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.
magicjava
And in response to my question..
The updated paper is 2008.
In fact, Kiehl and Trenberth don’t throw out any measurements in favor of climate models. In the 1997 paper they assume that incoming and outgoing energy balances. Why?
Because the instrument error means the measurement results are not accurate enough to be able to say whether energy in = energy out. In a non-warming and non-cooling world this would be true.
And there is a small challenge of whether the measurements of solar energy in is more accurate than the measurement of terrestrial energy leaving and reflected solar energy.
So there is an uncertainty around 5-10W/m^2.
In the updated 2008 paper, being good scientists they attempt to provide better numbers all around. In the case of the instrument error, there are still the same unknowns. So rather than fix energy in=energy out, they say, “well, the earth is warming up, how much by?”.
Anyhow, for those for whom the word “model” causes outrage.. look at the statement which was inaccurately quoted:
As you can see -first the number is pretty small, and second, the calculation is supported by the measurement of the increase in ocean heat (as you can see in The Real Measure of Global Warming ).
1W/m^2 out of 240W/m^2 – and you want to throw out the results?
For anyone wanting to learn a little about climate basics, read the whole original 1997 paper.
Willis: Technically speaking, climate sensitivity is the partial derivative of temperature with respect to energy (probably both incoming energy from the sun and energy radiated downwards by the atmosphere and clouds). Your post may be assuming that temperature is a linear function with respect to incoming energy. The relationship between T and W is certainly a very complicated one if conditions are dramatically different from today – a snowball earth or even an ice-age where the relative proportions of land and ocean change. For small changes in W and T, the relative is approximately linear and climate sensitivity can be treated as a constant.
The IPCC also worries about the time-scale associated with estimates of climate sensitivity. For a given dW, how long does it take for T to come to equilibrium? Does equilibrium include changes in the deep oceans and ice-caps? For models with the highest climate sensitivity, equilibrium of the atmosphere and upper ocean apparently requires decades.
Willis:
I am confused as to where you have gotten the 150 W/m^2 figure that you quote. I also think, in line with what scienceofdoom said, that what you have essentially calculated here is not the climate sensitivity but the sensitivity in the absence of feedbacks. In particular, what you have to recognize is that the distinction between forcings and feedbacks is somewhat arbitrary. For example, CO2 change is, in some sense, a feedback in the glacial – interglacial cycles but is a forcing in our current predicament. The thing is that you have to be consistent. What you have done is not consistent because you have presumably counted everything, e.g., including the water vapor, as a forcing in getting that 150 W/m^2 figure but then you have not counted any change in water vapor as a forcing in computing the resulting climate sensitivity.
Another way of putting it is this: If the warming due to the change in CO2 causes additional water vapor to go into the atmosphere, this water vapor will produce an additional radiative forcing…and if the additional warming causes ice melt that changes the earth’s surface albedo, this will also produce an additional radiative forcing. (And, the change in clouds would also produce an additional radiative forcing whose magnitude, and even admittingly, sign are uncertain.) Now, we usually call all of these things feedbacks instead of forcings and that is fine if we do so consistently. The problem is that I don’t think you have done so consistently…i.e., as near as I can tell, your “150 W/m^2” (which I don’t really understand anyway) counts everything as a forcing, not a feedback.
By the way, Jim Hansen has made a similar point recently about being consistent with what you call a feedback and a forcing…And, in fact, he has argued that what he calls the Charney sensitivity derived from the glacial – interglacial cycles considers changes in albedo due to changes in ice sheets as a forcing whereas any such changes in our current discussions are considered to be a feedback. Hence, he argues that the 3 C climate sensitivity for doubling CO2 is probably too small for our current “experiment”…and says it is more like 6 C when you properly consider the effects of the albedo changes due to changes in ice sheets. (Others question whether the ice sheet albedo effects would really be that large in our current climate and also how fast the ice sheet changes can occur…so, I am not saying his 6 C estimate is correct, but I think that his basic point about being careful what you consider to be forcings and feedbacks is.)
steven mosher (11:39:03) : Steve I guess you missed reading the part about patenting the idea. It was a rhetorical question. I cannot put smiley face at the end of the sentences.
