Umweltphysik für Alle
6) Regional and Global Circulation (Dec. 13, 2005)
• Global Circulation in the Atmosphere
• Hadley circulation
• Causes of the circulation
• Forces in the fluid systems on earth
• The Coriolis Force
• The Ekman spiral, High’s and Low’s
Buncefield
- Depot
Global Radiative
Energy Balance
Global Convection on a non-rotating Planet
Average global
circulation,
proposed by the
British scientist
George Hadley
(1685-1768) in 1735
Reality:
Earth is rotating
!Coriolis Force
Reality: Coriolis Force
N
1) Moving laterally outward
(south): circumferential
velocity increases
! object too slow
! deflected to the right
2) Moving laterally inward
(north): circumferential
velocity decreases
! object too fast
! deflected to the right
S
Vector notation :
!
! !
F = 2m ⋅ v × ω
2π
ω=
T
F = 2mv ω
3) Moving tangentially
(east): circumferential velocity
increases
! additional centrifugal force
! deflected to the right
4) Moving tangentially
(west): circumferential velocity
decreases
! less centrifugal force
! deflected to the right
The Coriolis Force
Gaspard Gustave de Coriolis,
(1792-1843, Paris)
Vector notation :
!
! !
F = 2m ⋅ v × ω
2π
Ω = Angular velocity of the earth’s
ω=
T
rotation = 2π/24h ≈ 7.3⋅10-5s-1
F = 2mv ω
Global Atmospheric Circulation Patterns - 1
Global Atmospheric
Circulation Patterns - 2
Coriolsi - force would
accelerate airmasses
transported from the
equator to the pole up to
the circumferential
velocity vC of Earth at
the equator
vC =
40000 km
≈ 1667 km / h
24h
! Circulation breaks in
several (i. e. 3) cells:
• Hardley-cell
• Ferrel-cell
• Hardley-cell (polar)
The Inter-Tropical Convergence Zone (ITCZ)
Near the equator (typically a few degrees north of the equator)
air from both hemispheres rises.
ITCZ from
Space
ITCZ
Sea-Level Pressure and Surface Winds
(January mean 1959-1997)
Mean January prevailing surface winds and centers of atmospheric pressure, 1959-1997.
Red line: InterTropical Convergence Zone (ITCZ).
(Source of Original Modified Image: Climate Lab Section of the Environmental Change Research
Group, Department of Geography, University of Oregon - Global Climate Animations).
Sea-Level Pressure and Surface Winds
(July mean 1959-1997)
Long-Range Transport Pathways
WCB
Asia
North
America
WCB
low level advection
Europe
Schultz,
Martin
MPI-Met, Hamburg
Isabelle Bey, EPFL, Lausanne
free trop. advection
Transatlantic transport and the
North Atlantic Oscillation (NAO) Index
NAO Index
NAO Index
North American ozone pollution enhancement
at Mace Head, Ireland (GEOS-CHEM model)
North American O3 (ppb)
r = 0.57
Li et al., 2002
NAO index = normalized surface pressure anomaly between
Iceland and the Azores
Atmospheric Mixing
(based on Potential Temperature)
Three Regimes of the Atmosphere
(based on Potential Temperature)
Potential temperature surfaces = surfaces of rapid adiabatic motion of air
Overworld
Middleworld
Underworld
Four-Box Model of Atmospheric Exchange
Southern Hemisphere
Stratosphere
τ ≈ 1-2 a
Southern Hemisphere
Troposphere
τ ≈ 3.5 a
Northern Hemisphere
Stratosphere
τ ≈ 1-2 a
τ ≈ 1.1 a
Northern Hemisphere
Troposphere
Forces in the Atmosphere
1) The Inertial Force
F(x)
F(x+∆x)
2) The Pressure Gradient force
A
∆x
3) The Gravitational force
4) The Coriolis force
A
5) The Friction force
FR
dz
v
The Pressure Gradient Force - Example
Pressure increases
F = p⋅A = −
F(x)
F(x+∆x)
⇒
A
dp
⋅∆
x⋅A
"
dx
V
F
dp
=−
V
dx
∆x
Net force
Example:
Horizontal pressure gradient:
!
