Be sure to read Part 1 first, now …
DEFINING THE rGHE THROUGH THE ERL.
How is the rGHE defined in the most basic way? If you have a planet with a massive atmosphere, the strength of its “greenhouse effect” is defined as the difference between its apparent planetary temperature in space and the physical mean global temperature of its actual, solid surface. The planet’s apparent temperature in space is derived simply from its average radiant flux to space, not from any real measured temperature. It is assumed that the planet is in relative radiative equilibrium with its sun, so is – over a certain cycle – radiating out the same total amount of energy as it absorbs.
If we apply this definition to Venus, we find that the strength of its rGHE is [737-232=] 505 K. Earth’s is [288-255=] 33 K.
The averaged planetary flux to space is conceptually seen as originating from a hypothetical blackbody “surface” or ‘radiating level’ somewhere inside the planetary system, tied specifically to a calculated emission temperature. This level can be viewed as the ‘average depth of upward radiation’ or the ‘apparent emitting surface’ of the planet as seen from space. Normally it is termed the ERL (‘effective radiating level’) or EEH (‘effective emission height’).
The idea behind the ERL is pretty straightforward, but does it accord with reality? The apparent planetary temperature of Venus in space is 231-232K, based on its average radiant flux, 163 W/m2. Likewise, Earth’s apparent planetary temperature in space is 255K, from its mean flux of 239 W/m2. In both of these cases, the planetary output is assumed to match its input (from the Sun), so one ‘simple’ method one could use to derive the apparent temperature of a planet is by taking the TSI (“solar constant”) at the planet’s (or moon’s) particular distance from the Sun, and multiply it with 1 – α, its estimated global (Bond) albedo, a number that’s always <1, finally dividing by 4 to cover the whole spherical surface. Determining the average global albedo is clearly the main challenge when going by this method. The most common value provided for Venus is 0.75, for Earth 0.296.
But does the resulting value really say anything about the actual planetary temperature? If the planet absorbs a mean radiant flux (net SW) below its ToA, then how this flux affects the overall system temperature very much depends on the system’s total bulk heat capacity. If it is large, the flux will have little effect, if it’s small, the flux will have a bigger effect.
Either way, what one tends to assume is that the planetary system needs to warm (that is, store up solar energy) until it has attained a temperature high enough for it to emit the same amount of energy per unit time as it absorbs: heat IN = heat OUT.
And in one way, this is of course correct.
The problem is to determine where this ideal ’emitting temperature’ is to be found. This is where the concept of the ERL comes in. And it is very much a ‘concept’ rather than a real ‘thing’. A planet’s energy budget, its heat balance with its surroundings (sun/space), isn’t really in itself tied to any single temperature. It only really concerns how much energy enters and thus how much energy needs to be expelled. It is only us humans and our mathematical devices that apparently feel the need to turn these fluxes or amounts of energy into specifically defined temperatures. We simply understand the concept of ‘temperature’ better than we understand the concept of ‘energy’. We feel temperatures, not energy. Temperatures are concrete, energy is abstract.
So we average the total amounts of energy exchanged into mean transfers, power density fluxes. We take all the energy and divide it by time and area and get a useful and easy-to-handle value: J/s/m2. The nice thing is, we can then enter this value into the Stefan-Boltzmann equation, describing the relationship between the surface temperature of an object and the potential thermal emission from that surface as a result of that temperature. And the operation of course works equally well both ways. One can just as easily find the object’s surface temperature from knowing the intensity of its thermal radiance. But, we will have to average …
So if we estimate that Venus at dynamic equilibrium with the Sun emits an average flux to space of 163 W/m2, then, without much ado, we can derive its apparent planetary temperature in space to be 231.5K. Perfoming the same calculation on Earth gives an apparent emitting temperature of 255K.
But what do these calculated temperatures actually signify? What are they? Are they real? Or are they just mathematical constructs?
Unless they can be connected directly to a global, isothermal blackbody surface somewhere within the planetary system, they are not real. They are just hypothetical quantities.
WHY IS THE rGHE ERL RAISED? WHAT IS IT SUPPOSED TO DO?
According to the rGHE hypothesis, a planet’s effective radiating level to space is lifted off the actual surface of that planet and into the massive atmosphere above it because this atmosphere, being IR-active, intercepts some of its thermal radiation meant for space, absorbing it down low and emitting it as its own from cooler air layers up high. The atmosphere is simply seen as the shell around the central sphere in Willis Eschenbach’s ‘Steel Greenhouse’ model. Before the atmosphere (the shell) is introduced, the planet’s (the central sphere’s) effective emitting surface to space coincides with its own. It both absorbs and emits the entire radiant flux from its heat source (the Sun) at its actual surface: 240 W/m2 IN, 240 W/m2 OUT. This is the lunar situation.
Then, as the atmosphere/shell is put in place around the planet/sphere, the planet is no longer directly connected with its surroundings. The atmosphere intervenes. It is basically ‘in the way’, the extended system’s new effective emitting surface to space. The central planet’s outward flux is now absorbed by the atmosphere, warming the atmosphere. The point is, the atmosphere needs to warm like this up to the point where it is able to emit an amount of energy per unit time to space to match the incoming flux from the Sun to the total system. Since the atmosphere is now the extended planetary system’s new effective emitting surface, absorbing the planet’s energy on the inside and emitting its own energy to space on the outside, and the system as a whole is still absorbing the same amount of energy from its heat source, the Sun, it follows that this balance is only reached at the point where the atmospheric temperature matches the planetary surface temperature before the atmosphere was emplaced.
So how is this supposed to work? The basic premise goes like this: The solid surface can only radiate one way – up. The atmosphere, on the other hand, absorbs only from below, but emits both up and down. Up to space and back down to the surface; the famous (or infamous) atmospheric “back radiation” or DWLWIR.
So if the shell, the atmosphere, absorbs 240 W/m2 from the planetary surface below, it emits only half to space (120 W/m2); the other half is recycled, back down to the surface it goes. So how can the ‘outer’ surface of the atmosphere shell warm so that it ends up radiating the 240 required W/m2 to space all by itself?
