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
Observed radiative budget
Implied energy transport:
requires fluid motions to
effect the implied heat
transport
Roles of atmosphere and ocean
net
ocean
atmosphere
Trenberth & Caron (2001)
Rotating vs. nonrotating fluids
Ω
f>0
f=0
f<0
Ω
u
φ
Ωsinφ
Hypothetical 2D atmosphere relaxed toward RCE
2D: no zonal variations

0

x
φ
Annual mean forcing —
symmetric about equator
A 2D atmosphere forced toward radiative-convective equilibrium
dQ
Te(φ,p)
dz
dt  c p dT

g
dt
dt
J
(J = diabatic heating rate per unit volume)
J
 dT w  
cp
dt
1
T T e 
, z
Hypothetical 2D atmosphere relaxed toward RCE
dT
dt

0

x
φ
w 1
T T e 
, z
Above the frictional boundary layer,
z 0
du fv g 
dt

x

u v 
u w 
u fv 0

t

y

z
Ω
r
Absolute angular momentum per unit mass
m ur r 2
ua cos a 2 cos 2 
dm
dt
m

u m 0

t
a
φ
Angular momentum constraint
m ua cos a 2 cos 2 
Above the frictional boundary layer,
dm
dt
m

u m 0

t
In steady state,
u m 0
φ
Angular momentum constraint
m ua cos a 2 cos 2 
Above the frictional boundary layer,
dm
dt
m

u m 0

t
In steady state,
u m 0
φ
Or 2) v, w 0 but m constant
along streamlines
Either 1) v=w=0
dT
dt
T
v
w

y
w 1
T T e 
, z

T


z
T = Te(φ,z)
1
T T e 
, z
u
sin 2 
a cos 
φ
0
15
30
45
60
U(ms-1)
0
32
134
327
695
(if u=0 at equator)
Angular momentum constraint
m ua cos a 2 cos 2 
Above the frictional boundary layer,
dm
dt
m

u m 0

t
In steady state,
u m 0
φ
Or 2) v, w 0 but m constant
along streamlines
Either 1) v=w=0
dT
dt
T
v
w

y
w 1
T T e 
, z

T


z
T = Te(φ,z)
1
T T e 
, z
u
sin 2 
a cos 
φ
0
15
30
45
60
U(ms-1)
0
32
134
327
695
(if u=0 at equator)
1) v 0 ; T T e 
, z
2) v 0
Near equator,
u m 0
solution (2) no good at
high latitudes

u

p
T e  A B2
 fpR

T

y
R
 ap

T
1

2sin  
u finite (and positive) in upper levels at equator;
angular momentum maximum there; not allowed
solution (1) no good at equator
Hadley
Cell
RB
 ap
T = Te
1) v 0 ; T T e 
, z
2) v 0
Near equator,
u m 0
solution (2) no good at
high latitudes

u

p
T e  A B2
 fpR

T

y
R
 ap

T
1

2sin  
u finite (and positive) in upper levels at equator;
angular momentum maximum there; not allowed
solution (1) no good at equator
Hadley
Cell
RB
 ap
T = Te
Observed
Hadley cell
v,w
In upper troposphere,
Structure within the Hadley cell
sin 2 
u ut a cos 
Hadley
Cell
T = Te
In upper troposphere,
Structure within the Hadley cell
sin 2 
u ut a cos 
J
Hadley
Cell
T = Te
v,w
Observed
Hadley cell
u
Subtropical jets
In upper troposphere,
Structure within the Hadley cell
sin 2 
u ut a cos 
Near equator,
u ut a2
But in lower troposphere,
Hadley
Cell
T = Te
u lt 0
(because of friction ).

u

p

T




ut
T d lnp
 

lt 

T  R 
T
R 
y

fp 
afp 
afp 
u  2a  
u
R 
R
p

lnp
2a 
u ut u lt 
R
2a u  23 a 3 3
ut
R
R
ut
3 3
  T d lnp const.   a 4
2R
lt

y
1
T~φ4
0.75
Te~φ2
0.5
0.25
0
0
0.25
0.5
0.75
1
x
In upper troposphere,
Structure within the Hadley cell
sin 2 
u ut a cos 
Near equator,
u ut a2
But in lower troposphere,
Hadley
Cell
T = Te
Vertically averaged T
very flat within cell
u lt 0
(because of friction ).

u

p

T




ut
T d lnp
 

lt 

T  R 
T
R 
y

fp 
afp 
afp 
u  2a  
u
R 
R
p

lnp
2a 
u ut u lt 
R
2a u  23 a 3 3
ut
R
R
ut
3 3
  T d lnp const.   a 4
2R
lt

y
1
T~φ4
0.75
Te~φ2
0.5
0.25
0
0
0.25
0.5
0.75
1
x
v,w
Observed
Hadley cell
T
Structure within the Hadley cell
In upper troposphere,
sin 2 
u ut a cos 
Near equator,
u ut a2
But in lower troposphere,
Hadley
Cell
T = Te
u lt 0
T>Te: diabatic cooling
(because of friction ).
➙ downwelling
y
T
v
w

y

T


z
1
T T e 
, z
1
T~φ4
0.75
Te~φ2
0.5
edge of cell
T<Te: diabatic
heating
0.25
➙ upwelling
0
0
0.25
0.5
0.75
1
x
The symmetric Hadley circulation
JJA circulation over oceans
(“ITCZ” = Intertropical Convergence Zone)
Monsoon circulations
(in presence of land)
winter
summer
Satellite-measured (TRMM) rainfall, Jan/Jul 2003
Satellite-measure (TRMM) rainfall, Jan/Jul 2003
deserts
South Asian monsoon
ITCZ
Heat (energy) transport by the Hadley cell
Poleward mass flux (kg/s) = Mut
Moist static energy (per unit mass)
E = cpT + gz + Lq
Net poleward energy flux
F = MutEut – MltElt
= M(Eut – Elt)
But
(i) Convection guarantees
Equatorward mass flux (kg/s) = Mlt
Mass balance: Mut = Mlt = M
Eut = Elt at equator
(ii) Hadley cell makes T flat across the
cell
➙ weak poleward energy transport
Roles of atmosphere and ocean
net
ocean
atmosphere
Trenberth & Caron (2001)