Classical Hadley circulation theories
and their shortcomings
Tapio Schneider
(Source: CLAUS, http://badc.nerc.ac.uk/data/claus/)
Classical Hadley circulation theories
and their shortcomings
Tapio Schneider
(Source: CLAUS, http://badc.nerc.ac.uk/data/claus/)
Classical Hadley circulation theories
and their shortcomings
Tapio Schneider
Easterlies
(Source: CLAUS, http://badc.nerc.ac.uk/data/claus/)
Classical Hadley circulation theories
and their shortcomings
Tapio Schneider
Westerlies
Easterlies
Westerlies
(Source: CLAUS, http://badc.nerc.ac.uk/data/claus/)
Earth’s surface winds
30°N
30°S
Speed:
m/s
(Source: NCEP/NCAR reanalysis)
Earth’s surface winds
30°N
NE Trades
30°S
Speed:
m/s
(Source: NCEP/NCAR reanalysis)
Earth’s surface winds
30°N
NE Trades
SE Trades
30°S
Speed:
m/s
(Source: NCEP/NCAR reanalysis)
Earth’s surface winds
Westerlies
30°N
NE Trades
SE Trades
30°S
Westerlies
Speed:
m/s
(Source: NCEP/NCAR reanalysis)
Earth’s rotation matters
“The causes of the General Winds have not been
fully explained by any of those who have written on
that Subject, for want of more particularly and
distinctly considering the Share the diurnal Motion of
Earth has in the Production of them.”
George Hadley, Phil. Trans., 39 (1735)
Hadley’s view of winds and the general circulation
30°N
Equator
30°S
Hadley’s view of winds and the general circulation
30°N
Equator
30°S
Hadley’s view of winds and the general circulation
30°N
Equator
30°S
Hadley’s view of winds and the general circulation
30°N
Equator
30°S
Hadley’s view of winds and the general circulation
“The NE and SE Winds within the
Tropics must be compensated by
as much NW and SW [Winds] in
other Parts; otherwise some
Change must be produced in the
Motion of the Earth round its
Axis.”
30°N
Equator
30°S
Eastward wind (January)
Pressure (mbar)
a
200
44
32
800
8
Easterlies
0
Westerlies
Westerlies
0˚
Latitude
50˚
(Schneider, Ann. Rev. Earth Planet. Sci., 2006)
Eastward wind (January)
Pressure (mbar)
a
200
44
32
800
8
Easterlies
0
Westerlies
Westerlies
0˚
Latitude
50˚
(Schneider, Ann. Rev. Earth Planet. Sci., 2006)
Eastward wind (January)
Pressure (mbar)
a
200
44 m/s
44
32
800
8
Easterlies
0
Westerlies
Westerlies
0˚
Latitude
50˚
(Schneider, Ann. Rev. Earth Planet. Sci., 2006)
Eastward wind (January)
Hadley cells
200
40
Pressure (mbar)
Ferrel
cells
800
8
Easterlies
0
Westerlies
Westerlies
0˚
Latitude
50˚
(Schneider, Ann. Rev. Earth Planet. Sci., 2006)
Hadley circulation confined to tropics
30°N
Equator
30°S
Hadley circulation confined to tropics
30°N
Equator
30°S
Extratropical macroturbulence transports angular
momentum into regions of wave generation
Macroturbulence in control
Any theory of atmospheric circulations and of climate must
be based on a theory of atmospheric macroturbulence.
Because we have no complete theory of macroturbulence,
“the causes of the General Winds still have not been fully
explained by any of those who have written on that
Subject” (Hadley).
But the Hadley circulation was generally thought not to
depend strongly on atmospheric macroturbulence. Let’s
examine whether that is the case.
The ideal Hadley circulation...
•
Conserves angular momentum m in upper branch
v̄∂ym̄ ⇡ 0
Since ∂ym̄ µ f + z̄ , this implies
with local Rossby number
•
Is energetically closed (no heat export)
•
Responds directly to variations in thermal driving
•
Result: fh ⇠
0 0 1/2
(Ht Dh) ,
Ymax ⇠
0 0 5/2
(Ht Dh)
(Schneider 1977; Schneider & Lindzen 1976, 1977; Held & Hou 1980)
Nearly inviscid axisymmetric theories
µ f4
( f + z)v = f (1
Ro =
Ro)v ⇡ S ⇡ 0
z/ f ⇡ 1
(Schneider 1977; Schneider & Lindzen 1976, 1977; Held & Hou 1980)
Nearly inviscid axisymmetric theories
µ f2
µ f4
Heating by Newtonian relaxation toward background state
(Schneider 1977; Schneider & Lindzen 1976, 1977; Held & Hou 1980)
Nearly inviscid axisymmetric theories
µ f2
µ f4
Result:
fh⇠ (Ht0D0h)1/2
Ymax⇠ (Ht0D0h)5/2
(Schneider 1977; Schneider & Lindzen 1976, 1977; Held & Hou 1980)
Off-equatorial heating
Slight displacement of heating off equator strongly amplifies
circulation (nonlinearity of AMC constraint)
Annual average circulation nonlinearly amplified
(Lindzen & Hou 1988)
‘Seasonal’ variations in nearly inviscid theory
Mass flux (10 9 kg s−1)
0
a
−50
f0 = 0, 2 , 4 , 6
−100
50
b
0
1
[Y(f0) + Y( f0)]
2
−50
−30 ̊
0̊
Latitude
30 ̊
(after Lindzen & Hou 1988; Walker & Schneider 2005)
Ideal Hadley circulation theory...
•
Is intuitively appealing (direct reponse to thermal
driving)
•
Appears to account for extent of circulation in
Earth’s atmosphere
But does it account for variations in Hadley circulation as
climate varies?
January streamfunction and angular momentum
Ro . 0.2
Ro . 0.5
(Schneider 2006)
Hadley cells and eddy momentum flux divergence
EMFD S
Angular (or zonal) momentum balance:
Eddy driven if Ro<<1
(Schneider 2006; Schneider et al. 2010; data source: ERA-40)
Eddy momentum flux phase speed spectrum
(Randel and Held 1991)
Earth-like Hadley circulations...
•
In the annual mean or during equinox are close to
limit Ro ! 0
•
Do not respond directly to variations in thermal
driving but respond via changes in eddy fluxes
We need to rethink Hadley circulation response, for
example, to ENSO and global warming