Class 15 - Earth, Venus, Mars - Dynamics 1

1. Atmospheres - Goody & Walker Chapter 4
2. New Solar System - Ch 13.
• Convection
• Latitudinal Heat Transport
• Global Circulation
• Effects of Rotation
• Earth - Water Cycle

Convection

ADIABATIC LAPSE RATE - dT/dz - drop in temperature of a blob of air as it rises without gaining or losing energy.

dT/dz = -g/cp

g= gravitational acceleration cp = Specific Heat Capacity at Constant Pressure

cp = squiggle R / M

M = mean molecular mass =<amu> 0.001 - e.g. air = 29 kg / mol

R = gas constant = 8.31 J K^-1 mol^-1

squiggle = 5/2 for monoatomic gas, = 7/2 for diatomic gas, = 9/2 for triatomic gas

UNITS: cp - (kg m^2 s^-2 K^-1 mol^-1 )/(kg mol^-1) = m^2 s^-2 K^-1

dT/dz = g/cp - m s^-2 /(m^2 s^-2 K^-1) = K m^-1

What's cp for E, V, M? What's dT/dz for Earth, Venus Mars?

 Gas M kg/ mole cp m2 s-2 K-1 g m s-2 -dT/dz K / km V CO2 44 x 0.001 850 8.87 10.4 E O2 , N2 29 x 0.001 1003 9.81 9.8 M CO2 44 x 0.001 850 3.71 4.4

So, Earth and Venus about the same - down in the troposphere - but at Mars the adiabatic temperature profile drops off more slowly with height.

- - - - - = adiabatic lapse rate, White line = actual lapse rate

- if cools faster than adiabatic - stable (cool air sinks)

- if cools slower than than adiabatic - unstable (warm air rises)

For example - here are data from Mars... A = adiabatic, C = condensation of CO2

Latitudinal re-distribution of energy

Heating at the equator - cooling at the poles

WHY less energy flux on Venus? Higher albedo (0.6 instead of 0.4)

WHY superrotation?

1. Venus rotation = 243 days
2. Upper atmospheric superrotation = 4 days
3. Column mass of atmosphere = 1000 m deep ocean
4. Thermal inertia time constant ~ century
5. Weak forcing, weak damping - mean flow only loosely coupled to forcing - ultimately solar heating - only 11% of which reaches the surface
6. Solar tides probably important
7. Requires large computer simulations that run for a very long time

Effects of rotation

WHY the coriolis force? What is the cause? Conservation of angular momentum.

Coriolis force:

1. Deflects to R in N hemisphere, to L in S hemisphere
2. Magnitude is proportional to angular velocity (spin rate)
3. Mantitude is proportional to the SPEED.

Here is a map of surface winds - not the narrow strips and the the enormous effect of land masses. And seasons.

Below is Fig 4.5 from G&W - note the jet streams - and their changes with seasons - left and right.

An effect of the rapid rotation on Earth is to produce the strong waves in the mid-high latitudes - producing cyclones (L) that hit the west of Europe and US (nasty weather in Britain and coasts of Oregan and Washington states) ...and some anti-cyclones (H). Fig 4-18

Fig 4-16 shows the effect of coriolis forces - they tend to balance the pressure gradient forces leading to circular winds - cyclonic winds anticlockwise and anti-cyclonic clockwise (opposite in southern hemisphere).

GEOSTROPHIC BALANCE

Earth - Water Cycle

Remember the calculations from homework about the latent heat of vaporization and condensation of water? Although the total amount of water in the atmosphere is small, the effects of latent heat on the dynamics can be substantial. Furthermore, the hydrological cycle is of huge planetary importance.