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The giant space ship example; Can you calculate surface temperatures given a moon sized interstellar space ship with its own atmosphere?
Topic Started: Dec 4 2011, 03:29 AM (1,491 Views)
gbaikie

Review
Quote:
 
We've been using 364 W/m2 on the dwarf planet...
If we boosted the Dwarf planet to 15C (which we have been taking as Earth's representative temperature), then the energy requirement for Dwarf would be 391 W/m^2....
The Earth is heated by 240 W/m2.


Dwarf: 1200 km radius. 18 million sq km. 1.8 x 10^13 square meters
364 W/m2. Total power:6.58 x 10^15 watts

Earth: 6378 km radius. 511 million sq km. 5.1 x 10^14 square meters
240 W/m2. Total power: 1.2 x 10^17 watts


End review and try something new.
Suppose instead dwarf heating entire planet at one time it heats in sequence 4 sectors, each section ran for 6 hours- each sector having 18 hours of downtime. And this roughly imitates earth and gives lots of a maintenance time, each of the sector will supply 6.58 x 10^15 watts which will providing 1456 watts per square meter. 364 W/m2 maintains 10 C. Each time the section start it will be cooler than it ended in last shift, but it adding 1092 watts per square meter of added heat during it's 6 hr shift.
The sector adjacent to sector staring it's shift will warmest section, and heat will be flowing from that sector before the coldest shift begins. As the coldest section warms it will flow heat to next sector to begins it's shift.
This could add stability to atmosphere. Analogous to easier to ride a bike which is moving.
And difference in heat from coldest to warmest is 1 or 2 degrees and difference isn't as much as there is on earth.

Oh, I see posted, with tungsten planet. :)
I was planning posting about something else, but got sidetracked with idea of imitating earth's day and night.
And I said earlier " Plus at 1/10th pressure, the sky isn't so high." It doesn't lower very much- something like less 10 km, and was figure that out. But probably quicker to load this Excel program you made.
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Chris Ho-Stuart
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gbaikie
Dec 11 2011, 01:46 AM
But probably quicker to load this Excel program you made.
I'd very much appreciate some feedback on whether you were able to unzip it and use it; and whether it's obvious or not how to use it!

Suggestions for additional features are welcome. Writing new features yourself is also great. I'm going to be extending the gas modeling to deal with CO2 instead of some hypothetical grey gas. The spreadsheet includes some liberal boiler plate for a license and copyright in the "readme" sheet. This lets you do almost anything you like with the spreadsheet as long as:

  • you don't sue me
  • you leave the copyright notice there when you are making other changes
  • you don't use my name without permission to promote anything you might develop from the spreadsheet

If people can stick to those obvious principles, then I encourage you and others to change it at will, use it anywhere, and share it with others.
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gbaikie

Quote:
 
Writing new features yourself is also great. I'm going to be extending the gas modeling to deal with CO2 instead of some hypothetical grey gas.


So changing grey gas number isn't suppose change any values?

Download it and looked interesting I fiddle with a bit and didn't have problems.
I don't have any experience using excel
So I proved any idiot can do it:)
Don't know if I can do much de-bugging- I tried putting Venus in there and of course said required +16 thousand watts/meter surface emission- not too surprising it's wrong.
And not sure I used right perimeters.
What the cp/cv gamma?
:)
Oh tried changing from .3 atm to .1 atm on dwarf and it didn't change height- should change it by
how high it requires a .3 atmosphere to go to get to .1 atm- so it should indicate somewhere as I said around 10 km difference.

Edited by gbaikie, Dec 11 2011, 08:15 AM.
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Chris Ho-Stuart
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gbaikie
Dec 11 2011, 05:57 AM
Quote:
 
Writing new features yourself is also great. I'm going to be extending the gas modeling to deal with CO2 instead of some hypothetical grey gas.


So changing grey gas number isn't suppose change any values?