This is where we enter the warming stage of the rGHE-concocted internal amplifying radiative transfer loop of the atmosphere/surface system. The atmosphere is always returning half the flux from the surface, in turn feeding the atmosphere with ever more energy, until the ‘net’ flux between them equilibrates at 240 W/m2:
Energy absorbed by the surface (sun+atm) ⇒ sfc UWLWIR ≻ ≺ atm DWLWIR = Net LWsfc-atm
240 ⇒ 240 ≻ ≺ 120 = 120
240+120 ⇒ 360 ≻ ≺ 180 = 180
240+180 ⇒ 420 ≻ ≺ 210 = 210
240+210 ⇒ 450 ≻ ≺ 225 = 225
240+225 ⇒ 465 ≻ ≺ 232.5 = 232.5
240+232.5 ⇒ 472.5 ≻ ≺ 236.25 = 236.25
240+236.25 ⇒ 476.25 ≻ ≺ 238.125 = 238.125
240+238.125 ⇒ 478.125 ≻ ≺ 239.0625 = 239.0625
240+239.0625 ⇒ 479.0625 ≻ ≺ 239.53125 = 239.53125
In the new steady state, the sphere/planet, the old emitting surface to space, from an elevated temperature of 303.3K, emits 480 W/m2 to the atmosphere, the new emitting surface to space. At this time, the atmosphere emits 240 W/m2 down to the surface, but also significantly up (out) to space, from an equilibrated temperature of 255K.
As you can gather from this, the steady state ERL temperature is achieved by the parallel warming of the surface and the atmosphere, and the warming of the surface (and thereby of the atmosphere) is accomplished not by the reduced flux from the new extended system to space, but directly by the addition of more and more “back radiation” from the warming (absorbing/emitting) atmosphere.
The upshot: The ‘raised ERL’ model of the rGHE mechanism for ‘extra’ surface warming turns out to be nothing more than another and simply a bit more convoluted version of the “heating by back radiation” narrative.
When it comes down to it, you cannot get the surface to warm some more – the rGHE way – by any other means than increasing the atmospheric “back radiation”.
This is what the concept of the (raised) ERL is ultimately all about. The atmosphere absorbs IR from the surface. Hence it also emits IR back down to it. Warming it. It isn’t really about the upward radiation through the ToA at all. It’s about the downward radiation to the surface. Guy Callendar’s original “sky radiation” idea.
It’s this funny diagram all over again:
Figure 1. (Derived from Stephens et al. 2012.)
TWO DIFFERING VIEWS ON HOW TO ATTAIN A THERMAL EQUILIBRIUM
The imagined ‘internal amplifying radiative transfer loop’ of the rGHE hypothesis is actually just a misconstrued version of the real-world situation.
There simply is no continuous radiative transfer of energy going on inside the atmosphere, looping up and down and back and forth, warming in all directions, getting bigger for each cycle, during the energy buildup towards the new steady state.
There is only a storing up of internal energy. As in any real-world, warming thermodynamic system.
This is the key to understanding: There’s a distinct difference between energy being statically accumulated inside a warming thermodynamic system and energy being dynamically transferred between thermodynamic systems.
If you don’t get this distinction, you won’t understand what’s going on.
What the rGHE hypothesis is essentially saying is that, in the new steady state, the solar flux is finally once again given a free pass all through the system: Conceptually, 240 W/m2 come in to the surface, warming it; the 240 W/m2 then move out from the surface, cooling it back, and is absorbed by the atmosphere, warming it; the 240 W/m2 then finally move out from the atmosphere, cooling it back, and ends up in space, where it originally came from. The overall temperature at this stage will thus not change. It warms as the Sun shines, and cools back down when the Sun’s out of sight.
The point is that, in addition to this lossless ride of the solar heat through the Earth system, there is now a continuously (and constant) cycling loop of radiative energy transfer up and down between the surface and the atmosphere, absolutely necessary to maintain the steady-state temperatures enabling this equilibrated situation to last. This transfer loop, in the steady state, is really a zero-sum game*, but that doesn’t mean it can be removed in any way. If it’s removed, then the entire Earth system will freeze cold.
*480 W/m2 up from the sfc, of which 240 go straight to space (the ‘solar flux’ part) and 240 to the atm, after which the atm returns those 240 back to the sfc, adding it to its 240 W/m2 in from the Sun and enabling it to emit 480 W/m2 up to space and the atmosphere in combination. In this way, 240 W/m2 always moves up and down between the sfc and the atm, while at the same time an equal flux always escapes to space:
The thing is, the orange internal atmospheric radiation loop in Figure 2 doesn’t really exist. It’s purely a figment of someone’s imagination. What exists is rather the statically stored ‘internal energy’ held within the thermal mass of the atmosphere system, giving it its steady-state temperature (and temperature distribution). There is no continuous thermodynamic zero-sum transfer game of radiative energy back and forth between the surface and atmosphere, keeping the temperatures up.
What the ‘radiationers’ perceive as the cause of the steady-state temperatures (the necessary, eternally cycling radiative transfer loop), is really just an apparent effect of those steady-state temperatures (actually caused simply by the storing up of ‘internal energy’). ‘Thermal radiation’ is called thermal radiation because it is the result of warmth, of temperature, not because it causes that warmth or temperature.
OUR PLANETARY NEIGHBOURS IN SPACE
We have talked about the apparent and/or potential ERL-driven rGHEs on Venus and Earth. We have yet to discuss Mars.
While Venus carries an enormously massive atmosphere, Earth’s is much more moderate in mass, density and pressure. Still, when compared to the Martian atmosphere, ours can practically be considered Venusian. Consider surface air pressure and density on the three neigbouring planets:
VENUS ……. sfc air pressure: 92 bar (92x) ………….. sfc air density: 66.5 kg/m3 (54.5x)
EARTH ……. sfc air pressure: 1 bar …………………….. sfc air density: 1.225 kg/m3
MARS ……… sfc air pressure: 0.0063 bar (/158) ….. sfc air density: 0.02 kg/m3 (/61.3)
So in a way, Earth’s atmosphere can be considered to be centred somewhere around the median point on a mass continuum between two extreme cases, the incredibly dense and heavy one on the one end and the incredibly thin and light one on the other.
The apparent radiatively/rGHE-driven ERL on Venus (and on Earth) is in actual fact an illusion. When comparing Venus and Earth directly, we soon realise how the strictly radiative story of the Venusian atmosphere is first and foremost one about depriving the planetary system and its different levels, significantly the surface, of solar heat, and that it is simply the enormous mass of the Venusian atmosphere, making it so much denser and deeper than Earth’s, that forces the low pressure/density/temperature levels much higher up above the solid surface:
Figure 3. A crude schematic comparing the overall planetary systems of Venus (a)) and Earth (b)) and their main heat fluxes IN/OUT. Note in b) that Earth’s lower, solid line tropopause is the global average one (at 12 km and 200 mb), while the upper, dashed line tropopause is the Hadley-cell (tropical/subtropical) one (at 16-17 km and 100 mb). What you will notice is how the ‘average depth of atmospheric upward LW radiation’ (the ERL) – the lowermost end of the orange arrows – on Venus is located at/around the actual tropopause, made up of a thick blanket of clouds, while on Earth it is located much further down, deep within the airy troposphere, a difference thought to reflect the general levels of atmospheric IR-opacity of the two planets. At the same time, you will observe how the Venusian atmophere reflects and absorbs nearly all of the incoming radiant heat from the Sun (the yellow arrows), preventing 97.4% of the potential solar heat input from ever reaching the actual, solid surface at the bottom, while Earth’s atmosphere, on the other hand, does the same to only a moderate extent (preventing 44.4%). The final point to bear in mind is how much higher above the surface you need to go on Venus (60-64 km) to get to the 200-100 mb level (the tropopause) than on Earth, a reflection of the monstrous mass of the Venusian atmosphere compared to Earth’s, putting a 92,000 mb pressure on the surface where Earth’s atmosphere merely exerts a thousand (1013 mb on average).
If the Venusian atmosphere had the same mass as Earth’s, if Venus received the same solar input as Earth and its troposphere had the same lapse rate, then its troposphere would climb up to the 200 mb level (like on Earth and ‘real’ Venus), at initially the same altitude (~12 km) above the surface (same mass and assuming same tropospheric temperature and ignoring differences in chemical composition, like heavy CO2 (Venus) vs. light H2O (Earth)), and from there on up to ~50 mb would be the thick, global, isothermal tropopause cloud layer, practically emitting the planet’s entire flux to space. However, the required flux to put out would be much smaller than Earth’s, because the same cloud layer would also reflect a much larger portion of the incoming solar:
Figure 4. a) The radiative/convective situation on ‘terrestrial’ Venus (an atmosphere having the same general level of EMR-activity as ‘real’ Venus, but the mass of Earth’s atmosphere). At Earth’s distance from the Sun (1AU), 341 W/m2 comes in to ‘terrestrial’ Venus. Its atmosphere then reflects 67-68% of the incoming solar radiation (as compared to ‘real’ Venus: 75% (Figure 3)), letting only 110 W/m2 through, and proceeds to absorb 60% of the remaining downward flux (as compared to ‘real’ Venus: 90%), so that the actual, solid surface only receives 44 W/m2 of solar heat for it to absorb. Since ‘terrestrial’ Venus’s atmosphere is almost completely made up of CO2 (like on ‘real’ Venus), it can only absorb upward surface IR within its specific, pressure-broadened spectral bands. Meaning a lot will go straight through. This freely escaping surface IR, will not reach straight to space, though. It will move up to the haze or cloud layers high up in the troposphere, absorbed by these instead. Three things to notice when comparing ‘terrestrial’ Venus in a) with Earth in b): 1) The required LW output from the Earth system is 2.2 times as big as the Venusian one (240 vs. 110 W/m2); 2) the Venusian atmosphere being a ‘cloud emitter’ and Earth’s being an ‘air emitter’ means that the latter will have to collect its aggregate flux from a much deeper part of the atmospheric column, on Venus, everything from below is ultimately captured by the cloud lid at the top; 3) on Earth, the surface absorbs 165 W/m2 worth of solar heat, nearly four times as much as the surface of ‘terrestrial’ Venus, whereas a mere 24 W/m2 are shed by non-radiative processes on Venus (basically, conduction>convection), a flux 4-5 times as weak as the equivalent one on Earth, but exactly the same as Earth’s conductive loss. Either way, nothing in this setup points to any particular radiative effects forcing the surface of ‘terrestrial’ Venus to be warmer than Earth’s.
Which leads us to the titanic mass of the Venusian atmosphere. Its mechanism for surface warming will be revealed a bit further on. First, our other planetary neighbour, the small, red one …
What, then, goes on on a planet with a tenuous atmosphere such as the Martian one, where the gas molecules are relatively few and far apart?
I’ll cut right to the chase: The mean global surface temperature of Mars, according to the ‘Thermal Emission Spectrometer’ (TES) instrument aboard the ‘Mars Global Surveyor’ (MGS), and so now generally accepted by NASA, is ~210-211K (based on multiple-year measurements with no real trend observed, albeit slight interannual differences). Its central estimate is corroborated by the overlapping and succeeding investigations of the ‘Mars Climate Sounder’ (MCS) spectrometer aboard the ‘Mars Reconnaissance Orbiter’ (MRO), plus in situ surface measurements from various landers like Viking 1 and 2 and Pathfinder.
Since the mean TSI (“solar constant”) at Mars’s average distance from the Sun (1.52 AU) is ~587 W/m2 and the Red Planet’s mean global albedo appears to be ~0.235 (TES gives 0.232, MCS 0.239), this means the absorbed solar flux at the ToA would be ~112.3 W/m2 (equivalent to Earth’s 239 W/m2), which would again be associated with a planetary blackbody temperature in space (equivalent to Earth’s 255K) of … ~210-211K.
Now isn’t that quite an astounding coincidence!?
Mars’s ‘effective/apparent planetary emission temperature in space’ happens to be exactly equal to its ‘physical surface temperature’.
Recalling the rGHE equation:
Tsfc = Terl + (Γ*H). For Mars, this gives: 210K = 210K + (2.5 K/km * 0 km)!
The planetary ‘effective radiating level’ on Mars is coincident with the actual, solid planetary surface. It appears not to be raised one single metre off the ground!
