Guest Post by Willis Eschenbach (@WEschenbach on X, my personal blog is here)
I got to thinking about how much the world will warm in the long run when the radiation absorbed by the surface increases. I figured I could use that to estimate the long-term climate sensitivity, which is usually expressed as how much the surface will warm if CO2 doubles. (2xCO2).
To begin with, I looked at the total amount of power absorbed by the surface, in watts per square meter (W/m2). This includes solar radiation from the sun, longwave radiation from the atmosphere, and advected heat, which is the power constantly being moved horizontally from the equator to the poles. Fig. 1 shows the result, both without (left) and with (right) advected heat. Note how the poleward advection of heat evens out the heating of the planet.
Figure 1. Surface power absorption both without (left) and with (right) advected power.
Now, the Stefan-Boltzmann equation relates radiated power to temperature. The formula says that the radiated power is a constant times the emissivity of the surface times the fourth power of the temperature. So … given that equation and the temperature of the Earth, how much should an increase of 1 watt per square meter (W/m2) warm up the planet? Figure 2 shows the calculated result.
Figure 2. Calculated theoretical temperature change using the Stefan-Boltzman equation, on the order of 0.2°C per W/m2. (Thanks to Arjan Duiker who pointed out below that the legend in the graphic is wrong, it should be C per W/m2.)
Note the variations in the calculated temperature changes due to temperature and emissivity. As expected, because of the fourth power relationship, a one-watt per square meter change makes more difference at the poles than in the tropics.
Next, I looked at the real-world relationship between the net absorbed power (including advection) and the temperature. Fig. 3 shows the result as a scatterplot of the temperature versus the total absorbed power.
Figure 3. Scatterplot, surface temperature versus net gridcell power absorption (including advection)
Note that the slope (trend) of the yellow line is the sensitivity of temperature in °C with regard to the net power absorbed by the gridcell.
This is a most interesting graph. First, the slope is almost constant from the extreme cold of the south pole up to about 26°C. This is a surprise, because the Stefan-Boltzmann equation would lead us to think the sensitivity should be greater in the cold regions. But apparently, this is offset by the advection of heat from the tropics to the poles.
Second, the clustering is very tight. This shows the close relationship between absorbed radiation and temperature at all levels of radiation.
Third, the slope goes almost flat at the highest temperatures. This means that no matter how much additional power is going to the warmest gridcells, they are not warming any further.
To understand more about the slope, Fig. 4 shows the slope overlaid on Fig. 3 along with the average value.
Figure 4. As in Figure 3, but with the red line showing the slope of the yellow trend line (right scale) and the area-weighted average trend.
A question arises. Is this average slope of ~0.14°C per W/m2 just a one-off, or is this a more permanent feature of the Earth’s climate? Will it change if the total power absorbed by each gridcell increases due to any reason?
To investigate that, I looked at the 25 individual years of CERES data. To start with, here’s the range of the gridcell absorbed power over the 25 years.
Figure 5. Boxplot, range of gridcell power absorbed by each of the 25 years of the CERES data.
Note that the range goes from 507 W/m2 up to 513 W/m2, a range of 6 W/m2. This is far more than the expected change from CO2.
Now look below at how small the change is in the expected sensitivity of temperature to surface power absorption.
Figure 6. Boxplot, range of temperature sensitivity for each of the 25 years of the CERES data.
Above, I rounded the sensitivity to 0.14°C per W/m2. Despite the absorbed power varying by 6 W/m2, the calculated average sensitivity only varies from 0.133 to 0.140°C per W/m2. This is small enough to be lost in the noise. So we can see that this relationship between temperature and gridcell absorbed power is a stable feature of the climate.
So … how does this all relate to the equilibrium climate sensitivity? To calculate that, we need to take a look at how the changes in the poorly-named” greenhouse radiation” relate to downwelling longwave at the surface. In other words, if the greenhouse radiation increases by 1 W/m2, how much does the downwelling radiation at the surface increase? Once again, I turn to the CERES data. Fig. 7 shows the result.
Figure 7. Scatterplot, surface downwelling longwave radiation versus top-of-atmosphere (TOA) “greenhouse” radiation.
Now we can put it all together:
Change in surface temperature per 1 W/m2 gridcell power absorption = 0.14 °C per W/m2
Change in TOA downwelling “greenhouse radiation” per doubling of CO2 = 3.7 W/m2 per 2xCO2
Change in gridcell power absorption per 1 W/m2 TOA “greenhouse” radiation = 1.46 W/m2 per W/m2
Expected change in temperature from a doubling of CO2 =
0.14 °C per W/m2 times 3.7 W/m2 per 2xCO2 times 1.46 W/m2 per W/m2 =
0.75°C per 2xCO2
Uncertainty analysis: the uncertainty in the slope can be estimated by taking the standard deviation of the slopes of the 25 individual years making up the average slope shown in Fig. 3. This is 0.006 °Cper W/m2. This also shows the temporal stability of this type of analysis
The uncertainty in the change in downwelling surface radiation is 0.069 W/m2 per W/m2.
The uncertainty in the estimated increase in CO2 forcing from a doubling of CO2 is 0.35 W/m2
Combined, this gives a final value of the climate sensitivity estimate of:
0.76 ± 0.08 °C per 2xCO2
… I had calculated a maximum estimated climate sensitivity of 1.1°C per 2xCO2. I said it was a maximum because it did not include the moderating effect of clouds and other phenomena on the changes.
This current estimate of 0.76 W/m2 per 2xCO2 includes not only clouds but all other weather phenomena that affect the sensitivity. So I would say that it is a best estimate, rather than a maximum estimate.
As always, comments and corrections welcome.
My best to all,
w.
My Customary Ask: When you comment, QUOTE THE EXACT WORDS you are referring to. I can defend my own words. I can’t defend your interpretation of my words. Thanks.
I’d like to know what the climate sensitivity of Methane is. Google AI says about 0.3C°
WUWT April 2014 OK back to your regular programing.
It is 7/30 of CO2’s according to W.Happer
Thanks, If the no feedback figure for CO2 is ~1.2K that comes to about 0.028K
Which confirms the ~0.3K that Google’s AI said
No, there is an order of magnitude difference between the two numbers.
The formula used today is slightly different from the one in the past. See Table 1 here for details. It’s not like CO2, so much per doubling. It depends on where it started and where it ends.
The formula in the citation yields a total increase since pre-industrial times of 0.65 W/m2.
Best to you,
w.
Thanks for the reply to my off topic question found in that 2014 WUWT post
The climate sensitivity of CO2 is about 1.2C° per doubling in the atmosphere
The climate sensitivity of CH4 is about (___)C° per doubling in the atmosphere
Can anyone fill in the blank?
If 3.3 W/m² = 1K of warming then the 0.65 W/m² gets ~0.2K or warming which is in the ball park of other answers I’ve gotten over the years.
The usual metric for climate projections/predictions is, “By 2100” and it would be nice if policy makers and media were to know or ask how much more warming methane is on track to produce by 2100 considering that its concentration increases ~7ppb every year.
But they don’t know or ever ask and continue to recite the Global Warming Potential numbers found in all the IPCC assessment reports. CH4 is 82.5 times more powerful at trapping heat than CO2 according to the IPCC’s AR6. Sounds scary but it appears to be less than a tenth of a degree by the end of the century.
Meanwhile we are feeding Bovaer to livestock so they emit less methane.
Climate sensitivity to so-called “greenhouse gasses” is utter tripe. Ice controls the radiation balance in both short wave reflection and OLR emissions. Most people get the short wave reflective aspect.
I asked MS Copilot for why ice dominates in the OLR region. This is the answer and I agree with it:
At an effective emission temperature of 255 K, Earth’s thermal radiation peaks near 11–12 µm, right in the centre of the atmospheric infrared window. In this spectral region, water vapour absorbs only weakly, because its rotational–vibrational lines do not significantly overlap the window. By contrast, solid ice has a much larger absorption coefficient at these wavelengths, meaning that if ice crystals are present in the atmospheric column, they interact far more strongly with radiation near the Planck peak for 255 K.
Because the upper troposphere at 255 K is extremely dry, water vapour is largely absent, but ice crystals can persist due to their slow sedimentation rates. Even very small concentrations of ice can therefore provide a radiatively active medium at the wavelengths where Earth emits most strongly. In this specific spectral region, the absorption cross‑section of ice exceeds that of water vapour by orders of magnitude, making ice the more effective emitter when it is present.
This leads to the important conclusion that at the effective emission temperature of 255 K, and at the dominant emission wavelength near 11–12 µm, ice—not water vapour—is the stronger emitter to space. While water vapour dominates infrared absorption and emission in the warm, moist lower atmosphere, the radiative physics at the emission altitude are governed by the spectral window and the materials still present there. Under those conditions, ice becomes the dominant radiating substance in the relevant part of the spectrum.
And of course it is no accident that the emission temperature is 255K because it is the high absorption region for ice.
Steve
Here’s an article that has a very revealing graph in it for a number of gases…
Resultant watts if the gas is removed from the atmosphere.
Keep it handy. 1.55/23.04= 6.7% of CO2 for CH4
https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2012GL051409
Thank you for your continuing efforts to bring rational analysis to the scientific debate. One hopes that those in the consensus community will begin to consider inputs from you, Will Happer and others who present arguments based on scientific reasoning evaluated against real world observational and experimental data.
The “Consensus Community” has real world models.
</sark>
Willis, your analysis indicates that the expected rise in temperature from a doubling of CO2 should be 0.75°C per doubling. As a point of clarification, my question is this ….
Would that 0.75C figure be the expected rise in Global Mean Temperature (GMT) with a doubling of atmospheric concentration of CO2 in the earth’s atmosphere — for example, for a rise from 280 ppm CO2 to 560 ppm CO2 as measured by the Keeling Curve?
Yes.
w.
Interestingly, you can use 400 and 800 ppm in Modtran, UChicago version, clear sky, tropical, fixed RH, and get 1.2 C per 2xCO2. You can also choose a different locality where the OLR would be more representative of the entire planet at 240 Watts TOA (IIRC temperate winter). This results in 0.8 C per 2xCO2.
One problem is that the “actual warming” as measured by say UAH at 0.13C per decade is almost twice as high.
For those so inclined a good Modtran tutorial is here:
https://www.aiche-cep.com/cepmagazine/may_2022/MobilePagedArticle.action?articleId=1788369&lm=1685661039000#articleId1788369
Willis,
Sorry, I should have been more specific….a problem is that the temp increase from UAH since 1979 is about twice as high as one would get from Modtran using the CO2 increase since 1979…personally I think the difference is due to ocean current upwelling variability on the couple of century timescale. The effect of elNino wind induced surface currents is clear on UAH on a couple of year timescale….why not general deeper ocean turnover on a much longer timescale ?
Assuming Willis’s estimate is correct, we will have to see 2 doublings of CO2 concentration from the pre-industrial level of 280 ppm to reach the Paris agreement target of 1.5 degrees. So 1120 ppm CO2. I don’t think anyone believes the earth holds that much fossil fuel. Maybe we can arrange for the Yellowstone super-volcano to blow.
One estimate I recall was that burning all the available coal, oil and natural gas, at one time, would increase the CO2 levels to around 800ppm, so it looks like 1120ppm is out of reach.
I’m surprised that the latest work done by Paul Burgess hasn’t even warranted a mention in passing. And it hasn’t. He puts ECS at ~1C and he has what he calls the “Oceanic-Solar-CO2 index”.
https://www.freespeechbacklash.com/sites/default/files/assets/library/download/Warming%20from%201983%20to%202025%20Final_Main_Paper.pdf
Puts Mann in the shade.
Thanks, Strativarius.
The main problem with the Burgess study is its circularity.
Burgess claims to avoid curve fitting by fixing ocean‑index weights and a scaling factor using 1900–1980 and then applying them “unchanged” to 1983–2025.
The problem is that the calibration procedure is a multiple linear regression of detrended HadCRUT against AMO, PDO, IOD, ENSO, and TSI, i.e., it optimizes weights to match the observed temperature wiggles in the very record that contains anthropogenic forcing, aerosols, and internal variability mixed together.
The issue here is that the AMO, PDO, ENSO, etc. are temperature-related indices. So he is using the temperature to … wait for it … predict the temperature.
Sorry. Gonna pass.
w.
He is using weighted Ocean temperature indices to calculate atmospheric temperature accurately, which indicates that the Oceans, which contain vastly more heat than the atmosphere and can store the solar input, are what controls the climate. He states that his algorithm is not predictive.
David, you say, “He states that his algorithm is not predictive.”
He calls his AMO, PDO, ENSO etc. datasets “predictor datasets”.
He says “Because the results of this work are so accurate in predicting all the temperatures from 1983 to 2025 so precisely …”
He says “Because several predictors are derived from sea-surface temperatures …”
I could go on and on, because he uses “predict” no less than 158 times in the paper, but I’m sure you see the problem with your claim.
w.
Yes he is very sloppy with the use of the word “predictive”. If one replaces “predicted” with “calculated”, then the intent of his algorithm is clear. The accuracy of the calculation is more than impressive and once again shows that the oceans control the climate.
He doesn’t predict, you have to know… before you can calculate.
Exactly. He also says once the lesser “well knowns” are better understood, they can be added instead of best guessing like IPCC do. Hence their efforrs result in an ensemble with a relatively huge range. At least he only needs one CO2 ECS. Anyone can contact him and debate any flaws.
Presumably this number is the transient version, before slow feedbacks (of course, more relevant to policy).
Regarding Figure 5 (Figure 7 as labelled): the ratio looks to be more than 1.46. I think I’m missing something here.
Jit, you say “this number is the transient version, before slow feedbacks”. Not true, which is precisely why I chose this method.
You see, what I’m describing is the equilibrium state of each gridcell—that is to say, given a certain amount of absorbed power, the temperature of each gridcell has settled out to a certain value. Note that it includes variations in the surface (land or ocean), the humidity, the clouds, the CAPE, and all other variables.
In other words, this is a long-term result including all “slow feedbacks”. It is a property of how the climate system works. And this is supported by the very small change in the slope despite the annual variations in gridcell power absorption.
w.
Thank, Jit. The surface has a range of about 9, and the TOA has a range of about 5. So 1.46 is correct.
w.
The above analysis is interesting, but continues the fiction that the CO2 forcing is responsible for global warming/cooling. Climate data shows that CO2 abundance lags temperature change. Since before the start of the 21st century, the slow logarithmic rise of CO2 forcing has been outstripped by the potent – long-lived greenhouse gases (GHG) we introduce into the atmosphere to make smart phones and air conditioners.
If there IS significant anthropogenic global warming, it is not due to CO2.
The effect of the potent GHGs has been modeled. The data is included in the AR4, 5, and 6 radiative forcing tables, so the IPCC agrees, but the IPCC is subtle.
The “change of playing fields” is used: writing all forcing as CO2 equivalents.
Using ‘metrics’ and modeled temperature anomalies, the narrative continues that CO2 must be suppressed (i.e. NO MORE fossil fuels), in spite of its obvious positive contribution to feeding billions of humans.
The IPCC has staked its future on ‘decarbonization’ – meaning actual removal of CO2 from the atmosphere – as if biology does not do that already. The branding of climate variation as climate change (i.e. anthropogenic) justifies any and all obfuscation since it transfers 100’s of $trillions into the pockets of the perps, the real goal, and bankrupts the rest of us.
Thanks, wh. My Spherical Cow analysis clearly shows that the temperature is set (as we’d expect from basic principles) by two factors—energy entering the system, and energy leaving the system.