The point is that CO2 is not a grey gas; accurate modeling of CO2 will require calculation of frequency dependent k values.

Quote:
 

Don't know if I can do much de-bugging- I tried putting Venus in there and of course said required +16 thousand watts/meter surface emission- not too surprising it's wrong.
And not sure I used right perimeters.


Venus is a good example. I used these parameters in the 8 available input places.

Radius: 6052 (a tad less than Earth)
Gravity: 8.9 (a tad less that Earth)
Surface temperature: 464C (very hot!)
Surface air pressure: 92 atm (very high pressure)
Cp: 0.8501 (check out the references at the "readme" sheet; one of them gives Cp and R for different planets
gamma: 1.2857 (using gamma = 1/(1-Cp/R) and R = 0.1889)
Lapse rate: I just used the DALR calculated, which is 10.47
k: 473

The choice of "k" is really only picking the number that happens to give the thermal emission to space at the correct value of 184.2 W/m^2

As expected, this is a higher k value than for Earth. Beyond that we can't say much, because neither planet has a grey atmosphere.

The values for the greenhouse effect magnitude are as expected, which is no surprise. The "k" value was chosen only on the basis of getting those results!

Quote:
 
Oh tried changing from .3 atm to .1 atm on dwarf and it didn't change hieght- should change it by
how high it requires a .3 atmosphere to go to get to .1 atm- so somewhere as said around 10 km difference.


Yes; that is an interesting consequence of the fixed lapse rate assumption. If the lapse rate is fixed all the way up the atmosphere, then the altitude at which you get a temperature of absolute zero depends only on lapse rate and surface temperature. Pressure makes no difference. Really. What happens with higher pressures is that the gas is just more dense. Maximum altitude stays unchanged.

Version 2 is going to remove the fixed lapse rate assumption, by identifying a tropopause and applying radiative equilibrium above that point. I don't expect it to make much difference to the magnitude of the greenhouse effect in most cases; but I'll have to see. It will be a more realistic model of the atmosphere; but the tropopause height I calculate won't be particularly accurate. I haven't attempted to do the moist adiabat, let alone model the environmental lapse rate. In reality, the troposphere on Earth tends to have lapse rates that are slightly unstable to convection; and there's a usually a point within the troposphere where the atmosphere has dried out and the dry adiabiat is the stable case up until the tropopause.
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Bug report... the calculation of the "Effective emission altitude" Ze, on row 36 of the Definitions sheet in version 1.1, takes a difference of a temperature in Kelvin and a temperature in Celsius, and so calculates a nonsense value. The value is not used anywhere else in the spreadsheet, so you can simply ignore that row for the time being. This will be fixed in the next version.
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gbaikie

I looking at dwarf sky.
I used just nitrogen and 37 tonnes liquid N2 per square meter is 3 times mass
as earth:
For dwarf with .3 need about 30 meters liquid nitrogen: 1:694:
http://chemistry.about.com/od/moleculescompounds/a/liquidnitrogen.htm
And: "At normal pressure, liquid nitrogen boils at 77 K (-195.8°C or -320.4°F)."
Also: density: 0.808 [need 37 meter instead of 30]
If air is 1 nitrogen gas is 0.9737
cubic meter of air is 1.2929 kg/m3 dry and 0 C. Nitrogen gas is 1.26 kg per m3
Pipe has 1 cubic meter per meter length
So have, pipe horizontal or zero gee:
37 times 694 is 25,678 meters at 77 K at 1 atm.
Double temperature twice it's volume:
154 K and 51,356 meters
And 283 K is 94,495 at 1 atm. 14.7 psi
1 psi is 1,389,076.5
1/10 psi is 13,890,765