N
dp 5 mBar 5 ⋅10 2 Pa
−3 Pa
− ∇p = −
≈
=
=
5
⋅
10
oder
dx 100 Km
m
10 5 m
m3
Acceleration at an air density of ρ ≈ 1.29 Kg/m3:
This corresponds to an acceleration of
≈14m/s per hour
! typical wind velocities in the atmosphere are
reached within hours.
dp
dx
1 dp
1
≈−
⋅ 5 ⋅10−3
a=−
ρ dx
1.29
m
≈ 4 ⋅10−3 2
s
ρa = F = −
Weather Map
1000 Km
http://www.ecmwf.int/servlets/chart
A
!
FP
The Force Triangle
!
FC
B
!
FR
!
v
!
FR
C
!
FC
!
FP
!
v
!
FR
!
FR
!
FC
!
FP
!
FC
!
FR
!
v
!
FC
Force triangle consisting of the pressure gradient force FP (blue), Coriolis-force FC (black) and friction force FR
(green). The direction of FR is always opposite to the direction of air flow, The direction of FC is perpendicular to
the direction of air flow v (red) i.e. the movement of an air-parcel.
There are three cases shown:
A)Close to the ground the friction force is relatively large, v points approximately in the direction of pressure
gradient force.
B) In intermediate altitudes there is already a considerable angle between FP and v.
C) In the geostrophic case (at several 100 m altitude) the friction force can be neglected and FC is anti parallel
to FP. The air parcel moves at right angle to the pressure gradient force.
The Ekman Spiral
Vagn Walfried Ekman (1874- 1954),
At the end of the 19th century, Fridtjof
Nansen made the observation that ice
bergs in the ocean tend to drift to the
right of prevailing winds. This lead
one of his students, Vagn Ekman, to
develop a theory explaining the role
of the earth's rotation on surface
currents. Over the course of his life,
Ekman made a number of important
con-tributions to the area of Geophysical Fluid Dynamics, and the
process of 'Ekman Pumping' bears
his name.
The Ekman Transport in the Ocean
When driven by wind, the
topmost layer of the ocean in the
Northern Hemisphere will move
to the right of the wind direction
(by about 45o) due to the Coriolis
force. The next "layer" down will
not feel the wind, but will feel the
friction caused by shear with the
topmost layer, which is directed
at about 45o to the right of the
wind direction. Due to the
Coriolis force, this lower layer will
flow to the right of the topmost
layer. Successive layers will flow
at more extreme angles to the
right of the wind direction and will
also flow more slowly than the
overlying layers. At some depth,
the flow will actually be in the
opposite direction of the wind
direction!
However, the average flow of the
column will be at a right angle
(90o) to the wind direction. This
net flow is known as Ekman
transport.
Air Flow in a High Pressure System - 1
1) Geostrophic flow above the
Ekman layer:
Pressure gradient force balances
Coriolis force
2) Flow in the Ekman layer:
Pressure gradient force plus
friction force balance Coriolis force
H
H
R
R
1020 hPa
1020 hPa
1010 hPa
1010 hPa
High Pressure System - 2
H
R
1020
hPa
1010 hPa
Descending air
"Leakage" only
close to the
ground
because of the
Ekman - Spiral
High Pressure System - Low Pressure System
H
L
Air in the high pressure
system rotates around
centre, air can only leak out
near the ground (friction!)
Air in the low pressure system
rotates around centre, air to fill
it up can only enter near the
ground (friction!)
! empties slowly
! fills slowly
! descending air heats up
! ascending air cools
! clouds dissolve
! clouds form
! "good weather"
! "bad weather"
Gyres in the Ocean
Summary