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.
Pamela Gray (06:55:38) :Addendum, internal variability cannot be “averaged”.
Then internal variability is not what I have in mind. What would you call PDO Pamela?
Invariant says:
Thanks. You should keep in mind though that I am not a climate scientist by any stretch of the imagination. I am a physicist who has been studying climate science as a “hobby”.
In terms of internal variability, I don’t really know although my general impression is that the belief is that completely unforced variability (i.e., not due to major volcanic eruptions, changes in solar forcing, …) is pretty small…probably a few tenths of a degree. But, if I get the chance, I’ll try to see where they talk about this in the IPCC report and point you in that direction.
Joel Shore (11:08:43) : I am a physicist who has been studying climate science as a “hobby”.
Thanks.
Me to, I am also a physicist who has been studying climate science as a “hobby”.
Looking forward to hear from you! Why cannot the climate equilibrium oscillate a couple of Kelvin? I’ve never heard a good reason! Since you are a physicist, you know that all fluxes are instantaneously given by the gradients, meaning that the reach for equilibrium one day may be pointless the next day. Although the forces point toward equilibrium, it is missed over and over again… And thinking of the yearly fluctuations does not make the issue easier either, I mean, a yearly variation of ~90 W/m² is quite astonishing, the forces discussed here are almost negligible in comparison.
Invariant (12:37:49) :
a yearly variation of ~90 W/m² is quite astonishing, the forces discussed here are almost negligible in comparison.
A pet peewee of mine too. People fight over the [purported] effects of a 0.1 W/m2 solar cycle variation and ignore the 90 W/m2 beam in their eyes.
Leif Svalgaard (13:23:15) : A pet peewee of mine too. People fight over the [purported] effects of a 0.1 W/m2 solar cycle variation and ignore the 90 W/m2 beam in their eyes.
Well you told me this Leif! 🙂 (I did not know).
Do you have some emprical data showing this?
God påske! 🙂
Invariant (13:59:55) :
Well you told me this Leif! 🙂 (I did not know).
Do you have some emprical data showing this?
Here is the past 15 [or so] years of actually measured TSI [normalized to SORCE]:
http://www.leif.org/research/Erl76.png
You can see that all curves fall just on top of one another [showing that the orbit is very stable – no barycenter nonsense] and that there are tiny wiggles from time to time. Those are the biggest solar active regions. The solar cycle variation is smaller than the thickness of the lines.
God påske! 🙂
Tak og til dig såvel.
gee leif – but that’s peak to peak, LOL. the RMS difference is less.
Invariant, the 90W/m^2 difference is due to the orbital distance – aphelion to perihelion distances. December is perihelion – meaning that the peak incoming power to the southern hemisphere summer is actually 90W/m^2 more than the peak power coming to the northern hemisphere during its summer.
What’s more interesting to me is that the SH temperatures tend to be slightly lower than the NH temperatures, despite this massive difference in forcing. The difference is evidently that the NH has most of the land surface while the SH has most of the ocean surface. Considering that ocean albedo is much lower than land albedo, something like less than 0.04 versus something in the realm of 0.15 to 0.19, not only does the SH summer have more power (90w/m^2 peak to peak) at the TOA than the NH, ignoring cloud cover, there would be another 34 w/m^2 of absorbed power ignoring also additional differences in TOA power.
Of course, if one insists on ignoring cloud cover albedo changes, one is then faced with massive increases in absorbed power resulting in lower temperatures. LOL.
What has to be going on is something in the line of LIndzen’s iris effect where the added forcing, especially over water, is resulting in more water vapor cycle and cloud cover albedo reduction of incoming power to the surface.
cba (14:45:21) :
gee leif – but that’s peak to peak, LOL.
So is the solar cycle effect…
the RMS difference is less.
I don’t know what you mean, or rather it doesn’t make much sense to compute RMS over a smooth curve…
December is perihelion
January 4th.
