EART 160: Planetary Science

20 February 2008

Last Time

• Elastic Flexure

• Paper Discussion – Titan Atmosphere– Tobie et al., 2005

• Planetary Atmospheres– General Description

Today

• Homework 4 due, 5 out– Oh, huzzah.

• Planetary Atmospheres– Atmospheric Structure– General Circulation– Thermal Balance– Origin / Geochemistry

Atmospheric Structure

Convection, Weather, Clouds

T increases with alt. Stable to convectionCools by radiation

Shooting stars burn up

Low density, heated by X-rays

Free electrons, ionsAffects radio wave propagation

Exobase – Height at which 1/e particles can escape

Heating due to UVabsorption by O3

Atmospheric Pressure

• Atmosphere is hydrostatic:

• Ideal Gas Law:

• Combining these two:

gdzzdP )(

NRTPV

zRT

gPP

RT

gP

dz

dP

exp0

P Pressure Densityg Gravityz HeightV VolumeN Number of MolesR Gas ConstantT Temperature Mass of one Mole

Assuming: Isothermal Atmosphere Constant Gravity

Scale Height

• Let H = RT/g:

• P = P0 e-z/H

• H is the scale height of the atmosphere– Distance over which P

drops by 1/e

• Mass of a column of atmosphere– Mc = P/g

Venus Earth Mars Jupiter Saturn Uranus Neptune

H (km) 16 8.5 18 18 35 20 19

Atmospheric Temperature• Of course, temperature actually does vary with height• If a packet of gas rises rapidly (adiabatic), then it will expand and,

as a result, cool• Work done in cooling = work done in expanding

pC dT

pC

g

dz

dT

• Combining these two equations with hydrostatic equilibrium, we get the dry adiabatic lapse rate:

Cp is the specific heat capacityof the gas at constant pressure

• On Earth, the lapse rate is about 10 K/km• What happens if the air is wet?

dPM

VdP

General Circulation

• Zonal Mean Circulation– Wind parallel to lines

of latitude

• Fastest Transport • What drives zonal

winds?– Angular Momentum

Conservation!– dv = -2 dR

R

R

Zonal Winds

• Westerlies– Near-surface winds that

blow from the west in mid-latitudes

• Trade Winds– Light winds that blow

from the east in the tropics

• Winds alternate between prograde (eastwards) and retrograde (westwards)

Hadley Circulation

• Parcels of atmosphere rise and fall due to buoyancy (equator is hotter than the poles)

• The result is that the atmosphere is broken up into several Hadley cells

• Each cell makes a band of zonal wind

Rotation Cells

• How many cells depends on the Rossby number (i.e. rotation rate)

v

RRo planet sin2

Venus

Ro = 0.02

1 Cell / hemisphere

Ro = 4

3 Cells / hemisphere

Earth Jupiter

Ro = 30

5 Cells / hemisphere

R: planet radius, : rotation rate, : latitude, v: wind speed

Zonal Winds on Giant Planets

• The reason Jupiter, Saturn, Uranus and Neptune have bands is because of rapid rotations (periods ~ 10 hrs)

• The winds in each band can be measured by following individual objects (e.g. clouds)

Atmospheric Dynamics

• Solve a set of coupled dynamical, radiative and possibly chemical equations. – General Circulation Models (GCM)

• Coriolis Force– Objects moving on a rotating planet get

deflected

• Geostrophic Wind– Balance Between Pressure Gradients and

Coriolis Force

Geostrophic balance• In some situations, the only significant forces acting are due

to the Coriolis effect and due to pressure gradients

• The acceleration due to pressure gradients is

• The Coriolis acceleration is 2 v sin

• In steady-state these balance, giving:

x

P

1

x

Pv

sin2

1

• The result is that winds flow along isobars and will form cyclones or anti-cyclones

• What are wind speeds on Earth?

L L

Hisobars

pressure

Coriolis

wind

Next Time

• Planetary Atmospheres– Thermal Balance– Climate Change– Origin and Loss