However, it is possible to construct an idealized thermos floating in space, with an inside chamber transparent to IR but infinite R value, and an outside surface that blocks incoming radiation whose inside surface is a perfect reflector of IR. So no conduction no convection only IR from the soup, coffee whatever to the next chamber. Fill the space where the vacuum would normally be with CO2.
The IPCC formula makes no difference as to anything except the forcing of the log of (C/CO). So with that in mind using the IPCC 5.35ln(C/CO) we get
ln 1000000 is 13.81 times 5.35 for 73.91 W/m2. According to IPCC whatever you have in the thermos will heat by 74 W/m2 indefinitly to vaporization and explosion.
Please don’t miss the point Steve I don’t think CO2 can do what is claimed and none of the information I have read demonstrates via physics, math, chemisty etc or whatever, over turns my understanding of the laws of thermodymanics, heat transfer etc.
My ultimate point is that if CO2 could increase heat energy through radiation then someone somewhere would have found a way to make money off the idea. But as of yet nothing even though we are told this has been know for a 100 years. Hog wash.
Honestly, I can’t find anything about a ‘colored’ black body. A Black body is a black body (or blackbody if you are so inclined). Either way, anything which as an emissivity (not equal to 1) is not a black body.
Unless there’s something changed in the last 20 years. Maybe: they are teaching all sorts of funky stuff these days (perhaps an object with a specific emissivity is classified as a specific ‘black body’ color? ). Even so, it’s an irrelevant argument: as I understand it, based on what had been demonstrated, if earth was a black body it [surface] would be 8 degrees cooler; as it has an emissivity, it is theorized to be 20 degrees cooler than what we measure today.
It seems like the prosecution is stating that the perpetrator accelerated from a stand still to 100mph when they breezed through the red light. The defense [Willis] is arguing that it’s only 50 yards from where the perpetrator started to the red light, so how can they be going 100 mph? Weather it’s 50 yards, or 60, or 20, or 70.235 is quite irrelevant; or what the shade of the red light is, or even the decimal accuracy of the radar gun used for measurement.
Does the theory hold? Are the results of Willis calculation so far off ? Is the principle employed sound? If not, why not? Can it be demonstrated that his theory is false? Are there any significant factors not accounted for?
In other words…
8 degrees cooler? That contradicts what can be found using Stefan-Boltzmann law, 255K or -18C. Or have I missed something?
http://answers.yahoo.com/question/index?qid=20090408183916AASBK1D
http://en.wikipedia.org/wiki/Black_body#Temperature_of_Earth
OceanTwo (12:58:04) :
if earth was a black body it [surface] would be 8 degrees cooler; as it has an emissivity, it is theorized to be 20 degrees cooler than what we measure today.
albedo, perhaps, rather than emissivity.
The 8C was not really used by Willis for anything, so it is perhaps not worth harping too much on it. There is also a possible confusion because you can talk of blackbody radiation as that which has a blackbody spectrum without the body be required to be black [the Sun is not black, for example]. More confusion comes from the statement: “That is to say, the net gain from our entire complete system, including clouds, surface albedo, etc..” where the clouds and surface albedo are not gains but deficits. Anyway, I may just have been too pedantic about this, but I was disappointed that the lead paragraphs were on something not actually used further on. The important things was the 20C difference.
Willis:
Re: wayne (04:27:21) :
I may have answered my own question to you.
Seems the 105 W/m2 might very well come from the 22 for Sensible Heat and 76 for Latent Heat. Those total 98, close but not exact to the 105.
Seems the K/T chart is organized in a confusing manner. Their fault, not yours. It should have been broken in three sections. The Input, the internal flows, and the output. That would tie the back radiation to the back radiation mathematically.
On the left, the SW radiation from the sun, the input, and it is pretty clear, then a dashed light gray vertical division.
Next is the internal energy flows. That is the atmosphere, clouds, the two upper pointing heats, sensible and latent, and the down dwelling back radiation on the far right. Then another vertical dashed light gray line.
What remains on the far right is the output section. That is all of the up dwelling radiation that gathers from the ground and from the center internal section.
That would de-mystify it a bit, mathematically anyway.
Willis, somewhat OT:
Some of your graphs are coming out vary fuzzy on this end. If you are getting these via screen captures, this might help. It works on xp anyway. Before capturing, turn the screen font edge smoothing off. On xp it’s standard or ClearType. Capture the picture then turn the smoothing back on. It does wonders on my machine, no more fuzziness! You get am exact pixel for pixel copy.
Willis Eschenbach (10:25:22) :
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?
“Thought experiments” have a long and proud history in science. They are widely used to examine conditions that we cannot replicate in a laboratory.
I agree wholeheartedly, but I am not convinced that anything meaningful
about the detailed properties of our climate system can be inferred by
thinking about a planet completely devoid of a climate system.
[quote scienceofdoom (12:30:53) :]
In fact, Kiehl and Trenberth don’t throw out any measurements in favor of climate models.
[/quote]
They do, readings that are more than 6 times higher than their estimate of 0.9. The CERES satellite shows an imbalance of 6.4 W/m-2. It’s right there in the paper. The sentence before the one I quoted. So is the reason why they threw it out: because it’s not expected by their models.
And yes, I think Trenberth’s model needs to be redone. I’ve given reasons why on this thread. Willis Eschenbach has given reasons why he believes the model can’t even work. In a nutshell, we need to start looking at reality rather than models.
Anyway, Willis has stated that Trenberth’s energy budget is not central to what he was trying to say, so I don’t want to clog up this thread with debates over it. If you’d like to respond to what I’ve posted here, I’ll let you have the last word on the matter.
Just curious (really) about one point. If the average temperature of the moon in sunlight is about 225F, how come the average temp of the earth in sunlight is so much lower? As far as I can see from the energy budget diagram, about half of the incoming radiation is either reflected by the atmosphere or the earth’s surface itself, or absorbed by the atmosphere on the way in (and some of the latter would be radiated down to the surface). So it seems that we should expect the average surface temp of the earth in sunlight to be not less than about 110F, i.e. about half that of the moon. True, this is reached or exceeded in the middle of the Sahara or Death Valley, but it seems very high for a global average. Am I wrong about this, or is there something wrong in my reasoning?
….maybe cooling by evaporation of water accounts for the apparent shortfall?
steven mosher (11:39:03) said:
In a thermos you build a vacuum chamber. You try to get as few as particles in there as possible to prevent conduction. Filling that chamber with anything would defeat the purpose of reducing the heat transfered by CONDUCTION. How do you prevent radiation through this vacuum? Easy, you put a SILVERED LINING on the metal.
That shiny metal “blocks” or reflects the IR. It does this much better than C02 does. C02 only “blocks” certain regions of Longwave.
Ahhh, that’s a much better explanation than I managed to produce. I forgot about the silver coating on the inside side of the outer sleeve … and yes, almost complete reflection is much better than 50% reflection.
Looks like I didn’t get my invite from CTM. Was hoping to meet you.
mkelly says:
There’s an awful lot of confusion in these couple of paragraphs but I’ll try to point out some of the major problems:
(1) In fact, if you postulate a system where incoming radiation gets in and (at least some of it) gets absorbed but any outgoing radiation cannot escape then indeed that system will keep heating up indefinitely. That’s what energy balance (essentially the 1st Law of Thermodynamics) says it has to do!
(2) In reality, in the case that you described, the system could never get hotter than the surface of the sun because, as the temperature rises, its emission of radiation will shift toward the shorter wavelengths and eventually it won’t be emitting mainly in the IR but rather in the visible where, by the assumptions of the problem (e.g, such radiation is able to get into the system), the radiation is able to escape.