What has to be going on is something in the line of LIndzen’s iris effect
And yet, in spite of all that, the 1 W/m2 solar cycle effect manages to sneak by the 90 W/m2 and make LIAs etc. 🙂
A very interesting plot Leif! Thank you for that. Now I have a question.
Do you have any idea what that plot might look like over the course of the glacial/interglacial cycles?
What I am getting at is this: Is the effect of the Milankovitch cycles limited to a change in the latitudinal distribution of solar radiation that reaches the surface, or does the TSI that reaches the TOA change as well?
This has been bugging me for a long time (I can’t find any info) and I would appreciate anything you could contribute.
Thanks in advance.
Leif Svalgaard (14:42:18) :The solar cycle variation is smaller than the thickness of the lines.
Thanks a lot Leif! Really appreciate it! 🙂 Regarding the 1 W/m² TSI variation, perhaps some people thinks that our climate can be charged like a capacitor over many cycles by this extra offset? You know, if you have a simple RLC oscillatory circuit, the capacitor and the inductance can be charged and discharged each cycle. However, increasing 1365 W/m² to 1366 W/m² is not a big increase (in magnitude) after all, and I doubt that the capacitor wil notice the difference.
Regarding my proposed climate variation of T = 287 ± 1.6 K with a characteristic cycle length of ~330 years, perhaps this is not so unlikely after all? I mean, we know that the climate is chaotic, and chaos almost always means scale invariance, implying that the rapid oscillations we see at a short timescale (years) also must be visible on a larger timescale (decades, centuries). Whether the magnitude of the variations also must be scale invariant is an interesting question, because if they are, then small oscillations (in amplitude) on a short timescale may be invariant with large oscillations (in amplitude) on longer timescales.
Joseph (15:53:09) :
What I am getting at is this: Is the effect of the Milankovitch cycles limited to a change in the latitudinal distribution of solar radiation that reaches the surface, or does the TSI that reaches the TOA change as well?
The average TSI [and all that reaches the TOA] over the year will not change measurably [as the average distance to the Sun is nearly constant]. The eccentricity of the orbit will change so the peak-to-peak swing will change [smaller the more circular the orbit is]. Another important changes will be in the phase of the curve, that is: when does it peak? A glaciation may hinge on the insolation at 65 degrees North during Northern summer.
Invariant (16:38:38) :
Regarding my proposed climate variation of T = 287 ± 1.6 K with a characteristic cycle length of ~330 years, perhaps this is not so unlikely after all?
If that 3.2 degree swing were due to TSI, it would mean a 60 W/m2 swing in TSI, which is not very likely. At least 100 times larger than what we would expect.
Leif Svalgaard (17:11:57) : If that 3.2 degree swing were due to TSI, it would mean a 60 W/m2 swing in TSI, which is not very likely. At least 100 times larger than what we would expect.
Wow! Then the interal variations must be powerful… What could it be? Monster PDO? ….
“Leif Svalgaard (14:52:12) :
cba (14:45:21) :
gee leif – but that’s peak to peak, LOL.
So is the solar cycle effect…
the RMS difference is less.
I don’t know what you mean, or rather it doesn’t make much sense to compute RMS over a smooth curve…
December is perihelion
January 4th.
What has to be going on is something in the line of LIndzen’s iris effect
And yet, in spite of all that, the 1 W/m2 solar cycle effect manages to sneak by the 90 W/m2 and make LIAs etc. 🙂
”
the RMS I’d use to get an average power difference over half a cycle so as to get a number related to how much more power goes to the SH in their summer versus to the NH in our summer time. This 90w/m^2 peak to peak annual variation looks like it corresponds to a sine function.
the solar cycle effect is a bit longer than the few months of seasonal change which means it should have more of an effect due to the total energy, but still, it’s and order of magnitude less than the seasonal.
anna v (23:40:42)
anna, I hate to say it, but that paragraph is entirely content-free. If you (or anyone else) have a problem with the numbers that I laid out in The Steel Greenhouse or in this post, or that Joel laid out, you’ll have to:
a) quote (not paraphrase or interpret but quote) the offending words and numbers, and
b) tell us exactly what is wrong where.
