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I'm Number 44

May I ask a question? I stress that I am not trying to do any original research, but only want to improve the GW article by explaining what is fundamental to the AGW hypothesis. I don't think the current article really explains it very well.

My question: I did some Googling and the Stefan-Boltzmann equation (or rather a derivative of it) seems to be fundamental. But there are two versions of it, as follows:

• S0/4*(1-alpha) = e*sigmaT^4
• S0/4*(1-alpha)+G = sigmaT^4

where alpha is albedo, S0 is a constant solar radiative flux (units W/m^2), T is temp in K, and sigma is a constant. The two sides of the equation both have units W/m^2.

In the first equation e is 'emissivity' which is unitless and is the ratio of energy radiated by a particular material to energy radiated by a black body at the same temperature. I think of it as an 'underpants factor'. You have a black body throbbing with radiation, which will cool unless you keep it warm. So you put some underpants on it, to keep the cold out, i.e. stop it radiating so much. Hence CO2 and water vapour are like thermal underwear to keep the earth warm (if e is 100%, the temperature is about -18 deg C, for if you solve for e with current temperature, assume 15 deg C, you find e is about 60%). I am assuming e is constant whatever the temperature for exactly the same material, is that correct? In reality e will change as the material of the atmosphere changes (more CO2, or more vapour).

In the second equation G is a number, units also W/m^2, which is a measure of the influence a factor has in altering the balance of incoming and outgoing energy in the Earth-atmosphere system. If you solve for G for 15 deg C, you get about 150 W/m^2.

My puzzle is whether G is also constant, if for other reasons (e.g. change in solar radiation, change in albedo) the temperature changes. Intuitively it won't be constant. Why represent it this way?

Apologise if I have misunderstood, and please correct any mistakes (I am quite new to this, but it is interesting). Again, I am not trying to do any research, just finding out some facts that could be put into layman's language and hopefully into the article. I think thermal underwear is a better analogy than greenhouses, e.g. HistorianofScience (talk) 11:52, 10 January 2010 (UTC)

I really don't think all this talk of underwear and throbbing bodies is appropriate. Please keep such impulses to yourself. Short Brigade Harvester Boris (talk) 19:24, 10 January 2010 (UTC)

You are the Walrus and you talk about throbbing bodies? --Stephan Schulz (talk) 19:28, 10 January 2010 (UTC)

My personal preference is for exploding underpants, but they banned them :-( William M. Connolley (talk) 19:31, 10 January 2010 (UTC)

Actually it was Long Johns I was looking for but couldn't find the category until now. Anyway I prefer the leather ones. Seriously, can anyone answer my question above ? HistorianofScience (talk) 19:37, 10 January 2010 (UTC)

I think you're looking for the one-sentence summary of the greenhouse effect, which is the earth is warmer with an atmosphere, because it receives heat from both the sun and the atmosphere. Your G, above, is the heat from the atmosphere. Put that way, it becomes obvious that G is not contstant, in time (long or short term) or space William M. Connolley (talk) 20:15, 10 January 2010 (UTC)

Thanks for the explanation but I'm still not sure I understand. Suppose we turned off the sun like an electric light. Then the earth no longer receives heat from the sun. Does it still receive heat from the atmosphere?

Until the atmosphere cools down, yes. Then no William M. Connolley (talk) 20:41, 10 January 2010 (UTC)

Surely not. Isn't the correct explanation that the atmosphere is acting like a blanket around the earth, preventing it from cooling as fast as a black body would?

No. You need to read what I wrote and understand it. Until you do, you will get nowhere William M. Connolley (talk) 20:41, 10 January 2010 (UTC)

So it's not heating the earth, it's preventing it from cooling as fast as it would in the black body case.