When vertical on 1/10 gravity world:
1/100th 13,890,765 is
138,907.65
So 37 meter liquid is 30 tonnes which weighs 3000 kg on 1/10 gravity
99% of 3000 kg is 2930 kg 2970 kg
On earth 30,000 kg of atmosphere would make 14.7 times 3 or 44.1 psi
4.41 psi bottom and minus .0441 psi or 4.365 psi at at top 1% section
Plus starting .1 psi before any gravity.
So give 4.51 psi bottom and minus .0441 psi which is 4.466

from gravity the 1/10th pressure, starts from 1/10 and doubles: 2/10/, 4/10, 8/10th 16/10th, 32/10th. Being 3.2 psi. And times by 40% gives 4.5 psi

So taking one section which 1% of entire length and
at .1 psi with 138,907.65 length, half length gives .2 psi at 69,454 meters
.4 psi is 34727 meters. .8 is 17,363 meters. .8 is 8682 meters
1.6 psi is 4341 and 3.2 is 2170 meter and finally 1550 meters gives 4.51 psi at bottom.
As pressure decreases from 4.51 psi to 3.2 psi the length will go from 1550 meters
to 4341 meters.
The following 15 of the 100 138,907.65 meter lengths which goes from the bottom
part of section starting at 4.51 to 3.88 psi. Which length range of 1550 to 3580 meters.
Or roughly adding 135. Or say start 120 add 3
1550 elevation meters Pressure Density .4516 kg per cubic meter
***************
1670 *--* 3220 *--* 4.46 *--* .4192 kg/m3
1793 *--* 5013 *-- * 4.42 *--* .3904
1919 *--* 6932 *--* 4.38 *--* .3648
2048 *--* 8980 *--* 4.34 *--* .3418
2177 *--* 11,157 *--* 4.3 *--* .3215
2311 *--* 13,468 *--* 4.26 *--* .3029
2448 *--* 15,916 *--* 4.22 *--* .2859
2588 -- 18,504 -- 4.18 -- .2705
2731 -- 21,235 -- 4.14 -- .2563
2877 -- 24,112 -- 4.10 -- .2433
3026 -- 27,138 -- 4.06 -- .2313
3178 -- 30,316 -- 4.02 -- .2203
3333 -- 33,649 -- 3.99 -- .2100
3490 -- 37,139 -- 3.95 -- .2006
3650 -- 40,789 -- 3.91 -- .1918

First section has 70 kg weigh or 700 kg of nitrogen
700 divide by 1550 is .4516 kg per cubic meter.
The other section would also have 700 kg
Edit: made mistake it's 30,000 kg and 1/100th
of this per section. Hmm. "99% of 3000 kg is 2930 kg"
Oh, should been 99% of 30,000 which 29,700.
So 300 kg, so need to times density .4285 to correct.
Drats.
So ground level has .1935 kg/m3 and 40,789 meter has
.0821 kg/m3.
A lot less dense then I thought it would be- the original
numbers were less but now even more the case.
Oh density would increase as temperature drops, at 40,000
even with low lapse rate it should be quite significant.
And 85% of atmosphere is above 40,000 meter.
So the average temperature of entire atmosphere would be very low.
So to be clear those density are not adjusted for temperature. It
would correct if temperature was 283 K

Earth has 1.29 kg per square meter at sea level at 0 C
"At sea level and at 15°C according to ISA (International Standard Atmosphere), air has
a density of approximately 1.225 kg/m3" http://en.wikipedia.org/wiki/Density_of_air
By about 7000 it is about half, or .6 kg per cubic meter
And Density at 16 km is around .16 kg per cubic meter:
http://www.pdas.com/m1.html
Edited by gbaikie, Dec 13 2011, 12:01 AM.
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gbaikie

I was looking for reference for velocity of atmospheric gas:

"Air molecules are never at rest. They undergo constant random thermal motions of a variety of types. The simplest type is that of uniform translation. The mean speed is about 500 m/s which is greater than the speed of sound (340 m/s). Each molecule has three degrees of translational motion: up and down, left and right, and backward and forward.
..
Air molecules take up only 0.1% of the volume they occupy. Thus air is a very sparse gas in which 99.9% of the atmosphere is vacuum. However there are 2.7 x 1019 molecules in every cubic centimeter of air. This high number density coupled with the large translational speeds implies that the air molecules are constantly colliding with each other. The mean time between collisions is 0.2 x 10-9 s. Thus an average molecule undergoes 5 collisions every nanosecond. (One nanosecond corresponds to the time it takes light to travel 30 centimeters in a vacuum.) The mean free path is the average distance traveled by a molecule before it collides with another molecule in the gas. Typically this distance is about 10-5 cm or about 500 to 1000 molecular radii. "
http://www.ems.psu.edu/~bannon/moledyn.html

There is more collisions occurring then I thought.
Not sure what to make of "99.9% of the atmosphere is vacuum"
what is meant by atmosphere- beyond the stratosphere? Surface level?
Venus "proves" one could have 92 sea level atmospheres.
And solid matter is said mostly open space- such as a wall, a brick, steel plating, etc.

One could say it isn't so much a molecule hits another molecule, but rather there so many molecules that they hit the molecule. Or a faster molecule hits less often.
It seems if molecules are traveling with mean velocity of 500 m/s in the higher atmosphere of dwarf, then large quantities of them would reach escape velocity.
I want find reference of molecule speed relative to air temperature. And whether any gases we could use travel at faster velocity at given temperature. I think mono-atomic gases- noble gases like argon do travel faster. Due not having paired rotational energy.

Add:
mean free path

The higher the density of gas, the smaller the mean free path (more likelyhood of a collision). The larger the molecules, the smaller the mean free path. The mean free path depends on the number density of the gas molecules and their size --- and nothing else
At sea level the mean free path of atmospheric gases is about 60 nm
At 100 km altitude, the atmosphere is less dense than where we live at the surface of the earth, and the mean free path is about 0.1 m (about 1 million times longer than at sea level)
http://itl.chem.ufl.edu/2041_u00/lectures/lec_d.html
Above also has graph showing gas velocity, but I don't temperature of gas on graph.

Oh here is calculator for gas velocity:
http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/kintem.html
mean velocity dry air at 260 K is 435.68 m/s
220 K: 400.7 m/s
160 K: 341.7 m/s
Edited by gbaikie, Dec 13 2011, 05:30 AM.
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Chris Ho-Stuart
Dec 4 2011, 11:52 AM
The easiest way to answer the original question is to simply use a Nitrogen/Oxygen mix in the starship atmosphere. Nitrogen and Oxygen are almost totally transparent to infrared radiation, which means that there is no greenhouse effect in the starship atmosphere. The thermal radiation emitted from the surface will pass straight out into space, pretty much the same as if there was no atmosphere at all.

Can we also assume that Nitrogen in addition to being almost totally transparent, also does not transfer energy [lose heat/energy] other than imparting energy through collision. That molecule collision in the atmosphere among exclusively nitrogen gas can impart kinetic energy, but doesn't cause nitrogen emit photons [radiate heat].

And that collisions of nitrogen gas with CO2 [or other gases] could cause these other gases to emit photons.

That we accept that this is true and applicable in an atmosphere:
"Electron impact excites vibrational motion of the nitrogen. Because nitrogen is a homonuclear molecule, it cannot lose this energy by photon emission, and its excited vibrational levels are therefore metastable and live for a long time.
Collisional energy transfer between the nitrogen and the carbon dioxide molecule causes vibrational excitation of the carbon dioxide, with sufficient efficiency to lead to the desired population inversion necessary for laser operation."
http://en.wikipedia.org/wiki/Carbon_dioxide_laser

Or that only way a N2 molecule can transfer any of it's energy is by collision with something other than other N2 molecules.
And if one has a pure nitrogen atmosphere this means nitrogen can only exchange energy with the surface of the planet. And that nitrogen is unable to directly radiate energy into space.
[N2 molecules frantically "trades" kinetic energy with themselves, but the "community" only "exports" energy to the surface- it can not "export" energy to space. It needs a middleman to radiate energy into space.]

