The Four Elements: A Quest for Atmosphere

This jour­nal entry is ded­i­cat­ed to plan­e­tary atmos­pheres, since this is prob­a­bly the most dif­fi­cult part of a worldbuilder’s jour­ney. Of course, you can have things eas­i­er way, say, if you have earth­like con­di­tions or you have addi­tion­al data laid out for you in case of a stan­dard star. But what if things were dif­fer­ent?

I’m going to explain each step, adding some the­o­ret­i­cal info as well. The Four Ele­ments series will cov­er top­ics such as the atmos­phere, the ocean, geo­log­i­cal activ­i­ty, inso­la­tion and plan­e­tary cli­mate. And maybe some­thing else I’ll find nec­es­sary to add.

The quest doesn’t start where one might think it does – not on a plan­et, but on a star. So, long before we can mod­el our plan­e­tary atmos­phere or any­thing else relat­ed to it, first we should con­sid­er stel­lar spec­trum. There are sev­er­al ways of get­ting it: tak­ing a real detailed spec­trum for exist­ing star or com­put­ing a syn­thet­ic stel­lar spec­trum. It all depends on your star of choice and how deep you are will­ing to go into details.

Why is this impor­tant? To design your own exclu­sive and unique plan­e­tary atmos­phere mod­el: maybe the air is so thin at alti­tude of 5 km, so your local peo­ple will nev­er go to the moun­tains, for exam­ple. What­ev­er it is, you’ll get the full set of nec­es­sary para­me­ters, some of which you might have had imag­ined, and some of which you prob­a­bly didn’t expect at all. Any­way, you will get to know your plan­et bet­ter.

Don’t be afraid of exper­i­ment­ing with things. They are not as hard or incom­pre­hen­si­ble as might appear to be.

Plan­et atmos­phere

The atmos­phere is an enve­lope of gas mix­ture around the plan­et. It is held down by grav­i­ty, and the weight of that gas is pres­sure (as in mass times g). The total pres­sure is the sum of par­tial pres­sures of gasses in the mix­ture. The par­tial pres­sure is the con­tri­bu­tion of a par­tic­u­lar gas con­stituent to the total pres­sure, and is found as the total pres­sure times the vol­ume frac­tion of gas com­po­nent.

The pro­por­tion of gas­es found in the atmos­phere changes with alti­tude. Dis­tinct lay­ers (such as tro­pos­phere, stratos­phere, etc.) are iden­ti­fied using ther­mal char­ac­ter­is­tics, chem­i­cal com­po­si­tion, mol­e­cule move­ment, and den­si­ty.

Indi­vid­ual mol­e­cules are mov­ing freely in gas and if their motion veloc­i­ty exceeds the planet’s escape veloc­i­ty, the mol­e­cules will escape into space from the out­er edge of the atmos­phere. A cer­tain amount will always exceed escape veloc­i­ty, and if that per­cent­age is too high, the atmos­phere will leak away in a geo­log­i­cal­ly short term. Thus, enough grav­i­ty is nec­es­sary to hold the atmos­phere. The out­er atmos­phere tem­per­a­ture plays a vital role in this process as well, since gas mol­e­cules trav­el faster with increas­ing tem­per­a­ture. The hot­ter the exos­phere is, the greater grav­i­ty must be. To keep things in bal­ance, worlds clos­er to their stars must be larg­er to hold atmos­pheres equiv­a­lent to those around cool­er worlds. Thus, atmos­pher­ic com­po­si­tion is also impor­tant, because lighter mol­e­cules move faster at the same tem­per­a­ture. Same sur­face grav­i­ty can keep one mol­e­cules, but can’t hold oth­ers; in case of Earth hydro­gen and heli­um are too light for our grav­i­ty.

Com­po­si­tion and pres­sure are not com­plete­ly free para­me­ters, though. They are influ­enced and mod­i­fied by chem­i­cal reac­tions with the sur­face of the plan­et (e.g. atmos­phere inter­ac­tion with crustal rocks over time in the car­bon­ate-sil­i­cate cycle), liv­ing things and pho­todis­so­ci­a­tion (stel­lar UV light breaks up the hydro­gen-bear­ing com­pounds like water, ammo­nia and methane) at the out­er edge of the atmos­phere. The atmos­phere changes over geo­log­i­cal time along with the evo­lu­tion of the star, life and loss of lighter gasses.

