Saturday, October 17, 2020

How Greenhouse Gases Heat the Surface Revealed

 Over many years Eli, your humble Bunny, has explained things about the Greenhouse Effect in words that even Mom Rabett of blessed memory would understand. The Cyanobacteria's Friend would say, the secret is at the top of the atmosphere where the outgoing radiation to space must match the incoming from  the sun and that means as greenhouse gases increase and the level of the atmosphere from which emission can reach space increases and colder, the surface must warm.

But how does the surface warm and in particular how does backradiation play a role. Thanks to Twitter,  Eli has found a splendid argument which he will put into these margins. Might even get published.

Dear friends, let us start. We got the sun. Let's ignore the absorption of sunlight in the atmosphere, the Foote effect, and say that it all hits the ground and is absorbed

Greenhouse gases prevent IR radiation from the surface reaching space directly

The atmosphere is transparent in the visible, but, there are many regions of the IR where absorption is high, including those regions where CO2 and H2O absorb. A handy dandy number to carry about is that at the surface the average distance light can travel in the CO2 spectral region is 10 meters (or about 35 feet for you unethical customary unit users).

Energy does not stay in the molecule that absorbs the IR photon, to be re-radiated later. This is not so, it is quickly degenerated to thermal motion (translation, zipping about) via collisions. Thermalization requires about a 10 μs at atmospheric pressure. So where does the emission come from the bunnies ask?

Well, there is a considerable thermal energy at room temperature, and even much lower. True this average energy is low compared to even the lowest vibrational excitation of CO2 (which would be ~1000 K), but it is enough that a small, but significant fraction of CO2 molecules are always found in excited levels which can emit in the IR (about 6% at room temperature).

Eli has explained this many times before. The two new things are to recognize that 

1. The amount of heat passing from one layer to the next has to be equal to the amount of heat absorbed from the sun and

2. the number of layers the heat must pass through depends on greenhouse gas concentration and ability to absorb IR.  Another way of thinking about this is that the IR energy emitted from the surface has to undergo a number of absorption/emission cycles before reaching space.

The figure below idealizes this showing that if there are effectively n layers each with an emissivity ε, that then the temperature at the bottom increases as the fourth root of n.  when you add up the contribution of all the layers. We also know that the temperature of each layer decreases linearly with altitude for everything except water vapor where it decreases much faster because of condensation.

Remembering that q is both the heat absorbed from the sun and the heat radiated to space and substituting q= εnσTn⁴ where To is the temperature at the surface (say 287 K) and Tn the effective radiative temperature at the top (~255 K) we get n~ 4 after estimating that the altitude whose temperature is 255 K is between 5 and 6 km, where the density is approximately 40% of that at the surface. 

So increasing greenhouse gas concentrations increases the number of layers, and decreases the separation between them which directly increases the surface temperature as n grows.

This is the mechanism by which the greenhouse effect warms the surface

If you are going to do a detailed calculation of the thermal structure of the atmosphere level by level, the separation between levels will depend on frequency as will the relative strength of different greenhouse gases. One of the tricky things is that greenhouse gases radiate at discrete fixed frequencies and the surface and clouds IR emit and absorb like black bodies, but more of that later.

So simply measuring the total absorption of a greenhouse gas at different frequencies in the atmosphere is not very useful.  

Total absorption throughout the atmosphere does not account for the average distance that an IR photon can travel before being absorbed and thus the number of layers. For example, if the distance at 14 microns IR photon travels before being absorbed in 1% water vapor is 1 km, and that for 400 ppm CO2, 10 m, then CO2 would have much more of a warming effect on the surface at 14 μ but both would absorb 100% of the IR over the path from ground to space (and how).

Tomorrow, the concept being elastic and Eli tired, the Bunny will show how using the average distance that IR can travel at different frequencies helps understand the roles that different greenhouse gases play.

9 comments:

Historyscoper said...

This kind of analysis is way out in left field.

[[the secret is at the top of the atmosphere where the outgoing radiation to space must match the incoming from the sun.]]

Zonk! It's impossible for a match to exist after massive amounts of incoming radiation are turned to work to create winds and weather after heating the surface and being conducted and convected back toward space, shedding their heat as they go.

[[the level of the atmosphere from which emission can reach space increases and colder, the surface must warm.]]

Zonk! Radiation laws are purely local, and there is no way that the sky can tell the ground what to do. Surface radiation is emitted based solely on the temperature created by absorbing solar radiation.

[[Well, there is a considerable thermal energy at room temperature, and even much lower. True this average energy is low compared to even the lowest vibrational excitation of CO2 (which would be ~1000 K), but it is enough that a small, but significant fraction of CO2 molecules are always found in excited levels which can emit in the IR (about 6% at room temperature).]]

Zonk! The Earth's surface temperature range is -50C to +50C, and the surface radiates Planck (blackbody) radiation on a power-wavelength curve based solely on its temperature. Too bad, CO2's absorption/emission wavelength of 15 microns has a Planck radiation temperature of -80C, the same as dry ice, which is outside this window, meaning that CO2 can't even interfere with surface radiation processes. 15 microns is closer to microwave, which isn't even heat.

Therefore CO2 can't reheat the Earth's surface with its own heat. Only the Sun heats the surface, and the atmosphere just helps cool it via radiation, conduction, evaporation, and convection, with the trace CO2 component just going along with the 99.6% of non-CO2 gases.

-80C isn't heat and can't melt an ice cube any more than a wet match can light a cigarette.

