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.
harrywr2 (07:21:49) :
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.
That’s essentially what I got out of it, also.
The actual energy flows in the atmosphere in this case are (mostly) irrelevant. The linearity is irrelevant. It seems we are trying to determine what the (theoretical) temperature of the earth is without an atmosphere.
And honestly, even at 20 degrees, it seems like you’d need a radical atmospheric change to significantly alter the atmospheric contribution. (Of course some people claim that the current and predicted CO2 change is a ‘radical’ change).
Maybe Willis *does* hate polar bears, who knows? they aren’t particularly friendly creatures, after all. 😛
Tempest in a teapot when you realize that there is not enough carbon out there for us to burn to double the CO2 in the atmosphere.
Why? Good question.
CO2 partitions 50 to 1 between water and air. It would take 50 times the CO2 that the atmosphere contains to double the CO2 in the atmosphere. One estimate is that, if we really tried, we might be able to raise the CO2 by 20%. We are fighting against a partition coefficient.
The temperature for a blackbody earth should be
T = (1368 watts/square meter)/(4* 5.67*10^-8 watts/square meter K^4)
gives a temperature of 278.683 K- Willis Eschenbach’s figure. What you’re all arguing about is whether or not you should throw the factor (1 – albedo) into the numerator. If you throw
in the clouds, you throw a (1-.3) into the numerator, you decrease the prior figure of 278.683 to 278.683 * (0.7^.25) = 254.909 -blackbody earth without greenhouse gases but with clouds
Derek (08:46:04) : No warmist I.
For anyone a question. If CO2 can cause an increase in temperature based on reradiation of IR then why are thermos bottles not filled with 100% CO2 instead of using a vacuum?
By the IPCC formula of 5.35ln(C/CO) you could get up to 75 W/m2 of extra “heat” going back into your coffee. OUCH!
Someone should patent this.
dr.bill,
Thanks for the clear response. Choice of albedo it is, then.
Alan D McIntire (09:00:18) :
The temperature for a blackbody earth should be […] a temperature of 278.683 K- Willis Eschenbach’s figure.
No, this is for a black blackbody, but the Earth is not black. It is very nearly a blackbody, but the albedo of the Earth without atmosphere [and clouds] is not zero, it is [as Willis points out] more like 0.15, thus a real Earth with atmosphere removed would be 20C cooler, not 8C.
Alan D McIntire (09:00:18) :
The temperature for a blackbody earth should be […] a temperature of 278.683 K- Willis Eschenbach’s figure.
No, this is for a black blackbody, but the Earth is not black. It is very nearly a blackbody, but the albedo of the Earth without atmosphere [and clouds] is not zero, it is [as Willis points out] more like 0.15, thus a real Earth with atmosphere removed would be 20C cooler, not 8C.
Using this logic, Mt. Everest should be only four or five degrees cooler than Saudi Arabia. Another example of the misuse of mathematics.
David L (07:50:25) :
mkelly (07:28:59) :
“Why is it that PV=nRT is never considered when figuring a surface ”
I’m afraid mkelly is quite correct.
The atmosphere is subject to the Earths Gravitational Field
This causes gravitational compression of the gases.
High school physics student would be expected to answer question below.
Typical HSPQuestion is” using the kinetic theory of gases
a/calculate the rms speed of a N2 molecule at STP
b/If this molecule moved vertically upward and had no further interactions how high would it get
c/ What would happen to the temperature as it went higher”
(Answers 517m/s,13.6Km,drops constantly)
Close enough for the black-body sensitivity which is 0.18 °C per W/m2, but we want to know the ‘climate-body’ sensitivity, and then you have to include the feedbacks.
Trenberth’s diagram shows that the system amplifies the external input (sun) by 2.4 so the resulting sensitivity is somewhere around 0.43 °C per W/m2, or 1,6 C per CO2 doubling.
This assumes todays gain of 2.4 will not change if the forcing increases, but it probably will, probably not linear. But since a 3.7 W/m2 increase is <1% of the initial, setting a 2.2-2.6 boundary should be safe (+/- 8% of initial) and then the sensitivity range becomes 0.40-0.47 or 1.48-1.73 C per CO2 doubling.
calcs:
Solar input to surface: 169 + (58+10)/2=203 W/m2 (/2 because only 1/2 downward)
Total to surface: 321+169=490
Gain: 490/203=2.41
Black-body sensitivity: (289^4-288^4)*5.678*10^-8=5.45 W/C=0.18 C/W/m2
This holds if we do not reach a Tipping Point, but the good thing is we already reached the cold-to-warm TP 10000 years ago, so the next TP will be a warm-to-cold TP.
Willis,
Thanks for your superb efforts and excellent way to get open discussion
I’m a little wary should we ourselves draw overly firm conclusions/convictions in the sense of taking the Kiehl/Trenberth graph figures as a given, and then drawing some overly firm conclusions therefrom
(All sorts of conjecture is absolutely warranted )
Isn’t this the same Kevin Trenberth referred to below?
I.E. Who admits in a private email we are not close to balancing the earths energy budget (and agreed by Tom Wigley) and therefore geoengineering would be hopeless, as we would not be in a position to evaluate it’s effect
If so what is the level of confidence in all the various fluxes shown in that diagram in the first place.?
It may well be that it’s just that I’ve not taken the time myself to study these particular aspects in depth required to get a personal comfort level
The Warmers are absolutely open to highly warranted criticism on multiple levels. I thought your robust 🙂 comments to Judith Curry and Ravetz were spot on. They reflected my views exactly.
Just a word of caution (very slight) that we not get ahead ourselves in term conviction/confidence
Warm Regards
brent
http://www.eastangliaemails.com/emails.php?eid=1056&filename=1255550975.txt
Kevin,
I didn’t mean to offend you. But what you said was “we can’t account
for the lack of warming at the moment”. Now you say “we are no where
close to knowing where energy is going”. In my eyes these are two
different things — the second relates to our level of understanding,
and I agree that this is still lacking.
Tom.
++++++++++++++++++
Kevin Trenberth wrote:
> Hi Tom
> How come you do not agree with a statement that says we are no where
> close to knowing where energy is going or whether clouds are changing to
> make the planet brighter. We are not close to balancing the energy
> budget. The fact that we can not account for what is happening in the
> climate system makes any consideration of geoengineering quite hopeless
> as we will never be able to tell if it is successful or not! It is a
> travesty!
> Kevin
>
An argument that is made on the basis of a Kiehl-Trenberth diagram makes me nervous for this type of diagram makes a muddle of thermodynamics. In the language of thermodynamics, there is no such thing as an “energy flow.” The only energy that “flows” is heat. In a Kiehl-Trenberth diagram, some of the “flows” are heat. Others are radiation intensities. It is clear that the “back radiation” is not heat for it “flows” from cold to hot matter; if it were heat, it could not flow in this manner, under the second law of thermodynamics. However, while we have a conservation principle for heat flows, we do not have one for radiation intensities. Thus, the proposition that the K-T diagram portrays some kind of “balance” is false.
Amazing to see so many using ‘wiki’… LOL
What is truly amazing is this: So many of you consider yourself scientists but, as seen in many, if not all posts, is that you cannot agree on actual numbers. I thought sciences, like mathematics, uses numbers that have been accepted by measurements that can be validated.
How is it that there are so many theories and only a few datasets to use? How can we almost NEVER agree on an answer? Why so many theories? Can’t someone just factually prove what is being presented… ever? Certainly, I am not saying we shouldn’t continue to push forward as new and enlightening evidence is brought forth via discovery, but, damn, I didn’t know science was so grey… shouldn’t it be either black or white, one or the other? I realize that some of these are just theories and can never be proven, but like AGW, the one’s claiming to KNOW MUST prove it via facts, or it should just be academia speaking for the sake of spurring on innovation/discovery and NOT be presented like it is the end all–unless it truly is.
Again, I am not saying that because Joe, Jim, Janet, and Jomojo all say it is fact, that one should stop looking, but let’s find out which measurements are the best, accurate and then all use the same info after analysis. How are there so many theories surrounding supposed fact-based research?
Steve Goddard (09:19:41) :
Another example of the misuse of mathematics.
Nonsense, it is of misuse of the physics.
If the earth’s atmosphere were only N2 and O2 would either of these gases absorb or emit radiation from the sun or earth. Sorry to expose my ignorance,but it is better to ask than to remain ignorant. This is a great blog,with great comments.
mkelly (09:08:39) said:
I don’t think this is a good argument. The devil is in the details.
1. Coffee is normally at a temperature that is outside the frequency range that CO2 efficiently absorbs.
2. Evacuating the thermos shell is to prevent conduction between the inner part of the shell and the outer part of the shell. CO2 will conduct much better than a vacuum.
So, it really depends on whether the losses due to conduction are higher or lower than the reduction in losses due to radiation.
Basil (04:38:24)
8°C if the no-atmosphere earth is considered to be a blackbody.
20°C if the no-atmosphere earth is considered to have present day surface albedo.
w.
Leif Svalgaard (05:59:34)
Leif, forgive me, but I’ve never heard a blackbody referred to as anything but a blackbody. What is the difference you speak of?
For a blackbody (which absorbs 100% of the energy that falls on it) the answer is 8°C. I’ve shown my work above. If you disagree, please show yours …
Willis Eschenbach (10:09:49) :
8°C if the no-atmosphere earth is considered to be a blackbody.
You do not understand what a blackbody is. The 8C is for a black blackbody. The Earth is not black, but is nevertheless very close to a blackbody. Take a white sphere and heat it to 400C, then take a black sphere and heat it to 400C, they both radiate the same amount. If not, we would violate the thermodynamics, where we could get work out of the radiative difference [use it to power a steam engine] between two bodies at the same temperature.
Basil (06:33:41)
My bad, surface albedo should be 0.15 rather than 0.16. Good catch. Makes no difference to the calculations in any case, which are not intended nor claimed to be more than a first-order estimate. I’ve changed it in the head post. Thanks for checking.
Anders L. (06:43:13)
“Thought experiments” have a long and proud history in science. They are widely used to examine conditions that we cannot replicate in a laboratory.
Willis Eschenbach –
Do you think you’re up to creating an energy balance diagram from scratch using actual data rather than James Hansen’s climate model the way Trenberth did?
Somebody with motivation has to do it and my plate is full at the moment with the Aqua satellite.
Enneagram states ”just one humble volcano will surpass any amount of anthropogenic “forcings””
Pinatubo released 42 Mt of CO2 (see http://vulcan.wr.usgs.gov/Projects/Emissions/Reports/Pinatubo/pinatubo_abs.html). Mankind releases 6 or 7 Gt of carbon per year (multiply by 44/12 to get CO2)
Claude Harvey (07:16:14)
Lots of people “suspect” I’m wrong about various things … but math beats suspicion every time.
Yes, the earth can be colder than it is now and still have an atmosphere. That is something entirely different from what I’m discussing, and is immaterial to my conclusions. If you think my blackbody calculations are off, show us the math. I’ve shown mine … your turn.
Ryan Stephenson (07:28:41)
Every calculation I’ve either seen or done has put geothermal heat a couple orders of magnitude smaller than the other flows, on the order of a tenth of a Watt per square metre. If you have other numbers, I’d like to see them.