Ter­res­tri­al-like plan­ets may obtain atmos­pheres from three pri­ma­ry sources: cap­ture of neb­u­lar gas­es, degassing dur­ing accre­tion, and degassing from sub­se­quent tec­ton­ic activ­i­ty. While cap­ture of gas­es is vital for gas giants, low-mass ter­res­tri­al plan­ets are unable to cap­ture and retain neb­u­la gas­es, which also may have large­ly dis­si­pat­ed from the inner solar sys­tem by the time of final plan­e­tary accre­tion. Atmos­pher­ic mass and com­po­si­tion for ter­res­tri­al plan­ets is there­fore close­ly relat­ed to the com­po­si­tion of the sol­id plan­et (Elkins-Tan­ton & Sea­ger, 2008a).

In case of humans and ani­mals the atmos­phere has lim­its on its com­po­si­tion. To be breath­able, it must have lev­els of mol­e­c­u­lar oxy­gen (O2) between 0.16 and 0.5 atm; high­er con­cen­tra­tions of oxy­gen are tox­ic (severe cas­es can result in cell dam­age and death), low­er than min­i­mum are not enough to sup­port human life. Hypox­ia (oxy­gen depri­va­tion) and sud­den uncon­scious­ness becomes a prob­lem with an oxy­gen par­tial pres­sure of less than 0.16 atm. Hyper­ox­ia (excess oxy­gen in body tis­sues), involv­ing con­vul­sions, becomes a prob­lem when oxy­gen par­tial pres­sure is too high. Our present atmos­phere con­tains 21% mol­e­c­u­lar oxy­gen (par­tial pres­sure of 0.21 atm).

Also, to pre­vent nitro­gen nar­co­sis under high pres­sures (the diver’s “rap­ture of the deep”) the par­tial pres­sure of nitro­gen (N2) must be less than 3 atm.

As for oth­er tox­ic stuff, the lev­el of car­bon diox­ide must be less than 0.02 atm to breathe indef­i­nite­ly, and less than 0.005 atm to avoid phys­i­o­log­i­cal stress­es. In case of CO2 con­cen­tra­tion above nor­mal lev­els the only hab­it­able places for humans might be high regions, like moun­tains. But then again, too lit­tle oxy­gen high­er up can be trou­ble­some.

Many plants, how­ev­er, can sur­vive and thrive in low oxy­gen-high CO2 envi­ron­ment. Earth’s plants will grow in many atmos­pheres that are unbreath­able to humans and ani­mals, unless the run­away green­house ruins the place com­plete­ly (like Venus).

By build­ing plan­et atmos­phere and cli­mate mod­els you can see what are the bound­aries for life under dif­fer­ent stars and atmos­pheres. How fast the atmos­phere thins upward? What are the prop­er­ties of lay­ers (alti­tudes, tem­per­a­tures, pres­sures, com­po­si­tion, ozone lay­er (ozone is also tox­ic), grav­i­ta­tion­al pull, etc.)? What is the cli­mate and weath­er pat­tern? The broad­er appli­ca­tions for the mod­el include your plan­et aero­space or colonization/terraforming his­to­ry, if applic­a­ble. The thick­ness of the atmos­phere has some con­se­quences. The thick­er it is (and/or the low­er the grav­i­ty), the eas­i­er flight is. Sound also trav­els bet­ter in a denser medi­um. Storms can be more intense if mass of mov­ing air is greater.

More detailed descrip­tion of atmos­pheres is beyond the scope of this arti­cle, but can be found on the Inter­net or in text­books. In fact, if you know lit­tle about how atmos­pheres work, fur­ther read­ing into sub­ject is required before build­ing any­thing. Some use­ful book titles are list­ed in my Library­Thing cat­a­logue, which is con­stant­ly grow­ing. My goal here is to describe the tools: what data for mod­els is required and how those mod­els can be used to pro­duce desir­able results.