This would mean that with pure Nitrogen atmosphere if one control the heat loss of the surface, or controls the interaction of the atmosphere with the surface, you control amount energy needed
to warm the atmosphere. If you have near zero loss of heat from surface, one has near zero loss of energy from the planet.

With nitrogen atmosphere one could ignore the non-existent radiation of the atmosphere to space and focus on the transfer of energy of the atmosphere to the surface.
One might interested what percent of the atmosphere molecule collide with the surface.
How long does it take for an average nitrogen molecule to hit the surface.
Could have a thermal reflective surface?
Could thin layer of cooled air inches above the surface reduce loses- would this be the case "without even trying"- since there is no sunlight heating the ground, the cold ground should "naturally" cause a layer of cool atmosphere near the surface?

Note, other gases or most other gases can also function in similar manner to nitrogen- I am not mentioning them from a desire to simplify. Whereas greenhouse gases are considered, to act differently.
Namely, CO2 is considered as agent that may to some degree take the KE from N2 as well as the surface and emit this energy as radiation. It's possible that CO2 or H2O may in some manner reduce energy loss, but CO2 or H2O at high elevation should be a net loss of energy/heat- they may export energy towards the surface, but are the only exporter of energy to space in the upper atmosphere. A examination of pure CO2 or H2O atmosphere would also be interesting.
It would seem that in such examples, the surface temperature could be more or less irrelevant- "all the action" occurring mostly in the upper atmosphere.

[In the real world one is going to have mixtures/impurities- Oxygen is common though commonly chemically reactive- and so mostly in various compounds, CO2 is common as is water, nitrogen and with Hydrogen and Helium dominating this universe.
NASA is sending a spacecraft [Dawn]to Ceres [and is at Vesta at present time]. Ceres may have a largely H20 atmosphere:
"There are indications that Ceres may have a weak atmosphere and water frost on the surface. Surface water ice is unstable at distances less than 5 AU from the Sun, so it is expected to sublime if it is exposed directly to solar radiation."
http://en.wikipedia.org/wiki/Ceres_%28dwarf_planet%29
So on Ceres' weak atmosphere H2O may be one of major gases. Anyhow it will be 2015 before Dawn reaches Ceres. And perhaps then see up close an atmosphere which could have H2O as main element as the atmosphere.]
Edited by gbaikie, Dec 15 2011, 12:53 AM.
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Chris Ho-Stuart
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gbaikie
Dec 15 2011, 12:45 AM
Can we also assume that Nitrogen in addition to being almost totally transparent, also does not transfer energy [lose heat/energy] other than imparting energy through collision. That molecule collision in the atmosphere among exclusively nitrogen gas can impart kinetic energy, but doesn't cause nitrogen emit photons [radiate heat].

And that collisions of nitrogen gas with CO2 [or other gases] could cause these other gases to emit photons.
In a mixed gas, all the different kinds of molecules end up at the same temperature, as they keeping colliding with each other. As well as this, all the molecules absorb and emit radiation depending on their own radiative properties.

Nitrogen has almost no interaction with radiation in either visible or thermal-IR bands. It does not absorb, or emit, those frequencies; it is transparent. Greenhouse gases are gases that absorb or emit in the thermal-IR bands, which are the bands where you get radiation emitted from a surface such as Earth's, with temperatures up to 320K or so. A mixture of N2 with even a very small amount of a gas that interacts strongly with thermal-IR will be heated up very effectively by thermal radiation. It's only the greenhouse gas that actually absorbs the radiation itself. But thereafter the energy is rapidly shared around with other molecules in the gas, so that the whole gas heats up.
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gbaikie

Chris Ho-Stuart
Dec 15 2011, 04:23 AM
gbaikie
Dec 15 2011, 12:45 AM
Can we also assume that Nitrogen in addition to being almost totally transparent, also does not transfer energy [lose heat/energy] other than imparting energy through collision. That molecule collision in the atmosphere among exclusively nitrogen gas can impart kinetic energy, but doesn't cause nitrogen emit photons [radiate heat].

