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The Atmosphere: Part 6: The Hadley Circulation. Composition / Structure Radiative transfer Vertical and latitudinal heat transport Atmospheric circulation Climate modeling. Suggested further reading: James, Introduction to Circulating Atmospheres (Cambridge, 1994) - PowerPoint PPT Presentation
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The Atmosphere:Part 6: The Hadley Circulation
• Composition / Structure
• Radiative transfer
• Vertical and latitudinal heat transport• Atmospheric circulation• Climate modeling
Suggested further reading:
James, Introduction to Circulating Atmospheres (Cambridge, 1994)
Lindzen, Dynamics in Atmospheric Physics (Cambridge, 1990)
Calculated rad-con equilibrium T vs. observed T
pole-to-equator temperature contrast too big in equilibrium state (especially in winter)
Zonally averaged net radiation
Diurnally-averaged radiation
Implied energy transport: requires fluid motions to effect the implied heat transport
Observed radiative budget
Roles of atmosphere and ocean
Trenberth & Caron (2001)
net
ocean
atmosphere
Rotating vs. nonrotating fluids
Ω
φ
u
ΩΩsinφ
f = 0
f > 0
f < 0
Hypothetical 2D atmosphere relaxed toward RCE
φ
x
0
2D: no zonal variations
Annual mean forcing — symmetric about equator
A 2D atmosphere forced toward radiative-convective equilibrium
Te(φ,p) dQ
dt cp
dTdt
g dzdt
J
(J = diabatic heating rate per unit volume)
dTdt
w J cp
1 T Te , z
Hypothetical 2D atmosphere relaxed toward RCE
dTdt
w 1 T Te , z
φ
dudt
fv g zx
0
u t
v uy
w u z
fv 0
m ur r2
uacos a2 cos2
a
r
φ
Ω
dmdt
m t
u m 0
Above the frictional boundary layer,x
0
Absolute angular momentum per unit mass
Angular momentum constraint
dmdt
m t
u m 0
φ
Above the frictional boundary layer,
In steady state,
u m 0
m uacos a2 cos2
Angular momentum constraint
dmdt
m t
u m 0
φ
Above the frictional boundary layer,
In steady state,
u m 0
Either 1) v=w=0 Or 2) but m constant along streamlines
dTdt
w 1 T Te , z
T = Te(φ,z)
m uacos a2 cos2
φ 0 15 30 45 60U(ms-1) 0 32 134 327 695
v Ty
w Tz
1 T Te , z
v, w 0
u a sin 2cos
(if u=0 at equator)
Angular momentum constraint
dmdt
m t
u m 0
φ
Above the frictional boundary layer,
In steady state,
u m 0
Either 1) v=w=0 Or 2) but m constant along streamlines
dTdt
w 1 T Te , z
T = Te(φ,z)
m uacos a2 cos2
φ 0 15 30 45 60U(ms-1) 0 32 134 327 695
u a sin 2cos
v Ty
w Tz
1 T Te , z
v, w 0
(if u=0 at equator)
u m 0
2) v 0
solution (2) no good at high latitudes
1) v 0 ; T Te , zNear equator, Te A B 2
up
Rfp
Ty
Rap
12 sin
T RB
ap
u finite (and positive) in upper levels at equator; angular momentum maximum there; not allowed
solution (1) no good at equator
Hadley Cell
T = Te
u m 0
2) v 0
solution (2) no good at high latitudes
1) v 0 ; T Te , zNear equator, Te A B 2
up
Rfp
Ty
Rap
12 sin
T RB
ap
u finite (and positive) in upper levels at equator; angular momentum maximum there; not allowed
solution (1) no good at equator
Hadley Cell
T = Te
Observed Hadley cell
v,w
Structure within the Hadley cell
Hadley Cell
T = Te
In upper troposphere,
uut a sin 2cos
Structure within the Hadley cell
Hadley Cell
T = Te
In upper troposphere,
uut a sin 2cos J
Observed Hadley cell
u
v,w
Subtropical jets
Structure within the Hadley cell
Hadley Cell
T = Te
Near equator,
In upper troposphere,
uut a sin 2cos
uut a 2
But in lower troposphere,
ult 0(because of friction ).
10.750.50.250
1
0.75
0.5
0.25
0
x
y
x
y
T~φ4
Te~φ2
up
Rfp
Ty
Rafp
T
T afp
Rup
2 aR
u lnp
lt
ut T d lnp 2 a
R uut ult
2 aR
uut 2 3a3
R 3
lt
utT d lnp const. 3a3
2R 4
Structure within the Hadley cell
Hadley Cell
T = Te
Near equator,
In upper troposphere,
uut a sin 2cos
uut a 2
But in lower troposphere,
ult 0(because of friction ).
10.750.50.250
1
0.75
0.5
0.25
0
x
y
x
y
T~φ4
Te~φ2
up
Rfp
Ty
Rafp
T
T afp
Rup
2 aR
u lnp
lt
ut T d lnp 2 a
R uut ult
2 aR
uut 2 3a3
R 3
lt
utT d lnp const. 3a3
2R 4
Vertically averaged T very flat within cell
Observed Hadley cell
T
v,w
Structure within the Hadley cell
Hadley Cell
T = Te
Near equator,
In upper troposphere,
uut a sin 2cos
uut a 2
But in lower troposphere,
ult 0(because of friction ).
10.750.50.250
1
0.75
0.5
0.25
0
x
y
x
y
T~φ4
Te~φ2
T<Te: diabatic heating
➙ upwelling
T>Te: diabatic cooling
➙ downwelling
edge of cell
v Ty
w Tz
1 T Te , z
The symmetric Hadley circulation
JJA circulation over oceans
(“ITCZ” = Intertropical Convergence Zone)
Monsoon circulations(in presence of land)
summerwinter
Satellite-measured (TRMM) rainfall, Jan/Jul 2003
Satellite-measure (TRMM) rainfall, Jan/Jul 2003
ITCZSouth Asian monsoondeserts
Heat (energy) transport by the Hadley cell
Poleward mass flux (kg/s) = Mut
Equatorward mass flux (kg/s) = Mlt
Mass balance: Mut = Mlt = M
Moist static energy (per unit mass)
E = cpT + gz + Lq
Net poleward energy flux
F = MutEut – MltElt
= M(Eut – Elt)
But
(i) Convection guarantees
Eut = Elt at equator
(ii) Hadley cell makes T flat across the cell
➙ weak poleward energy transport
Roles of atmosphere and ocean
Trenberth & Caron (2001)
net
ocean
atmosphere
