Solar Sensitivity

Guest Post by Willis Eschenbach [SEE UPDATE AT END]

In my previous post, “Global Scatterplots“, I discussed how a gridcell-by-gridcell scatterplot of the entire globe could be used to gain insights into the relationship between two variables. The variables I discussed in that post were the cloud radiative effect (CRE) as a function of the temperature. At the end of that post, I threatened as follows:

I will return to what I’ve learned from other gridcell scatterplots in the next post.

So as foretold in the ancient palimpsest texts … he’s baack!

For this expedition into global scatterplots, Figure 1 shows the surface temperature as a function of the amount of solar power that’s actually entering the climate system. This available solar power is the top-of-atmosphere (TOA) solar, minus the “albedo reflections”, which are the amount of sunlight reflected back to space by the clouds and the surface.

Figure 1. 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.

I’ve mentioned before how I love the surprises that science brings. The surprise for me in this was that there are three very distinct regimes shown in Figure 1.

The left side of the plot, below around 100 W/m2 available solar, shows the areas near the poles where there’s little available solar power. In those areas, the temperature rises very quickly with increasing solar power.

Then there’s a long basically straight-line section from ~ 100 W/m2 available solar up to around 300 W/m2.

And finally, from about 310 W/m2 to 360 W/m2, there is a flat straight line, with no slope at all.

That last was the biggest surprise to me. Once the average available solar power is above 310W/m2, you can add up to an additional 50 W/m2 without increasing the surface temperature one bit. And remember, these are not short-term changes. This reflects the effects of an additional 50 W/m2 applied over decades and centuries.

Hmmm … an increase of 3.7 W/m2 from a doubling of CO2 is supposed to cause a 3°C temperature rise. But here’s a part of the world where a change of 50 W/m2, more than ten times as large, does … nothing. However, I digress …

How large a part of the world shows this insensitivity? Figure 2 outlines the areas below 100 W/m2, where there is a steep rise of temperature with increasing solar, and the areas above 310 W/m2, where there is NO rise of temperature with increasing solar.

Figure 2. Available solar power (TOA solar minus albedo reflections), Pacific-centered and Greenwich-centered views. Areas in red outlined in cyan/black do not change temperature with increased average solar input. Polar areas in blue outlined in white/black show where the temperature is very sensitive to increased solar input. Dotted horizontal lines show the tropics and the arctic/antarctic circles.

Note that the red areas that are insensitive to increased solar input are all in the tropics, and are virtually all ocean. They cover half of the tropical area or about 22% of the planet’s surface.

The blue areas of high temperature sensitivity to solar variations, on the other hand, only cover about 8% of the planet.

Returning to Figure 1, recall that I said that “The slope of the cyan/black line shows the change in temperature for each 1 W/m2 change in available solar.” Figure 3 shows exactly that, the slope of the cyan/black trend line in Figure 1.

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

Here we see the same three regions that we can see in Figure 1. At the left, below ~ 100 W/m2 of available solar, the sensitivity of temperature to changes in solar input is quite high. (Remember that this is not the climate sensitivity to CO2 changes. It is the sensitivity to available solar.)

Then, from 100 W/m2 to 300 W/m2, the sensitivity is basically unchanged, averaging 0.16 °C per W/m2.

Finally, above ~ 310 W/m2 of available solar, the temperature is totally insensitive to changes in available solar power.

Note that this means that solar power has to rise by about six W/m2 to raise the temperature of 70% of the planet by 1°C … and remember that in half the tropical ocean, 22% of the planet, that same six W/m2 increase in available solar doesn’t do doodly-squat to the temperature. (“Doodly-squat”? That’s a technical scientific term for zero.)

Conclusion? Simple.

It takes ~ 5 W/m2 of additional solar input to raise the surface temperature by a single degree C.

Let me close with the threat from my previous post, viz:

I’ll leave this here, and I will return to what I’ve learned from other gridcell scatterplots in the next post.

Best regards to everyone on a foggy coastal day,

w.

I IMPLORE YOU: When you comment, quote the exact words you are responding to. I can defend my own words. I can’t defend your rephrasing of my words. Thanks.

[UPDATE] A commenter said that my saying the situation was stable “over decades and centuries” is a little presumptuous. I answered:

True … but I am judging that on the lack of change on either a yearly average or a 5- year average basis.

Also, the slope shown in Figure 3 is the parameter of interest since it shows dY/dX, the change in the Y variable with respect to the X variable. And that slope changes very little, year to year or decade to decade.

Here, I just made this graph up special for you. It shows yearly averages, rather than the 21-year average as shown in the head post.

Figure 4. As in Figure 3, but showing 21 individual years rather than a 21-year average.

Note that other than right at the poles there is very, very little change in the slope (sensitivity of temperature to changes in solar input) regardless of which year you pick.

Also, I’ve looked at the same analysis using Berkeley Earth temperature data and CERES radiation data. It shows the same thing you see above—very sensitive where there’s little sun, ~ 0.16 °C per W/m2 over ~70% of the earth, and 0.0 °C over ~22% of the earth.

Finally, recall that we are looking at gigantic, planetary-scale patterns of relationships between the two variables. These will not be affected by much smaller local variations, as verified by the graphic above.

And that taken together convinces me that we are looking at stable, long-term relationships. This is what I expected from the start since each gridcell has had millennia to settle into those planetary-scale patterns of temperatures and available sunshine.

Regards,

w.

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Tom Halla
October 16, 2022 10:12 am

With that sort of nonlinearity for solar radiation, it is no wonder it would be easy to make a model that goes wrong. No increase from 310 to 360 is notable.

Mr.
Reply to  Tom Halla
October 16, 2022 10:45 am

Yes models can only ever produce a projection of outcomes based upon what we think we know will hold true based upon the quantifications we assign to all the elements.

If a modeler decided to list all the possible variations to all the elements along with all the possible influences that weren’t included in the model, they might well conclude that the old tea leaves or chicken entrails provide just as useful a basis for prediction as the slaved-over model.

n.n
Reply to  Mr.
October 16, 2022 11:16 am

Chaos in characterization (i.e. incomplete, insufficient) and processing (e.g. numerical) of nonlinear signals limits prediction to the scientific domain (i.e. near-frame).

Last edited 1 month ago by n.n
Reply to  Mr.
October 16, 2022 12:18 pm

Yes models can only ever produce a projection of outcomes based upon what we think we know will hold true based upon the quantifications we assign to all the elements.

obviously you never worked with non deterministic perturbation
models.

Mr.
Reply to  Steven M Mosher
October 16, 2022 2:12 pm

Can’t say that I have.
Do they put out more accurate results than the suite of climate models we have had for these past 3 decades or so?

MarkW2
Reply to  Steven M Mosher
October 16, 2022 3:48 pm

Non-deterministic perturbation models are useful but are also, inherently, approximations. The reliability of findings from ANY climate models looking into the future for anything other than very short periods will be no better than tea leaves or chicken entrails. Claiming otherwise is absurd.

Streetcred
Reply to  MarkW2
October 16, 2022 4:20 pm

Has there ever been a time when Musher made an intelligent comment here ? I’ve been reading this blog for around 2 decades & cannot recall such an occasion.

Reply to  Streetcred
October 16, 2022 5:13 pm

Well, it wasn’t on WUWT, but this was my all-time favorite series of Mosh comments:

http://rankexploits.com/musings/2012/tell-me-whats-horrible-about-this/#comment-89946

http://rankexploits.com/musings/2012/tell-me-whats-horrible-about-this/#comment-89954

http://rankexploits.com/musings/2012/tell-me-whats-horrible-about-this/#comment-89957

Especially:
http://rankexploits.com/musings/2012/tell-me-whats-horrible-about-this/#comment-89959

http://rankexploits.com/musings/2012/tell-me-whats-horrible-about-this/#comment-89961

http://rankexploits.com/musings/2012/tell-me-whats-horrible-about-this/#comment-89965

http://rankexploits.com/musings/2012/tell-me-whats-horrible-about-this/#comment-89966

http://rankexploits.com/musings/2012/tell-me-whats-horrible-about-this/#comment-89967

http://rankexploits.com/musings/2012/tell-me-whats-horrible-about-this/#comment-89983

http://rankexploits.com/musings/2012/tell-me-whats-horrible-about-this/#comment-89989

http://rankexploits.com/musings/2012/tell-me-whats-horrible-about-this/#comment-90004

http://rankexploits.com/musings/2012/tell-me-whats-horrible-about-this/#comment-90020

http://rankexploits.com/musings/2012/tell-me-whats-horrible-about-this/#comment-90022

http://rankexploits.com/musings/2012/tell-me-whats-horrible-about-this/#comment-90033

http://rankexploits.com/musings/2012/tell-me-whats-horrible-about-this/#comment-90035

http://rankexploits.com/musings/2012/tell-me-whats-horrible-about-this/#comment-90109

http://rankexploits.com/musings/2012/tell-me-whats-horrible-about-this/#comment-90224

http://rankexploits.com/musings/2012/tell-me-whats-horrible-about-this/#comment-90232

http://rankexploits.com/musings/2012/tell-me-whats-horrible-about-this/#comment-90240

beng135
Reply to  Dave Burton
October 17, 2022 11:00 am

Dave Burton, wow, those are painful to read.

Chad W Jessup
Reply to  Streetcred
October 16, 2022 8:00 pm

I completely understand your perception, but he has commented intelligently on other websites plus his own website.

Willem Post
Reply to  Willis Eschenbach
October 17, 2022 5:58 am

Willis,
Your work would be even greater with a chart starting at 50 W/m2 for the South Pole, to 350 W/m2 for the tropics, and 50W/m2 for the North Pole.

The flat area would be in the middle of the graph.

The Northern and Southern Hemispheres are quite different.
Would the data sets not be different as well?
The NH has warmed more than the SH

beng135
Reply to  Streetcred
October 17, 2022 10:58 am

Streetcred, I have a hazy memory of him making one possibly, maybe, long ago? IIRC, he did do some decent detective work regarding the Climategate fiasco.

Last edited 1 month ago by beng135
Tim Gorman
Reply to  MarkW2
October 17, 2022 5:16 am

The non-deterministic perturbation models are only useful if you can assume that at least some of the outputs are valid. How do you do that with climate models where almost none of the outputs match real world observations? You can’t just assume that the most common output is valid, it has to be validated in some manner or another. That never seems to happen with climate models. The average of the ensembles are just *assumed* to be a valid output.

MarkW2
Reply to  Tim Gorman
October 17, 2022 5:44 am

I agree, Tim, and should have said “can be useful” rather than “are useful”. However, I wasn’t just referring to climate models.

Tim Gorman
Reply to  MarkW2
October 17, 2022 12:27 pm

I understand. I was just using your post as a place to post a reply about the subject.

MARTIN BRUMBY
Reply to  Steven M Mosher
October 16, 2022 6:14 pm

I think you misspelled that penultimate word. Try beginning with ‘mas’.

Julian Flood
Reply to  Steven M Mosher
October 16, 2022 9:34 pm

Mosh, you could usefully use your undoubted skill with data to quantify the areas of oceans/seas/lakes which are warming faster than the simple CO2 hypothesis can explain. Black Sea, Red Sea, Lake Superior, Eastern Mediterranean, Baikal, Lake Tanganyika etc etc.

If pollution caused the 1910 to 1940 warming (and Wigley’s blip) then a lot of the AGW data jiggery-pokery is unnecessary.

JF

Tim Gorman
Reply to  Steven M Mosher
October 17, 2022 5:12 am

If your model gives different outputs over different runs due to processing variability then how do you know what the *true* output is? It won’t be just the output that is seen the most often unless the model actually matches reality. In fact, you can’t even be sure that the range of outputs encompasses reality unless you have some method of determining the model is “good”. You can’t just assume that a valid output exists somewhere in the varying outputs. They *can* all be wrong!

ferdberple
Reply to  Steven M Mosher
October 17, 2022 7:10 am

Non deterministic perturbation
models.
======
How about a roll of the dice. The outcome is probabalistic not deterministic. The toss provides the perturbation.

Monopoly qualifies as a non deterministic pertubation real estate investment model.

Last edited 1 month ago by ferdberple
PCman999
Reply to  Steven M Mosher
October 17, 2022 10:29 am

“obviously you never worked….”

Don’t understand why you stated that last sentence – was it meant as an insult or only people in the climate disaster club should be allowed to discuss the issue?

W.E. has worked with huge climate models and yet comes up with great insight just using R and a standard computer.

And just about anyone can look at a temperature graph (especially if anomalies are shown on top of the ~15°C average) of the last ~200 centuries and see that there’s no such climate crisis that so many scientists would bet their lives on.

Matthew Schilling
Reply to  Steven M Mosher
October 18, 2022 11:19 am

And that’s what Climate Modelers are doing – creating non-deterministic perturbation models!
Or something.

MARTIN BRUMBY
Reply to  Mr.
October 16, 2022 6:12 pm

They might indeed and with justice.

But, gazing into my crystal ball, I see zero signs that they will.

Back to the Lalalal-fingers in ears-“I can’t hear you….” and “worse than we thought – send more money…”

Gary Pearse
Reply to  Tom Halla
October 16, 2022 6:08 pm

I think I see where this going. In the equatorial band, above 310W/m^² the added energy goes into evaporation, driving earth’s heat engine, (delta Enthalpy). Below 100W/m^², the heating doesn’t arise significantly from solar heating but from polar bound warm currents carrying equatorial heat to the cooling end of the heat engine.

Possibly this could be proved by calculating what the temperature should be over the equatorial band without evap and see if it matches what the temp is minus what it should be without the warm currents. The assumption would be that “should-be-heating” is directly related to the angle of incidence on each m^² of the globe.these derived difference should be ~ equal.

Gary Pearse
Reply to  Gary Pearse
October 16, 2022 6:11 pm

derived differences

Joe Born
October 16, 2022 10:29 am

This post’s Fig. 1 put me in mind of the discussion accompanying a recent Richard Lindzen paper‘s Fig. 4.

Aden
October 16, 2022 10:41 am

Here’s a question I can’t get a straight answer too. How much lag is there in the system?

If you look at seasons, end of December is the solstice. However winter is december to january which implies a lag of a month.

However, if we look at daily temperatures, the “forcing” is turned off at night, and you have drops of the order of a degree an hour or more. Depends on where you are. Low over the ocean, more over land, much more over a desert. That implies the lags are on the seasonal timescale instantaneous.

What’s the cause of the difference?

Rud Istvan
Reply to  Aden
October 16, 2022 11:54 am

The diurnal lag depends on specific humidity, which adds thermal inertia to the atmosphere. The seasonal lag (to summer/winter solstice) is on order 2 months, mostly thanks to land/ocean thermal inertia.

RickWill
Reply to  Aden
October 16, 2022 3:43 pm

How much lag is there in the system?

From the perspective of annual sunlight, land temperature in the mid latitudes lags by about 1 month. Ocean surface temperature lags the sunlight by about 2 months in the mid and high latitudes.

In the tropics, the ocean surface temperature LEADS the sunlight by about 25 days in the Pacific. Shorter time in the Atlantic. That is because the surface temperature is dominated by cloud feedback in the tropics and it takes up to a month for the atmospheric water to build to the temperature limiting level. The Arabian Sea is very good indicator of this. Most of it hits 30C before the monsoon sets in:
https://earth.nullschool.net/#2022/05/09/0000Z/ocean/primary/waves/overlay=sea_surface_temp/orthographic=-298.37,15.14,654/loc=70.503,11.152

Actual data on thermal response to sunlight is presented here:
https://wattsupwiththat.com/2022/10/04/surface-temperature-response-to-solar-emr-at-top-of-the-atmosphere/
As show here, sunlights is by far the dominant player in surface temperature over ocean and land in the mid latitudes. The changing solar intensity due to orbital changes explain the observed trends in temperature across the globe. The Northern Hemisphere will continue to see higher summer temperature and wetter (snowier) winters. The Souther Hemisphere is the reverse with temperature extremes moderating.

The long term temperature trends are driven by thermal capacity and albedo changes. The Meditteranean Sea and other land locked water ways are latitudinally constrained. They store heat over centuries and respond to centennial scale trends in solar forcing. The oceans have much longer time lags that depend on where the sea ice is being formed.

Ice covered land and ocean cannot exceed 0C. Once the ice is sustained over an annual cycle it takes a long time to melt. The air surface temperature in the low sunlight months is dominated by the advection of warm air. The South Pole currently gets the highest single day solar input of anywhere on the globe and yet the surface temperature does not exceed 0C because it is a 2000+m thick ice block. Same goes for much of Greenland. Minimum temperature over ice blocks is sensitive to fairy farts because there is next to no thermal inertia in the atmosphere above. A 10C variation in average temperature when the low point is -55C means nothing because the high point is inevitably 0C.

kwinterkorn
Reply to  RickWill
October 16, 2022 4:08 pm

Add to this complexity that prevailing winds almost continuously transport sea air onto the continents and continental air to the seas.

Curious George
October 16, 2022 11:05 am

A great piece of work. Surprising!
A little nitpick: “over decades and centuries” is a little presumptuous when based on 30+ years of data.

Joe Born
Reply to  Willis Eschenbach
October 16, 2022 2:37 pm

That Lindzen paper‘s discussion accompanying its Table 1 may be relevant; it infers from paleo data that the major changes in global-average surface temperature have resulted from changes in tropics-to-polar temperature difference, with very little change in the tropical temperature itself.

Also, I think there’s speculation that much of that polar change is a change in the difference between the surface and the tropopause without a lot of change in the tropopause temperature itself.

Joe Born
Reply to  Willis Eschenbach
October 17, 2022 4:18 am

I greatly appreciate that; among my character flaws is zero patience for dealing with arcane data formats, so I’d probably never get around to analyzing those data first-hand.

Obviously your plot deals with a time scale much smaller than Dr. Lindzen’s table does, but it’s still tantalizing.

RickWill
Reply to  Willis Eschenbach
October 16, 2022 4:02 pm

Which is what I expected from the start, since each gridcell has had millennia to settle into those planetary-scale patterns of temperatures and available sunshine.

The sunlight is not constant at any point on the globe from one year to the next. It is continually changing due to orbital changes. That is why Antarctica and the Southern Ocean are cooling and the northern hemisphere is warming.

This table covers 1000 years of April 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
Currently trending up 0.4W/m^2 per century. That will be causing a rising trend in NH mid latitude temperature. There are significant swings =year-to-year as well due to orbital changes.

November sunlight at 60S is trending down at 0.6W/m^2 per century:
-0.500  397.549763
   -0.400   397.039478
   -0.300   396.537025
   -0.200   396.042597
   -0.100   395.556374
    0.000   395.078532
    0.100   394.607107
    0.200   394.144579
    0.300   393.691333
    0.400   393.247755
    0.500   392.814223

This will influence the regional temperature in January due to the thermal lag. These are real changes in solar forcing not make believe.

The globe has to warm up because the peak solar input is moving northward and there is more land in the NH that responds faster and over a wider range to solar input than the ocean.

DMacKenzie
October 16, 2022 11:08 am

So the almost 0 C temp change per Watt of available solar from 310 to 360 corresponds to the steep part of the CRE 27 to 30 C from your post 2 days ago. Obviously you are saving the best for last…..PS I like your % of Earth’s surface lines, but you haven’t done that on Fig. 3, of course your prerogative as chief data dabbler…..

October 16, 2022 11:11 am

I told you.
The extra heat is from earth.
Just think about it. My books say that T is going up 3K per km down.
So to get an increase of 0.5K you only need a change of 200 m of the inside of earth…

https://breadonthewater.co.za/2022/08/02/global-warming-how-and-where/

DHR
October 16, 2022 11:13 am

Doodly squat? And all this timeI thought it was diddly squat! Something new from Willis every time.

another ian
Reply to  DHR
October 16, 2022 1:48 pm

“Doodly squat” – “The random pencil writes and having writ”?

navy bob
Reply to  DHR
October 16, 2022 5:36 pm

Coined originally in 1957’s “Red Hot” by Billy.Lee Riley & the Little Green Men, to wit: “My gal is red hot. Your gal ain’t doodly squat.” Willis clearly goes way back.

michael hart
October 16, 2022 11:13 am

Fig. 3 Hmmm… qualitatively similar to something observed during the recent rise of atmospheric CO2? Pronounced warming at the poles, virtually zero for much of the hottest, sunniest places, and gentle warming in between?

Richard M
Reply to  michael hart
October 17, 2022 7:07 am

Last I looked there hasn’t been any “Pronounced warming” at the south pole.

Andrew Chantrill
October 16, 2022 11:14 am

Dear Willis,

Thank you for another fascinating post. A couple of comments:

In Figure 1 there appears to be a figure of eight in the 100 – 300W/m2 range. In the UK I get a similar relationship between sunshine hours and average temperature, but if I introduce a lag of a month in the temperature (i.e. temperature in June compared to sunshine in May) I get a very good correlation and the figure of eight disappears. I wonder if the same would happen with your data.

Secondly a recent post I saw looked at CERES data from 2001 to 2020, and this suggests CO2 has little effect:

https://phzoe.com/2022/06/10/20-years-of-climate-change/

I don’t have the skills to reproduce this, but would be very interested to know if you support the claims made.

I very much appreciate your posts.

Reply to  Andrew Chantrill
October 16, 2022 11:52 am

Andrew,

The influence of the increase in CO2 2000-2010 (22 ppmv) was measured in the specific wavelengths of CO2 back radiation (about 0,2 W/m2 increase) at two measuring stations with a full spectrum of incoming IR:
https://escholarship.org/content/qt3428v1r6/qt3428v1r6.pdf

If that has an effect in the full energy balance is a question of how much other factors (clouds…) affect that balance…

Andrew Chantrill
Reply to  Ferdinand Engelbeen
October 16, 2022 1:24 pm

Thank you!

Reply to  Ferdinand Engelbeen
October 16, 2022 5:33 pm

Feldman et al 2015 measured downwelling longwave IR “back radiation” from CO2, at ground level, under clear sky conditions, for a decade. They reported that a 22 ppmv (+5.953%) increase in atmospheric CO2 level resulted in a 0.2 ±0.06 W/m² increase in downwelling LW IR from CO2, which is +2.40 ±0.72 W/m² per doubling of CO2.

However, ≈22.6% of incoming solar radiation is reflected back into space, without either reaching the surface or being absorbed in the atmosphere. So, adjusting for having measured at the surface, rather than TOA, gives ≈1.29 × (2.40 ±0.72) per doubling at TOA, and dividing by ln(2), yields:

  𝞪 ≈ 4.47 ±1.34 (which is 3.10 ±0.93 W/m² per doubling of CO2)

That’s nearly identical to what van Wijngaarden & Happer 2021 (and see also 2020 & 2022) calculated for CO2’s ERF at the mesopause (similar to TOA):

  𝞪 = 4.28 (which is 2.97 W/m² per doubling)

However, Feldman’s uncertainty interval is wide enough to also encompass the Myhre 1998 / IPCC estimate of 𝞪 = 5.35 ±0.58 (which is 3.7 ±0.4 W/m² per doubling). It does preclude the SAR’s higher estimate of 𝞪 = 6.3 (which is 4.4 W/m² per doubling; see SAR §6.3.2, p.320).

I wish Feldman had continued their experiment longer. With 20 years of data they probably could have narrowed their confidence interval enough to preclude that high Myhre 1998 estimate which the IPCC still uses.

Last edited 1 month ago by Dave Burton
Reply to  Dave Burton
October 16, 2022 6:22 pm

Feldman only concerned himself with two locations in [I think?] Oklahoma and Alaska.

How is that of any use to anyone?

There’s massive amount of horizontal heat transfer.

I think his research is useless, and can’t be used to make any judgments whatsoever by any side in the debate.

So I don’t think he needed to continue his “research”, as it was flawed from the beginning.

Kind regards, -Z

Reply to  Zoe Phin
October 17, 2022 12:51 am

Dear Zoe,

Feldman’s research indeed was only at two stations, but they have proven that the influence of increasing CO2 is measurable, even the effect on downwelling IR radiation by the seasonal amplitude of CO2 in the NH (caused by vegetation) was measured.
There is no reason to assume that this is not the case at the many other stations where downwelling IR radiation is measured:
https://scienceofdoom.com/2010/07/17/the-amazing-case-of-back-radiation/

If that has much effect within the natural noise of many other influences, is a matter of time. One can’t prove or disprove that the sea level is rising within the large noise of waves and tides after a year. Only after some 30 years of data, one can deduce it statistically…

Steve Keppel-Jones
Reply to  Ferdinand Engelbeen
October 18, 2022 7:26 am

Ferdinand, no one has measured DWLWIR at the surface… read more closely and you can see the tricks they use to “invent” it from whole cloth, using fake physics.

Reply to  Steve Keppel-Jones
October 18, 2022 8:58 am

Sorry, they measured the whole spectrum, line by line, of downwelling IR.
Not only Feldman did that, but many more at a lot of places, a.o. at the South Pole, where they had no overlaps with water vapor which is virtually absent there:
https://scienceofdoom.com/2010/07/24/the-amazing-case-of-back-radiation-part-two/ Fig. 11.

The full spectrum as measured at Oklahoma is at page 6 of
https://escholarship.org/content/qt3428v1r6/qt3428v1r6.pdf
Integrating the height of every line and its wavelength gives you the total downwelling energy that is radiated back to the surface: about 300 W/m2.

The second graph at that page shows the difference between the measured downwelling and the calculated downwelling according to Hitran…

Steve Keppel-Jones
Reply to  Ferdinand Engelbeen
October 20, 2022 11:36 am

Okay, let me clarify my statement: no one has measured DWLWIR at night at ambient temperature. The AERI instruments are cryogenically cooled to liquid nitrogen temperatures, which is therefore measuring something else entirely.

Steve Keppel-Jones
Reply to  Steve Keppel-Jones
October 21, 2022 7:02 am

In case that wasn’t clear enough, Ferdinand, there are two problems with your statement “Integrating the height of every line and its wavelength gives you the total downwelling energy that is radiated back to the surface: about 300 W/m^2”. The first problem is that you wrote “energy” and then you wrote a number in W/m^2, which are not the same type of quantity. Mixing up those two ideas would get you an “F” on your physics exam. But even worse than that, you left out the critical qualifier: radiated back to the surface if the surface temperature were below 77 Kelvin, the temperature of the AERI sensor. Where on Earth are you expecting to find those kinds of temperatures?

The Real Engineer, CEng etc.
Reply to  Steve Keppel-Jones
October 24, 2022 1:37 am

It seems to me that we are back in the realm of faulty thermodynamics again. Zero heat is absorbed by the surface if it is warmer than the alleged “CO2 back radiation”. This has to be the ultimate error, and I agree totally with Steve above. This continuous swapping of energy and temperature is ridiculous, the rules are very clear (2nd Law), and the only way to get to the claimed result is to ignore the surface temperature completely. At 77k the result is not real. At night the absorbed energy should be zero, (space temperature is less than 77k), and is the control measurement, where is it?

Steve Keppel-Jones
Reply to  The Real Engineer, CEng etc.
October 24, 2022 9:56 am

Yes, Real Engineer, we are absolutely deep into the realm of faulty thermodynamics. Everything Willis writes on this topic is in that realm. But he is not alone, all of official climate science is right there along with him. Even the Encyclopedia Britannica definition of the Stefan-Boltzmann law makes this error. It is very pervasive. The most common manifestation is, as you said, to ignore the surface temperature completely and convert the temperature of an object (perhaps the atmosphere, or a pyrgeometer sensor sitting on the ground) directly into power, as if it were radiating all of its thermal energy to deep space. But slightly more subtly, they make these liquid nitrogen cooled sensors to measure IR, and pretend that this is the same measurement that would be obtained at ambient surface temperature, if only they could figure out how to do it. That is of course not how thermodynamics works. Not even close.

Richard M
Reply to  Ferdinand Engelbeen
October 17, 2022 7:27 am

When you increase CO2 you will see increases in IR in all directions. Feldman only measured the changes in downwelling IR. Without taking into account the changes in upwelling IR those numbers are useless. Same problem exists in almost all output from radiation models. Only looking at downwelling IR is meaningless.

In addition, feedback to changes in downwelling IR at the surface, what I call boundary layer feedback (BLF), almost completely negates whatever warming effect it might have. You will see a little enhanced evaporation and some increases in conduction from the surface to the atmosphere.

Since almost all the IR that Feldman measured (99.9%) comes from within the boundary layer and the BLF returns most of that energy right back into the boundary layer, the net result is no change.

Most of BLF is due to conduction. This form of energy transfer is almost entirely ignored by climate science because the net is small. However, massive amounts of energy are moving back and forth due to pico second level collisions of the atmospheric molecules with the surface. This is what keeps the boundary layer and surface temperatures in a steady state. BLF in this case is primarily a small increase in the amount of energy being conducted from the surface to the atmosphere.

Reply to  Richard M
October 18, 2022 6:43 am

As far as I have understood the whole investigation (radiation was learned mostly in my student age, some 65 years ago…), Feldman used upgoing radiation as well, to correct the intensity of downwelling radiation and used balloon humidity measurements to calculate the back radiation of water vapor.

I did find that the surface (grass in the case of Oklahoma) emits a relative “ideal” black body spectrum in the IR bands where CO2 is active (over 97%), thus the difference between the incoming and outgoing spectra should show the specific back radiation of the different GHGs.
Interesting is the downwelling spectra found at the South Pole, where water vapor is almost absent, see Fig. 11 at:
https://scienceofdoom.com/2010/07/24/the-amazing-case-of-back-radiation-part-two/

“feedback to changes in downwelling IR at the surface, what I call boundary layer feedback (BLF), almost completely negates whatever warming effect it might have.”

I don’t follow that. If a (near) blackbody absorbs IR energy of whatever wavelength, the only way that it can get rid of that extra energy is by heating up, or its radiation energy stays exactly the same and you are destroying energy. If that results in more evaporation or more turbulence is secondary…

The Real Engineer, CEng etc.
Reply to  Ferdinand Engelbeen
October 24, 2022 1:42 am

But it does not Ferdinand, unless the incoming radiation source (CO2) is warmer than the surface. Radiation Physics and “ideal” black bodies assume the “black body” is at a very low temperature (because any energy in it will have been radiated to the surroundings) but this is never the case in a real situation, unless in deep space.

Richard M
Reply to  Ferdinand Engelbeen
October 24, 2022 2:43 pm

Yes, the energy gets absorbed and heats the surface. However, that surface is under constant bombardment from atmospheric molecules as well as radiation. Energy is also exchanged when these collisions occur. The heat can very easily get used to energize one of the molecules that comes into contact with the surface.

The overall exchange of energy will follow the 2nd law with more energy transferred from the surface if it is warmer. Since increasing DWIR warms the surface (and cools the atmosphere) you end up increasing this conductive exchange from the surface to the atmosphere. This effectively cancels the temporary warming. Within microseconds the energy state has returned back to where it was.

Yes, I’m ignoring other possible energy transitions here but given the high rate of collisions at the surface and the fact that all the atmospheric molecules are involved, conduction should be the primary method.

Since there are trillions of these events per second you end up looking at it statistically. The 2nd law keeps the atmosphere and surface near thermal equilibrium. More CO2 based radiation to the surface is returned mainly via conduction back to the atmosphere to maintain the equilibrium.

If the surface happens to be a water molecule you will also see some increase in evaporation. Once again, the energy has been returned to the atmosphere.

Ireneusz Palmowski
October 16, 2022 11:16 am

“A gas is characterized by compressibility, that is, a change in pressure with a change in the volume of the vessel in which the quantity of gas under consideration is enclosed. The compressibility of gases means that a different amount of heat must be supplied by heating the gas by 1C at a constant pressure, and a different amount at a constant volume. In the former case, there is an expansion, that is, an increase in volume. This can be interpreted as an expansion of the gas, which causes it to cool down, i.e. more heat must be supplied to achieve a 1C increase in temperature. If the gas is heated at a constant volume, there is a “peculiar compression” of the gas, because the gas seeks to increase in volume when it is heated. From these considerations, it follows that the specific heat of a transformation realized at constant pressure (isobaric transformation) will always be greater than the specific heat of a transformation realized at constant volume (isochoric transformation).”
The vertical temperature gradient can be calculated from the formula: gravitational acceleration/specific heat of air at constant pressure. However, the specific heat of air at constant pressure increases with increasing solar energy, so the vertical temperature gradient can decrease during the day and increase at night.
It is very likely that the specific heat of air at constant pressure reaches limits, so the vertical temperature gradient in the troposphere cannot fall below a certain value.

Last edited 1 month ago by Ireneusz Palmowski
mkelly
Reply to  Ireneusz Palmowski
October 16, 2022 11:55 am

Attached is a table of specific heats for various gases.

The Cp of air is equal to the Cv plus the work energy necessary to account for PV or enthalpy.

4A8103D3-FB0C-4EA4-9F28-FB099BE35CCB.jpeg
Ireneusz Palmowski
Reply to  mkelly
October 16, 2022 2:32 pm

At 300oK (26.85oC), Cpo is 1005 J/(kg x K).
9.81/1005=0.0098 K/m, so 0.98 K/100 m.

Ireneusz Palmowski
Reply to  mkelly
October 17, 2022 4:54 am

The gradient value of 0.98 K per 100 meters applies to dry air.
If the air consisted only of water vapor, the vertical temperature gradient would be about 0.5 K per 100 meters.

mkelly
Reply to  Ireneusz Palmowski
October 17, 2022 6:33 am

The values in the table are for dry air. That is the basic lapse rate. Yes you need to incorporate WV once you get below about 10000 feet.

DHR
October 16, 2022 11:22 am

So above 310 W/m2 the tropical oceans loose energy as fast as it is delivered. By evaporation I suppose? Your thunderstorm cooling mechanism?

Rud Istvan
October 16, 2022 11:46 am

WE, most excellent. Three related longish observations.

First I have a testable hypothesis for 310-350 SWR region causing no change in surface temperature in your figure 1.
It cannot be cloud related per se, because you subtracted albedo reflected SWR. The SWR solar energy is reaching the tropical oceans (figure 2) but not affecting its surface temperature. That means there must be an equivalent energy removal mechanism.
I mentioned in my comment to your previous cloud feeback post (on the Bode feedback method of estimating ECS) that ARGO is showing almost exactly twice the ocean rainfall of CMIP5 and CMIP6 models. That rainfall is the needed surface energy removal mechanism, because rain comes from condensed water vapor, which itself removes the heat of evaporation from the ocean surface with the water vapor formation, then releases it at altitude as the rain condenses inside clouds thanks to the lapse rate.
This is an easily testable hypothesis since the ARGO data is all on line at UCSD, and contains lat/lon. I don’t have the requisite skill set, but simply mapping the actual ARGO ocean rainfall (inferred from near surface salinity) to your figure 2 provides the observational test of the explanatory hypothesis. The ARGO data is ‘good’ since 2007, plenty of overlap time for a good test.

Second, also foreshadowed in my comment on Bode ECS to your last post, there are now 3 MAJOR climate model problems:

  1. Christy has been pointing out for years that the models produce a tropical troposphere hotspot that does not in fact exist. There is one model exception, INM-CM5 in CMIP6. And INM-CM5 specifically took special care to parameterize ocean precipitation per ARGO. Which leads to
  2. ARGO shows almost exactly twice the ocean precipitation as CMIP5 and 6. That means about half of the modeled water vapor feedback, which is the likely point 1 root cause.
  3. Your last post proved a moderately negative cloud feedback, which IPCC and climate models say is significantly positive. In Bode f terms, IPCC +0.17, WE Ceres observed -0.03. They got the SIGN wrong! Moreover, per my previous Bode comment, IPCC WVF 0.5/2 per ARGO minus negative cloud 0.03=f 0.22, which via Bode almost exactly matches the observational energy budget method ECS estimates ~1.65 derived completely differently.

Third, three serious defects means the IPCC climate models are useless, their projections worthless. Three strikes and you are out. A BIG deal, since all the climate alarm is based on future model projections since nothing has happened yet:

  1. Arctic summer sea ice has not disappeared.
  2. Sea level rise has not accelerated.
  3. Children still know snow…

Highest regards.

cerescokid
Reply to  Rud Istvan
October 16, 2022 1:47 pm

“….IPCC climate models are useless, their projections worthless.”

The more one digs and the more one waits, the more that statement becomes obvious.

The last few decades will be fertile territory for social psychology case studies later this century.

Rud Istvan
Reply to  Willis Eschenbach
October 16, 2022 4:04 pm

Well, again you got there before me. Now no need to do the envisioned experiment I am personally incapable of compsci wise. But I remain a dogged follower/publicist with a broad overview of the battleground.

RickWill
Reply to  Willis Eschenbach
October 16, 2022 5:07 pm

And this means the evaporative cooling increased.

This conclusion is wrong. The change above 26C is due entirely to mid level convergence to more powerful convective towers. Warm pools always get more precipitation than they generate in evaporation.

Ocean regions cooler than 28C are inevitably mid level divergence zones and upper level convergence zones. Regions warmer than 28C are inevitably the reverse unless they are near land and the more powerful towers draw mid level moisture from them. That is the only way ocean surface temperature can exceed 30C – divergence of mid level moisture that disrupts convective instability..

The attached diagram shows the energy balance at a tropical buoy over 17 days when it was temperature regulating at 30C. Almost zero surface heat flux. The 200W/m^2 surface sunlight was almost all evaporation and that limits it to 7.6mm/day but average precipitation was 10.5mm/d.

Warm pools in the Indian Ocean typically make 15mm/d rainfall but are only evaporating 7mm per day. Regions at 26C can evaporate about 9mm/d but rainfall averaged about 5mm/d. These regions lose latent heat to the warm pools nut gain much more from sensible heat transfer in the upper level.

The other point about the 30C column is that it loses some 190W/m^2 in sensible heat due to high level divergence. The difference in enthalpy between a 30C base column and 29C base is significan.

Buoy_Thermal_Balance.png
Last edited 1 month ago by RickWill
Joe Born
Reply to  RickWill
October 17, 2022 4:31 am

Can you direct us to a higher-resolution version of that diagram? I’m unable to read it, and I think it will come in handy when I re-read your three-part series.

Joe Born
Reply to  Willis Eschenbach
October 17, 2022 10:12 am

Much appreciated.

Gary Pearse
Reply to  Willis Eschenbach
October 16, 2022 9:04 pm

So this explains why there is no increase in temperature above 310 to 360W/m² incident solar. It goes into enthalpy change. I speculated from this, that the apparent rapid temperature rise per W/m² in the segment from 50 to 100W could be largely due to warmed ocean currents at the cool end of the heat engine and not due to solar insolation at the higher latitudes. Perhaps I misunderstood what you presented.

lgl
Reply to  Willis Eschenbach
October 17, 2022 4:31 am

“Here’s one of my favorite graphics.”

Which still does not show evaporative cooling because that water evaporated far away.

Last edited 1 month ago by lgl
lgl
Reply to  Willis Eschenbach
October 17, 2022 11:45 am

Yes, I think this is the fifth time through the years I have added the very important piece of information that rainfall in a particular spot does not equal evaporative cooling.

ferdberple
October 16, 2022 11:58 am

Willis,

I did a quick paper on Fig 1 from Global Scatterplots. Can’t really explain the result. Comments welcome.

https://www.transfernow.net/dl/202210162aqxM2Dl

October 16, 2022 12:10 pm

Note that this means that solar power has to rise by about six W/m2 to raise the temperature of 70% of the planet by 1°C … and remember that in half the tropical ocean, 22% of the planet, that same six W/m2 increase in available solar doesn’t do doodly-squat to the temperature.

note all of this neglects the real cause of warming:
the reduction of cooling to space

Mr.
Reply to  Steven M Mosher
October 16, 2022 3:17 pm

the real cause of warming: the reduction of cooling to space

And this was demonstrated by one of those non deterministic perturbation
models, right?

Wim Röst
Reply to  Steven M Mosher
October 16, 2022 3:45 pm

Steven Mosher: “note all of this neglects the real cause of warming:
the reduction of cooling to space”

WR: The lower stratosphere cools better than before, not showing (as stated) a ‘reduction of cooling to space’. Lower stratosphere temperatures go down, not up:
UAH 1979 Jan. Globe 1.14°C
UAH 2022 Aug. Globe -0.40°C
A cooling by 1.54°C. Cooling trend: -0.27°C/decade
Source: https://www.nsstc.uah.edu/data/msu/v6.0/tls/uahncdc_ls_6.0.txt

Lower stratospheric cooling excludes ‘reduction of cooling to space’ as a possible cause for [surface] warming.

PCman999
Reply to  Wim Röst
October 17, 2022 3:13 pm

If the slight increase in CO2 made its way to the stratosphere would that lead to increased cooling?

Or would the Troposphere holding on to a little bit extra of heat because of CO2 absorbing and remitting some back to the direction of the surface, leave less heat to go to the stratosphere?

Wim Röst
Reply to  PCman999
October 18, 2022 4:42 am

PCman999: “If the slight increase in CO2 made its way to the stratosphere would that lead to increased cooling?”
 
WR: I think so, yes. Probably the following happened:
1.    From 1979 to 2021 CO2 rose by about 23%, NOAA data. By nearly a quarter. CO2 is well dispersed up to a height of 80 km. In the lower stratosphere CO2 is able to radiate to space more effectively than from lower elevations. given the low pressure / the wide spacing of molecules at those elevations and given the very low content of the main greenhouse gas water vapor H2O. Logically, the presence of a higher number of CO2 molecules results in more energy absorbed by them, by collisions with other molecules and therefore the higher quantity of CO2 molecules is able to radiate a higher quantity of energy to space. The result of higher CO2 in the lower stratosphere must be the cooling of the lower stratosphere. But there is more.
2.    Enhanced high convection in the tropics (because of surface warming) injects more water vapor in the lower stratosphere, further distributed by the Brewer-Dobson circulation. Even when the quantity of extra water vapor is very low, its cooling effect is high: water vapor radiates at many wavelengths that are not absorbed by CO2: stratospheric radiative cooling by H2O molecules must be very effective in reaching space. A small number of extra H2O molecules results in a large extra cooling of the lower stratosphere.
 
As a result of the colder stratosphere, the temperature gradient of the lower stratosphere with the surface is enlarged. The result of a higher gradient is a stronger energy transport between the surface and stratosphere, finally resulting in the cooling of the surface, in a stronger cooling of the lower stratosphere, and in the cooling of the Earth.

Wim Röst
Reply to  PCman999
October 18, 2022 5:18 am

PCman999: “Or would the Troposphere holding on to a little bit extra of heat because of CO2 absorbing and remitting some back to the direction of the surface, leave less heat to go to the stratosphere?
 
WR: A rise in CO2 results in small initial warming for the surface. Some warming will be the first, but not the final result. Like other ‘complex systems in equilibrium’, warming results in the activation of cooling processes. By evaporative surface cooling, by enhanced convective cooling, and by enhanced tropical cloud cooling most of the initial CO2 surface warming already disappears. What remains is a cooling stratosphere which is resulting in a higher temperature gradient with the surface. Over time, this higher temperature gradient probably results in taking away about all of the remaining warming.
 
The Modern Warming as observed after the Little Ice Age is [natural] warming by advection (by oceans and atmosphere) and by related [natural] processes, resulting in higher atmospheric water vapor, especially over the highest latitudes of the Northern Hemisphere: in and around the Arctic. Arctic warming results in a smaller gradient between the North Pole and the equator. The smaller gradient will result in less poleward advection and so in less warming: again temperatures will be nearing the old equilibrium point.
 
Total result: over time, a highly stable surface temperature as controlled by the H2O molecule, but temporarily influenced by the chaotic behavior of the ocean-atmosphere system, and (on longer timescales) by orbital changes.

The role of orbit is more important than assumed. The reason is the enhancement of orbital latitudinal warming/cooling by the main greenhouse gas water vapor, the quantity of which is going up and down with every temperature change for that specific latitude. Because of water vapor, every change in orbit will have a higher-than-expected temperature effect. By a change in orbit, a change in the advection of energy over latitudes will result, and the effect(s) of advection on the quantity of latitudinal water vapor has to be added. Water vapor is our main greenhouse gas. Water vapor cools (the surface) and water vapor warms (the atmosphere) as long as it is able to remain in the atmosphere. Convection is decisive for the time water vapor can remain in the atmosphere. And the latitudinal surface temperature is decisive for the quantity of water vapor in the air and so for convection.
 
Surface warming leads to H2O evaporative cooling. Higher evaporative cooling leads to more water vapor in the atmosphere, which stimulates convective cooling and tropical cloud cooling. Higher rising and stronger convection lead to a cooling stratosphere, as does rising CO2. The higher stratosphere-surface gradient will lead to further surface cooling until the former equilibrium state is reached.
 
All processes are activated/deactivated on their own time scales. Each process has its own ‘cycle’ and all cycles are combined in a multitude of possibilities, making exact future predictions more or less impossible. Looking back to temperature graphics of the past, all those ‘superimposed individual cycles’ did lead to unpredictable patterns. Which does not mean that Climate in its complexity cannot be understood. But to understand the basics of Climate, the immense role of the H2O molecule must be studied and understood.

To summarize: the warming effect of CO2 must be about zero. H2O sets and regulates surface temperatures for each orbital and continent/ocean setting.
.

Matthew Schilling
Reply to  Wim Röst
October 19, 2022 8:10 am

We live on a water planet with a temperature range that enables that water to easily cross between the three states of solid, liquid, and gas. Like virtually everything else at all scales in the universe, our water planet is spinning – spinning in close proximity to a lively star. That gives an impetus for things to mix and swirl and throb. Our water planet is also blessed with a relatively large moon, which also keeps things churning and mixing on our world. The result? Water dominates our climate.

The effect on our water planet of slight changes in a trace atmospheric gas are more like a stone tossed into a lake than like a boulder dropped into a bathtub.

Climastrology is all hype. It is 1) a convenient subtext for domineering and micromanaging masses of people; 2) one of the only ways left to simultaneously inflate the Communists’ balloon while deflating the Capitalists’; and 3) a convenient excuse to keep the execrable sophistry of Malthusianism afloat for another generation of condescending morons.

Climastrologists, along with racial arsonists, are the useful idiots doing yeoman’s work for those who have their eye on the ultimate prize: Wiping out billions of people, and subjugating the rest.

Last edited 1 month ago by MattXL
Jim Gorman
Reply to  Steven M Mosher
October 17, 2022 5:59 am

Spoken by someone who deals with simple averages.

A daily total reduction in cooling would result in a constant increase of both Tmax and Tmin. In other words, every day would be warmer than the day before. That obviously doesn’t occur.

How about seasonal? Well that would mean each season would be warmer than the previous year.

Maybe, just maybe, a reduced rate of cooling is being seen. That would mean it takes longer at night to shed the daytime warming. That is a totally different scenario than a total reduction in cooling at all times.

Reply to  Steven M Mosher
October 17, 2022 7:23 pm

This is the most important
thought in this debate: Additional CO2 raises the altitude at which the Atmosphere is transparent ton15 micron radiation, thus reducing the temp at which the atmosphere radiates to Space, thus reducing energy lost to Space, thus increasing energy retained in the Atmosphere. But just exactly how much? This is really the only question here.

October 16, 2022 12:33 pm

Those big red blobs over the tropical oceans tell you why that extra energy isn’t increasing the surface temperature. It is evaporating water. Evaporation is an endothermic process which cools the surface. Condensation at the bottom of clouds is an exothermic process so that energy is being transported from the surface to the bottom of clouds. Thunder clouds in the tropics transport that energy to the stratosphere. Try your scatter plot on dew point/frost point and see what you get.

Ireneusz Palmowski
Reply to  Fred Haynie
October 16, 2022 1:42 pm

The temperature at the tops of typhoon clouds in the South China Sea is approaching -90 degrees C. This shows how low temperatures in the lower stratosphere actually are.
comment image

bill
Reply to  Ireneusz Palmowski
October 17, 2022 12:23 pm

but in degrees Kelvin still hot.

Jeff L
October 16, 2022 12:35 pm

We always hear about how the arctic / antarctic are showing the greatest effect from “global warming”. From figure 1, those regions do show the highest sensitivity to a changes in radiation, so this is internally consistent.

Given the 3.7W/m^2 per CO2 doubling number quoted in this post, along with with figure 1 that a global average “sensitivity” should be able to be calculated. It seems the atmosphere shouldn’t care where the power comes from – the sun or back-radiated energy from CO2. So, would the general math be as such: For each region, see what % of the earth is in that region, what the expected delta T would be for that region for an increase in 3.7W/m^2 (per the trend curve fit), then do a pro-rata average based on what % of the earth each region represents. And there you go the … you have a globally averaged number for “climate sensitive to CO2”.

If I am reading the Conclusion of this post right, perhaps a quick of the envelope number is as such:

Conclusion of this paper : 5 W/m^2 to raise the planet by 1 deg C
Proportionally, (3.7W/m^2 / 5W/m^2) *1°C = 0.74 °C
So, a doubling of CO2 = 3.7 W/m^2 = 0.74 °C …. climate sensitivity empirically derived at 0.74 °C/doubling .

…. which is way below any alarmist view & pretty much destroys the CAGW hypothesis with observed data. That would be pretty cool!

Anyone want to comment of the maths here? Improve on them? Refute this hypothesis? Would love to hear others thoughts on this.

Curious George
Reply to  Jeff L
October 16, 2022 12:48 pm

The AGW is threatening to make Siberia, Alaska, Canada, and Patagonia habitable. It must be stopped at any cost!

Arjan Duiker
Reply to  Jeff L
October 16, 2022 12:55 pm

Agree, but take into account advection as well. That will make things a bit more complicated. But still, high climate sensitivity seems very very far from likely.

Michael Lorrey
October 16, 2022 12:57 pm

 At the left, below ~ 100 W/m2 of available solar, the sensitivity of temperature to changes in solar input is quite high.”

I’d suggest you next look at how changes in solar cycles affects these <100W/m2 areas as well as how changes in aerosols and other particulates impacts cloud cover and resulting temps in these areas.

RickWill
Reply to  Michael Lorrey
October 16, 2022 5:58 pm

I’d suggest you next look at how changes in solar cycles affects these <100W/m2 areas 

There is solid evidence that the surface temperature in the Nino34 region is influenced by solar cycles. This can have some bearing on the intensity of ENSO. Likely contributing to the extent of the current La Nina because it has occurred near the bottom of the influence from the solar cycle.

I go into some detail on solar influence in this note:
https://wattsupwiththat.com/2022/10/04/surface-temperature-response-to-solar-emr-at-top-of-the-atmosphere/
I have not shown the correlation with cosmic rays but found it to be slightly better correlated than the sunspot. Regression coefficient of 8% rather than 6%.

Timing of ENSO is independent of solar activity. Current thoughts are that salinity changes trigger the swing. Evaporative power reduces with salinity so that could be the key factor in the phase switch. Warm pools are always mid level convergence zones so lower salinity than cooler regions that have mid level divergence. .

PCman999
Reply to  RickWill
October 17, 2022 3:24 pm

What could alter the salinity on such a large scale, far away from any glaciers?

Or are you saying that an area off the western coast of South America gets boiled more than normal for some reason, gets a bit more salty due to evaporation and then hits some critical level that causes a ‘knee’ in the evap/temp curve so the cooling from evap drops and temps in that region of water go up?

What throws the cycle back the other way? Just time and currents eventually bringing in more water?

October 16, 2022 1:33 pm

” Figure 1 shows the surface temperature as a function of the amount of solar power that’s actually entering the climate system. This available solar power is the top-of-atmosphere (TOA) solar, minus the “albedo reflections”, which are the amount of sunlight reflected back to space by the clouds and the surface.”

Before any conclusions are made based on these data:
They should be analyzed to determine if they are accurate or could have large margins of error. Conclusions may be easy, but defending the quality of the data used for that conclusion may be difficult. The data quality analysis should be performed with the goal of discrediting the data, and the people who collect the data — pointing out every possible weak spot.

A large majority of the short articles on climate science have conclusions without an analysis of the data quality leading to those conclusions. If the data used are available to the general public, it’s suspicious when one person uses those data for a conclusion that appears to be unique. If the data are reliable, and the conclusion based on them is logical, it’s puzzling why that conclusion would not be a majority consensus among scientists. There are so many wrong conclusions and predictions concerning climate science that one ought to be suspicious of every one of them. Science requires skepticism.

Editor
October 16, 2022 2:02 pm

Hi Willis – You are using ‘available solar power’ as the top-of-atmosphere (TOA) solar, minus the “albedo reflections”, which are the amount of sunlight reflected back to space by the clouds and the surface. So these numbers are independent of any “greenhouse effect” (I assume that “reflection” doesn’t include the effect of greenhouse gases). The surface temperatures, however, include the “greenhouse effect” including the effect of man-made CO2. Man-made CO2 has increased significantly over your 21-year period, and we can therefore expect to be able to estimate TCR (Transient Climate Response) from your data. Looking at your Figure 4, I estimate TCR at zero. Is that a reasonable estimate?

Incidentally, if “albedo reflections” does include the “greenhouse effect” then I would estimate that TCR is still remarkably small – about 5% of the observed surface warming over the 21-year period..

Editor
Reply to  Willis Eschenbach
October 16, 2022 4:30 pm

Yes I understand that, but it seems that an additional inference might be obtainable from your data?

RickWill
Reply to  Willis Eschenbach
October 16, 2022 6:04 pm

the total power available to the system.

It is not the total power available. It was only the thermalised component. All ToA solar EMR is available.

The thermalised portion is not fixed. The unthermalised solar EMR is a KEY component of THE CLIMATE SYSTEM.

Matthew Schilling
Reply to  RickWill
October 19, 2022 7:44 am

I think Willis’ “available to the system” is the same as your “thermalised component”. If it’s reflected at TOA it isn’t “available to the system”… therefore it cannot join the “thermalised component”.

A C Osborn
Reply to  Mike Jonas
October 17, 2022 1:45 am

Mike, surely the ocean’s reaction to any form of energy must be the same whether it is Solar or DWIR?
More energy = more evaporation.
In fact the response to DWIR should be even even higher because it is all surface action due to it’s lack of penetration power.

David A
Reply to  A C Osborn
October 18, 2022 3:41 pm

Surely it is dramatically different. LWIR is entirely absorbed at the surface “skin” layer of water, where much if said energy goes into accelerated evaporation, increased water cycle and atmospheric heat movement created ( hence clouds and potential negative feedback there as well)

Whereas much of SWR penetrates the ocean surface up to several hundred feet and has a very long residence time within the oceans before being released, and therefore has more warming potential than LWIR.

Last edited 1 month ago by David A
Bruce of Newcastle
October 16, 2022 2:26 pm

The effect of liquid water availability would be interesting to examine.

Desert vs forest/jungle vs plains vs ice, plus of course actual ocean.

I hypothesize that the response in desert gridcells will be much steeper, since lack of soil moisture, vegetation and free water would prevent the moderating effect of latent heat of evaporation and cloud cover.

Likewise icecap has little available evaporatable water – and from the data the poles clearly show a big response.

RickWill
Reply to  Bruce of Newcastle
October 16, 2022 6:08 pm

Land surface in the mid latitudes responds in half the time and twice the range in temperature for the same solar input as water. It takes 14W/m^2 to shift typical mid latitude land 1C. It takes 28W/m^2 to shift deep water basins like the Med 1C.
https://wattsupwiththat.com/2022/10/04/surface-temperature-response-to-solar-emr-at-top-of-the-atmosphere/

Clyde Spencer
October 16, 2022 2:26 pm

Willis, you said,

In those areas, the temperature rises very quickly with increasing solar power.

Is this a suggestion that the poles (particularly the notoriously cloudy Arctic) are sensitive to changes in cloudiness and that it might help explain the 2-3X more rapid warming in the Arctic?

RickWill
October 16, 2022 3:08 pm

The attached top chart is similar to your figure 1 but covers only oceans and considers total solar radiation rather than just thermalised short wave. It depicts the different convective regimes as well.

The two images show the ocean temperature and the reflected short wave above oceans.

This highlights that the only ocean surface that sustains temperature above 30C is influenced by land. The reason is that convective towers over land can develop higher convective potential than those over water because the base temperature can rise beyond 30C.

OST_Solar_Response.png
Joe Born
Reply to  RickWill
October 17, 2022 4:59 am
October 16, 2022 3:18 pm

Good on you, Willis. It’s nice to see someone doing climate PHYSICS for a change. What is happening over land may be even more interesting than over the ocean. Local Climate Sensitivity is highest in the dry cold regions of northrn Canada and Siberia where CO2 has a greater effect in inhibiting night-time cooling. See http://paradigm2.net.au/reid-and-nielsen-2022/ .

Javier
October 16, 2022 3:25 pm

Once the average available solar power is above 310W/m2, you can add up to an additional 50 W/m2 without increasing the surface temperature one bit.

Two important points to consider:

  1. The Sun delivers the same amount of energy every year plus minus 1 W/m2 due to the solar cycle. There are no additional 50 W/m2.
  2. Solar energy is absorbed in the photic layer of the ocean. No change in surface temperature does not mean no change in absorbed energy by the climate system. The subsurface heat content follows the solar cycle even though it shouldn’t, due to the small energy change.

The tropical SST cap has been known for a long time. Figure 1 is another way of looking at it.

Editor
Reply to  Javier
October 16, 2022 4:35 pm

re 1. Willis isn’t referring to a change in the sun delivering an extra 50 W/m2, he’s referring to Earth locations where solar input differs by 50 W/m2 and temperature doesn’t differ at all.

RickWill
Reply to  Javier
October 16, 2022 7:39 pm

The Sun delivers the same amount of energy every year plus minus 1 W/m2 due to the solar cycle. 

This statement is WRONG. You state energy then provide a measure in power flux. You need to learn the difference because it is important for understanding climate.

The power flux is never constant at the same point on Earth at the same time each year. It has never been and never will be.

About 500 years ago, the solar power flux peaked over the Southern Hemisphere. The peak intensity is now moving northward and will continue that trend for about 9kyr.

Mid latitude surface temperatures are very highly correlated to solar intensity. – in fact everything else is noise from a global perspective. The response of land to solar forcing in the mid latitudes is faster and more responsive in terms of temperature change than over oceans. So as the sun’s view of land increases when it is closest to Earth the global surface temperature must increase.

This is the solar power flux in April at 30N for the last 500 years and the next:
-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
Hardly constant.

Once you understand the difference between power and energy you might begin to understand the driver of climate change – solar forcing..

Steve Keppel-Jones
Reply to  RickWill
October 19, 2022 5:37 am

That is true, Rick, but I think even your correction could use a bit of refinement. How about we stop referring to the climatologists’ purpose-invented phrases “solar flux” and “solar forcing”, and instead use an actual physics term for measuring intrinsic radiation energy, namely temperature? The solar radiation has a temperature of about 5000 K, because that is the surface emission temperature of the object that emits it. In order to do anything with that number (e.g. calculate energy flow, heat, work, and power), you need to know the temperature (and reflectivity) of the target object first. No target object, no power.

Most of the people here (presumably through honest ignorance, except for Willis, who actually works at it) (and of course, almost all of official climatology, presumably deliberately in their case) seem to have no clue how any of this works, and so we had better start with the fundamentals…

ferdberple
October 16, 2022 3:32 pm

About 1/3 of the earth’s surface is in the area of high evaporative cooling from fig 1 of scatterplots. This area is also the warmest.

This would seem to support the notion that the bulk of the heavy lifting to cool the planet’s surface is not IR. It is the convection via evaporation/condensation from the warm oceans.

The energy budget cartoon that is so popular does not show this at all. It has only a very minor role shown for evaporative cooling.

David A
Reply to  ferdberple
October 18, 2022 3:53 pm

Which is exactly what LWIR striking the oceans surface does.

RichardT
October 16, 2022 3:42 pm

One of my favorite Willis plots:

Should We Be Worried? – Watts Up With That?

Fits nicely here.

Loren C. Wilson
October 16, 2022 3:50 pm

Willis, as usual a very interesting analysis. One thing you could do to the scatter plots is to color code them for latitude, or perhaps ocean versus land surface. This might give even more insight to the data.

RickWill
October 16, 2022 5:33 pm

It takes ~ 5 W/m2 of additional solar input to raise the surface temperature by a single degree C.

I think you are referring to thermalised input rather than actual available EMR.

I have shown that the surface temperature response to solar EMR available at the top of the atmosphere varies widely. In the mid latitudes the land requires a change of approximately 14W/m^2 to shift the temperature 1C.

Over mid latitude, latitudinally constrained ocean basins, it takes around 28W/m^2 to move the temperature 1C.

The Southern Ocean requires 198W/m^2 to shift the temperature 1C.

The tropical ocean temperature is negatively correlated with available solar EMR.

So with peak solar input gradually moving northward, the planet has to warm because more land surface is getting higher solar input and oceans, dominating in the SH, getting less solar input.
https://wattsupwiththat.com/2022/10/04/surface-temperature-response-to-solar-emr-at-top-of-the-atmosphere/
Solar EMR is the dominant determinant of the surface temperature, both land and ocean, in the mid latitudes by a long margin. Surface ice is key factor in high latitudes. The tropical oceans are limited to 30C irrespective of the amount of solar EMR.

Joe Born
Reply to  RickWill
October 17, 2022 5:09 am

What do you mean by “thermalized”? My best guess is you mean total top-of-the-atmosphere solar radiation (at some latitude and longitude) net of what’s reflected. That is, the total that’s absorbed and thereby contributes to molecular kinetic energy before being re-radiated. But that’s just a guess.

RickWill
Reply to  Joe Born
October 17, 2022 2:18 pm

Solar EMR not thermalised is reflected. Reflected radiation is not converted to heat.

However the thermalised portion of the available EMR is not constant. It is a function of Earth’s albedo and that is constantly changing, mostly due to variation in cloud. There are long term trends because the sun’s view of Earth is always changing and different surfaces as well as their atmospheric column offer a different response to the solar EMR.

Joe Born
Reply to  RickWill
October 17, 2022 2:41 pm

Thanks. It’s what I suspected, but I hadn’t seen others use that terminology in this context before.

Rich Davis
October 16, 2022 5:34 pm

Bravo!
And thanks for a new word: palimpsest

ResourceGuy
October 16, 2022 5:46 pm

Better let the big guy know sooner than later to save a few billion measly dollars.

White House pushes ahead research to cool Earth by reflecting sunlight (cnbc.com)

angech
Reply to  ResourceGuy
October 16, 2022 6:26 pm

Steven M Mosher
“Yes models can only ever produce a projection of outcomes based upon what we think we know will hold true based upon the quantifications we assign to all the elements.

obviously you never worked with non deterministic perturbation models.”

Aha, the good old set of models that do not include models that work like models.
Got it.

Steven M Mosher
“note all of this neglects the real cause of warming:
” the reduction of cooling to space”

I think I know what he means to say
the reduction of warming to space, perhaps.
After all if cooling effects cannot go into space it would have to cool on the earth.
how cooling the earth warms the earth is another matter.

Sam Shicks
October 16, 2022 6:23 pm

These results don’t surprise me and are inline with how I would compute Planck Response.

If E is the surface emission and Ts is the surface temperature and SB is Stefan Boltzmann’s constant, then

dE/dTs = 4 x SB x (Ts)^3 which equals Planck Response. Not the IPCC version

For

Ts = 320K, Planck Response = 7.432 (W/m²)/K, Based on this one, 7 W/m² would = 0.94°C increase
Ts = 300K, Planck Response = 6.1 (W/m²)/K
Ts = 270K, Planck Response = 4.46 (W/m²)/K
Ts = 230K, Planck Response = 2.76 (W/m²)/K

No change above 320K makes sense too since because of longitudinal transport.

Reply to  Sam Shicks
October 16, 2022 8:32 pm

No change above 320K makes sense too since because of longitudinal transport

Sam, I think you mean the latitudinal (meridional) transport (advection) of the Hadley Cell.

Bob Wentworth
Reply to  Sam Shicks
October 18, 2022 1:02 pm

What significance do you attribute to this version of the “Planck response”?

It has nothing to do with the planet’s response to radiative forcing at TOA.

It does give the planet’s response to how surface emissions will change with surface temperature.

Based on this one, 7 W/m² would = 0.94°C increase

That 7 W/m² is at TOA, not at the surface.

Surface emissions and TOA emissions are different, because some surface emissions are absorbed by the atmosphere.

Currently, only a fraction 0.6 of surface emissions reach TOA.

So, 7 W/m² equates to 7/0.6 ≈ 11.7 W/m² at the surface.

So, your surface-level “Planck response” could be applied to that 11.7 W/m² to predict temperature change.

Or, you could convert your surface Planck response to a TOA Planck response (the usual definition) via the equation [TOA Planck response to surface temperature changes] = 0.6 × [Surface Planck response to surface temperature changes]

No change above 320K makes sense too since because of longitudinal transport.

Yes, but… that longitudinal transport means any increase in heating might not raise temperatures in the tropics, but it will result in even more heating at high latitudes.

Sam Shicks
Reply to  Bob Wentworth
October 19, 2022 3:20 pm

Planck Response should always be based on the response at the surface and not the TOA. What we are interested in is the change is surface emission with respect to a change in surface temperature. From this, we can compute the response to a change in greenhouse effect. The 0.6 that you reference comes from the planetary heat balance equation. This represents a combined surface/atmospheric emissivity and should not be used for Planck Response. Please explain this to the IPCC.

At 2xCO2, the Greenhouse effect will increase by 3W/m² (Dr Happer). This will force the surface to radiate an additional 3 w/m² and the surface temperature will increase 0.55°C. The Planck Response is 5.49 (w/m²)/K

Single Layer.jpg
Bob Wentworth
Reply to  Sam Shicks
October 19, 2022 4:14 pm

At 2xCO2, the Greenhouse effect will increase by 3W/m² (Dr Happer). This will force the surface to radiate an additional 3 w/m² and the surface temperature will increase 0.55°C. The Planck Response is 5.49 (w/m²)/K

You are missing a key piece of the puzzle.

If the initial ΔGHE is 3 W/m², then sure, assuming a particular right emissivity the surface response could be 5.49 (w/m²)/Km, yielding a 0.55℃ increase.

But, you’re not done at that point. That shifts surface emissions by 3 W/m², but that only shifts emission at TOA by 3 × 0.6 = 1.8 W/m². So, there is still a 1.2 W/m² imbalance at TOA to be corrected, a ΔGHE of 1.2 W/m² remains for the surface to respond to.

So, surface shifts by another 1.2/5.49 = 0.22℃. But wait! While that increased surface emissions by 1.8 W/m², it only increased emissions at TOA by 0.6×1.8 =1.1 W/m², leaving a remaining ΔGHE of 0.5 W/m² (rounding errors are arising) to respond to, and so on.

Summing the infinite progression, the final response will be 1/(1-.4) = 1.7 times larger than the response that happened during the first round.

That’s what your procedure misses.

Thats why others calculate the Planck response to be about 1.7 larger than what you’re asserting it to be

Sam Shicks
Reply to  Bob Wentworth
October 19, 2022 6:21 pm

You’re doing the energy balance wrong!

Once you account for the increase in Greenhouse Effect, there is no imbalance at the TOA. The energy in from the sun must equal the energy out at the TOA which is the case in my energy balance.

There is no infinite progression.

The system of equations are solved simultaneously. If you need a link to this procedure. It can be found at the University of Colorado State.

https://www.acs.org/content/acs/en/climatescience/atmosphericwarming/singlelayermodel.html

Bob Wentworth
Reply to  Sam Shicks
October 19, 2022 7:35 pm

The system of equations are solved simultaneously. If you need a link to this procedure. It can be found at the University of Colorado State.

I solved a more sophisticated version of that Colorado State simplified atmosphere model here. (It’s a multi-layer model including a tuning parameter f which is not emissivity, but fraction of spectrum absorbed by layers. Adding emissivity could be done trivially, but it wouldn’t produce particularly interesting effects. Changing f does produce interesting effects; it can be used to produce an effective TOA forcing.) (The “atmospheric energy recycling” conceit of the title is somewhat frivolous; I know thermal physics doesn’t really work that way, but one can always analyze the result, after the fact, as if some fixed recycling fraction was involved. Despite that side show, the thermal analysis of a multi-layer radiative atmosphere in that essay is correct.)

One limitation of the Colorado State model is that it seemingly provides no mechanism that could correspond to radiative forcing. (In my multi-layer model, changing the parameter f can be used to implement a radiative forcing.)

The model assumes the equilibrium relative GHE effect (SLR – OLR)/SLR = 1/2 always. Changing the equilibrium relative GHE by a small increment is the essence of forcing. The model seemingly can’t address that.

So, I don’t see how one could use that model to correctly address analyzing the response to forcing.

Once you account for the increase in Greenhouse Effect, there is no imbalance at the TOA. The energy in from the sun must equal the energy out at the TOA which is the case in my energy balance.

No, it’s really not. Your model does not achieve TOA energy balance.

Let’s work it out:

Step 0: Prior balanced state

SLR0 = 𝜀σ T0⁴
OLR0 = Sn = absorbed solar irradiance
EXH0 = OLR0 – Sn = 0 (Excess heat imbalance at TOA)
GHE0 = SLR0 – OLR0

Step 1: Immediately after forcing

ΔSLR1 = SLR1 – SLR0 = 0
ΔT1 = 0
EXH1 = ΔEXH1 = ΔF = 3 W/m²
ΔOLR1 = ΔSn – ΔEXH1 = 0 – ΔF = -ΔF
ΔGHE1 = GHE1 – GHE0 = ΔSLR1 – ΔOLR1 = 0 – (-ΔF) = ΔF = 3 W/m²

Step 2: Surface responds to ΔGHE1 = ΔF; SLR rises by an amount ΔGHE1 = 3 W/m²

ΔSLR2 = SLR2 – SLR1 = ΔF
Also ΔSLR = ΔSLR1 + ΔSLR2 = ΔF = 3 E/m²
ΔT2 = T2-T1 = (T/(4 SLR)) ΔF = 3/5.49 = 0.55°C
Also ΔT = ΔT1 + ΔT2 = 0.55℃

However, when surface emissions increase by ΔSLR2 = ΔF = 3 W/m², OLR does NOT increase by the same amount. Instead:

ΔOLR2 = OLR2 – OLR1 = (OLR/SLR) ΔSLR = 0.6 × 3 = 1.8 W/m²

This means that the net change in ΔOLR from step 0 is
ΔOLR = ΔOLR1 + ΔOLR2 = (-3 + 1.8) = -1.2 W/m²

Energy imbalance at TOA is
ΔEXH = ΔSn – ΔOLR = +1.2 W/m²

The change in GHE relative to step 1 state is:
ΔGHE2 = GHE2 – GHE1 = ΔSLR2 – ΔOLR2 = (3 – 1,8) = 1.8 W/m²

The net change in GHE relative to step 0 is:
ΔGHE = ΔSLR – ΔOLR = (3 – (-1.2)) = 4.2 W/m²

So, increasing SLR has also increased GHE (albeit by a smaller amount)

So, in summary, after your adjustment which you assert produces balance, I find an imbalance

ΔEXH = +1.2 W/m²

And some additional GHE (ΔGH2 = 1.8 W/m²) has shown up as a result of your which has yet to be addressed by any temperature change.

* * *

My check of your claim indicates that your answer does NOT result in TOA energy balance.

You imply you confirmed balance using the Colorado state model, but I don’t see how you could have correctly done that, since the model provides no mechanism for introducing a forcing, as far as I can tell.

If you used that model, how did you apply it?

Last edited 1 month ago by Bob Wentworth
Sam Shicks
Reply to  Bob Wentworth
October 20, 2022 2:26 am

I will look thru your multi layer model in more detail. At first glance, I think I may know what separates us. Do all your atmospheric layers have an emissivity of 1? If so, therein lies the difference.

I have used a multi-layer (2-layer) model from Colorado State which is explained in this link

https://biocycle.atmos.colostate.edu/shiny/2layer/

I put it in mathcad and in excel. The effect of adding more insulating layers to the atmosphere just forces the surface temperature to increase. I get the same planck response at the surface.

This link explains multi-layer better which I am aligned.

https://www.acs.org/content/acs/en/climatescience/atmosphericwarming/multilayermodel.html

It’s a basic energy balance and the equations are solved simultaneously.

I am not a fan of CO2 Forcing Concept because in my opinion, from a standpoint of changing CO2 concertation, there is no radiative imbalance at the TOA. True that it varies during the year as albedo changes and solar flux varies. But with respect to a change in CO2, it can be assumed balanced. Unless you can prove to me that the over sized evaporator we have for oceans has zero margin in it.

2XCO2 = 0.55K (9-13-22).jpg
Last edited 1 month ago by Sam Shicks
Bob Wentworth
Reply to  Sam Shicks
October 20, 2022 3:44 pm

I have used a multi-layer (2-layer) model from Colorado State. / This [ACS] link explains multi-layer better which I am aligned.


Thanks for those links. It is really interesting to pick apart the subtle difference between the different models.

It turns out there are three similar but distinct models in play here.

The Colorado State model is nonphysical, except when 𝜀=1:

  • Kirchoff’s radiation law tells us that the absorptance of a layer also equals 𝜀, which means the transmittance of the layer would need to be (1-𝜀), as is assumed in the ACS model. Yet, the Colorado State model always assumes zero layer transmittance.
  • So, while I really like their interactive solver, the Colorado State model seems to be nonsense when 𝜀ᵢ < 1.

The model I used, and the ACS model both include emissivity (my parameter f actually is emissivity, in retrospect), but rely on different implicit assumptions about how atmospheric absorption depends on frequency/wavelength. Both models make the simplifying implicit assumption that the spectrum of thermal radiation does not change between layers. However, this is achieved in different ways:

  • The ACS model implicitly assumes that the absorption coefficient, and hence the emissivity, is independent of wavelength or frequency.
  • The model in my essay assumes the absorption coefficient is high in some parts of the spectrum (so that near total absorption occurs within a layer) and negligible absorption occurs at other wavelengths/frequencies.

I think the assumption about spectral dependency in the model I analyzed is a bit closer to reality than the assumption of the ACS model, but neither assumption captures the full complexity of the spectral response.

So, I think both models (my prior model and the one from ACS) are useful―and they’ll produce slightly different results.

One consequence of the differing assumptions is that atmospheric layers are defined differently.

  • In the model I used, layers must be optically “thick” so that at the relevant wavelengths nearly all thermal radiation is absorbed within each layer. Consequently, layers are assumed to have the same mass of atmosphere, not the same vertical height in kilometers.
  • In the ACS model, they’re free to choose layer thickness however they like. They seem to implicitly suggest choosing equal thicknesses as measured in kilometers. Their results are also valid for equal-mass layers, but then the emissivities would be the same for all layers.

Do all your atmospheric layers have an emissivity of 1? If so, therein lies the difference.

No, though I might have mistakenly said that at one point. As I’ve sorted it all out, it turns out that f is the net emissivity of a layer, averaged over all wavelengths.

It’s just that the ACS and the model I analyzed make different assumptions about about the spectral dependency of emissivity/absorption.

I am not a fan of CO2 Forcing Concept because in my opinion, from a standpoint of changing CO2 concertation, there is no radiative imbalance at the TOA. True that it varies during the year as albedo changes and solar flux varies. But with respect to a change in CO2, it can be assumed balanced.

I agree that there is generally not a literal imbalance at TOA as CO₂ concentration increases, since the climate system constantly seeks to restore energetic balance.

(There may be some transient imbalance that occurs while the system works to return to equilibrium. The IPCC AR6 WG1 report estimates a current unresolved imbalance of 0.7 W/m².)

But, changing the concentration of CO₂ does have an impact on the system, and the question is how to characterize that impact.

What we ultimately care about is how the changing concentration will affect temperature. That’s what is reported via estimates of TCR or ECS.

But, calculations of TCR and ECS involve a lot of complicated modeling, and are difficult to reason about.

The radiative forcing value ΔF is based on a hypothetical scenario. It’s the imbalance at TOA that would occur if we could instantly change the concentration and then measure the imbalance at TOA before the system (especially surface temperature) had any chance to react to restore energetic balance at TOA.

Although this scenario is purely hypothetical, it has two virtues:

  • The value of ΔF associated with a change in concentration is reasonably straightforward to calculate, using radiation propagation models.
  • It’s possible to reason about how the value of ΔF will translate into a change in surface temperature after the system restores equilibrium and returns the TOA imbalance to zero.

So:

  • I agree that, in practice, there is typically little actual radiative imbalance at TOA.
  • Yet, there still needs to be some way of assessing how changing the concentration of CO₂ will affect temperature.

If you don’t want to use the value of ΔF (which is admittedly calculated using a hypothetical scenario) as the basis for analysis, what would you propose to use as a basis for analyzing how temperatures will behave as the radiative properties of the atmosphere change due to changes in the concentration of CO₂?

Bob Wentworth
Reply to  Sam Shicks
October 22, 2022 3:56 am

In my other comment, I claimed the Colorado State model ignores transmittance and so is non-physical when emissivity isn’t 1. On closer examination, their diagrams make this mistake, but their radiation budget equations appear to be correct. So, maybe it’s just sloppy presentation, and the model they are simulating is actually correct (and equivalent to the ACS model).

Bob Wentworth
Reply to  Sam Shicks
October 19, 2022 8:09 pm

I see the Colorado State work does also include a more complex multi-layer model on another page.

And, while it’s a poor substituted for something that in some way mimics GHGs, one can see what happens in the model if one simply increases absorbed insolation by ΔF. The answer isn’t what you claim it to be; in the single-layer model, the temperature change is twice as large as what you predict.

Last edited 1 month ago by Bob Wentworth
Sam Shicks
Reply to  Bob Wentworth
October 19, 2022 3:33 pm

High latitudes are most sensitive for two reasons

  1. The surface temperature needs to change more because the Planck Response is less
  2. Latitudinal transport

This is where most of the warming takes place which isn’t so bad.

Julian Flood
October 16, 2022 9:21 pm

Given the correct resources I could warm parts of the planet with no changes in solar input, just by altering albedo. The Sea Of Marmara shows how. This enclosed sea is polluted by oil, surfactant, sewage and agricultural run-off. It is warming much faster than the average. The same effect can be seen all around the planet where albedo is reduced by pollution.

A big inadvertent experiment was carried out in WWII, namely the Battle of the Atlantic. It left an irreducible blip in the temperature record. I wonder, why the blip?

Now if only we could think of a pollutant that would spread on water when spilt in tiny quantities. Hmmm. Ruf and Evans found that microplastic didn’t do lower albedo, but the pollution that gathered on their gyres did. And that Ben Franklin chap even demonstrated a likely candidate on a Clapham Common lake.

I wonder if there’s a connection between pollution levels of a water body and how fast it is “global” warming?

JF
Lake Michigan must be a good place to look. Isn’t there some sort of marine science place near there?

RickWill
Reply to  Julian Flood
October 17, 2022 2:33 pm

All land locked water bodies in the northern hemisphere will be warming faster than the oceans at the same latitude. They are getting more sunlight and significantly more in April and May.

Land locked water bodies do not experience the same temperature limiting process as open oceans. Convective instability is disrupted over the water because they are inevitably mid level divergent zones which inhibits cloudburst over the water.

This table shows how solar EMR is changing in May at 40N last 500 years to next 500 years:
 -0.500   442.025049
   -0.400   442.409040
   -0.300   442.800035
   -0.200   443.197592
   -0.100   443.601278
    0.000   444.010670
    0.100   444.426501
    0.200   444.847249
    0.300   445.272359
    0.400   445.701259
    0.500   446.133362
This increase in solar EMR will cause a long term upward trend in temperature of land locked water bodies because they cannot sustain the temperature limiting process observed in open oceans.

Sam Shicks
Reply to  Julian Flood
October 19, 2022 3:23 pm

I could warm the planet by factoring in increase in urban sprawl. Urban sprawl has increased approx 0.6% of NH land mass. Even more if you consider south of 60° latitude. This causes cloud reduction due to Urban Heat Island Effect and thus less albedo and more incoming solar.

Izaak Walton
October 16, 2022 9:56 pm

These graphs do not show anything like what Willis is claiming. The local temperature does not depend only on the local incident solar power. Rather as should be clear and obvious to everyone energy received at the equator goes to heating the poles. This is clear from Willis graphs. Thus you cannot derive the solar sensitivity from these graphs. Fig. 3 for example should really be “temperature sensitive per change in latitude” and clearly moving closer to the equator will have a different effect than increasing the global amount of sunlight received. And there is no way you can predict how the climate will change to redistribute any additional energy stored by the greenhouse effect.

M Courtney
Reply to  Izaak Walton
October 17, 2022 12:00 am

So the idea is that the extra energy from sunlight at the equator is transferred to the Poles without doing much in the way. And it only has an effect where the sun shines least?
That’s possible. But some mechanism and evidence would be useful. And what causes the boundaries of the regions?

  • Where does “transfer away” start and end and why?
  • Where does “keep transfering” start and end and why?
  • Where does “start warming here” start and end and why?

Surely the more probable answer is that the energy from the Sun goes into phase changes wherever moisture is available. Therefore it has little effect on temperature where the air is humid and a lot more where it is dry? This also allows for non-poleward winds occuring.

Izaak Walton
Reply to  M Courtney
October 17, 2022 1:30 am

At a very rough level you can look at what would be the black body temperature
at each point given the amount of sunlight received. At the poles the temperature is about 50 degrees higher than what you would expect while at the equator it is a lot less. So clearly a lot of energy is moving polewards and heating things up.

If you look at something like the gulf steam then it clearly plays a major role in moving heat from the equator to the poles. As do Hadley cells.

Ireneusz Palmowski
Reply to  Izaak Walton
October 17, 2022 2:45 am

There is a problem with transporting energy in winter to high latitudes, when the circulation in the stratosphere and troposphere are combined.
comment image

Bob Wentworth
Reply to  Ireneusz Palmowski
October 18, 2022 12:36 pm

Could you explain what you want us to see in these charts? (And how is the vertical axis defined? Is that pressure in millibars?)

It looks like there are high wind speeds in the stratosphere. Given how little air there is there, does that amount to much lateral heat transfer?

Looks like troposphere winds are greatest in the middle latitudes.

I don’t see anything that explains to me why you would say “There is a problem with transporting energy in winter to high latitudes, when the circulation in the stratosphere and troposphere are combined.”

Ireneusz Palmowski
Reply to  Bob Wentworth
October 19, 2022 12:44 am

You can see it better in this graph. The wind in the winter startospheric polar vortex is so strong that it controls circulation in the troposphere up to the 500 hPa level. In America, this level is referred to in forecasts as the “winter polar vortex.” Note that the direction of the stratospheric wind in summer does not affect the wind in the troposphere.
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https://www.cpc.ncep.noaa.gov/products/stratosphere/strat-trop/
https://ds.data.jma.go.jp/tcc/tcc/products/clisys/STRAT/

Bob Wentworth
Reply to  Ireneusz Palmowski
October 19, 2022 1:15 pm

Nice chart, thanks.

Is this northern hemisphere?
Are warm colors blowing toward or away from the pole?

Bob Wentworth
Reply to  M Courtney
October 18, 2022 12:27 pm

Surely the more probable answer is that the energy from the Sun goes into phase changes wherever moisture is available. Therefore it has little effect on temperature where the air is humid and a lot more where it is dry? 

The extra energy from the Sun can only go into phase changes if the humidity is continually increasing day after day, which it is not. So, that can’t be the explanation.

But some mechanism and evidence would be useful. And what causes the boundaries of the regions?

The “transfer away” region occurs where there is powerful convection that takes heat away from the surface and sends it high into the atmosphere, where some of the heat is radiated to space and the rest is circulated by air currents to other latitudes.

That occurs predominantly in the tropics, where the sunlight is intense enough to drive powerful evaporation and convection.

Ireneusz Palmowski
Reply to  Izaak Walton
October 17, 2022 12:52 am

This is how the temperature changes in high latitudes depending on access to sunlight.
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Trick
Reply to  Willis Eschenbach
October 17, 2022 8:13 am

Willis asks: “why do all the gridcell datapoints fall in the three nice ~ straight lines in Figure 1?”

The x-coordinate leaves out significant power inputs to natural surface temperature at its extremes.

One reason for the change in slope at the left x-extreme is, while I don’t know the world record for the lowest downwelling (DW) radiative power flux from the atmosphere, I have read a value of min. DW being around 130 W/m^2 for Arctic winters.

For example, at the left end, including at least nature’s min. DW 130 for the -50C point (for which it is already naturally included) when added to the “solar minus albedo reflection” would then plot a much different slope.

Also, local temperature at each gridcell, under reasonably normal (or avg.) conditions, does not drop below the dewpoint as measured. This is why forecasters are taught that on a clear day with light winds, the late afternoon dew point is a good estimate for the eventual minimum overnight temperature.

These are two ingredients of local gridcell surface temperature not included in your x-coordinate & serve to, at least partially, answer Willis’ question.

Last edited 1 month ago by Trick
Izaak Walton
Reply to  Willis Eschenbach
October 17, 2022 1:13 pm

Willis,
you have it backwards. The fact that the grid cell data points fall in three nice
~ straight lines is evidence that the temperate doesn’t depend on locally available solar polar.

Suppose you had a black body in thermal equilibrium with the incidence solar radiation. Then the temperature would go as the fourth root of the available solar power due to the Stefan-Boltzmann law. So the fact that the temperature is linear with solar power shows that there must be a lot of transport of energy due to things like advection. Thus the local temperature depends not only on the locally available solar power but also on the solar power at the equator and elsewhere and there is no way to untangle the effects using the plots that you show.

Bob Wentworth
Reply to  Willis Eschenbach
October 18, 2022 12:46 pm

these are datapoints from all over the planet … and everywhere there is some given available solar power, the surface temperature is related to the amount of solar power… this kind of scatterplot shows the full, real-world relationship between available solar and temperature.

Actually, this issue of advection shows that you are muddling together local and global effects.

Data points with low levels of available solar power are not from “all over the planet” (they’re from polar regions) nor are data points with high levels of solar power are not from “all over the planet” (they’re from the tropics).

So, the points at the left of the chart are all characterized by advective heating, and the points at the right of the chart are all characterized by advective cooling.

When radiative forcing is applied, advective cooling will change, because advective cooling is a function of global temperature patterns, not a local effect.

When advective cooling patterns change, the curve will shift. Maybe not enough to change its overall shape, but enough to invalidate any gridcell-by-gridcell predictions about temperature changes.

Ireneusz Palmowski
October 17, 2022 3:06 am

La Niña correlates very well with the increase in the strength of the solar wind magnetic field.
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Strong spikes in the solar wind can be seen to hinder subsurface heating in the western Pacific.
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Last edited 1 month ago by Ireneusz Palmowski
D Boss
October 17, 2022 5:04 am

Such incredible, succinct analyses showing the utter failure of the “groupthink” inherent in so called learned persons! I am again and again amazed at how many areas of so called science often miss the forest for the trees, or fail to perform even the most rudimentary testing of concepts, theories or “what they’ve been taught”.

While I applaud Willis’ acumen and works, I do not believe he is some superman of analysis. Why haven’t similar, and rather simple on their conceptual face data testing been done before? Because stupid humans do what they are told and are chastised when they challenge the knowledge base that they have been taught.

Isn’t “science” supposed to be primarily about testing whether an idea, theory or hypothesis is correct? Increasingly it appears to be filled with more dogma and blind faith than major religions.

Excellent work Willis, keep on doing your thing!

Tim Gorman
October 17, 2022 5:56 am

WE,

Congrats on a simple, easy to understand analysis. The fact that this subsumes all of the poorly understood biosphere physics into one, straight forward, combined total is a masterpiece.

At the risk of offering a contested opinion, this also shows me the folly of trying to determine a “global average temperature”. A GAT simply can’t describe what your analysis displays. As such it is useless in determining what is happening to the Earth, at least to me. As a corollary it also makes the climate models useless as well. Now, if the models reproduced what you have provided here then they would be offering something that people could actually use to see what is going on in our biosphere.

ferdberple
October 17, 2022 6:57 am

Willis, can you post the temperature data for the 64800 grid-cells by year?

Thanks, Ferd

Ichneumon
October 17, 2022 8:00 am

Once the average available solar power is above 310W/m2, you can add up to an additional 50 W/m2 without increasing the surface temperature one bit.

Your global map shows that these 310+ areas are in the tropical oceans. Tropical waters continually circulate and mix. Mixing water averages out its temperature. Thus it’s no surprise that those areas maintain about the same average temperature, the energy differentials even each other out.

This doesn’t mean that say an additional 40 W/m^2 wouldn’t raise that equilibrium temperature, of course it would.

This reflects the effects of an additional 50 W/m2 applied over decades and centuries.”

Ocean mixing also goes on over decades and centuries.

Matthew Schilling
Reply to  Ichneumon
October 18, 2022 11:39 am

Would it help to picture three buckets with different sized holes at the bottom? “Water” entering and leaving the buckets is actually heat content. The size of a hole increases as the “water” (heat) level increases.

Near the equator, the hole at the bottom of the bucket is so big, it’s nearly impossible to add any more “water” to the bucket. At the poles, the hole is so small, any trickle in will efficiently raise a bucket’s “water” level. In between, the bottom hole ranges in size – larger nearer the equator and smaller nearer the poles.

David A
Reply to  Matthew Schilling
October 18, 2022 5:18 pm

Mathew, not sure how that applies to the question.

Matthew Schilling
Reply to  David A
October 18, 2022 7:38 pm

(I think I meant it as a general comment vs. reply to yours. Sorry)

David A
Reply to  Ichneumon
October 18, 2022 5:17 pm

You make a valid point about ocean residence time of solar insolation over the oceans, as some of that is lost to the atmosphere for a time. I do not know of any studies that strive for an understanding of disparate W/L SWR ocean residence times.

beng135
October 17, 2022 8:39 am

Thanks, Willis. You may be about the only person studying this line of research. And it very much contradicts the conclusions of the corporate, so-called climate science.

PCman999
October 17, 2022 10:21 am

If the science ever gets settled, it will be because of the work of a brilliant person with the initials W.E.

You make things so easy to see and understand – thanks 10^1000 times.

Steve Keppel-Jones
October 17, 2022 11:23 am

Willis, you wrote:
It takes ~ 5 W/m2 of additional solar input to raise the surface temperature by a single degree C.”

Since you told us that solar (or any) EMR is a form of energy, which is true, what units should we measure it in?

October 17, 2022 1:03 pm

Willis,

Again you made almost the same mistake that you made with your previous post. This graph says nothing about sensitivity – at all. This shows a gradient for how variability in solar relates to surface temperature LOCALLY. It does not show how much GMST changes per 1 W/m^2 perturbation of the earth’s energy imbalance. Sensitivity by definition is:

dT = λ*dF

Where λ is sensitivity and dF is a change in radiative forcing (a perturbation of EEI) and dT is a change in GMST. Graphing the gradient between solar and temperature locally doesn’t demonstrate anything about sensitivity. The curve may look identical if EEI = 0.

Doubling CO2 causes roughly a 3.7 W/m^2 perturbation of EEI. If Ein is 240 W/m^2 then Eout decreases to 236.3 W/m^2. The surface MUST warm until that imbalance at the top of the atmosphere is resolved. Sensitivity estimates how much GMST increases at a new equilibrium – that is when Ein – Eout = 0 again.

Since the IR we’ve experienced a ~2.2 W/m^2 increase in RF, and the surface has responded with ~1.2 C warming with a current EEI of about 0.8 W/m^2. That means 2.2-0.8 = 1.4 W/m^2 is roughly equal to 1.2 C/λ. That’s a λ of 1.2/1.4 = 0.86 C/W/m^2. That means ECS is about 0.86*3.7 = 3.17 C. That’s how ECS is calculated.

Bob Wentworth
Reply to  Scott J Simmons
October 18, 2022 12:17 pm

Again you made almost the same mistake that you made with your previous post. This graph says nothing about sensitivity – at all. This shows a gradient for how variability in solar relates to surface temperature LOCALLY. It does not show how much GMST changes per 1 W/m^2 perturbation of the earth’s energy imbalance.

I’d like to offer a different way of saying what I think you’re saying, to capture the same facts you’re raising in a way that make the relevance to what Willis is arguing clearer, for at least some readers. (It’ll help me, if not anyone else.)

* * *

One problem is that Willis keeps looking at TOA energy imbalance and surface energy fluxes as if they are interchangeable. For example, Willis writes:

“an increase of 3.7 W/m2 from a doubling of CO2 is supposed to cause a 3°C temperature rise. But here’s a part of the world where a change of 50 W/m2, more than ten times as large, does … nothing.”

“It takes ~ 5 W/m2 of additional solar input to raise the surface temperature by a single degree”

No importance at all seems to be given to the fact that 3.7 W/m² is at TOA while 50 and ~ 5 W/m² are at the surface.

Yet, there is a multiplier effect between TOA ΔF and the surface. In particular:

  • Overall, the gross multiplier is (surface emissions SLR/outgoing emissions OLR) = (398/240) = 1.7. But, the marginal multiplier (the multiplier for small changes ΔSLR/ΔF) can be different.
  • Note that surface emissions ΔSLR change by 5.5 W/m²/℃. The short-term sensitivity is the “Planck sensitivity” 3.2 W/m²/℃, which means that the short-term response to forcing involves a multiplier ΔSLR/ΔF = (5.5/3.2) = 1.7.
  • Since the industrial revolution 2.2 W/m² of forcing (with 0.8 W/m² of that forcing still unrealized) has led to a ~1.2℃ (which corresponds to ΔSLR = 1.2×5.5 = 6.6 W/m²) that corresponds to a multiplier ΔSLR/ΔF = 6.6/(2.2-0.8) = 4.7 W/m². So, over that time period, when longer term feedbacks have been allowed to take effect, the marginal multiplier has been ΔSLR/ΔF ≈ 4.7.

So, the size of the multiplier between TOA and the surface depends on whether one is talking short term or long term.

But the multiplier is NEVER 1, and Willis keeps saying things that presume a multiplier of 1, that TOA and surface energy fluxes are interchangeable.

The multiplier effect IS one measure of the GHE. Pretending that the multiplier is 1 (when it’s observationally not 1) is a way of assuming that there is no GHE (which I I’m confident Willis does not intend to do).

* * *

Another other problem is that Willis assumes one can predict temperature changes on a purely local basis.

The scatterplots Willis looks at suggest to him that, locally, changing surface irradiance by ΔS leads to typical temperature change ΔT.

But, what that leaves out is: That temperature shift ΔT leads to some corresponding change in the local energy imbalance at TOA, call it ΔEI_local

All those local energy imbalances add up to some net Earth energy imbalance ΔEEI = [Sum over] ΔEI_local

For the current set of gridcell temperatures, it works out that the global energy imbalance is about 0.8 W/m².

But, any global energy imbalance means global temperatures need to change until that imbalance is rebalanced towards zero.

Willis is suggesting that if a forcing of 3.7 W/m² happens, one can simply pretend local sunlight levels have increased by 3.7 W/m² and then use his curve to predict the changes. Setting aside the fact that one needs to apply a multiplier (so 3.7 3.7 W/m² goes to 1.7×3.7 = 6.3 W/m² at the very least), Willis’s procedure doesn’t consider what his proposed temperature changes will do the the global TOA energy imbalance. If his procedure doesn’t lead to changes that match that 3.7 W/m² of forcing, then there will be some residual ΔEEI which will drive additional temperature changes.

Willis’s procedure falsely assumes that temperature changes can be determined on a purely local basis, and fails to take into account that there are certain global factors that need to be taken into account. In particular, globally, for there to be equilibrium, energy in must equal energy out.

Willis’s procedure doesn’t account for that balance, or ensure that an appropriate balance will exist after his procedure is applied.

* * *

I hope this alternate way of expressing your/Scott’s points is helpful to someone.

Reply to  Bob Wentworth
October 20, 2022 7:17 am

All good points. I set up a toy model spreadsheet that lets me do these types of calculations pretty quickly. With surface emissivity of 0.98, even if we take a no feedback sensitivity of 1.14 C, doubling CO2 (3.71 W/m^2) causes a ΔG of 6.1 W/m^2, so a multiplier of ΔG/ΔF = 1.6x, whereas with feedbacks, if ECS = 3 C, that jumps up to 16 W/m^2, a multiplier of ΔG/ΔF = 4.3x.

Bob Wentworth
Reply to  Scott J Simmons
October 20, 2022 4:04 pm

Sounds good.

What I particularly like is your framing is that you’re expressing things in terms of the multiplier between the change in actual Greenhouse effect (G = SLR-OLR), ΔG, relative to a change in radiative forcing, ΔF.

ΔF is a largely hypothetical quantity (since we never measure climate in a state where the system hasn’t had a chance to shift away from ΔF being the observed TOA energy imbalance).

So, conceptually:

  1. One characterizes the effect of changing the concentration of CO₂ via a quantity ΔF, which reflects a hypothetical non-equilibrium situation, but is relatively straightforward to compute.
  2. One calculates the change in GHE, ΔG, that would occur in the less hypothetical situation (i.e., equilibrium but without non-Planck feedbacks) or in an even less hypothetical situation (TCR or ESC, where the only thing hypothetical is the exact change in GHG concentrations).

Hmm. I’m not sure if that will add clarity for anyone else. But I’m liking thinking in terms of ΔG, and in terms of the multiplier ΔG/ΔF.

Reply to  Bob Wentworth
October 21, 2022 6:47 am

What’s interesting to me is how nearly constant ΔG/ΔT is, where ΔT is equilibrium GMST.

If ECS = 1.14 C, then ΔG/ΔT = 6.10/1.14 = 5.35 W/m^2/C
If ECS = 3.00 C, then ΔG/ΔT = 16.18/3.00 = 5.39 W/m^2/C
If ECS = 4.50 C, then ΔG/ΔT = 24.46/4.5 = 5.44 W/m^2/C

So a ΔG/ΔT value says pretty much nothing about climate sensitivity. Given the error margins of these values, the same ratio is consistent with probably just about any reasonable estimate for ECS.

Last edited 1 month ago by Scott J Simmons
Bob Wentworth
Reply to  Scott J Simmons
October 21, 2022 2:49 pm

I take it that’s what you’re seeing in your spreadsheet?

I’m curious about the assumptions the spreadsheet makes. And, I’m wondering how those assumptions correspond to my analysis below, which is exact, within the limits of looking only at linearized first-order effects.

What’s interesting to me is how nearly constant ΔG/ΔT is, where ΔT is equilibrium GMST… So a ΔG/ΔT value says pretty much nothing about climate sensitivity. 

I think it’s entirely to be expected that ΔG/ΔT says pretty much nothing about climate sensitivity. Why would you expect it to?

* * *

To explain my response, let my share the results of my linearized analysis.

By my reckoning the change in temperature in response to a forcing can be expressed in either of the following two ways (as show at the end of this comment):

ΔT = T [ΔF + ΔSn + SLR Δ’g] / (4 OLR)
ΔT = T [ΔGHE + ΔSn] / (4 SLR)

where the second equation is equivalent to

ΔGHE/ΔT = q = 4 SLR / T – ΔSn / ΔT

and where

T = surface temperature
ΔF = radiative forcing at TOA due to change in GHG concentration
Sn = net absorbed solar irradiance
g = GHE/SLR = normalized greenhouse effect
OLR = outgoing longwave radiation at TOA
GHE = SLR – OLR = greenhouse effect
SLR = surface longwave radiation emissions
ΔX is small change in X
Δ’g is the post-forcing (i.e., feedback-induced) change in g

Note that, in the first equation above, all “feedback” in response to a forcing shows up via either an albedo change which creates a non-zero ΔSn, or via a post-forcing change in the normalized greenhouse effect, Δ’g. Because ECS doesn’t match the Planck response (4 OLR / T), ECS must reflect changes to these quantities.

I notice from these results of my analysis that:

  1. ΔT is expected to change with ΔF
  2. ΔGHE/ΔT is NOT expected to change with ΔF, except to the extent that a change in absorbed insolation (ΔSn) is induced as a feedback process (or to the extent that changes become large enough that the linearized analysis is no longer accurate and second-order effects need to be taken into account)

So, looking at what my analysis indicates, it seems to me to be completely unsurprising that ΔGHE/ΔT doesn’t vary much with ΔF. I wouldn’t expect these to have much relation to one another.

I’m almost surprised that ΔGHE/ΔT changed in your model, since I’m guessing you’re not factoring in albedo feedback? Or are you?

Of course, the more likely option is that your result just reflects the way that d(SLR)/dT = 4 𝜀 σ T^3 = SLR / T shifts with temperature.

That’s not something reflected in my linearized results, but it could well be showing up in your analysis.

Bottom line: I don’t think that looking at ΔGHE/ΔT (or ΔG/ΔT in your notation) is likely to tell us much of interest in relation to climate sensitivity in response to radiative forcing.

* * * * * * * * * * * * * * * * * * * * * *

SUPPORTING ANALYSIS

Let me set some context for how I understand things.

I’ll expand how I see change in surface emissions SLR relating to forcing and to the change in GHE.

Energy balance at TOS looks like:

Sn – TXH = OLR = SLR – GHE = (1-g) SLR

where
Sn = net absorbed sunlight
TXH = TOA excess heating (imbalance)
OLR = outgoing LW at TOA
SLR = surface emitted LW
GHE = SLR – OLR =
g = relative GHE = GHE/SLR

Let’s further stipulate that

g = 𝜂 𝚪

where 𝚪 is the (positive) lapse rate. So

Sn – TXH = (1 – 𝜂 𝚪) SLR

Suppose that initially we are in equilibrium, so TXH =0

A forcing happens. This involves

TXH = ΔF = 𝚪 SLR Δ𝜂
Δ𝜂 = ΔF/(𝚪 SLR)

with nothing else changing.

In general, the formula for small changes in the energy balance equation is

ΔSn – ΔTXH = (1 – 𝜂 𝚪) ΔSLR – 𝜂 SLR Δ𝚪 – 𝚪 SLR Δ𝜂

From above, let’s replace ΔTXH with TXH and Δ𝜂 with ΔF/(𝚪 SLR) + Δ’𝜂 where Δ’𝜂 is any feedback-level change in 𝜂. This yields:

ΔSn – TXH = (1 – 𝜂 𝚪) ΔSLR – 𝜂 SLR Δ𝚪 – 𝚪 SLR Δ’𝜂 – ΔF

Require TXH = 0 for equilibrium and rearrange, to find

(1 – 𝜂 𝚪 ) ΔSLR = ΔF + ΔSn + 𝜂 SLR Δ𝚪 + 𝚪 SLR Δ’𝜂

Let’s try to get this back in terms of g (where g=𝜂𝚪).

Δg = 𝜂 Δ𝚪 + 𝚪 Δ𝜂

So prior equation becomes

(1 – g) ΔSLR = ΔF + ΔSn + SLR Δ’g

where Δ’g is the post-forcing change in g.

Solving for ΔSLR yields

ΔSLR = [ΔF + ΔSn + SLR Δ’g] / (1 – g)

* * *

Ok, but I want to relate this to ΔGHE, so let’s compute that:

GHE = SLR – OLR
ΔGHE = ΔSLR – ΔOLR

But after coming back to equilibrium, ΔOLR = ΔSn so
ΔSLR = ΔGHE + ΔSn

* * *

But let’s do these in terms of ΔT not ΔSLR

d(SLR)/dT = 4 𝜀σ𝛵^3 = 4 SLR / T

so

ΔT = (T / (4 SLR)) ΔSLR

With results from above:

ΔT = T [ΔF + ΔSn + SLR Δ’g] / (4 SLR (1 – g))
ΔT = T [ΔF + ΔSn + SLR Δ’g] / (4 OLR)

ΔT = T [ΔGHE + ΔSn] / (4 SLR)

Let’s solve the latter for ΔGHE/ΔT = q:

4 SLR ΔT = T q ΔT + T ΔSn

q T ΔT = 4 SLR ΔT – T ΔSn

ΔGHE/ΔT = q = 4 SLR / T – ΔSn / ΔT

Reply to  Bob Wentworth
October 21, 2022 9:07 pm

I think it’s entirely to be expected that ΔG/ΔT says pretty much nothing about climate sensitivity. Why would you expect it to?

I don’t and wouldn’t. But I suspect Willis does, at least to some extent, since he said it takes ~5 W/m^2 to increase surface temperature by 1 C, though it’s unclear to me what he thinks that ~5 W/m^2 is. But he seems to think that means sensitivity must be small.

Your math looks similar to mine, though mine is more simple. I didn’t account for lapse rate and held g constant at 0.4.

Bob Wentworth
Reply to  Scott J Simmons
October 21, 2022 9:39 pm

I suspect Willis does [expect that ΔG/ΔT says something about climate sensitivity], at least to some extent, since he said it takes ~5 W/m^2 to increase surface temperature by 1 C, though it’s unclear to me what he thinks that ~5 W/m^2 is. But he seems to think that means sensitivity must be small.

Good point.

He seems to have the impression that forcing ΔF should directly drive surface temperature change by changing ΔSLR correspondingly. I don’t think he a coherent picture of how the varying ingredients relate, so there’s no really coherent way of mapping his thoughts onto the coherent model that you and I (and many others) appear to share.

I think Willis and others somehow imagine that ΔF is a flux that shows up at the surface and so should drive temperature as ΔT = ΔF /[d(SLR)/dT] = ΔF / [4 SLR / T]

And, when that doesn’t check out, they assume someone else must be making a mistake, rather than realizing that ΔF simply doesn’t directly correspond to the equilibrium changes at the surface.

It probably doesn’t help that, instantaneously, ΔG does increase by an amount ΔF, which makes it look like ΔF is showing up at the surface, and all they have to do is increase SLR by ΔF to compensate for the increase in ΔG. But, of course as soon as they increase SLR, they don’t create equilibrium as they imagine would “of course” be the case. In actually, ΔG keeps increasing as ΔSLR is increased, only coming to equilibrium when ΔG has increased by a total of ΔF/(1-g) (before non-Planck feedbacks are taken into account).

A lot of the confusion seems to involve people expecting the linkages between parts of the system to be more direct and straightforward than wha the actual physics indicates.

Bob Wentworth
October 17, 2022 1:12 pm

Hi Willis. Thanks for your post. However, I’m quite certain your logic is wrong.

  • Over a year ago, in my post Thunderstorm World: A Model to Explore Ideas from Willis Eschenbach, I demonstrated that with a simple climate model I could roughly reproduce the sort of scatterplot features you’re seeing, but that in my model, “following the curve” was NOT a valid way of predicting what would happen in the presence of global warming. This offered an “existence proof” demonstrating that your hypothesis about using scatterplots to make predictions could fail, at least given some not unreasonably assumptions about climate dynamics. One failure is arguably sufficient to invalidate the logic as something that ought to be trusted.
  • Earlier today, I posted a comment on your recent Global Scatterplots post in which I spelled out in considerable detail why your logic in thinking shifting-along-the-curve-predicts-outcome-of-warming is mistaken. I also pointed out that your empirical test of your approach didn’t address the fact that your hypothesis would be invalidated if the curves you offered for different time periods shifted just tenths of a degree to the right between the first and the last interval.

Now to this latest post…

Once the average available solar power is above 310W/m2, you can add up to an additional 50 W/m2 without increasing the surface temperature one bit.

My TW model crudely reproduced that behavior in my Figure 6, albeit that plot used SW+LW on the x-axis. I could run the model again and plot just SW, if it would add value.

This reflects the effects of an additional 50 W/m2 applied over decades and centuries.

That it would be a persistent phenomenon doesn’t surprise me; it was the equilibrium state in my model that showed similar behavior, so there would be no reason for it to change.

an increase of 3.7 W/m2 from a doubling of CO2 is supposed to cause a 3°C temperature rise. But here’s a part of the world where a change of 50 W/m2, more than ten times as large, does … nothing.

It’s not the same kind of change, so it’s not an apt comparison.

Note that the red areas that are insensitive to increased solar input are all in the tropics, and are virtually all ocean. They cover half of the tropical area or about 22% of the planet’s surface.

I
n my TW model, the insensitive zone covered not just the tropics, but all the way out to around 42º degree latitude North and South (Figs. 2 and 3). Yet that was NOT a barrier to the average surface temperature rising in response to radiative forcing.

Returning to Figure 1, recall that I said that “The slope of the cyan/black line shows the change in temperature for each 1 W/m2 change in available solar.” Figure 3 shows exactly that, the slope of the cyan/black trend line in Figure 1

You are assuming that temperature is ONLY a function of available solar power, not just in the current version of the world, but in all accessible versions of this world.

My TW model produces a curve qualitatively similar to yours (albeit in terms of SW+LW ― I can confirm the SW-only version if this turns into a dialog). However, that curve is determined by the temperature in the upper troposphere.

In the model, when I inject radiative forcing, the temperature of the upper atmosphere increases, and all the surface temperatures in the “insensitive zone” increase as well. That part of the curve does NOT stay the same.

I explained in my comment on your other post that your hypothesis works if only absolute surface temperature matters when it comes to what happens in the atmosphere above―yet we know that convection onset is dependent on the temperature gradient to the upper atmosphere, so that relative temperature matters as well. And upper atmosphere temperature is NOT a purely local phenomenon. There’s a lot of horizontal heat transport that evens out high altitude temperatures across latitudes. That means that absolute temperature at the surface doesn’t change in lockstep with relative temperature to the upper troposphere in a way that brings one gridcell to a circumstance that a prior gridcell had already experienced. Instead, the gridcell comes into a combination of absolute and relative temperatures that was not part of the global context of the gridcells that defined the prior version of the curve.

Note that this means that solar power has to rise by about six W/m2 to raise the temperature of 70% of the planet by 1°C … and remember that in half the tropical ocean, 22% of the planet, that same six W/m2 increase in available solar doesn’t do doodly-squat to the temperature.

I don’t agree, based on both the behavior of my model and the logical flaw in your argument. I don’t see reason to believe that that 70% of the planet is necessarily insensitive in the way that you seem to believe it is.

In my TW model, which reproduces the “insensitivity” behavior, when I added radiative forcing, the global average surface temperature rose―as did surface temperature in the “insensitive zone.”

I really don’t think that “insensitive zone” means what you think it does.

* * *

Thoughts?

Respectfully,
Bob

Last edited 1 month ago by Bob Wentworth
Bob Wentworth
Reply to  Bob Wentworth
October 17, 2022 2:33 pm

For what it’s worth, I did rerun the TW model plotting only SW radiation on the x-axis instead of SW+LW and the results remained qualitatively quite similar.

Ireneusz Palmowski
Reply to  Bob Wentworth
October 17, 2022 11:53 pm

I think that the basis for the calculation can be solar radiation reaching the upper troposphere, because it can significantly affect the vertical temperature gradient. On all planets with a sufficiently dense atmosphere, the troposphere is determined by a fairly constant vertical temperature gradient.

Bob Wentworth
Reply to  Ireneusz Palmowski
October 18, 2022 11:06 am

On all planets with a sufficiently dense atmosphere, the troposphere is determined by a fairly constant vertical temperature gradient.

It depends what you mean by “fairly constant.” On Earth, the lapse rate in the tropics is much different than the lapse rate in polar regions (which is closer to small absolute lapse rate, near vertical temperature profile). Those differences in lapse rate are very important to how our climate behaves.

I only recently realized that the Greenhouse effect (GHE) is strongly effected by lapse rate. At a lapse rate of zero (isolthermal temperature profile), there would be zero greenhouse effect―TOA would radiate at the same level as the surface.

So, at any given location, the size of the GHE (measured as surface thermal emissions not reaching space) is a function of these things:

  1. Concentration of persistent GHEs like CO2
  2. Concentration of responsive GHEs, i.e., water vapor
  3. Clouds
  4. Lapse rate
  5. Surface temperature (since that acts as a weight which determines how many surface emissions there are to potentially be lost)

You weren’t necessarily advocating for it, but pretending lapse rate is constant everywhere would grossly distort the way that radiative forcing from the GHE influences climate.

solar radiation reaching the upper troposphere, because it can significantly affect the vertical temperature gradient. 

Ok, I can see an effect insofar as it drives how much convection and tropical storm formation there is likely to be, both of which affect lapse rate.

I think that the basis for the calculation can be solar radiation reaching the upper troposphere,

Hmmm.

Which calculation are you trying to help?

In my TW calculation using that as the x-axis would just slightly stretch out the part of the graph where odd things are happening. In Willis’s version with real data, it would somewhat alter the shape of the curve in that region, which might be interesting.

But, neither solar radiation reaching the surface nor solar radiation reaching TOA is a reasonable proxy for radiative forcing due to increases in CO2, because neither of them incorporate the fact that radiative forcing from CO2 changes locally, depending on the local lapse rate.

Ireneusz Palmowski
Reply to  Bob Wentworth
October 19, 2022 12:25 am

When I say that the vertical temperature gradient is constant, I mean the global mean vertical temperature gradient. What happens if we assume that the troposphere, due to its density (caused by gravity), warms from the upper layers? Then we find that greenhouse gases are actually cooling the surface, because the vertical gradient decreases as water vapor increases.
It seems that the heat capacity of the troposphere is constant (fluctuates within a small range), so the global temperature increase is limited.

Last edited 1 month ago by Ireneusz Palmowski
Bob Wentworth
Reply to  Ireneusz Palmowski
October 19, 2022 1:15 pm

What happens if we assume that the troposphere, due to its density (caused by gravity), warms from the upper layers? 

Are you suggesting heat flow from the cooler upper layers to the warmer lower layers? (If so, that would be a violation of the 2nd Law of Thermodynamics.)

We know that the troposphere warms from (a) heat transfer up from the surface and (b) absorbed sunlight (much of which happens in low altitude clouds).

Then we find that greenhouse gases are actually cooling the surface, because the vertical gradient decreases as water vapor increases.

Convection generally keeps the lapse rate from getting vertical enough to really wipe out the GHE. Hight moisture makes the curve somewhat more vertical, but it’s still not vertical enough to wipe out the GHE.

This is directly checkable. GHE = (Surface emissions) – (Outgoing emissions at TOA)

There must be data for that.

Ireneusz Palmowski
Reply to  Bob Wentworth
October 20, 2022 4:25 am

No, it is not the “layers” that heat up, it is the incoming solar energy that heats up the troposphere, reaching ever denser layers of the atmosphere, all the way to the surface. Only the Sun is the source of heat, not the “layers.”

Bob Wentworth
Reply to  Ireneusz Palmowski
October 20, 2022 4:25 pm

I don’t know how to interpret your words “it is the incoming solar energy that heats up the troposphere, reaching ever denser layers of the atmosphere, all the way to the surface.”

That’s ambiguous enough that I can’t agree or disagree.

* * *

Here are something unambiguous that I know how to say:

The Sun is the ultimate source of all atmospheric heating. But, the Sun first delivers 2/3 of its energy to the surface, not directly to the atmosphere. So, everywhere in the atmosphere, a majority of solar heating occurs below that point, not above above it.

David A
October 17, 2022 1:29 pm

Quoting Willis; “Conclusion? Simple. 
It takes ~ 5 W/m2 of additional solar input to raise the surface temperature by a single degree C.”

And a 5W/m2 increase in LWIR raises the surface T ????

Would it not likely be less, perhaps considerably? After all, said energy over the oceans is utilized mostly in evaporate energy, possible negative feedback.

Will Wallace
October 17, 2022 1:31 pm

How ironic, more CO2, plant food, is not an existential threat to the planet, and CO2 is not the control knob for climate. Why is it that whatever the political class touches, they cause pain and suffering?

The Real Engineer, CEng etc.
October 18, 2022 12:43 am

It is very interesting that Willis has just found a bit of actual thermodynamics from climate data. This flatline is caused by… it is the first law of thermodynamics, that is that heat only flows from hot objects to cold ones. This probably needs a bit of explanation here, because the radiant energy from the sun does not have an obvious temperature, and is always assumed to be “very hot”. This is not strictly speaking true, the wavelength of the thermal energy is directly related to the “temperature”, because it is really energy transfer we are talking about, temperature is only an indicator of energy. Once the surface temperature matches the thermal profile of the incoming energy, temperature cannot increase! Discussion welcome!

Bob Wentworth
Reply to  The Real Engineer, CEng etc.
October 18, 2022 10:40 am

it is the first law of thermodynamics, that is that heat only flows from hot objects to cold ones.

Actually, that’s the 2nd Law.

At that’s not what’s causing the flatline, and least, not in the way you seem to be suggesting.

The flatline is caused by the onset of powerful tropical convection and thunderstorm formation. These efficiently convey heat from surface to the atmosphere, and shade the surface from sunlight.

The heat doesn’t just disappear, however. It i transported to higher latitudes and causes warming there.

the wavelength of the thermal energy is directly related to the “temperature”, because it is really energy transfer we are talking about, temperature is only an indicator of energy. Once the surface temperature matches the thermal profile of the incoming energy, temperature cannot increase! Discussion welcome!

So, yes, it’s true that the “thermal profile’ of sunlight means nothing can be raised to a higher temperature than the Sun by shining sunlight on it. That’s around 6000 K, so is not relevant to why things might not get hotter than a certain level on Earth.

However, it’s not well understood that the limitation of sunlight not being able to warm things to hotter than the temperature of the Sun doesn’t necessarily have anything to do with wavelength.

As you say, temperature is an indicator of energy. So, all that matters in determining the temperature of an illuminated object is: how much energy is is receiving, and how hot does it need to get to lose heat at an equal rate?

Wavelength doesn’t generally factor into that.

So, why can’t a giant magnifying glass or solar concentrator raise objects at the focus to higher than the temperature of the Sun?

It’s not about wavelength, but is the result something obscure called the Etendue of sunlight. That places limits on how much it can be concentrated.

Steve Keppel-Jones
Reply to  Bob Wentworth
October 20, 2022 11:50 am

That conclusion about etendue is slightly misleading, I think, Bob. Etendue prevents you from concentrating light from an area onto an arbitrarily small point, but does not explain why a target object cannot get hotter than the source. That limitation is a first-law consequence. Xkcd explained this well: https://what-if.xkcd.com/145/

Bob Wentworth
Reply to  Steve Keppel-Jones
October 21, 2022 12:41 am

Thanks for the reference to that great XKCD What If? writeup by Randall Munroe.

However, after reading Randall’s writeup, I don’t see why you would suggest that a target object not getting hotter than the source is “a first-law consequence” and not a consequence of conservation of Etendue.

The 1st LoT (conservation of energy) of course applies, but doesn’t seem to be in any way the key to the issue.

The 2nd LoT (heat flows spontaneously only from warmer to cooler) does, of course, tell us that it has to be true that concentrating light can’t make the target hotter than the source.

But, leaving the explanation at the level of “the 2nd LoT forbids it” doesn’t fully clarify the how and why of focused light not being able to make something hotter than the source.

As Randall explains, the principle of Etendue does explain it (more specifically than does invocation of the 2nd LoT).

As Randall says:

There’s another way to think about this property of lenses: They only make light sources take up more of the sky; they can’t make the light from any single spot brighter, because it can be shown that making the light from a given direction brighter would violate the rules of étendue. In other words, all a lens system can do is make every line of sight end on the surface of a light source, which is equivalent to making the light source surround the target. If you’re “surrounded” by the Sun’s surface material, then you’re effectively floating within the Sun, and will quickly reach the temperature of your surroundings.

So, I’m glad to have a chance to explore this issue a bit more fully, but I stand by my conclusion that the reason concentrated sunlight can’t raise the temperature of a target to beyond the temperature of the Sun:

  • may be understood as being a consequence of the rules of étendue and
  • doesn’t have anything to do with the wavelength / spectrum of sunlight.

To be more precise, the constraint has to do with the combination of the rules of étendue and the Stefan-Boltmann law, which says that the radiative flux at the surface of the Sun has a value 𝜀 (Tsun)⁴. Those two together guarantee that that the radiative flux delivered to the surface of the target can’t be greater than 𝜀 (Tsun)⁴, which is what guarantees that light absorbed by the target can’t possibly raise the temperature of the target to higher than Tsun.

Notice that the argument nowhere depends on the particular wavelengths that predominate in sunlight.

Going back to the original comment, it said:

“the wavelength of the thermal energy is directly related to the “temperature”, because it is really energy transfer we are talking about, temperature is only an indicator of energy. Once the surface temperature matches the thermal profile of the incoming energy, temperature cannot increase”

In view of the full picture we’re now getting, having read Randall’s explanation and noting the relevance of the SB law, it seems fair to say that:

  • Sunlight does effectively have a “temperature” (characteristic of the temperature of the emissive surface of the Sun)
  • That “temperature” of sunlight is associated with multiple characteristics of the light, including not only its wavelength/spectrum, but also its étendue and the intensity of radiant flux at the source.
  • It is the latter two characteristics (étendue and radiant flux at the source) which guarantee that concentrated sunlight can’t cause a target to exceed the temperature of the Sun; the wavelength/spectrum of sunlight doesn’t enter into that conclusion.
Steve Keppel-Jones
Reply to  Bob Wentworth
October 24, 2022 10:27 am

Good points for discussion, Bob, and you are right, I should have said 2nd law instead of 1st. My takeaway from Randall’s lovely writeup, though, is that etendue is related to the direction of photons (itself a bit of a slippery concept, they travel in waves, not necessarily straight lines), and not to their temperature (which is very closely related to wavelength by Wien’s law). Temperature, of course, is a measure of energy. Since emission temperature is directly related to wavelength, and the 2nd law prevents a target object from getting hotter (temperature) than the source, I think the wavelength is a critical part of the conclusion, and etendue isn’t.

(That’s not to say that I have any clue what would happen if you could simply get rid of etendue somehow! I am sure that it is just as fundamental as the 2nd law, and everything is tied together whether we realize it or not.)

Randall’s main point is that although you can redirect light all day long and anywhere you want, you cannot “intensify” it (make it brighter, therefore more energetic, therefore hotter) passively. That requires extra energy as input.

Bob Wentworth
Reply to  Steve Keppel-Jones
October 24, 2022 11:38 am

etendue is related to the direction of photons (itself a bit of a slippery concept, they travel in waves, not necessarily straight lines)

There are two distinct ways of thinking about light, the classical interpretation or the quantum interpretation. For many purposes, the classical interpretation is just fine. The concept of étendue is most often used by those working within the classical perspective; so, it’s usually not thought of as being about photons.

From a classical perspective, conservation of étendue means: if you take light from a given source and squeeze it to fit through a smaller opening, it will be spreading out over a wider range of angles; or you can reduce the range of angle, but then you’ll need a larger area to gather all the light.

* * *

photon… temperature (which is very closely related to wavelength by Wien’s law).

You would be surprised at how little relationship there is between temperature and wavelength.

You might want to read this essay of mine, in response to someone over-interpreting Wien’s law.

A few points are worth noting:

  • If one object has double the temperature of the other, the two objects will still be emitting light at ALL of the same wavelengths. Given the wavelength of a particular bit of light, there is no way whatsoever of determining the temperature of the source.
  • As temperature shifts, this only shifts the peak of the emission spectrum, and the relative intensity at different wavelengths. The range of wavelengths emitted his huge, compared to the shift in peak wavelength that is associated with modest temperature changes.
  • The “peak” wavelength that Wien’s law gives you is completely dependent on the particular way that you plot the graph of the spectrum (e.g., as a function of wavelength, or frequency, or log-frequency, or something else). There are actually multiple forms of Wien’s law to reflect that reality, though only the one for plotting as a function of wavelength is widely none. For different ways of plotting the spectrum, the peak occurs at an entirely different place. The “peak” is entirely an artifact of the way that you choose to plot the spectrum. It has very little relation to any actual physics.

Since emission temperature is directly related to wavelength, and the 2nd law prevents a target object from getting hotter (temperature) than the source, I think the wavelength is a critical part of the conclusion, and etendue isn’t

In my long comment to Real Engineer, I explicitly worked through the analysis of how concentrating sunlight affects the temperature of the object being illuminated.

  • Wavelength appears nowhere in that analysis. It’s simply not relevant.
  • I did use étendue in my analysis; it was critical to understanding how, in a solar concentrator, there is a coupling between how much energy an object can receive from a source, and to what extent that object continues to radiatively “see” the environment around it.

So, I continue to disagree with your thesis that wavelength is somehow of primary importance.

That’s not to say that I have any clue what would happen if you could simply get rid of etendue somehow! I am sure that it is just as fundamental as the 2nd law, and everything is tied together whether we realize it or not.

Yes, all sorts of principles fit together to form a coherent, self-consistent whole.

The 2nd Law and conservation of étendue are different sides of the same coin.

Randall’s main point is that although you can redirect light all day long and anywhere you want, you cannot “intensify” it (make it brighter, therefore more energetic, therefore hotter) passively. That requires extra energy as input.

Yes. And, it is unexpectedly subtle, what it means to “intensify” light. In some common notions of intensity, certainly focusing sunlight into a tiny spot “intensifies” the light. It’s within the context of a particular technical notion of “intensity” that if’s fair to say, lenses “can’t make light brighter.”

Interesting stuff.

Steve Keppel-Jones
Reply to  Bob Wentworth
October 26, 2022 6:03 am

Very interesting stuff indeed, and not necessarily all that intuitive! I will have to think about the relationship between 2nd law and etendue some more, and why you say that etendue is more important than wavelength in applying that law. Certainly although temperature is related to wavelength, you cannot determine temperature from the wavelength or energy of a single photon, and I don’t think I tried to imply that. As you say the temperature only affects the peak of the distribution, and there is a lot of overlap between energies of individual photons at similar object temperatures.

The relationship between classical and quantum descriptions of light probably trips up a fair number of people, and I see some confusion on that point around here. But for thermodynamics work, as you say, the classical descriptions are generally entirely adequate. (In quantum land, thermodynamics doesn’t really apply, since notions of time dependence, entropy, work, and power are pretty much totally absent.)

I’ll get to your other posting below in a bit…

Bob Wentworth
Reply to  Steve Keppel-Jones
October 26, 2022 8:48 am

I will have to think about the relationship between 2nd law and etendue some more, and why you say that etendue is more important than wavelength in applying that law.

When it comes to calculating actual temperatures and heat exchange, one almost never “applies” the 2nd LoT. Rather, one does calculations based on energy flows and temperatures, and it’s always an emergent consequence that the 2nd LoT is honored.

It’s not always true that étendue is more important than spectrum (which seems like a better characterization than talking about wavelength, as if there was only a single wavelength that mattered). It depends on the situation being analyzed, whether étendue or spectrum will affect energy transfer:

  • When you are concentrating light to an extreme, then it is étendue that prevents the energy transfer from getting high enough for the temperature of the object of interest to exceed the temperature of the heat source.
  • If you are applying a hypothetical extreme GHE, then it is spectrum that prevents the energy transfer from getting high enough for the temperature of the object of interest to exceed the temperature of the heat source: as the two temperatures get close, it is no longer possible for the atmosphere to let in light from the source, while “trapping” emissions from the surface, due to shifts in the emission spectrum.
  • When it comes to examining temperatures in the context of climate, étendue probably never matters, and spectrum matters only when one gets into precise calculations—at a crude level, it’s unimportant.

Determining temperatures is always about energy transfer. Various factors can affect energy transfer to varying “degrees.”

In quantum land, thermodynamics doesn’t really apply, since notions of time dependence, entropy, work, and power are pretty much totally absent.

All of those (except perhaps “work”?) do get engaged with quantum mechanically at times. But, they’re mostly easier to deal with in the classical realm.

The Real Engineer, CEng etc.
Reply to  Bob Wentworth
October 21, 2022 10:37 am

Sorry Bob but you are confusing yourself. Yes with a lens I can raise an object to a high temperature, but not if I simply put a black object in sunlight. With a lens or mirror concentrator I am collecting more energy per unit area, and focusing it at a point but that has little to do with the sun surface temperature. Temperature is not the parameter that is important here, it is energy only. The electrical analogy is the voltage between two points, but the controlling power is the actual energy transfer. The voltage needed to transfer that current (energy) depends on the circuit resistance (Ohms law).

Back to your point (and mine), the actual temperature of an object in sunlight depends on: solar irradiance (W/m2), emissivity (equal in loss or gain of energy), convective loss, radiated energy (W/m2), and most important the relative temperature of the object and the radiation absorber and the convective absorber. Lets forget convection transfer, as almost everyone always does and examine an ideal black body for a moment. All of the incoming radiant energy is absorbed and the temperature of the body rises until the radiated energy matches the incoming energy. It does not rise forever, and given an ideal absorber around it (at 0k) will hardly rise at all.

When objects change in temperature the radiated thermal spectrum changes, the higher the temperature the shorter the wavelength of some radiated energy. This is how IR thermometers work, the ratio of some arbitrary long and short wavelength detectors outputs. The overall intensity doesn’t matter, just the ratio outputs of the detectors with suitable wavelength filters over each.

The question then is the thermal resistance of the atmosphere to space (very cold).
Our problem is that the heat gain and loss to the Earth are very closely balanced, and the degree of balance varies greatly with atmospheric conditions, clouds, water vapour content etc. and the emissivity of the surface that again varies fairly widely depending on ground type and cover.

I see the problem in these terms as I am not interested in “greenhouse gases” as such, or anything else that is used as a point of confusion more than anything very useful. Greenhouse gases will vary the thermal resistance of the atmosphere in some very calculable and measurable way, and we see this directly with clouds and night-time cooling rates. The feedback effects alleged are irrelevant, there is exactly one mechanism of heat loss for radiation, and probably one which is convection from the surface to the cold outside of the atmosphere. The effect of “feedbacks” is only to change the apparent thermal resistance to heat loss, again a very understandable and measurable thing. I think this is a very suitable thermodynamic description of the climate change argument, and may be an insight into why no one has made much scientific sense for a long time. Willis’s insights above fit my description rather well, but of course anyone may disagree.

Bob Wentworth
Reply to  The Real Engineer, CEng etc.
October 22, 2022 3:18 am

Sorry Bob but you are confusing yourself.

I’m pretty sure I’m not even slightly confused about my understanding of the issues. There is, however, apparent confusion between us, with a lack of mutual understanding happening. 

I wonder what we can do to sort out that imperfect communication?

With a lens or mirror concentrator I am collecting more energy per unit area, and focusing it at a point but that has little to do with the sun surface temperature. Temperature is not the parameter that is important here, it is energy only.

Yes, it’s “energy only” and I am entirely focused on energy. I am interested in temperature only insofar as it affects energy flows.

When it comes to some thermodynamic issues, the way temperature affects energy flows is critical.

In the case of hypothetical super-efficient solar concentrators, even the Sun’s temperature becomes relevant to the energy flows.

* * *

To spell that out more precisely, let’s work with the energy flow per unit time and area, in particular, the radiance (measured in W/m²) of SW and LW radiation. (It’s call irradiance when it is inbound to a system, but the term radiance can be used more generally, for inbound or outbound fluxes. Radiance also has other names.) 

I will denote radiance by the symbol E:

  • Es = the Sun’s emission flux – radiance at the surface of the Sun
  • Eo = the solar irradiance averaged over the surface of the target object

The laws of étendue guarantee that, even after concentration:

Eo ≤ Es

It happens that the Stefan-Boltzman law tells us 

Es = 𝜀s σ Ts⁴

where 𝜀s and Ts are the emissivity and temperature of the Sun. So, the SB law and the laws of étendue together guarantee that

Eo ≤ 𝜀s σ Ts⁴

This is ENTIRELY a matter of constraining the amount of ENERGY flowing to the object at the focus on the solar concentrator.

Yes, energy is what is important. But, contrary to what you are saying, the surface temperature of the Sun is important to determining how large that energy flow could potentially be.

My later analysis in this comment shows explicitly that (in the absence of  losing irradiance to absorption or reflection, an ideal solar concentrator could raise an object to the temperature of the Sun’s surface, but not hotter. Again, on at least a theoretical basis, the temperature of the Sun’s surface is relevant.

I was originally drawn into this discussion because you had written “the wavelength of the thermal energy is directly related to the “temperature”… Once the surface temperature matches the thermal profile of the incoming energy, temperature cannot increase!”

I was concerned that your words might indicate you had some confusion about what it meant to “match the thermal profile of the incoming energy”, perhaps you thought that matching the “thermal profile” related to with matching the wavelength in sunlight, since that’s all you wrote that seemed to identify what you might mean by “thermal profile.”  But matching the “thermal profile,” DOESN’T have anything to do with wavelength. The “thermal profile” of sunlight that matters in that regard has to do with etendue and radiance in combination. Those collectively determine how much energy can be delivered to an object.

* * *

The electrical analogy is the voltage between two points, but the controlling power is the actual energy transfer. The voltage needed to transfer that current (energy) depends on the circuit resistance (Ohms law).

Are you trying to say that the temperature difference is analogous to voltage, that the temperature difference is what determines the rate of energy transfer? And that, beyond determining the rate of energy transfer, the temperature difference isn’t so important?
If so, then I agree with you.

* * *

This comment eventually addresses everything in your comment, and provides an excess of explicit analysis as well. (I include analysis for the full range of theoretically possible solar concentrators.)

But, for the moment I want to skip ahead to the end of your comment.

The question then is the thermal resistance of the atmosphere to space (very cold).

I used to focus on the “thermal resistance” of the atmosphere. It’s “sort of” right. But, it doesn’t really support understanding as well as it could, because it is based on a roughly linear relationship between heat flow and temperature difference, and radiative heat transfer isn’t remotely linear.

I’ve realized that, instead of thinking about thermal resistance,  it’s more helpful, at least for quantitative purposes, to think about the “effective emissivity reduction” provided by the atmosphere.

Average planetary equilibrium surface temperature can be expressed as:

Ts = [Sn / (σ 𝜀 𝛾ₜ (1 – g) )] ^(¼)

where 

  • Ts is average surface temperature
  • Sn is absorbed solar irradiance, 
  • 𝜀 is the weighted-average surface emissivity
  • 𝛾ₜ is a factor greater than one associated with non-uniform surface temperatures that effectively boosts emissivity, slightly lowering the average surface temperature
  • g is the normalized greenhouse effect, g = (1 – [outgoing emissions]/[surface emissions]) = 0.4 on Earth at present. A nonzero value of g is possible only because things in the atmosphere absorb or scatter longwave radiation. A nonzero g value effectively decreases emissivity, raising the temperature. On Earth, the formula says that the nonzero value of g increases the average surface temperature T by about 35℃.

The above formula is an EXACT result, with NO approximations or assumptions. The only thing the formula relies on are the definitions of the various quantities involved.

As you can see, everything that affects temperature shows up in this formula as either altering that amount of absorbed sunlight, or as altering the effective emissivity of the planet.

“Thermal resistance,” with its assumption of a relatively fixed ratio between heat flow and temperature difference, isn’t a great fix to a phenomenon in which heat flow scales as the fourth power of temperature.

I see the problem in these terms as I am not interested in “greenhouse gases” as such, or anything else that is used as a point of confusion more than anything very useful. Greenhouse gases will vary the thermal resistance of the atmosphere in some very calculable and measurable way, and we see this directly with clouds and night-time cooling rates

Yes, Greenhouse gasses do vary the thermal resistance of the atmosphere, or more clearly (at an analytic level), the effective emissivity of the planet, in very calculable and measurable ways.

That makes it rather puzzling why you are “not interested” in them, or why you seem to think that considering them is “not very useful.” What do you mean by that?

The feedback effects alleged are irrelevant, 

In what sense are they irrelevant?

In my planetary temperature formula above, feedbacks alter absorbed solar irradiance, surface emissivity, the temperature variation distribution and hence the term 𝛾ₜ, and especially the normalize greenhouse effect g. They alter every factor that goes into determining average surface temperature. It seems odd to call them “irrelevant.”

there is exactly one mechanism of heat loss for radiation, and probably one which is convection from the surface to the cold outside of the atmosphere.

If you talk at a sufficiently gross level, then any complex system can be alleged to be just “one” thing. The question is what you’re achieving by doing that?
Are you saying that talking about “feedbacks” is addressing a level of detail which is an unhelpful diversion, in a context where people don’t understand the primary effect―so it’s a waste of time to bring in secondary effects.

If that’s what you’re saying, then I might agree with you.

The effect of “feedbacks” is only to change the apparent thermal resistance to heat loss, again a very understandable and measurable thing. I think this is a very suitable thermodynamic description of the climate change argument, 

Yes, at a gross level, the core of it all is that increasing Greenhouse gas concentrations changes the effective emissivity of the planet (or more crudely the thermal resistance of the atmosphere), thereby increasing the average surface temperature.
There would probably be less confusion circulating if that core understanding was more widely understood.

and may be an insight into why no one has made much scientific sense for a long time. Willis’s insights above fit my description rather well, but of course anyone may disagree.

Are you citing Willis as an example of someone whose insights above fit the description of not making much scientific sense?

If so, then sadly, I must agree with you, though I respect how hard and creatively he tries.

* * *

Now, back to the remainder of your comment. My response may be a bit excessive, in terms of the level of analysis offered.

I was really curious to work through exactly how it all works when a solar concentrator is involved.

Sorting that out was inspired by the XKCD What if? analysis discussed in another comment.

* * *

the actual temperature of an object in sunlight depends on: solar irradiance (W/m2), emissivity (equal in loss or gain of energy), convective loss, radiated energy (W/m2), and most important the relative temperature of the object and the radiation absorber and the convective absorber. 

Agreed. I’m about to write out an equilibrium energy balance equation for the object put what you’re talking about into concrete terms.

I am going to do one thing that may be a little fancier than what you were thinking of. I want to account for what happens if a solar concentrator is present. If we set the concentration ratio to 1, that will reduce things to the special case of no concentrator.

* * *

It took me much of the day to figure out how to handle a solar concentrator in a rigorously correct way that obeys the laws of étendue. The one simplification that thinking about concentrators forced me to make was to assume that the object we are investigating the temperature of is spherical.

One implication of that assumption is that, with no concentrator present, the solar irradiance averaged over the surface of the object is:

Eo = Ei/4 = Et (1-𝛼)/4  {when concentration ratio R=1}

where

  • Et = the Total Solar Irradiance (TSI)
  • Ei = (1-𝛼) Et = the incident solar irradiance measured normal to the sunbeam, just before entering on the solar concentrator (or illuminating the object directly in the absence of a concentrator)
  • 𝛼 = net atmospheric absorption and  reflection of incoming sunlight

Earth’s TSI is Et = 1361 W/m², and on an area-averaged basis, 185 W/m² out of 340 W/m² reach the surface, so we can take atmospheric absorption and reflection as 𝛼 = 0.46, so that atmospheric transmittance is (1-𝛼) = 0.54.

Thus, on average, Ei/4 = 185 W/m².

The strength of our solar concentrator can be parameterized by either of two related parameters:

  • F — the fraction of what the object radiatively “sees” that is the Sun; while (1-f) represents the fraction of what the object radiatively “sees” that is the local environment. What I mean by radiatively “sees” technically refers to the radiation view factor for radiative heat transport. 
  • R  — the concentration ratio, indicating by what factor the object is receiving more solar energy than it would have in the absence of the solar concentrator

More information on these parameters:

  • F ranges from a minimum of Et/Es ≈ 2.1e-5 at Earth’s orbit to a theoretical maximum of 1. (Et/Es is the ratio of TSI at Earth’s orbit to the radiance emitted at the surface of the Sun.)
  • R ranges from a minimum of 1 to a theoretical maximum of Es/Et = 1/(Et/Es) ≈ 4.6e4
  • F = R⋅(Et/Es)
  • R = F/(Et/Es)

The solar irradiance the object receives averaged over its entire surface area is:

  • Eo = R⋅Ei/4 = F⋅(1-𝛼) Es

From this, we see that R indicates how much the rate of solar radiation energy being received is boosted above the rate of solar energy that would be received without a concentrator; and F indicates how close the rate of solar radiation energy being received is relative to what would be received if the Sun’s surface effectively surrounded the object.

* * *

I will write out the energy balance equation for the object in equilibrium, and we can see if that matches how you think things work:

In equilibrium, (energy in rate) = (energy out rate), so:

ao⋅Eo + [(1-F)⋅𝜀o⋅σ⋅Te⁴] = [𝜀o⋅σ⋅To⁴] + NRH(ΔT)

where
 

  • (Temperature superscripts above indicate the fourth power)
  • F = fraction of what the object radiatively “sees” is the Sun; i.e., view factor from object to the Sun
  • (1-F) = fraction of object illuminated by environmental thermal radiation; i.e., view factor from object to the environment
  • ao = shortwave absorptivity of target object
  • 𝜀o = longwave emissivity of target object
  • To = temperature of target object
  • Eo = average irradiance illuminating the surface of the target (¼ incident solar irradiance if no concentrator)
  • Te = temperature of environment
  • ΔT = To- Te = temperature difference between object and environment
  • NRH(ΔT) = non-radiative heat transfer rate from object to environment (i.e., heat loss from convection and conduction)

Energy gain terms are:

  • ao⋅Eo = target’s rate of energy absorption from sunlight, averaged over the surface. (The view factor F doesn’t explicitly appear in this term because it has been implicitly included in the definition of Eo; the view factor would become explicit if we substituted in Eo = F⋅(1-𝛼) Es.)
  • (1-f)⋅𝜀o⋅σ⋅Te⁴ = target’s rate of energy absorption from environmental blackbody thermal. (If there is no concentrator or for most commonplace solar concentrators, (1-F) is so close to 1 that it’s entirely normal to omit this term; it would be relevant for the real concentrators that have achieved temperatures of thousands of Kelvins. I’ve included it just so we can find out what happens in the case of the best possible hypothetical concentrator.)

Energy loss terms are:

  • 𝜀o σ To⁴ = target’s rate of emitting thermal radiation
  • NRH(ΔT) = rate of non-radiative (e.g., convection) heat transfer to the environment

Does that align with your thinking (aside from all the complications I’ve added to reflect solar concentration)?

(If you haven’t previously encountered the notion of “radiation view factor”, the inclusion of that might be unexpected. As I said, in the case of the Sun, it’s unimportant to include this for any practical purposes; I’m including it so we can look at theoretical extreme cases.)

* * *

Lets forget convection transfer, as almost everyone always does and examine an ideal black body for a moment. All of the incoming radiant energy is absorbed and the temperature of the body rises until the radiated energy matches the incoming energy. 

Ok, in my formulation, that means NRH(ΔT) = 0 and at = 𝜀t = 1. 

Then the equilibrium energy balance equation becomes

 To = [Eo/σ + (1-F)⋅Te⁴]^(¼)    {Exact}

(The superscript on temperature is the 4th power, in case it’s not legible.)

If the object temperature Tt is a lot higher than the environmental temperature Te, that’s about as far as we can go. But, if ΔT is small compared to To, then I show below that

To ≈ Te +  Eo/(4σ⋅To³)   {For small ΔT}

* * *

It does not rise forever, and given an ideal absorber around it (at 0k) will hardly rise at all.

I agree that it doesn’t rise forever. My formulas indicate the final equilibrium temperature.

However, I don’t agree that “given an ideal absorber around it (at 0k) will hardly rise at all.”

If I set the environmental temperature to Te = 0, then the exact formula for Tt becomes To = [Eo/σ]^(¼)  It there is no concentration of sunlight, so R=1, then for the previously calculated value of Eo when R=1, one finds

To = 239 K / -34℃

I don’t know what starting temperature you were assuming, but given an environmental temperature of 0 K, I’d assume the object started at near 0 K. In my mind, rising to a temperature of 239 K / -34℃ would not be “hardly rising at all.”

But, maybe you meant something else?

* * *

For what it’s worth, for a perfect solar concentrator, with F=1, then Eo = (1-𝛼) Es where Es is the radiance at the surface of the Sun, and the temperature would turn out to be

To = 4,970 K

That’s cooler than the Sun just because 46% of the solar irradiance was assumed to have been absorbed in the atmosphere.

If one assumed no absorption (𝛼=0) and perfect concentration (F=1), then the object would reach the same temperature as the surface of the Sun.

I found one claim that real solar concentrators have achieved 2300 K.

* * *

When objects change in temperature the radiated thermal spectrum changes, the higher the temperature the shorter the wavelength of some radiated energy. This is how IR thermometers work, the ratio of some arbitrary long and short wavelength detectors outputs. The overall intensity doesn’t matter, just the ratio outputs of the detectors with suitable wavelength filters over each.

I’m aware of all that.

* * *

Our problem is that the heat gain and loss to the Earth are very closely balanced, and the degree of balance varies greatly with atmospheric conditions, clouds, water vapour content etc. and the emissivity of the surface that again varies fairly widely depending on ground type and cover.

Why do you see this as a problem?

The balance exists primarily on a global average basis. Advection provides a lot of lateral transport, and there is nowhere near balance on the basis of radiation alone, in most locations.

Most of those variations have been well-studied, and are usually understood at the level of averages in each individual map gridcell,

So, in what sense is the “our problem”?

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 
ANALYSIS DETAILS: SMALL ΔT CASE

If ΔT = Tt – Te is much smaller than Tt, and F is much smaller than 1, it can be shown that it’s approximately true that

To⁴ – (1-F) Te⁴ 
= To⁴ – (1-F) (To – ΔT)⁴ 
≈ To⁴ – (1-F) (To⁴ – 4 To³ ΔT) + (smaller terms)
= F⋅To⁴ + 4 To³ ΔT + (smaller terms)

(The ΔT term includes temperature to the 3rd power, in case it’s not legible.)

So the energy balance equation becomes approximately

Eo/σ = F⋅To⁴ +  4 To³ ΔT

ΔT ≈ Eo/(4σ⋅To³) – F⋅To/4 

If ΔT is small enough for this to be a valid approximation, F will be so small the final term is negligible. So

ΔT ≈ Eo/(4σ⋅To³) 
To = Te +  Eo/(4σ⋅To³)   {For small ΔT}

So, that’s the small-ΔT result for the object temperature To that corresponds to thermal equilibrium.

Steve Keppel-Jones
Reply to  Bob Wentworth
October 24, 2022 10:34 am

I am not sure if Real Engineer will follow up to this post, Bob, but I will reply to this part of it, where you wrote, near the top:

“in particular, the radiance (measured in W/m²) of SW and LW radiation. (It’s call irradiance when it is inbound to a system, but the term radiance can be used more generally, for inbound or outbound fluxes. Radiance also has other names.) I will denote radiance by the symbol E:

  • Es = the Sun’s emission flux – radiance at the surface of the Sun”

I think you are already confused by this point in your posting. You can’t measure “radiance” of an object, or “flux”, in W/m^2, in isolation from any other object. There isn’t any such thing. You can only measure Watts when you have a temperature differential between two objects, and then the S-B law comes into play. The Sun does not emit Watts intrinsically. Light in general is not measured in Watts. It is measured in temperature (or Joules, or electron-volts, all equivalent). See if you can correct this part of your thinking, and then see what the rest of your posting would look like…

Bob Wentworth
Reply to  Steve Keppel-Jones
October 24, 2022 12:38 pm

Bob: in particular, the radiance (measured in W/m²) of SW and LW radiation. (It’s call irradiance when it is inbound to a system, but the term radiance can be used more generally, for inbound or outbound fluxes. Radiance also has other names.)

By the way, due to some bad Wikipedia content, I got that wrong. “Radiance” is not an umbrella term that include “irradiance.” It has different units.

It’s “irradiance” or “flux density” when received by a surface, and “radiant exitance” when emitted by a surface.

* * *

You can’t measure “radiance” of an object, or “flux”, in W/m^2, in isolation from any other object. There isn’t any such thing. You can only measure Watts when you have a temperature differential between two objects, and then the S-B law comes into play. The Sun does not emit Watts intrinsically.

You seem to be echoing ideas from a frankly muddled way of thinking that is making its way around the internet. I have a Ph.D. in Applied Physics with a sub-specialty in a subfield of applied optics. In my experience, what you’re describing is not how scientists think about these issues.

Worse, what you are describing is not even a viable, self-consistent way of thinking about things (unless some very subtle adjustments are made that I’ve never seen be present in the discussions I’ve seen floating around on the internet).

Note that not all thermal emissions are detected by a means that has anything to do with temperature differences.

That’s the preferred technology for detecting the “flux” in W/m^2 for only a very limited range of the electromagnetic spectrum.

For both shorter and longer wavelengths, the detection technologies have nothing to do with temperature. Planck’s law and the Stefan-Boltzmann law are found to operate at all the wavelengths that don’t rely on temperature differences for detection, so why shouldn’t they operate in the same way for those wavelengths as well?

The Sun provides a good example for thinking through how problematic your hypothesis is.

The Sun generates 386 yottawatts (386e24 W) of heat internally, through nuclear fusion.It is a fundamental principle of thermal physics that, in equilibrium, the temperature of an object will be the temperature at which the rate of energy coming “in” and the rate of energy going “out” are equal. This principle allows us to explain the temperature of the Sun’s surface.The Sun has a radius of about 6.9e5 meters, and so a surface area of 6e18 m². That means it needs to get rid of energy at a rate of 6.4e7 W/m² in order to maintain a steady temperature.According to the SB law, the Sun will emit radiation with that much power if its surface has a temperature of 5800K — which is the Sun’s observed surface temperature.Under your hypothesis, the Sun isn’t really putting out any power unless there is an object for it to exchange power with. But, if one looks out into the universe, it’s mostly nothing in every direction. Stars and planets make up only an infinitesimal fraction of the night sky. So, most of the light that the Sun emits will never interact with another object.So, under your hypothesis, the Sun does NOT emit that 386 yottawatts of energy.In that case, under your hypothesis, the Sun is generating 386 yottawatts of energy, but losing only an infinitesimal fraction of that.Therefor, under your hypothesis, heat should keep on building up inside the Sun, and its temperature should be endlessly rising.We don’t observe that happening. So, your hypothesis is falsified.
Do you disagree with something in my analysis?

How could what you are saying possibly be true, and still have thermal physics make correct predictions?

* * *

Light in general is not measured in Watts. It is measured in temperature (or Joules, or electron-volts, all equivalent).

Of course light is measured in Watts.

If it’s not, how are you possibly going to measure the light emitted by a non-thermal source like an LED or a laser?

Light from those sources is in no way associated with any particular temperature (misinterpretations of Wien’s law notwithstanding).

Temperature, Joules, and electron-volts are absolutely not equivalent.

The latter two are units of energy; temperature is something entirely different, even if temperature and energy are in some ways related.

A given temperature change can correspond to wildly different amounts of energy, depending on the context.A photon with a given energy could have been emitted by a source at almost any temperature.Energy is a fundamental concept that arises (in a subtle way) from the time-translation-invariance of the laws of nature.Temperature is a statistical concept, meaningful only in the context of large numbers of particles or photons.Both conceptually and practically, temperature and energy are very different things.

* * *

See if you can correct this part of your thinking, and then see what the rest of your posting would look like…

I’m curious how you could analyze temperatures in complex situations, given your way of thinking. I predict it could predict correct answers in some simple scenarios, but that when things get complicated, it just won’t be workable.

Last edited 1 month ago by Bob Wentworth
Bob Wentworth
Reply to  Steve Keppel-Jones
October 24, 2022 1:25 pm

One thing I left out…

Light in general is not measured in Watts. It is measured in .. Joules

The definition of “Watts” is “Joules per second.” Watts is the rate at which energy arrives or leaves.

Light is energy moving. So, it’s incoherent to argue that light is about energy, but not about Watts. When energy moves, that’s measured in Watts.

* * *

Light in general is not measured in Watts. It is measured in temperature…

There is a who field of knowledge called “Radiometry” which relates to the measurement of light. Look at the list of units they use in radiometry for measuring light. None of those units are temperature.

Last edited 1 month ago by Bob Wentworth
Steve Keppel-Jones
Reply to  Bob Wentworth
October 26, 2022 2:05 pm

It is fascinating that you managed to get a PhD (Piled higher and Deeper) in Applied Physics while being so confused about the fundamentals of radiation, energy, and power.

Your fundamental misunderstanding is that EMR is not intrinsically power. That is nonsense. It is energy, in the form of a wave(function). This is a very fundamental definition and you must be very careful to understand it. Clear your mind of “how scientists think about these issues”, because most of the scientists thinking about these issues are trying to confuse you, and many of them deliberately. Remember that the fundamental unit an individual photon possesses is an electron-volt. Not an electron-watt. An electron-volt is a fraction of a Joule. Not a fraction of a Watt. You need to get this clear in your mind before you can understand any other part of this discussion. Nothing else will make the slightest bit of sense until you do, and instead, you will find yourself making nonsensical statements like these:

“Note that not all thermal emissions are detected by a means that has anything to do with temperature differences.”

and

“detecting the “flux” in W/m^2 for only a very limited range of the electromagnetic spectrum”

Hmm… I am not the one who is being inconsistent here.

Instead, my contrary claim, consistent with all the laws of physics, is that all thermal emissions, throughout the whole spectrum, are indeed detected by a means that definitely has something to do with temperature differences. This is much more consistent than what you wrote. What detection methods are you thinking of that don’t rely on temperature differences somehow? Certainly pyrgeometers do, and CERES space-borne radiometers, and AERI cryogenically cooled surface bolometers. All of them. Indeed the laws of physics demand this, and no one can escape them.

Then you wrote this equally nonsensical statement:

“Of course light is measured in Watts.”

It isn’t, because that’s not an intrinsic characteristic. Light has an intrinsic characteristic (among others) of wavelength, related to electron-volts, or Joules, and then multiples of those are aggregated as temperature, which is of course also a measure of energy. But, and this is the important bit, that is not the same as Watts.

Thus, when you look very closely at all the radiometry techniques, they all require a temperature differential, and then they measure a power from this, which is being produced by radiative energy flow. That is entirely valid as far as it goes, but claiming that they are measuring some sort of “intrinsic” power of the radiation in Watts isn’t, because, as I said, that is not an intrinsic characteristic. It depends on the temperatures of both the source and target, i.e. it is extrinsic. To pull this sleight-of-hand off, they usually suppress the exact temperature differential they based their measurement on, which is highly disingenuous and misleading on their part. (See if you can find, for example, the actual temperature of the thermistor heat sink on the CERES radiometers. I couldn’t, and not for lack of looking.) They are not violating the laws of physics, but they are being very fuzzy about how they are using those laws to come up with their results. They try to hide the temperature difference way down in the fine print on page 77 or so. But it is always there.

(In the case of pyrgeometers, they use the S-B equation incorrectly to convert negative power readings to fake positive ones, in order to invent a radiant greenhouse effect. Very sneaky! You can’t trust these slippery eels!)

Of course there is a trivial exception to this rule, which is that with no temperature differential you can nevertheless successfully and accurately measure a power of 0 watts of radiant energy flow. But I hope I don’t have to point that out before you try to use it as a counterexample to what I wrote.

Anyway, you then asked a series of questions based on your misunderstanding, like where does the Sun’s energy go, and how do LEDs work. We can get into all that, but we need to start with correct fundamentals. EMR is energy, not power. Let me know when you are ready.

Bob Wentworth
Reply to  Steve Keppel-Jones
October 26, 2022 9:37 pm

You seem to be hanging your hopes (for falsifying mainstream climate science) on the idea “EMR is energy, not power” and that that this means individual radiation power fluxes “aren’t real”—or something like that?

It appears as if you accept that radiative heat transfer between things at different temperatures is real.

If so, then perhaps your thesis is that:

  • Radiative heat transfer between things at different temperatures is real.
  • Aside from that, and power flows associated with thermal radiation is not real.

Is that anywhere near what you’re saying?

If so, it creates a possible problem, and, even it you have a solution for that, that thesis is not going to take you where you apparently want to go:

  1. Potential Problem: If radiation can transfer power only when that power is part of radiation heat transfer from one thing to another, then that would seemingly create a problem–how can the Sun and the Earth cool themselves into space? The Sun needs to shed the heat it produces from internal fusion reactions. The Earth needs to shed the heat it absorbs from the Sun. According to (my guess of) your hypothesis, power can be associated with radiation only when there is something at a lower temperature for radiation to transfer heat to. In your interpretation of things, how is heat transferred to space?
  2. Doesn’t help falsify the GHE: The idea that radiation can’t transfer power creates some inconvenience, but as long as your thesis accepts the reality of radiative heat transfer between something warmer and something cooler (and have a rationale for radiation being able to carry heat into space), then your thesis is not a problem (not even a minor hiccup) for GHE theory. Everything about the GHE can be expressed in either a “radiation power flow” perspective or in a “radiation heat flow” perspective. I imagine your thesis asserts that the first perspective “isn’t real.” Yet, the two perspectives are mathematically identical, producing 100% identical predictions. And, the latter perspective is entirely consistent with the constraints you apparently want to place on what is considered “real.” So, I don’t see how your thesis gets you anywhere that you would want to go.

But, maybe I’m jumping the gun, since you haven’t fully spelled out your thesis of how things do work. Maybe that’s yet to come?

* * *

Clear your mind of “how scientists think about these issues”, because most of the scientists thinking about these issues are trying to confuse you, and many of them deliberately.

I’m sorry to hear that you’ve had that experience. For what it’s worth, I’ve never personally witnessed an interaction where I thought the scientist was actively trying to confuse someone, though I’ve seen plenty of confusion resulting.

Would you be willing to consider the possibility that there’s just a communication gap that’s hard to cross, and most scientists aren’t very good at crossing that gap?

I think the world would function better if we were willing to give each other the benefit of the doubt.

* * *

Bob: Note that not all thermal emissions are detected by a means that has anything to do with temperature differences.”

Steve: Instead, my contrary claim, consistent with all the laws of physics, is that all thermal emissions, throughout the whole spectrum, are indeed detected by a means that definitely has something to do with temperature differences. This is much more consistent than what you wrote. What detection methods are you thinking of that don’t rely on temperature differences somehow? Certainly pyrgeometers do, and CERES space-borne radiometers, and AERI cryogenically 

We may be talking past one another due to some nuances in this topic.

Perhaps I should have phrased my claim differently.

What I meant was, for some types of EM radiation measurement in the IR range, they use pyrometers and bolometers and pyrgeometers may involve sensing heat transfer by allowing an element to warm up, and then measuring that warming effect. That is an approach that specifically relates to, and relies upon, radiative heat transfer.

But, not all detection of thermal EM radiation relies on heat transfer.

At shorter wavelengths, e.g, the visible range (where we can detect the Sun’s thermal emissions), they use semiconductor detectors like CCDs and CMOS detectors, which don’t rely on any heating effect from the detected photons, but instead absorbed photons generate electrical charge which is then measured..

At longer wavelengths, they detect thermal radiation using glorified radio receivers. The “cosmic microwave background radiation” is thermal radiation from the early universe. It was discovered using a big microwave dish (anecdotally, I used to play volleyball on a court next to that dish). Yes, they had to chill the sensor to a very low temperature to reduce noise levels sufficiently to measure the signal. But, the detector basically detected the signal because of the way the EM radiation wiggles electrons around, not because any measurable heat was being transferred.

* * *

And not all EM radiation is “thermal” radiation, yet the same detectors detect it:

  • Radiation from an LED or laser or klystron or radio antenna is NOT thermal radiation. (In the case of an LED or a laser, there is nothing in the device that is at a temperature associated with the light emission, and in all the cited cases, the radiation has characteristics very different than those of thermal radiation.)
  • The same detectors that detect thermal EM radiation can detect the EM radiation produced by those non-thermal sources. So, the nature of detecting EM radiation doesn’t seem to simply be inherently about temperature differences.

But, I don’t understand what point you’re trying to make. So, maybe we’re talking at cross purposes.

Steve: Then you wrote this equally nonsensical statement: 

Bob: “Of course light is measured in Watts.”

Steve: It isn’t, because that’s not an intrinsic characteristic.

Hmmm… Of 17 quantities that the SI system of units has standardized as relevant to the measurement of electromagnetic radiation, 14 involve Watts. So, it seems a bit strong to call the idea of measuring light in Watts “nonsensical.” Certainly, many people do measure EM radiation in terms of Watts.

it isn’t [measured in Watts], because that’s not an intrinsic characteristic. Light has an intrinsic characteristic (among others) of wavelength, related to electron-volts, or Joules, and then multiples of those are aggregated as temperature, which is of course also a measure of energy. But, and this is the important bit, that is not the same as Watts.

In classical electromagnetism, power is an inherent characteristic of the radiation, specified by the Poynting vector.

In quantum mechanics, power is a characteristic of an ongoing flux of photons, not something usefully applied to an individual photon. So, if each photon has an energy of 1.2 eV = 2.0e-19 Joules, then a flux of 5e18 photons/second has a power of 1 Watt.

Watts or Joules/second is a measure of how fast energy is flowing. Given that EM radiation is the only form of energy that is always, intrinsically, moving, it seems a little odd to argue that the unit for measuring the movement of energy is not relevant to EM radiation.

What do you have against Watts anyway? Don’t you believe in radiant heat flow? That’s measured in Watts. So, your objection isn’t really about Watts, is it—it’s about something else?

* * *

EMR is energy, not power. 

Saying EM radiation is energy but not power is like saying that water is gallons, not gallons per minute. Water isn’t actually either of those things. It’s water. But, it has various characteristics that can be useful to measure.

Light is not energy. It’s light. It carries energy, and when there are more than a few photons, it also carries power, since power is simply the movement of energy.

* * *

I don’t want to get mired in a philosophical argument about what sort of measurements are morally or epistemologically superior to others.

Can we try to ground the discussion in the practical, i.e., what actually affects outcomes?

* * *

when you look very closely at all the radiometry techniques, they all require a temperature differential, and then they measure a power from this, which is being produced by radiative energy flow. 

Where do semiconductor-based light detectors fit into your thoughts about all this? They don’t operate in that wavelength range, but they do detect thermal radiation.
 

That is entirely valid as far as it goes, but claiming that they are measuring some sort of “intrinsic” power of the radiation in Watts isn’t, because, as I said, that is not an intrinsic characteristic. It depends on the temperatures of both the source and target, i.e. it is extrinsic.

In the case of semiconductor detectors for shorter wavelengths (and for longer wavelengths with microwave detectors like the one they used to detect the cosmic microwave background radiation), the way it works is:

  • The detector has a certain internal “noise” level, and that noise level is affected by temperature. The temperature needs to be cool enough that the noise level is low enough that the detector can detect the radiation it’s observing without it being swamped by the noise. However…
  • Once the noise level is low enough to observe the “signal” (the radiation being measured), the measured value remains essentially at a fixed level as the detector is cooled further.

So, in that sense, it doesn’t seem fair to call the power level of the radiation being detected “extrinsic”: the power measured is the same for any measurement device, regardless of its temperature—as long as that temperature is low enough for the detector to do its job.

To pull this sleight-of-hand off, they usually suppress the exact temperature differential they based their measurement on, which is highly disingenuous and misleading on their part. (See if you can find, for example, the actual temperature of the thermistor heat sink on the CERES radiometers. I couldn’t, and not for lack of looking.)

I haven’t done any investigation of the CERES radiometers and how they work.

However, unless they’ve made a design error, I imagine that the “thermistor temperature heat sink” doesn’t matter, as long as it’s cool enough.

For a properly designed detector, the inferred power of the radiation being detected should be the same for any measurement device, no matter what their temperatures―as long as those temperatures are sufficiently low.

(Yes, I imagine that they infer or compute the measurement values they report, but practically all modern detectors involve some sort of inference.)

* * *

But, I imagine perhaps I’m stepping into the middle of a “hot button” issue for you, talking about that in particular.

* * *

In the case of pyrgeometers, they use the S-B equation incorrectly to convert negative power readings to fake positive ones, in order to invent a radiant greenhouse effect. Very sneaky! You can’t trust these slippery eels!)

I haven’t looked into pyrgeometers.

Steve Keppel-Jones
Reply to  Bob Wentworth
October 28, 2022 10:50 am

Well, perhaps we are talking at cross purposes. But two simple questions should clear things up, I hope:

1) Under what conditions do you think the magnitude of the Poynting vector would be 0?

2) What direction do you think the Poynting vector poynts (sorry, couldn’t resist) on Earth’s surface at night?

Bob Wentworth
Reply to  Steve Keppel-Jones
October 28, 2022 3:10 pm

1) Under what conditions do you think the magnitude of the Poynting vector would be 0?

I’ll go with the simplest interpretation, and assume you are talking about the time-averaged Poynting vector (rather than considering time scales comparable to the EM radiation cycle time).

In that case, the Poynting vector at a particular location will be zero if:

  • There are no EM waves passing through that point; or
  • There are EM waves passing through that point, but they are traveling in opposing directions, so that the Poynting vectors associated with individual waves cancel one another out, yielding a net Poynting vector of zero magnitude.

2) What direction do you think the Poynting vector poynts (sorry, couldn’t resist) on Earth’s surface at night?

Assuming the atmosphere is colder than the surface (as I expect is always the case in the ways that matter), then the Poynting vector poynts up.

Bob Wentworth
Reply to  Steve Keppel-Jones
October 29, 2022 9:03 pm

I’m curious. Did my answers about the Poynting vector clear things up? Where is our conversation at this point? I’m still interested in understanding how you are thinking about all this.

Steve Keppel-Jones
Reply to  The Real Engineer, CEng etc.
October 19, 2022 5:50 am

Willis only ever finds actual thermodynamics by accident. I would have said that the radiant energy from the sun does have an obvious temperature, though, doesn’t it? It would be about 5000 K, which is approximately the surface temperature of the sun. The radiant energy from the Earth would have a temperature of about 288 K.

Matthew Schilling
October 18, 2022 11:07 am

Doesn’t this three-segmented scatterplot hint at saturation levels? The far north is “starving” for energy. Levels of “energy hunger” decrease as one approaches the equator and increases as one approaches either pole.

Also, doesn’t the top, horizontal segment align with Willis’ insight about tropical storms AND with RickWill’s insight about a hard upper limit to open ocean temperatures?

JDubya_Mesa
October 19, 2022 6:27 pm

Do you have a paper with your theory, equations, etc. that you could post here? It would be interesting to see.
I did some work 30 years ago in grad school on the solar effect on the atmosphere, simple work, and my prof rejected it. I left the field of this topic to pursue semiconductor.
It would be interesting to see the equations and models, just for interests.
Great piece.