Extratropical Cyclones
– Genesis, Development, and Decay
Xiangdong Zhang
International Arctic Research Center
Basic Facts
Extratropical cyclones is a major weather maker for mid
and high latitudes.
 Size: roughly 1000-2500 km in diameter;
 Intense: central pressure ranging from 970-1000 hPa;
 Lifetime: 3-6 days to develop, and 3-6 to dissipate;
 Movement: generally eastward at about 50 km/hr;
 Peak season: winter;
 Formation: along baroclinic zone or from transition of
tropical cyclones.
Outline
Goal: Understand cyclone from simple model to complex
dynamics
• Classic surface-based polar-front model – Bergen Model
• Surface – upper troposphere coupling – understanding from
kinematics
• Interactions between dynamics and thermodynamics – a more
complex vorticity dynamics
Bergen Cyclone Model (BCM)
Mechanism of cyclone development: Baroclinic instability
Z
Warm
cold
Unstable
Stable
Baroclinic Instability: Available potential energy (APE)  kinetic energy
(air movement -> wind)
Center of
Gravity
h
h≈0
Unstable
Stable
Are we satisfied with BCM so far?
Questions we could not answer:
• How do upper level waves disturb the surface
cyclone formation?
• How can surface cyclone be maintained when air
mass fills in?
How does ageostrophic wind redistribute air mass
and links upper level waves to surface cyclone
development?
planetary waves at 500 hpa
a weather chart at 500 hpa
Surface – upper troposphere coupling
• Geostrophic wind: the wind when it is in perfect
geostrophic balance:
1
f k ´ vg = - Ñp
r
• Ageostrophic wind: difference between the actual
wind and the wind when it is in perfect geostrophic
balance:
va = v - v g
ds
dV
1 dp
1 dp
=s + (- fV )n Force Balance
Free Atmosphere
dt
r ds
r dn
s
dV d (V s) dV
ds
=
=
s +V
dt
dt
dt
dt
dV
1 dp
s=s
dt
r ds
d s = s dq
t+1
t
s
dS
s component
t
dq
ds
ds
= dq
ds
ds
dS
dq
s
dS
R
n
d s dq d s
ds
ds
ds V
=
= R
= dt
= n
(dt ® 0)
dt dt d s
dt d s
R ds
dt R
1 dp V2
1 dp V2
ds
V
1 dp
- fV = - fVg - fVa =0
V = V n = (- fV )n
r dn R
r dn R
dt
R
r dn
n
component
V 2 <0: cyclonic curving
Ageostrophic wind: Va = fR >0: anticyclonic curving
Ageostrophic wind when the air curves cyclonically:
• The centripetal
acceleration breaks the
geostrophic balance;
• The ageostrophic wind
points the opposite
direction of the
geostrophic wind.
V2
Va = - < 0
fR
vt-1
va
Low Pressure
Pressure Gradient Force
Centripetal
Acceleration
vt
vt+1
Coriolis Force
High Pressure
Sub-geostrophic wind: slower than the geostrophic wind.
Ageostrophic wind when the air curves anticyclonically:
• The centripetal
acceleration breaks the
geostrophic balance;
• The ageostrophic wind
points the same direction
of the geostrophic wind.
Va = -
V
>0
fR
2
vt+1
High Pressure
Coriolis Force
Centripetal
Acceleration
vt
va
vt-1
Pressure Gradient Force
Low Pressure
Super-geostrophic wind: faster than the geostrophic wind.
Ageostrophic wind when the air speeds up:
• The pressure gradient
increases and air blows
toward lower pressure
side;
• The ageostrophic wind
points the left of the
geostrophic wind.
Low Pressure
Pressure Gradient Force
vt-1
va
vt
Coriolis Force
High Pressure
Ageostrophic wind when the air slows down:
• Opposite.
Summary I: Curvature effects (uniform pressure gradients
along the flow)
Summary II: Effects from varying pressure gradients along
the flow
Low Pressure
Divergence
Convergence
Pressure Gradient Force
CF > PGF
(PGF decrease)
PGF > CFP
(PGF increases)
Coriolis Force
Convergence
Divergence
High Pressure
old
new
Upper level driver
From 2007 Thomson Higher Education
Are we satisfied with kinematics so far?
Questions we could not answer:
• How does temperature impact cyclone
development?
