Modeling planets

[Thorsten]

I'm current;y working on a pet science project - some code which simulates the conditions on exoplanets. It's still in its infancy so far - I have a numerical planar n-body solver to cover orbital dynamics and can compute planet trajectories in single and double star systems, get solar irradiation and gross radiative heat balance and am now going into the nitty-gritty details of the thermal physics - thermal inertia of various surface materials, position-differential heat balance and such like, absorption properties of the atmosphere dependent on composition, gross scales of weather patterns,...

Here is the first serious result of my calibration case - Earth. Shown is the temperature distribution in the absence of heat transport by the atmosphere (current radiative temperature).

It's summer in the southern hemisphere, so most of the incoming sunlight hits the southern latitudes. Daily temperature variation is really substantial on land (it cools off quickly without an atmosphere once the sun is down), much less on water (thermal inertia is much higher) - Asia, North America and Europe have cooled substantially due to the lack of sunlight. Antarctica is pretty cool even at noon since it has high albedo. Globe-averaged temperatures are actually quite okay, indicating that the gross balance is okay, just the transport is missing.

Noon over Africa...



... Australia...



... and South America.



I have to say, it's pretty cool what one can achieve with a little work. Once the dynamics for Earth is calibrated, I'll have a go at Helliconia (for those who haven't read the novels, it's a planet orbiting a sun-like star which in turn orbits a blue giant on an eccentric orbit of 2700 years - so it periodically freezes over at apoapsis and thaws at periapsis, giving rise to a periodic destruction of civilization. I suspect the irradiation pattern from two suns is pretty weird...

[Philosopher]

Sounds interesting! What are the units on the temperature?

As a side note, I wonder what it would look like with the cubehelix color scheme...

[PINTO]

Looks like that'd be in Kelvin, no?

Does look interesting, keep us updated!

[Thorsten]

It's Kelvin... and I'm not going to fiddle with aesthetics like colors of the plotting program at this stage

[Thorsten]

With a crude model of heat transport by the atmosphere, temperature variations become more reasonable:

A summer day in the northern Hemisphere





Winter day in the northern Hemisphere:





Spring:





What's missing is changing albedo of water with light incident angle (which would make tropics hotter and poles cooler) and the effect of clouds (which would keep the tropics much hotter by avoiding the IR radiative colling during the night). And of course real weather phenomena.

But it's actually doing remarkably well for such a simple code. Right now I'm computing Mercury as next test case - which has a very weird daylight pattern.

[gsagostinho]

This is really fascinating, Thorsten!

[www2]

Thorsten.
Nice
And can i download the code under BSD, MIT or (L)GPL?

[Hooray]

what do you want to do with the code ??

[MIG29pilot]

Perhaps he wants to take the ufo for a spin?

[Thorsten]

what do you want to do with the code ??

I dunno. The main motivation to write it was to quickly get a handle on how the conditions on a fictional world would be like. I've assembled quite a bit of material over the years on things like radiative balance, tidal heating, habitability envelope, atmospheric absorption cross sections... but it is rather tedious to do all the computations by hand. Now I can just define a config file and surface maps, shove them through a parser and run the simulation.

Ultimately I want to understand details like weather patterns. I'd like to know things like what the weather would be like on a world which is tidally locked to a red dwarf (it'll be stormy), what the windspeeds would be, how high thunderstorms would tower.

I can't really go there, but I can work out how it'd be.

And can i download the code under BSD, MIT or (L)GPL?

It's just on my harddisk, and it's not documented at all. I guess sooner or later I''ll make it available in some form - possibly GPL.

[Thorsten]

For those who don't know, Mercury as a test case is actually far from boring. It rotates very slowly, in a resonance pattern, which means that it needs two orbits for each rotation. That in turn means that the movement of the sun across the sky is determined by both the orbit ('year') and the rotation ('day'). However, since the orbit is eccentric, the yearly progression varies - it's faster at periapsis and slower at apoapsis.

If you plot the progression of a 'day' as seen from the ground, you get this:



The sun actually pauses in the sky for an extended period of time and even moves slightly backward.

For the temperature distribution of the planet, that has the interesting consequence that the spots which happen to have the sun right in the zenith when it pauses in the sky get extra-hot. In addition, the orbit is in periapsis when this happens, so the distance to the sun is also smallest. It shows up pretty clearly when plotting the 2-orbit averaged irradiation:



Also plotting temperature distribution at apoapsis



and periapsis



show this effect quite clearly.

Moving onward to a first glimpse at Helliconia, we start with the longyear summer (Helliconia and Batalix at periapsis with respect to Freyr).

During the conjunction of Batalix and Freyr, there is just a single lightspot illuminating the planet:



Half a year later, Batalix and Freyr illuminate opposite hemispheres of the planet and there is daylight practically everywhere:



Here the stronger spot is Freyr, the weaker Batalix.

(still need to define surface maps for Helliconia - the novels give the layout of the continents etc. )

[MIG29pilot]

For those who don't know, Mercury as a test case is actually far from boring. It rotates very slowly, in a resonance pattern, which means that it needs two orbits for each rotation.

So the days literally stretch into years, eh?

[Thorsten]

In case anyone is interested in what I've been up to, here's a home-made calculation of the Greenhouse effect for Earth.

It's pretty amazing how good even a simple model can be - for doubling CO2 content in the atmosphere I get a direct forcing of 0.7 K whereas the really sophisticated climate models utilizing full atmospheric transport codes get 1.05 K.

I guess I got partially lucky - I was hoping to get the right order of magnitude, getting such a change to 30% accuracy is too good to be true.