Energy entering the system is regulated by albedo. Energy leaving the system is regulated by the poorly-named “greenhouse effect”.
So yes, CO2 and other GHGs do affect the temperature. The question is, how much?
My analysis says that a doubling of CO2 will result in about 3/4 of a degree C of warming. Pre-industrial CO2 was about 285 ppmv. Current CO2 is about 420 ppmv. This would imply a CO2 warming of log2(420 / 285) * 0.75 = 0.4°C … which is trivially small.
w.
Exactly, and as you noted, including the albedo and other feedbacks, acts to reduce even that small effect to near zero. The small net GHG effect cannot justify the destruction of an entire energy system.
Emblemsvag (INTERNATIONAL JOURNAL OF SUSTAINABLE ENERGY
2024, VOL. 43, NO. 1, 2355642) analyzed what Germany could have achieved with those wasted hundreds of billions of Euros.
In addition to Emblemsvag’s sums, the entire wind turbine and PV system must be replaced every 20 years, compared with the 50-75 years for base power, requires a backup system that is equally as expensive, and then requires a clean up and recycling of the enormous debris of the wind turbine and PV facilities which will easily double the original wasted expenditure.
ALL this waste, do not forget, was aided and abetted by activist ‘scientists’ who paid no price for their sycophancy, but instead received prizes and accolades.
ps. The spherical cow is the great way to put super-serious climate catastrophe predictions where they belong.
Yes, but the estimate on the energy leaving the system is a lower-bound because even CERES does not have the proper observation geometry to measure the oblique specular reflection off water — particularly near glancing angles. By luck, that is somewhat compensated for by the cosine effect that reduces the intensity of impinging light per unit area. However, it is not an exact, or even a correct solution.
Actually, even rough terrestrial materials, like dirt clods and corn stalks, have high reflectance at angles of incidence approaching glancing. The shape of the reflectance curve, is however, different from water. It is something that I haven’t measured, despite having a large database for opaque minerals.
The reflection of light from below the surface of the water is the sum of diffuse reflectors, principally suspended sediment near the shore, ocean bottom in shallow water, and plankton in deep waters.
The surface, reflecting specularly, varies with the angle of incidence, but it is forward reflectance for all but small angles of incidence. Satellites with a synoptic view, miss that completely in most cases, only ‘seeing’ the retro-reflectance. Additionally, the reflectance varies with the complex (as in the sq. rt of -1) refractive index, which also varies significantly with the wavelength.
The Extinction Coefficient (absorbance) is related to the emissivity. The hypothetical Black Body is much like your “spherical cow” — it doesn’t exist. It is only approximated for regions of the electromagnetic spectrum that are strongly absorbing, such as the infrared. That is, wavelengths for which the terrestrial materials have large extinction coefficients.
Your first-order approximation to the problem may turn out to be close enough for government work. However, until you or someone else does the calculations correctly, we won’t be sure.
I see some sanity at my alma mater. Wait until others find out about the econ department.
Hi Willis, 0.75°C per 2xCO2. I would think it hard/dni to separate CO2 from all possible other causes. Eg, land use. In effect CO2 is a proxy. Which means your figure may be more significant than simply a co2 metric.
darn near impossible
Like UAH measuring 0.017 C/year GMST rise.
The thermal sensitivity of the atmosphere to CO2 is a big fat zero.
Correlation is not cause no matter the stunning handwavium smoke & mirrors.
Hey, does this work for me??
“My Customary Ask: When you comment, QUOTE THE EXACT WORDS you are referring to. I can defend my own words. I can’t defend your interpretation of my words. Thanks.”
Earth is cooler with the atmosphere/water vapor/30% albedo not warmer. Near Earth outer space is 394 K, 121 C, 250 F. 288 K w – 255 K w/o = 33 C cooler -18 C Earth is just flat wrong. Dividing 1,368 by 4 to average 342 over Spherical ToA is wrong.
Ubiquitous GHE heat balance graphics don’t balance and violate LoT. Refer to TFK_bams09.
Solar balance 1: 160 in = 17 + 80 + 63 out. Balance complete.
Calculated balance 2: 396 S-B BB at 16 C / 333 “back” radiation cold to warm w/o work violates Lot 2. 63 LWIR net duplicates balance 1 violating GAAP.
Kinetic heat transfer processes of contiguous atmospheric molecules render surface BB impossible. By definition all energy entering and leaving a BB must do so by radiation. Entering: 30% albedo = not BB. OLR: 17sensible & 80 latent = not BB. TFK_bams09: 97 out of 160 leave by kinetic processes, 63 by LWIR = not BB. As demonstrated by experiment, the gold standard of classical science.
For the experimental write up see:
https://principia-scientific.org/debunking-the-greenhouse-gas-theory-with-a-boiling-water-pot/
Search: Bruges group “boiling water pot” Schroeder
RGHE theory is as much a failure as caloric, phlogiston, luminiferous ether, spontaneous generation and several others.
When GHE fails the entire CAGW house of cards implodes like the Titan submersible.
Why, exactly are \the words of my three points incorrect.
Spare us the ad hominems, insults and changing the subject to esoteric, convoluted, hocus pocus.
The whole whacko phiisics of “Climate Scientology” is falling apart. Without USA funding and propaganda, AR7 is floundering. The dire quandary is that ocean heat content and net radiation have been parting ways since aligned in 2015.
Notably, ocean heat content in the Southern Hemisphere is decelerating and trending to decline within two decades. Meanwhile ocean heat content in the northern hemisphere continues to accelerate. The rising net radiation imbalance in the Southern Hemisphere is now well above the ocean heat uptake. And it is not explained be equatorial advection because net radiation imbalance in the NH also exceeds ocean heat uptake.
These issues cannot be resolved with some magic and without the involvement of the groups operating ARGO and CERES.
Once ocean heat content in the SH is declining, the whole pile of claptrap is dead. Ocean heat has been the touchstone for the Global Warming™ BS.
No GHE = No CAGW.
It is absolutely wrong. It assumes incoming insolation is spread over 24 hours and is the same everywhere. The solar radiation absorbed by the surface (land and ocean) varies by the angle of incidence that the radiation encounters on the earth. Directly under the sun, that is, at 0° of incidence, the “cos θ = 1” means everything is absorbed. While at 90°, that is, at the poles, “cos 90 = 0” and nothing is absorbed.
This is complicated by the fact that the sun’s position over the earth is not constant causing the seasons.
Consequently, a point on the equator is exposed to 1368 and so is the North Pole. The difference is the angle of incidence.
Because of the T⁴ in SB, it is important to use the true insolation to find the temperature at any point on the earth. One can not assume it is linear in an average.
The use of SB questionable anyway due to the earth not being a black body. The surface that absorbs insolation is a heat sink. Some of the insolation is diffused into the heat sink and is not immediately reradiated. This has the effect of skewing the resulting radiation and also reducing the effective radiating temperature.
Here are two graphs I have made using my weather station data and soil temperatures from Kansas State University.
These illustrate the complicated processes of the Earth’s reaction to insolation. They can truly only be analyzed with gradients that include time and trig functions.
“Dividing 1,368 by 4 to average 342 over Spherical ToA is wrong.”
No it’s correct, it uses proper geometry to calculate the average amount of solar radiation per m^2 reaching the Earth’s surface in the absence of atmospheric effects.
It is wrong. The spherical wave front from the sun has expanded to the point that the earth sees it as a plane wave. A plane wave has the same intensity at every point on the plain. Think of a bed sheet pulled taught and having a basketball thrown at it. Every point on the sheet will touch every point on the ball with exactly the same intensity.
At 1360, every square meter of one half of the earth is exposed to 1360 at a given point in time. What changes? The angle of incidence!
No, the Earth is exposed to 1360xcross section of the spherical Earth, when this radiation reaches the Earth’s surface it is spread over the Earth’s surface area, so the average amount of solar radiation per m^2 reaching the Earth’s surface is given by:
1360xcross section/surface area, since cross section/surface area = 1/4 the average is 1360/4 QED
Phil – It’s a lost cause… I tried here:
https://wattsupwiththat.com/2025/11/24/a-world-without-air/#comment-4135274
to convince Jim that parallel flux hitting an oblique surface results in lower flux density impinging on that surface. He couldn’t get it.
If you want to try as well…
He couldn’t get it because using your logic the surface area expands. Instead of the 45deg ray impinging on 1m^2 it impinges on 2m^2. Meaning the surface area exposed to the sun insolation all of a sudden must be assumed to expand by a factor of 2.
For a ray impinging at a 45deg angle, the vertical component is 0.7, not 0.5.
At local noon the 1m^2 insolation at 45º will impinge on √2 m^2 therefore the insolation at the surface will be 1360/√2 W/m^2. Expanding that over the illuminated surface gives an average of 1360/2, allowing for the rotation of the Earth over 24hrs will include the unilluminated surface therefore over the whole surface of the Earth the average will be 1360/4 as I posted previously!
At local noon the 1m^2 insolation at 45º will impinge on √2 m^2 therefore the insolation at the surface will be 1360/√2 W/m^2.
That is not true. EM waves can be absorbed, reflected, or transmitted. Planck realized this applies to “heat” radiation EM as well as visible light which is also EM waves.
IR therefore obeys optical physics. This well proven theory shows that absorbed energy is dependent on the angle of incidence.
Your description requires ALL incident energy be absorbed, just over larger and larger areas. That can be true with a point source close enough that the spherical wavefront does not appear as a plane wave.
However, the earth is distant enough from the sun that the wavefront appears as a plane wave. A plane wave has the same intensity at every point of the wave. What the earth experiences has negligible variation across the area of the plane wave.
That means every square meter on the earth receives 1360 (reduced by albedo). What is absorbed is based on the angle of incidence.
It also means that a point at 45° absorbs “1360 • cos 45 = 1360 • 0.7.
Here is a screenshot from a meteorology textbook that you can peruse.
This example uses sin (1-Θ) which is the same as cos 60.
This text book is downloadable.
Practical Meteorology, ROLAND STULL, The University of British Columbia Vancouver, Canada
https://geo.libretexts.org/Bookshelves/Meteorology_and_Climate_Science/Practical_Meteorology_(Stull)
Unfortunately you don’t appear to understand what ‘impinge’ means!
The textbook you quoted agrees with me: “Because the solar radiation is striking the parking lot at an angle, the radiative flux into the parking lot is half the solar irradiance.”
Your ‘flat Earth’ theory doesn’t apply, the Earth is a sphere!
Ed I understand, the gormless twins stick to their guns no matter how wrong they are. Our trying to explain that the integral of T^4 versus time is not T^5/5 being another recent case in point! However if they are not corrected someone reading their nonsense might think they’re right.
You have yet to show one scintilla of math supporting your claim while I have shown you the math showing you are wrong.
You simply can’t differentiate between “rate” and “quantity.
So all you have left is Argument by Denigration, usually known as “Attack to the person”.
Where have you shown that the integral of T^4 over time is T^5/5?
You are fighting a losing battle. The radiative balance at the top of the atmosphere ISN’T EVEN OF THE SAME THING! One is mostly shortwave and the other longwave. The rates *can’t* be of the same value. Even if they were of the same thing since one happens over 12 hours and the other over 24 hours THE AVERAGE VALUES CAN’T BE THE SAME if they are to provide the same total quantity. Nor are they associated with the same functional equation. One is sinusoidal and one is exponential decay. You *still* haven’t shown how the average of a sinusoid over 12 hours can be the same as the average of an exponential decay over 24 hours!
The only way to compare the two is to integrate both over the applicable time period or each and then normalize the total quantities to an arbitrary time interval. You may as well use one hour as 24 hours.
And at each point the measurement uncertainty ADDS. Finding the integrals is really nothing more than summing all the measurements which means that the measurement uncertainty ADDS with each iteration step in the integration. The final measurement uncertainty of the normalized values is quite likely in the tens digit – when you are trying to find differences in the unit digit or tenths digit.
It’s all non-physical garbage. Once you’ve done the integrations there is NO JUSFITIABLE REASON to try and normalize them to an arbitrary time period to come up with an intensive property value.
Just change the trenberth diagram to show joules in and joules out over a 24 hour period and be done with it!
You bring up a good point.
Is the ~160 incoming a 24 hour average or a 12 hour average? Is the 398 outgoing a 12 or 24 hour average?
The earth radiates over 24 hours while it only receives insolation over 12 hours. You can’t equate rates over different time periods.
Hard to believe that the earth only receives an average of 160 during 12 daylight hours and emits an average of 398 over 24 hours.
This post was clearly made on April Fools’ day!
I believe Happer and Wijngaarden found the ~same
“Change in TOA downwelling “greenhouse radiation” per doubling of CO2 = 3.7 W/m2 per 2xCO2”
“Downwelling” is a stone cold violation of LoT2, i.e. cold to warm wo work. The 333 “back” is a consequence of a calculated BB 396 surface. This is just flat wrong.
Upwelling 396 16 C BB/333 “back”/63 2nd copy is trash. Erase GHE loop from the graphic and balance still valid.
I could not spot the surface emissivity you used.
0.9 to BB is wrong
I figure it is on the order of 15% to 20%.
See annotated TFK_bams09
Nicholas, you say “Downwelling” is a stone cold violation of LoT2, i.e. cold to warm wo work.”
Sorry, but that’s not true. See my post.
Or Dr. Roy Spencer’s post.
w.
“If the atmosphere didn’t exist, the Earth’s surface would lose IR radiation directly to the cold depths of outer space,”
Nonsense.
No atmosphere and naked Earth bakes in the 250 F solar wind.
Do your experiment in a vacuum where there are no kinetic effects.
This whole “back” “net” radiation is a fabrication to make GHE seem to work, a consequence of the BB surface.
No BB = no “back” ‘ no GHE
What surface emissivity did you use??
Nicholas, you ask, “What surface emissivity did you use??”
I used the MODIS/Terra Land Surface Temperature/Emissivity Monthly L3 Global 0.05Deg CMG V061 for the land, and a constant 0.985 for the ocean based on the discussion here.
w.
0.985 is just flat wrong.
That is more than arrived from the Sun.
I love folks who simply shriek “THAT’S WRONG” and think they’ve established something.
w.
A black body requires that all energy leaving does so by radiation.
60% to 80% of the energy leaving the Earth’s surface does so by kinetic modes so a BB is impossible.
Because of the significant (60% per TFK_bams09) non-radiative, i.e. kinetic, heat transfer processes of the contiguous participating atmospheric molecules the surface cannot upwell “extra” energy as a near Black Body. .
EVIDENCE:
As demonstrated by experiment, the gold standard of classical science.
For the experimental write up see:
https://principia-scientific.org/debunking-the-greenhouse-gas-theory-with-a-boiling-water-pot/
Search: Bruges group “boiling water pot” Schroeder
“A black body requires that all energy leaving does so by radiation.”
A black body is also assumed to be at internal equilibrium. I.e. it is *not* a heat sink with thermal resistance and internal temperature gradients. It is assumed to absorb all EM it encounters and emit the same amount of radiation.
As usual with climate science they have to simplify things so far to make their theories work that nothing is actual reality. It’s not physical science.
“A black body requires that all energy leaving does so by radiation.”
No, it requires that it radiates based on its temperature with an emissivity of 1.
“A black body requires that all energy leaving does so by radiation.”
You don’t understand what a black body is hence your error about the Earth’s surface emissivity is.
A black body emits solely based on its temperature, whether it is also losing heat via other mechanisms is irrelevant, it will still emit with an emissivity of one.
