Lately there’s been a bit of back-and-forth discussion going on on the so-called ‘Gravito-Thermal Effect’ (GTE) at a few notable climate blogs, like The Hockey Schtick, Tallbloke’s Talkshop, Clive Best and even Judith Curry’s Climate Etc. (in fact, this is where the lengthiest discussion thread on the subject is to be found).
To me the whole thing appears to arise from a fundamental misunderstanding of the adiabatic process (see the end of the post).
Something called the ‘Loschmidt Effect’, after a proposal in the 1870s by the Austrian scientist Josef Loschmidt, seems to lie at the heart of the GTE argument. Tallbloke brought it out from relative obscurity in a post in early 2012. A quote from a textbook describes the proposed effect as follows:
“Loschmidt claimed that the equilibrium temperature of a gas column subject to gravity should be lower at the top of the column and higher at its base. Presumably, one could drive a heat engine with this temperature gradient, thus violating the second law. (…)
Loschmidt’s rationale for a gravitational temperature gradient is straightforward. Consider a vertical column of gas in a uniform gravitational field (acceleration g) of height (z = h). Gas molecules (mass, m) at the top of the column possess mgh greater gravitational potential energy than molecules at the base. Thermal motion with (against) the direction of the field increases (decreases) molecular kinetic energy. This net kinetic energy can be transferred from the top to the bottom of the column via collisions. No net particle flow from top to bottom is required since energy transfer is mediated by collision; thus, this is heat conduction, not convection. If this gravitationally directed motion is eventually thermalized, one can write from the first law: mgz = CvmΔT, where Cv is the specific heat of the gas at constant volume (Trupp notes that Cv should be replaced by Cp). From this, a vertical temperature gradient can be intuited:
dT/dz = -∇zT = g/Cv
For a typical gas (e.g., N2) with Cv (N2) ≈ 1100J/kgK, in the Earth’s gravitational field, one estimates∇zT ≈ 10-2K/m. This is nearly the well-known standard meteorological adiabatic gradient, where Cp replaces Cv.”
First of all, I don’t see how this would be a violation of the 2nd Law. Isn’t it simply a version of the ‘refrigerator effect’, where you apply an external force to the system, doing work on it so as to counter the natural tendency of heat to flow from hot to cold? The gravitational pull at one end skews the distribution of both mass and energy in this particular system, forcing even heat conduction to tend towards the denser and more energetic end. If you were to simply switch off gravity in this situation, the internal distribution of the system would immediately and spontaneously equalise, making the sample homogeneous, mass flow from more dense to less dense, heat flow from warmer to cooler. There’s no inherent violation of any thermodynamic laws here as far as I can see.
Secondly, for the life of me I cannot see this ‘Loschmidt effect’ as being of significance to real, observable atmospheric temperature gradients at all. It seems to be a mere ‘relativistic’ effect, where gravity indeed produces a drag on time, matter and light, but where, if this effect is to be of much consequence, you would need incredibly strong gravitational forces and/or – in the case of the gas sample in question – an incredibly high column over which the pull could work. Yes, in our atmosphere, gravity sees to it that the surface air is quite significantly denser than the air around the tropopause (about 4 times as dense). But this circumstance alone won’t make the temperature of the denser surface air any higher than that of the more tenuous tropopause air, because there is much more energy per volume down low, but also more mass, so in an equilibrated situation the two will tend to cancel and create an isothermal profile. That is, barring any heat inputs to (or outputs from) our system.
This is the whole clue: You need to ‘thermalise’ the system to make it run. Even Loschmidt seems to understand this. An adiabatic lapse rate can only be realised at the point where air masses actually start moving up and down. And they won’t do that in a hydrostatic equilibrium with no heat inputs or outputs whatsoever.
There absolutely will not be a temperature gradient similar to a potential adiabatic lapse rate in an atmospheric column with no radiative heat transfers to/from the system (IN down low and OUT up high) and no convective response. There is no way.
This is where I don’t get the GTE argument. What is it actually trying to say?
Is it saying that, even with no heat input from the Sun, no convection and no radiative cooling of air masses to space, a temperature gradient would naturally form in an atmospheric column, simply from gravity and its specific heat alone?
I don’t know. I hope not. Because that would just be … nuts!
The point is, we do have solar radiative heating down low, we do have radiative cooling to space up high, we do have convection in between. That’s how and why we have a tropospheric temperature gradient. The gravitational pressure and density gradients do not alone create a temperature gradient. You need heating/cooling and movement of air masses to accomplish that, I’m sorry. Yes, the (dry) adiabatic lapse rate is just g/Cp. But it applies specifically to vertically moving air. By definition. Without vertically moving air, it is but a potential gradient, not an actual gradient.
True, the value of the DALR is not in any way dependent on convection. Only gravity and specific heat. ~10K/km. However, its realisation in the atmosphere (through the mean ‘environmental lapse rate’ (ELR)) is crucially dependent on convection. A pretty important distinction to make …
The ALR is just a theoretical (potential) gradient, a template for the actual gradient – the ELR – to stick to.
Be all this as it may, the atmosphere does indeed insulate the solar-heated surface of our Earth, forcing it to be warmer than if the atmosphere weren’t there. And it does so through its mass.
I’ve discussed the mechanisms with which it does so earlier.