Because I can’t respond to a claim that there may be double counting somewhere in some unspecified “famous energy budget”, that’s far from enough information.
Thanks,
w.
cba (20:02:25) :
the RMS I’d use to get an average power difference over half a cycle
Just integrate over the half-cycle to get a physically meaningful number. But, no matter what, the yearly variation completely swamps the solar cycle variation, which is why Milankovitch works so well, because it exploits that fact.
lgl (03:42:02)
I’m not sure why that’s relevant. First, it’s not “at 6 km”, it is at the tropopause, which varies in altitude. The point is that ∆W, the change in radiation between the two situations, is 150 W/m2
My understanding is that that is the equilibrium forcing, and that the feedbacks are taken up in the temperature response. This is supported by the Hansen figure (which is clearly including all feedbacks) of 3.95 W/m2, and a temperature response of about 2°C.
But if you have a citation to say otherwise, bring it forwards, that’s how science works.
Joel Shore (07:02:54)
I understand that very well, Joel. My point is that the forcing Fs* is one of the “forcings defined below”, and it does include feedbacks of all types. That’s why I used the Fs* numbers …
It is also why I say it makes little difference which one you choose, because the difference between Fa and Fs* is only a few tenths of a Watt/m2 (Fa = 4.12, Fs* = 3.95 W/m2).
I think that Luboš Motl has a very good discussion of this.
http://motls.blogspot.com/2010/03/black-body-limits-climate-sensitivity.html
I think he is more likely to be correct.
Richard,
Just went over Lubos article (5 minutes worth at 6am) and there’s much to be said for it – not that I fully gleaned all of it at this hour of the day in such a short time. I do have some problems with it though.
Clear skies with surface radiation only account for about half of the Earth’s surface. Clouds block the rest with substantial ability. Clouds are not water vapor but are particles of liquid and solids which are no longer behaving as single molecules with well defined spectrums but are rather continuum radiators like larger solid and liquid objects. These are blocking the surface outgoing radiation and absorbing it. They are also radiating back down and radiating outbound at their characteristic temperature. However, this radiation outbound is a continuum at a lower temperature and it is above most all of the h2o vapor in the atmosphere and above both a good bit of the co2 AND it’s starting at pressures that are lower than the surface value and pressure is an important requirement for ghg absorption as it is required to spread the spectral lines out so as to permit greater capture.
Another problem with Lubos’ presentation is that the atmosphere in clear sky conditions is going to block about 30% of the radiation emitted from the surface. One needs just a bit more T to compensate.
For clear skies, radiation out of the atmosphere calculates to be around 270w/m^2, significantly more than a BB radiator around 288k. For an overall balance with 235 or 239 w/m^2 absorbed incoming solar, that means the cloud cover portion must radiate less than that through the balance of the atmosphere above the clouds. This throws in a new parameter, cloud cover fraction, which has an effect both on incoming and on outgoing radiation.
Willis Eschenbach (21:16:47) :
“The point is that ∆W, the change in radiation between the two situations, is 150 W/m2”
But radiation isn’t the only change. You are also jumping from the surface to the tropopause (or whereever, I thought TOA in this context was the 255 K height)
I have already cited IPCC in
lgl (11:16:12) : (and Gavin before that)
In other words, the radiative forcing corresponding to a doubling of the CO2 concentration would be 4 Wm-2. To counteract this imbalance, the temperature of the surface-troposphere system would have to increase by 1.2°C (with an accuracy of ±10%), in the absence of other changes. In reality, due to feedbacks, the response of the climate system is much more complex. It is believed that the overall effect of the feedbacks amplifies the temperature increase to 1.5 to 4.5°C”
Similar from a old Hansen paper: http://epa.gov/climatechange/effects/downloads/Challenge_chapter2.pdf
“A simple radiative calculation shows that doubling atmospheric C02 would raise the mean level of emission to space, averaged over the thermal emission spectrum, by about 200m. (Cf. discussion in the section below on empirical evidence of climate sensitivity.) Since atmospheric temperature falls off with altitude by about 6C/km, the planet would have to warm by about 1.2 C to restore equilibrium if the tropospheric temperature gradient and other factors remained unchanged. In general, other factors would not remain unchanged, and thus the actual temperature change at equilibrium would differ from the one in this simple calculation by some “feedback” factor,f,”
cba (05:47:25) : This throws in a new parameter, cloud cover fraction, which has an effect both on incoming and on outgoing radiation.
