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.
Leif,
I don’t buy the white 400C sphere and the black 400C sphere radiating the same. The fact that the white sphere is white has altered its emissivity and its radiation. It’s no longer a black body but a grey body. You can’t extract energy from the two spheres initially as the white sphere will also have lower absorption to go with the lower emissivity and so you won’t get a net flow of heat from the black sphere to the white. Maxwell’s demon still naps even though the total radiation from the two spheres initially is not the same.
Willis,
Yes, your post was a bit confusing because you didn’t show the math for the two cases until your follow up comments. I originally agreed with Leif until I re-read your post a couple of times to get your point. And, as others have pointed out, why didn’t you use the derivative with respect to power of S-B at mean global temp to get your sensitivity? The error is relatively small (0.18 vs. 0.13 K(C)/W) but it’s still a bug, or were you claiming that the sensitivity is something other than black body?
Willis,
to measure the actual sensitivity of the atmospheric absorption you’re going to have to have similar albedo, despite its unreal conditions. That means before and after albedo of 0.307 despite a lack of atmosphere or of atmospheric absorption. The numbers are an average temperature of 288K with the associated surface radiation of 390 w/m^2. Balance occurs with about 239w/m^2 making it out of the atmosphere – leaving 150 w/m^2 to be absorbed in the atmosphere or blocked in the atmosphere. Note that some of this is due to ghgs and some due to cloud blocking.
doing the comparisons for various warming values:
33 deg C = 34/ 150 = 0.23
18 deg C = 18/150 = 0.12
8 deg C = 8/150 = 0.05 deg C rise per W/m^2 power increase
keeping albedo constant means we have 342 W/m^2 – 107 = 235 w/m^2 which corresponds to a bb temperature of 254 or about 34 deg C.
Note that even the 34 deg C rise due to the current atmosphere corresponds to only 0.8 deg C rise for a 3.7 w/m^2 forcing increase due to a co2 doubling.
Applying an increase in absolute humidity based on constant RH and a 2 deg C increase in temperature, one finds that h2o vapor (ignoring cloud formation) results in only about 1/3 of the power increase due to the co2 doubling (it’s about 3.1 w/m^2 for an increase of 30% based on a 5 deg C rise)which means that most of such a 2 deg C rise doesn’t have a mechanism to cause the increase. That is even assuming the rise of 5 deg. C, the co2 + h2o vapor increase doesn’t have enough forcing to generate even a 2 deg. C rise. Less warming results in even lower forcing from h2o vapor.
Willis
A few points
Your TOA figure of 147 seems wrong, from the diagram. You seem to be using the radiation that ORIGINATES at the TOA and not including the radiation making it THROUGH FROM LOWER LEVELS – 237 w/M^2 on the diagram
“1. The climate models assume that there is a large positive feedback as the earth warms. This feedback has never been demonstrated, only assumed.”
Well I would say rather estimated from calculations. Just because it may not have been adequately demonstrated does not automatically mean it isn’t valid
“2. The climate models underestimate the increase in evaporation with temperature.”
I can’t comment on whether they do but the question is what impact does this have on energy balance. What altitude does this additional heat get transported to before it condenses out?
“3. The climate models do not include the effect of thunderstorms, which act to cool the earth in a host of ways . “.
Yes, conceivably they do, but what is the quantitative impact of that? What percentage of the energy transport in the atmosphere could be attributed to Thunderstorms. Is it a significant percentage or small enough that it can be ignored as a 2nd or 3rd order effect. Or simply subsumed into the general circulation within a cell in the model. A qualitative idea about a possible factor is only useful if you can get a handle on how important that factor is quantitatively.
“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.”.
How can the effect of CO2 be ‘tuned to the temperature record’? Surely the effect of CO2 is used to estimate the radiative balance consequences. Any tuning to the temperature record is then about relating radiative balance to temperature change. And the UHI effect won’t be that big. 70% of the surface temperature is oceans – no UHI. Most of the worlds land area isn’t in cities, no UHI. If it is the historical record being used, even in cities, UHI was much lower in the past.
“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.”
See my comments at 4 about UHI. Also isn’t aerosol effects also analysed by modelling and measuring the optical properties aerosols?
“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”
See my comments at 3 about quantifying such statements. How much do winds speeds increase relative to the current speed of the Jet Stream for example. Also, what if any impact does any of this have on vertical mixing and energy transport to higher altitudes which could increase outgoing radiation. Greater mixing at one altitude does not necesarily result in changing the vertical heat balance for that level, just the horizontal distribution of that heat.
You don’t mention increasing contributions from Methane, Ozone, Nox. You don’t discuss long term albedo change due to decline of ice coverage or vegetation change. You don’t discuss the consequences if cooling due to aerosols declines due to humanity trying to clean up our emissions. You don’t mention that the capacity of the air to hold water vapour does not go up exponentially with temperature, so increased evaporation will be balanced by increased precipitation.
There is a lot you don’t mention Willis
HankHenry:
The sun warms the bottom of the atmosphere and the top of the oceans. When a gas or liquid warms it expands and so rises because it is less dense.
So the oceans are very stratified in temperature – because the top is warmer and gets further warmed by the sun.
But the atmosphere experiences a lot of convective overturning as the warmed air at the bottom rises up. So the atmosphere is more mixed.
You can see more about this at Why Global Mean Surface Temperature Should be Relegated, Or Mostly Ignored
PS More technical note, yes the top of the stratosphere gets warmed as well due to the O2-O3 process. But most of the sun’s energy then travels through the “transparent” atmosphere and so warms the surface of the earth and the surface of the oceans.
Tsk Tsk (20:11:34) :
I don’t buy the white 400C sphere and the black 400C sphere radiating the same.
My argument goes like this:
Consider a solid white sphere with an opaque interior in empty space far from everything. In its interior it has a nuclear reactor that heats the sphere [by conduction] to a temperature of 400C. This means that the electrons just inside the surface due to thermal jiggling will be accelerated constantly [in random directions]. Accelerated charges radiate determined by their acceleration. Since we stipulate that the sphere stays at the same temperature it must radiate corresponding to the thermal jiggling determined by that temperature.
The same must hold for a black sphere, or a green sphere, etc. The radiating, accelerated electrons don’t know what color the sphere has. The energy emitted must equal that generated by the reactor.
“Temperature of a body at the distance of the earth from the sun, with an albedo equal to that of the earth: about 20°C cooler than the present earth.
TOA radiation from the present earth: about 150 W/m2
Since 150 W/m2 TOA radiation gives a warming of about 20°C, this gives a climate sensitivity of about half a degree for a doubling of CO2. This is only one-sixth of the UN IPCC canonical value of 3°C.
I don’t care if I’m off by 10%, this is a first-order analysis. My answer is way below the IPCC answer, that’s the issue, not the exact details.”
Couple questions.
First, it’s well known that earth’s average temperature is about 15 C. Is that suppose to be air temperature or temperature of the ground or surface of oceans. I assume it’s air temperature in the shade and on sea level elevation. Or simply the average air temperature of the ocean [since a large part of the surface of the Earth is covered by oceans- and therefore one can basically ignore all the land with it’s all of varying elevation.
Now you talking about an imagined airless world with the same albedo as earth. It seems then that you talking about the surface temperature- as you have removed the air.
Take Mars [a nearly airless world] it’s “air temperature” varies widely depending upon whether it is a meter or two above the surface:
“The daytime SURFACE temperature is about 80 F during rare summer days, to -200 F at the poles in winter. The AIR temperature, however, rarely gets much above 32 F. ”
http://www.astronomycafe.net/qadir/q2681.html
“The problem with measuring the temperatures on Mars is that they change in time and space in radical ways,” he said. “On Mars Pathfinder, for example, over a distance of only 40 centimeters (about 16 inches) up and down a little mast, we had three temperature sensors. They often measured temperatures that differed by about 15 degrees Celsius — that’s about 25 degrees Fahrenheit.”
http://www.space.com/news/mplmet_991201.html
Re: DavidB (Mar 17 15:30),
A contributor posted the following link
http://isccp.giss.nasa.gov/products/browsesurf1.html
where one can find the “surface skin temperature”.
It is higher than the air at 2meters temperature that is used in all the calculations.
Mind you, it is the surface skin temperature that should be used in black body formulae, because it is the solids/liquids that radiate as T^4.( I think the atmosphere is something like a T^6 and in any case has small heat capacity with respect to the surface). Nobody uses the “surface skin temperature” in all these radiation budgets.
In any case, my physicist trained brain gives up with all the hand waving and double counting that goes on in “climate science”.
Why are we worried about a black body earth when there is, and never will be such a thing. I see the point, saying a perfect black body would only be 8°C colder doesn’t allow the tiny CO2 increase much latitude to increase temperatures. But in reality we have a 30°C difference caused by our atmospheric blanket, therefore a 3-4°C increase is less impossible, and at the same time quite significant.
Joel Shore (12:34:08)
Joel Shore (20:05:18)
Much as I’d like to do this all the time, I do have a life. Anyhow, 11 PM here, I’m back in the saddle.
