If there were no atmosphere on top of our solar-heated terrestrial surface, then Earth’s mean global surface temperature would likely be about 80 degrees lower than what it actually is (209 rather than 289K). And this would be in spite of the fact that in this case the solar heat input to the global surface would be almost 80% larger on average (296 rather than 165 W/m2).
Much of this cooling of the mean would simply come as a result of greatly amplified temperature swings between day and night and between the seasons. The larger the planetary surface temperature amplitudes in space and time, the lower the mean global planetary surface temperature needs to be to maintain dynamic radiative equilibrium with the Sun. This is why the Moon is so cold.
So we need to get this straight: The Earth’s surface would be a much colder place without an atmosphere on top of it. Even with much more solar heat absorbed. There is no escaping this. The lunar surface is about 90K colder than ours, on average.
SO WHAT DOES OUR ATMOSPHERE DO?
The short answer: It insulates the solar-heated surface.
Well, so how does it do this?
Mainly in four ways, three of which concern suppressing the effectiveness of convective cooling of the surface at a certain temperature.
Why is this important? Why convective cooling?
Consider a hypothetical single-room house. The room is evacuated (no air) and completely and evenly insulated on all sides by a 0.25 m thick wall of say balsa wood (thermal conductivity (k): 0.048 W/m K), a strong lumber of low density (containing lots of pockets of air). In the middle of the room there’s a tiny oven burning steadily from a constant supply of fuel. The house’s surroundings are also a vacuum, just like the room inside, only the outside vacuum is boundless, like space. The emissivity of both the inner and the outer surfaces of the wall is assumed to be 1 (like a blackbody).
Now, the tiny central oven, the only heat/energy source in this setup, burns so that the temperature of its outer surface facing the inner walls of the room naturally adjusts to emit the same isotropic flux of radiant heat at all times towards the walls, meaning that if the temperature of these walls rises, the temperature of the outer surface of the oven must also rise accordingly.* When this constant radiant heat flux reaches and is absorbed by the inner surface of the balsa-wood wall, its mean intensity is 240 W/m2.
*See the earlier discussion of how and why this must be here.
In order for the temperature of the inner surface of the house’s wall facing the evacuated room surrounding the tiny central (and constantly burning) oven to stop rising, that is, for it to reach a dynamic equilibrium with its heat source (the oven) and thus its steady-state temperature, its mean heat input (Qin) – 240 W/m2 – needs to be matched by its mean heat output (Qout). Since the heat output from an object can never in nature move in the direction of its heat input, this means that, in the steady state, 240 joules will have to pass each second through each square metre of wall, 0.25 m on to its outer surface, facing space. This particular heat transfer can in effect only occur by way of conduction (there could also be radiation moving the energy forward through the internal air-filled cavities, but we’ll assume this transport, for the sake of argument, to be fully negligible).
Now, since the outer surface of the house’s wall faces the vacuum of space, it can only deliver its heat to it via radiation. And since, in the steady state, the heat delivered from the outer surface of the house’s wall to space will have to match the heat supplied to it through the wall from the wall’s inner surface, facing the oven, its steady-state temperature (according to the Stefan-Boltzmann law) will need to be 255K.
The question then is: If the inner wall surface absorbs (and passes on) a heat flux worth of 240 W/m2 (radiative IN, conductive OUT) and the outer wall surface absorbs (and passes on) a heat flux of the exact same size (conductive IN, radiative OUT), at a steady-state temperature of 255K, what is required for the 240 W/m2 to pass through the wall, from the inner to the outer surface?
A temperature difference across the thickness of the wall. That is, a temperature gradient.
Since heat can only spontaneously move from warmer to cooler and since the heat in this case moves from the inner to the outer surface of the wall, it follows that the inner surface, in the steady state, needs to be warmer than the outer one.
Note, just as much energy moves into and out of the inner surface as ‘heat’ as what moves into and out of the outer surface per unit of time and area. But the former is still warmer than the latter.
Ok. So how much warmer? Well, let’s see. We’ll use Fourier’s fairly straightforward conductive heat transfer equation:
Q/A = -k ∇T
where Q/A is power (J/s) per area – the power density flux or ‘conductive heat flux’: W/m2,
k is the thermal conductivity of the material/medium through which the heat is conducted: W/m K, and
∇T is the temperature gradient through the material: K/m.
We know already that the heat flux is 240 W/m2. We also know that the wall is 0.25 m thick, that the outer surface of the wall is at 255K and that the thermal conductivity of balsa wood is 0.048 W/m K.
What we want to know is the steady-state temperature of the inner surface of the wall:
240 = -0.048 * ((255 – x)/0.25)
-5000 = (255 – x)/0.25
-1250 = 255 – x
x = 1505 K
The inner surface of the wall of our hypothetical house will not reach its steady state until it has warmed to 1505 K (1232 °C).