Could cover fraction! A most useful concept it seems. Are we monitoring this with the required precision?
it’s undoubtedly tied up in measurements of albedo – which have been few and far between so to say. There are some direct measurements of that going on as well that are in better shape than direct albedo measurements but I doubt it’s being done to the precision and coverage required. I’m probably oversimplifying too as there are different types of clouds with different effects. Khiel and Trenberth used the assumption of three types of clouds. Looking at Lindzen’s Iris concepts, it would seem that there is different albedo based upon the make up of the particular cloud type – like size of particulates involved in seeding the cloud.
My cloud cover fraction is the ultra simplified concept presuming the existence of a ‘generic’ cloud with average effects and then combining it with the clear sky area to get a better understanding of a simplistic cloudy+clear model.
What one has is a pair of straight line functions. These are incoming power density which ranges from 341w/m^2 in clear sky to a much lower value, like 10% of that for total cloud cover. One then has outgoing power which for clear skies is around 270W/m^2 (390 surface radiation – actual absorption by ghgs – something around 100 to 120 w/m^2 absorption (note that the 150 w/m^2 from 390-239 w/m^2 is for the actual mixed atmosphere of cloudy & clear) . The outbound IR in full cloud coverage is virtually total – but the cloud tops are going to radiate a continuum from their intrinsic T so there is no total blockage, only a reduction to something more like 200 or 210 W/m^2 so that the average becomes the same as the average incoming – around 239 w/m^2. These two lines intersect at a point on the cloud cover fraction axis – around 0.62 or so which represents the cloud fraction where there is balance.
While simplistic, it is more sophisticated than a clear sky only analysis.
Like you and some of the others in this thread, I’m involved professionally in physics (& astronomy) and not climatology or planetary science. Considering my current sleep patterns and the rest of my schedule these days, I have very little time at the moment for either sleep or for ‘hobby’ armchair climatology studies I’ve been doing the last couple of years.
cba (15:21:04) : I’m probably oversimplifying too as there are different types of clouds with different effects. Khiel and Trenberth used the assumption of three types of clouds.
Thanks. I’ve read a couple of papers by Trenberth, and I must say that there is something fishy going on, it is not anything near being well founded physics with some intuition and arguments based on insight, to me it seems mostly like a collection of (unfounded) claims…
Willis Eschenbach says:
No, Fs* is the one that Hansen et al. note Gregory et al. say “is obtained by
regressing the flux at the top of the atmosphere against the change in surface air temperature, with the flux at zero temperature change being the estimated forcing”. If you are looking at the flux at zero temperature change, there is no way that this flux includes the effects of the water vapor feedback because the water vapor feedback depends on there being a temperature change!
I admit that the Hansen et al. paper is a little bit unclear and you can mistakenly misinterpret it in the way that you have. However, the evidence that this interpretation is just plain wrong is all around you. I would suggest that you actually entertain this possibly rather than to continue to cling to your notions that make essentially no sense on the grounds that you can find language in the Hansen et al. paper that is ambiguous enough so that you could read as supporting it (and ignoring the language such as that I have pointed out that clearly demonstrate that such an interpretation is incorrect).