# Scatterplot Sensitivity

Guest Post by Willis Eschenbach

This is the third post looking at the use of 1° latitude by 1° longitude gridcell-based scatterplots. The first post, Global Scatterplots, looked at a gridcell-based scatterplot of surface cloud radiative effect (CRE) versus temperature. The CRE measures how much clouds either warm or cool the surface through the combination of their effects on shortwave (solar) and longwave (thermal) radiation.

Figure 1. Original caption: Scatterplot, surface temperature (horizontal “x” axis) versus net surface cloud radiative effect (vertical “y” axis). Gives new meaning to the word “nonlinear”.

The slope of the yellow/black line shows the change in CRE for each 1°C change in temperature. Note the rapid amplification of the cloud cooling above about 25°C.

The second post, Solar Sensitivity, used the same method to investigate the relationship between available solar power (top-of-atmosphere [TOA] solar minus albedo reflections) and temperature. Here’s the graphic from that post.

Figure 2. Original caption: Scatterplot, gridcell-by-gridcell surface temperature versus available solar power. Number of gridcells = 64,800. The cyan/black line shows the LOWESS smooth of the data. The slope of the cyan/black line shows the change in temperature for each 1 W/m2 change in available solar. The data in all of this post is averages of the full 21 years of CERES data.

As before, the slope of the cyan/black line shows the change in surface temperature per one W/m2 change in available solar power.

In this one, the points of interest were the three roughly straight sections, particularly the right one. In that section, additional solar power isn’t raising the temperature.

Figure 3 below shows the slope of the cyan/black line versus available solar power.

Figure 3. Original Caption: Slope of the trend line in Figure 2. This shows the amount of change in the temperature for a 1 W/m2 change in available solar.

This method of looking at the data is of great interest because it reveals long-term relationships between the variables. Each gridcell has had thousands of years to equilibrate to its general current temperature and available solar power. So looking at the temperatures of both nearby and distant gridcells with slightly different available solar power shows long-term relationships between solar and temperature, not what happens with a quick change.

Next, it’s of value because the slope is relatively insensitive to changes in average temperature or average available solar. Changes in average temperature merely move the cyan/black line up or down, but this causes very little change in the slope on the cyan/black line.

Similarly, changes in average solar move the cyan/black line left or right. And changes in both average temperature and average solar displace the data diagonally … but none of these change the variable of interest, the slope of the cyan/black line, in any significant manner.

Now, for this post I wanted to look at the relationship between the very poorly named “greenhouse” radiation and surface temperature.

And what is greenhouse radiation when it’s at home?

All solid objects, including the earth, emit thermal radiation. It’s how night-vision goggles work. They allow us to “see” that radiation.

Some of the radiation from the earth goes directly to outer space. But some is absorbed by the atmosphere. This is eventually re-radiated in all directions, with about half going up and half going back towards the earth. This downwelling (earth-directed) longwave thermal radiation is called “greenhouse radiation”.

Now, a smart guy named Ramanathan pointed out that we can actually measure the amount of this greenhouse radiation from space. For every gridcell, we take the amount of radiation emitted at the surface. From that, we subtract the radiation escaping to space. The remainder is what was absorbed by the atmosphere and re-directed downwards—the greenhouse radiation.

So I wanted to see what happens to surface temperatures when greenhouse radiation changes. But there’s an immediate problem. The amount of greenhouse radiation goes up and down whenever the surface temperature changes. If the surface is warmer and radiating more, more is absorbed by the atmosphere, and as a result of the increase in surface temperature, greenhouse radiation is larger.

To remove that difficulty, we can express the greenhouse effect as a percentage of upwelling (directed to space) longwave surface radiation. This takes the direct effect of surface temperature on greenhouse radiation out of the equation. Figure 4 shows the resulting relationship between surface temperature and the greenhouse effect as a percentage of upwelling radiation.

Figure 4. Scatterplot, gridcell-by-gridcell surface temperature versus greenhouse radiation percentage. Number of gridcells = 64,800. The red/black line shows the LOWESS smooth of the data. The cyan/black line’s slope shows the change in temperature for each 1 W/m2 change in available solar. The few negative gridcells are at the poles, and they show the effect of the importation of heat from the tropics.

And here is the corresponding graph of the slope, once the percentages are translated back into W/m2.

Figure 5. Slope of the trend line in Figure 4. This shows the amount of change in the temperature for a 1 W/m2 change in greenhouse radiation.

This has both similarities and differences from the warming due to changes in available solar shown in Figure 3 above. Both start out high on the left, and both end up with a low unchanging slope on the right. However, the greenhouse warming is much larger in the middle. This leads to a global area-weighted average climate sensitivity of 0.58°C per 1 W/m2 additional greenhouse radiation.

This in turn equates to about 2°C per doubling of CO2. This is about the same equilibrium climate sensitivity found by Nic Lewis in his recent study Objectively combining climate sensitivity evidence, viz:

The resulting estimates of long-term climate sensitivity are much lower and better constrained (median 2.16 °C, 17–83% range 1.75–2.7 °C, 5–95% range 1.55–3.2 °C) than in Sherwood et al. and in AR6 (central value 3 °C, very likely range 2.0–5.0 °C).

Finally, this method gives a climate sensitivity estimate for each gridcell. Here is that map, showing how much the surface temperature is estimated to change for each additional W/m2 of greenhouse radiation.

Figure 6. Expected temperature change resulting from a 1 W/m2 increase in greenhouse radiation.

This makes some sense. The blue areas are the location of the intertropical convergence zone and the Western Pacific Warm Pool. They are generally covered with cumulus and thunderstorm clouds. These act as a 100% absorber of upwelling radiation … so any additional CO2 will make little difference. In addition, temperatures in these areas are up near the maximum, so they won’t warm much from increased greenhouse or solar radiation.

Well, there are probably more insights to be drawn from all of this. But this post is long enough, so I’m going to leave it there. I’m sure, for example, that I can get better results by subdividing the data, both by north/south hemisphere and by land vs ocean. That will do a better job of only comparing like with like. But sadly, there are never enough hours, in either a day or a lifetime

And as usual, what I’ve found brings up more questions than answers. I view my writings in some sense as my ongoing lab notebook, where I get to have a permanent record of what I’m finding, and you get to learn about things when and as I learn about them.

My very best to you all, and thanks for your continued interest, participation, and critiquing of my ongoing investigations into the mysteries of this amazing universe,

w.

My Perennial Request: When you comment please quote the exact words you are discussing. It avoids all kinds of misunderstandings.

Previous Work: There’s an index to my work here, divided up by subject matter. Click on any of the headers below to go to that section.

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Bob Jameson
October 21, 2022 10:27 am

Thanks for all the hard work you put into this site.

Dave Yaussy
October 21, 2022 10:30 am

Thanks for the research, and thanks for explaining it so clearly.

john b
October 21, 2022 10:32 am

Your analysis coupled with the work by Happer really seems to put a damper on the crowd that squawks that continual CO2 increases will be the death of the planet.

Dorn
Reply to  john b
October 21, 2022 11:57 am

Agree. Each watt in the north takes us 100m downslope or 100km south. That’s not a thermageddon, but still changes the environment a lot.

But there’s no way stopping China, when we know how disastrous the European energy policies have been to Europe.

This is our last chance. Not to avoid the greenhouse effect, global warming and climate change, but our last chance to admit our chosen green policies just give China an economic and military advantage that it will exploit to subvert us.

Willem Post
October 21, 2022 2:54 pm

Western EXPENSIVE green policies (primarily variable, intermittent wind, solar and batteries) cannot be emulated by China, India and most of the rest of the non-western world, because their economies cannot afford such silliness.

The western world has been able to afford its EXPENSIVE green policies, only because of low-cost fossil fuels.

Low-cost fossil fuels will not return again, ever!!
The Russia/Saudi/Iran, etc., partnership will aim for high oil and gas prices.

Europe and Japan will be at the greatest disadvantage, because both have a gross lack of domestic fossil fuels.

Kent Gatewood
Reply to  Willem Post
October 21, 2022 3:26 pm

How much coal and natural gas does Europe still have?

I assume those fossil fuels can be Sasolled into a liquid form.

richardw
October 21, 2022 11:46 am

I don’t claim to understand it all, but your work looks mightily impressive!

Rud Istvan
October 21, 2022 12:01 pm

An IPCC observation, triggered by Nic’s new paper and your independent finding.
AR6 based on CMIP6 raised the MINIMUM probable ECS to 2.5C from 1.5C in AR5. Nic redid Sherwood to find ~2. WE independently found ~2. The only two CMIP6 models below 2 were INM CM4.8 and CM5.0. They produced 1.9 and 1.8 respectively. And neither produced a tropical troposphere hotspot, while all the others incorrectly did. This seems to show conclusively that both CMIP6 and IPCC are biased hot, producing climate alarm when none is objectively warranted.

Other BIG IPCC alarms have also proven false:

1. Arctic summer sea ice did not disappear.
2. Sea level rise did not accelerate.
3. Buffered ocean did not ‘acidify; the GBR is doing fine despite Cook University claims otherwise and firing Peter Ridd for challenging those false claims.
Rud Istvan
Reply to  Rud Istvan
October 21, 2022 12:30 pm

Further ECS observations based on the last sentence of Nic’s abstract “values between 1.5C and 2C are quite plausible.” Nic’s earlier EBM work gave about 1.65C. Calendar’s 1938 curve gives 1.68. Lindzen’s Bode feedback method using WE scatterplot slight negative cloud feedback gives something just under 1.7 when halving the IPCC WVF f =0.5 based on the new ARGO ocean rainfall findings twice what is modeled.

But whatever ECS actually is, anything 2 or under proves IPCC AR6 alarm bias and cancels the IPCC alarm.

Herbert
Reply to  Rud Istvan
October 21, 2022 3:26 pm

Rud,
The three current papers that are relevant here are Nic Lewis 2022 as you mention and W&H 2021 which provided us with a detailed and accurate model that shows only modest warming from a doubling of CO2 and GHG of 2.2 C to 2.3 C inclusive of likely water vapour feedback but not counting the feedback due to changes in cloudiness.
As Andy May says, “both the magnitude and sign of Net cloud feedback to surface warming are unknown. Lindzen has shown it is likely negative ( cooling) in the tropics but outside the tropics no one knows.”
Lastly, “Ronan Connolly and 22 co-authors ( Connolly et al 2021) took a comprehensive look at the literature on solar variations as a cause of warming.
They concluded that much of the warming in the Northern hemisphere, and possibly all of it may have been due to solar variability, not CO2.
Using plausible assumptions and estimates of the solar impact on climate Ronan Connolly and his colleagues found the Sun could have provided anywhere from zero to 100% of the forcing necessary for recent warming.
In short, the magnitude of natural variability is simply not known with sufficient precision” .( h/t Andy May ,”The Great Climate Debate”).

Tom Abbott
October 22, 2022 10:11 am

“In short, the magnitude of natural variability is simply not known with sufficient precision””

That’s the heart of the matter.

Herbert
Reply to  Willis Eschenbach
October 23, 2022 11:46 pm

Willis,
Thanks.

Wim Röst
Reply to  Rud Istvan
October 22, 2022 6:22 am

Rud Istvan: “the new ARGO ocean rainfall findings twice what is modeled”.

WR: “Argo ocean rainfall findings twice what is modeled” is a very important fact. Thanks for mentioning again. Double as much oceanic rainfall requires double as much oceanic evaporation or, results in double as much oceanic evaporative cooling. To be added: ….% enhanced convective surface cooling and …% tropical cloud cooling.

Is it possible to give model results for double as much oceanic evaporation?

Jeff L
October 21, 2022 12:08 pm

Assuming the data & methodology are solid, from a purely scientific point of view, why wouldn’t any one accept this as the bottom line as it is driven by observed data?
Interestingly, this conclusion is also consistent with a much more simple but also data driven approach I put together for WUWT several years ago:

https://wattsupwiththat.com/2014/02/13/assessment-of-equilibrium-climate-sensitivity-and-catastrophic-global-warming-potential-based-on-the-historical-data-record/

In hindsight, this was really a blend of TCR & ECS, so it is consistent that it just a little lower than the estimate here.

mkelly
October 21, 2022 12:09 pm

All that thermal radiation showing it’s “power”.

Jim Gorman
October 21, 2022 12:10 pm

Willis,

My only picky thing is that half up and half down isn’t correct. It is the same in all directions. Otherwise you would need to measure in all directions to use Planck’s or S-B to find the temperature.

Planck discusses this.

This allows one to know the temperature of something by aiming an IR thermometer at just one point instead of measuring all sides.

Jim Gorman
Reply to  Jim Gorman
October 21, 2022 12:25 pm

PS:
You have hit upon some research that should have been done years ago. You would have thought people writing models would have checked some of this to validate their assumptions.

Keep up the good work!

Jim Gorman
Reply to  Willis Eschenbach
October 21, 2022 4:04 pm

Sorry no. An equal amount goes north, east, south, west, up, down, sideways up, sideways down. The flux is equal in all directions. That’s one reason steradians are used to describe the power in a given solid angle.

Half and half means you need to add them to get the total, and that isn’t right.

I don’t mean to be picky but for lay people they need to understand the correct radiation pattern.

Don
Reply to  Willis Eschenbach
October 21, 2022 8:58 pm

Radiation flux is equal in all directions, but radiation in other than a vertical direction is replaced by radiation from other areas of the gas so there is no net energy flow other than up or down. That is the reason half is up and half is down, but that is approximate given there is a temperature gradient.

Jim Gorman
October 22, 2022 7:39 am

Don,

Why is up and down different that all other directions, especially if radiation is equal in all directions? Is absorption different in different directions?

Don
Reply to  Jim Gorman
October 22, 2022 2:12 pm

In the atmosphere in any horizontal slice at any altitude other than above the ToA there are an infinite number of molecules in horizontal directions. Any East radiation in a slice from molecules will be matched by west radiations from other molecules in the slice. Thus there is no net radiation East and West in that slice.

Up and down is different as the number of molecules is limited by the surface and space. Further there is a temperature gradient favoring radiation from lower altitude molecules that isn’t matched by molecules at altitude. In fact measuring radiation at any altitude you would find there is more energy going up than going down even including the GHE. Therefore radiation up or down is not balanced by radiation down or up. Net result is all radiation that leaves the atmosphere is going up or down.

The short answer to the question is each molecule radiates equally in all directions but the ensemble radiates in preferred directions.

Jim Gorman
October 22, 2022 5:48 pm

Your answer has nothing to do with the radiation being emitted. Somehow you have jumped into absorption and it’s effects. That has nothing to with what is radiated by a small volume described by Planck as “dτ”. Where and how fast that emitted IR is absorbed has no effect on what is radiated.

JCM
October 21, 2022 12:20 pm

I don’t quite follow – can you provide a numerical example?

For instance:

For a condition of

OLR = 240
Surface Temp = 288K
Surface Flux ~ 390

Atmospheric Effect Quotient = OLR / Surface Flux = 240/390 = 0.62
Difference Surface and OLR = Surface Flux – OLR = 390 – 240 = 150

Atmospheric Upward Emission = Surface Flux / 2 = 390/2 = 195
Surface Window to Space = OLR – Atmosphere Upward Emission = 240 – 195 = 45

OLR = Window + Atmospheric Upward Emission

Surface Flux = Surface Window + Atmosphere Absorbed

Atmosphere Absorbed = Surface Flux – Surface Window = 390 – 45 = 345

In this example, what is the downwelling as a % of upwelling?

Atmospheric LW Effects:

LW down = LW up – Window
Near the surface LW down = LW up – Surface Window
Near the surface LW down = 390 – 45
Near the surface LW down = 345

Near the surface LW down = Atmosphere Absorbed = 345
Near the surface LW up = Surface Flux = 390

Thx

Jim Gorman
October 21, 2022 12:45 pm

Part of your problem is working with averages. Example – CO2 absorbed radiation is partially thermalized to N2/O2. Some part of that is stored until it can lose energy to a radiative gas by collision at a later time. Same way with the surface, soil for example, stores heat until later when the sun sets.

Look at 288. Is the surface at 288 throughout the day? Is the surface radiating 390 throughout the day? Is your 0.62 constant throughout the day? T^4 is involved here, so absolute numbers are important.

That makes using averages almost impossible to use in getting a correct answer.. This really should be done with gradients that include time and thermodynamic processes.

JCM
Reply to  Jim Gorman
October 21, 2022 12:52 pm

Understood. it was just examples values of what might be found in an isolated CERES grid cell so I can understand what is meant by “downwelling as a % of upwelling”. I am not trying to make any point.

JCM
Reply to  Willis Eschenbach
October 21, 2022 3:07 pm

Thank you.

The Ramanathan definition speaks to atmospheric radiative density, or opacity.

It may be worth noting that there is no overall trend in this parameter over the observational period. The atmospheric radiative density remains unchanged overall. And yet, temperature has increased.

Where it should be recognized that the balance of the atmosphere is multifaceted, and not driven only by LW, as broadly advertised to the public. A notion enforced by anti-skeptics who dwell obsessively on LW radiative properties. They exhibit a giant blind spot.

Where atmospheric balance is described by:

F = solar absorbed
K = convection
A = Atmospheric absorbed LW
Au = Atmosphere Upward Emitted LW
Ad = Atmosphere Downward Emitted LW

Where for the balance of the system:

F + K + A – Au – Ad = 0

Considering A – Au – Ad are derived from one another, as illustrated in my post above, and the fact there is no observed trend in this net value…

it can be deduced that the only degrees of freedom are F (solar absorbed) and K (total convection). It is conceivable that it is one, or both, of these parameters that is driving the observed changes. It should also be noted that F and K are related in cloud nucleation. Where F is largely dependent on K.

Reducing further, it is the ratio of F/K that is the only degree of freedom exhibited in the system during the CERES period of record. A perturbation which is miles apart from the LW radiative obsession.

It should be noted additionally that both F and K are the two largely unknown parameterized factors in GCMs. Meanwhile, they appear to be the most influential factors on the system during the observational period. A conundrum.

Last edited 5 months ago by JCM
RickWill
October 21, 2022 4:48 pm

The atmospheric radiative density remains unchanged overall. And yet, temperature has increased.

The average surface temperature has increased.

Surface temperature outside the tropics is highly responsive to solar intensity and that is constantly changing due to the orbit.

Different surface have vastly different response to solar forcing.

For example, the solar intensity peaked at the South Pole at 545W/m^2 about 4,500 years ago. It is now down to 527W/m^2. However it is not easy to shift the temperature of the South Pole above 0C but the peak sunlight has been reducing. No amount of sunlight will shift the temperature of a 2000m thick ice block very much. On the other hand when there is no sunlight. for months the surface temperature depends mostly on atmospheric heat transport rather than the stored heat in the ice block or geothermal heat.

Moving north to the Southern Ocean at 65S, the December solar intensity peaked at 500W/m^2 3,800 years ago. The Southern Ocean has sluggish response to solar intensity but is cooling at a rate of 0.66C/century. It takes a change of 198W/m^2 to currently shift the Southern Ocean surface temperature 1C.

Another example is April at 45N. It bottomed at 344W/m^2 5,300 years ago. It is now at 357W/m^2 and will reach 367W/m^2 in 4,700 years. Central USA land at this latitude requires only 13W/m^2 to shift the temperature 1C and 1 month to respond. So May temperature has to be increasing, likewise June and July. The July sunshine at 45N is close to the minimum solar intensity so expect August temperatures to rise strongly in coming centuries.

Generally the peak solar intensity is moving north and will have most impact on boreal summer land temperature. It is going to get hotter and has nothing to do with CO2. The average temperature is increasing because more land is being exposed to increasing sunshine but less water. Land responds over a wider range of temperature for a given change in solar intensity than land.

JCM
October 21, 2022 5:00 pm

Hi RickWill,

I was going to add additional addendums which exactly tie into your ideas. The changing solar intensity by latitude is tightly intertwined with K, and associated pressure dynamics. Personally, I think there is more to it but your contributions are not to be discounted. Your observation that “different surfaces have vastly different response to solar forcing” is on point. This is inextricable from K.

And K has associated feedbacks with F. This is not well understood, where feedbacks in current mainstream discussion are exclusively to do with LW.

Last edited 5 months ago by JCM
RickWill
Reply to  Willis Eschenbach
October 22, 2022 2:23 pm

You made the claim that each grid has been in equilibrium for thousands of years. I have stated the clear fact that the solar input at any location is never constant.

Every grid on your globe responds differently to the solar input. Building and melting ice mountains for example are cumulative processes that reflect integrating the power input over thousands of years. So 10W/m^2 over a thousand years is going to make a massive change in certain locations.

Another example, ocean thermal expansion and contraction reflect thousands of years of accumulated energy flows.

The current coupled climate models are integrating make-believe surface energy imbalance into ocean heat uptake. It is the key belief that drives runaway global warming.

JCM
Reply to  Willis Eschenbach
October 21, 2022 6:39 pm

ok – keep pushing. The limit comes from the unobservable, and discounted properties. It is in fluxnet where reality will come to fruition https://fluxnet.org/sites/site-summary/. It is the convenience of observation tools which limits conceptual frameworks. When LW radiometers were coupled with modtran, our prospects for advancement was diminished. This was when the climate system was reduced to LW radiative properties. However, there is a rich history which precedes this reductionism. This gives hope for getting out of the rut of the past 30-40 years.

Last edited 5 months ago by JCM
JCM
Reply to  Willis Eschenbach
October 21, 2022 7:09 pm

I guarantee any fluxnet tower operator has a much deeper appreciation of earth system dynamics, and the complexities involved, compared to the crop of derivative climate ‘researchers’ polluting the literature with their GCM derived ‘experiments’. I can’t even imagine the hollow emptiness I would feel to be leveraging a GCM as an actual surrogate for the earth system in my research, and yet 99/100 researchers do exactly that. Where hypotheses are not tested against the real world, but in GCM-land. A farcical notion of research.

Last edited 5 months ago by JCM
Nelson
October 21, 2022 12:43 pm

Interesting data as always.

I am surprised by the differences in Fig 3 & 5. I would have thought they would have been more similar. My intuition fails as to the reason for the shape of figure 5.

Wim Röst
October 22, 2022 5:20 am

It would be interesting to see the maps (both projections) for ‘Greenhouse radiation W/m2’ for the numbers used in figure 5. Then we can see where on Earth we find the 130 W/m2 peak sensitivity and the 80 W/m2 low of figure 5. Willis, could you produce those maps?

Wim Röst
Reply to  Willis Eschenbach
October 24, 2022 5:28 am

Willis, you are right, Figure 5 has its peak at 1.2°C. At about 70 W/m2, 110 W/m2, and 180 W/m2 we find the same average temperature change per W/m2. For all other values, the same is visible: the ‘response’ (if it is ‘a response’) is different for different grid cells. This seems to indicate that ‘other factors’ than Greenhouse Radiation set surface temperatures. Or, ‘natural factors’ play the main role.

Therefore, my question: is it ‘sensitivity for greenhouse radiation’ that we are looking at, or are we looking at ‘the end result of a complex climate system’? If the last is the case, possibly the whole climate system will react when input changes and the end result might be that there will be no warming left (or just a very little bit of warming). In that case, the ‘sensitivity’ for a W/m2 of Greenhouse Radiation would be zero or near zero, although the initial greenhouse warming effect for each grid cell will be something like in figure 5.

(As you know, I am of the opinion that surface temperatures are [nearly] fully dominated by the surface cooling system, based on evaporation, convection, and tropical clouds. This impedes that the ‘final sensitivity’ for extra greenhouse gases should be about zero – apart from ‘system changes’ that surely will follow when the radiative input somewhere changes. In that case, ‘sensitivity’ (for greenhouse radiative input) is a very dangerous term, causing a lot of unnecessary scare, because the surface temperature end result of extra radiative input will be close to what we see now. The complex system will change, but the fact that we don’t know how exactly does not justify all kinds of assumptions like ‘initial sensitivity’.)

Wim Röst
Reply to  Willis Eschenbach
October 24, 2022 5:31 am

When I look at both figures 6, what I think to see is nearly completely local ‘Greenhouse radiative warming’ by water vapor and clouds, the main players in the greenhouse surface warming effect.

Don
October 21, 2022 12:52 pm

When critics arrive, I would expect two areas will be mentioned.

1. Broadband solar heating is not the same as narrowband IR heating.
2. All of the energy not radiated to space in the CO2 band does not return to the surface. For example, a CO2 molecule in an excited state passes it’s kinetic energy to an O2 molecule. That molecule sometime later collides with some other molecule releasing radiation at some unknown frequency not in the CO2 band. Lost energy not returned to the surface.
Macha
October 21, 2022 3:48 pm

Yep. Those night vision glasses aren’t lit up much without a living being in view. Even darker looking up and most of my camping experience is the ground is cold at night.
Chemistry explains reactions using activation energy. Below a threshold no reaction occurs. As per full spectrum sunlight and TOA zenith sun 120C, it’s not the same as average 10um LWIR.

Gary Pearse
October 21, 2022 1:27 pm

“The few negative gridcells are at the poles, and they show the effect of the importation of heat fom the tropics.”

Re your scatterplot fig. 2 in this post, which was the subject of the immediate previous post, I had a comment, the gist of which was as in the quote above.

https://wattsupwiththat.com/2022/10/16/solar-sensitivity/#comment-3621582

The relationship between “available solar” and surface temperature isn’t a pure one. Rather, it is confounded by enthalpy change in evaporation in the equatorial band which is the flat T section, and, on the cold end, the rapid rise in T vs W/m² is almost all due to importation of heat in ocean currents and atmospheric flow.

What you could calculate quantitatively from this (possibly) would be the the solar energy that went into enthalpy change in the tropics and its distribution in sensible heat (net of direct solar warming) via air and ocean that warmed the extra-tropics. Your first post (as per figure 1) is a pure relationship.

TimTheToolMan
Reply to  Gary Pearse
October 21, 2022 1:47 pm

“The few negative gridcells are at the poles, and they show the effect of the importation of heat from the tropics.”

Perhaps Willis has analysed this in detail to come up with that explanation but my intuition tells me the negative grid cells are due to atmospheric temperature inversion.

RickWill
October 21, 2022 2:26 pm

Each gridcell has had thousands of years to equilibrate to its general current temperature and available solar power.

No location on Earth has constant solar intensity over hours, days, months, years, decades, centuries or any other time frame you choose.

That means no single location can ever be in equilibrium with its solar input.

Your prediction of sensitivity in Figure 6 fails because Antartica and the Southern Ocean have a sustained cooling trend throughout the satellite era.

Northern Hemisphere mid latitude spring/summers have to warm because the solar intensity is increasing. The reverse is occurring for the Southern Hemisphere.

Surface temperature in the mid latitudes is highly correlated to solar intensity – regression coefficient 96 to 97% over an annual cycle making due allowance for the thermal lag. With the intensity always changing, there can never be equilibrium. So your basic premise is false.

This is past 500 years and next 500 years for solar intensity at 30N:
-0.500  407.814408
-0.400  408.231635
-0.300  408.649215
-0.200  409.066813
-0.100  409.484100
0.000  409.900750
0.100  410.318143
0.200  410.734184
0.300  411.148357
0.400  411.560133
0.500  411.968970

Last edited 5 months ago by RickWill
Macha
October 21, 2022 3:52 pm

Rick, much of the southern polar vortex is observed by Erl Happ.
https://reality348.wordpress.com/
Beware…lots of chapters and charts.

DMA
October 21, 2022 2:40 pm

“Finally, this method gives a climate sensitivity estimate for each gridcell. Here is that map, showing how much the surface temperature is estimated to change for each additional W/m2 of greenhouse radiation.”
“The point of the paper is that the direct effects of greenhouse gases on the thermal radiation to space is much smaller than the average person realizes. This is the radiation that gets rid of solar heating. A 100% increase of CO2 (doubling) only reduces radiation to space by 1%.” Will Happer.
Considering the small change of temp for each new W/m2 and Happer’s statement that doubling will change the forcing by 1% we shouldn’t expect much warming from more CO2.

RickWill
October 21, 2022 2:49 pm

Each gridcell has had thousands of years to equilibrate to its general current temperature and available solar power.

If you did this entire analysis over a singly month time frame, you would get different results. That would clearly demonstrate that the temperature equilibrium you are claiming is anything but equilibrated.

RickWill
Reply to  Willis Eschenbach
October 21, 2022 6:31 pm

But you have stated that each 1X1 degree grid is thermally stabilised. over thousands of years when it cannot be possible because the solar intensity is never constant over any time frame – even from year-to-year let alone thousands of years. It varies tens of W/m^2 at any location for any particular month over thousands of years. .

The fact that you get a different result each month proves that it is not stabilised.

RickWill
Reply to  Willis Eschenbach
October 21, 2022 6:51 pm

My reason for pointing out that your basic premise is wrong is to encourage you think about why the average surface temperature is changing. You have a misguided belief that the solar intensity at any given location is constant from year-to-year.

If you understand that surface temperature in the mid latitudes is highly correlated to solar intensity AND that the solar intensity is always changing then you begin to understand something about real climate change. Not made up stuff about CO2 and greenhouse gasses.

One simple question that you should try to answer – Why is your Figure 6 predicting warming in the Southern Ocean when the evidence over 40 years is that the Southern Ocean is cooling?

R_G
October 21, 2022 11:09 pm

I do not think that Figure 6 shows predicted warming. It shows hypothetical situation what will happen if there is an increase of 1W/m2 of incoming radiation.

RickWill
Reply to  Willis Eschenbach
October 22, 2022 2:26 pm

And I have shown you that solar intensity due to orbit changes agree with the observations.

So again you have arrived at the point where “greenhouse” gasses do not alter the energy balance but you still persist in the idea that there is a “greenhouse effect” impacting the energy balance.

October 21, 2022 3:29 pm

Willis, please provide figure 6 also in an Atlantic centered version, Europeans will be grateful.

Reply to  Willis Eschenbach
October 22, 2022 1:47 am

Willis, Thank you, I see in figure 6 in Europe that you plot a sensitivity of one °C per W/m2, which means per CO2 doubling of 3.7 W/m2 a sensitivity of 3.7K.

Am I right to conclude that this above the IPCC mean of 3 degrees ECS?

October 21, 2022 4:01 pm

It is interesting to see that there is a breaking point at approximately 27 Celsius, since that is also the threshold temperature in seawater for triggering hurricanes.

When the sea is above 27 Celsius, the hurricanes get stronger, and when it is below, they get weaker.

I guess that there is a quite strong correlation between air temperatures and sea temperatures. That mean that the hurricanes can be some of the reason for the breaking point in air at 27 Celsius.
/Jan

michael hart
October 21, 2022 6:59 pm

Willis, I hope it’s just my imagination that your closing tone seems a bit valedictory.

michael hart
Reply to  Willis Eschenbach
October 22, 2022 4:23 pm

as in “end of” or “last”. “Here is my legacy” sort of stuff.

Kevin kilty
October 21, 2022 7:30 pm

Well, these plots are interesting, but I am unsure what lessons regarding CO2 sensitivity to draw from them. Let’s look at Figure 2 as an example. It looks like there are three domains. Form the surface temperatures plotted one is polar, a second is the temperate latitudes, and the last is the tropics. It looks like an interesting alternative rendition of the three cells of the general circulation that many of us learned somewhere in school (Hadley, Ferrel, Polar cells).

I thought an informative exercize would be to take the surface temperature in each domain and apply the stefan-boltzmann (SB) law with a surface emissivity of 0.97. Down in the polar domain at 233K this SB result would be $162Wm^{-2}$ whereas Willis’s plot shows a bit over 50. Thus, the net solar irradiance is incapable of supporting observed surface temperature. What makes up the deficit of $112Wm^{-2}$ is heat transferred from lower latitudes. In comparison, in the colder parts of the temperate zone at say 273K the corresponding deficit is something like $155Wm^{-2}$; and finally in the tropical zone there is still a deficit, but it is smaller — on the order of $90 Wm^{-2}$.

At first blush the results for the tropical cell might surprise a person because one would think that an excess of net solar irradiance in this region is what provides the excess energy transported to higher latitudes; yet there is actually a deficit. However, there is also a very large greenhouse effect in the tropics because the surface is warm and atmosphere humid. In mid-latitudes in summer, the greenhouse effect is around $130 Wm^{-2}$; that is, even in the warm season in mid-latitudes some support for surface temperatures must come from poleward transport of heat out of the tropics. This, I think, is an interesting result — the greenhouse effect in the tropics provides a great deal of support for surface temperature everywhere else on our planet.

There is a lot of information in the graph, a lot more information that is probably blurred by averaging over so many variations, but I am not sure that it makes a tight argument for a particular CO2 sensitivity because the water vapor feedback is still a topic of contention.

JCM
Reply to  Kevin kilty
October 21, 2022 8:10 pm

Look into the vast difficulties in closing surface energy budgets. A simple google search of “surface energy budget closure” reveals the vast uncertainties in the system. Surface energy budgets have never been resolved to better than 10-20 W m-2 and yet we’re told to accept forcings a magnitude less as self-evident. The uncertainties are far more than ‘water vapor feedback’. This is loose jargon from radiation theorists. Closing surface energy budgets is the holy grail of boundary layer climatologists, and yet radiative physicists get away with mere approximations and claim authority. There are a zillion factors involved that are not yet determined…

Geoff Sherrington
October 21, 2022 10:01 pm

JCM
You summarise my main concern. No way am I suggesting concerns should put an end to this exploration, only that in time refinements and more data might change the story. Uncertainty in TOA radiation balance is problematic. Geoff S

Kevin kilty
October 22, 2022 6:25 am

Even with all the effort put into this version 4 of EBAF its one-sigma uncertainty is still $5 Wm^{-2}$ which is greater than the alleged effect doubling of CO2.

Dave Fair
October 22, 2022 10:51 am

As NASA oh so politely and obscurely puts it: “Note: Determining exact values for energy flows in the Earth system is an area of ongoing climate research. Different estimates exist, and all estimates have some uncertainty.﻿

JCM
Reply to  Dave Fair
October 22, 2022 11:41 am

That’s for sure. Because the vast majority of energy flows within the Earth system are not measured. It is convection K which relates surface temperature to OLR.

Where at the surface, flux is dominated by evapotranspiration. At the cloud deck flux is dominated condensation. At TOA flux is dominated by radiation.

The vast majority of flux within the atmosphere is dominated the convection K. This is not directly observable. Movements of mass, tangible heat flows, and latent transmittance of heat.

Any perturbation to evaporative flux at the surface has the same effect as a TOA radiation perturbation. Any perturbation to condensation effectiveness in cloud has the same effect as a TOA radiation perturbation.

Net radiation does not account for surface temperature, evapotranspiration does. Net radiation does not account for temperature in the cloud deck, condensation does.

For example, a moist meadow has a higher net radiation than a bright concrete, and yet the meadow has a lower temperature. Go figure. Radiation enthusiasts struggle with that.

Furthermore, condensation in cloud controls the humidity profile aloft, IR window variability, and OLR spectral properties.

These processes cannot be accounted for by LW conjecture. It is K which controls heat dynamics within the system, and the spectral characteristics of OLR.

Izaak Walton
October 21, 2022 9:19 pm

Willis,
You interpretation of the scatter plots is not correct. Below Fig. 2 you state that
the slope of the cyan/black line shows the change in surface temperature per one W/m2 change in available solar power.”

which is incorrect given that each point on the plot represents a different point on the earth
and thus has a fixed location. There is no reason to expect that increasing the available solar power in Sydney for instance would produce the same climate as moving inland to the outback (on the same latitude) or further north since the ocean currents and winds are different in each location.

What the slope shows at best is what happens if you move location. Which is a very different thing from increasing the solar forcing while staying in the same location.

Izaak Walton
Reply to  Willis Eschenbach
October 21, 2022 11:44 pm

Willis,
what your scatter plot shows is what how the temperature changes as you move closer to the equator. And that temperature is a function of both the locally available solar power and the energy transported from the equator by the current climate. There is no valid way to use the slope of that graph to make predictions about what might happen if the locally available solar power increased.

Changing the globally available solar power will also change the flow of energy about the globe and in ways that you cannot predict from your scatter plots.

Nelson
Reply to  Willis Eschenbach
October 22, 2022 7:55 am

Willis what the intuition on why 1 w/m2 of back radiation warms so much more than 1 w/m2 of additional solar?

Izaak Walton
Reply to  Willis Eschenbach
October 22, 2022 9:25 am

Willis you say that “Figure 3 shows that over large areas of the planet, for each additional W/m2 of available solar, local temperatures increase by about 0.16°C.”

This is wrong. Fig. 3 shows that over large areas of the planet if you MOVE from one spot to another one that receives 1W/m^2 more sunlight then the temperature increases by 0.16 C. This does not imply that if you say in the same spot and increase the sunlight by 1W/m^2 then the local temperature will increase by the same amount as previously.

This is perhaps clearly seen near the poles. Europe is warmed by the gulf stream meaning for example that the UK is 5 degrees warmer than the coast of Canada at the same latitude. So an additional W/m^2 of sunlight in the UK is not going to make much difference since it won’t change the stream of the gulf stream.

Marinus
Reply to  Willis Eschenbach
October 24, 2022 2:44 pm

What is the impact of cleaner air on the temperature?
Over the last 40 years the global radiation as measured in De Bilt has increased from approx. 925 J/cm2 to over 1000 J/cm2. This is caused by less clouds.

October 21, 2022 11:55 pm

This article suggests a +2 degree C. TCS
Similar estimates can be made on the back of an envelope
The right answer, of course, is “no one knows the exact TCS,
and especially the exact ECS (after several centuries)

Estimated changes since 1850 assuming all warming
was caused by CO2, which is just a worst case assumption:
(1) My Back of Envelope Estimate:
CO2 up about 50% since 1850
Global average temperature up about 1 degree C
If +1 degree C. in 50 then, then expect approximately +2 degrees C.
after CO2 has doubled — up 100% At +2.5 ppm per year, it would take
3 years for the 415ppm CO2 level to increase +50%

(2) The IPCC AR6 TCS estimate:
IPCC 2021 AR6 WG1 says doubling CO₂ leads to forcing of 3.78 W/m² (p. 945) which leads to a TCR (70-year timescale) response of +1.8℃ (1.4-2.2)

For those two estimates, of +2.0 and +1.8 degrees C.:
Both assume CO2 is the only cause of global warming, which is a worst case assumption, and unlikely to be true

This in turn equates to about 2°C per doubling of CO2.”

So it appears we have yet another similar guess at TCS, using a different methodology. which appears to confirm the IPCC TCS estimate, not exactly what most readers of this website were hoping for?

Alexy Scherbakoff
Reply to  Richard Greene
October 22, 2022 2:40 am

When you make a connection between CO2 increase and temperature rise you will always have that connection. Regardless of the real reason of temperature rise.

Reply to  Alexy Scherbakoff
October 22, 2022 3:49 am

I stated that I was making a worst case assumption — that CO2 caused the entire temperature rise since 1850. I did not want a side issue of exactly what percentage of the CO2 rise was caused by CO2 I never said I believed CO2 is the only variable that causes global warming, because it is not.
.

Alexy Scherbakoff
Reply to  Richard Greene
October 22, 2022 4:47 am

I wasn’t aiming at you. I was referring to them. I could have said ‘When one makes……’

Reply to  Richard Greene
October 22, 2022 3:45 am

TYPO CORRECTIONS:
If +1 degree C. global warming was caused by a 50% CO2 increase then expect approximately +2 degrees C. after CO2 has doubled — up 100%

At +2.5 ppm per year, it would take 83 more years for the current 415ppm CO2 level to increase +50%

Last edited 5 months ago by Richard Greene
Geoff Sherrington
Reply to  Richard Greene
October 22, 2022 6:03 pm

RG,
You forget thet the temperature record shows peaks and troughs in years before CO2 became trendy. You cannot just double an extrapolation. Simply, invalid math. Geoff S

Geoff Sherrington
Reply to  Richard Greene
October 22, 2022 6:01 pm

RG,
Some readers here, researchers to whom I have spoken, are more interested in the results of scientific studies than “… what most readers of this website were hoping for”.
How can you possibly know what most readers were hoping for? Geoff S

DMacKenzie
October 22, 2022 6:08 am

Willis,
Generally, and over-simplified, I am of the opinion that the planetary temperature is controlled by cloud cover which is in turn controlled by the amount of water vapor in the air, which is in turn controlled by the amount of sunlight striking water-wet surfaces of the planet, with cloud cover randomized by highly variable weather patterns everywhere. Point 2 would be that water vapor in the air emits more IR photons back to the surface….until such point clouds form and start reflecting much more incoming sunlight back to outer space than the H2O emits in downward IR. This is where one can often find it assumed that water vapor will triple the CO2 warming effect.
But your graphs show little or no surface temperature dependency to increased GH downwelling IR where the planet is ALREADY warm and has high water vapor content….ignoring clouds for a moment…. I think this means that upwelling IR from water vapor through the atmospheric window to outer space is a more important factor than one would anticipate (not sure who that one might be).
This might explain why spectrum integration programs like modtran, using a surface temperature offset and fixed RH (not fixed absolute humidity) seem to come up with a lower ECS…

I’m thinking NSAIDS might fix the headache….

Last edited 5 months ago by DMacKenzie
DMacKenzie
October 22, 2022 6:18 am

Or maybe it shows that warm places are “temperature increase limited” by advection to higher latitudes.

October 22, 2022 7:46 am

Or that the water vapor greenhouse effect competes with the CO2 greenhouse effect. If true, the result would be that added CO2 would most increase global warming in cold, dry areas during the coldest months of the year, and at TMIN, rather than in the tropics, during the warmer months of the year, and at TMAX.

That is exactly what has happened since the 1970s, especially in the Northern Hemisphere. I’ll be awaiting my Nobel prize nomination.

Geoff Sherrington
Reply to  Richard Greene
October 22, 2022 6:06 pm

RG,
Then explain this, please. What turns off the CO2 tap? Geoff S
http://www.geoffstuff.com/uahoct.jpg

Richard M
October 22, 2022 9:19 am

One of the problems is this approach includes cloud radiative effects with GHG effects and then computes single number for downwelling radiation. In Dubal/Vahrenholt 2021 they attempted to look at both situations. I think Willis needs to do the equivalent to get a usable value.

Richard M
Reply to  Willis Eschenbach
October 25, 2022 6:32 pm

As far as I can tell, the data includes cloud effects. How did you remove them?

Robert W Turner
October 22, 2022 7:58 am

So the atmosphere is semi-solid stationary matter, convection is not a thing, and all LWR emitted from Earth comes from the surface.

Richard M
October 22, 2022 8:42 am

Now, a smart guy named Ramanathan pointed out that we can actually measure the amount of this greenhouse radiation from space. For every gridcell, we take the amount of radiation emitted at the surface. From that, we subtract the radiation escaping to space. The remainder is what was absorbed by the atmosphere and re-directed downwards—the greenhouse radiation.

Isn’t this only true for clear skies? Otherwise, you include cloud effects. Once those are included you eliminate any possibility of finding the effects of greenhouse gases. And, when you use data that includes cloud effects you cannot gain any knowledge about whether that data tells you what would happen when GHG concentrations change. Hence,

This in turn equates to about 2°C per doubling of CO2.

is somewhat overstating what the data is showing.

They are generally covered with cumulus and thunderstorm clouds. These act as a 100% absorber of upwelling radiation … so any additional CO2 will make little difference.

Yup, this is the most important finding. Remember, the GHE for CO2 is supposed to operate high in the atmosphere above the clouds. In fact, above the clouds is the best place to measure it. Yet, you found almost no effect.