That is pretty bloody hot! In fact, it is way too hot for balsa wood. The temperature gradient through the wall at this point would have to be -5000 K/m, a drop in temperature of 50 degrees per cm!
Why is such an incredibly steep gradient required?
Simple answer: Because balsa wood is a terrible conductor of heat. If our wall were instead made of aluminium, a light metal and a first-rate conductor, then the temperature of the inner surface would need to be no more than 0.3 degrees warmer than the outer one in the steady state for the full 240 W/m2 to be conducted right through, down a gradient of -1.2 K/m (0.012 K/cm).
In practical terms, the balsa wood walls of our hypothetical room would never be able to reach a steady state, a dynamic equilibrium between its heat input from the central oven and its heat output through to the outside. It would just continue to warm slowly, but surely, until we could no longer be bothered waiting, or until the wooden walls eventually started to shrivel and smoulder from its own hotness.
The point to take home from this exercise, this admittedly highly idealised thought experiment, is that the balsa wood, being such a poor thermal conductor, makes for a brilliant insulator:
- The less effective the heat is moved through the insulating system (the wall), from where it’s originally absorbed (at the inner surface, IN from the oven) to where it’s finally emitted (from the outer surface, OUT to space), the stronger its insulating effect, and the higher the ‘absorbing surface’ temperature needs to be in order to be able to pass the heat through the system to the ’emitting surface’ sufficiently fast to reach dynamic equilibrium between heat IN and heat OUT.
This is also the governing principle behind the ‘atmospheric insulating effect’.
As I guess most people have already understood, the hypothetical setup described above is a simple model of the ‘Sun-Earth-space’ composite system, where 1) the central oven represents the Sun (which, however, does not itself need to warm in order to supply a constant radiant heat flux to Earth as the Earth warms; it is way too far away, and far too much hotter than Earth for this to occur), 2) the vacuum between the oven and the inner surface of the wall represents space in the Sun > Earth heat transfer, 3) the inner surface of the wall represents Earth’s surface, 4) the wall proper, between its two outward-facing surfaces, represents the atmosphere (essentially, the troposphere), 5) the outer surface of the wall represents the ToA, and 6) the outside vacuum represents space in the Earth > space heat transfer.
So the atmosphere basically acts as a ‘conductive insulating layer’ – kind of like styrofoam or foam rubber – wrapped around the solar-heated surface, hindering the solar heat absorbed by the surface on its route back out to space.
The funny (?) thing is that air is an even worse conductor of heat than balsa wood. In fact, heat would conduct twice as effectively through balsa wood as it would through pure air, which at room temperature has a thermal conductivity of a mere 0.024 W/m K.
The good thing is that in an open volume of air, much larger than the tiny cavities inside the balsa wood lumber, subjected to gravity and heated from below, our atmosphere being a perfect example, a mechanism for the movement of energy emerges that is much, much more effective than the pure molecule-to-molecule conduction of heat, even immensely more effective than conduction through a slab of aluminium. It is called convection (or ‘advection’), and involves the movement of the heated medium itself (which means it only operates in fluids (liquids and gases), not in solids).
Convection – in our atmosphere – simply substitutes for (supersedes) conduction as the real ‘transporter of heat’ from (inner/lower) ‘absorbing surface’ to (outer/upper) ’emitting surface’.
However, even convection needs a temperature gradient, just like conduction, through the system in question in order to be able to do what it’s supposed to do – transfer energy from the heating end to the cooling end of the system. It can simply make do with a much, much gentler one …
But since, with a massive atmosphere, being able to absorb heat from the surface that was originally meant for space, the final emission of this energy back out of the Earth system will be delayed by having to go through an intermediate, internal transfer process on the way, the movement of bulk air from the surface to the atmospheric level(s) or regions from where it can be freely radiated to space, the ‘absorbing surface’ – the solar-heated liquid/solid surface of the Earth – will by natural necessity end up warmer than the ’emitting surface(s)’ aloft in the atmosphere.
To illustrate this, let’s go back to our strange little house in space with the balsa wood walls.
If the much more effective heat transfer mechanism of convection moved the heat through the 0.25 m wall rather than conduction, then the inner surface facing the oven (the equivalent of Earth’s surface) would not need to be anywhere near as hot for balance between heat IN and heat OUT to be achieved. But it would still need to be ever so slightly warmer than the outer surface facing the surrounding space (the equivalent of ToA or Earth’s effective radiating ‘surface’), although hardly discernible over a 0.25 m distance.
If there were no wall at all (no atmosphere), however, only the inner surface facing the surrounding space directly, then there would no longer be any need for it to become warmer than 255K. Then all its heat loss would be by radiation alone, and it would be straight from the surface itself. The ‘inner’ surface would’ve become the actual radiating surface to space.
The point here being: As soon as some of the surface energy is transferred as heat to the atmosphere rather than directly to space, be it through radiation, conduction or evaporation, a delaying process is initiated that will eventually force the steady-state surface temperature up.
At this stage, people might wonder where I’m going with all this. Is he actually endorsing the ‘raised effective radiating level (ERL)’ explanation of the rGHE?
To this I would say: Yes and no.
I endorse the general principle behind this explanation in the broader sense already expounded above. What I do not endorse is the notion that this is somehow a consequence simply of the atmosphere’s IR-opacity. There are two major reasons for this:
- The atmosphere is not dependent on being able to absorb IR radiation from the surface for it to warm; it would’ve warmed with or without this ability, simply from being directly convectively coupled with the solar-heated surface below. The atmosphere is, however, dependent on being able to emit IR radiation to space for it to cool. Or else, energy transferred from the surface to the atmosphere would have no real means of getting out of the Earth system; it would rather pile up … be ‘trapped’ within. This is an unacceptable scenario in a real universe.
- The Earth system doesn’t actually possess a final single 2D ‘radiating surface’ to space as does our balsa wood wall. The Earth system radiates its heat to space from a full 3D ‘radiating volume‘, spanning the entire depth of atmosphere from the actual liquid/solid surface at the bottom to the ToA at the top. It is thus impossible to tie Earth’s total radiant heat flux to space to any one specific temperature. The 255K value simply becomes a mathematical construct arrived at by calculating backwards from the total flux itself.
No, as I pointed out to begin with, the ‘atmospheric insulating effect’ is very real, but it arises from the simple fact that the atmosphere is massive, not as a consequence of this atmosphere being opaque to outgoing IR as opposed to some hypothetical case where it’s not. (I’ll elaborate on this crucial point in the next post.)
As mentioned, the atmosphere suppresses the overall cooling rate of the global surface at a certain temperature by inhibiting the effectiveness of its own convective circulation, and it mainly does so in three ways. But the first thing it does is evening out the global temperature differences across the planetary surface. The thicker it is, the more evened out the temperatures become:
- The atmosphere (as does – importantly – the global ocean) reduces the surface temperature amplitudes both spatially (from equator to poles) and temporally (between day and night and summer and winter). Space doesn’t (and pure regolith does it only temporally and to a relatively minor extent). The atmosphere does this by holding on to (‘capture’ and ‘store’ for a while, significantly away from the surface itself) and spreading most of the absorbed solar heat before it’s being released back out of the system. It holds on to it through its thermal mass and latent heat. It spreads it via natural heating-induced pressure/density circulation.
- The atmosphere is warm. Space isn’t. Which means that the atmosphere basically acts as a massive thermal barrier through which surface heat needs to travel up along a certain temperature gradient constrained by gravity in order to be able to get out of the Earth system. The temperature gradient determines – to a first approximation (see points 3. and 4.) – how much the surface and, in turn, the lowermost layers of the atmosphere need to warm before effective convective cooling of the surface becomes fully operative.
- The atmosphere exerts a pressure on the surface. Space doesn’t. By having a weight (mass times gravity) and a density (mass per volume), the atmosphere presses down on the surface, restricting the average ability of water molecules to escape our global surface through evaporation, hence its main heat loss mechanism, at a particular surface temperature. Evaporation, as it happens, is a major driver of atmospheric convective circulation on Earth.
- The atmosphere is ‘sluggish’. Space isn’t. By possessing inertia and a certain inherent ‘sluggishness’ (molecular density, weight and viscosity), the atmosphere resists heating and cooling, near-surface turbulent flow and steep horizontal temperature/pressure differentials leading to strong surface wind shear, all of which would work to enhance convective surface cooling. Compare Mars and Venus. The light atmosphere of the former is so responsive and turbulent that its constant erratic fluctuations makes it hard to even settle on an average state. The heavy atmosphere of the latter, on the other hand, is almost completely non-responsive and non-turbulent (until you get very high up above the surface), the thick ‘air’ along the surface hardly moving at all, and only in a sludgy, near-perfect laminar flow. The Earth’s atmosphere sits somewhere in between these two extremes.
The atmosphere, in short, through its mass simply resting on the solar-heated surface, demands a certain kinetic level to be reached before the smooth, adequately efficient loss of surface heat is allowed. Space has no such limiting ‘blanket’ tendency, other than perhaps the speed of light …
An atmosphere insulates like this:
- Without an atmosphere, the planetary surface equilibrates radiatively with its sun and stabilizes at a physical global mean steady-state temperature quite far below the hypothetical blackbody emission temperature corresponding to the averaged radiative heat balance (if the balance is an average 296 W/m2 IN, 296 W/m2 OUT, the ideal, evened out BB temp would be 269K, but due to large spatial and temporal swings in temperature, the actual mean will be lower, on Earth likely around 209K).
