Download The unpredictable nature of the atmospheric jet stream

The unpredictable nature
of the atmospheric jet
stream
Frank Selten, KNMI
Satellite view of the general circulation
water vapour channel
•
what sets the atmosphere into motion?
•
what causes the strong westerly jets?
Differential heating
Net cooling in high latitudes
Net warming in tropics
Poleward heat transports
5 PW = 300 x world energy consumption
Available potential energy due to differential
heating sets the atmosphere in motion
unstable
L
Cold air
H
Warm air
pressure higher
in warm air region: air
starts flowing towards
lower pressure
gravity force
height
stable
pressure
H
L
extra-tropics
tropics
no pressure gradient
Hydrostatic balance: the pressure is approximately equal to the weight
of the air column above: warm air is lighter, pressure drops less quickly with height
Hadley cells
Hadley Cells
Ferrel Cell
Ferrel Cell
Between equator and 30 degrees: direct mean poleward transport
by the thermally driven Hadley circulation
In the poleward moving air, westerlies develop:
conservation of angular momentum,
an apparent force in the rotating earth frame deflects particles to the right
13
Geostrophic balance
• In the extra-tropics on synoptic spatial and temporal
scales the flow is approximately in a geostrophic balance
(Law of Buys Ballot):
the coriolis force balances the pressure gradient force.
Low
Fp = -dP/dy
U
f = 2Ωsinφ is coriolis parameter
Ω= angular velocity of the earth
High
Fcor = -f U
Valid for small Rossby number:
Klimaatcursus
Velocity U and spatial scale L of
synoptic motions set a time scale on
the order of days, long enough to feel
the rotation of the earth
In the upper branch of the Hadley
circulations strong westerlies develop
zonal mean zonal circulation
General circulation observed
zonal mean meridional circulation
Thermal wind balance
Combines the hydrostatic balance with the geostrophic balance:
A horizontal temperature gradient leads to an increase of the geostrophic
wind with height that is a vertical wind shear.
Cold air
Warm air
L
H
pressure becomes higher
in warm air region:
a geostrophic flow develops
proportional to the pressure
gradient
dp/dy = f U
dp/dy increases with height
so does zonal wind U
no pressure gradient
y
Klimaatcursus
Strong horizontal temperature gradients
•
what drives the jetstream: radiation imbalance at
the top of the atmosphere: net heating of tropics,
net cooling of poles: creates temperature gradient,
pressure gradient, flow: westerlies due to rotation of
the earth: == subtropical jet: two approximate
balances: geostrophic and hydrostatic balance
•
jetstream unstable: baroclinic instability: available
potential energy is converted into kinetic energy of
storms by lowering the center of mass of the
atmosphere: warm air rises, cold air sinks in extratropical storms: storms reduce the temperature
gradient which gets restored by the radiation
imbalance
Baroclinic instability
Instabilities develop if horizontal temperature gradients/
vertical wind shears become too large
Baroclinic instability
• Small disturbances grow through conversion
of available potential energy of the
background flow into kinetic energy
• Hydrostatic en geostrophic balance lead to a
typical spatial scale of disturbances that
become unstable first as temperature
gradients cross a critical value
A baroclinically growing wave
warm air is advected underneath the upper air ridge: growth !
warm air rises
Westward tilt with height
cold
cold air sinks
L
warm
cold air is advected underneath the upper air trough: growth !
Baroclinic wave observed
At 500 hPa
At surface
Role of the ‘eddies’ in climate
• Transport heat poleward
• Transport water vapor
• Transport westward momentum into the jet region: vortex
stripping through wave breaking: eddy driven jet
• Mix air masses
•
strong scale interactions: jet steers the storms,
storms feedback on the jet: zonal - blocked flow
transitions: implications for local weather: stripping
effect of breaking waves; mixing of momentum to
the surface: waves can form jets: eddy-driven jets
Position of subtropical and eddydriven jets
•
strong subtropical jet - weaker southward displaced
eddy-driven jet
•
North Atlantic Oscillation (NAO): multi-scale
interactions, split-single jet transitions, large impact
on European climate
Rotation of the earth: Rossby wave motions
Rossby waves: conservation of absolute vorticity
d ⎛⎜ζ + f ⎞⎟ = 0
⎟
dt ⎜⎝
⎠
ζ : relative vorticity
f = 2Ωsinφ : planetary vorticity
Rossby waves move westward in the planetary vorticity field with respect to the flow
The phase speed depends on the wavelength: long waves move faster
Dispersive character:
c=U − β2
k
β =δ f
δy
for a wave of the form:
ζ = Acos(k(x−ct))
L = > 30 days
Standing waves
M= <30 days
> 6 days
Retrogressing
waves
H= < 6 days
Baroclinic waves
Rennert and Wallace, 2009
A toy model of the extra-tropical atmosphere
E.N. Lorenz, 1984: “Irregularity, a fundamental property of the atmosphere”,Tellus, 36A, 98-110
X
The Lorenz 84 system
dX = −Y 2 − Z 2 −aX +aF
dt
dY = XY −bXZ −Y +G
dt
Y
•
•
•
•
•
Z
dZ =bXY + XZ − Z
dt
Interaction of a wave (Y,Z) with a zonal flow (X)
Solutions depend on parameters F, G, a and b
Solutions are found by numerical integrations
Solutions in the 3D phase space: trajectories
Solutions in real space: traveling wave on a zonal flow
ζ (x,t)= X(t)×ζ zonal (x)+Y (t)×sin(kx)+ Z(t)×cos(kx)
Strange attractor
X
Z
Y
• Sensitive dependence on initial conditions
• Evolution never exactly repeated
Solutions in phase space
X
y
z
•
unstable periodic orbits: quasi-periodic behaviour
of waves in the jetstream
•
origin of Rossby wave energy: tropical convection
with upper level divergence, mountain ranges,
baroclinic instability, barotropic instability
•
traveling and standing waves lead to
teleconnections: correlations between wind/
pressure fluctuations over large distances: example
tropical forcing experiment
•
weather regimes: multiple equilibria, interaction
with mountain ranges, stationary waves, resonant
interaction: in low-order models: chaotic transitions
between zonal and block flows along preferred
paths, continuous temporal spectrum, limited
predictability due to sensitive dependence on initial
conditions
Crommelin, 2003
“zonal”
stable
Zon
al
flo
w
unstable
= forcing
“blocked”
stable
Dynamisch seminarium
Homoclinic and heteroclinic orbits
PDF in chaotic regime
Conclusion: UPO’s as remnants of heteroclinic
connections guide transitions between
regimes on the chaotic attractor
Ingredients: orographic and barotropic
instability
•
jet stream influenced by: a interaction with diabatic
heating processes (condensation, radiation), b
interaction with earth surface (land/ocean/sea-ice), c
turbulent heat and momentum transports
•
predictability from lower boundary (soil moisture, sea
surface temperatures, sea-ice cover) on the seasonal
time-scales
•
climate change due to CO2 increase: jets will respond to
change in radiative forcing: need to compute feedbacks
from a-b-c: high-resolution coupled atmosphere-oceanland sea-ice models with radiative transfer, moisture and
clouds, aerosols
•
examples: pole ward shift due to shift in baroclinic
zones, high pressure over British Isles due to
cooling sub polar surface waters in summer, shift in
stationary waves due to change in tropical
convection, hints of change in regime frequencies
•
detection of change difficult due to existence of
large internal fluctuations
“Warming Hole”
MSLP
SAT
Reduced upward heat
flux
Z500
Sens. + latent
heat flux