Cooling of Atmosphere Due to CO2 Emission: A Critical Analysis

[DEMcMillan]

Convection has been linked to CO₂ and heat transfer from Earth’s surface. The abstract mechanism is “absorption” and has heating leading to convection. The reply strings, especially chjoaygame’s, generated a model without the original heat transfer problem in a cloudless and dust-free troposphere.

chjoaygame pointed out that CO₂ raises the density of air. This property fascinated me several years ago because water vapor has the opposite effect. Water vapor addition makes air more buoyant, carrying the water vapor upward, usually until the water vapor condenses into haze, fog or clouds. While buoyant water vapor-containing air is rising heavier dry air elsewhere is descending to replace it as pressure gradients develop. Water vapor entry is a major mediator of vertical motion in the troposphere. The easily mixing adiabatic troposphere is disrupted as water vapor adds energy by changing in state. Rising CO₂ accelerates this process but doesn’t change the rate of heat transfer to and within the troposphere. My numerical calculations failed to portray any substantial change in tropospheric heat distribution. More rapid mixing actually stabilized its convective heat distribution. Liquid and solid water-mediated temperature inversion is the major inhibitor of tropospheric mixing, giving us smog and other urban and regional problems. But in general inversion has only a limited effect on radiation balance.

The major role of Earth’s convection is the movement of heat from the tropics toward the poles. The atmosphere’s role is to drive the oceans great streams to transfer heat. The trade wind Easterlies are generated by high air descending and returning to the tropics. The resulting Western flow is due to conservation of angular momentum. Ocean water transmits far more heat than the atmosphere itself. The sea surface temperature in the Temperate and Frigid zones is raised and the Tropics lowered by the steady ocean water anti-cyclonic movement. Periodically, characteristically in November and December, this process breaks down and the Earth’s weather changes. In a year, the trade winds return and the briefly heated Earth cools in proportion to its previous heating, but now over two years. One can wager that the jet streams benefit from the Easterlies loss. The stratospheric velocity increase brings on storms that would not otherwise ascend the continental mountains. How such behaviors affect radiation into space is not clear. The marked tropical rise is incorporated into a general planetary rise. The descent path from the jet streams has not been identified but must sweep more directly back to the tropics. The overall system’s effect is to raise surface temperatures. The effect of stratospheric temperatures is less clear. I used 1997-8 as a test year for convection breakdown. http://www.cpc.noaa.gov/products/stratosphere/temperature/ The upper and lower stratosphere don’t show any clear change in temperature during this period. Where does carbon dioxide’s molecular weight fit in? How does it make the Earth’s energy balance negative in general? The ultimate balance must be radiative and thermal.

I would like to point out to vanesch that none of the cited models allow treatment of the IR emissive nature of the atmosphere itself that markedly reduces the greenhouse gas line by line radiative return to the Earth’s surface. Gray body and optical depth maneuvers act only to hide the modeling deficiency. https://www.physicsforums.com/showthread.php?t=261966

 

[Andre]

I don't know. As I said, I never used these codes. It takes time and effort to plunge into a scientific computing program like that. I know similar codes (not in the public domain at all) for nuclear radiation transport (in my opinion, the two categories of problems are very similar, that's why I think I can have the pretension to open my mouth in this kind of discussion). Now, nuclear radiation transport codes are very accurate because real working stuff is based upon them, like power reactors, radiation protection and criticality avoidance in radiochemical plants ; we can't permit ourselves to have ununderstood fudge factors and group think or we all blow ourselves in the air ! So these codes are tested against a lot of known test cases.

But probably optical radiation transport is harder than nuclear radiation transport because there are molecular interactions and things like that. Nuclear radiation transport codes usually do not include hydrodynamical effects in themselves: you have to couple different codes in order to achieve that. Convection by itself, as a hydrodynamical problem, is already extremely difficult. Add to that things like condensation and so on, and you have something very hard to do ab initio. So I guess - although I don't know - that these codes are doing just the radiation transport, with all matter "fixed".

To really find out, you should look into the user manuals. I could very well be totally wrong.

Let's do a bit of back side of the envellope educated guessing first:

As the absolute/relative humidity is course directly affecting water vapor feedback, let's see what is required to get those increased values. For ballpark figures, from http://www.usclivar.org/Organization/Salinity_WG/workshoppresentations/Evp-salinityLisanYu.pdf here let's assume average annual evaporation of a meter per year. That's 2.74 liters (2740 g) per m2 per day or 114 g per hour is 0.032 gram per second. It takes 2500 joule to evaporate one gram of water, so for 0.032 gram that's 79 joule per second per square meter or 79 W/m2

Now to keep relative humidity constant when increasing the ambient temperature of 15 C to 16 C, suppose a dewpoint of about 9 degrees we see http://www.humirel.com/All_about_humidity-calculation2.htm a decrease of 67% to 63%. Obviously we also have to raise the dewpoint one degree to get back to 67% Now the absolute humidity calculated http://www.humirel.com/All_about_humidity-calculation2.htm goes from 9 gram/m3 at a dewpoint of 9 degrees to 9.6 gram/m3 at a dewpoint of 10 degrees, an increase of 7%. To sustain an increase of 7% more water vapor in the atmospere it seems logical that the rate of evaporation also has to increase by 7% as well, which in turn requires 7% more energy. Hence I'd need 7% of 79 W/m2 or 5.5 W/m2 extra to maintain constant relative humidity. So how much excess energy is there to get that positive water feedback in? Weren't we talking about 3-4 W/m2. So is anything wrong here?

 

[vanesch]

To sustain an increase of 7% more water vapor in the atmospere it seems logical that the rate of evaporation also has to increase by 7% as well, which in turn requires 7% more energy. Hence I'd need 7% of 79 W/m2 or 5.5 W/m2 extra to maintain constant relative humidity. So how much excess energy is there to get that positive water feedback in? Weren't we talking about 3-4 W/m2. So is anything wrong here?

The point is that there will be increased condensation too somewhere and that will then act as a heat source of equal importance (5.5 W/m2 in your example: somewhere, these 5.5 W/m2 will be returned). Of course, everything will depend on *where* this condensation will take place and hence *where* the latent heat which has been subtracted from the ground by increased evaporation, will be rendered to the atmosphere (and act as a source of heating). If this is low in the atmosphere, then the heat which was extracted by evaporation, will be rendered on the spot, and in this case, the evaporation heat loss (as well as the condensation heating) will not have to be included in the balance. If it is higher up, then of course, this will act as a heat vector.

What's also a matter, is that water vapor is a lighter gas (18 amu) than air (28 or 32 amu), and hence water vapor (even not hot) is a drive for convection. As I said somewhere else, it is the main drive for the convection in cooling towers (where the heat source is in fact on top: one makes hot water (in the form of drops) fall from the top of the cooling tower down into the cooler air).

 

[chjoaygame]

Andre and vanesch PF Mentor, the chance of a "single photon" (IR), emitted from the Earth surface, to escape to space.

The chance of escape depends very much on the wave number within the IR band. There is an "atmospheric window" of wave numbers, rather arbitrarily but reasonably defined in detail as from 720 cm^-1 to 1260 cm^-1 by Miskolczi, in which the chance of escape of a single photon is quite good, better than 1/2, variably dependent on the water vapour content and CO₂ content, as well of course as on cloud fraction. Outside the window, the chance of escape of a "single photon" is extremely small, practically zero. This is why is it is not overly useful to think of the atmosphere as "grey".

There are thus two regimes for IR in the atmosphere, the window and the non-window. In the window, the optical depth is less than 1. Outside the window, the optical depth is perhaps 30.

The window is translucent, partly transparent. It is, as it were, variably "muslin curtained" by water vapour and CO₂. The water vapour content varies from place to place, usually being largest near the equator and least at the poles, and quite rapidly from time to time. The CO₂ content is less rapidly variable. There is a small spatial variation with latitude, and a seasonal cycle, and in the time it has been measured over the past decades a slow drift of increase. Also the window is variably "venetian blinded" by clouds, which are practically opaque in the window, but of course are patchily or fractionally distributed in space, as well as variable in time.

Outside the window, where the cloudless atmosphere is opaque to IR, the propagation of heat from the land-sea surface to the lower skin of the atmosphere, and through the atmosphere except in its upper reaches, is described by the diffusion limit of the radiation transfer equation (Mihalas and Mihalas 1984). Fourier's law of heat diffusion reigns here. Though very widely customary, it is not good physics to try to speak or think here of "radiative transfer" as distinct from conductive-convective-evaporative transfer. The radiative part of the heat transfer is much better thought of as part of the diffusion-conduction. Both ponderable matter and radiation share inseparably in the conduction of heat. The mean free path of the IR "single photons" is some tens of meters, a distance over which the temperature of the air changes only a little, because of convection. It is thus futile to think separately of "radiative transfer" from the land-sea surface outside the window. In other words, the commonly touted story of "back-radiation", from the bulk of the atmosphere to land-sea surface, is futile, poor physics, confusing or misleading, practically meaningless outside the window. Outside the window, the rate of transfer of heat from land-sea surface to lower atmospheric skin is directly proportional to the local temperature gradient, as expressed by the Fourier heat diffusion law, and one can forget a separate radiative transfer here.

Inside the window, one is interested in separate radiative transfer of heat from the land-sea surface. The mean free path of "single photons", when the air is relatively dry and the CO2 relatively little, can be hundreds of kilometers. The very importantly and greatly variable IR radiative flux through the window, direct from the land-sea surface to space, is on the order of magnitude of 60 W m^-2. In a cloudless sky, the notion of "back-radiation" does not arise here.

Consequently, the overwhelming varying, and nearly the only, flow, of back radiation from atmosphere to land-sea surface is from the lower surfaces of clouds. Because it arises from clouds which are cooler than the land-sea surface, it is fractionally less in magnitude than the radiation from land-sea surface through the window which is blocked by the clouds. The clouds are good radiators in the IR because they are practically opqaque to IR. From the upper surface of clouds there is also radiation through the window direct to space. Overall the clouds are cooled by the window radiation because they have window radiation reaching them only from below, while they radiate nearly equally both upwards and downwards.

The land-sea surface is partly warmed by the back radiation downwards through the window from the clouds. On the other hand, the net cooling of the clouds by the window radiation leads eventually to convection of cooler air from altitude down to the land-sea surface and thus eventually to a greater temperature gradient driving diffusion from land-sea surface to atmosphere; this partly cools the land-sea surface to partly offset the partial warming by the clouds' window back radiation.

The 24-hour partial result of this mechanism is slight warming of the land-sea surface and slight cooling of the clouds. This tends to increase the vertical temperature gradient, the lapse rate, and tends to increase convection, both horizontal and vertical.

Apart from the window back radiation outside the window wave numbers, and its consequences, the clouds hardly affect intra-atmospheric radiative heat transport, because outside the window the atmosphere is practically opaque anyway. Of course latent heat and convective transport are important in clouds.

But during the day the clouds exert another kind of radiative effect, in another, non-IR wave number regime. They reflect, from their upper surfaces directly back to space, a big fraction of the visible sunlight that hits them. This is described as albedo. This is a strong cooling effect of clouds during the day, affecting the whole atmosphere and land-sea surface. On the other hand, at night, the clouds exert a slight warming effect on the lower atmosphere and the land-sea surface because of their window back radiation and its consequences.

I have not seen the above account written elsewhere, so far as I can recall, but then I have an appalling weakness of memory.