How can this be?
Mars does after all possess a massive atmosphere lying on top of its solar-heated surface. It’s not impressively massive in any way, a mere 25 teratonnes where Earth’s is 5148. But it’s still there. And most importantly, it is significantly IR-active, made up of ~96% CO2. It does absorb outgoing radiation from the ground.
In fact, the Martian atmosphere contains a lot more CO2 than Earth’s atmosphere does. Each cubic metre of atmosphere above each square metre of Martian surface holds
~28 ~26 times (!) as many CO2 molecules as does a similar volume over a similar area on Earth. This would be equal to 10,400 ppm in our atmosphere, or 1.04% of it. Which is quite comparable to Earth’s average global atmospheric boundary layer content of all IR-active substances, mainly including water.
So how come our ERL is (allegedly) lifted 5-6 kilometers up in the air, while Mars’s stays firmly on the ground, when the total IR-opacity of the two atmospheres are in fact rather similar? Yes, water clearly absorbs wider across the EMR spectrum than what CO2 does, so Earth’s atmosphere would effectively be more IR-opaque than Mars’s. But that doesn’t explain why the Martian ERL apparently isn’t raised at all.
What makes the whole difference is of course the overall mass, the total molecular density of the atmosphere. Regardless of the specific content of actually IR-active constituents …
On Mars it is quite easy to show how silly the whole ERL concept really is. Because on Mars, the atmospheric IR window stands pretty wide open, the only significant absorber being CO2 (although aerosols/dust and the few tiny clouds do contribute):
Figure 5. Left diagram: From Bandfield et al. 2013 (Figure 1); Right diagrams: From Pierrehumbert 2011 (Figure 3b), caption stating: “The panel to the left shows a summer-afternoon emission spectrum for Mars observed by the TES instrument on the Mars Global Surveyor. Its accompanying temperature profile was obtained from radio-occultation measurements corresponding to similar conditions. (…) squiggly arrows on the temperature profiles indicate the range of altitudes from which IR escapes to space.”
I’ll exemplify how silly it might get.
Let’s assume that, of the incoming solar flux below the ToA (112 W/m2), about 15 are absorbed by the atmosphere and its dust particles. This leaves 97 W/m2 of incoming heat to be absorbed by the surface. So the surface also has 97 W/m2 to shed, as total heat.
Well, the surface holds a mean temp of 210-211K, so emits an UWLWIR ‘flux’ (its S-B-calculated radiance) of 112 W/m2. Of this, ~75 W/m2 is directly lost to space through the atmospheric window. Looks more like 95 W/m2 from the spectras in Figure 5? I agree. But let’s ignore that for now. Hopefully, you’ll see where I’m going with this.
The Martian surface absorbs a solar flux of 97 W/m2. It then emits 75 of these straight back out to space. The surface also loses some heat to the massive atmosphere above by way of conduction>convection; let’s assume it amounts to an average of 10 W/m2. This leaves [97-75-10=] 12 W/m2 to be transferred as radiant heat from the surface to the atmosphere.
97 IN, [75+12+10=] 97 OUT. Heat balance.
What, then, about atmospheric “back radiation”? Well, the surface, from its temperature (210-211K), emits 112 W/m2, but only [75+12=] 87 of them escape as radiant heat, so one would expect the atmosphere to make up the balance by providing a DWLWIR ‘flux’ of [112-87=] 25 W/m2. This way, the surface ends up absorbing a total radiant input of [97+25=] 122 W/m2, which is handled by emitting back out 112 W/m2 and losing the final 10 through non-radiative processes.
[97+25=] 122 IN, [112+10=] 122 OUT. Energy balance.
But what now of the atmosphere’s budget?
The atmosphere absorbs 15 W/m2 directly from the incoming solar, 10 via conduction>convection from the surface, and 12 through radiant heat transfer from the surface, a total of [15+10+12*=] 37 W/m2 (*UWLWIR 37 – DWLWIR 25). Since the surface, as we saw above, emits 75 of the system’s required aggregate flux of 112 W/m2 to space, it rests upon the atmosphere to shed the remaining heat, meaning, just those 37 W/m2.
But from where exactly? From what level? Or levels? Is this level (or are these levels) determined by the atmospheric IR-opacity? Or by its temperature? Or by both? Or by something else entirely?
Let the silliness begin.
The atmosphere absorbs heat from three different sources: 1) from solar SW radiation, 2) from surface LW radiation, and 3) from surface conduction>convection. Originally, three separate ‘batches’ of energy.
So, how high up must the energy transferred from the surface via conduction>convection (the 10 W/m2) go before it can be emitted to space?
If we follow ERL logic, it cannot escape until it has reached an altitude of ~38 km above the surface, the air layer holding an average temperature of 115K (assuming a Martian mean global environmental lapse rate of 2.5 K/km). One can only assume this is because the IR-opacity of the atmosphere won’t allow it to escape any sooner. Even though it’s 10 W/m2 already from the start, when moving out of the relatively ‘warm’ surface …
What about the 15 W/m2 in from the Sun? 33.2 km. The 12 W/m2 from surface LW? 36 km.
Does this make any sense? Or do we have to add all three batches together first and only then decide? 15+12+10= 37 W/m2. This is what (in this particular setup) the Martian atmosphere actually emits to space, after all.
So, does that mean the ERL is really situated about 20.4 km above the planetary surface?
If this were true, then Mars’s apparent temperature in space would be 150K rather than ~210-211. It’s not.
We might try to argue that the 150K is the apparent temperature of the Martian atmosphere, not of the planet as a whole.
But then we’re no longer talking about the planetary ‘effective radiating level’, the actual ERL as defined, are we? That’s the solid surface, after all, there’s no question about it. We’re only talking about the ‘average (or apparent) depth and temperature of atmospheric upward radiation’. Based solely on the Stefan-Boltzmann connection. We don’t know if this is physically the average depth of radiation. We only assume it to be so from our understanding/interpretation of the temperature-radiance relationship of blackbody surfaces. 37 W/m2 is simply the amount of energy the Martian atmosphere has to put out to space. And that’s all there is.