A brief summary:
This is how the atmosphere makes the Earth’s surface warmer – much warmer – than the maximum pure solar radiative equilibrium temperature (because it sure does!):
- It has a mass and therefore a ‘heat capacity’. This means it is able to warm. It does so by being directly convectively coupled with the solar-heated surface below it. Regardless of whether that atmosphere contains radiatively active gases (so-called ‘GHGs’) or not, it will warm – conductively > convectively; on our real Earth, like this: conductively/radiatively/evaporatively > convectively. The atmosphere is able to warm. Space isn’t. Therefore the atmosphere sets up a temperature gradient away from the solar-heated surface that has a finite (sub-max) steepness. Space doesn’t. The atmosphere thus INSULATES the surface. Energy is not able to escape the surface as fast as it’s coming in before it has warmed to a higher mean temperature than before the atmosphere was put in place.
- It has a mass and therefore a weight (it’s in a gravity field, after all). Space doesn’t. This affects the surface energy escape rate in two ways: i) The expanding air lifting convectively from the surface air layer and into the atmosphere at large is heavy – it needs to be pushed upward against gravity. AT EQUAL TEMPERATURE, this circumstance makes it harder for energy to escape the surface convectively at the same rate with the atmosphere being denser (more mass per volume). ii) The atmosphere having a weight means it exerts a pressure on the solar-heated surface above 0. Unlike space. A higher atmospheric pressure/density makes it harder for energy to escape the surface than with a lower pressure AT EQUAL TEMPERATURE by suppressing the evaporation rate from the oceans. The weight of the atmosphere is not a rigid barrier. But it functions by the same principle – setting limits to convection/evaporation from a heated body.
If there is any ‘Gravito-Thermal Effect’ of the atmosphere on the surface temperature, this is it … The surface temperature needs to be set first, for this is the baseline from which the tropospheric temperature profile climbs up. The surface heats first and from it, the heat propagates upwards towards the tropopause via convection.
In other words, the surface temperature is simply determined by the balance point between the incoming and the outgoing heat fluxes. At the point where the outgoing flux finally matches the incoming flux, we have reached our steady state temperature.
If each average square metre of the global surface of the Earth absorbs 165 joules worth of energy (as heat) from the Sun every second, then, to balance this, each average square metre of the global surface of the Earth also needs to shed 165 joules worth of energy (as heat) every second. It cannot manage this just like that. Not with a massive atmosphere on top.
While the incoming heat from the Sun is purely radiative, the outgoing heat derives from several different source mechanisms – radiative, conductive and evaporative. For the surface heat loss to be effective, the energy transferred to the air layers directly above it through these three mechanisms, needs to be constantly removed at a certain pace, so that new energy can take its place. It can only ever hope to attain such a pace through the movement of the air itself – convection. So the efficiency of convective uplift in reality puts a limit to the transfer of energy as heat from the surface to the lowermost air layers of the atmosphere. If the air isn’t lifted up and away fast enough, bringing the surface energy with it, then when new energy comes along from below, it will all start piling up in the surface air layer, which in turn will reduce the transfer rate from the surface itself, due to a decreasing temperature gradient back down. Energy will thus start accumulating at/below the surface. And we get warming. Higher temps to promote faster uplift. The only goal for the surface in the end is to pass on its absorbed energy as fast as it comes in. As one can well gather from the above, it can only accomplish this upon equilibrating at a certain mean temperature level. This level is NOT -18°C.
Finally, how does the adiabatic process actually work? What is an adiabatic process?
It is NOT – as far too many people seem to believe – the process of uplift (or subsidence) of air in the atmospheric column. That’s convection.
When you lift an object, it doesn’t get any cooler from its mechanical KE (kinetic energy) being turned into gravitational PE (potential energy). You simply ‘charge’ the object with energy to be expended on its way back down, were you finally to let it drop.
The adiabatic process is only the expansion/compression of the air. Not the lifting or sinking. In the atmosphere it just so happens that you need to move the air up or down to change the external pressure on it. If you could change the external pressure in any other way, you wouldn’t need to move the air at all. The lifting itself will not change the temperature of the air, only its speed/work potential on the way back down. Lifting something is a mechanical (Newtonian) process, not a thermodynamic (adiabatic) one. Changing mechanical KE into gravitational PE and back when moving up and down a gravity well is real enough; it simply has no bearing whatsoever on temperatures. The exchange of energy across system boundaries in the form of ‘heat’ [Q] or ‘work’ [W] (like in thermodynamic processes) does.
Thus, the expansion and compression of lifting/sinking air is the only adiabatic process going on in the atmosphere. Expanding air cools adiabatically by doing work on its surroundings (thus losing internal energy [U]), against the external pressure. Air being compressed warms adiabatically from the surroundings doing work on it (it thus gains internal energy).
This is intimately linked to the 1st Law of Thermodynamics:
ΔU = Q – W
Where U is the internal energy of the system (air parcel), Q is the net transfer of energy as heat to/from the system, and W is the energy transferred to/from the system by work being done by/on the system.
For incremental steps in a so-called quasi-static (reversible) process:
dU = δQ – δW
dU = δQ – PdV
In an adiabatic process, the transfer of ‘heat’ [Q] across the system boundary is 0 by definition, so the entire change in system internal energy [dU], and thus temperature, T, is due to the pressure-volume work [PdV] being done by/on the system:
dU = – PdV
The adiabatic process in one simple formula.
Read about adiabatic processes, lapse rates, atmospheric stability/instability and convection: