Guest Post by Willis Eschenbach
OK, a quick pop quiz. The average temperature of the planet is about 14°C (57°F). If the earth had no atmosphere, and if it were a blackbody at the same distance from the sun, how much cooler would it be than at present?
a) 33°C (59°F) cooler
b) 20°C (36°F) cooler
c) 8° C (15°F) cooler
The answer may come as a surprise. If the earth were a blackbody at its present distance from the sun, it would be only 8°C cooler than it is now. That is to say, the net gain from our entire complete system, including clouds, surface albedo, aerosols, evaporation losses, and all the rest, is only 8°C above blackbody no-atmosphere conditions.
Why is the temperature rise so small? Here’s a diagram of what is happening.
Figure 1. Global energy budget, adapted and expanded from Kiehl/Trenberth . Values are in Watts per square metre (W/m2). Note the top of atmosphere (TOA) emission of 147 W/m2. Tropopause is the altitude where temperature stops decreasing with altitude.
As you can see, the temperature doesn’t rise much because there are a variety of losses in the complete system. Some of the incoming solar radiation is absorbed by the atmosphere. Some is radiated into space through the “atmospheric window”. Some is lost through latent heat (evaporation/transpiration), and some is lost as sensible heat (conduction/convection). Finally, some of this loss is due to the surface albedo.
The surface reflects about 29 W/m2 back into space. This means that the surface albedo is about 0.15 (15% of the solar radiation hitting the ground is reflected by the surface back to space). So let’s take that into account. If the earth had no atmosphere and had an average albedo like the present earth of 0.15, it would be about 20°C cooler than it is at present.
This means that the warming due to the complete atmospheric system (greenhouse gases, clouds, aerosols, latent and sensible heat losses, and all the rest) is about 20°C over no-atmosphere earth albedo conditions.
Why is this important? Because it allows us to determine the overall net climate sensitivity of the entire system. Climate sensitivity is defined by the UN IPCC as “the climate system response to sustained radiative forcing.” It is measured as the change in temperature from a given change in TOA atmospheric forcing.
As is shown in the diagram above, the TOA radiation is about 150W/m2. This 150 W/m2 TOA radiation is responsible for the 20°C warming. So the net climate sensitivity is 20°C/150W-m2, or a temperature rise 0.13°C per W/m2. If we assume the UN IPCC canonical value of 3.7 W/m2 for a doubling of CO2, this would mean that a doubling of CO2 would lead to a temperature rise of about half a degree.
The UN IPCC Fourth Assessment Report gives a much higher value for climate sensitivity. They say it is from 2°C to 4.5°C for a CO2 doubling, or from four to nine times higher than what we see in the real climate system. Why is their number so much higher? Inter alia, the reasons are:
1. The climate models assume that there is a large positive feedback as the earth warms. This feedback has never been demonstrated, only assumed.
2. The climate models underestimate the increase in evaporation with temperature.
3. The climate models do not include the effect of thunderstorms, which act to cool the earth in a host of ways .
4. The climate models overestimate the effect of CO2. This is because they are tuned to a historical temperature record which contains a large UHI (urban heat island) component. Since the historical temperature rise is overestimated, the effect of CO2 is overestimated as well.
5. The sensitivity of the climate models depend on the assumed value of the aerosol forcing. This is not measured, but assumed. As in point 4 above, the assumed size depends on the historical record, which is contaminated by UHI. See Kiehl for a full discussion.
6. Wind increases with differential temperature. Increasing wind increases evaporation, ocean albedo, conductive/convective loss, ocean surface area, total evaporative area, and airborne dust and aerosols, all of which cool the system. But thunderstorm winds are not included in any of the models, and many models ignore one or more of the effects of wind.