But how come the elevated ‘average depth and temperature of atmospheric upward radiation’ doesn’t raise in the least the solid surface temperature above the apparent planetary temperature on Mars? How come the fact that some of the surface IR is absorbed by the Martian atmosphere still doesn’t do anything at all in terms of forcing the surface temperature to be higher than the overall planetary one?
THOSE are the questions I would like for you to focus on. Because THOSE are the key to ulocking the mystery! The mystery of what really forces surface temps: atmospheric mass or radiation?
Let me give you a couple of clues:
From UniverseToday.com (June 2008): “Temperature of Mars”
“Mars follows a highly elliptical orbit, so temperatures vary quite a bit as the planet travels around the Sun. Since Mars has an axial tilt similar to Earth’s (25.19 for Mars and 26.27 for Earth), the planet has seasons as well. Add to that a thin atmosphere and you can see why the planet is unable to retain heat. The Martian atmosphere is over 96% carbon dioxide. If the planet had an atmosphere to retain heat, the carbon dioxide would cause a greenhouse effect that would heat Mars to jungle like temperatures.”
From Space.com (Aug 2012): “What is the Temperature of Mars?”
“Mars’s atmosphere is about 100 times thinner than Earth’s. Without a “thermal blanket,” Mars can’t retain any heat energy.“
The first quote is the ‘funniest’. Author Jerry Coffey can’t seem to connect the dots of his own observations: Mars has such a thin atmosphere that it can barely retain any heat. This makes the Martian surface cold. The exceedingly thin atmosphere, however, is made up of 96% CO2. So if only the atmosphere were much thicker than it is, enabling it to retain heat (like the atmosperes of Earth and Venus), then the CO2 would all of a sudden cause the surface of Mars to heat! So not the acquired atmospheric thickness itself. Not its newfound ability to retain heat. No, its content of CO2 specifically, which already in its thin state is up to 96% (and thus 26 times the absolute concentration of Earth’s atmosphere!), but which is then apparently unable to heat anything. For some odd reason …
A classic example of the kind of mental contortions of self-deception that a steadfast ‘radiationer’ will perform in order to make his expected reality fit with reality itself. The never-ending effort to reduce his constantly recurring cognitive dissonance.
Tim Sharp at Space.com keeps it more honest. At least in what he writes.
The reason why there is no apparent raised ERL and hence no rGHE, as defined, on Mars, the reason why its atmosphere cannot radiatively raise its surface temperature above the planetary one, is very simple: The atmosphere is way too thin. It can barely retain any heat.
It doesn’t matter if 96% of it is CO2. It can do nothing as long as the bulk of the atmosphere remains as rarefied as it is.
Which naturally raises the question: If the atmosphere got thicker and the surface of Mars grew warmer as a result, would it then be the radiative properties of its CO2 molecules that caused the extra heating? Even though they apparently do nothing in the present state …
Think about it, and consider this:
THE (REAL) MECHANISM EXPLAINED
What will normally happen in Earth’s relatively dense IR-active atmosphere is the following (a crude, general description):
A CO2 molecule – for instance – in the near-surface air absorbs a 15 μm wavelength IR photon from the surface, is excited from having its energy content boosted, but collides almost immediately with a nitrogen (N2) or oxygen (O2) molecule, giving up its newly gained surplus energy to this one by conduction. In other words, it doesn’t get to reemit this energy in the form of another photon to fall back to its former state. It rather passes it on conductively by collision.
The denser the air, the harder it will be for the CO2 molecule to reemit rather than pass on the absorbed energy conductively, meaning, the higher the ratio of gained energy lost by molecular collisions to that lost by reemission events.
The N2 and O2 molecules (making up 99% of our bulk atmosphere) thus statistically ending up with this extra energy transferred from the surface, will help to maintain the overall temperature of the atmosphere by moving a little bit faster. They need to do this, because at the same time higher up the air column, other molecules are moving a little bit slower from losing energy to space. However, there is no balance to be obtained from air molecules moving faster and faster down low (from absorbing heat from the surface, the ‘hot reservoir’) and molecules moving slower and slower up high (from emitting heat to space, the ‘cold reservoir’), if there is no natural process to connect the two levels. Then the temperature difference between them would simply grow ever larger, the gradient from hot to cold ever steeper. A highly unstable situation that could never be sustained (simply not tolerated) within a massive volume of gas subjected to gravity and heated from below.
No, what will happen is of course this: The warmed air down low will become less dense (from the faster-moving molecules) and float up spontaneously to higher levels through natural buoyancy to equilibrate with its surrounding air masses, automatically keeping the steady temperature gradient in place. Likewise, only the other way around, the cooled air up high will become more dense (from the slower-moving molecules) and spontaneously start to subside in order to equilibrate at lower levels. In this way, the layers of air up through the column is always sure to be replaced (too warm by cooler, and too cool by warmer), the constant organised circulation or ‘turnover’ of air masses in the troposphere ensuring the stable distribution of energy and hence temperature from top to bottom. Radiative processes simply work to stimulate this natural turnover circulation, keeping it running smoothly and stably (through a net ‘warming’ tendency down low, and a net ‘cooling’ tendency up high).
In this way, the excess energy from the surface is certain to always ‘leak’ upward through the troposphere by the movement of the heated air itself.
High up in the atmosphere, the air density is much lower. In fact, already at 5 km up the atmospheric column, the air density is reduced to 60% of the surface value. At 10 km, it’s down to a third, and at 15 km the air is no more than ~15% as dense as it is at the surface. (Also, the air up there is colder, so the gas molecules travel more slowly through space.) This means that the CO2 molecules do not collide with other air molecules as often as further down, which means their chances of emitting in the form of a photon any surplus energy it might possess or acquire are better.
Most of the energy transferred from the surface (or the Sun) to the atmosphere as heat, is ultimately held by N2 and O2 molecules (ending there by way of diffusion/conduction), but since these molecules are not themselves able to effectively release this energy to space in the form of radiation, thus also letting the atmosphere cool back from the original absorption, they have to transfer their surplus energy (once again by way of collisions) to the actual IR-active constituents of the atmosphere, like CO2 (and, much more importantly, H2O), in order for these to do the job and rid the extended Earth system of it. This process is easier to accomplish the higher up the air column (down the pressure/density gradient) you get, for the reason mentioned just above.
What is the corollary of this?
Moving from the initial to the final (steady) state of warming, what the solid surface needs to do is feed and thereby fill the massive atmosphere above it with (internal) energy, up to the point where the atmosphere, functioning as the now extended planetary system’s new effective emitting surface to space, is able to radiate away as much heat as what the total system originally absorbed from the Sun.
* * *
I must once again stress the distinction between what is perceived (by the ‘radiationers’) as a continuous output of thermal radiation associated solely with the specific temperature of the air, and the temperature of the air itself. You can only ever tranfer energy away from a system in dynamic thermal equilibrium that at some point earlier has been transferred to it. What is radiated from the atmosphere (to space) is simply the energy previously absorbed from the Sun by the planetary system. The radiative output from the surface/atmosphere system to space is ONLY to match the solar input; no more, no less. The temperature of the system is related ONLY to its static content of internal energy. The only quantities acting as dynamic transfers to/from the system is the incoming ‘net SW’ and the resulting outgoing LW (‘OLR’) at the ToA. And that’s it.
Conceptually, one can view the ‘Sun>surface>atmosphere>space system’ as a grand energy conveyor belt, with solar SW radiation as the heat input (Qin) to the heating end (sfc), convection as the transporter of Earth’s resulting internal energy (U) from heating end to cooling end, and finally terrestrial LW radiation as the heat output (Qout) from the cooling end (tropopause).
Imagine an open tank brimful of water. This tank with all its water would represent our steady-state atmosphere and all its stored-up internal energy (enduing it with a steady-state temperature and temperature distribution).
If we were to connect a pipe to the bottom of the tank and open the valve to let the pipe supply the tank with, say, 240 new litres of water every minute (4 l/s), this would be equivalent to our Sun supplying our planetary system (conceptually via the solid surface) with an average energy (heat) input of 240 W/m2.
Where would the water added at the bottom go? It would become part of the total volume of water contained within the tank. However, at the same time, the tank would also necessarily – being brimful – overflow by the exact same amount of water from the top. The new bottom water would ‘push’ the old top water out. In this way, the total volume would never change, the outflow would always match the inflow.
This is effectively what goes on in our atmosphere in the steady state as well. As new heat from the Sun is added from the bottom of the atmosphere, the whole convective air column above shifts upward, ‘pushing out’ the exact same amount of heat from the top. In between is only the (rather slow) bulk movement of internal energy. The energy is always there, stored up, but it is never released to space unless there’s an extra ‘heat push’ from below.* Heat IN > gained (‘new’) internal energy at the bottom replacing lost (‘old’) internal energy at the top > heat OUT. A conveyor belt.
*No, energy released during the night is not energy released independently of an extra ‘heat push’ from below. The output simply always lags the input, the response is extended rather than direct (2+0 = 1+1 rather than 2+0 = 2+0), the terrestrial LW intensity can never match the daytime solar heat, but is more consistent, spread out in time, so still manages to expend the original gain over a full cycle.
* * *
So, at what point will the surface/atmosphere system stabilise (equilibrate)? At what time is enough energy ‘filling’ the system? In what state, in what condition or configuration will as much heat as what comes in be able to be emitted out as well?
The troposphere, the lowermost part of the atmosphere, in direct thermal contact with the solar-heated surface, inflates, its outer edge (the tropopause) lifting (it can move in no other direction) through the upward propagation of surface heat by bulk air movement. As this occurs, the troposphere is warmed and expands thermally, stretching the air column so that both the pressure and the density gradients become gentler, the scale height (H) would increase, meaning you would have to go higher from one specified pressure or density level to one reduced by a factor of ~2.72 (e). To provide some examples: If the surface temperature of Titan (Saturn’s largest moon, and the only moon in the solar system with a substantial atmosphere) happened to rise from its actual 94K to Earth’s 288, then its scale height would increase from 20.5 to almost 63 km! That is, you would all of a sudden have to move 63 rather than 20.5 km up into the atmospheric column, from the
1.47 1470 mb surface pressure, to reach the 541 mb level. On Venus, if you went from its actual surface temp of 737K to Earth’s 288, its scale height would drop from 15.8 to below 6.2 km, so even if the surface air pressure remained at 92 bar, the 34 bar level (first scale height) would be located almost 9 km closer to the ground.
If the Earth’s global surface cooled to 210K, then its first scale height (1013 – 373 mb) would go down from ~8.4 to 6.1 km, its second (373 – 137 mb) from 6.8 to below 5 km. In other words, rather than being ~15.2 km above the surface*, the atmospheric 137 mb pressure level would be located slightly above 11, more than 4 kilometres further down the column.
*In reality, Earth’s 137 mb pressure level is at ~14.2 km, not 15.2; the calculation above is after all pretty crude, not taking into account how the scale height changes with every increment of ascent, not just from one scale height to the next. The principle stands, though.
So how come Earth’s global surface isn’t at 210K rather than 288? If the tropopause itself stays at the same pressure level anyway, only further down?
Simply because in this state, the air column from surface to tropopause would be far too compressed. Just as much atmospheric mass would be contained between the two levels in the 210K scenario as in the 288 one, but would fill a vastly smaller volume. The air pressure (and density) gradient(s) would necessarily be quite a bit steeper in the cold scenario than in the warm. And the air density would increase significantly all the way from the surface to the tropopause, the root of its steeper exponential curve shifted to the right on the x-axis.
This situation would be an intolerable one; unstable and unsteady. The original solar heat could not be radiated away at an adequate level of efficiency from the Earth system (energy would still escape by radiation to space from every atmospheric layer, of course; just not at the required rate).
The system would have to warm in order to stretch the tropospheric column back out. Why? Because of the relatively high mean (column aggregate) frequency of molecular collisions preventing the absorbed surface heat from escaping in sufficient amounts per unit time by radiation to space, keeping it rather ‘locked away’ as molecular KE inside the conductive/convective thermal mass of the troposphere.
There will be a balance struck in this regard between gravity, atmospheric mass (pressure/density), atmospheric composition (molecular size), and temperature, sorting out the tropopause height in between them. Compositionally defined degree of IR-opacity does not enter this equation. A massive atmosphere is an IR-active one. If it weren’t, it couldn’t get rid of its absorbed heat.