Emissivity does *NOT* dictate temperature at any point in time. It only specifies the radiation from a specific temperature. A black body has no specific heat capacity, it’s temperature can change instantaneously. The earth is *NOT* a black body, it has a specific heat capacity. It’s temperature at any point in time is determined by the HEAT in over time and the HEAT out over time.
If the heat-in and heat-out operate over different time intervals then emissivity does *not* determine the temperature of the earth at any point in time. Thus the climate science assumption that the average radiative flux in and average radiative flux out is garbage. You will *never* measure the value of radiative flux out from the earth anywhere near a value of 300-odd joules/sec thus the *ACTUAL* temperature of the earth using this non-physical joules/sec will never approach the temperature calculated from the joules/sec inward from the sun. If the radiative flux from the earth never reaches anywhere near the size of the flux-in then how does it ever reach the temperature needed by its emissivity to generate a “balanced” flux.
If this assumption was true, then neither Planck’s equation nor Stefan-Boltzmann equation would be true. Both equations were developed from black bodies that were homogenous and isotropic, with no other heat transfer mechanisms operating.
From Planck’s Theory of Heat Radiation.
Max Planck. The Theory of Heat Radiation by Max Planck (English Edition) – Unraveling the Mysteries of Heat Radiation: Max Planck’s Groundbreaking Theory in English (p. 29). Prabhat Prakashan. Kindle Edition.
No conduction of heat takes place because it is isotropic. Planck’s entire work is dependent on this.
Seems your rules of engagement don’t apply to you.
Thank you for the link to the Science of Doom website. The author appears to know what he is talking about and even knows about the (real) index of refraction and (imaginary) extinction coefficient that constitute the complex refractive index of materials. Few people do.
True. SoD knows whereof he speaks.
w.
“It states that the net flow of thermal energy which we call “heat” goes from hot to cold each and every time without exception…”
LoT says nothing about “net” of any sort!!
If this “net” were real there would be refrigerators without power cords.
Seen any??
“Net” is a useful term! Every body with a temperature above 0K radiates energy in all directions, and receives energy from all bodies within “sight” according to their temperature and distance. The resulting “temperature” (internal energy without phase change) is therefore the “net” effect of all the energy exchanges involved. Two close bodies at the same temperature are exchanging energy. Try putting your hand between two candles!
The term ‘body’, meaning objects comprised of condensed matter, is the key. What you’re describing does not apply to gases, including the so-called GHGs, whose spontaneous emissions of ‘photons’ is effectively quenched within 10 meters or so of the Earth’s surface by collisions with non-GHG species, i.e. O2 and N2. See:
https://andymaypetrophysicist.com/wp-content/uploads/2025/01/Shula_Ott_Collaboration_Rev_5_Multipart_For_Wuwt_16jul2024.pdf
aka “stuff.”
It’s the kinetic stuff not IR.
Two candles is a bogus analogy.
Sigma (T1^4 – T2^4) is not a net figure, it is the amount of energy a refrigeration loop, i.e. work, must remove from A1 to cool it to A2.
Problem is, T^4 is W/m^2 which is power density, not energy.
which is why you have to integrate over time to find total energy and it’s not going to give you an average of a mid-point value.
My experiment demonstrates that the so called “net” is the kinetic processes cooling the system not “back” radiation.
Your post’s graphic does not balance & violates GAAP & LoT.
This graphic is not an energy balance, it is an energy-flow graphic which is energy-flow; i.e. power. The graphic shows the same power entering the atmosphere as leaving the atmosphere which is wrong. Power is lost getting through the atmosphere.
Strictly speaking a W is power not energy.
3.412Btu/Eng h or 3.6 J/SI h.
No, it’s not.
It’s the BB surface upwelling that is wrong.
396 BB/333 “back”/2nd 63 IR is trash.
Nicholas, that’s not my post’s graphic. That’s Kiehl/Trenberth’s graphic. Go complain to them.
w.
You used it as figure 2 in your suggested post.
It’s trash like all the others.
Are you really this unable to read? Here’s the figure I used.
It is NOT the figure you show above.
You posted the Kiehl/Trenberth figure, which is NOT energy-balanced.
w.
This “net” concept is straight out of some heavily papered PhD’s butt!! much like caloric & phlogiston.
“Now, the Second Law of Thermodynamics is only about net flows. It states that the net flow of thermal energy which we call “heat” goes from hot to cold each and every time without exception.”
No, it does not.
You just made this up.
From my BSME in 1978 through 35 years of application I never encountered this “net” concept.
Mostly because it does not exist.
Nicholas, you say: “From my BSME in 1978 through 35 years of application I never encountered this “net” concept.” Did you sleep through all your classes? I got a BSME in 1981 and an MSME in 1984, and I encountered this “net” concept all the time!
Consider J.P. Holman’s “Heat Transfer”, which I used for an ME course back in the 1970s. A more recent edition (but with very little changed) can be found online here:
https://pdfcoffee.com/qdownload/heat-transfer-jp-holman-ed10-pdf-free.html
Chapter 8 covers radiative heat transfer. In it, you will find many phrases such as “the net radiant heat exchange” and “the net energy exchange”. The diagrams, such as Figure 8-8, clearly show this two-way exchange.
Here is a very popular heat transfer textbook written by MIT ME professor John Lienhard
https://ahtt.mit.edu
It completely agrees with how radiative heat transfer was taught at MIT when I studied ME there.
Chapter 10 covers radiative heat transfer. It immediately introduces the concept as “The problem of radiative exchange”. (There is a quick introduction in Chapter 1.) The very first figure shows “two arbitary surfaces radiating enery to one another”. It then says, “The net heat exchange, Qnet, from the hotter surface (1) to the cooler surface (2) depends on the following influences…”
Because I keep seeing claims like yours, I have looked closely at many other heat transfer texts lately. Every single one of them covers the topic in this manner, where the resulting net heat transfer is a result of radiative exchange.
Or going back further, consider this by Rudolf Clausius, who did more than anyone else to formulate the 2nd LoT:
“What further regards heat radiation as happening in the usual manner, it is known that not only the warm body radiates heat to the cold one but that the cold body radiates to the warm one as well, however the total result of this simultaneous double heat exchange is, as can be viewed as evidence based on experience, that the cold body always experiences an increase in heat at the expense of the warmer one.”
(DIE MECHANISCHE WÄRMETHEORIE von R. CLAUSIUS, 1887, translated)
Nicholas and others, LISTEN TO ED BO! The idea of a net radiative exchange, involving flows in both directions, is Thermo 101. Anyone denying it can be safely ignored.
A funny truth. If you light a candle on a clear day, the sun gets warmer. Of course, the NET flow is sun to candle, but the flow in the other direction is real as well.
Here are some online texts that discuss the issue. Do a search for the word “net ” (including the space) to locate discussions of net two-way radiative heat transfer.
NASA: THERMAL RADIATION HEAT TRANSFER Volume Ill
Siegel & Howell – Thermal Radiation Heat Transfer
ON-LINE APPENDICES TO
Thermal Radiation Heat Transfer
7th Edition, Taylor and Francis, 2021
w.
First. let me reiterate that much of the current discussion concerns black body radiation. Radiation is not “heat”, it is an EM wave that is an energy carrier.
The SB equation really only works for temperatures of black bodies. It can not predict the amount of heat being absorbed and what ∆T will occur at a given level of radiation.
The ME’s here should know this. The heat equation is:
Q = m•c•∆T.
What does this tell you? That the amount of “heat” being added to a system is dependent on three things, the mass, the specific heat, and the change in temperature.
So, how does one handle the earth? I am going to address only the land and a temperature change from sunrise to noon of a square meter of typical soil 4 inches deep. Insolation warms the soil increasing its heat content. How much heat is added? Let m = 140 kg, c = 1000 J/kg•k, and ∆T = 4°C.
Q = 140•1000•4 = 560,000 J.
Let’s check this figure. 164 W/m² = 164 J/sec•m². Let’s use 6 hours converted to seconds.
60•60•6 = 21,600 sec.
21,600•164•1 = 3,542,400 J
560,000 J versus 3,542,400 J, why the difference? The soil is storing some of the “heat” which will be released later. This also means only about 6/7ths of the incoming insolation is used in heating the air. That value is then split into radiation and conduction/convection.
Additionally, insolation starts at zero, builds to a maximum at “noon”, then diminishes to zero again as a sine function. An average of insolation does not capture the entire range of temperature raised to the fourth power.
As you can see from the attached graphs, there is a disconnect between insolation, soil temperatures, and air temperatures in time of day. It is obvious that insolation does not directly translate into air temperature or soil temperature. More power to anyone that has a mathematical explanation.
Jim: Most of your post is irrelevant to the issue of whether there is radiative exchange or not. And then you get hung up on semantics.
The sources Willis and I have cited here are all careful to refer to “thermal radiation”. Many people who are not so careful use the term “blackbody radiation” to refer to the more general subject of thermal radiation. This generates a lot of confusion in the blogosphere.
You say that “radiation is not ‘heat’, it is an EM wave that is an energy carrier.” But in most cases, any absorbed radiation is thermalized, yielding what everyone refers to as “heat”. And note that Clausius uses the term “radiates heat”.
Then you say that “the SB equation really only works for temperatures of black bodies.” But if you get past the first 2 or 3 pages of an introductory textbook chapter on radiative heat transfer, you will find modifications to the SB equation that can be used for real-world applications.
One of the first modifications used is the “gray body” approximation, where the emissivity/absorptivity value is constant across the entire range of frequencies of interest. This turns out to be a very good approximation for many of the substances we are concerned with here, notably seawater. Willis uses a well-supported value of 0.985 for seawater, not much different from the “perfect” value of 1.0 for an ideal blackbody.
(Comically, Nicholas advocates using a value of about 0.16 for the emissivity of seawater, because he refuses to believe there is downwelling radiation from the atmosphere. He calculates that there is a resulting (net?) upward flux of 63 W/m2 compared to a blackbody flux of 396 W/m2, so he forces the emissivity to be 63/396 = 0.159 instead of acknowledging the 333 W/m2 downwelling flux.)
Before we can use your equation for temperature change, we have to figure out what the value of Q is. You are really using the equation in the form:
DeltaT = Q / (m * c)
Important, but completely downstream from what we are discussing here.
I said:
EM waves do not have a “temperature”. Temperature only occurs after absorbtion and the amount of “heat” is determined by the heat equation Q=mc∆T. That is the reason the SB equation can’t be used to determine the amount of “heat” except for when dealing with a black body.
You are mixing two different things, absorption and heat. Specific heat values and mass control temperature.
Here is an example.
How many joules does it take to raise 1 gram of water 1°C (25 to 26°C)?
How many joules does it take to raise 1 gram of typical soil 1°C (25 to 26°C)?
Will they have the same temperature rise when exposed to the same intensity of flux?
It isn’t hard to compute. You know the flux value. You can compute joules by using a fixed elapsed time, say 10 sec and 1 square meter. Then use the same mass (1 kg) when computing the ∆T. I think you’ll find the temperature rise is pretty much controlled by the specific heat value, and not the flux.
That is where the misuse of flux intensity to calculate temperatures fails using the SB equation. You claim saltwater has an almost perfect emissivity like a black body. That means what comes in immediately goes out. That sounds like little heating is being done.
How do you heat a black body with radiation if that occurs?
I have expounded continually that instaneous and averaged values are too simplistic. Gradients are needed with time as part of the descriptions. There is a reason calculus was a requirement for learning thermodynamics. Simple algebra just didn’t cut it. The same with AC circuit analysis or Statics and Dynamics for structural analysis.
Jim: I’m sorry, but your post is just a combination of irrelevancies, misunderstandings, and outright errors.
In my post, I was simply refuting (with solid sources) Nicholas’ assertion that there is no such thing as “net” radiative transfer. That is all. You keep bringing up other topics in response.
You say: “EM waves do not have a ‘temperature’.”
I never said, or even implied, that they do.
Responding to my paragraph about the commonly used gray body approximation, you say that I am “mixing two different things, absorption and heat. Specific heat values and mass control temperature.”
I am mixing up nothing. I mentioned neither heat nor temperature here. I just stated the completely standard definition of a gray body, and a commonly accepted value for seawater.
Your lengthy example is completely irrelevant to my arguments, and in no way contradicts them.
Then you say that I “claim saltwater has an almosts perfect emissivity like a black body. That means what comes in immediately goes out.”
NOOO!!! It means no such thing! I’ll ask you the same thing I asked Nicholas: Did you sleep through heat transfer class?
Saying that an object acts like a gray body with emissivity of 0.985 means several things, but not that. First, it means that it absorbs 98.5% of radiation incident on it, because absorptivity must equal emissivity (Kirchhoff’s radiation law).
Second, it emits 98.5% as much thermal radiation as an ideal blackbody would at that same temperature, whatever that temperature is. So at 15C (288.15K), and ideal blackbody would emit:
Q = 5.67×10^-8 * 288.15^4 = 390.9 W/m2
A gray body with emissivity of 0.985 would emit:
Q = 0.985 * 5.67×10^-8 * 288.15^4 = 385.0 W/m2
It does NOT mean that it would “immediately” re-emit 98.5% of radiative energy that it emits.
You say: “That is where the misuse of flux intensity to calculate temperatures fails using the SB equation.”
Hmmm… My kitchen infrared thermometer and my fever infrared thermometer do a very good job of using flux intensity to calculate temperature. And I have cross-checked them against other types of thermometers. From the reading I’ve done, they assume an emissivity of about 0.95, which is very common for the things you point them at.
I have no quarrel with your assertion that you need further equations (in general differential equations) to determine temperature profile of an object, but again, it is irrelevant to the point I was making about radiative exchange and “net”.
“ “net” radiative transfer”
Net radiative transfer doesn’t determine temperature. It’s just that simple.
” calculate temperature”
Meaning you must know the specific heat and thermal inertia of the measuring device. S-B won’t tell you that. The measurement sensor is not a black body.
“, but again, it is irrelevant to the point I was making about radiative exchange and “net”.”
If you can’t determine temperature from the flux value then you can’t use flux balance as a metric for temperature balance either. The conclusion is that the radiative balance meme is useless since it doesn’t determine HEAT TRANSFER amounts.
I’ve posted on here several times that radiative (i.e. flux) balance will *never* occur. Heat-in happens over half of a day. Heat-out happens over the full day. For heat-in and heat-out to balance there simply cannot be equal flux-in and equal flux-out. Trying to equate flux-in and flux-out in some kind of “energy” balance is not possible. Since the heat-in and heat-out curves are complex combinations of sinusoids and exponential decays the mean values of heat-in and heat-out are *not* simple arithmetic means.
I have yet to see anyone actually document how the flux-in and flux-out means are arrived at. Why is that?
When does the heat-out from the earth reach its maximum value? Daytime or nighttime?
Tim, you say: “Net radiative transfer doesn’t determine temperature. It’s just that simple.”
But you cannot determine temperature without knowing the net radiative transfer. It’s just that simple!
Then you say about my infrared thermometers: “you must know the specific heat and thermal inertia of the measuring device.”
Actually, no! Once the sensor reaches steady-state condition, the specific heat and thermal inertia are irrelevant. (They determine how fast the steady-state condition is reached, but that occurs very, very quickly in these infrared thermometers.) In steady state conditions, the radiative flux is enough to determine temperature.
One of the first things you learn in an introductory thermodynamics class is how to define a “control mass” and carefully note all of the energy fluxes in and out. This must be done before you start creating the dynamic equations for resulting temperature.
And it is very common when there are repetitive cycles of power inputs and outputs to use averages for a first cut approximation. In my professional engineering capacity, I work with pulsed power systems all the time, and everyone in the field uses this averaging for ballpark numbers. You do have to be careful when there are non-linearities, but for a first cut, it gets you close, and helps to bound the real values that require more detailed analysis.
By the way, elsewhere in this thread, you say:
“’A black body requires that all energy leaving does so by radiation.’
A black body is also assumed to be at internal equilibrium. I.e. it is *not* a heat sink with thermal resistance and internal temperature gradients. It is assumed to absorb all EM it encounters and emit the same amount of radiation.”
Every assertion here, except for “it is assumed to absorb all EM it encounters” is just wrong! You obviously don’t have the technical foundation to grasp the issues at hand.
https://wattsupwiththat.com/2026/03/21/chasing-elusive-climate-sensitivity/#comment-4177658
Elsewhere you discuss the integral of T^4 flux over time, and assert this has the form of T^5/5. NOOOOO!!!! You only get the T^5/5 form if you integrate over temperature T. This is a high school math error, and completely blows any arguments you make out of the water.
https://wattsupwiththat.com/2026/03/21/chasing-elusive-climate-sensitivity/#comment-4177734
The RATE of transfer doesn’t determine the temperature. It’s the integral of the rate that determines temperature. The integral of the Joules/sec determines the joules transferred. It is the joules transferred that determines the temperature.
ΔT = ΔQ/(m)(c)
The ΔQ is the number of joules transferred. It is a *time* dependent value.
The rate-in does *NOT* have to be the same as the rate-out. You can’t balance the rate-in with the rate-out unless they both occur over the same interval of time – which is not true for the Earth. rate-in occurs for half a day. rate-out occurs for a full day. The net transfer of energy has to be based on calculating in and out over different time periods. The math simply doesn’t work to say the average rate-in equals the average rate-out.
It’s like saying that a car travelling at 10 mph for 12 hours covers the same distance as a second car travelling at 10 mph for 24 hours. The distances simply can’t be the same! The math doesn’t work. The average rate for the second car has to be 5 mph for 24 hours. 10 mph ≠ 5 mph.
The RATES don’t balance for the cars. The RATES don’t balance for net HEAT transferred when one occurs for 12 hours and the other for 24 hours.
And exactly when is the earth in a steady-state condition? If your instrument is measuring the same RATE out and in at the same moment in time then it can’t be correct. It would be saying that the car at 10 mph for 12 hours covers the same distance as a car at 10 mph for 24 hours.
The problem is not the averaging. The problem is the difference in the intervals over which the repetitive cycles of power inputs and outputs happen!
If the average input is over a period Interval1 and the average output is over a period Interval2 and Interval1 ≠ Interval2 then the average input and output rates can *not* be equal. They will never balance in value.
Radiative flux is a RATE, not a quantity. Joules/sec is no different than miles/hour. It is the quantity that must balance, not the rates.
“Every assertion here, except for “it is assumed to absorb all EM it encounters” is just wrong! You obviously don’t have the technical foundation to grasp the issues at hand.”
Oh, malarky! A black body is an IDEALIZED object that *is* in thermal equilibrium internally, including inside the object as well as on the surface of the object. Do you need a quote from Planck to confirm this? I’ll get it for you if you need it.
The *real* issue here is that it doesn’t matter. You can’t balance rates in and out if they occur over different time periods. Just like two cars travelling at the same rate over different time periods covering the same distance. If the same distance is travelled (i.e. the same amount of heat is input to the system as is lost from the system) over two different time periods then the AVERAGE rates can’t be the same.
Tim, you just keep getting more and more ridiculous! You keep arguing against points I never made.
You say: “The RATE of transfer doesn’t determine the temperature. It’s the integral of the rate that determines temperature.”
But you have to know the RATE before you can integrate! So my point stands! Have you ever actually calculated integrals? From your egregious error in trying to integrate T^4 over time, I suspect not!
You say: “The rate-in does *NOT* have to be the same as the rate-out.”
I never said it did, or even implied that it did. In fact, my claim that you need to know the “net radiative transfer” obviously means that it could be, and in general will be, non-zero!
All your subsequent rantings are against a point that I NEVER made!
You say: “And exactly when is the earth in a steady-state condition?”
I never said it was. I said that the sensors in my infrared thermometers were, which is correct.
You say: “A black body is an IDEALIZED object that *is* in thermal equilibrium internally, including inside the object as well as on the surface of the object.”
Several points here: First, an idealized blackbody is in “local thermal equilibrium”, which is very different from general “thermal equilibrium”. Many objects are in LTE but not total TE. You would be well advised to learn the difference.
Second, an ideal blackbody emits a radiative flux density of Sigma*T^4, regardless of the radiative flux coming in, which could be greater than, or less than, this. So the assertion that “what comes in immediately goes out” is just WRONG!
Third, we have very good real-world measurements that show that many physical substance – like liquid water – have absorptive and emissive properties very close to an ideal blackbody.
You go on at great length about what you refer to as “different time periods” for radiative inputs and radiative outputs. Huh! The fundamental time period for both inputs and outputs is a full day. Of course, they don’t match each other throughout the day – during daylight, inputs generally exceed outputs, so temperture increases, and at nighttime outputs generally exceed inputs, so temperature drops. But the dominant period for both is the same 24 hours.
Why do you continue to miss the point? Yes, you have to know the rate. BUT THE RATES DON’T HAVE TO BE EQUAL, they don’t have to balance. What has to balance is the values of the integral.
∫(rate-in)dt | 0 to π = ∫(rate-out)dt | 0 to 2π
rate-in ≠ rate-out
Balancing of the flux flows will never happen when the integral limits are different.
If rate-in is sin(t) and t is from 0 to π then the average value is 0.6.
If rate-out is e^-x and t is from 0 to 2π then the average is 0.16
It’s actually far more complicated than this since the instantaneous rate-out value from 0 to π is also a function of the instantaneous temperature change from the sin(t) input.
I notice you do not show what my error actually is!
If rate-out is determined by T^4 then what is the integral of T^4?
∫T^4dT = T5/5
This does, of course assume that T is a constant. In actuality it is a decaying exponential, e^(-x).
I’ll leave it to you to try and evaluate that integral. I can assure you that it won’t generate an average rate-out value that is equal to the rate-in value.
So it is *MY* point that still holds. You cannot assume that the average rate-out value is equal to the average rate-in value. The values will never be the same and so assuming a balance in the two values is wrong. It requires assuming that the rate-in and rate-out operate over the same time intervals and a subject to the same functional relationship.
This is the same kind of non-physical assumption that climate science is famous for, e.g. the “average” diurnal temperature of the earth’s atmosphere is (Tmax + Tmin)/2.
“Third, we have very good real-world measurements that show that many physical substance – like liquid water – have absorptive and emissive properties very close to an ideal blackbody.”
Malarky! The difference of the Earth from a black-body is obvious when looking at the diurnal temperature profile. The maximum temperature of the Earth occurs HOURS later than maximum insolation. That is *NOT* the profile of a blackbody.
A blackbody has no specific heat value. You cannot say that a blackbody heats up by x degrees per joule.
Assuming the Earth is a blackbody is just one more non-physical assumption made by climate science.
All of these kinds of non-physical assumptions result in an uncertainty associated with any attempt to determine the effect of CO2 that overwhelms any differences used to determine the effect itself.
Malarky! This is just one more non-physical assumption made by climate science.
The amount of heat injected into the biosphere from the sun happens over HALF OF A DAY.
So what? It does *NOT* mean that flux in equals flux out at any point in that 24 hours. Meaning the average value for each flux *has* to be different.
Then how can you ASSume that the average flux-in equals the average flux-out?
I asked you once about when the flux out is at max. You didn’t answer. Can you answer now? At least you admit that there *is* an output during the day.
What is the input at night? 0 (zero)?
Output happens over the entire 24 hour period. Input only happens over approximately half of the 24 hour period. How can the average rate-in equal the average rate-out?
Tim, everytime I think you can’t get more ridiculous, you prove me wrong!
You say: “Yes, you have to know the rate. BUT THE RATES DON’T HAVE TO BE EQUAL.”
As I keep saying: I NEVER SAID THEY WERE EQUAL. And again, the fact that I am talking about a NET variable means very clearly that I am arguing that they do not need to be equal.
Then in your math, you use: ∫(rate-in)dt | 0 to π. If you are talking about the solar input then ∫(rate-in)dt | 0 to 2π has the same value because the ∫(rate-in)dt | π to 2π is zero!
I explained earlier what your error was in integration:
“Elsewhere you discuss the integral of T^4 flux over time, and assert this has the form of T^5/5. NOOOOO!!!! You only get the T^5/5 form if you integrate over temperature T. This is a high school math error, and completely blows any arguments you make out of the water.”
In this post you dig yourself deeper by asserting: “This does, of course assume that T is a constant.” Ummm, there is no point in integrating over T if it is constant!
The fact that you cannot recognize this very basic math error even after it is pointed out to you tells me that you are just far out of your depth here.
You say: “You cannot assume that the average rate-out value is equal to the average rate-in value. The values will never be the same and so assuming a balance in the two values is wrong.”
Once again, I NEVER SAID THEY WERE EQUAL!!!! In a response to Jim, I presented the 1st LoT equation for integrating the rates over a 24-hour period as:
DeltaSystemEnergy24 = EnergyIn24 – EnergyOut24
“DeltaSystemEnergy24” is a VARIABLE. Nowhere is it required to be 0.
You say: “The difference of the Earth from a black-body is obvious when looking at the diurnal temperature profile. The maximum temperature of the Earth occurs HOURS later than maximum insolation. That is *NOT* the profile of a blackbody. A blackbody has no specific heat value. You cannot say that a blackbody heats up by x degrees per joule.”
I have no idea where you get these ridiculous notions about blackbodies, but they are just plain WRONG! The notion of an idealized blackbody is simply about the surface radiation properties. It absorbs all incident radiation upon it, and it radiates with a flux density of Sigma * T^4, where T is the instantaneous surface temperature.
As I explained above, this is the output flux density “regardless of the radiative flux coming in, which could be greater than, or less than, this. So the assertion that “what comes in immediately goes out” is just WRONG!”
There is NOTHING in the definition of a blackbody that says that the body has no specific heat value and no thermal inertia. If the output flux is less than the input flux, the body temperature increases. If the output flux is greater than the input flux, the body temperature decreases.
You say: “The amount of heat injected into the biosphere from the sun happens over HALF OF A DAY.”
But it repeats over a full day. So my assertion that the fundamental period is a full day is correct. If you did a Fourier transform on insolation flux values over time, by far the dominant period/frequency would be diurnal.
You say that the idea that there is a dominant 24 hour period for both inputs and outputs “does *NOT* mean that flux in equals flux out at any point in that 24 hours.”
Once again, I NEVER SAID THAT IT DID!
Then you say that this “Mean[s] the average value for each flux *has* to be different.”
NO IT DOES NOT! The average values do not *have* to be the same, but they *can* be – there is nothing preventing it!
You ask: “Then how can you ASSume that the average flux-in equals the average flux-out?”
I never made any such ASSumption!l
Then you ask: “I asked you once about when the flux out is at max. You didn’t answer. Can you answer now?”
All right, the maximum surface temperature is usually in the early afternoon, so this is when the flux output is greatest.
You ask: “What is the input at night? 0 (zero)?”
The shortwave solar input at night is zero. But the downwelling longwave input is not zero. And it is greater with high humidity than low humidity, greater on a cloudy night than a clear night.
Next you ask: “Output happens over the entire 24 hour period. Input only happens over approximately half of the 24 hour period. How can the average rate-in equal the average rate-out?”
Seriously? You think that if the two profiles are different “shaped”, their average values MUST be different?
Let’s take a toy example: Input flux is 2X for 12 hours, 0 for 12 hours. Output flux is 1X for all 24 hours. Both average to 1X over the 24-hour period. (I am not saying this is exactly what happens, just illustrating how it is possible.)
It is increasingly clear that both the math and the physics of this topic are completely beyond you!
If they are not equal then the Trenberth diagram is garbage since it is trying to equate in and out flux rates. Which has been my argument from the beginning.
Are you now agreeing that the Trenberth diagram is garbage?
Trenberth doesn’t show the NET variable. It shows the flux rates!
Huh? We are talking AVERAGE VALUES of the rates. x-in/12 ≠ x-in/24! Trenberth uses RATES, not quantities.
You are *still* trying to substitute QUANTITY for RATE.
“I have no idea where you get these ridiculous notions about blackbodies, but they are just plain WRONG! The notion of an idealized blackbody is simply about the surface radiation properties. It absorbs all incident radiation upon it, and it radiates with a flux density of Sigma * T^4, where T is the instantaneous surface temperature.”
If the flux intensity is related to T, then the flux intensity in, which is determined by the temperature of the generating black body (body1), does *NOT* have to match the flux intensity out since the receiving black body (body2) does *NOT* have to be at the same temperature as the other body (body1).
An ideal black body is in internal thermal equilibrium. The inside of the black body is the same temperature as the surface of the black body. It is that temperature that determines the outgoing radiating flux.
Trenberth requires assuming that the radiating flux in and out are the same, the very definition of “balance”. It’s not a correct assumption.
If it doesn’t change temperature and immediately start to re-emit heat it has received then how do two bodies ever reach equilibrium?
That’s not an answer. Of course there is nothing preventing it – EXCEPT THE DIFFERENT TIME PERIODS FOR THE HEAT-IN AND HEAT-OUT!
If a blackbody had a specific heat capacity then it couldn’t be assumed to be in equilibrium internally and it *would* have thermal inertia. Thus it would not emit according to Planck’s law. In other words it wouldn’t be a blackbody at all. You are confusing an ideal blackbody with the real world.
Once again, SO WHAT? The heat that gets injected occurs over a half day, not the full day. The fact that it is repeated still doesn’t lead to being able to equate the RATES of heat-in and heat-out!
Actually no. You would have at least three waveforms, a +/- f and a DC component.
Again, so what? You would have a whole series of frequencies. The amplitude at 1/day would be about 0.5 and at 2/day would be about .4. Almost equal. The rest of the harmonics would make up the difference which would make the function look like a half-wave rectified cosine wave. That’s hardly making the diurnal period a “dominant* one.
They *have* to be if you want their integrals to match. In this case if the integrals don’t match then you are either injecting more heat then you are losing or you are losing more heat than you are gaining. What happens to the earth is dependent on the HEAT injected/lost. Not on the rate at which each happens while it is operative. One way the earth would be a molten ball by now or it would be a frozen ball.
The average rate over 12 hours can’t be the same as the average rate over an hour or you get a mismatched heat integral. Thus balancing RATES requires assuming that the earth only loses heat at night – meaning any physical outward measurements of radiative flux will *never* read what you expect from the non-physical assumption.
Only if you assume that the heat-in and heat-out have the same waveform! They aren’t the same. One is a rectified cosine and the other is a exponential decay where half of it is dependent on the cosine input!
What is equal is the TOTAL HEAT, the integral of the rates, not the rates themselves!
You are trying to convince everyone that
[∫cos(t)dt]/t = [∫e^-tdt]/t
(and also assumes the sun insolation is a perfect cosine)
But the average of the left side is something like sin(t)/t and of the right side is (1-e^-t)/t
Those average values will *not* equate. They both converge on 1 as t
-> 0 but that hardly applies here.
I have yet to see any actual math from you that shows you can equate flux rates using averages when the functions are so different.