Note that the climate sensitivity figure of half a degree per W/m2 is an average. It is not the equilibrium sensitivity. The equilibrium sensitivity has to be lower, since losses increase faster than TOA radiation. This is because both parasitic losses and albedo are temperature dependent, and rise faster than the increase in temperature:
a) Evaporation increases roughly exponentially with temperature, and linearly with wind speed.
b) Tropical cumulus clouds increase rapidly with increasing temperature, cutting down the incoming radiation.
c) Tropical thunderstorms also increase rapidly with increasing temperature, cooling the earth.
d) Sensible heat losses increase with the surface temperature.
e) Radiation losses increases proportional to the fourth power of temperature. This means that each additional degree of warming requires more and more input energy to achieve. To warm the earth from 13°C to 14°C requires 20% more energy than to warm it from minus 6°C (the current temperature less 20°C) to minus 5°C.
This means that as the temperature rises, each additional W/m2 added to the system will result in a smaller and smaller temperature increase. As a result, the equilibrium value of the climate sensitivity (as defined by the IPCC) is certain to be smaller, and likely to be much smaller, than the half a degree per CO2 doubling as calculated above.
“What is the temperature on the moon?”
First, remember that heat is the thermal unit of measure that “flows”, not temperature. Temperature is a result of heat content, defined as the average translational kinetic energy of atoms and molecules, and is dependent on the mass and specific heat of the object (such as air). There is less specific heat (and less mass) for a planet with no atmosphere than one with atmosphere. So if the amount of energy were the same for both cases, the temperature would be higher for the planet with no atmosphere. But heat is lost radiatively (black body radiation) and the atmosphere will prevent some of this loss, but itself also radiates it’s heat back to the earth and out to space. Quite a complicated system to figure out exactly as Willis nicely shows in his graphic.
There is no atmosphere on the moon, so there’s no air temperature (there’s no air to absorb heat), only surface temperature (the surface absorbs heat). When the sun is hitting the surface, it’s very hot. When the sun isn’t hitting the surface, it’s very cold because, having lost whatever heat it had by radiation. One side is hot, the other cold, and the average works out to be about -10F.
This illustrates the problem I have with a single term like average global temperature. Statistically if I put one foot in boiling water and one foot in ice water, the average is luke warm and I should feel fine. Some stations show an increase in temperture, others show a decrease. What’s the average? If North America becomes an ice sheet but Antarctica melts and becomes a jungle, and the average global temperature is still zero, should we be concerned? Is this global climate change? It’s certainly local climate change!!!!
Scientists should be focussed on the thermal budget and not a meaningless average global temperature that is dependant on so many other factors. I guess thermometers are cheap and everyone can read them…it’s harder to track the energy. But that’s the core of the problem. Is the earth retaining too much of the solar energy it receives and not allowing the proper balance to radiate back into space? When a climate scientist shows me these fundamental calulations and experiments on the heat budget then I’ll believe we have a problem.
In closing, a guy who lived in my neighborhood in 1902 wrote in his diary that yesterday (in 1902) was 58F….Today (2010) the high is 47F……not warmer for you climate scientists keeping score at home.
Willis Eschenbach (01:08:38) :
On a blackbody earth the current distance from the sun, it would only be 8°C cooler.
You are misunderstanding this. There is a difference between a ‘blackbody’ [20C cooler] and a ‘black body’ [8C cooler]. The correct answer to your question as stated is 20C cooler.
[quote ScientistForTruth (05:42:08) :]
[Quoting Trenberth]
“Increasing concentrations of carbon dioxide and other greenhouse gases have led to a post-2000 imbalance at the top-of–atmosphere (TOA) of 0.9±0.5 W m-2 that produces “global warming”
[/quote]
I’ll just add that the 0.9 Wm-2 Trenberth uses _does not_ come from measurements. It comes from Hansen’s climate model. Actual measurements give a higher or lower number than 0.9, depending on what measurement you use.
So, Trenberth is basically saying “Global Warming is 0.9 Wm-2 because Hensen’s climate models say it is so.”
This is an excellent website that explains the fundamental concepts of Physics for those of you new or “rusty” on these concepts.
http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html
Click on “Heat and Thermodynamics” for links to those concepts, under that link click on “Radiation” to read about Stefan-Boltzman.
I think you are right Willis.
They have actually calculated the 33K greenhouse effect wrong.