And that collisions of nitrogen gas with CO2 [or other gases] could cause these other gases to emit photons.
In a mixed gas, all the different kinds of molecules end up at the same temperature, as they keeping colliding with each other. As well as this, all the molecules absorb and emit radiation depending on their own radiative properties.

Nitrogen has almost no interaction with radiation in either visible or thermal-IR bands. It does not absorb, or emit, those frequencies; it is transparent. Greenhouse gases are gases that absorb or emit in the thermal-IR bands, which are the bands where you get radiation emitted from a surface such as Earth's, with temperatures up to 320K or so. A mixture of N2 with even a very small amount of a gas that interacts strongly with thermal-IR will be heated up very effectively by thermal radiation. It's only the greenhouse gas that actually absorbs the radiation itself. But thereafter the energy is rapidly shared around with other molecules in the gas, so that the whole gas heats up.
So I getting that you saying that CO2 absorbs radiation- from other greenhouse gases or the ground.
And that a molecule of N2 can collide with the CO2 and gain that energy.

And if so, I am not sure I can agree.

As I understand it, the N2 molecule can have 3 "types" of energy. The speed the molecule is traveling. The spin of the molecule. And vibration of the molecule.

I am uncertain about the vibration of the N2 molecule- the amount or significance
of any N2 vibration. I don't know how to begin to quantify it.
The spin of N2 molecule I also don't understand very well.

The velocity of the molecules seems the most obvious and most understandable.
It seems to me that the most significant "element" of any gas temperature is the velocity
of the gas molecules. No molecule speed- no temperature.

Now, if CO2 molecule could transfer energy to a N2 molecule, how would this energy be expressed?

Would it increase the N2 molecule's velocity?

I tend to believe it's asymmetrical.

I think a CO2 molecule absorbs a part of infrared radiation. I don't know how long it holds this energy. Or how much energy it can absorb. I think it could release this energy when it's in a collision. And therefore the rate absorption and emission could be related to rate of collisions.

I think another possibility is that CO2 also gets energy from collisions [it apparently does this with a CO2 laser, so it could also do it in a atmosphere] would transform motion of gas molecules into radiate energy or maybe it converts spin and/or the vibrational energy.
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Here now is version 2 of the spreadsheet. To download, click on this link.

This version now considers convection within a grey atmosphere. The file is actually hosted at a free file hosting service, rather than being provided as a post attachment, since it is a bit bigger than the attachment limit. The following changes will be apparent from version 1.

  • On the first worksheet (definitions) we have as before a column marked "Inputs", where there are green cells in which values can be entered; and a column marked "Values", where all values in use are recorded. There is now also an additional column marked "%change", which gives the difference between values recorded in the default example planet and the values calculated. This makes it easy to alter one input, and observe all the consequences on other values.
  • As inputs and values, temperatures are given in Celsius, and pressure in atmospheres, without using additional rows for the SI units actually used in calculations.
  • In the green input cells in the definitions worksheet, you can enter text of form "*###", where ### is a number. This uses the default number multiplied by that number. For example, "*1.1" will use as the input the default value increased by 10%. The resulting actual value used appears in the "Values" column.
  • The formatting of the "Integration" work sheet is cleaned up a lot, to be informative for those who want to follow the integration calculation. It also provides some green input cells where users can override the values carried forward from the definitions sheet; useful (to me!) for debugging the integration; and hence probably useful to others as well who want to delve into the details or make modifications. These input cells should all be cleared for the integration to properly represent the inputs from the definitions sheet. There are warnings supplied, on both worksheets, when such overriding is in place.
  • Calculations for a constant lapse rate throughout the entire atmosphere are still available. As well, there is a calculation of the energy imbalance at each layer of the atmosphere considered. In the troposphere, the atmosphere tends to lose more energy by radiation than it gains. The difference is made up by convection, which supplies additional energy needed to maintain the lapse rate. The integration worksheet gives backradiation, cooling rates and convection at each level of the atmosphere, under the constant lapse rate assumption. A negative cooling rate indicates a breakdown of the assumptions under which the adiabatic lapse rate is stable. This is characteristic of the atmosphere above the tropopause.
  • The integration is now extended with a new calculation that identifies where the tropopause appears, and adjusts the calculation method above that point to be a radiative equilibrium. Rows of the integration worksheet are shaded light blue above the tropopause. Note that the constant lapse rate assumption locates the tropopause differently from the more accurate calculation! This shows up in the shading as well.
  • As for version 1, the lapse rate row also accepts the text "DALR", which uses the dry adiabatic lapse rate as the lapse rate.
  • Some minor changes in appearance; fonts, layout, colors, etc. (This version should load better into older versions of Excel.)
  • There are changes in the internal coding, which do not materially alter the behaviour other than what is mentioned above; with the exception of the bug fix, mentioned previously for calculating the effective emission temperature.


