Earth's Climate Explained

A simple and synthetic explanation by Glenn Tamblyn

Atmospheric Physics is a tricky subject, and sometimes even the experts miss some details. Figure above, the basic feature that controls Earth’s temperature, the temperature lapse rate. From a paper by Glenn Tamblyn

I found by chance an extremely well written text by Tamblyn on Quora. In my experience, even people who are supposed to know about climate change, sometimes miss some basic elements of the physics involved. So, I suggest that you take a look at this text — you might learn something you didn’t know. I did. For instance I had missed how the surface temperatures of Venus, Earth, and Mars are related to the respective heights of the effective emission altitude. Amazing! See also a more detailed paper by Tamblyn

Glenn Tamblyn is not a climate scientist, but a mechanical engineer expert in climate. It may be the characteristic of coming from a different field that makes him able to express some concepts so clearly. He is, among other things, part of the Skeptical Science Team. I haven’t been able to find his email to ask his permission to reproduce this text, but since it was published in a public site I think it is not covered by a copyright, and I am sure he won’t object to seeing it published here. If some readers have a contact with him, please let me know in the comments

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By Glenn Tamblyn

The greenhouse effect (GHE) depends on 3 things.

1. Radiative balance and required radiation temperature.

2. Effective emission altitude

3. Atmospheric Lapse Rate.

Radiative Balance.

The earth receives energy from the Sun. This arrives at the Earths orbit with a strength of 1361 watts/m^2 of the earths frontal area. Around 30% of the sunlight arriving is reflected by clouds, the surface and the atmosphere. This doesn’t contribute to the planets energy balance. The remainder is absorbed. If the earth just absorbed this energy and couldn’t get rid of it again the planet would just warm and warm. Radically! This is enough heat to boil the oceans dry in less than a 1000 years if the planet couldn’t get rid of it.

But get rid of it it does, by radiating the energy back out to space as infrared light. If these two heat flows balance, the amount of heat here on earth doesn’t change and climate is pretty stable. This is a dynamic stability however, the amount of heat arriving from the sun varies over the year, how reflective the earth is varies, and the suns output varies very slightly over a roughly 11 year cycle. But these are all cycles and they balance out.

In order to radiate enough energy the earth, or importantly, the right part of it, needs to be at the right temperature. The hotter it is the more it radiates. So if the earth isn’t warm enough, it isn’t radiating enough, things are out of balance, and it warms until it is in balance. The converse applies if it is too warm, it radiates too much and cools. So with the seasonal cycles, it is always ‘seeking’ to come back into balance.

So how warm does it have to be? Since the radiation comes from the entire surface, the amount that needs to be radiated per m^2 is the ratio of the planets frontal to total surface area - 1/4. So it needs to radiate 1361 *0.7/4 = 238 watts/m^2 from each square meter of the surface, on average. Although different parts of the surface are at different temperatures, the average will end up being 238.

So what temperature does something need to be to radiate 238 watts/m^2, We can work this out from an equation in thermodynamics, the Stefan–Boltzmann law - Wikipedia. When we solve this equation to work out the temperature we get 255 degrees Kelvin, or -18 Celsius.

The average temperature should be -18 C, but actually the average surface temperatures is more like +15 C - 33 degrees warmer. Something is keeping the earth much warmer than it should be. Note I slipped in the word ‘surface’ there. This matters in the next part.

Effective Emission Altitude.

Greenhouse gases absorb infrared radiation (IR). So the IR that is radiated up from the surface can be partly absorbed by those gases in the atmosphere. How partly? Around 90% of the IR that is radiated from the surface doesn’t get out to space, not directly. This energy is absorbed and spread around all the molecules in the atmosphere, it is thermalised. The 10% that does get out is in wavelengths where the GH molecules aren’t active.

But it doesn’t end there. GH molecules can and do also radiate IR. Randomly, in all directions. So only some of this reradiation is radiated up. And all their reradiation is in the wavelengths that they absorb in so none of this reradiation can get to space, it is reabsorbed by other GH molecules, or if close to the ground, by the surface. So it still isn’t getting out to space. So how do we solve radiative balance?

When the atmosphere is like this, absorbing virtually everything, it is said to be optically thick. However, as we go higher in the atmosphere its density drops and drops, the number of all molecules in a volume of air is lower, and the number of GH molecules is also lower. Eventually, high enough, the number of GH molecules has dropped low enough that some radiation no longer gets absorbed. Radiation upwards can now start to get out to space. The atmosphere is becoming optically thin at this altitude. However this altitude where the transition starts varies significantly for different wavelengths of IR. Because the GH molecules have different likelihoods of absorbing (and thus also emitting) at different wavelengths.

