EVAT 554 OCEAN-ATMOSPHERE DYNAMICS LECTURE 8 LARGE-SCALE ATMOSPHERIC CIRCULATION (Reference: Peixoto & Oort, Chapter 3,7)

LARGE-SCALE ATMOSPHERIC CIRCULATION

IDEALIZED ATMOSPHERIC CIRCULATION THERMALLY-DIRECT CIRCULATION FOR AN IDEALIZED NON-ROTATING EARTH

Vertical temperature profile THERMAL PROFILE Vertical temperature profile Temperatures increase with altitude in the stratosphere (10 - 50 km) due to absorption of UV light by ozone (O3). There is limited exchange of material between the troposphere and the stratosphere (i.e., across the tropopause)

THERMAL PROFILE Simplest possible reasonable model for surface temperature steady no motion no thermal diffusion no water Ignore GHGs Consider global mean surface temperature, Ts esTS4 =(1- a0)S0/4 TS4 =(1- a0)S0/4es Tearth = [( 0.7)(343 W m-2)/(1)(5.67 x 10-8 W m-2 K-4)]1/4 = 255 K (-18 C) +33K (GHG) = 288K Earth S0 = 1370 W m-2

THERMAL PROFILE Simplest possible reasonable model for surface temperature steady no motion no thermal diffusion no water Ignore GHGs Consider surface temperature as a function of latitude esT4 =(1- a)S/4 T4 =(1- a)S/4es Assume small latitudinal variations about the global mean temperature TS linearization T4 =(1- a)S/4es 4T3 DT =[(1- a)/4es] DS T3 ~TS3 DT =[1- a(f)][S0 /16es TS3] (cosf-2/p) Where: DS~S0[cosf- 2/p]

DT =[1- a(f)][S0 /16es TS3] (cosf-2/p) THERMAL PROFILE TS DT =[1- a(f)][S0 /16es TS3] (cosf-2/p)

DT =[1- a(f)][S0 /16es TS3] (cosf-2/p) THERMAL PROFILE TS DT =[1- a(f)][S0 /16es TS3] (cosf-2/p)

GLOBAL ENERGY BALANCE 343 W/m2

EIN =S( )  (S/4)(1- a)cosf GLOBAL ENERGY BALANCE EOUT = esT4 EIN =S( )  (S/4)(1- a)cosf

GLOBAL ENERGY BALANCE Why don’t the tropics continue to heat up and the poles continue to cool?

GLOBAL ENERGY BALANCE Eout Ein

Advective heat transport GLOBAL ENERGY BALANCE Eout Ein steady no motion no thermal diffusion no water Advective heat transport

THERMALLY-DRIVEN CIRCULATION

THERMALLY-DRIVEN CIRCULATION Approximate circulation as steady, linear, two-dimensional (meridional-vertical plane) We will derive the circulation as a perturbation that arises in response to a mean imposed thermal gradient THERMALLY-DIRECT CIRCULATION FOR AN IDEALIZED NON-ROTATING EARTH

THERMALLY-DRIVEN CIRCULATION Approximate circulation as steady, linear, two-dimensional (meridional-vertical plane) Vertical momentum balance We will derive the circulation as a perturbation that arises in response to a mean imposed thermal gradient Boundary conditions: Start out assuming horizontally uniform surface pressure (1) no slip (2) no normal flow v’=w’=0 Pole Equator Meridional momentum balance v’=w’=0 v’=w’=0 v’=w’=0 THERMALLY-DIRECT CIRCULATION FOR AN IDEALIZED NON-ROTATING EARTH

THERMALLY-DRIVEN CIRCULATION Approximate circulation as steady, linear, two-dimensional (meridional-vertical plane) Continuity equation Not zero for compressible fluid! Boundary conditions: (1) no slip (2) no normal flow (linearized) v’=w’=0 Pole Equator v’=w’=0 v’=w’=0 zero near boundaries v’=w’=0 Implies the circulation pattern shown! THERMALLY-DIRECT CIRCULATION FOR AN IDEALIZED NON-ROTATING EARTH

HADLEY CELL CIRCULATION THERMALLY-DRIVEN CIRCULATION Approximate circulation as steady, linear, two-dimensional (meridional-vertical plane) HADLEY CELL CIRCULATION v’=w’=0 v’=w’=0 v’=w’=0 v’=w’=0 Pole Equator THERMALLY-DIRECT CIRCULATION FOR AN IDEALIZED NON-ROTATING EARTH

HADLEY CELL CIRCULATION Hadley Cell Circulation is a thermally direct circulation that transports sensible heat poleward N Equator S

HADLEY CELL CIRCULATION Hadley Cell Circulation also transports latent heat owing to different adiabatic lapse rates for dry and moist air Dry/Cold Dry Adiabatic warming (rapid) Moist Adiabatic cooling (gradual) Dry/Warm Moist/Hot N Equator S