I'm doing a bit of double checking that the coding is all correct; but in any case, here it is. If anyone finds bugs or errors I'll be very glad to hear of it.



Edited by Chris Ho-Stuart, Dec 19 2011, 02:09 AM.
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gbaikie

Hi Chris looking at revised program.
Earth and Venus are as though there was no sunlight and is heated from surface. Correct?
And it seem you have greenhouse effect gases, but how those value changed?
Never actually understood got you meant grey gases, maybe this is my problem
Can I see for example what 50% humidity does to affect dwarf temperature.
Or these greenhouse effect sort of like place values and work in progress?

edit: In readme you mention darker orange having values to do with greenhouse-
I see orange on definition page and i guess orange on integration page are
slightly darker- is that orange on integration meant by darker orange?
Edited by gbaikie, Dec 19 2011, 07:26 AM.
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Chris Ho-Stuart
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gbaikie
Dec 19 2011, 07:20 AM

Earth and Venus are as though there was no sunlight and is heated from surface. Correct?


Correct. It is important to recognize that this spreadsheet is not intended to represent the planets accurately, but to represent your space ship example. It does not deal with sunlight at all. In Venus in our solar system, there is plenty of solar heating within the atmosphere, which alters the temperature profiles. The physics of how the greenhouse effect works is unchanged; but there is more going on than only a greenhouse effect. Your star ship problem is a useful simplification in which other complications can be ignored.

You should think of the Venus example in the spreadsheet as being a bit like Venus used as a starship. I should add this to the readme sheet!

Quote:
 

And it seem you have greenhouse effect gases, but how those value changed?
Never actually understood got you meant grey gases, maybe this is my problem


I am looking at a gas which absorbs all frequencies equally well. That's what "gray" means. For the starship, the atmosphere can even absorb shortwave without complicating things at all, because there is no incoming radiation to worry about.

In fact, solar absorption within a real planet's atmosphere does not make much difference as long as the solar energy input to the atmosphere is not enough to prevent convection. In that case, you still have a temperature profile determined by the adiabatic lapse rate, and you can calculate the flux of radiation from the surface up through the troposphere just as I have done in the spreadsheets; although with a real gas you need to consider different frequencies separately. I will get to that in version 3. That's where you should see the difference between grey gas and real gas more clearly.

Above the troposphere things look very different. Here the equilibrium lapse rate is determined by radiation only, without any convection. For example solar absorption in Earth's stratosphere causes temperature to increase with altitude. The effect of the stratosphere on radiation up from the surface, however, is negligible, because this part of the atmosphere is so thin. The "effective radiating altitude" on Earth is well below the stratosphere.

Quote:
 

Can I see for example what 50% humidity does to affect dwarf temperature.
Or these greenhouse effect sort of like place values and work in progress?