(3) The IPCC formula is not a magical formula that holds for any container with a concentration of CO2 in it. It is a formula obtained from detailed line-by-line radiative (or even radiative-convective) transfer calculations in the actual earth’s atmosphere. Among other things, the actual temperature profile of the atmosphere with height and the other IR-active constituents like water vapor play an important role. See here for further discussion: http://www.aip.org/history/climate/simple.htm#L_0623
I have one question regarding the Kiehl/Trenbeth radiation budget scheme : I have the understanding that since some quite extraordinary papers
Gerlich & Treuschchner (1989), Robitaille, etc. this kind of ‘budget’ was heavily falsified for basic physics reasons ?
I’m wondering whether these papers had eventually to face rebuttals in peer reviewed papers…
Ar this stage I’m not aware of any, and would just conclude that they represent the current stage of physics, which mean that next IPCC report’s science basis would be interesting to draft
DavidB says:
It is the global radiation in and out that half to balance, not the local one. The heat transport in the earth’s atmosphere and the thermal inertia relative to the diurnal variation means that the earth’s temperature goes through less extreme ranges. If the earth rotated much slower and/or if there was less thermal inertia (e.g., not so much ocean) and/or if there was less convective processes in the atmosphere to mix things then there would be more extreme temperature ranges.
Roy Spencer on clouds and negative feedback. May be evidence for Lindzens’ Ifrared Iris
Part 1
Part 2
Thank you, Willis, this is interesting.
It’s a common calculation in the senior-level course of radiation heat transfer to show the Earth’s radiation exchange temperature with the Sun is (about) 280K, then the extra 8K are observed from satellites
In other words, isn’t this pretty common knowledge to people with a BS in mechanical engineering etc?
Also recommended:
Nir Shaviv: “On Climate Sensitivity and Why it is Probably Small”
http://www.sciencebits.com/OnClimateSensitivity
Willis
A bit old but I really liked your thunderstorm post from some months ago
To Joel Shore: Thanks. Those are good points. The influence of the oceans as a heat store is probably the key factor. In the interior of the continents there is a much larger diurnal range than over or near the oceans, and even there convection currents must carry the extremes of daytime heat away from the surface. I’m just a curious newbie to these subjects, so please forgive my errors and oversights.
You’ve also got to adjust for emissivity. The earth’s albedo would be maybe 0.15 without clouds, but it would also would not emit as a black body- what would the emissivity be? I’ve read estimates that the oceans’ emissivity is about 0.94, what would it be for land only, about 0.9?
in that case, you’d figure in a correction of ( 1 – 085/.9)^0.25
‘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.’
One liter of liquid water contains 55.56 moles of water molecules and occupies 1000 mls or one litre. At STP, as a gas, this would generate a volume of 1244.544 liters; giving a ratio of 1,244.544:1.
The globally-averaged annual precipitation is 990 millimetres (39 in), or 0.27 mls/cm2 per day; so that during the day/night cycle, on average, each cm2 of the planet generates and then collapses one third of a liter of volume, or an ingot 336 cm or 3.36 meters.
I think Willis’s estimate makes sense on other grounds.
Using the diagram the atmosphere receives its energy primarily from the Surface.
If you look at the Surface energy flux balance, you get a sensitivity between 0.095 and 0.15 DegC/W/m^2, depending on what assumption is made on evaporation.
(This number makes no allowance for “feedbacks” eg greater back-radiation due to increased CO2 and water vapour concentrations, or lesser solar radiation absorbed into the surface due to increased cloud cover. However it is interesting that if the surface temperature rises by the median IPCC estimate of 3 DegC for a doubling of CO2, the 3.7W/m^2 “radiative forcing” at the top of the atmosphere would necessarily need to be a huge “surface forcing” of between 22 and 32 W/m^2 at the surface. )
The usual IPCC calculations, without feedbacks, use a TOA sensitivity of around 0.3. This is then assumed to apply throughout the troposphere, right down to ground level. But that sensitivity is between twice and thrice the surface sensitivity, and I reckon that the assumption that the temperature change at TOA translates to the same temperature change at the surface cannot be sustained without invoking magic, or unless the sensitivities are in fact similar.
Willis’s calculation brings the TOA sensitivity in line with the surface.