No William M. Connolley (talk) 20:41, 10 January 2010 (UTC)

And the heat energy it is losing should be identical, at the instant the sun turns off, to what it was receiving from the sun. If that is correct, G is the difference between the W/m^2 that the black body would emit, and the W/m^2 actually emitted. No? HistorianofScience (talk) 20:35, 10 January 2010 (UTC)

As a very very broad-brush approximation, the atmosphere receives no heat directly from the sun, since it is transparent to SW. The atmosphere is heated by LW from the earth (which itself, of course, is ultimately sourced from SW from the sun absorbed at the earth's sfc. Can you cope with maths? If you can, this is easily written down - indeed it is somewhere, I only need to point you at it William M. Connolley (talk) 20:41, 10 January 2010 (UTC)

I can cope with maths. HistorianofScience (talk) 20:46, 10 January 2010 (UTC)

Would it be more like those rude transparent underpants then? HistorianofScience (talk) 20:50, 10 January 2010 (UTC)

Fine. Writing it all out is quicker than finding it, so... simplifying, the sun shines 4S units on the uniform earth (and since the area of a circle is 1/4 the area of a corresponding sphere the 4 drops out), which is a black body (forget albedo for the moment, it makes no real difference). The atmosphere is transparent to SW, and can be considered as a single layer not in conductive contact with the surface. There is no diurnal cycle, all is averaged out, all is in equilibrium.

So at the sfc (with atmosphere) we have the following equation:

S + G = rT^4

(the surface is black, captures all solar SW and transforms it into LW which it re-radiates) and G is the radiation from the atmosphere. Meanwhile, in the atmosphere,

2G = rT^4

(the atmospheric layer is totally opaque to the surface LW, is itself isothermal, and being a layer radiates both up and downwards). As it happens G = r(T_a)^4 but we don't care about that for tihs analysis.

Hence, S + G = 2G, hence S = G, hence T_1 = (2S/r)^0.25. Meanwhile, in the absence of the atmosphere, we clearly would have T_2 = (S/r)^0.25. T_1 > T_2 (by a factor of 2^0.25) and (T_1 - T_2) is the greenhouse effect.

William M. Connolley (talk) 21:02, 10 January 2010 (UTC)

Also, this and the linked also refers, but is harder William M. Connolley (talk) 21:12, 10 January 2010 (UTC)

Thanks (appreciated).

How do you get from S + G = rT^4 to 2G = rT^4 without the assumption that S=G (which you later derive). The intervening bracketed "the atmospheric layer is totally opaque to the surface LW, is itself isothermal, and being a layer radiates both up and downwards). " seems like an explanation, but I didn't understand it.

The atmospheric layer absorbs all the surface LW, which is the rT^4. It is in equilibrium. It radiates , equally, upwards and downwards, G. So it gains rT^4 and loses 2G, so those two are equal William M. Connolley (talk) 22:05, 10 January 2010 (UTC)

If the earth receives all the SW, then reflects it back to the layer, why do you say earlier that the layer heats the earth? Why isn't it the other way round.

No, it doesn't reflect the SW - it is assumed black. It absorbs all the SW and re-radiates it as LW. Yes, "the earth heats the atmosphere" can also be regarded as true William M. Connolley (talk) 22:05, 10 January 2010 (UTC)

Thanks for taking the time. HistorianofScience (talk) 21:51, 10 January 2010 (UTC)

Thanks for your explanation which I am afraid I still don't really follow. I don't see how 'the earth heats the atmosphere' and 'the atmosphere heats the earth' can both be true.

• If it is true that none of the SW affects the atmosphere and that the earth reflects LW as a result, then the earth is the cause of the warming. Indeed couldn't we ignore the sun entirely, turn it off and install a large amount of patio heaters all round the earth pointing upwards at the sky: this would have the same effect.
• I didn't understand the both directions stuff "It radiates , equally, upwards and downwards". Maybe it does, but, unless there is a net outflow of LW heat energy from the earth to balance the SW coming in, the temperature of the earth will not be at equilibrium. A net flow can only be in one direction, by definition.
• The net outflow from the earth must be exactly balanced by the outflow at the edge of the atmosphere, otherwise the atmosphere would continue heat up. The atmosphere is hotter than the earth's surface because the outflow from the atmosphere has to occur at a higher temperature than the same outflow from the earth. So, the earth is the 'efficient cause' of the heating of the atmosphere, surely. HistorianofScience (talk) 20:05, 12 January 2010 (UTC)

You've dropped down into words (some of which are wrong: as I've said before, Earth doesn't reflect LW. It is black in LW). It is clearer if you use maths. Or pix, perhaps. Lets try:

                          |
                   G ^    V Solar input. (4S ->) S
                     |
                ----------------------------
                Atmosphere. Emits G, up and down, thermal radiation. Absorbs S+G.
                ----------------------------
                     |    |
                     |    V Solar straight through - atmos transparent, still S
                   G V
                                      ^ S+G
                                      |
                -----------------------------
                Sfc. Abs S(SW)+G(LW). Thus emits (S+G)(LW). Thus S+G = rT^4

Clear now? William M. Connolley (talk) 20:13, 12 January 2010 (UTC)

Sorry, apart from the bit about not reflecting LW (that seemed picky, unless I misunderstood it), which of my claims was wrong? I said that the net outflow from earth to atmosphere has to be upwards. And that this outflow has to be exactly equal to the outflow from the atmosphere into space. Your diagram is incomprehensible. And what about Greenhouse effect where it says "Radiation is emitted both upward, with part escaping to space, and downward toward Earth's surface, making our life on earth possible." This is entirely wrong isn't it? It gives the impression that we are safe because only part of the radiation escapes to space, but the rest is trapped behind & keeps us snug and warm. The reality is that the net outflow from the earth has to be exactly balanced by the outflow at the edge of the atmosphere into space. Otherwise the atmosphere would keep on heating up until equilibrium was restored. HistorianofScience (talk) 20:31, 12 January 2010 (UTC)

The unclearness of the diagram is the omission of the causality. You have the atmosphere radiating G downwards, e.g. Yes but where does the G come from? If we were to start with turning on the sun like a switch, at that instant there would be no G from the atmosphere. In which case the first thing to hit the earth would be S. Then earth would emit (not reflect) S. With no G. HistorianofScience (talk) 20:43, 12 January 2010 (UTC)

Like I say, you need the maths and the pix, not the words. The diagram is a steady state. We can re-draw it, if you like, for an Earth at 0K above which the sun has just been turned on:

                          |
                   0 ^    V Solar input. (4S ->) S
                     |
                ----------------------------
                Atmosphere. At 0K. Doesn't radiate.
                ----------------------------
                     |    |
                     |    V Solar straight through - atmos transparent, still S
                   0 V
                                      ^ 0
                                      |
                -----------------------------
                Sfc. Abs S(SW)+0(LW). At 0K. Doesn't radiate.

So now in this pix you see that the atmos is still in equilibrium, at 0K, but the Earth isn't: It is absorbing S but radiating nothing. So it will warm up, yes? So after a bit we get something like this:

                          |
                   0 ^    V Solar input. (4S ->) S
                     |
                ----------------------------
                Atmosphere. At 0K. Doesn't radiate.
                ----------------------------
                     |    |
                     |    V Solar straight through - atmos transparent, still S
                   0 V
                                      ^ G_T
                                      |
                -----------------------------
                Sfc. Abs S(SW)+0(LW). Has warmed up somewhat, to T. Emits rT^4, call this G_T.

So now the sfc has warmed up somewhat, so it is emitting G_T in the LW. Now the atmosphere isn't in balance: it is absorbing G_T but emitting nothing, since it is at 0K. So it will warm up. So it will start emitting downwards an warm further. And eventually we end up with the equilibrium solution William M. Connolley (talk) 21:47, 12 January 2010 (UTC)

Sorry for any inconvenience. — the Man in Question (in question) 10:21, 14 January 2010 (UTC)

PD initial thoughts

Misplaced Pages:Arbitration/Requests/Case/Climate change/Proposed decision looks about as stupid as I'd expected, though not as stupid as some others expected. The failure of any meaningful remedies for admin involvement, which wrecked the CC probation, is a flaw. But to be fair, the PD is capable of becoming moderately sensible with the correct votes. The real test is who votes for that William M. Connolley (talk) 11:15, 23 August 2010 (UTC)

Wikipedia_talk:Arbitration/Requests/Case/Climate_change/Proposed_decision#Statement_by_WMC, in case you missed it William M. Connolley (talk) 22:43, 26 August 2010 (UTC)

Now Wikipedia_talk:Arbitration/Requests/Case/Climate_change/Proposed_decision/Statements#Statement_by_WMC I think William M. Connolley (talk) 10:51, 3 November 2020 (UTC)

PD continuing thoughts

FoF thoughts

Misplaced Pages:Arbitration/Requests/Case/Climate change

This arbitration case has been closed and the final decision is available at the link above. The following is a summary of the remedies enacted: