Guest Post by Willis Eschenbach
I’ve been wanting to [take] another look at the relationship between net top-of-atmosphere (TOA) radiation changes on the one hand and changes in temperature on the other. As a necessary prelude, I finally have gotten round to an oft-postponed task, that of looking at the thermal lag in different areas of the planet. This is the lag between a change in TOA radiation and a corresponding change in surface temperature. Figure 1 shows my results.
Figure 1. Lag in months between the changes in TOA radiation and the corresponding changes in temperature.
As always when working with CERES data, I find that every graph brings surprises. For example, the wet land areas respond more quickly to changes in TOA radiation than do the dry land areas. Not sure I understand that. Also, you can see the quick response in the Inter-Tropical Convergence Zone (ITCZ) just above the equator in the Pacific. This suggests that the water-thunderstorm cycle transfers the energy more readily to-from the surface, with less thermal lag.
Now, I admit that there are more accurate ways of calculating the lag. However, my method gives the lag to the nearest month, so the error won’t ever be more than half a month. Here is the relationship between raw temperature and TOA radiation at a randomly chosen point in the Atlantic:
Figure 1a. Scatterplots of net TOA radiation versus surface temperature at 35°N, 10°W. Letters in the graphs are the initial letters the months, JFMAMJJASOND. All trends given are in degrees C per 3.7 W/m2 of TOA radiation change (the change expected from a doubling of CO2). Click image for larger version.
As you can see, the actual best fit for the lag is slightly more than two months, but not as large as three months. However, we won’t get much error using the 2 month lag.
In any case, having that lag data, I was able to see what the trend was between temperature and TOA radiation given the lag in each cell. Figure 2 shows that result. I have given the trend in temperature per 3.7 watts per square metre (W/m2) increase in TOA radiation. This is the change in the amount of downwelling TOA radiation that the IPCC says will result from a doubling of CO2. In other words, the graph shows the immediately change in temperature that (might) theoretically result from a doubling of CO2 IF ALL ELSE STAYED UNCHANGED. Of course, things wouldn’t stay unchanged, because change is the rule, not the exception …
… in any case, Figure 2 below shows the relationship between TOA radiation and temperature, with the trend calculated using the gridcell-by-gridcell lag:
Figure 2. Change in temperature per 3.7 W/m2 change in net TOA radiation. All gridcell trends have been calculated using the thermal lag indicated in Figure 1.
This is the raw trend of the relationship between the net TOA radiation and the appropriately lagged temperature response.
However, we still have a problem. This is that because of the thermal lag, the surface temperature doesn’t get as high as it would if there were no lag and the thermal response were instantaneous. I discussed in Time Lags in the Climate System how we can estimate the reduction in amplitude due to the thermal lag. In general, as you might expect, the longer the thermal lag, the smaller the change in temperature.
Once I’ve adjusted the amplitudes upwards to allow for the reductions in amplitude caused by the thermal lag in each gridcell, I get the results shown in Figure 3. This is an estimate of the Transient Climate Response (TCR), which is the short-term response to an increase in net TOA forcing.
Figure 3. Best estimate, transient climate response (TCR) in degrees C per doubling of CO2 (3.7 W/m2 change in TOA radiation.) It differs from Figure 2 in that the amplitude has been increased as a function of the thermal lag.
As is expected, this adjustment increases the overall expected thermal response to the change in net TOA radiation. Note that this adjustment reduces the land/ocean difference, but without removing it entirely. I take this as support for the method being used.
So what can we learn from this? Well, first off, the transient climate response (TCR) value of 0.44°C per 3.7 W/m2 shown in Figure 3 is pretty small compared to the IPCC values. For the 18 climate models that reported results in the IPCC Fourth Assessment Report (AR4), the mean TCR is 1.8 ± 0.1 °C (std. err. of mean) per doubling of CO2. My results in Figure 3 are less than a quarter of their results.
Finally, how does the transient climate response (TCR) relate to equilibrium climate sensitivity (ECS)? The ECS is the long-term response to a change in TOA radiation after all succeeding adjustments have occurred. ECS is the sensitivity that people usually discuss.
Well, the relationship shown by the AR4 models linked above is that the ECS is about 1.82 ± 0.1 (std. err. of mean) times as large as the transient climate response (TCR). With a TCR from Figure 3 of 0.44 degrees C per doubling of CO2, that would put the equilibrium climate sensitivity at 0.8 ± 0.03 degrees C per doubling of CO2.
By comparison, the average of the 18 AR4 climate models linked to above is an equilibrium climate sensitivity of 3.2 ± 0.2 degrees C per doubling of CO2. This is about four times larger than my results.
Please note that I make no overarching claims regarding the accuracy of these measurements and estimates. They represent my best effort in my continuing quest to understand the relationship between the TOA radiation and the temperature.
Regards to all,
w.
Usual Note: If you disagree with someone, please have the courtesy to quote the exact words you think are incorrect so that we can all understand your objection.
Math Note: Using the method in my post linked above, the multiplication factors to increase the amplitude of the temperature cycle based on the individual gridcell thermal lags are 1.0, 1.7, 2.9, and 4.8 for lags of 0, 1, 2, and 3 months respectively. In other words, amplitudes are not increased for 0 months lag; for a one month lag, all amplitudes would be multiplied by 1.7; and so forth.
I have calculated the length of the lag by using the cross-correlation function (ccf) and selecting the lag with the greatest correlation. I understand that there are likely better ways to establish the more precise value, but using the ccf was quick and did what was required.
Data Note: I’m using the CERES EBAF dataset. For the surface temperatures I’ve converted the (calculated) upwelling surface longwave radiation dataset to the corresponding blackbody temperatures. The data starts in March 2000 and ends in February 2014.
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Shouldn’t the caption text that starts with “All trends given are in degrees C per 3.7” be associated with figure 2 instead of 1?
“shurely shome mishtake?”
water vapour should increase in the warmer summer months while co2 should decrease because of photosynthesis but water vapour should decrease in cold winter months as co2 increases because of photosynthesis stopping. can co2 really have a lagged effect on increasing temperature when its maximum effect is during the colder winter months when temperatures are falling.
When the air is dry, temps fall like a rock at sunset, everywhere the air is dry it’s the same.
Modern warming isn’t from Co2, it’s from the ocean cycles, and remember we didn’t discover the PDO until after CAGW was hypothesized as the cause.
Willis,
Perhaps too late..
I think you have misunderstood what climate science is specifically trying to calculate (as collated in various IPCC reports).
The question is, if the temperature is perturbed, what is the change in top of atmosphere radiation? For example, if surface temperature increased 1K, what is the TOA radiation (flux) change?
If there was no positive or negative feedback, the 1K increase would lead to an increase in outgoing longwave radiation (OLR) of 3.6 W/m^2 (example in Clouds & Water Vapor – Part Eight – Clear Sky Comparison of Models with ERBE and CERES). Various results (including the example paper shown in the linked article) show that OLR doesn’t increase by 3.6 W/m^2, instead something like 2 W/m^2, indicating some positive feedback.
What you are looking at in your article is the change in surface temperature from a change in net TOA radiation (OLR – absorbed solar radiation). This is quite a different perspective (causality in the other direction) so obviously you are not going to see the same result.
Given the respective heat capacities involved I suspect it would be amazing to see a large change in the surface from a TOA net change. That said, I have just in the last 2 weeks been downloading and trying to understand the raw data from CERES & AIRS (along with the “model based” NCAR reanalysis data) for the last 14 years and don’t feel like I yet have a useful interpretation of your results.
scienceofdoom:
What you are looking at in your article is the change in surface temperature from a change in net TOA radiation (OLR – absorbed solar radiation). This is quite a different perspective (causality in the other direction) so obviously you are not going to see the same result.
Even if they were speaking of the same causality direction, though, Mr. Eschenbach’s calculations would not be very relevant to what I understand TCR and ECS to be. The earth is like a complicated low-pass filter, and Mr. Eschenbach measures its response to a high-frequency stimulus. TCR is its response to a 70-year ramp, while ECS is the DC response. My comment here illustrates that by reference to a “two-box” model. You may prefer different parameters.
That second paragraph was supposed to be a block quote. I must have used the wrong tags.
Joe Born, May 26, 2015 at 2:57 am:
“Even if they were speaking of the same causality direction, though, Mr. Eschenbach’s calculations would not be very relevant to what I understand TCR and ECS to be.”
Well, most of all, Eschenbach’s use of ‘net ToA radiation’ is mixing cause and effect into one parameter, so is only confusing the issue and is not providing any useful results. You can’t determine climate sensitivity to an increase in CO2 and/or WV looking at these data. The ‘net SW input’ (solar) leads lower tropospheric temps by 2-3 months on average, while ‘LW output’ (terrestrial OLR) lags lower tropospheric temps by 0-1 months on average. The OLR at ToA simply tracks tropospheric temps as a true radiative effect should and does, no gradual divergence either upward or downward over time to be observed.
SOD,
What if there is no change in surface temperature but instead a change in lapse rate slopes ?
Are you aware of the concept of hydrostatic balance?
Do you realise that a surface beneath an atmosphere radiates less photons as a result of an increase in collisional activity and therefore that a surface at 288K beneath 1 bar pressure of atmospheric mass actually only radiates as if the temperature were at 255K without such an atmosphere?
Stephen Wilde,
I think we have attempted discussion of climate science before. I suggested equations were important for helping us distinguish between entertainingly bad ideas and science. Equations are found in physics textbooks and are used as reference points between correct science and fantasy.
I recommend interested readers to follow that exchange.
If however you are not the author of the comments in that article let me know and I may review your comment here.
scienceofdoom, May 26, 2015 at 1:03 am:
“The question is, if the temperature is perturbed, what is the change in top of atmosphere radiation? For example, if surface temperature increased 1K, what is the TOA radiation (flux) change?
If there was no positive or negative feedback, the 1K increase would lead to an increase in outgoing longwave radiation (OLR) of 3.6 W/m^2 …”
Peculiar. There is no overall increase in OLR allowed if an “enhanced GHE” caused that 1K temp rise of yours. The 3.6 (or 3.7?) W/m2 increase in outgoing LW in this case would be back up to the original level. A sudden doubling in CO2, for instance, would reduce the OLR at the ToA by 3.7 W/m2, forcing the surface to warm by 1K for the Earth system to be able to once again put out those final 3.7 W/m2 and balance the budget – back to square one, only 1K warmer. In the real world, the CO2 increase is incremental, so we never get to see that sudden plunge in OLR, because the Earth system continuously adjusts by gradually increasing its temperature parallel to the increased forcing, keeping the OLR trend flat over time while the surface and the troposphere warms.
SOD,
That was me but I have moved on since and now see where you have been going wrong.
Perhaps you could reply to my above comment here so that I can assess the validity of your response.
I don’t think one needs equations at this point. The dry adiabatic lapse rate slope clearly shows how the rate at which photons are emitted declines with increasing density through an atmosphere to the surface.
For a non GHG atmosphere at 1 bar pressure the surface must be at 288k in order for it to radiate to space at 255k past the conducting and convecting barrier of atmospheric mass.
Stephen Wilde:
“..and therefore that a surface at 288K beneath 1 bar pressure of atmospheric mass actually only radiates as if the temperature were at 255K without such an atmosphere?”
This statement is not correct. Thermal radiation from a surface is governed by the Stefan-Boltzmann equation, r = %epsilon;σT^4 – the factors are the material properties (emissivity) and the temperature of the surface.
Therefore, the atmosphere pressure above is irrelevant for the emission of radiation from a surface. There is no possibility of confusion about this. No possibility of confusion, that is, for people who can look up an equation and understand an equation.
..my last comment should have: r= εσT^4
SOD,
The S-B equation does not apply to a surface sandwiched between two grey bodies which are exchanging energy by conduction and convection.
It must be applied from a point external to the object being observed so that there is no conduction or convection passing between the two locations.
On that basis it must be applied from a point in space which is near enough to a vacuum for present purposes.
Earth radiates 255K to space exactly as predicted by S-B.
S-B tells us nothing about the pattern of heat distribution within an atmosphere surrounding a planet nor about the temperature of the surface beneath that atmosphere.
Climate ‘science’ has negligently applied the S-B equation to a surface beneath a conducting and convecting atmosphere. It was never designed for that purpose.
Conduction and convection are slower than radiation so there will always be temperatures higher than S-B within a planet / atmosphere system and the temperatures will reflect the mass density distribution.
Stephen Wilde:
“The S-B equation does not apply to a surface sandwiched between two grey bodies which are exchanging energy by conduction and convection.”
Hilarious.
Here are two textbook extracts for emission of thermal radiation.
Whenever I produce multiple textbook extracts on the emission of thermal radiation, no one ever produces a textbook which says anything different.
After you produce your textbook with a different equation I will comment further. Otherwise there is no point.
Emission of thermal radiation is in the form of photons.
You seem not to have understood your text books.
Collisional activity between molecules transfers kinetic energy by conduction directly between them through contact which reduces the total energy of the warmer molecule. That reduces the probability of photon emission from the warmer molecule.
The same packet of kinetic energy cannot be used to emit a photon if it is being transferred directly between molecules by contact.
On average, overall, the frequency of photon emission declines as one moves down through atmospheric mass because collisional activity is increasing in its stead.