So progressively, as we go up, more and more wavelengths start to be able to escape to space, until essentially all of it can. This was my reason for referring to the surface earlier. Most of the IR to space doesn’t come from the surface, it comes from higher in the atmosphere. Although the height of this transition varies with altitude, we can still meaningfully talk about the average altitude where the emissions arise - the effective emission altitude. On Earth that is about 5 km up. And this is determined by the concentration of GH gases in the atmosphere. With more GH gases the average altitude is higher.

So, for radiative balance, since the average height that emissions are coming from is 5 kilometers, and the intensity of emission depends on temperature, this 5 km altitude needs to be at the right temperature to keep things balanced. It needs to be at -18 C. And it is. The average surface temperature is +15 C and air temperatures drop by 6.5 C for every km that we go up, so the 5 km layer is at 15 -(6.5 * 5) = -18, close enough.

So the earth is radiating to space correctly. It is radiating as a -18 C body. Just that it isn’t coming from the surface. Is this coincidence? No.

Atmospheric Lapse Rate.

The lower atmosphere cools as we go up due to the Environmental Lapse Rate - Wikipedia has a discussion here. Lapse rate - Wikipedia. This is driven by vertical air movement and condensation. And the atmosphere cools at -6.5 C/km. Not just to the 5 km level but above that as well. This is an active vertical mixing process that drives this. So it moves heat up and down to produce a 6.5/km gradient AND a temperature at 5 km of -18 C because radiative balance forces that. So this mixing process drives temperatures in the rest of the air column to have a value relative to the 5 km level. Meaning the surface temperature is 15 C. And the temperature at 10 km is around -51 C.

This is the GHE in a nutshell. Radiative balance drives the emission temperature, GH gas concentrations determine what altitude will be at that temperature, and the mixing engine of the Lapse Rate sets the temperatures in the rest of the air column.

This is all averages, there are still cycles, local variations, the lapse rate differs from place to place depending on how much condensation is occurring, and the effective emission altitude varies a bit from place to place, particularly driven by variations in the water vapour content of the air. But the big picture looks like this.

So, if we were to increase the concentration of GH gases so the average altitude of transition to optical thinness was now 5.5 km up what would happen? 5.5 km is at -21.25 C, not warm enough to generate enough radiation to space. The earth isn’t in balance. What now happens is heat builds up in the system. At first a lot of it has to go to warming the oceans, but eventually the 5.5 km level has to warm to 18 C to restore radiative balance. And the Lapse Rate engine adjusts the rest of the air column around this and the surface temperature is now 18.25 C. Global Warming (there are some other details I have left out, particularly that the size of the Lapse Rate decreases because in a warmer world there is more evaporation and thus more condensation).

The crux of it is that the height difference between the surface and the effective emission altitude is required to have a GHE. On Earth that is 5 km. So Earth is the first case of a GHE.

Venus is our next case. It’s atmosphere is 95% CO2 with masses of clouds at the top and 95 times the mass of Earths atmosphere - at the surface it is as much a thin liquid as a thick gas. So it’s emission altitude is over 50 km above the surface. And it’s Lapse Rate is higher - 10.2 - 10.4 C/km - since there is no water and no condensation. So it’s GHE produces a temperature difference at the surface of more than 500 C. The surface temperature is hot enough to melt lead because the emission altitude is so high.

Next is Mars, another case. Although its atmosphere is also almost all CO2, it is so thin that its emission altitude is very low. Mars has a GHE of 6 C or so.

Next is Saturns moon Titan, which has a GHE and an anti-greenhouse effect. Anti-greenhouse effect - Wikipedia. This happens when most of the sunlight absorbed by a planet is is absorbed higher in the atmosphere but the emission altitude is lower than that. Titan has a high haze layer, then GH gases in its atmosphere. The GHE would raise the surface temperature by 21C but the anti-GHE lowers this by 9 C so the surface is actually 12 C warmer. Methane is the main GH gas on Titan,but in cold, reasonably dense atmospheres you can also get absorption and emission occurring when molecules that aren’t normally GH gases are colliding - nitrogen and hydrogen in this case.

Other planets have atmospheres influenced by lapse rates, that is universal if there is an atmosphere where vertical circulation can occur while the atmosphere is optically thick. In contrast in thin atmospheres that are also optically thin, mixing is rarer and radiation dominates the formation of the temperature profile.

Planets around other stars are expected to have GHE’s if they meet the right conditions. Atmospheres where the emission and absorption altitudes differ and mixing can occur. So the universe should have gazillions of cases of the GHE.