• How does external and internal heating and
impact cyclone development?
Vorticity dynamics
Thermal wind Balance: VT = Vg2－Vg1 =
Vorticity:
z g1 = z g2 - z T
500 hPa
level 2
¶z1 ¶z2 ¶zT
=
¶t
¶t ¶t
With certain approximations, we have:
Surface
level 1
Petterssen’s Development Equation
(Carlson (1998))
Cyclone Development Equation
Az 2 vorticity advection at 500 hPa
AT surface-500 hPa layer-averaged temperature advection
S
H
surface-500 hPa layer-averaged adiabatic heating/cooling
surface-500 hPa layer-averaged diabatic heating/cooling
Positive Vorticity Advection (PVA)
N
Negative Vorticity
5x10-5 s-1
10x10-5 s-1
15x10-5 s-1
20x10-5 s-1
Positive Vorticity
E
Negative Vorticity Advection (NVA)
N
Negative vorticity
4x10-5 s-1
8x10-5 s-1
12x10-5 s-1
16x10-5 s-1
Positive vorticity
E
Effects of Vorticity Advection Az 2
Ridge
For a Typical Synoptic Wave:
500 mb
Trough
• Areas of positive Az 2 (PVA)
are often located east of a
trough axis
• PVA increases the surface
vorticity ζ1 and leads to the
formation of a surface low or
cyclone
PVA
NVA
Effects of Temperature Advection AT
• Areas with maximum warm AT (WAA),
one has
, which leads to
an increase in surface vorticity ζ1
and the formation of a surface low
or cyclone
WAA
Effects of Diabatic Heating H
• Strong diabatic heating (H >0) always helps to increase surface vorticity ζ1
• Diabatic heating includes radiation, latent heat release from cloud and
precipitation, and sensible heat exchange
Effects of Adiabatic Heating S
• When S < 0, there is whole layer (surface-500 hPa) convergence, which leads to
a decrease in surface vorticity and unfavors the development of surface low
• Upper level (above 500 hPa) divergence is needed for cyclone development!
Note:
We can have:
¶w
¶u ¶v
= -( + ) = -D
¶p
¶x ¶y
w = w ps - D*(p - ps )
Therefore:
S = w ps (g d - g ) - D(p - ps )(g d - g )
From continuation equation:
If there is no surface forced vertical velocity ( w p = 0 ) and the surface-500 pha layer-averaged
convergence (D < 0) leads to S < 0 , unfavorable to cyclone development.
s
Surface Cyclone Development
 The surface cyclones intensify due to
WAA and an increase in PVA with height
→ rising motion
→ surface pressure decreases
 With warm air rising to the east of the
cyclone, and cold air sinking to the west,
potential energy is converted to kinetic
energy (baroclinic instability) and the
cyclone’s winds become stronger
Rising
500mb
PVA
WAA
SFC
Pressure
Decrease
System
Intensifies
Surface Cyclone Development
Weather of Extratropic Cyclone
Occluded Front:
Cold with strong winds
Precipitation light to moderate
Significant snow when cold enough
Warm Front:
Cloudy and cold.
Heavy precipitation
Potential sleet and freezing rain
From gsfc.nasa
Cold Front:
Narrow Band of showers and
thunderstorms
Rapid change in wind direction
Rapid temperature decrease.
Warm Sector:
Warm
Potential showers and thunderstorms
Surface weather chart
12Z, Wed, Nov 9, 2011
surface cyclone
500 hPa weather chart
12Z, Wed, Nov 9, 2011
How did upper level waves
support the developing
surface cyclone
• Occurred before a trough
and after a ridge
advection of + vorticity
advection of warm air
divergence due to curvature
divergence due to deceleration
500 hPa trough
surface cyclone
Single synoptic scale cyclone process can cause highly
variable surface wind field and impact sea ice
Xiangdong Zhang, IARC
Climatological characteristics of northern hemispheric
cyclone activity
Winter
Summer
cyclone count/frequency
Climatological characteristics of northern hemispheric
cyclone activity
Winter
Summer
cyclone central SLP
Summary
• Cyclone is a prominent element of weather system, impacting
our daily life.
• Genesis, development, and decay of cyclones result from 3dimensional, interactive processes between dynamics and
thermodynamics.
• Better understanding of cyclones has important implications
for improving weather forecast and climate change
assessment.