Geoff Sherrington
Reply to  Richard M
October 22, 2022 6:14 pm

Willis,
What happens when you continue the Ramanathan path “ The remainder is what was absorbed by the atmosphere and re-directed downwards—the greenhouse radiation.”?
That “re-directed downwards” then meets clouds or not, it meets the ground and heats it, it meets the oceans that some claim cannot be heated much this way, it meets ice. Tose now hotter parts of the globe emit IR upwards, some of which goes to space, some to clouds etc and we are back at where we started with another cycle.
Don’t you have to integrate the flows over repeating cycles until they fizz out because some part of the puzzle cannot go any further? Like summing a Taylor’s expansion? Geoff S

frankclimate
October 22, 2022 10:19 am

Very interesting approach, Willis. However I’m not quite sure if it’s the last word. Your “ECS-pattern” ( Fig. 6) should be replicated in some way in the spatial trends of the GMST, albeit some possible internal variability, not captured by the “ECS-pattern”. Especially the contrast in warming between the East Pacific and West Paciific ( the pattern effect in the real world, reducing the ECS) shoud be to see in your Fig.6. This is not the case:

Therefore I have some doubts if your approach is valid enough. It also could be, that your outcome ( ECS= 2.2) is the same as in Lewis (2022) by chance?
best Frank

frankclimate
Reply to  Willis Eschenbach
October 22, 2022 11:37 pm

Hi Willis, this (“GHG not a main driver”) would mean that there are other forcings ( the IPCC AR6 lists them, i.e. vulcanos, aerosols, solar variations, land use changes..) which overwhelm the GHG impact. However youself make a quantification: you find an ECS of 2.2 K/2*CO2 with strong spatial differences . This MUST have an impact on the global temperature trends since 1950 IMO. If you were right you should discuss these differences with observations.

arjan duiker
October 22, 2022 2:54 pm

Dear Willis, thank you for sharing these very impressive results.

You say “This in turn equates to about 2°C per doubling of CO2″. One of the most recent (and probably most accurate) average forcing values for 2xCO2 is from Happer/Wijngaarden and amounts 3.0 W/m2. In reality, there’s a certain distribution over the globe, I presume; low latitutes higher values than higher latitutes. If that’s the case (but I’ve a hard time finding literature about that) the higher forcing values would coincide with the non-sensitive area’s you’ve presented in figure 6.

Would it make a lot of difference taking that into account do you think?

ferdberple
October 22, 2022 8:25 pm

Willis

Kindly post the temperature data by year and grid cell so we can validate your work. As I understand temperature is not part of the raw CERES data. Rather you have derived it from upwelling radiation.

thanks, Ferd

ferdberple
Reply to  Willis Eschenbach
October 23, 2022 6:37 am

Hi Willis

Kindly post the temperature data by year and grid cell. I believe the generally agreed standard is to release both data and methods behind a paper.

For example: The controvesy over Phil Jones and Steve McIntyre and access to temperature data.

As I recall there was considerable criticism at the time over the failure to release temperature data, even though as with Berkley, the data could be derived from another source.

This situation appears very similar.

Thanks, Ferd

Last edited 5 months ago by ferdberple
ferdberple
Reply to  Willis Eschenbach
October 24, 2022 5:58 am

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3126798/

Data Sharing by Scientists: Practices and Perceptions
“Data sharing is a valuable part of the scientific method allowing for verification of results and extending research from prior results.”

https://www.nature.com/articles/s41597-022-01428-w

A focus groups study on data sharing and research data management

Sharing scientific research data has many benefits. Data sharing produces stronger initial publication data by allowing peer review and validation of datasets and methods prior to publication1,2. Enabling such activities enhances the integrity of research data and promotes transparency1,2, both of which are critical for increasing confidence in science3,4.

ferdberple
Reply to  Willis Eschenbach
October 24, 2022 6:30 am

https://www.nature.com/articles/s41597-022-01428-w
A focus groups study on data sharing and research data management

After publication, data sharing encourages further scientific inquiry and advancements by making data available for other scientists to explore and build upon2,3,4,5. Open data allows further scientific inquiry without the costs associated with new data creation4,6.

======
especially important for us unpaid researchers and hobbyists.

Richard M
October 23, 2022 6:14 am

I was trying to understand what might cause figure 5. It appears to show a highly variable warming effect related to the GHE. My best guess is that it, in fact, is related to clouds. Might be interesting to build a similar graph for cloud cover to see if they match up.

ferdberple
October 24, 2022 6:07 am

https://climatedataguide.ucar.edu/climate-data/global-surface-temperatures-best-berkeley-earth-surface-temperatures

Key Limitations

Anomaly fields are highly smoothed due to the homogenization and reconstruction methods, despite being gridded at 1×1 degree

The homogenization approach may not perform well in areas of rapid local temperature change, leading to overestimates of warming at coastal locations and underestimates at inland locations

======
Why would highly smoothed BEST data be highly correlated with a CERES outgoing surface radiation derived dataset? Why would satellite data be smoothed? Polar orbits provide global coverage. Why would smoothed data be highly correlated with unsmoothed data?

Scott J Simmons
October 24, 2022 10:43 am

Willis,

There are at least three problems with your post:

1. What you’re calling “the greenhouse effect as a percentage of upwelling radiation” is the normalized greenhouse effect, g, which is approximated by G/Fs, where G is the greenhouse effect and Fs is the upwelling LW surface flux. The calculation isn’t exact, though, which is the first problem with your post. What is clear is that G/Fs increases with temperature, but not by much. If we start at T = 288 K and double CO2 with an ECS of 2 C, the resulting g = 0.399%. If ECS = 3 C, then the resulting g = 0.407%.
2. Your graph has practically nothing to do with climate sensitivity. Sensitivity by definition is the equilibrium warming at the surface that occurs per unit change in radiative forcing at the top of the atmosphere, not at the surface. That is, if the earth’s energy imbalance increases by 1 W/m^2 and the result of that is 0.81 C, then sensitivity is 0.81 C/W/m^2 and ECS = 0.81*3.71=3 C. If ECS = 2 C, then sensitivity is 2/3.71 = 54 C/W/m^2. For any increase in EEI, there is always a larger increase in LW surface flux. If ECS = 2, then doubling CO2 (3.71 W/m^2) results in ~11 W/m^2 increase at the surface, so using the surface LW flux will always cause you to underestimate sensitivity.
3. Furthermore, it should be obvious that you’re not looking at equilibrium temperatures at all, since EEI is currently 0.8 W/m^2.

Your calculations are completely wrong – they fail to grasp what sensitivity actually is.

Scott J Simmons
Reply to  Willis Eschenbach
October 24, 2022 12:56 pm

Multiple errors continue:

I have no clue what you mean by “The calculation isn’t exact”.

You can calculate g in multiple ways, and G/Fs is one. Another is 1-(T0/T1)^4, where T0 is the earth’s effective temperature (255 K) and T1 is current temperature (~288 K). The values are similar but not the same. I believe the IPCC treats it as a constant 0.4 because it simply doesn’t change that much.

Figure 4 clearly falsifies your claim…

No, it doesn’t. You just made a scatter plot of local temperatures and local g, but g is properly calculated with global surface temperature, and G/Fs doesn’t change by much with a change in GMST. In fact, it changes as I calculated. The numbers don’t lie. Check my math if you doubt me.

I’ve calculated the top-of-atmosphere forcing change in the manner defined by Ramanathan—TOA LW radiative forcing is equal to surface upwelling LW minus TOA upwelling longwave.

What you calculated is NOT top of the atmosphere forcing change. You calculated the greenhouse effect, which is what you described. But that is NOT the top of the atmosphere forcing change. If doubling CO2 causes 3.71 W/m^2 change in EEI (top of the atmosphere forcing change), the greenhouse effect increases by ~16 W/m^2 if ECS = 3 C. Your confusion here is a big part of the problem.

in such a complex system, there is never complete equilibrium on any time scale.