Joel, the 150 W/m2 is what I estimate as the TOA downwelling forcing. See Figure 1 above. Kiehl/Trenberth give a higher figure, but their diagram is not physically possible. But use either number, it doesn’t matter.
This number perforce includes everything. It includes whatever water vapor feedback (or forcing) exists at the current earth temperature. It includes the cloud feedbacks (or forcings) that exist at the current earth temperature. By definition, it includes each and every feedback that exists, known and unknown, measured and unmeasured.
Now, the combination of all of those forcings and feedbacks keep our lovely planet about 18 above what it would be if the atmosphere disappeared. So ~ 18C is the ∆T in the equation.
And without an atmosphere, the TOA forcing would obviously be zero, so 150W/m2 is the ∆F in the equation.
Since the sensitivity for a doubling of CO2 is 3.7*∆T/∆F, that gives on the order of half a degree for a doubling of CO2.
Now, if you have an explanation for why 150 W/m2 of downwelling TOA longwave radiation gives us on the order of 20°C of warming, but another 3.7W/m2 might give us 4.5°C of warming as the UN IPCC claims, I’m more than happy to listen.
w.
PS – I note that someone above called you “Troll Shore”. Folks, I’ve got good news and bad news. Joel is a physicist, understands the math, and is one of the few AGW supporting trained scientists with the balls to post here. So cut out the personal attacks. They are repulsive in any case, and totally unmerited in Joel’s case. I disagree with him a lot, but he is absolutely not a troll.
mkelly (12:51:59)
Filling a thermos with CO2 (or any other gas) increases the heat loss in a thermos. In just the same way, conduction/convection by the atmosphere of sensible heat in the climate system increases the heat loss. Sorry, your idea doesn’t work, it makes the thermos bottle (also called a “Dewar flask” or a “vacuum flask”) less efficient. That’s why it’s a vacuum flask … see my post called The Steel Greenhouse for further discussion.
Mattias, Sweden (13:09:09)
Yes.
They are using the amount of sunlight remaining after cloud albedo and surface albedo. I’m using the full amount of sunlight that would shine on a black body at the distance from the sun of the earth.
Re: Willis Eschenbach (Mar 17 23:19),
They are repulsive in any case, and totally unmerited in Joel’s case. I disagree with him a lot, but he is absolutely not a troll.
Truly said. I have had interactions with Joel and I confirm this.
pochas (15:07:53)
Interesting, thanks for the link. Shaviv uses an entirely different empirical measurement technique over six time periods to estimate the climate sensitivity, and gets numbers that center around 0.5W/m2 … doesn’t mean he or I are right, but it is of interest.
Brian P (15:29:16)
Thanks. I consider it my most insightful piece of scientific work. It’s here if someone hasn’t read it.
Alan D McIntire (15:31:54)
My bible, Geiger’s “Climate Near The Ground”, puts the IR emissivity of the earth at around 0.95. Geiger also says “The surface will be treated as a blackbody [for longwave emission/absorption] throughout the remainder of the book since, for the range of natural surface emissivities, the departure of Tr [blackbody radiation temperature] from Ts [true surface temperature] is small.”
To calculate the difference, if we take the albedo as 0.15 and TOA insolation as 342W/m2, for a blackbody we get a temperature of -5.6°C. Using an emissivity of 0.95 we get -2.1°C.
Since using the emissivity makes the calculated climate sensitivity even smaller, I have taken the blackbody figures as the conservative route, to avoid people saying I was picking the numbers to favour my argument.
Alan D McIntire (16:21:39)
No, no, no. I’ll keep going over this until everyone gets it. According to the UN IPCC, climate sensitivity is the change in surface temperature divided by the change in TOA forcing … yes, I know, it’s a really dumb measurement, but there it is. I suspect it was specifically chosen by AGW supporters because downwelling TOA radiation can’t be measured directly … but perhaps that’s just my paranoia speaking.
cba (17:25:23)
Above I cited the ERBE satellite measurement for clear-sky albedo of 0.123. And I recalculated the sensitivity using that number. If you don’t like that surface albedo estimate, I fear you’ll have to take it up with the ERBE folks.
Harry Lu (17:59:59)
The emissivity of the earth in the less than 4um range is generally taken to be 1. Most natural substances (including bright white things like snow) have IR emissivities of around 0.95 or higher. Geiger gives inter alia fresh snow 0.986, cotton 0.980, water 0.960, coniferous forest 0.970, etc. Human skin is 0.98 …
sky (18:15:08)
As I pointed out above, the change from blackbody conditions to current earth conditions includes every known and unknown variable … so no, I have not forgotten atmospheric pressure.