Wake up that you're preaching a fake physics hoax and master real radiative physics with my free online lesson:

http://www.historyscoper.com/thebiglieaboutco2.html

- T.L. Winslow

Max Planck's ghost said...

Max Planck's ghost
Did he just say "Radiation laws are purely local,?"

Thermal radiation is generally a long-range phenomenon. The mean free path for a photon may be as short as 10^-10 m (e.g., absorption in a metal), but can also be as long as 10^+10 m or larger (e.g., the sun's rays hitting earth).
Should have done your homework before commenting.

EliRabett said...

A good rule for physicists is never to argue with Max, as he points out that electromagnetic radiation and gravity are both long range forces.

OTOH Zonker is ripe for derision. Energy can neither be created nor destroyed, but it can be transformed. It's called conservation of energy. Sunlight transformed into heat, heat into wind, wind back again to heat, and then radiated into space

THE CLIMATE WARS said...

Eli should also remind the bunnies to look up from the grass frequenly. for liquid water is a powerful good absorber around 10 microns, and the first cloud droplet a thermal IR photon sees may be its last.

Since most climates feature millimeters or more of precipitable water overhead, the weather has a big say in the free path



EliRabett said...

You need to adjust your high resolution FT

http://rabett.blogspot.com/2020/10/no-overlaps.html

Chris A. said...

@Historyscoper

"Only the Sun heats the surface, and the atmosphere just helps cool it via radiation, conduction, evaporation, and convection,[...]"

Which means, that the transport of energy away from the surface is on average MUCH slower than the transport of energy to the surface, which is near to light speed, since the surface is fed it's nergy by the sun.

Combine this simple fact with the other simple fact that the laws of thermodynamics force the surface to get into steady state regarding incoming and outgoing energy, and you will find that there MUST be a higher temperature compared to a surface that could radiate energy to space freely.

So the cause of this higher temperature must be, whatever prevents the free radiative exchange from surface and space. Let's look what we have there... oh! What? Wait...

Why should anybody take a sophisticated "radiative physics" lecture from someone who can't even grasp much more fundamental physics to start with?

Barton Paul Levenson said...

H: Zonk! It's impossible for a match to exist after massive amounts of incoming radiation are turned to work to create winds and weather after heating the surface and being conducted and convected back toward space, shedding their heat as they go.

BPL: The power input to the Earth has to match the power output. If there is more coming in, the Earth heats up indefinitely. If there is more going out, it cools down to absolute zero.

H: Zonk! Radiation laws are purely local, and there is no way that the sky can tell the ground what to do.

BPL: It emits radiation which warms the ground.

H: Surface radiation is emitted based solely on the temperature created by absorbing solar radiation.

BPL: No, there isn't enough absorbed from the sun alone to account for the surface temperature. Do the math.

H: Zonk! The Earth's surface temperature range is -50C to +50C, and the surface radiates Planck (blackbody) radiation on a power-wavelength curve based solely on its temperature. Too bad, CO2's absorption/emission wavelength of 15 microns has a Planck radiation temperature of -80C, the same as dry ice, which is outside this window, meaning that CO2 can't even interfere with surface radiation processes. 15 microns is closer to microwave, which isn't even heat.

BPL: Wien's law only applies to the peak of the curve. You can't take pieces out of the spectrum and assign a Wien's law temperature to them.

H: Therefore CO2 can't reheat the Earth's surface with its own heat. Only the Sun heats the surface, and the atmosphere just helps cool it via radiation, conduction, evaporation, and convection, with the trace CO2 component just going along with the 99.6% of non-CO2 gases.

BPL: Wrong again. See above.

H: -80C isn't heat and can't melt an ice cube any more than a wet match can light a cigarette.

BPL: Your temperature is not derived legitimately. See above.

H: Wake up that you're preaching a fake physics hoax and master real radiative physics with my free online lesson:
http://www.historyscoper.com/thebiglieaboutco2.html

BPL: If you have proof it's a hoax, produce it. If you have no proof, STFU.

Alan said...

Eli, I believe your analysis is flawed. Your equations for energy transport between layers neglect convection. However, in the troposphere convective heat transport is dominant over radiative transport, which is why the temperature gradient closely follows the linear adiabatic lapse rate.

Of course radiation is dominant for heat transfer to space (the only factor, in fact). This occurs around the height where the atmosphere becomes optically thin.

The end result is that it doesn't much matter what the mean free path is for IR radiation near the surface -- opaque is opaque. What's important is where the atmosphere stops being opaque.

EliRabett said...

Hi Alan,

It is true that this argument neglects convection, but it is also true that radiation accounts by far for the major thermal energy transport mechanism in the troposphere the net of which is heat flow. The reason for this confusion is two fold.

The formal definition of heat is net thermal energy transport (FWIW Eli has become very formal in separating heat flow from thermal energy flow to avoid confusions but usually people are sloppy about this and it leads to confusion if not purposeful disruption)

IR radiation absorbed in the atmosphere is rapidly (10 μs) converted into thermal You can't tell how any specific packet of energy got there or left.
see http://rabett.blogspot.com/2018/09/heat-has-no-hair.html for details

So you can't draw any conclusions by subtracting the upwards and downwards radiation and then comparing it to the convective upwards flow. Best you can do is allocate contributions by proportion.

The back radiation comes from ALL of the sources pushing thermal energy into the atmosphere, from the convective and radiative heat transfer from the surface. Neglecting the Foote Effect, direct absorption of sunlight, surface radiation accounts for about 3/4 of this