Cli­mate dynam­ics mod­el

The MIT­gcm (MIT Gen­er­al Cir­cu­la­tion Mod­el) is a numer­i­cal mod­el designed for study of the atmos­phere, ocean, and cli­mate dynam­ics. MIT­gcm is freely avail­able to all and can be run on a home pc or lap­top, and is enough to play with your plan­et in detail.

There are some oth­er mod­els, such as NASA/GISS 4×3 Atmos­phere-Ocean Mod­el or the Com­mu­ni­ty Earth Sys­tem Mod­el (CESM).

Run­ning the NASA/GISS mod­el requires a sig­nif­i­cant invest­ment in time and mon­ey, and it is designed to run on mul­ti­proces­sor machines. It can repro­duce the sea­son­al and region­al mean val­ues and vari­a­tions of cli­mate quan­ti­ties such as tem­per­a­ture, pres­sure, pre­cip­i­ta­tion, cloud cov­er, and radi­a­tion with rea­son­able degrees of pre­ci­sion, and many oth­er things. I do not rec­om­mend this one for our pur­pose (though, if you own a mul­ti­proces­sor work­sta­tion, you can try).

The CESM is also designed for sim­u­lat­ing Earth’s cli­mate sys­tem, but, as with the NASA/GISS, it is not sim­ple at all. It is a cou­pled cli­mate mod­el com­posed of five sep­a­rate mod­els simul­ta­ne­ous­ly sim­u­lat­ing atmos­phere, ocean, land, land-ice, and sea-ice.

How­ev­er, before you can mod­el weath­er and cli­mate, an atmos­pher­ic lay­ered mod­el is required. You can take earth­like mod­el (e.g. Stan­dard Atmos­phere) or you can make your own. For the lat­ter pur­pose you’ll need anoth­er piece of code, described in the sec­tion below.

Pho­to­chem­i­cal and radiative/convective atmos­phere mod­els

The cou­pled pho­to­chem­i­cal and radiative/convective atmos­phere mod­el was used to study earth­like plan­ets around dif­fer­ent types of stars: F2V, G2V (Sun), K2V (Segu­ra et al., Astro­bi­ol­o­gy, 2003) and M stars (Segu­ra et al., Astro­bi­ol­o­gy, 2005); Gren­fell et al. 2006, 2011; Kast­ing et al. 1996.

This mod­el requires stel­lar spec­trum, which can be tak­en from the data­base or syn­the­sized. Some spec­tra are hard to find. The ones used by Segu­ra et al. can be tak­en from the VPL site.

Stel­lar flux great­ly influ­ences chem­i­cal process­es in the atmos­phere and bio­log­i­cal process­es on the plan­et. Each star has its indi­vid­ual flux “sig­na­ture”.

In Segura’s mod­el the “Earth” is assumed to be at a dis­tance equiv­a­lent to 1 AU in the extra­so­lar plan­et sys­tem. The orbital radius is scaled accord­ing to stel­lar lumi­nos­i­ty, and the plan­et is then moved inward or out­ward until its cal­cu­lat­ed sur­face tem­per­a­ture is 288 K. Also, the term “mix­ing ratio” has the same mean­ing as “mole frac­tion”.

Temperatures. Credit: Segura et al. 2003
Tem­per­a­tures. Cred­it: Segu­ra et al. 2003

The plan­et around the F star devel­ops a thick­er ozone lay­er because of the abun­dance of short-wave­length UV radi­a­tion (lamb­da < 200 nm) that can dis­so­ci­ate mol­e­c­u­lar oxy­gen.

Ozone number density. Credit: Segura et al. 2003
Ozone num­ber den­si­ty. Cred­it: Segu­ra et al. 2003

The sur­face UV flux increas­es with decreas­ing par­tial pres­sure of O2, but the behav­ior is very non­lin­ear. Good UV shield devel­ops above 10^−2 of present atmos­pher­ic lev­el of O2.