You, and climate science, seem to always assume that (Xmax+Xmin)/2 is the average of anything, including flux rates. The real world just doesn’t work that way.
What systems have you done using averages when there is a temperature term to the 4th power? That is a rather large nonlinearity. I’d be interested in what power system has that large of a factor involved.
And, on land what is the control mass being discussed?
Look at the Trenberth radiation diagram. Climate science quite literally ignores any transfer functions introduced by the 1st absorbing mass, that is the land/ocean masses.
“That is a rather large nonlinearity”
The breakpoints of sunrise and sunset represent non-linearities that are simply not considered by climate science. Yet it is those non-linearities that determine the time intervals for heat-in and heat-out! Climate science just assumes that both heat-in and heat-out are constant over the entire 24 hour diurnal period. Thus it follows that the average heat-in is equal to the average heat-out allowing a “balance” in the flux-in and flux-out.
It is *exactly* like assuming that two cars with the same velocity cover the same distance even though one travels for twice the time of the other. Just ignore the time intervals and assume everything is equal.
The point is that the “net radiation” is not simple to calculate except under very specific conditions. Both black and grey bodies are assumed to immediately have their temperatures in raised upon absorption resulting in radiation at the new temperature. That alone should tell one that there is a time element in determining the rate of change in the net flux. That means one can not equate fluxes except at the condition of temperature equilibrium.
Tim had a good explanation.
Look at this graph. Where exactly would the fluxes ever balance?
The emissivity is not the question. The question has to do with WHEN the emissions are equal with the absorptions when using fluxes to balance energy flows.
Averages are absolutely the worst way to deal with exponential functions containing trig functions.
Jim, you ask: “What systems have you done using averages when there is a temperature term to the 4th power?”
I didn’t say that I had worked with 4th-power effects; I said non-linearities. Please learn to read!
The effecct I was thinking about was applying pulsed on/off voltage to a circuit with significant inductance, which results in a sawtooth current waveform. The resistive power loss at any instant is I^2 times R. Because of this non-linearity, the sawtooth waveform has higher losses (and generated heat) than a constant current at the average value.
You ask: “on land what is the control mass being discussed?”
That’s an interesting question. Above, you cited the equation Q = m * c * DeltaT. Implicitly, you defined your control mass by setting “m”. Effectively, the climate models define many, many control masses of the land, sea, and air, calculating inputs and outputs for all of them. (I am certainly not claiming they do this perfectly, or even well enough to be useful, but they do it.)
You say: “one can not equate fluxes except at the condition of temperature equilibrium.”
As I told Tim, the very fact that I talk about net radiative flux means that it is NOT zero in general, so I am not trying to equate fluxes at any particular time!
You quote Tim as saying: “Since the heat-in and heat-out curves are complex combinations of sinusoids and exponential decays the mean values of heat-in and heat-out are *not* simple arithmetic means.”
Actually, this is wrong. As you keep saying, you must integrate these flux rates over a time interval to get energy in and energy out. As an example, let’s use 24 hours as our time interval. So we have the integrated quantities EnergyIn24 and EnergyOut24.
The First Law of Thermodynamics tells us that:
DeltaSystemEnergy24 = EnergyIn24 – EnergyOut24
To get the mean values, we just divide these integrated values by the 24-hour time period. So the mean (rate) values by the 24-hour time period.
To be sure, because of the non-linear relationship between temperature and radiative flux rates, you cannot say the same about mean temperatures. But you most certainly can about the input and output rates themselves.
What are sunrise and sunset except non-linearities?
Then how does the Trenberth diagram make any sense? If the values of the flux-in and the flux-out are not equal at all points in time then how can their averages be the same? The average value of a sinusoidal input and an exponential decay have the same average value over the same time period?
Energy is not flux. Energy is joules. Flux is joules/time.
To get the mean values of what? Heat? or Rate of heat transfer? You are equating heat-in and heat-out over the 24 hour period, NOT THE RATES OF HEAT TRANSFER. The Trenberth diagram is equating RATES. You keep jumping from HEAT to rate.
Now this is downright surreal!
I started by talking about power fluxes in Watts (or power flux densities in W/m2). Jim insisted that energy (“heat”) was the important quantity, so I integrated over time (24 hours) to get the heat energy value.
As I explained, if you just divide the value integrated over time by the time interval, you get the mean RATE. (The explanation got a little garbled during editing.) Apparently, this is too difficult a concept for you.
You say: “The Trenberth diagram is equating RATES. You keep jumping from HEAT to rate.”
I went from rate to heat for Jim, but sometimes it is clearer to talk about RATES. It’s not hard for most people to keep up!
The rate of energy absorption and emission are not conceptually equivalent to heat.
If I add 1000 joules to 1 kg of a substance A at 20°C with a given specific heat value, ∆T may be 4°C. If I add 1000 joules to 1 kg of another substance B at 20°C, the ∆T may only be 1°C.
Since T_total determines the radiated flux, which substance radiates more?
The problem is that this ignores the heat storage of soil and oceans. Both bodies diffuse heat into their interiors for later release. That can be hours, to monthly, to seasonal. This heat will not be reflected in a flux leaving those bodies. This is called heat inertia. It is very visible on the graphs I have posted.
By attempting to “balance radiative” flux, the Trenberth diagram missed all this. Let me add that fluxes are an intensive property. They must be converted to extensive properties such as through the heat equation.
Again this ignores heat inertia of the land and oceans. It is common knowledge that oceans can preserve OHC for periods as long as centuries. Land warms slowly and cools slowly. The direction is seasonal and a 24 hour “average” will not encopass the variation.
The rates are intensive properties. You can’t just assume they will be equivalent. Changes in temperature (∆T) across a boundary is dependent on both mass and specific heat of a substance. If you wish to average properties, you should use “Q”.
Jim, you say: “this [the energy balance equation] ignores the heat storage of soil and oceans.”
It does no such thing! In my equation:
DeltaSystemEnergy24 = EnergyIn24 – EnergyOut24
the quantity “DeltaSystemEnergy24” is the “Q” in your equation:
Q = m * c * DeltaT
This IS the heat storage! The product m*c is the “heat inertia”. You keep using equations when you have no idea what they actually mean!
Be careful of who and what you accuse people of not knowing.
No, “DeltaSystemEnergy24” is not Q in the heat equation. “Q” is the number of Joules it takes to raise the temperature 1°C. If one KNOWS the total number of Joules added to a substance AND the specific heat of a substance, AND the mass of the substance, the anticipated temperature rise (∆T) can be calculated. That temperature rise is part of what determines the emitted flux.
Your equation is short at least one item, stored heat for longer than 24 hours. When heat is stored for periods longer than 24 hours, the energy equation you have will not balance.
If that wasn’t the case, soil would not warm day by day in spring time. Conversly, soil would not begin to cool in the fall. This is the danger in using averages of intensive properties like, flux and temperature.
You are conflating energy and themodynamic heat. They are not equivalent. Joules of energy absorbed and joules of heat can be equal only in very specific circumstances. Most of the time, equating them is conceptually wrong. There are too many processes at work where energy is transformed to something oth
er than heat.
Jim, you say: “Be careful of who and what you accuse people of not knowing” in response to my claim that “You keep using equations when you have no idea what they actually mean!”
I’m afraid your latest post just confirms my point!
Upthread, YOU introduced the equation:
Q = m•c•∆T
into the discussion, explicitly stating that that Q is energy in Joules, and that it is the integral over a time period of the rate of flux.
So we could be on common ground in the discussion, I integrated the rates I was talking about over a 24-hour period, yielding the 1st LoT equation for the day:
DeltaSystemEnergy24 = EnergyIn24 – EnergyOut24
All the terms in this equation are energy in Joules. So I used YOUR equation where Q is the energy in Joules.
But now you say: “No, “DeltaSystemEnergy24” is not Q in the heat equation. “Q” is the number of Joules it takes to raise the temperature 1°C.” That shows that you do not even understand the equations that YOU introduce!
Then you say: “Your equation is short at least one item, stored heat for longer than 24 hours. When heat is stored for periods longer than 24 hours, the energy equation you have will not balance.”
What??? My equation is the most basic statement of the 1st Law of Thermodynamics, expressed over the time period of interest. The change in STORED energy is the difference between the energy input and energy output over that period. If the input is greater than the output over that period, the stored energy increases.
You are concerned what happens when “heat is stored for periods longer than 24 hours”. Well, that (obviously) depends on what happens in future periods. Let’s say that in our first 24 hours, inputs exceed outputs, so the stored energy increases. If over the next 24 hours, inputs equal outputs, so the change in stored energy for this period is zero, but the increase in stored energy from the first 24 hours remains. This is basic, basic thermodynamics, but it is beyond you!
After focusing on “stored heat” time after time, you accuse ME of “conflating energy and thermodynamic heat”. While it is true there are other ways of storing energy, you are changing the terms of the discussion here from the terms YOU introduced!
This is getting incredibly tedious. You simply do not have the background context to deal capably with these issues.
Both of these statements assume the energy from both the sun and atmosphere are additive at the surface thereby raising the temperature of the surface. This is impossible. It results in a series of ever increasing energy flows between the two objects.
In this diagram, the surface temperature is controlled by the sun. The sun’s insolation is a constant and the surface doesn’t cool. It stays at the temperature derived from 164 w/m². In essence it is at equilibrium with the sun.
Anyway one cuts it, a decrease in the cooling rate of the warm body is a reduction in entropy. It means that entropy would decrease which is impossible in nature without work being done.
It must be remembered that temperature is a measure of sensible heat. One can not discuss energy flux without also dealing with temperature, i.e., heat. They are linked. If the cold body raises the hot bodies temperature from where it should be (an increase in heat), a decrease in entropy has occured.
Here is a textbook that discusses this.
Callen’s axiomatic formulation shows that spontaneous heat flow from cold to hot (increased temperature) is forbidden because it would reduce total entropy.
Planck also discussed entropy at length with the same result.
I owe you $25.
I have a bank account (T1) with $2000 in it.
You have a bank account with $1000 (T2) in it.
I write a check to you for $25.
My bank account has $1,975 in it.
Your bank account has $1,025 in it.
Hot to cold w no net hocus pocus.
Figure 2 from your post.
Originating from the Sun.
169 – 22 – 76 = 1st 71.
Originating from a magical, theoretical, “What if?” S-B at 16 C calculation that fills the denominator of the emissivity ratio & is 116% of ISR, 245% of the surface violating LoT 1
392 BB – 321 “back” = 2nd 71 duplicate violating GAAP.
How come the 1st 71 is not shown??
If it is missing, there is no way this graphic balances.
Mistake or deceit??
If it appears both places one loop can be erased. Delete the imaginary, hocus pocus magical one.
Energy is a thermal property.
Heat is a thermal process, energy in motion flowing from hot to cold.
Using power flux, W/m^2, for balance is dumb. It is chosen to toggle between power flux and temperature which is misleading.
A balance is done in Btu/Eng h or kJ/SI h.
You will never convince a religious fanatic. I have pointed Willis at proofs of the nature of E-M field and it is beyond his understanding.
https://pubs.aip.org/aip/acp/article/1531/1/11/922276/125-years-of-radiative-transfer-Enduring-triumphs
For some reason most people readily grasp the nature of gravitational field interaction and the communication between two two masses at the speed of light but do not grasp the same communication for light (or EMR) itself between two objects at different energy levels. Hence the desire to shift the T^4 terms outside brackets. It leads to a whole world of confusion and lack of clarity that is exploited by the “greenhouse” nonsense..
Rick, if you’re going to accuse me of lack of understanding, how about if you have the spine to link to what you said and what I responded? I’ve had it with vague unsubstantiated nasty accusations.
w.
You wrote this:
The part I have highlighted is wrong. Longwave radiation from atmosphere to surface does not exist unless there is a temperature inversion. You are removing brackets in an equation where the terms cannot be separated physically. It is like saying that the gravitational force on an object is only related to its mass and nothing to do with other masses that it is commiunicating with through the gravitational field.
There have been numerous times when I have provided you with links to Mischenko’s papers and you clearly have not understood them because you are still doing what the climate clowns do.
Your normal practice is to edit out the things that you disagree with when you lose your point.
More accusations, now that I’m a “climate clown” and I “edit out” things I disagree with, but you still don’t have the albondigas to link to where I supposedly did these things.
Since you appear to be hard of reading, let me repeat this from the head post:
“When you comment, QUOTE THE EXACT WORDS you are referring to. I can defend my own words. I can’t defend your interpretation of my words. Thanks.”
Next, you say:
“Longwave radiation from atmosphere to surface does not exist unless there is a temperature inversion.”
This is true about NET longwave radiation. However, it’s not true about individual radiation flows. There is a constant flow of radiation between objects, as well as between objects and radiatively active gases.
You cite Michael I. Mishchenko. Let me cite “An Introduction to Atmospheric Radiation”, KN Liou, 2002.
Liou describes the standard two‑layer greenhouse description based directly on Liou’s framework and commonly used in modern atmospheric‑radiation analyses (emphasis mine):
“We are assuming that each layer is at a constant temperature and absorbs all infrared radiation energy impinging on it, and then emits infrared radiation out its top and its bottom in equal amounts (because the layer emits infrared radiation energy in both directions equally).”
I’m sure you can figure out where the IR coming out of the bottom of the atmosphere is going … but if you can’t, in the same derivation, Liou explicitly states the consequence for the surface:
“At Earth’s surface, there is the incoming solar radiation energy that is absorbed and the tropospheric downward emitted infrared radiation, equivalent to three times the incoming solar radiation energy that is absorbed.”
What Mishchenko did in his most interesting article was to put the field of radiometry on a solid theoretical basis derived from first principles. This was indeed an advance for the field.
However, what he did NOT do is show that the use of radiometers in the normal manner using the normal radiative transfer theory causes problems or gives inaccurate results.
Mishchenko writes:
This is fearmongering without evidence. The paper provides:
• No examples where WCR measurements fail
• No quantification of errors introduced by the standard radiative transfer theory
• No climate applications where his admittedly valid first-principles-based microphysical approach changes results
Basically, Mishchenko’s paper says “WCRs give the right answer but for the wrong reasons”, which is true.
Mishchenko admits that in his conclusion, saying that “These firmly established facts make the combination of the radiative transfer equations and a WCR useful in some well-defined applications and help “rescue” the majority of documented uses of the phenomenological radiative transfer theory”.
This clearly suggests the practical impact is negligible. If the standard radiative transfer theory has been producing incorrect results for climate science for 125 years, show us the errors.
Best regards,
w.
Your post shows you appreciate that you now know you are using a non physical sum to arrive at a number that has no physical relevance. So you are learning. Which proves I was wrong calling you a religious fanatic. To make my point on why you should use physics rather than sums that give an answer is to highlight the errors as you asked.
The southern ocean surface is cooling not warming.
OLR is increasing not decreasing on average. But not everywhere; notably just north of the Equator is reducing
Albedo is reducing on average but not everywhere; notably just north of the Equator it is increasing
Ocean heat content in the SH is decelerating not accelerating while CO2 continues to rise.
Ocean heat content increase is concentrated in the region of the Ferrel cells in both hemispheres. Both regions show a net radiation loss not gain. That means OHC is the result of accelerated advection from tropics to poles not localised GHE.
Net radiation is going up faster than ocean heat uptake.So missing heat is increasing!!
Ocean surface temperature levels off at 30C and there is no surface temperature response to ToA solar forcing above 425W/m^2.
None of these observations are explained by GHE.