Robinson and Catling (2014) has found an interesting relationship between the average tropopause height on planets/moons in our solar system possessing massive atmospheres and the atmospheric pressure at that height:
Figure 6. (Robinson & Catling’s Figure 1.)
This diagram suggests that this fairly narrow and strangely common general tropopause range (50-200 mb) is no coincidence at all. It happens to be centred around somewhat of a ‘universal’ atmospheric balance point between convection and radiation, establishing itself as high as the surface heat (or solar heat absorbed at depth) of a planet with a substantially massive atmosphere will need to go or be brought for it to be finally and adequately radiated to space, irrespective of the specific level of IR-opacity of this atmosphere as defined by the concentration of its actually IR-active species, rather depending simply on the overall pressure/density/temperature of the bulk air. What gives the atmosphere, or layers therein, their real IR-opacity is simply their total molecular density (directly associated (along with temperature) with the rate of molecule collisions).
Let’s just quickly relate this to Earth and to our two next-door sister planets, Venus and Mars.
At the 180-200 mb level in the atmosphere of Venus (~61 km) and Earth (~12 km), there is quite exactly the same amount of molecules in a cubic metre of air, although the terrestrial ones, being lighter than the Venusian ones, move a bit faster (even if the air at that level is actually colder, 235 K on Venus, 210 on Earth),
while the Venusian ones (CO2) are bigger than the terrestrial ones (N2 and O2).
The crucial difference between Venus and Earth, though, is simply that, on Venus, the ideal atmospheric air density levels (60-65 km) consist of (is completely filled by) thick, nearly impenetrable and all-covering cloud layers, on Earth (10-15 km) mostly of pure air with only scattered clouds here and there. A dense, constant, global cloud blanket such as the Venusian one, being a fairly effective broadband (black/gray body) emitter, is able to radiate almost the entire planetary flux to space all by itself from a relatively shallow atmospheric stratum, quite closely related, in fact, to its physical temperature. There is no coincidence in the main Venusian cloud layers being situated where they are. Their height is an equilibrated one.
A single shallow layer of air is not itself capable of radiating the full flux of a cloud deck, even at the same temperature. Hence, an ‘air-emitting atmosphere’ needs to collect its aggregate flux from a far thicker portion of the column than what a ‘cloud-emitting atmosphere’ has to. This is in effect the difference between Venus and Earth (and Mars).
Finally, what about Mars?
On Mars, even the surface air density (and pressure) is way lower than the required value(s) for an effective planetary emitting “surface”. Still, that doesn’t mean the atmosphere isn’t radiating, that it can’t emit radiation to space. It does so all the way from the surface and several tens of kilometres up the column. After all, surface (and solar) heat is transferred to it, both radiatively and non-radiatively, so it naturally also has to get rid of it somehow. The tenuous Martian atmosphere radiating just doesn’t work to raise the apparent planetary emitting level (and thus temperature) off the ground, that’s the thing …
WHAT A LOAD OF EXTRA ATMOSPHERIC MASS WILL DO
In Figure 7 we have doubled Earth’s atmospheric mass (a)), without changing its average degree of EMR-activity at all (still ~0.5%), to compare it with ‘real’ Earth (b)).
What will happen?
The two Earths are located at the same distance from the Sun, their rotation periods and their axial tilts are equal, their mean global tropospheric lapse rates are also set to be the same, considering that both planets’ gravity, atmospheric specific heat and release rate and distribution of latent heat from water condensing in the air column are also assumed to be the same.
The only difference is in the total mass of their atmospheres. At the planetary surface, the atmospheric pressure is doubled in Earth a). Its surface air density is also initially twice as high as on Earth b), but this could change with the temperature (thermal pressure). As you will observe, the tropospheric column in a), containing exactly two times as much atmospheric mass as column b), is far from twice as high in the initial state. In fact, while column b) is 12 km high (from the solid surface at 1000 mb to the global average tropopause at 200 mb), column a) is ‘only’ 4-5 km higher (from the solid surface at 2000 mb to the global average tropopause at 200 mb), quite exactly as high as the Hadley-cell (tropical/subtropical) tropopause on our present Earth. The reason for this is simply that both atmospheric pressure and density fall off exponentially, not linearly.
The solar input is the same, but the total reflectivity of the doubled atmosphere planetary system in a) will likely go up a little bit (potentially more layers of clouds). Also, the doubled atmosphere will likely absorb more of the ‘SW net’ down from the ToA, having a deeper column with a denser lower troposphere and more layers of cloud. It’s hard to appraise the exact amount, but it probably wouldn’t be a lot more, considering a substantial part would already be absorbed in the upper two thirds of the column, significantly by clouds (and ozone even above the tropopause). As you can see from Figure 7, I’ve increased the reflected portion from 101 to 111 W/m2 (global albedo up from 29.6 to 32.6%) and the atmospherically absorbed portion from 75 to 95 W/m2 (from 31.3 to 41.3%).
This means that the global surface of Earth a) on average absorbs a solar heat flux of 135 rather than one of 165 W/m2 (b)), and 230 W/m2 are what needs to go out to space through the ToA rather than 240.
Next stage: Getting the heat back out.
Doubling the mass, pressure and density of an atmosphere has implications for its IR absorption/emission profile. The surface thermal radiation will be absorbed across a shallower layer down towards the ground, which means less heat will move out from the surface in the form of radiant loss. At the same time, the LW emissions to space will be able to accumulate from a deeper column, so that the ERL will most likely be situated a bit farther below the tropopause on Earth a) than on Earth b).
In the end, though, these things will not matter all that much. What matters most is the extended depth of atmosphere that the doubled mass naturally provides. From the 200 mb level (the tropopause) and 12 km down, the pressure, air density and IR-opacity of the two columns are more or less identical and proceed along the same exponential course, assuming equal temperatures.