Brian G Valentine (19:25:34)
Fallacy of the false dilemma. There are lots of other possibilities. They might be partly right. Their facts might be right but their conclusions wrong. Their being wrong might not imply a perpetual motion machine.
cba (20:14:47)
No. I am trying to figure out the changes relating to the atmosphere. To do this, I have to see what the temperature would be without the atmosphere. Accordingly, I have to remove the cloud albedo (which is part of the atmosphere).
scienceofdoom, ok but my question still stands. On the continents temperatures at a depth of a few feet below the frost line will represent something pretty close to the annual average surface temperature (but no colder) while the temperature in the depths of the ocean is *colder* than the average surface temperature. (Remember that the geothermal gradient of the earth is something like 25-30 C per kilometer so by this extrapolation the bottoms of the oceans with an average depth of 3.7 km should be very very warm). This is the main point I am trying to drive home, namely, that on the continents the earth below the frost line (or at comparable depths for tropical latitudes) is no cooler than the average surface temperature while in the oceans most of the ocean is cooler than the average surface temperature. Once one starts thinking about temperatures a short distance beneath the surface of the earth it strikes one as quite surprising. I believe that so much cold ocean water (3.9 C overall average according to my encyclopedia) suggests that the earth is really quite different than a simple black body model. Rather there must be substantial movement by advection of heat along and across the surface of the globe; otherwise there would not be so much of the ocean’s water at the same average temperatures as polar or sub polar regions. My guess is that on the earth there is a general motion of heat poleward (at the surface but not at oceanic depths) and further that because air is dryer in cold polar regions, heat is radiated away more effectively in those regions. The Earth is much different than the idealized black body radiator of our imaginations. I am suggesting that the earth with its oceans is probably better at radiating than a true black body with a strictly solid stable surface and that the prime evidence of this is the great coldness of the subsurface ocean.
Glenn Tamblyn (20:44:12)
The UN IPCC says that the climate sensitivity is the temperature change divided by the change in downwelling TOA longwave radiation. That is to say, radiation that ORIGINATES at the TOA. So that’s what I have used. If you want to use the upwelling radiation as well you are free to do so … but then you are not measuring climate sensitivity as defined by the IPCC.
You are right, that does not mean it is not valid. However, call me crazy, but I tend to put more stock in things that have been demonstrated to exist …
If the evaporation is underestimated, their cooling effect on the surface is underestimated. How much? I don’t know, and it’s very hard to measure. But we know that the effect is to increases the calculated climate sensitivity. Wind cools the surface, look into your own experience if you doubt this.
I give some numbers on this here. I don’t know if you’ve ever lived in the tropics, but if you, you would not say they were a third order effect …
CO2 is the only thing in the models that provides a mechanism for gradual modeled warming. Since the models are tuned to the past, if the temperature rise is overestimated, the effect of CO2 needs to be larger to mimic the temperature rise. This is true no matter the size of the UHI effect.
Also, GISS estimates the temperature of large parts of e.g. the Arctic Ocean (where there is no temperature data) from the surrounding land.
Did you bother to read Kiehl?
My point is that regardless of the size of all of those effects, they all tend to increase the calculated climate sensitivity. I listed them as some of the possible explanations for why the models come up with huge sensitivities. You don’t like them, fine … what’s your explanation?
As I have mentioned several times, the current state of the earth includes all forcings, known and unknown, measured and unmeasured, the ones you mention and more. All of them are reflected in the surface temperature and the TOA forcing. So you are right, I didn’t mention cosmic rays or CMEs or planktonic sulfur compound emission that increases clouds when plankton get too hot or a host of other things … and it makes no difference to my estimate of climate sensitivity. The net result of all of them is a warming of about 20°C and a downwelling TOA radiation of about 150W/m2.
Re: Willis Eschenbach (Mar 18 00:01),
It is infrared that is important at these temperatures.
various emissivities:
http://www.icess.ucsb.edu/modis/EMIS/html/em.html
0.95 is closer for soils. .985 for oceans. Sand can go as low as o.75 ( think deserts).
There is still the assumption that average air temperature at 2 meters is the same as average surface skin temperature. It is not.
http://isccp.giss.nasa.gov/products/browsesurf1.html
It is obvious in Africa, and also the changes when one blinks from surface to air.
look at the antarctic. These are the average mean annual. they have options per month also.
They have the data there also but I do not have the tools to use it ( ftp, Fortran)
gbaikie (21:53:59)
You raise an interesting point. The average surface air temperature is generally considered to be a reasonable approximation of the actual surface temperature. In general the surface is warmer than the air during the day, and cooler than the air during the night. So for the purpose of this first-order analysis, the difference in the averages doesn’t make a difference.