M stars emit very lit­tle near-UV radi­a­tion (200−300 nm), but active M (and, in fact, ear­ly K) stars emit lots of UV radi­a­tion short­ward of 200 nm (chro­mos­pher­ic emis­sion). One can there­fore split mol­e­c­u­lar oxy­gen (and, hence, make ozone), but the ozone pho­to­chem­istry is very dif­fer­ent. Methane in Earth’s atmos­phere is most­ly destroyed in chem­i­cal reac­tions trig­gered by UV-flux at 310 nm. In atmos­pheres near M stars the life­time for methane is long.

Syn­thet­ic stel­lar spec­trum

If you have a star type that is not on the VPL list of spec­tra, acquir­ing a syn­thet­ic spec­trum is where you’ll have to start build­ing your mod­el. There are numer­ous ways and soft­ware pack­ages to com­pute a syn­thet­ic spec­trum, but the eas­i­est one is to use the BaSeL inter­ac­tive serv­er: it saves time and san­i­ty. This tool presents a user-friend­ly inter­face of an inter­po­la­tion engine, that allows on-line com­pu­ta­tions of syn­thet­ic stel­lar spec­tra for any giv­en set of fun­da­men­tal para­me­ters Teff, log g and [Fe/H]. More info about BaSeL is found in “The BaSeL inter­ac­tive web serv­er: a tool for stel­lar physics”. Please note that fun­da­men­tal para­me­ters are tak­en from the real star’s data or com­put­ed stel­lar evo­lu­tion mod­el.

# Have fun and more mod­el­ing to fol­low.

Jeno Marz
JENO MARZ is a science fiction writer from Latvia, Northern Europe, with background in electronics engineering and computer science. She is the author of two serial novels, Falaha’s Journey: A Spacegirl’s Account in Three Movements and Falaha’s Journey into Pleasure. Marz is current at work on a new SF trilogy. All her fiction is aimed at an adult audience.

3 Comments

  1. I’m real­ly glad to have found your blog. These world­build­ing posts have been real­ly use­ful for me.

    In the past I have tried and giv­en up on the NASA/GISS and CESM mod­els and I have played with sim­pler edu­ca­tion­al GCMs. NASA/GISS and CESM were just well beyond my capa­bil­i­ties. Both com­put­er assets and appar­ent­ly intel­lec­tu­al capac­i­ty.

    From what you’re say­ing, the MITGCM is rea­son­ably easy to deal with(as such things go), so I’m feel­ing a bit men­tal­ly under­en­dowed that I can’t get the thing run­ning. Per­haps at some point you could post a run-through of set­ting up and run­ning the gcm. “MITGCM for Dum­mies” would be even bet­ter, but at least I, per­son­al­ly, would real­ly appre­ci­ate a basic run-down. I know tuto­ri­als and docs exist for the pro­gram, and maybe once I can get a men­tal foothold on run­ning the thing they’ll start to make more sense, but it’s dif­fi­cult to find usage instruc­tions hid­den in all the physics text­book ele­ments.

    1. Hi Astro­g­ra­ph­er, thanks for drop­ping by.

      I haven’t been doing any mod­el­ing late­ly because I’m work­ing on my tril­o­gy of novel­las now. There’s a lot of writ­ing going on. I will have a pause before I will dive into writ­ing nov­els to get to it. 

      I plan to run a plan­e­tary atmosphere/ocean MIT­gcm mod­el some time (hope­ful­ly) next year, since I need the out­put for the nov­els. I have to decide on (read: cal­cu­late) quite few things for my fic­tion­al plan­et before putting them into my mod­el. When I’m done, I will post my detailed steps and results here on my blog.

      MIT­gcm only seems sim­ple, but in real­i­ty it is rather com­pli­cat­ed if you are not deal­ing with ocean/atmosphere sci­ence pro­fes­sion­al­ly, since there is a lot of “tun­ing” to do. 

      I sug­gest using Ubun­tu 10.10 or anoth­er ver­sion of Lin­ux for the run. If you are good with Lin­ux, no big deal here. If not, you will need an dual boot/clean instal­la­tion or a vir­tu­al machine in any case. 

      Cheers, J

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