with the polar front. Note that the front must tilt with height
otherwise a pressure discontinuity forms above the surface (∂p/∂z  1/T)
Source: wikipedia
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Formation of weather systems
The commonest depiction of the formation of a
weather system is the so-called Norwegian Model
(e.g. Bjerknes and Solberg 1922)
i.e. a small cyclonic perturbation grows on the polar front, pushing warm air poleward and
cold air equatorward
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Norwegian model of mature cyclone
This was the first depiction in the
literature of the schematic structure
of a cyclone. All cyclones are different
and most don’t look quite like this.
But there are some salient features
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Shapiro-Keyser model
Frontal fracture
Warm seclusion
Isotherms
A front is a region of strong temperature gradient. In the Norwegian model the cold
front is the dominant feature; in the S-K model the warm front dominates
From Schultz et al 1998
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Why do cyclones form?
Pressure is the weight of the air above you. So, if the
pressure falls there must be less air above you – there must
be divergence of air from the column above you
u v
divergence 

x y
We can formally express the wind as the sum of two
components:
U = Ug + Ua
Ug is the geostrophic wind and Ua the ageostrophic wind.
Now the divergence of Ug is zero.
u g
vg
  g z    g z 
 
  
  0


x
y
x  f 0 y  y  f 0 x 
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Ageostrophic wind
Divergence is a property of the ageostrophic wind. We can write this as
follows:
dU
 - gp z - f k (Ug  Ua )
dt
 - f k Ua
1 dU
 Ua  k
f
dt
i.e. the ageostrophic wind is proportional to acceleration, and is
directed to the left (in the NH) when the flow accelerates
Ua, and hence divergence, is greatest at jet stream level. Indeed the
pattern of the jet stream can initiate cyclone development
http://www.ncas.ac.uk
Convergence and divergence around a maximum in the jet stream
Ua
n
A
dU
dt > 0
dU < 0
dt
acceleration
Jet
B
Isotachs
Diagrams show a section of a 300
mb chart with a jet streak – a wind
maximum.
This induces C and D patterns in the
air either side:
Convergence
Divergence
Jet
Divergence
Convergence
C gives descent (p increase at
surface)
D gives ascent (p decrease at
surface)
“Vacuum cleaner effect”
http://www.ncas.ac.uk
Convergence and divergence forced by meanders in the jet stream
Divergence
U
Trough
Ridge
Ridge
Convergence
Air has to slow down to go round a trough, because the pressure gradient force must
now provide a centripetal acceleration as well as balancing the Coriolis – therefore
Coriolis force must weaken. The opposite is true in a ridge.
Trough-ridge patterns (short-wavelength Rossby waves) set up the conditions where lowlevel cyclones develop. But these patterns are themselves generated by the weather
systems! So it’s chicken and egg…..
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Growth of weather systems
Jet stream
Surface cyclone advects cold air south
behind it and warm air north ahead of it.
This changes the average temperature of
the troposphere in those regions,
intensifying the upper-air pattern
Growth of cyclone
-> distortion of jet stream
-> more ageostrophic motion
-> continued divergence
-> growth of cyclone
This process is called baroclinic
instability. It requires conditions in the
upper and lower troposphere to match
up
http://www.ncas.ac.uk
Warm conveyor belt
Green: low altitude
Yellow: high altitude
Low-level airstream flowing along and ahead of the
cold front, and up and over the warm front.
The most prominent airflow in a cyclone
Very important for transporting pollutants out of the
boundary layer
This picture shows a kata-cold front, where the main ascent is over the warm front (anawarm front). It is possible for most of the WCB flow to be up the cold frontal surface –
this would be an ana-cold front.
http://www.ncas.ac.uk
Conveyor belt patterns: airflow w.r.t depression centre
Occluding cyclone. As the surface
low intensifies, first the CCB then
the WCB start to turn cyclonically.
Mature cyclone, on the point
of occluding
Bader et al 1995
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Thermal wind equation
Geostrophic relation in p coordinates takes the
form:
g
Ug  k p z
f
By differentiating this wrt pressure, we can
derive an expression for wind shear, vertical
gradient of horizontal wind:
 Ug
 1
g
g
r
 z 
 k p    k p    - k p T 
p
f
f
f
 p 
 g 
using ρ=p/rT from the ideal gas law
So, vertical wind shear  horizontal T gradient:
Jet streams and fronts are intimately linked
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