Using convoluted, unphysical sums to arrive at an answer does not display understanding and leads to muddled thinking. The sort of thinking that gives rise to GHE.
Placing Hansen’s energy balance diagram that Nicholas highlighted in the various UNIPCC reports proves they are unscientific junk.
Y’know, Rick, against my better judgment, I decided to discuss this with you. I didn’t want to because you endlessly insult me. But I decided to make this a test case.
In response to my raising a number of points regarding Mishchenko, you haven’t quoted and rebutted a single one of them.
Instead, you say:
“Your post shows you appreciate that you now know you are using a non physical sum to arrive at a number that has no physical relevance. So you are learning.”
Piss off. The first rule of pig wrestling just came into play. Go insult someone else. I’m done with your nastiness.
w.
You admitted you now know you are using non-physical sums to arrive at an answer. I know your answer is wrong and I listed all of the observations that prove your answer wrong. All those observations that cannot be explained by GHE theory. You made no effort to show how GHE theory explains those observations.
Where I was educated I had to show step-by-step how I arrived at an answer. If I stumbled across the right answer but the method was wrong I got no marks. You know your methods is wrong and I know your answer is wrong. Because the ECS that you define is so close to zero that it is unmeasurable.
I usually do not comment on your rubbish ECS but I thought I would point out to Nicholas that he was wasting his time and you have proven that.
“Albedo is reducing on average but not everywhere; notably just north of the Equator it is increasing”
The greening of the earth *has* to be a part of the reduction in albedo. That greening puts some of the incoming heat into heat sink transfer (i.e. ocean and land) as opposed to reflection back to space making the whole thing a time function. Averages won’t work properly because of this.
‘Basically, Mishchenko’s paper says “WCRs give the right answer but for the wrong reasons”, which is true.’
Exactly. In other words the phenomenological physics (Mishchenko’s term) that mistakenly equates atmospheric ‘radiance’ with the ‘directional flow of radiant energy’.
In practice this has lead to the mistaken belief that the bulk of energy transfer through the troposphere (outside of the atmospheric window) is attributable to radiant transfer by GHGs, rather than to bulk convection initiated by the thermalization of excited GHGs by collisions with non-IR active gas species within meters of the Earth’s surface.
And this, unfortunately, has lead to decades of climate alarmism, manifested mainly through the vilification of mankind’s CO2 emissions.
From the conclusion of Mishchenko’s paper:
“Paraphrasing the famous pronouncement by Willis Lamb, Jr. that “there is no such thing as a photon”, we can conclude that there is no such thing as the specific intensity [radiance] allegedly quantifying multidirectional flow of electromagnetic energy.”
Frank, it seems you missed the part about it being the “right answer’.
w.
Willis, I don’t think so. With all due respect, I think when Mishchenko (and others) refer to the ‘right answer’, they’re talking about how the temperature gradient (lapse rate) of the troposphere, as derived from the RTE, matches that measured by radio sondes, NOT how energy is actually transported through the troposphere.
As you well know, if one feeds the temperature, pressure and atmospheric composition into a radiative transfer model, one can obtain the spectral radiance for that level of the troposphere. (van Wijngaarden & Happer, among many others, have published several papers where they’ve done exactly this).
Alternatively, one could measure the radiance at that same level, using a suitable ‘WCR’ located at that point, and then back-solve the RTE to obtain temperature, which obviously should match that measured by the radio sonde. In other words, they get the right answer, i.e., temperature, but that doesn’t mean that energy transfer through the troposphere occurs via the spontaneous absorbtion and emission of IR by GHGs.
Note, it’s not necessarily a bad thing to get the right answer for the wrong reason – we all make use of many heuristics, some of which don’t bear up to scrutiny, to navigate through life. But if the wrong reason opens the door to abuse, that’s a problem, hence the need to take a good look at the ‘phenomenological’ physics espoused by KN Liou.
It’s not “bulk transfer” if it happens in all directions and emitted energy is captured again within meters as happens near the ground.
On the other hand it’s very much bulk transfer higher in the atmosphere where the upwards component is increasingly emitted without subsequent capture.
I didn’t say ‘bulk transfer’, but ‘bulk of’, as in the majority of.
More importantly, however, you need to explain how the spontaneous emission of energy from ground level CO2 atoms in their excited state occurs when these atoms are 50K times more likely to undergo non-radiative deactivation (thermalization) via collisions with non-IR active gas species.
Yes, just above the ground the vast majority of the energy radiated from the ground is indeed captured and transmitted to the surrounding molecules.
But then its just statistics. Collisions either add energy for potential subsequent radiation or remove it back to the atmosphere. There are a LOT of molecules and some of them do radiate and its more and more with altitude (and lower density).
We know how much energy leaves the earth because over 24 hours, its the same as the energy that arrived from the sun.
From there, we can measure the various ways the energy moves upwards in the atmosphere to escape and the Trenberth diagram is that answer.
If you think conduction and convection account for far more than Trenberth, then you can make an objective argument for the energy flows but I’ve only ever seen subjective arguments which are basically worthless.
Tell you what, Tim, why don’t you stop trolling and just review this attachment. And then let me know exactly what you believe Shula & Ott got wrong and why we should believe Trenberth’s little cartoon.
https://andymaypetrophysicist.com/wp-content/uploads/2025/01/Shula_Ott_Collaboration_Rev_5_Multipart_For_Wuwt_16jul2024.pdf
So from that article, I expect you believe there is no such thing as emitted radiation by the atmosphere at sea level? Is that your position?
Tim, that’s not at all what they say. Looking at CO2 at SL, their calculations show that CO2 in its excited state is 50K times more likely to be returned to its ground state by non-radiative deactivation than via spontaneous emission. There is still a radiative field, whose radiance we can measure [f(T)], but it’s isotropic and does not convey energy in any direction to the extent implied by Trenberth’s EEB cartoon. This all excludes, of course, the energy conveyed by the so-called atmospheric window.
What S&O do say is that because GHGs collide with non-IR active gas species, there is no direct linkage between radiation emitted from the surface and that emitted to space at TOA. Instead there is convective troposphere where energy emitted by the surface is preferentially converted to sensible heat and then lifted aloft to various altitudes where this sensible heat is preferentially converted back to radiation, which can then radiate out to space. (As an aside, please note that even radiative transfer authorities like vW&H are very clear that CO2 does not spontaneously radiate to space below 80km, or so).
One last point about our convective troposphere – as rising air parcels expand, they are doing work and their entropy increases, hence the process is irreversible, negating the possibility of so-called ‘back radiation’. So there is a so-called GHE that keeps us warmer than what the S-B equation would imply based on TOA emissions. But it’s convective (just like a ‘real’ greenhouse), not radiative.
It is what they say.
And their figure 9 confirms it. They claim near extinction and no downwards radiation at the surface. It’s right there.
What they don’t do is actually calculate how much radiation there is.
Tim, I don’t see any discrepancy between what they said:
“The process of thermalization results in the near extinction of most radiation in the absorption/emission of the GHG bands a very short distance from emission at the Earth’s surface.”,
and what you said:
“Yes, just above the ground the vast majority of the energy radiated from the ground is indeed captured and transmitted to the surrounding molecules.”
They’re saying the surface radiation is captured by the GHGs near the surface. But they then claim there is essentially no emitted radiation by the atmosphere near the surface. The specifically say “Thermalisation prevents back radiation from GHGs”
Its very clear from their figure 9 which I cant seem to post a picture of because WUWT has issues for me and images.
But it seemed to post anyway.
“We know how much energy leaves the earth because over 24 hours, its the same as the energy that arrived from the sun.”
But the value of the amount of energy leaving per unit time, i.e. the flux leaving, is not the same as the flux that initially came in. Heat transfer *is* a time function, not a Black Body radiative process. And if you are going to use “averages” then those averages must be based on integrating the component fluxes, not on minimum and maximum temperatures. Heat-in happens in a 12 hour period, heat-out happens over a 24 hour period. Not a black body process in any way, shape, or form.
Trenberth’s diagram isn’t meant to be representative of any actual flows just like the global average surface temperature isn’t representative of any actual surface temperature.
It does, however, put a perspective on the flows.
It really doesn’t put a perspective on the flows unless the time differentials are also included. Flux out will NEVER equate to flux in (except perhaps at a single crossover point). Thus the average flux out and the average flux in will never be the same. Thus trying to “balance” flux-in and flux-out can’t give you a usable answer.
There will *never* be a balanced radiation value in and out. Thus a “radiation budget” is a phantom. All the Trenberth diagram is good for is to show that there is a flux in and a flux out – that’s not much of a perspective.
They are the same. That’s the thing about averages, they do account for variations over time. If they weren’t the same then we’d be warming or cooling. So arguably at the moment the average flux in is slightly greater than the average flux out.
“They are the same. That’s the thing about averages, they do account for variations over time.”
How can this be true? It’s the HEAT that determines temperature, not the flux. Heat is the integral over time of the flux.
When do you think the earth is at maximum flux-out? Nighttime?
If the flux values out and in are the same then how does the earth not cool wind up a frozen ball since it will lose twice the amount of heat over 24 hours than it takes in during the day from the flux-in which only occurs over a twelve hour period?
The average of T^4 is *NOT* the same as the average of T. The average of T^4 over an interval is related to T^5/5 by the integral. The average of T is related to T^2/2 by the integral. The value of T^5/5 will *not* be the same as the value of T^2/2 over the same interval let alone over different time intervals.
The average value of T from 0 to pi (daytime) is *NOT* the average value of T from 0 to 2pi (daytime + nighttime).
The daytime temperature curve is not even a perfect sinusoid. It is a complex function of heat-in and heat-out. The earth *does* radiate (i.e. lose) out even during the day. So the daytime temperature function is f(sin,e^-x). Sine from the rotation of the earth with respect to the sun and e^-x from the radiation flux outward during the day.
One more time. Flux-in occurs over a half day. Flux-out happens over a full day. The flux value out *has* to be less than the flux value in at all points or you would see the earth become a frozen ball as it loses more heat than it gains over a 24 hour day. If the flux-out value is *always* less than the flux-in value then how can the average values be the same?
It seems that what is being said that heat-in has to balance with heat-out but then the non-physical happens by equating heat-out and heat-in with flux-out and flux-in. The fluxes are RATES of heat transfer, not the amounts of heat transfer over time. Flux-out and flux-in won’t even balance in a two object system of black bodies until equilibrium. If there is a hotter object and a cooler object then S-B tells you that the flux-out and flux-in at both objects won’t balance either since the temperatures are different.
The flows are measured in terms of energy, not “heat” and the average is both over time and area. That’s why Trenberth’s diagram is a measure of energy flows, not temperatures.
Since the time intervals for incoming and outgoing are DIFFERENT, the averages of the flows simply can’t be the same value.
If the incoming averages 10 units/hour over 12 hours then the outgoing can’t average 10 units/hour over 24 hours or you will get double the amount out than you get in! It *has* to be 10 units/time over 12 hours and 5 units/time over 24 hours for there to be balance.
It is the amount of *HEAT* that determines temperature, not the rate of transfer.
1360 W/m^2 input is a rate. It’s a rate integrated over 12 hours (approximately). The rate that matches that input over 24 hours cannot average 1360 W/m^2 or you will lose more heat than you gained.
So how do you balance rates?
You simply do not lose heat via radiation only during night hours. You also lose heat via radiation during the day. It’s a 24 hour period.
It’s basically like saying that a car travelling 10 mph for 12 hours will cover the same distance as a car travelling at 10 mph for 24 hours. The math simply doesn’t work. If each car covers the same distance then the second car can only average 5 mph for the 24 hours. 10 mph ≠ 5 mph. So how can you draw a diagram balancing RATES?
You’re making strawman arguments. The time over which the average is calculated is obviously longer than a part day. Think of it as an average over all time if you like. Then its easy to see that your argument becomes irrelevant.
Where is temperature shown in Trenberth’s diagram?
“You’re making strawman arguments. The time over which the average is calculated is obviously longer than a part day.”
You are arguing a non-physical assumption. Determining the average rate-in *HAS* to be done over the period of time it occurs.
I give you the car analogy again. Let car1 travel for 2 hours at v1 velocity (equivalent average flux-in for the earth). Let car2 travel for 1 hour at v2 velocity (equivalent average flux-out for the earth). In order to balance rates the velocities must match, v1 = v2. You are trying to argue that each car will travel the same distance in the overall time period of 2 hours.
It’s *exactly* the same trying to assume that the average flux-in and average flux-out for the Earth must balance. THEY CAN’T. Either the flux-in has to be half (i.e. v1 = v2/2) or flux-out has to be twice (v2 = 2v1).
Climate science assumes that rate-in and rate-out are equal values as heat-in and heat-out. It is heat-in and heat-out that has to balance, not rate-in and rate-out. Temperature is determined by total HEAT, i.e. joules of energy, not by the rate of transfer of joules.
Absolute nonsense.
Let’s say a car travels west at 1 km per hour for an hour and then east at 2 km per hour for half an hour. It does that every day.
What is the average distance from the starting point at the end of the day after a year of doing that? It’s 0 even though the rates and times were different.
In the case of the Trenberth diagram, rates have nothing to do with average net energy flows because they’re all averaged out.
I get that you have concerns about specifics concerning rates but there’s a time and place where they matter. You can’t generalise their importance to everything.
“Let’s say a car travels west at 1 km per hour for an hour and then east at 2 km per hour for half an hour. It does that every day.”
One rate is 1km/hour and the other rate is 2km/hour. Are the rates equal? Do they balance?
What balances is the INTEGRAL OF THE RATE OVER THE TIME INTERVAL FOR EACH. 1km/hour integrated over 1 hour = 1 km. 2km/hr integrated over .5 hour = 1km.
THE INTEGRALS MATCH, NOT THE RATES!
“In the case of the Trenberth diagram, rates have nothing to do with average net energy flows because they’re all averaged out.”
1360 W/m^2 IS A RATE. It is joules/sec-m^2. 340 W/m^2 IS A RATE. It is joules/sec-m^2.
1360 is *NOT* an AMOUNT of energy, it is a rate of energy flow. Since flows occur over time you have to integrate over time to get the total energy. JUST LIKE YOU HAVE TO DO WITH THE CAR!
The Trenberth diagram is *NOT* in terms of amounts of energy, it is in terms of the rate of energy flows. And energy flows (like 1km/hr vs 2km/hr) do *not* have to be equal if the time intervals are different.
Do you *really* think 1km/hr and 2km/hr are equal?
If they are *not* equal then how can their average value be equal?
An average rate of 1km/hr for an hour means your average velocity was 1km/hr. An average rate of 2km/hr for a half hour means your average velocity was 2km/hr. If you didn’t average 2km/hr you wouldn’t have travelled 1km in a half-hour!
You can’t balance rates over different time intervals. 1360 W/m^2 insolation annually is generated from 12 hours per day of sun (give or take). Equating the radiation flux outbound annually to 1360 W/m^2 would require assuming that outbound radiation only occurs for 12 hours per night (give or take). That is a decidedly non-physical assumption! Rather than making a non-physical assumption like this (which climate science is famous for) why not just integrate the actual rates over the time period they occur and see how the total quantities in and out balance? You have everything you need to calculate the quantities.
Yes, but the average works out just fine. The average distance from the starting point over the year is still 0.
For the Trenberth diagram, the averages of energy flows over the time they used (at least months and maybe years or even all time) are all valid and balance.
How does your argument about rates alter the Trenberth diagram?
Let me put it this way, you can definitely say there is an average energy flow associated with convection over a period. You can say the same for latent heat of vaporisation. You can put them on the same diagram because they apply to the same period.
There is just no room for your concern to be an issue.
But they then become useless for calculating temperature at any point in time. With a T⁴ factor,, any smoothing, which averaging does, decreases the ability to have accurate calculations.
Tell you what. Take this graph, and using an average value of insolation from the graph and calculate what the average temperature should be using the SB equation.
Here is what I get.
Avg insolation of a sine – 750•0.7 = 525
Insolation with albedo – 525•0.7 = 368
SB calculation – (368/5.67×10⁻⁸)⁰.²⁵ = 284K
284K – 273 = 11°C = 52°F
That is a long way from the average temperature over 24 hours.
You continue to make the elementary error of integrating T^4 with respect to T instead of t (time) thus arriving at T^5/5. clearly incorrect
The correct integral is ∫Tdt not ∫TdT.
T is a time function therefore you integrate over time. It is the area under the temperature curve that determines the heat input/heat output.
Similarly for radiative flux. The flux is determined by the temperature, T^4. If you want to know the actual joules radiated overtime you have to integrate the flux curve which is joules/sec, it is a *time* function.
Why do think I keep telling you that to get total quantities you have to integrate over the time interval involved? Why do you think I keep telling you that the radiative flux is related to the temperature?
If you have the temperature profile then the radiative flux profile is nothing more than T^4 at every point on the temperature curve. If the temperature curve is plotted against time then the radiative flux curve will have a “x” value of time as well.
I am *not* integrating over temperature, T. I am integrating over time, t. 12 hours and 24 hours is time, t. 12 hours and 24 hours is *NOT* temperature.
If y = f(cos(t), t) why do you think I would integrate against dy? If y = f(T^4, t) why do you think I would integrate over T?
I still think you are confused over a rate (i.e. joules/sec an intensive property) and a quantity (i.e. joules). If joules/sec in is a cosine function and joules/sec out is an exponential function their average values will *not* be the same even over the same time period let alone over differet time periods.
You and climate science are just plain assuming that if the average “in” rate is 1 W/m^2 then the average “out” rate must be 1 W/m^2. That’s not physical. The average of a cosine rate from 0 to pi is not the same as the average of an exponential decay rate over 0 to 2pi, especially when the exponential decay curve is dependent on the cosine rate from 0 to pi.
“I am *not* integrating over temperature, T. I am integrating over time, t. 12 hours and 24 hours is time, t. 12 hours and 24 hours is *NOT* temperature.”
“If y = f(cos(t), t) why do you think I would integrate against dy? If y = f(T^4, t) why do you think I would integrate over T?”
Because you integrated over Temperature (T) not Time (t) as shown by this quote:
“If rate-out is determined by T^4 then what is the integral of T^4?
∫T^4dT = T5/5”
“The average of T^4 is *NOT* the same as the average of T. The average of T^4 over an interval is related to T^5/5 by the integral.”
As I pointed out an elementary mathematics error!
Obviously you’re embarrassed that you made such an error and are trying to cover up.
You can’t seem to be able to differentiate between “rate” and “quantity”.
The average rate is *NOT* the same as the total quantity. You integrate the rate curve over time to get an average rate. You integrate the quantity over time to get a total quantity. The average rate and the total quantity are not necessarily related when you have different functions describing the rate. E.g. the average value of an exponential decay is *NOT* the same as the average of a constant slope decay.
Arrrrgh! I told myself I wasn’t going to waste any more time refuting your nonsense, but this is too ridiculous to pass up!
You integrate the RATE curve over time to get the QUANTITY. You can divide this QUANTITY value by the time period you integrated over in order to get the AVERAGE RATE.
You claim that “you integrate the quantity over time to get a total quantity”. NOOOO! You get some value with units of (quantity * time) that probably doesn’t have any useful meaning.
If you go 30 km/hour (rate) for 2 hours, then 50 km/hour (rate again) for 2 hours, the distance (quantity) you travel is (30 * 2) + (50 * 2) = 160 km.
You can divide this distance by the 4 hour total time span to get (160 km / 4 hours) = 40 km/hour average rate.
Mathematically you can integrate the distance (quantity) value over time, but you don’t get a result that is very meaningful.
In the first 2 hours, the distance has a value D = 30 * t (with t in hours). If you integrate this over the time period, you get 30 * (t^2 / 2). Evaluating this at t = 0 and 2, you get a result of 30 * (4/2) – 0 = 60 km*hours. What does this even mean for the issue at hand? The units alone should tell you something is amiss.
And despite Phil and I pointing this out to you multiple times, you still haven’t come to grips with your fundamental mathematical error where you claim that the integral of T^4 over time (not over temperature) has the form T^5/5. Any high school math teacher would just mark this as completely wrong.
It is painfully clear that you don’t really understand the most basic issues at play here.
From post:”“At Earth’s surface, there is the incoming solar radiation energy that is absorbed and the tropospheric downward emitted infrared radiation, equivalent to three times the incoming solar radiation energy that is absorbed.””
the incoming solar radiation is in fact heat, thermal radiation. There is a temperature difference between sun and earth with sun at a higher temperature.
The IR from the troposphere is not heat and can’t cause the surface to increase in temperature.
Where and how does the troposphere multiply three times the conducted and convected energy from the surface?
mkelly, I’ve explained this over and over and over. See my posts “The Steel Greenhouse“, “People Living In Glass Planets“, and “The R. W. Wood Experiment“.
And for folks like you, RickWill, and Frank from NOVA who think the poorly-named “greenhouse effect” doesn’t exist … why is the Earth some 50°C warmer than would be expected from the Stefan-Boltzmann equation?
No vague handwaving, please, and lay off the childish insults.
w.
‘…why is the Earth some 50°C warmer than would be expected from the Stefan-Boltzmann equation?’
There is a ‘greenhouse effect’, but like its namesake at the local garden center, the hold-up in tropospheric heat transfer is convective not radiative, and is much more consistent with your Figure 3, above, in addition to your many excellent posts here at WUWT that explain ‘Emergent Phenomena’ and take down the alarmists’ ‘CO2 Roolz’ narrative.
Sorry, Frank, but I have no idea what physical process you are describing.
w.
I’m fairly certain you do, but here’s a link to refresh your memory:
https://andymaypetrophysicist.com/wp-content/uploads/2025/01/Shula_Ott_Collaboration_Rev_5_Multipart_For_Wuwt_16jul2024.pdf
Their central claim is that there is negligible radiation at ground level but they dont actually calculate it. Funny, they calculate everything else except the actual figure of their central claim.
No matter, I did with the help of ChatGPT and the answer is a lot because there are a LOT of molecules involved.
Feel free to check it, because it undermines their paper and your position.
≈1.6×10^11 molecules/cm3/second
I politely said, “Sorry, Frank, but I have no idea what physical process you are describing.”
You replied “I’m fairly certain you do …”
Now you’re accusing me of lying? What is with you people? Maybe your friends pretend to not know something, but me, I tell the truth as best I know it, and I had NO IDEA WHAT PHYSICAL PROCESS YOU WERE DESCRIBING!!!
Pass. Hard pass. I won’t engage with charming folks like you who think adults discuss contentious issues by hurling childish insults.
Have a good life, and go accuse someone else of lying. I won’t stand for it.
w.
PS—That paper is a joke. Claiming that downwelling longwave radiation doesn’t exist, when it has been measured thousands of times all over the planet both by scientists and automated instruments, is “flat-earth” level nonsense.
Heck, you can FEEL IT. On a cold clear winter night, when a cloud comes over you can feel the warmth from the big increase in downwelling longwave radiation … and you claim it doesn’t exist? Buy a damn standoff thermometer, you can measure it yourself.
Like I said.
Hard pass.
Willis, I am deeply sorry to have given you offense and to have impugned your integrity. These were not my intent. Also know that I do concur with a great deal, but not all, of your work on WUWT. So what I wrote above in that regard was by no means disingenuous or intended to curry your favor.
As to your PS, let me begin by saying that I don’t know anyone knowledgable in the subject of IR who claims ‘that downwelling long wave radiation doesn’t exist’.
First, there’s radiation emitted in the atmospheric window, all of which originates from condensed matter, i.e., the surface, dust, water droplets, etc. As you note this can bodily be felt when a cloud comes in on an otherwise cold winter night or detected by a standoff thermometer.
Second, there’s also localized radiation (radiance) from GHGs outside the atmospheric window that can be detected in the immediate location of a pyrgeometer. But this in itself is not evidence of ‘back radiation’ from higher up in the atmosphere, which has never been measured, only modeled.
As for your comment that the paper is a ‘joke’, perhaps a proper public critique of it’s points on WUWT would be warranted, if only to allay the skepticism of ‘us people’ who are aware that there are serious physicists, e.g., Michael Mishchenko and Freeman Dyson, who have serious doubts about the application of radiant transfer theory to climate science.
Frank, your gracious apology is accepted, and we can move forwards.
Below is a good analysis of the problems with the paper from my favorite AI. Usual rule applies. If you think something is incorrect about it, please quote what you think is wrong and show us why.
w.
The paper claims that standard greenhouse theory is physically wrong in the lower atmosphere because collisional thermalization of infrared‑active gases overwhelms spontaneous emission, so the usual picture of surface photons being repeatedly absorbed and re‑emitted (“back radiation,” radiative forcing) cannot operate in the troposphere. Instead, greenhouse gases are said to convert surface infrared into sensible heat within a few meters of the ground, after which convection and latent heat transport carry energy upward, and only at higher, thinner levels do greenhouse gases (mainly water vapor, plus ozone and CO₂ aloft) efficiently radiate to space, making CO₂’s role in setting surface temperature modest and undermining radiative‑transfer‑based GCMs.
To support this, the authors cite laboratory relaxation and quenching measurements showing that at near‑surface pressure, collisional deactivation of vibrationally excited CO₂ is 4–5 orders of magnitude faster than spontaneous emission, implying nearly all absorbed infrared energy is converted to kinetic energy of the air rather than being re‑emitted as photons. They argue this “destroys” the radiation field in greenhouse bands near the surface, so there is no meaningful upward radiative flux to propagate through stacked atmospheric layers, and they extend this to an atmospheric picture where radiation in greenhouse bands re‑enters the radiation field only at altitudes where the collisional rate falls enough for spontaneous emission to matter.
Hug 2012 CO₂ band measurements https://www.eike-klima-energie.eu/wp-content/uploads/2016/12/Hug-pdf-12-Sept-2012.pdf
Siddles et al. CO₂ vibrational relaxation https://www.sciencedirect.com/science/article/abs/pii/0022369776900616
Cannemeijer & de Vries CO₂ bending mode relaxation https://www.sciencedirect.com/science/article/abs/pii/0022407374900760
Roduner & Kruger on thermalization irreversibility https://www.sciencedirect.com/science/article/abs/pii/S1359028613000663
From this, they reinterpret the satellite “CO₂ notch” in outgoing longwave radiation (OLR) as largely water‑vapor emission overlapped by CO₂ and then collisional transfer, with water vapor again doing most of the actual cooling to space. They emphasize that water vapor dominates emission across the thermal‑IR spectrum, with smaller contributions from ozone and CO₂ at specific heights, and connect the observed near‑linear relation between OLR and surface temperature to convective (Newtonian) cooling rather than Stefan–Boltzmann behavior, arguing this is evidence that convection and latent heat, not radiative transfer, govern the energy balance.
Wijngaarden & Happer 2020 greenhouse gas radiation paper https://www.yorku.ca/anderson/DT/WThermal-Radiationf.pdf
Koll & Cronin 2018 OLR–surface T relationship https://www.pnas.org/doi/10.1073/pnas.1809868115
Historically, they trace greenhouse theory from Arrhenius through Schwarzschild’s radiative equilibrium model for the solar atmosphere and argue that climate science misapplied a radiative‑equilibrium framework designed for the Sun to Earth’s moist, convecting atmosphere. They claim mainstream texts conflate collisionally induced line emission with blackbody radiation, misapply Kirchhoff’s law (derived for macroscopic bodies in thermodynamic equilibrium) to gas molecules, and assume each atmospheric layer is a small greybody obeying Planck’s law, leading to the Schwarzschild radiative‑transfer equation and the concept of “back radiation,” which they reject as physically impossible under strong thermalization.
Arrhenius 1896 greenhouse paper (historical) https://pubs.rsc.org/en/content/articlelanding/2010/ay/c003442k
Schwarzschild 1906 solar atmosphere equilibrium paper https://www.digizeitschriften.de/dms/resolveppn/?PID=GDZPPN002497679_0041
Goody & Yung “Atmospheric Radiation: Theoretical Basis” https://global.oup.com/academic/product/atmospheric-radiation-9780195102918
They use van Wijngaarden & Happer’s line‑by‑line work as an example of this allegedly flawed paradigm, criticizing the use of Planck functions and Einstein A coefficients in dense air where collisions dominate, the assumption of local thermodynamic equilibrium (LTE) in the lower atmosphere, and the entire layered absorption–emission picture needed for radiative forcing. In their view, greenhouse gases “facilitate” energy flow by enabling radiation to space at high altitude rather than “trapping” heat, so the standard definitions of greenhouse effect and radiative forcing lack physical basis.
Wijngaarden & Happer greenhouse gas primer https://www.yorku.ca/anderson/DT/GreenhousePrimerArxiv.pdf
(continued below because of wordpress’s stupid word count restrictions)
(PART TWO)
They extend this critique to global climate models (GCMs), noting that CMIP6‑class models such as NASA GISS‑E2.1 rely on complex radiative‑transfer cores and tuning for top‑of‑atmosphere (TOA) energy balance, with many parameterizations and adjustable parameters. They argue that because the underlying radiative‑transfer picture is wrong, these models can only encode the assumption that CO₂ causes warming rather than test it, and they invoke comparisons suggesting models have run “hot” relative to satellite‑based temperature records to label large GCM ensembles an “expensive and worthless pursuit.”
Kelley et al. 2020 NASA GISS‑E2.1 model description https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2019MS002025
Christy & McNider satellite vs model temperature trends https://journals.ametsoc.org/view/journals/clim/30/2/jcli-d-16-0333.1.xml
Compared with mainstream atmospheric physics, their starting point—very rapid collisional deactivation in dense air—is standard, but current radiative‑transfer theory already uses this: LTE in the lower atmosphere, non‑LTE higher up, and line‑by‑line integration of gas absorption and emission rather than treating individual molecules as blackbodies.
Radiative‑convective models explicitly combine radiation and convection, reproduce observed spectra and fluxes reasonably well, and yield CO₂ radiative forcings consistent with observed changes in OLR and downwelling infrared. Surface and satellite measurements show substantial downward longwave radiation and trends matching increased greenhouse gases and water vapor, which the paper does not quantitatively reproduce under its claim that “back radiation” is impossible.
Liou “An Introduction to Atmospheric Radiation” (LTE, radiative transfer) https://link.springer.com/book/10.1007/978-1-4757-4309-7
Harries et al. 2001 spectral evidence for greenhouse strengthening https://www.nature.com/articles/35066553
Myhre et al. 1998 CO₂ forcing parameterization https://agupubs.onlinelibrary.wiley.com/doi/10.1029/98GL01908
Etminan et al. 2016 updated GHG forcings https://agupubs.onlinelibrary.wiley.com/doi/10.1002/2016GL071930
IPCC AR6 Chapter 3 model evaluation summary https://www.ipcc.ch/report/ar6/wg1/downloads/report/IPCC_AR6_WGI_Chapter03.pdf
Overall, the paper is a technically literate skeptical critique that usefully emphasizes rapid thermalization and the dual collisional–radiative role of greenhouse gases and underscores that tropospheric energy transport is not purely radiative. Its main weakness is the jump from that correct microphysics to broad claims that back radiation is impossible, radiative forcing has no physical basis, and GCMs are worthless, without offering a quantitative alternative that matches the diverse radiative observations that standard radiative‑transfer‑based frameworks already explain reasonably well.
