Pre-ample

OK, OK, OK - what's with the Tequilibrium formula? What IS the right value of To in Teq=To (1-A)^1/4/a^1/2(where a is distance from the Sun in AU) ? Answer - depends on what you use for So (since To = (So/4s)^1/4. I looked up the formula in a variety of reference books and values of So used vary from 1360 to 1380, values of To vary from 279K to 285K, and A varies from 0.36 to 0.39. You would think with the 4th root it would not make so much difference. (There is also an issue of emissivity which we are just ignoring.) I sent a message to the LASP SORCE guys who should be able to tell us what the most accurate value to use for So. In the meantime, I suspect the source of the To=288K value is using the actual average temperature of the surface of the Earth - that's WITH the 33K GH effect added. Woops.

From Greg Kopp, LASP

We're measuring 1361 W/m^2 from SORCE, much lower than the traditional 1366. We have several improvements in the SORCE Total Irradiance Monitor (TIM) over previous ones and the instrument has been more thoroughly analyzed as a primary standard than any other, so we believe these newer measurements. That's not to say the rest of the community believes it yet though! So you're safe using either 1361 or 1366, and you'll find people believing whichever number you choose.
Yes, this is due to the difficulty in making these absolute measurements. I have a plot of all TSI instruments' data at
http://spot.colorado.edu/~koppg/TSI/index.html
that shows the degree of scatter in the measurements. Prior to SORCE, there had been a lot of adjusting instrument's values to get them to match the expected 1366, or even ignoring data from individual channels in a multi-channel instrument because they were "too high" or "too low". So these earlier instruments have some degree of inadvertent cross-calibration in them that explains some of their apparent agreement.
I wish I had a better answer for your students; but this is the process of measurements in science...

Dip is a large sunspot group that developed on the Sun. Here are the TIM observations compared with previous ones...

So, if you use So=1361 then To=278.3 K. For So=1366 then To=278.6 K. I think 4 sig figs are too many, given the uncertainties in the measurements and the underlying assumptions of the formula. I recommend that To=279 K or even 280 K is probably good enough for most purposes.

Class 22 - Atmospheric Evolution 3

Mars

Mars Pictures

Earth vs. Mars - first the facts

Temperature Profile

Note: Temperature profile is adiabatic in the first scaleheight, cooling slower than adiabatic above (due to absorption of solar energy). This profile is at the equatorial Viking 1 site. Here you can see that the profile did not have temperatures as low as the condensation of CO2 temperature. There are places where the temperature is cooler - towards the poles, at higher altitudes on mountaintops and CO2 - as well as the (tenuous) water vapor will condense. See images of clouds under pictures above.

Winds - showing large-scale Hadley cells. Net result is the transport from the equator of both mass (CO2) and energy (via evaporation at the equator and the release of latent heat to higher latitudes).

Seasonal Variations

Note the ~50% variations in total pressure of the atmosphere over a Mars year. (50%? That's HUGE! Even at the top of Everest the pressure is reduced by only 1/e or ~30% on Earth. On Mars this is a 50% variation in "sea level" pressure).

(left of diagram) Northern Summer = longer & cooler - Southern Winter = longer (& cooler)

(right of diagram) Southern Summer = shorter & hotter - Northern Winter = shorter (& warmer)

According to local expert Mike Mellon, the HOTTER summer of the SOUTH does not make up for the summer being SHORTER - and the winter being LONGER- so, averaging the temperature over the year Taverage (south) < Taverage (north). Hence, residual CO2 cap in south and not north. It does not explain why the southern ice cap is smaller. Or offset from the south pole.

Polar Caps

Compare with Antarctica - 4,500 km across, 3.5-4km thick - and Greenland - 900 x 2000 km, 2-3 km thick

Below: Here is the topography."Shaded relief maps of (left) north and (right) south polar topography of Mars. The projection is polar stereographic from latitude 72° to the poles. The red contours in each hemisphere represent the approximate extent of the residual ice caps (denoted by high albedo), while the blue contours trace regions of elevated polar layered terrains. (Credit: MGS MOLA and RS Science Teams)" Note the offset of the small, south polar cap.

So - ice/dirt layered regions about same size. Size of ice cap bigger at south - yes - contrary to expectation for the colder pole - a mystery....

Check out these cool pictures of the textures of the northern and southern polar cap regions...

Measurements of water (inferred from the absorption of neutrons by hydrogen atoms) - both summer.

Seasonal variation of the North polar cap - covered in CO2 frost in winter (green) - bare water in summer (blue)

Remember - Taverage (south) < Taverage (north) and northern summer is longer ->more CO2 sublimation (delayed few months from N summer solstice)

Above is the seasonal variation in atmospheric CO2 - below for H2O - same effect of longer northern summer -> more sublimation of water from the northern polar region

Summing up - the LONGER northern summer is more important than the hotter, but shorter southern summer - in terms of generating CO2 and in sublimation of H2O - hence sublimation of all CO2 frost from northern hemisphere, but some residual (permanent) CO2 polar frost in the south. Why is S polar (water ice) cap smaller? Good question.

Longer-Term Climate Variations

Large (+- 10 degrees) variation on the obliquity leads to substantial variation of climate.

Long-Term Climate Evolution

Suggests volatiles brought in by comets or icy planetesimals. Same as Earth and Venus.

So, what about liquid water on Mars? Was Mars ever WARM AND WET? Well, sometimes

Sometime around 3.7 billion years ago the volcanism stopped sending gases into the atmosphere, the magnetic dynamo turned off, the greenhouse effect turned off and Mars began to freeze.

Persistently, perhaps, early on - for enough time to develop life???? More than stromatalites?

The problem is that if you just add more CO2 to make a greater greenhouse effect to compensate for the faint early Sun, the amount of CO2 need is so high that clouds will condense, increase the albedo and cool Mars down. Somehow, the trick is to make the clouds of large particles which absorb heat..... or something else. Add CH4? This remains a big current issue.

But that's not the end of the story.... Mars surface features tell us that there were periods with water on the surface more recently....

Below is a more complicated carbon dioxide - silicate cycle that allows for temporal variation in temperature.

So - volatile inventory of Mars (stored in polar caps, as permafrost, atmosphere) slowly lost. Mars' interior cools down, less geology, little outgassing....... fizzle, fizzle,.....zzzzzzzzzzzz..........

EROSION

First, let's dispel a myth - erosion is not the primary source of geological change on Earth - plate tectonics is. Erosion is just the small scale gology that wears down the plates and make pretty features like rivers and canyons. We notice it most because it happens on closer to human time scales (while the cm per year motion of plates is not noticable unless you use GPS locators).