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.
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.