Of course, but that’s besides the point. In order to calculate sensitivity, you need to calculate the dT at equilibrium with dF, where dF is a TOA forcing change (change in EEI). Since EEI is almost never exactly 0, you have to account for EEI in any estimate of sensitivity, which you simply did not do. This is the proper formula to calculate sensitivity using a simple energy balance equation:

λ= ΔT/(ΔF – EEI)

Here λ is sensitivity, ΔT is a change in GMST (not local temperature), ΔF is a forcing change at TOA and EEI is the earth’s energy imbalance. If you plug in empirical values for these, with ΔT = 1.2 C, ΔF = 2.2 W/m^2 and EEI = 0.8 W/m^2, you end up with a λ of about 3 C.

the warming over the entire 20th century was only 0.2%.

Again, that’s besides the point. Current GMST is 1.2 C warmer than the 1850-1900 mean. so 1.2/288 = 0.4%, but whatever number you want to use for that percentage, you didn’t calculate sensitivity at all.

And until you give me a seriously calculated uncertainty on your imbalance number, I’ll let that one go…

Loeb estimated it to be 0.77 ± 0.06 W/m^2 from 2005-2019.

Loeb, N. G., Johnson, G. C., Thorsen, T. J., Lyman, J. M., Rose, F. G., & Kato, S. (2021). Satellite and ocean data reveal marked increase in Earth’s heating rate. Geophysical Research Letters, 48, e2021GL093047. https://doi.org/10.1029/2021GL093047

except to note that your claimed imbalance is tiny … you’re pointing at a difference that makes no difference.

Whether you call it tiny or large doesn’t matter. But it does make a difference. If EEI is 0.77 W/m^2 that means that 0.62 C additional warming is built into current conditions (ECS = 3 C), or about 0.42 C additional warming if ECS = 2 C. If you ignore EEI, as you have done, you can calculate TCR, but you can’t calculate ECS.

I’m analyzing the worldwide relationship of greenhouse radiation and temperature, and the imbalance you mention is lost in the noise.

You did plot the relationship between g and T, but you did NOT calculate anything approximating ECS.

Jim Gorman
Reply to  Willis Eschenbach
October 24, 2022 2:38 pm

And until you give me a seriously calculated uncertainty on your imbalance number, I’ll let that one go except to note that your claimed imbalance is tiny … you’re pointing at a difference that makes no difference. I’m analyzing the worldwide relationship of greenhouse radiation and temperature, and the imbalance you mention is lost in the noise.”

Hear, Hear!

Scott J Simmons
Reply to  Jim Gorman
October 24, 2022 5:21 pm

As I said,

Loeb estimated it to be 0.77 ± 0.06 W/m^2 from 2005-2019.

Loeb, N. G., Johnson, G. C., Thorsen, T. J., Lyman, J. M., Rose, F. G., & Kato, S. (2021). Satellite and ocean data reveal marked increase in Earth’s heating rate. Geophysical Research Letters, 48, e2021GL093047. https://doi.org/10.1029/2021GL093047

ferdberple
October 25, 2022 1:42 pm

Willis Eschenbach
October 22, 2022 11:10 pm
Yes, I’ve derived the temperature. Yes, it is indistinguishable from say the Berkeley Earth data.
=====================
Willis Eschenbach
February 23, 2015 9:26 am
Thanks, Paul. I converted using the standard S-B relationship, which is that
Radiation = S-B_constant * emissivity * temperature^4
For the surface radiation I used the CERES calculated upwelling surface radiation, the EBAF-SURFACE dataset called “surf_lw_up_all”.
=====================

Willis,

Is the above how you derived the surface temperatures from upwelling radiation??

Looking at your excel ceres data for example, for

Year Month 2000 3
surf_lw_up_all 392.35 w/m2
allt2 13.88 C
SB-temp BB 15.264 C (mismatch)

Using S-B with 392.35 w/m2 yields 15.264 C but you have the temp as 13.88 C.

As a double-check, I repeated this exercise using the global average from the CERES EBAF 4.1 data directly with similar results.

Please explain this discrepancy. Thanks, Ferd

ferdberple
Reply to  Willis Eschenbach
October 26, 2022 6:37 am

I have repeatedly warned of this problem on WUWT. That average radiation cannot be used to infer average temperature using S-B because of non-zero statistical variance.

As such using monthly radiation averages from CERES EBAF 4.1 cannot match Berkley Earth except by chance.

Even using realtime gridcell radiation data from CERES is a problem because a gridcell is an arbitrary measure and there is no guarantee the scanners will exactly sample the gridcell. Averaging radiation will be required to infill, which invalidares infering temperature via S-B.

Kindly show the formula that allows you to determine average temperature from CERES average radiation. I contend no such formula exists given present knowledge.

Thanks, Ferd

Last edited 4 months ago by ferdberple
Jim Gorman
October 26, 2022 7:52 am

Climate science is full of this. S-B, Planck, etc. are all exponential functions. They are also based upon a static or momentary point in time. The next small increment of time the temperature will be different.

That is why gradients are necessary. Gradients define actual heat loss or gain in a uniform manner. For example, does copper lose heat faster than iron when starting at a similar temperature? Does humid air lose heat faster than dry air.

That’s why I had to take calculus before taking thermodynamics. Does soil or water lose heat faster than CO2? By what amount and why?

ferdberple
Reply to  Jim Gorman
October 27, 2022 7:36 am

There is a good explanation (below) of the problem in using average radiation to infer average temperature. As Bob Wentworth explains, average radiation only gives you an upper bound for average temperature, unless you have zero variance over the surface and time.

Clearly this is not the case when dealing with CERES monthly averages, where radiation for a grid square is unlikely to remain constant. Thus my request to Willis that he post his grid square temperatures for independent validation.

Looking at CERES own 10 year averages, using the Willis formula from 2015 I calculate an average surface temperature for the earth of 16.4 C. Clearly this must be an upper limit as the generally agreed average surface temp for the earth is 15C or lower.

https://ceres.larc.nasa.gov/documents/DQ_summaries/CERES_EBAF_Ed4.1_DQS.pdf

Table 4-1. Global mean TOA and surface fluxes and CREs for EBAF Edition 4.1 and Edition
4.0 for July 2005 to June 2015 (W m-2). pg 13
All-sky Ed4.0 Ed4.1 Ed4.1 – Ed4.0
Surface
LW up 398.3 398.3 0.0

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https://wattsupwiththat.com/2021/06/04/mathematical-proof-of-the-greenhouse-effect/
Mathematical Proof of the Greenhouse Effect
1 year ago Guest Blogger
Guest post by Bob Wentworth, Ph.D. (Applied Physics)

There is a mathematical law, first proven in 1884, called Hölder’s Inequality… Hölder’s Inequality says it will always be the case that:

⟨T⟩⁴ ≤ ⟨T⁴⟩

In other words, the fourth power of the average surface temperature is always less than or equal to the average of the fourth power of the surface temperature.

It turns out that ⟨T⟩⁴ = ⟨T⁴⟩ if T is uniform over the surface and uniform in time. To the extent that there are variations in T over the surface or in time, then this leads to ⟨T⟩⁴ < ⟨T⁴⟩.

(One of the reasons the surface of the Moon is so cold on average (197 K) is that its surface temperature varies by large amounts between locations and over time. This leads to ⟨T⟩⁴ being much smaller than ⟨T⁴⟩, which leads to a lower average temperature than would be possible if the temperature was more uniform.)
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