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 Tvs. 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

φ

uΩ

Ωsinφf > 0

f < 0

f = 0

Hypothetical 2D atmosphere relaxed toward RCE

φ

2D: no zonal variations

∂∂x ≡ 0

Annual mean forcing —symmetric about equator

A 2D atmosphere forced toward radiative-convective equilibrium

dQdt

cpdTdt g dz

dt JTe(φ,p)

(J = diabatic heating rate per unit volume)

→ dTdt Γw J

cp

≈ − 1 T − Te, z

Hypothetical 2D atmosphere relaxed toward RCE

dTdt Γw − 1

T − Te, z

φ

dudt− fv −g ∂z

∂x 0

∂u∂t v ∂u∂y 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

RAP3

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 Γw − 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 ∂T∂y w ∂T

∂z Γ − 1 T − Te, z

v, w ≠ 0

u a sin 2cos

(if u=0 at equator)

u ∇m 02) v ≠ 0

solution (2) no good at high latitudes

1) v 0 ; T Te, zNear equator, Te A − B2

∂u∂p R

fp∂T∂y R

ap1

2 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 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 ≈ a2

But in lower troposphere,Vertically averaged T very flat within cellult ≈ 0

(because of friction ).

10.750.50.250

1

0.75

0.5

0.25

0

x

y

x

y

T~φ4

Te~φ2

∂u∂p R

fp∂T∂y R

afp∂T∂

→ ∂T∂

afpR∂u∂p ≈

2aR ∂u

∂ lnp

→ lt

ut ∂T∂ d lnp ≈ 2a

R uut − ult

≈ 2aR uut ≈ 23a3

R 3

→ lt

utT d lnp ≈ const. 3a3

2R 4

Observed Hadley cell

T

v,w

Structure within the Hadley cell

Near equator,

In upper troposphere,

u

Hadley Cell

T = Te

ut a sin 2cos

uut ≈ a2

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 ∂T∂y w ∂T

∂z Γ − 1 T − Te, z

The symmetric Hadley circulation

JJA circulation over oceans

(“ITCZ” = Intertropical Convergence Zone)

Monsoon circulations(in presence of land)

summerwinter

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