# Class 14 - Earth, Venus, Mars - 4

1. Atmospheres - Goody & Walker Chapter 3 pp44-61
2. New Solar System - Ch 13.
• Recap EVM - pressures, scaleheights, composition, temperature
• Radiative Transfer - quantifying the greenhouse effect

## Earth, Venus, Mars Atmospheres

### Pressures, scaleheights

 VENUS EARTH MARS SURFACE PRESSURE (bar) 92 1 0.006 SCALEHEIGHT (km) 16 8 11 COLUMN MASS (kg/m2) 1.0E+06 1.0E+04 1.6E+02 TOTAL MASS (kg) 4.8E+20 5.2E+18 2.3E+16 COLUMN No. DENSITY (/m2) 1.5E+31 2.2E+29 2.3E+27 SURFACE No. DENSITY (/m3) 9.01E+26 2.52E+25 1.95E+23 SURFACE DENSITY (kg/m3) 6.58E+01 1.21E+00 1.42E-02 . . . . < /p>
 EARTH VENUS MARS Scaleheights 1 2 1.4 Surface pressure 1 92 0.006 Surface number density 1 36 0.008 Column number density 1 68 0.01 Total atmospheric mass 1 92 0.004

Remember -

Column mass density = Mc = Po/g

Column number density = Nc = Mc /(<amu>mp) = no H

### Composition WHY are these the compositions of these planets' atmospheres?

First - what comes out of volcanoes - Hawaii in this case...

80% water

12% CO2

6.5% SO2

1.3 % N2

0.6% H2

0.4% CO

... What happened to the water critically depends on T

... What happened to the CO2 critically depends on the presence of liquid water.... < /a>

QUANTITATIVELY

Resevoirs in units of 10^12 kg of carbon, rates of transfer in units of 10^12 kg of carbon per year.

... And what happens to the water depends on the Temperature which depends on the amount of greenhouse gasses.....

### Temperature where hPa is the same as mbar

THE LAYERS & PAUSES - these plus thermosphere, ionosphere, homosphere, heterosphere, exosphere, homopause, exobase, etc. NOTE the size of a scale height in each case compared with the height of the troposphere - the troposphere is about 2-3 scaleheights.   How do we QUANTIFY this greenhouse effect? How do we MODEL the absorption/ radiation?

First start with a very, very simple model..... see Chapter 3 pages 52-61 of Goody & Walker

NOTE - Te = Teff is the EFFECTIVE temperature - that's the & quot;temperature" that is derived by measuring all the (blackbody - or thermal radiation) IR flux from a planet (e.g. by flying over it or from an IR telescope on Earth) and saying what temperature object would be emitting this amount of flux?

The OPAQUE SLAB MODEL - sometimes called "grey model" - does not depend on wavelength.

Assumptions:

1. Each layer totally absorbs all light coming into it and radiates at its own temperature
2. There are no additional heat sources (no heating from the inside of the planet, no additional absorption in one of the layers)

Starting at the top of the atmosphere and working down layer by layer, equating the flux into each layer with the flux out

Layer 0 - T1 = Teff

Layer 1 - sT24 = sT14 + sT14 ....so, T 24 = 2T14

Layer 2 - sT34 + sT14 = sT24 + sT24 ....so, T34 = 2T 24 - T14 = 4T1< sup>4 - T14= 3T1< sup>4

.....

Layer N - TN4 = NT 14

So, if you imagine you keep going down the layers until you reach the surface of the planet - where the temperature is Tg - then you can envisage an expression

Tg4 = (1+t) Teff4

where we call t = OPTICAL THICKNESS (why (1+t) rather than t? Good question. I have no idea - probably due to some alternative derivation).

Earth: t = (Tg/Teff)4 -1 = (288K/255K)< sup>4 -1 = 0.6 - the Earth's atmosphere is thin - not even one totally absorbing layer.

Venus: t = (Tg/Teff)4 -1 = (750K/238K)< sup>4 -1 = 98 - Venus atmosphere is very thick (G&W quotes a surface temperature of 700 K and gets t = 68 - but the book was before the Soviet landers on Venus).

NOTE: This quantity t = (Tg/Teff)4 -1 = OPTICAL THICKNESS - we shall introduce a related quantity e = OPACITY in the next class.

The next step would be to add heating and cooling due to absorption and radiation... and make a much more complicated model. Rates are in units of Kelvin per day

In reality.... it's further complicated....by the fact that there are horizontal variations - some places have clouds, some do not. And there are vatiations with latitude.... etc. But, when you average over the globe, for Earth, this is what you get for a NET RADIATION BUDGET - visible light in (sunlight) - and IR light out (thermal radiation). units are Watts per square meter. Here's a color version.... And the Sun varies with time.... .... now that we have heated up the atmosphere - what about moving it around - next.....