The Albedo figure used in the 33K calculation is 0.3 which includes the effects of solar reflection by clouds. But then the calculation excludes the positive greenhouse contribution of those same clouds. You can’t include one without the other.
So everything should start over at the beginning and say an atmosphere without any greenhouse gases would be 20K cooler.
Put water vapour/clouds back in, and you have -13K from cloud Albedo and something around +17K to +25K from the water vapour/cloud greenhouse effect so you do get something like +16K to +8K greenhouse effect from CO2/non-water vapour GHGs.
After that, the Stefan Boltzmann equations are logarithmic so one needs to calculate the K/W/m2 impact at each individual differential rather than take the total temperature K / total forcing change [which is one of the problems with the greenhouse theory – they stop using the differential].
Once you get close to the 390 watts/m2 total forcing, the differential is 0.18K / W/m2.
“The surface reflects about 29 W/m2 back into space. This means that the surface albedo is about 0.16 (16% of the solar radiation hitting the ground is reflected by the surface back to space). ”
Another question. 29/.16 = 181.25. I don’t see ~181 in the diagram. I do see 29+169=198 (168 absorbed, and 29 reflected).
Is this CBO scoring, or .gov accounting? I.e. 181 is close enough to 198 for government work?
Bill Illis (06:15:41) :
I think you are right Willis.
I think he is not.
“If the earth had no atmosphere, and if it were a blackbody …”
Yes, but it does have an atmosphere, and it most certainly is not a blackbody, so why is this entire exercise relevant?
“The Wikipedia article is using the amount of sun after albedo losses, which is about 235 W/m2. That gives the colder value you quote above.”
Just a simple question. The wikipedia equations regarding radiating in all directions and receiving only in one direction seem to suggest the calculation assumes the sun is a point source, and the earth a hard disk. In actual fact, the sun has a finite size and slightly more than half the earth’s surface is being irradiated at any time. In addition, the atmosphere itself tends to increase the size of the cross sectional area – which could both increase and decrease the temperature of the earth.
Finally, I really wish people would stop reproducing these rubbish static models of the atmosphere. The atmosphere is a dynamic system with convectional currents taking heat from the surface up above otherwise blocking layers. The hysteria about global warming, is essentially a static view of the atmosphere (both in terms of time and space), in contrast I would suggest the sceptic view is a dynamic view whereby the climate not only varies in time, but it doesn’t stick around the surface but in contrast there are dynamic convective currents taking hot air high into the atmosphere where gases with a high emissivity (CO2!) enable the heat to escape.
Think about it this way
Why does hot air rise to create thermals …. it is because cold air descends! (Ha ha got you!) OK, a bit flippant, but if cold air didn’t descend, then we’d be left with a vacuum at the surface much like the space between Al Gore’s ears.
Hot air rises because cold air descends and so we should stop focussing on what is heating the air, and start asking the question: What is cooling the air?
Now, the answer is pretty obvious: the heated air is loosing its heat by the emission of IR, and therefore anything that helps to increase the emission of IR … like e.g. a complex molecule with a high IR interaction … what could that be? CO2? helps to cool the planet! That is to say, any molecule able to absorb IR is also (at the same temperatures) able to emit CO2 and so is just as capable of being a global cooler as being a global warmer!
The warmists see the atmosphere as a big blanket keeping us warm. In contrast I think the sceptical view should be to see the atmosphere as a huge cooling system taking heat from the surface of the earth up into space. The more CO2, the better the cooling system, and if like the warmists, we were to ignore the other effects of CO2, we also could create a hysteria that adding CO2 will dramatically increase the effectiveness of the world’s cooling system and lead to runaway global cooling.
OK, that’s far too simplistic but no less simplistic than the rubbish about CO2 causing runaway warming!
Anders L. (06:43:13) :
““If the earth had no atmosphere, and if it were a blackbody …”
Yes, but it does have an atmosphere, and it most certainly is not a blackbody, so why is this entire exercise relevant?”
Understanding if the earth is warming due to greenhouse gases has everything to do with the thermodynamics of the system. If you can’t explain the heat gain and the heat loss of this system then you don’t understand the system and shouldn’t be scaring people into doom and gloom scenarios.
Consider this, satellites orbiting the earth are in “vacuum” and being irradiated by the sun. Plus they contain electronics that generate heat. Here on earth my Pentium stays cool because air circualtes around it. How do you cool a pentium in a vaccum??? I’ll give you a hint “Black Body Radiation”. You ever see those giant sails on the space station? Some are solar panels, some are cooling radiators.
Now if scientists and engineers can use the basic concepts of physics to allow satellites to work in orbit, the Rover drive all over Mars, and the hubble space telescope develop great images, and in every case without freezing or melting down in a vacuum, then those same concepts should be able to explain the temperature on earth and it’s response to solar flux, greenhouse gases, and radiative cooling to name just a few.
Comparing the system with an atmosphere and without leads to a basic understanding of the maximum and minimum of the system. In calculus it’s understanding the limits of the equation. This helps in framing what’s going on in the middle.
[quote Leif Svalgaard (06:36:25) :]
Bill Illis (06:15:41) :
I think you are right Willis.
I think he is not.
[/quote]
I think the skeptic community would be well served if we built out own energy balance model, rather than using one based on numbers James Hansen pulled out of his ass, which is all Trenberth’s model is.
Starting with data from the CERES satellite would be a good idea, IMHO. Building a model that changes with conditions rather than just giving a hard-coded answer would be a good idea too. And being honest about things we don’t know, like where extra energy is going, would also be a plus.
Willis:
According to the chart of the past 450,000 years of reconstructed global temperatures for planet earth (the one The Goracle likes to wave about), the last Ice Age saw temperatures of at least 9 to 10 degrees C below today’s. I believe we had an atmosphere back then.
I think your “black body” calculation is off by a country mile. I admire much of your work, but suspect you got wrapped around your own axle on this one.
>Leif Svalgaard (05:59:34) :
>>Willis Eschenbach (01:08:38) :
>>On a blackbody earth the current distance from the sun, it would only be
>>8°C cooler.
>You are misunderstanding this. There is a difference between a ‘blackbody’
>[20C cooler] and a ‘black body’ [8C cooler]. The correct answer to your
>question as stated is 20C cooler.
Yes, this distinction is important – as I understand it, a “black” blackbody earth would be 8 degrees colder, whereas a blackbody earth would be 20 degrees colder. However, does this matter for the energy flux diagram and Willis’ conclusions?
Anders L. (06:43:13) :
““If the earth had no atmosphere, and if it were a blackbody …”
Yes, but it does have an atmosphere, and it most certainly is not a blackbody, so why is this entire exercise relevant?”
Because it’s a discussion on how sensitive the earths climate is.
One set of scientists says that if you modify one little part of the atmosphere there are going to be gigantic changes the climate.
I believe Willis is attempting to show if you just completely got rid of the atmosphere altogether the climate wouldn’t change that much.
Of course it would be hard to breath and the polar bears would surely die in Willis’s example.
Basil (06:33:41) :
This means that the surface albedo is about 0.16 (16% of the solar radiation hitting the ground is reflected by the surface back to space). ”
Should we thank the chinese for so kindly lowering that albedo?..with Carbon soot they lower it but with SO2 they increase it. But all this is nonsense as just one humble volcano will surpass any amount of anthropogenic “forcings”.
Interestingly I don’t see any part of this diagram to account for geothermal heat from underground. Even under the UK (not known for its volcanic activity) the ground at 3000meters depth is about 90Celsius. That underground heat energy must be percolating up to the surface eventually and contributing to the background temperature at sea level.
Interestingly, the bottom of the ocean cannot be lower than 4Celsius. If it fell below this it would freeze, and then the ice, being less dense than water, would float to the surface, where it would then melt in the sun. So the deepest ocean trenches cannot be lower than 4Celsius, even though in principle they can be getting almost no energy directly from the sun. Complicated isn’t it?
The Moon doesn’t have a lot of geothermal energy or ocean’s that refuse to freeze. It is relatively easy to understand why it gets close to absolute zero at night and above boiling point during the day. Fortunately we are well insulated from such extremes.