Consider this:
i) At the top of the atmosphere there is little or no collisional activity so molecules at 255K radiate to space at 255K
ii) Inside a solid body ,beneath its surface, there is little or no emission of photons , it is all collisional activity in the form of conduction but the surface will radiate at 255K in the absence of an atmosphere.
It follows that if one then adds an atmosphere one moves from a vacuum to a solid over a greater distance so that conduction takes over progressively from photon emission as density increases.
The DALR draws that line through the atmosphere from the vacuum of space to the solid surface below.
Conduction, in progressively taking over from photon emission, causes the surface temperature to rise. Less photons are emitted from a surface beneath an atmosphere RELATIVE TO THE TEMPERATURE. The surface still radiates 255K to space but it must be at 288K to hold the weight of the atmosphere off the ground in hydrostatic balance AT THE SAME TIME.
Convection within the mass of the atmosphere smears the temperature difference between the surface and space across a distance equivalent to the height of the atmosphere.
Thus the mass induced greenhouse effect which was the standard explanation from established science 50 years ago.
Unfortunately, the astrophysicists who took over climate science know nothing about the effects of non radiative energy transmission within atmospheres.
So, SOD,
How exactly do you propose that a molecule can emit photons at the same rate both with and without collisional energy transfers going on at the same time and a convective circulation to maintain as well?
Where in the S-B equation is any consideration given to ongoing conduction and convection?
How can you and your chums possibly show that it is correct to apply S-B to a surface beneath the conducting mass of a convecting atmosphere?
How much of your site has been a waste of space and of the time of readers and yourself?
The correct way to see the situation is to recognise that on average every radiating molecule from surface to space is radiating at 255K as per the S-B equation.
Every such molecule then carries an additional load of internal energy ‘worth’ 33K. That additional energy is derived entirely from conduction.
For molecules at the surface that 33K is in the form of sensible kinetic energy and at the top of the atmosphere that 33K is in the form of non-sensible potential energy.
The DALR marks the point of transition between kinetic and potential energy up the entire vertical column.
Any molecules that find themselves too warm relative to their height will rise and any that are too cool will fall. The hydrostatic process makes that inevitable.
If radiative molecules become warmer than 255K then they rise and in the process cool both by additional radiation to space and conversion of KE to PE until they are radiating at 255K once more.Whilst rising they distort the DALR to the warm side.
If radiative molecules become cooler trhan 255K then they fall and in the process warm both by additional absorption of IR from the surface and conversion of PE back to KE until they are radiating at 255K once more. Whilst falling they distort the DALR to the cool side.
SteveW wrote: “The correct way to see the situation is to recognise that on average every radiating molecule from surface to space is radiating at 255K as per the S-B equation.”
Scientists measure the absorption spectrum at different pressures and temperatures because the line-shape of the absorption bands changes modestly with pressure (collision broadening) and temperature (Doppler broadening). It is laughable to suggest that we don’t know how pressure effects absorption and emission.
SteveW wrote: “Where in the S-B equation is any consideration given to ongoing conduction and convection?”
The molecules radiating according to the S-B equation don’t “know” that they are part of a larger system that may or may not also be involved in convection and conduction. Molecules conduct when they collide and gain or lose kinetic energy. Some collisions create an excited vibrational state. SInce collisional excitation and relaxation is much faster than emission or absorption of a photon in the troposphere and stratosphere, molecules radiate at a rate that depends on temperature and excited state energy (Planck’s function B(lamba,T) ). Convection represents motion of a large group of molecules and vertical convection requires in unstable lapse rate. All three processes operate INDEPENDENTLY according laws that have survived numerous experimental test.
Furthermore, molecules don’t have any way of sensing the local pressure so that they can determine how frequently to radiate a photon. The Boltzmann distribution of molecular speeds for a given temperature controls the likelihood that a collision will produce an excited vibrational state, so temperature determines the fraction of molecules that are in an excited state. Pressure is a bulk property that emerges when a large number of molecules are confined in a particular volume.
Molecules don’t conspire to produce a predetermined outcome (such as the whole atmosphere radiating as if it were 255 degK); circumstances and laws produce a particular outcome. People conspire to produce a pre-determined outcome.
SteveW wrote: “How much of your site has been a waste of space and of the time of readers and yourself.”
In this post at WUWT, Willis doesn’t recognize that he has mistaken radiative imbalance for radiative forcing when calculating an perverted form of TCR, a measure of climate sensitivity. When his mistakes are pointed out by someone who understands them, there is no response. You won’t find such mistakes and irresponsibility at SOD. You will find references to articles and information likely to be reliable.