I'm not planning to consider humidity at all. The thing about humidity is that it changes the adiabatic lapse rate, due to the effects of condensation in rising air. To consider that, you need to go to a more advanced model, such as MODTRAN. You can play with MODTRAN at this link.

What you CAN do with the spreadsheet is alter the lapse rate, and see what impact that has on things. A weaker lapse rate will give a weaker greenhouse effect.

What that means is humidity plays a double role. It increases absorption (which strengthens the greenhouse effect) and it reduces the lapse rate (which weakens the greenhouse effect). As it turns out, the strengthening effect is greater than the weakening effect; but there's no quick and easy law to show it has to be that way. It's a matter of detailed observation, or else of detailed calculations -- both of which confirm that the net effect of greater humidity is a stronger greenhouse effect.

Try this. In the spreadsheet, enter "Earth" as the example. This will use an absorptivity co-efficient or 171.95, which was simply the value chosen to give about the right value for emission to space.

Now enter "DALR" in the lapse rate cell (row 18). This uses a lapse rate of about 9.76, rather than the 6.5 used by default.

You can see the consequences in the %change column.

The lapse rate has increased by just over 50%. The emission at the top of the atmosphere (row 35) has deceased by nearly 5%. That is, there is a larger difference between the surface temperature and the temperature of emission to space. The greenhouse effect is now stronger; up 9.2% from 33.85 degrees to 37 degrees.

I've just noticed that row 20 should be retitled from "Atmosphere total height" to "Total height for all-troposphere case", or better, just left out.

Quote:
 

edit: In readme you mention darker orange having values to do with greenhouse-
I see orange on definition page and i guess orange on integration page are
slightly darker- is that orange on integration meant by darker orange?


Oops. That's out of date. There is no darker orange now in version 2. I'll update the readme sheet appropriately. Thanks!

Cheers -- Chris
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Chris Ho-Stuart
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I've been busy and had limited time to work on this; but for the time being here's a slightly updated version 2.2.

Download link: Starship-v2.2.xls. Minor clean up applied.

My major reference for much of the theory I am applying is Principles of Planetary Climate by Ray Pierrehumbert. The integration sheet now includes also an additional column for an alternative calculation of the all-troposphere grey atmosphere using evaluation of a direct integral. There's a comment on the page describing how this works. It gives the same result as my original more direct layer by layer method, which is reassuring that I have the maths correct.

There are a couple of interesting points. For an atmosphere that is optically thick (a high k value, as is used for the Dwarf sample atmosphere) there is a theoretical dividing line between a deep troposphere and a shallow troposphere with the gamma value of the atmosphere at 4/3

Above 4/3, and the tropopause is low in the atmosphere. This is the expected case, with the bulk of the atmosphere as nitrogen and oxygen, which are around 1.4.

Try this. Alter the value for gamma on the first sheet, using the Dwarf example. By default, it is 1.4. Try entering 1.32, and then 1.34, and observe the sudden change in the height of the tropopause. This is another indication I am on about the right track; this is a theoretically expected behaviour.
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gbaikie

"Try this. Alter the value for gamma on the first sheet, using the Dwarf example. By default, it is 1.4. Try entering 1.32, and then 1.34, and observe the sudden change in the height of the tropopause. This is another indication I am on about the right track; this is a theoretically expected behaviour. "

Ok, so atmosphere lowers and requires more energy input.
I have no idea why. Can't remember what gamma is. This isn't heated by sunlight, but bond albedo- what surface is made of- should still a have affect- is that what gamma is.
If want lots people turning it knobs, maybe easy way to look definitions.
Ok look it up- does that mean if used helium or hydrogen [gases with high heat capacity] one lowers gamma. Oh, Hydrogen doesn't have high specific heat- but argon does. And Co2 is lower. Or does this have nothing to do gases and mainly with lapse rate?
Anyhow play around it bit
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