Why is it that PV=nRT is never considered when figuring a surface temperature of the earth. It is a valid scientific formula. It explains the normal use of STP when saying under what conditions you did your test etc. As such 0 deg C is what the earth with an atmosphere has as a temperature and the 33 deg C warm up from GHG is really only 15 deg. at max.
Also if IR goes from 4-60 micro and the band for CO2 is 14-15&16 accounting for any over absorbtion then all CO2 can only get 5.4% of total reradiation. Of that 5.4% human input to CO2 is roughly 3% ergo 3% of 5.4% is .0016. The best that human CO2 can do is .0016 of any longwave radiation. If you use TOA of 247 W/m2 then .4 W/m2 is max for human input. It is probably less than that.
Frank Schroeder (07:19:28) :
Yes, this distinction is important – as I understand it, a “black” blackbody earth would be 8 degrees colder, whereas a blackbody earth would be 20 degrees colder. However, does this matter for the energy flux diagram and Willis’ conclusions?
To be frank, I can’t tell what his conclusions are.
Your theory seems to be Swiss cheese on this one Willis.
mkelly (07:28:59) :
“Why is it that PV=nRT is never considered when figuring a surface ”
I don’t believe it applies in any significant way. Gas temperature by this equation changes given a change in volume, moles of gas, or pressure. but it says nothing of surface temperature.
In the earth’s atmoshere there is no change of volume (it’s the boundless sky..bounded only by gravity), no change in pressure (except small barometric changes when fronts move around) and there’s really no change in moles of gas (unless you consider the tiny fractional increase in CO2). Plus the ideal gas law only applies in the ideal cases…in this marginal increases in moles of CO2 it wouldn’t be an accurate equation anyhow.
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David L (07:50:25) :
mkelly (07:28:59) :
“Why is it that PV=nRT is never considered when figuring a surface ”
I don’t believe it applies in any significant way. Gas temperature by this equation changes given a change in volume, moles of gas, or pressure. but it says nothing of surface temperature.
In the earth’s atmoshere there is no change of volume (it’s the boundless sky..bounded only by gravity), no change in pressure (except small barometric changes when fronts move around) and there’s really no change in moles of gas (unless you consider the tiny fractional increase in CO2). Plus the ideal gas law only applies in the ideal cases…in this marginal increases in moles of CO2 it wouldn’t be an accurate equation anyhow.
**************
Isn’t the ideal gas law used to calculate the adiabatic lapse rate?
David L (07:50:25) :
Are you saying that the 5.3million giga tons of atmosphere has no effect on the earth’s temperature? If I leave T as an unknown in the formula and use standard pressure for P and figure for a volume up to say 100km I get a temperature of 0 deg C.
The term STP means standard temperture and pressure. If it is standard to have 0 deg C at one atm then that should apply to the surface of the earth also.
I realize air is not an ideal gas but then again we use radiation formula that were meant for cavities and black bodies with no depth.
Is anyone going to consider the second law of thermodynamics and “back radiation” supposedly “warming” the earth’s surface. ?
Quite simply anything based off the bunkum IR budgets,
is bunkum itself.
That is a shame Willis because your recent post(s) regarding thunderstorms (atmospheric heat pipes) is damned excellent, and a great leap forward in our understanding. I particularly have to mention the illuminating “sun’s eye view” you used, brilliant.
Excellant posts by Brian W, Ryan Stephenson, David Haseler and David L. to mention only a few.
The rest, this place is becoming a warmists site.
As a corollary it would be interesting to look at historic situations. For example, when the Earth had no ice caps what was the sensitivity? At the height of glaciation what was the sensitivity? That might put some bounds on the problem.
“1. The climate models assume that there is a large positive feedback as the earth warms. This feedback has never been demonstrated, only assumed.”
I would agree with this statement as it applies to a global scale. But positive water vapor feedbacks do occur on smaller spatial and temporal scales (Dessler, Lindzen, Pielke).
The error occurs in trying to generalize these situations to the entire atmosphere. As you point out, all the negative feedbacks come into play canceling or even reversing the potential effect.