- A massive atmosphere is placed on top of the solar-heated surface. It starts holding surface heat back, spreading it from relatively hot areas to relatively cold ones, evening out the temperature amplitudes. This naturally raises the global mean. The thicker the atmosphere, the more the amplitudes are cut down. But by itself, this process could only ever raise the global mean as far as the ideal BB emission temperature corresponding to the particular planetary radiative balance. At this point, the global surface would be isothermal both in space and time. Mars is very far from this situation. Earth is quite far from it, but still much closer. Venus is pretty much there.
- The drawback (as seen from a surface perspective) of placing an atmosphere on top of a solar-heated planetary surface is that clouds and areosols and the air molecules themselves prevent parts of the incoming solar heat from ever making it to the ground, reducing its heating potential, by reflecting and scattering and absorbing significant parts of the solar radiation. The averaged 296 W/m2 no-atmo surface input (the lunar value) is reduced in this way, on Earth, to a mere 165 W/m2. That’s nearly an 80% cutback. Which means that the target for the atmospheric process of evening out the temperature amplitudes on our planet would be 232K rather than 269K.
- However, this is where the mass of the atmosphere comes into proper play. The surface becomes directly convectively coupled with the atmosphere, and immediately starts shedding some of its energy to it rather than to its ultimate heat sink, space, warming the atmosphere in the process. The surface heat thus being transferred to the massive atmosphere above piles up in the atmosphere (it is ‘trapped’, it never reaches space, but goes rather into accumulation, extending the quasi-surficial ‘internal energy’ storage of the planetary system, on Earth encompassing the land, ice and biosphere, the ocean, and the atmosphere) and distributes there in a very specific pattern, warmer down low, cooler up high, up to the point of thermal balance, a steady state where the energy and temperature distribution from the surface up to what is called the ‘tropopause’ is forced to settle around a gravity-constrained (pressure/density) gradient. In this state of dynamic equilibrium there is finally a mean balance being achieved between the heat coming in through the ToA and into the surface and the heat going out from the surface and out through the ToA. Any ‘new’ heat coming in from the Sun and going out from the surface after this stage is considered ‘surplus energy’ and needs to be shed from the Earth system as a whole to space. However, it will have to do so by first moving through the warm atmosphere, along the naturally set up temperature gradient. The surface excess energy is thus transported by convection from the heating end (the surface at the bottom) through to the cooling end (the tropopause at the top). In other words, the atmosphere acts like a ‘conductive’ insulating layer around the constantly solar-heated planetary surface, putting certain limits on the heat transfer rates away from the surface.
- The upward movement of air from the lowermost layer of the atmosphere, directly warmed from (and/or buoyed by) surface>air heat transfer, the de facto mechanism facilitating the effective cooling of a solar-heated surface under a massive atmosphere, is far from unrestricted in its operation at some particular temperature (kinetic level). It is limited mainly by three atmospheric mass properties: (1) the atmospheric temperature (gradient), (2) the atmospheric pressure, and (3) the degree of atmospheric ‘sluggishness’.
- (1) The gentler the tropospheric vertical temperature gradient, the slower the relative upward movement of air for a particular level of surface heating. In other words, the more the surface needs to warm in order to sufficiently increase the rate of convective heat transfer up and away from the surface (compare the balsa wood wall analogy). This is probably the more important temperature-raising factor on Mars (adiabatic lapse rate: 4.3 K/km; environmental lapse rate: 2.5 K/km).
- (2) The heavier the atmosphere, the greater the surface pressure and the harder water (H2O) would find it to evaporate from the surface of a planet at a particular temperature. In other words, the warmer a watery surface would need to be to sustain an adequate rate of evaporation, to balance a certain level of solar heat input. This is most likely the most important temperature-raising factor on a water world like Earth.
- (3) The thicker and heavier the atmosphere, the more sluggish it becomes, and the more resistant to change (non-responsive) – and hence, stable – it gets. Horizontal temperature/pressure differentials will be smaller, leading to slower and more steady wind regimes. At the same time, the air moving along the surface will tend towards more laminar and less turbulent flow, reducing the vertical component of surface air movement. Finally, the temporal (diurnal/seasonal) temperature/pressure differentials will be smaller, leading to more stable vertical gradients, a situation which in turn inhibits efficient convective uplift. This is most likely the most important temperature-raising factor on Venus, whose surface air is nearly isothermal in space and time, super-heavy and sludgy, almost non-responsive to external forcing, moving extremely slowly in a near-perfect laminar manner and with a highly stable lapse rate from the surface and several tens of kilometres up.
Finally, I will need one more post on this topic to address the obvious issue of radiation. Why doesn’t a planet’s own thermal radiation matter in the end when it comes to its mean steady-state surface temperature? Bottom line: It’s an effect, not a cause of the temperatures ultimately set by the other processes discussed in this post.