Wednesday, January 6, 2010

What if there were no Greenhouse Effect?

Roy Spencer recently put up a post on his blog, reposted at WUWT, on the old chestnut of "What would the world be like without the greenhouse effect?". His thesis: "there would be no weather on Earth without the greenhouse effect." That, and some other things he wrote, are wrong.

But first, let's look at how "no GH effect" could be implemented. The simplest way is just to imagine that the Earth had the same gas constituents, but somehow they magically lost their ability to absorb and emit thermal IR. Roy S goes further, saying:
"So, let’s imagine an extremely cold Earth and atmosphere, without any water vapor, carbon dioxide, methane or any other greenhouse gases – and with no surface water to evaporate and create atmospheric water vapor, either."
That's a big change, but let's go with that.

Heat engines and weather

The Earth's atmosphere is often described as a big heat engine, generating weather. It is. A heat engine creates motion from transferring heat from a hot source to a cool sink. Sunlight creates lots of differential heating - between regions of different albedo, different latitudes, and between night and day regions. The latitude difference creates the classic Hadley cell. Hot air in the tropics rises from the surface, moves polewards, and descends in mid-latitudes, warming the cooler surface there. The warm source is maintained by an excess of sunlight over IR loss, and the cool sink is maintained by a corresponding deficit. This happens independently of the greenhouse effect.

The Hadley cell combines with the Coriolis effect to yield trade winds (the part of the cell where the replacement air flows back, cooled, from mid-latitude to tropics, and the mid-latitude westerlies (roaring forties), produced by the angular momentum transported from the tropics. Lots of weather there, and not due to the GHE.

Adiabatic Lapse Rate

Roy says "[without GHE]...Only the surface and a shallow layer of air next to the surface would go through a day-night cycle of heating and cooling. The rest of the atmosphere would be at approximately the same temperature as the average surface temperature. And without a falloff of temperature with height in the atmosphere of at least 10 deg. C per kilometer, all atmospheric convection would stop."
This is a common misunderstanding of the dry adiabatic lapse rate. It is not related to upper air cooling due to GHG emission. It happens in any gas (eg pure N2) which is in motion in a gravity field (g=9.8 m/s^2). It is something a like a reverse Carnot cycle. Imagine that you had a balloon with 1 kg gas (say N2), in an isothermal atmosphere under gravity, and you perform the following cycle.
1. From an initially isothermal state, you raise it rapidly by 1 km. The air expands adiabatically and cools (by 9.8 K). Because it is denser than the surrounding air, work is done to raise it.
2. The balloon is then held still until it warms to the ambient temperature, absorbing heat from the high altitude. It expands further, doing wasted work displacing gas.
3. The balloon is then quickly lowered 1 km. It is compressed, becoming hotter than ambient (by 9.8K), so work is needed to pull it down.
4. Again, the balloon is allowed to cool to ambient, delivering heat to the lower altitude. The cycle can repeat.
This is a classic heat pump. You do work, and move a fixed amount of heat downward in each cycle. Actually, in this case work is not required, because source and sink are at the same temperature, and the work is wasted. But the process can also be carried out with any lapse rate up to the dry adiabat of 9.6 K/km, and then true heat pumping is done, and heat goes from cooler to warmer.

The cycle has neutral effect if there is already a lapse rate (negative temperature gradient) of 9.8 K/km. For then the gas in the balloon is always at ambient temperature. It requires no work to raise it, and transfers no heat on arrival.

You might worry about whether there is some effect due to the external air being displaced up or down. OK, just imagine there are two balloons, one lowered just as the other is raised, so then there is no nett displacement of the atmosphere.

This is how the dry adiabatic lapse rate is maintained. Atmospheric motions, driven by the above mentioned heat engine, do the work. Whenever the gradient is less than the dry adiabat, heat is drawn downwards, until it is restored - well, almost (see next section).

Moist adiabat, etc

In reality, the dry adiabat is not always attained. There are processes which tend to conduct heat down any temperature gradient. The heat pump process that I described works against these, but can no longer maintain the full 9.8 K/km. These processes include:
1. Molecular conduction (heat diffusion) - very small
2. Turbulent heat transport - larger
3. Latent heat transport - can be larger again. But it requires that actual phase change occurs - evaporation and condensation, within the cycle. It enhances turbuleny transport, because the air carries more total heat.
4. Rosseland radiative transport. This is an enhanced thermal diffusion involving repeated absorption and emission of IR (by GHGs). It's often overlooked, and I'll talk more about it in a future post.

The postulates of Roy S would remove the leakage mechanisms 3 and 4, actually reinforcing the dry adiabat.

Spencer's error

Roy says "And without a falloff of temperature with height in the atmosphere of at least 10 deg. C per kilometer, all atmospheric convection would stop.". And that's his error. It wouldn't stop - it just has to be driven, by the atmospheric heat engine, as it is now. And that heat engine just needs regions of different temperature, which there would certainly be, with or without the GHE. In fact, the main latitudinal driver would work in much the same way.

A world without the GHE

So what would it be like? The conventional calculation is 33 C colder (for the same albedo), and that seems to me about right. There would still be latitude differences, and day/night differences, as well as land warm spots due to albedo variation. There would still be strong atmospheric motion - in fact the main circulations (eg Hadley) would still exist. The dry adiabatic lapse rate of 9.8 K/km would be almost universal. There would still be a tropopause somewhere, because at some altitude the atmospheric motions will reduce, the heat pump will fade, and heating from UV absorption by ozone etc will become more significant.


  1. Correct, and in fact Spencer later admits this in his article. His article is self contradictory.

  2. Cut and paste not working here is just as annoying as it is at Pielke, Jr.'s blog.

    I think you're wrong about the excess of sunlight vs IR emission in the tropics being independent of the greenhouse effect. If you're wrong about that, the rest of the analysis fails so I'd like to see some sort of reference as to why you think this is true.

  3. "4. Rosseland radiative transport. This is an enhanced thermal diffusion involving repeated absorption and emission of IR (by GHGs). It's often overlooked, and I'll talk more about it in a future post."

    Do you have an estimate of the relative importance of this?

  4. Dewitt,
    On the excess of sunlight, for the earth as is, that is surely not controversial? For the tropics, heat enters as sunlight, leaves as IR, and there is lateral heat transport from the tropics via Hadley cell, ocean currents etc. Heat is conserved, lateral flow is poleward, so sunlight must exceed IR.

    Whether that would be true without GHG could be disputed. My thesis is that there is energy in the latitude temp differences to drive a heat engine, and therefore such an engine will be continued, if it can get started.

    On cut/paste, this seems to be a blogspot issue. I found it at RP's too. It works if you have an identity, eg Google. I now use that everywhere - it seems troublefree, and makes life easier. But I'll see whether I'm allowed to countermand the cut/paste restriction.

  5. A quick google says that the Rosseland model is used when you can treat the gas as a gray body with an optical thickness greater than three. Since the Earth's atmosphere isn't gray and the average optical thickness is less than 2 (with the possible exception of a very warm and humid day in the tropics, the proverbial 90 F, 90% RH), how does this apply?

  6. Carrick "Do you have an estimate of the relative importance of this?"
    Funny you should ask - I've been working on that. Rosseland transport is just a way of conceptualising and calculating radiative transport in the regime where radiation is reasonably frequently absorbed and emitted. So you could say, of the 235 W/m2 radiated from the surface, about 40 W/m2 is in the AW, and is emitted without absorption. At a gues, there might be 20-30 W/m2 emitted at wavelengths that have a probability of up to say 60% of being absorbed. In that range, the Rosseland approx is increasingly effective, but not totally.

    Beyond that level, the Rosseland description of radiative transport is very good. In the upper troposphere, radiative transport is dominant, and so you could say that about 170W/m2 of the 235 are conveyed thus.

    Of course, as radiative transfer gets closer to the Rosseland model, the transfer itself gets less effective. Rosseland transport is just enhanced diffusion, down a temperature gradient, where the diffusivity is proportional to the mean free path of photons.

  7. "Diffusivity"? I meant conductivity.

  8. Dewitt,
    The complete Rosseland model has the gas temperature in turn determined by the radiative balance, and to simplify that, you need a gray-body model. But if you take the temperature gradient as a given, you can use the Rosseland formula for individual wavebands.

    The restriction to OD<3 is the equivalent of my probability of capture >60%. It's more restrictive, but the line is fuzzy. Again, the restriction applies to wavebands. The average OD may be <2, but many bands are higher.

    I'm recommending Rosseland not for quantitative accuracy but for concept value. It's accurate for OD>3, say, but still a useful way of thinking at lower OD. The reason it's useful is that it links IR transport to the temp gradient.

  9. Nick,

    For the Earth as it is, there is definitely excess insolation vs absorption up to about 45 degrees latitude where it becomes excess emission over insolation. But I think you're begging the question by assuming that would also hold in the absence of a greenhouse effect. A quick and dirty MODTRAN calculation has emitted radiation with 375 ppm CO2 at 287.8 W/m2 at 100 km looking down with surface emission (0 km looking down) at 417.3 W/m2. Eliminate CO2, most water, ozone and methane and you get 397.5 W/m2 at 100 km looking down with the the major features being nitrous oxide and a little bit of water above 10 km. Looking up, radiation from the atmosphere is cut to 48.1 W/m2 compared to 347.9 under standard conditions. That says to me that the major driving force for advection is not the temperature difference between the poles and the equator, but the excess heat trapped by the greenhouse effect at low latitude.

    But even if the trade winds develop to push air towards the tropics which then has to come down somewhere, how does that increase the lapse rate? Or would you just see a stable high pressure zone in the tropics with minimal vertical movement to balance the forces? I don't think the answer is as obvious as you seem to think.

    IMO, this is also part of the reason for polar amplification of temperature change. The other part being the effect of humidity on atmospheric heat capacity.

    As far as vertical convection even with water vapor as a working fluid, there is no driving force with an isothermal atmosphere because there will be no condensation as you move a packet of air upward. Even the diurnal cycle of cloud formation is driven by the fact that the lapse rate is positive and close to the adiabatic rate. Near as I can tell, what you would get would be formation of an inversion layer at night by conduction which would then disappear during the day. But it's not at all clear that the maximum lapse rate during the day would exceed the adiabatic rate and start convection.

  10. It's 235 w/m2 from the TOA, not the surface, which emits ~383 W/m2 at 288.2 K (emissivity 0.98).

    For high optical density and local thermal equilibrium (collisional heat transfer dominates over radiative transfer which is considered to apply for most of the atmosphere), how does the Rosseland model differ from the standard heat conduction model? In Physical Meteorology, except for very close to the surface, heat transfer by conduction is ignored.

  11. Dewitt,
    With the Modtran calculation, with GHG's gone everything would be cooler, so the surface radiation figures would change.

    But I do think it is simpler than that. With or without GHG's, there would be a latitude temp gradient - hottest in the tropics. That provides energy to drive a Hadley cell. Once you have winds you have turbulence and lots of up-down motion.

    The ideal adiabat (9.8 K/km) doesn't vary with GHG. But conformity with it would. The reason is that the work done (by winds) to maintain the lapse rate is work done to pump heat down to mreplace heat that leaks up, by conduction and other transport driven by the temp gradiant. That includes the Rosseland transport, with moves heat down a temp gradient, and depends on GHG. With that gone, much less work is needed.

    I think it's not right that you need to exceed 9.8K/km to have thermal convection. Above that level you have instability, but below you can get convection provided there is energy to drive it. This can come from any thermal inhomogeneity, allowing heat to flow from hot to cold. Hadley cells are the big one, but there's all the local effects - sea breezes, the thermals that gliders chase etc.

    On 235 W/m2, I count the nett flow - basically 235 W/m2 through the atmosphere, with a bit added as you go up to allow for insolation thermalised in the atmosphere.
    And yes, near the surface it isn't all IR (LH etc). But I'd offset the 383 with the back-radiation.

    Rosseland radiation does go by the heat conduction formula. That's why it is useful. But it is enhanced - it has a much higher conductivity. So it is different from thermal conduction - much bigger, and can't be ignored.

  12. For the purpose of the thought experiment, jack up the solar constant so the blackbody temperature is the same as if there were a greenhouse effect. Of course that gets tricky. Is there still latent heat transfer and how much? My guess would be that it would still exist, but at a much lower rate and be, like diurnal temperature variation, largely restricted to the boundary layer with evaporation during the day and condensation during the night.

    Both of us seem to be doing a lot of arm waving. I don't think either of us is going to accept the others point of view without something more quantitative.

    Almost all of the references to the Rosseland model that I can find are for much higher temperatures than 300K (stellar atmospheres, thermal cracking furnaces, etc.). Does it really make a difference at normal atmospheric temperature? And isn't it effectively already included in the measured thermal conductivity of air?

  13. "And isn't it effectively already included in the measured thermal conductivity of air?"
    No, it wouldn't a lab scale (OD>3?). The Rosseland model is just an approximation that works for IR transport at the murky end of the range - where OD>3, say. It goes by other names - I first encountered it as a P0 model.
    As with all IR, you tend to hear about it at higher temperatures, except in the atmosphere, where the combination of long distances and relatively small other fluxes makes it important.

    Latent heat transfer is just another form of convective transfer. I think of LH as just a delta fn in the specific heat scale. And LH is important because it increases the effective SH of the convecting gas.