If you look once more at the two scenarios in Figure 7 above, you should be able to appreciate from this what will have to be the end result. The more massive atmosphere still has to get its surface heat up to the atmospheric pressure/density/IR-opacity levels from where it can be effectively radiated to space. This is still the upper two thirds of the tropospheric column, from the tropopause at 200 mb and maybe 10 km down. But since this section of atmosphere is now located much higher above the surface, and since the lapse rate is still the same, this will inevitably force the average surface temperature to rise significantly.
If the 249-250 K level in column b), its ‘average depth of upward radiation’ (ERL), corresponding to a BB emission flux to space of 220 W/m2 (the total atmospheric flux, added to the sfc atm window flux of ~20 W/m2) is at around 5.8-6 km above the ground, then the 247-248 K level in column a), its ERL, corresponding to a BB emission flux of ~213 W/m2 (atm flux + sfc atm window flux of ~17 W/m2), situated about a kilometre further down from the tropopause than in column b), would still be at around 9.5 km above the surface. Extrapolating the normal lapse rate down from this level would give an average surface temperature of [(9.5 * 6.5) + 247.5 =] ~309.5 K.* Compare this to the global average in Scenario b): 288K. That’s a 21.5 degree increase!
* * *
*It is important here to point out how it is the surface that warms first. It warms (solar energy accumulates) as long as it cannot get its heat out (convectively) as fast as it comes in (radiatively). It thus needs to warm the atmosphere above to thermally inflate and stretch it, up to the point where a radiative/convective equilibrium is achieved and able to be maintained. The radiative/convective equilibrium is what keeps the average tropospheric temperature gradient aligned with the adiabatic lapse rate in a dynamic steady state. Radiation heats at the bottom and cools at the top of the atmospheric column, so is working towards steepening the gradient. Convection counteracts this tendency, lowering the gradient back down, by moving heat from the heating end at the bottom (cooling it) to the cooling end at the top (warming it). Convection is simply tasked with bringing the surface heat from the planet’s ‘old’ emitting surface (the actual, solid one) to the ‘new’ at the top of the tropospheric column. The two contrary processes of radiation and convection thus find a balance in a so-called ‘radiative-convective equilibrium’, making sure that the observed average of the ever-fluctuating environmental lapse rate corresponds to the ideal, hypothetical adiabatic lapse rate, on Earth, 6.5 K/km.
Now, there are a couple of requirements for this particular balance to be found and maintained:
- The convective engine, bringing the energy from the heating (absorbing) end to the cooling (emitting) end, up through the troposphere, needs to be at a certain level of efficiency.
- The radiative cooling from the top of the troposphere (top of convection, really) also needs to be at a certain level of efficiency.
These two points are required in order for the extended planetary system to balance its (solar) input with its overall output. As much heat per unit time must exit as what enters. This is true for the system as a whole, but also significantly for the surface itself. The two are tightly connected.
But it is always the surface that warms or cools first! The troposphere just follows …
* * *
So, how would the surface heat budgets look?
On Earth b), at 288K, there is 165 W/m2 of incoming from the Sun, and 53 (radiant) + 112 (conductive+evaporative) W/m2 of outgoing terrestrial heat.
On Earth a), at 309.5K, there is 135 W/m2 of incoming from the Sun, perhaps ~35 W/m2 of radiant heat loss (significantly reduced from Scenario b)), and about 100 W/m2 of non-radiative heat loss.
What is worth noting here is that, although there is less heat moving out of the global surface via non-radiative processes on Earth a) than on Earth b), even with a considerably higher mean surface temperature, this is not a point of inconsistency. It’s an effect fairly easily attributed to the substantial increase in atmospheric pressure/weight and density at the surface, making it harder for the convective engine to run at sufficient speed (see previous post). A stronger ‘driving force’ is required to ‘push’ the surface heat out and up.
Remember now that the Venusian atmosphere is not 2x the mass of Earth’s, but 92x …!
Does this mean the massive atmosphere of Mars does nothing to force its solar-heated surface to be warmer than if the atmosphere weren’t there? Not quite. There is one more effect caused by the mass of an atmosphere that raises the average surface temperature of a planet: The evening out of temperature amplitudes. This effect is potentially larger than what you might at first think. It occurs also on Earth and Venus. In fact, the effect is much bigger there than on Mars, simply because their atmospheres are more massive. The pattern is pretty consistent:
Moon: no atmosphere – huge spatio-temporal temp swings > Mars: light atmosphere – pretty large swings > Earth: moderately massive atmosphere – moderate swings > Venus: extremely massive atmosphere – practically no swings.
The larger its surface temperature amplitudes, the colder a body can be on average and still maintain a radiative equilibrium between input and output. Courtesy of the ^4 exponential relationship between radiative output and temperature. When a surface fluctuates between being very hot and very cold, it radiates so much during the hot periods (or from the hot regions) that it can remain in the cold for a longer period of time (and keep larger areas cold) and still balance its budget. Hence, its average temperature drops.
Temperature swings (or spatio-temporal differences, rather) enable the surface of the body to put out more radiation than what its physical temperature average would suggest. The larger the differences (in space and time), the more it puts out relative to its mean temp. The Moon, for instance, puts out 3.5 times as much LW to space from its global surface over a year as what its actual average global temperature of 197K would imply.
What a massive atmosphere does, then, in more ways than one, is cutting down these amplitudes. It basically reduces the heating rates during the day and the cooling rates during the night. In addition, it spreads (circulates) the heat from warmer regions to cooler ones.
Cutting down the amplitudes means elevating the average global/annual surface temperature. In other words, Mars would be a colder world – on average – without its atmosphere, because its temperature swings would be even much larger than they are (closer to the lunar range).
The difference between the apparent planetary temperature in space and the average global temperature of the planet’s physical surface, is 505K on Venus, 33K on Earth and 0K on Mars. The more massive the atmosphere, the higher up the conceptual ERL (the effective planetary emitting “surface”) is pushed. On Mars it isn’t pushed up at all, because the air density already at the surface is low enough for the solar heat to escape to space at an adequate pace. On Earth, we have to move a few kilometres up to reach such levels, and on Venus we have to climb a few tens of kilometres.
It’s all really straightforward:
- The more mass in an atmosphere, the deeper its air column, and the higher up you need to go to find sufficiently thin layers of air. Hence, the ‘massive’ ERL is pushed up. Pulling the average surface temp up along with it …