Thanks, Willis. It will take some time for me to work through the AI summary. A priori, it seems very complete and even-handed, the main criticisms arising in the last paragraph:
‘Its main weakness is the jump from that correct microphysics to broad claims that back radiation is impossible, radiative forcing has no physical basis, and GCMs are worthless, without offering a quantitative alternative that matches the diverse radiative observations that standard radiative‑transfer‑based frameworks already explain reasonably well.’
Much to consider, but it would be nice if AI would specify the ‘diverse radiative observations that standard radiative‑transfer‑based frameworks already explain reasonably well’.
Thanks again.
Sure. Here’s what it says is reasonably well-explained …
w.
===
1. TOA infrared spectra and the CO₂ “notch”
Satellite instruments (e.g., Nimbus IRIS, AIRS, IASI) have measured high‑resolution outgoing longwave radiation (OLR) spectra at the top of the atmosphere, showing the CO₂ band near 15 µm, strong water‑vapor bands, ozone features, and the atmospheric window. Line‑by‑line radiative‑transfer models (e.g., LBLRTM with HITRAN spectroscopy) reproduce the detailed shape and magnitude of these spectra, including the depth and width of the CO₂ “notch” and its dependence on surface and atmospheric temperature, within observational and spectroscopic uncertainties.
Increases in greenhouse forcing inferred from the outgoing longwave radiation spectra of the Earth (Harries et al. 2001) https://www.atmos.washington.edu/~dennis/321/Harries_Spectrum_2001.pdf
Using IASI to simulate the total spectrum of outgoing long‑wave radiation https://acp.copernicus.org/articles/15/6561/2015/acp-15-6561-2015.pdf
Nimbus 4 IRIS spectra in the 750–1250 cm⁻¹ region https://ntrs.nasa.gov/citations/19740043639
AER LBLRTM line‑by‑line radiative transfer model repository https://github.com/AER-RC/LBLRTM
2. Spectral “fingerprints” of greenhouse‑gas changes over time
By differencing TOA spectra taken decades apart, researchers detect changes concentrated in greenhouse‑gas bands (especially CO₂), with some compensating changes in window regions. The observed spectral differences between 1970s and 1990s OLR match the patterns predicted by radiative‑transfer calculations driven by the measured rise in CO₂ and other gases, both in spectral shape and approximate magnitude, providing direct, spectrally resolved evidence that increased greenhouse gases have altered TOA radiation as theory predicts.
Increases in greenhouse forcing inferred from the outgoing longwave radiation of the Earth (Harries et al. 2001) https://pubmed.ncbi.nlm.nih.gov/11268208/
3. Surface downward longwave radiation (DLR) and trends
Surface radiation networks (e.g., BSRN and national networks) measure downward longwave radiation, which varies with atmospheric temperature, humidity, clouds, and greenhouse gases. Radiative‑transfer models constrained by observed profiles and cloud properties reproduce the magnitude and variability of DLR at many sites. Multi‑decadal analyses show significant upward trends in DLR, and the decomposition into clear‑sky and cloud contributions using the same radiative‑transfer tools is consistent with increased greenhouse gases and water vapor.
Trends in surface radiation and cloud radiative effect at four Swiss sites (Wild et al. 2019) https://acp.copernicus.org/articles/19/13227/2019/
4. Direct clear‑sky surface radiative forcing by CO₂
High‑resolution spectroscopic measurements under clear skies have detected small but statistically significant increases in DLR specifically within CO₂ bands over roughly a decade. These increases track the observed rise in atmospheric CO₂ and closely match radiative‑transfer calculations using the same CO₂ changes and atmospheric profiles, providing a direct, spectrally resolved observational confirmation of surface radiative forcing by CO₂.
Observational determination of surface radiative forcing by CO₂ (Feldman et al. 2015) https://pubmed.ncbi.nlm.nih.gov/25731165/
5. TOA broadband fluxes and cloud radiative effects (CERES)
Broadband TOA shortwave and longwave fluxes from CERES, including global means and spatial patterns, are broadly consistent with radiative‑transfer‑based model calculations using observed temperature, humidity, and cloud distributions. Cloud radiative effects (CRE) diagnosed from CERES and from model perturbations of cloud properties show similar magnitudes and patterns, supporting the use of standard radiative transfer to link atmospheric/cloud changes to TOA flux variations.
CERES top of atmosphere flux product description https://svs.gsfc.nasa.gov/31059/
Explaining recent cloud radiative effect anomalies and trends in observations (AGU abstract) https://ui.adsabs.harvard.edu/abs/2020AGUFMGC1150004R/abstract
6. Radiance closure and vertical radiative heating/cooling rates
Radiance‑closure studies compare measured high‑spectral‑resolution radiances with line‑by‑line model output using collocated profiles, typically finding small residuals dominated by line‑parameter uncertainties. Likewise, calculated vertical profiles of longwave cooling and shortwave heating (from line‑by‑line or band models) agree with profiles inferred from observations and are consistent with known dynamical structures, including CO₂‑related cooling in the middle atmosphere and ozone heating in the stratosphere.
Performance of the Line‑By‑Line Radiative Transfer Model (LBLRTM) (Alvarado et al.) http://rtweb.aer.com/docs/alvarado2013.pdf
CO₂ radiative cooling in the middle atmosphere (Fomichev et al.) https://agupubs.onlinelibrary.wiley.com/doi/
Thanks, this is very helpful. One of these days I’ll have to learn how to use AI. Btw, which provider are you using?
I use perplexity.ai. But as with all AI, you have to give it some very serious prompt instructions to keep it between the ditches.
w.
Truer words have never been spoken.
I use AI to fix syntax. Every app, every programming language have their own syntax. It all runs together (do I need ; at the end of each statement? What is the line continuation symbol, _ or | ) And then it is like a TV detective show. The first 3 arrests are always someone who didn’t do it.
Wils asked:
Long wave radiation from Earth is mostly from ice at 273K or cooler. When the surface is at 303K, the atmospheric column can cycle through convective instability in thermal equilibrium. Tiny amounts of CO2 are not going to alter that cyclic equilibrium.
Any atmospheric column with more than 30mm water column and warmer base temperature above 285K can support convective instability.
Cyclic instability requires a level of free convection (LFC) to form. That is the point in the atmosphere where radiant energy loss is balanced with radiant energy gained. The atmosphere above is cooling and compressing due to condensing or solidifying water vapour while the atmosphere below is gaining heat through radiant transfer from the surface below and sunlight above as well as convective transport from below.
The LFC forms a ceiling or barrier for convection. So radiation prevails above and results in cooling due to loss of contact with the surface. That causes the formation of ice at high altitude which is the main emitter to space.
If you use proper physics you would use atmospheric absorption rather than the wrong concept of back radiation that does not exist.
I go into a good deal of detail on the absorption aspect in the linked article:
https://wattsupwiththat.com/2025/07/17/toward-a-deterministic-model-of-cloud-development-over-ocean-warm-pools/
I include an important chart from that article:
?quality=75&ssl=1
Aa you can see, there is no ocean surface able to radiate at higher temperature than 273K because the radiation is mostly coming off ice.
So what is described as a “greenhouse effect” is better described as an “ice effect”. And small quantities of CO2 are not going to alter the ice effect.
The ice effect runs out of puff at 303K base temperature because the ice that forms above 14000m in very thin atmosphere during convective overshoot hangs around for a long time and is responsible for regulating the surface temperature.
So if you throw out the muddled thinking on back radiation, you start to see how the atmosphere actually works to cause lower average radiating temperature than the surface temperature. It is due to ice. And ice forming processes occur at precise temperature for given pressure with no known influence from minute amounts of CO2.
Being bored with you, I asked perplexity.ai to read a couple of my previous posts and answer you. Here’s that answer.
Regards,
w.
===
Your two posts already contain everything needed to see why the commenter’s “ice effect / no back‑radiation” story fails and does not answer why Earth is warmer than a no‑atmosphere Stefan–Boltzmann temperature.
From “A Matter of Some Gravity,” you show that in an isolated, non‑radiating system with gravity and an atmosphere, the second law forbids a persistent temperature gradient that can do work; left alone, the system must become isothermal. Any scheme that tries to get a permanently warmer surface solely from pressure or gravity is therefore equivalent to a perpetual‑motion machine and cannot explain Earth’s warmth.
A Matter of Some Gravity – Watts Up With That?
https://wattsupwiththat.com/2012/01/13/a-matter-of-some-gravity/
From “The Steel Greenhouse,” you demonstrate with a simple radiative two‑shell model that adding an intervening radiating layer between a heated surface and cold space necessarily raises the surface temperature, even if there is no convection and no adiabatic lapse rate at all. The only requirements are that the shell absorb some of the surface’s radiation and emit isotropically; then, by energy conservation, the surface must warm until its emission is high enough that the net upward flux to space matches the imposed heating.
The Steel Greenhouse – Watts Up With That?
https://wattsupwiththat.com/2009/11/17/the-steel-greenhouse/
Those results imply: (1) gravity and pressure alone cannot maintain a warmer surface; and (2) a greenhouse‑type warming arises purely from radiative exchange, without needing an adiabatic lapse rate. With that in mind, here’s what is wrong with the commenter’s explanation.
He says longwave emission is “mostly from ice at 273 K or cooler,” so “no ocean surface is able to radiate at higher temperature than 273 K because the radiation is mostly coming off ice.” Interpreted in steel‑greenhouse terms, he is simply saying that the effective emitting surface to space is often a cold, high‑altitude, cloudy/icy layer rather than the warm surface. That is exactly the greenhouse effect: a radiating shell above the surface intercepts IR and emits to space from a colder level, while also emitting downward to the surface.
He then argues that “tiny amounts of CO₂” cannot affect a convective “cyclic equilibrium” capped at a level of free convection and regulated by ice formation around 14 km, claiming this thermostat “runs out of puff” at about 303 K. But your gravity argument shows that without radiative coupling to a cold reservoir, convection and gravity cannot sustain any such engine. Change the radiative properties of the column (including CO₂) and you necessarily change the cooling profile that maintains his convective cycle, so his equilibrium is not independent of greenhouse gases.
He also insists “back radiation does not exist,” preferring only to talk about absorption. Yet your steel shell must emit both upward and downward to be in radiative equilibrium; the downward emission is what raises the surface temperature above the bare‑rock value. The downward flux is a physically necessary part of the energy balance. Denying its existence contradicts the very mechanism your toy model (and real radiative‑transfer theory) relies on.
Finally, his idea that an ice‑based LFC sets a hard, CO₂‑independent upper limit near 303 K is just another way of saying “cloud‑ice structures plus convection regulate surface temperature.” But as your gravity thought‑experiment makes clear, such a thermostat only works via radiative exchange with space from those ice levels; without radiation, phase change and convection cannot maintain a stable gradient. Altering greenhouse gas concentrations changes the altitude and temperature at which outgoing radiation balances absorbed solar, which in turn shifts where such ice structures and convective tops must sit. So his “ice effect” is not an alternative to the greenhouse effect; it is one particular manifestation of it.
Restating your original question in your own framework: Stefan–Boltzmann at the top of atmosphere tells you the planet must emit like a 255 K blackbody to balance absorbed sunlight. Observed surface temperature is ~288 K because greenhouse gases and clouds create one or more radiating shells between the surface and space. Those shells absorb much of the surface IR and emit both up and down; the top of the system still emits 240 W/m² to space, but the surface must emit more than 240 W/m², so it equilibrates at a higher temperature. Convection and the lapse rate shape the vertical profile, but as you have shown, the existence of the greenhouse effect—and the fact that Earth is tens of degrees warmer than the SB effective temperature—follows from radiative transfer and energy conservation alone.
So now you believe everything Perplexity AI comes up with after directing it to give the answer you want.
It simply shows you are not willing to understand and learn.
The Perplexity response is just garbage. It clearly has not understood what I wrote.
You know you are using muddled unphysical concepts so why persist.
If you are incapable of understanding what I have written then at least use Grok to assess what I have written. It is far less biased than the other large language models.
All AI is based on consensus “science” so they are useless in any case but Grok is the least useless. And Grok is able to get to the correct answer faster with the right guidance.
Rick, you say:
I didn’t give it any directions as to what answer to give.
You seem to believe that insults are a valid scientific response.
Again, insulting a result means nothing. If you think any part of it is wrong, as I’ve asked you over and over, then QUOTE THE EXACT WORDS you think are wrong, and show us why.
More useless handwaving.
OK. I asked Grok. The answer is below.
w.
The commenter’s explanation is an attempt to reframe the standard greenhouse effect mechanism under a new label (“ice effect”) while downplaying or dismissing the role of greenhouse gases (especially CO₂) and the concept of downward (“back”) radiation. It draws directly from a July 17, 2025, article on Watts Up With That by Richard Willoughby, which uses the exact chart you provided (Chart 6 from CERES satellite data) as its centerpiece “evidence.”
Here’s a clear breakdown of what the commenter (and the article) is claiming, why the chart appears to support it superficially, and why it doesn’t actually solve — or replace — the reason Earth’s surface is warmer than its effective blackbody temperature.
Core claim in plain terms· The outgoing longwave radiation (OLR) that escapes to space over warm tropical oceans almost always comes from temperatures ≤ 273 K (freezing point of water), even when the ocean surface is much warmer (up to ~30 °C / 303 K).
· Therefore, the radiation Earth emits to space isn’t coming from the warm surface — it’s mostly emitted by high-altitude ice crystals (in cirrus clouds or anvil tops of thunderstorms).
· Convection (rising warm, moist air) transports heat upward. At high altitudes, the air cools radiatively, water vapor condenses/freezes into ice, and that ice becomes the main emitter to space at cold temperatures.
· This creates a self-regulating cycle: convection only “fires” strongly above certain thresholds (e.g., >285 K surface, >30 mm precipitable water), forming a “level of free convection” (LFC) ceiling. Ice forms, regulates heat loss, and caps surface temperatures around 30 °C.
· The whole process is driven by absorption of surface IR by the atmosphere (mostly water vapor) + convection + ice physics — not by “back radiation” (which the author calls nonexistent or muddled) and not significantly by CO₂ (“tiny amounts” can’t alter the ice-driven equilibrium).
In short: “The planet radiates from cold ice high up → the surface can stay warm while the effective radiating temperature stays low → no need for a CO₂ greenhouse effect; it’s really an ‘ice effect’.”
What the chart actually shows (real data, real pattern)The scatterplot is from CERES (satellite-measured OLR) over ice-free ocean 1°×1° grids on March 20, 2025: – X-axis: local surface (skin/sea) temperature. – Y-axis: effective radiating temperature inferred from OLR via Stefan-Boltzmann (T such that σT⁴ = observed OLR). – Almost all points fall below the 273 K freezing line, even over the hottest ocean surfaces.
This is a known feature of deep tropical convection: over warm pools, towering cumulonimbus clouds form, their icy anvil tops spread out near the tropopause (~15–17 km, temperatures 190–220 K), and those cold ice surfaces emit most of the OLR to space. The surface radiation is strongly absorbed below and re-emitted higher up from colder levels. That’s why local OLR can be low (cold ERT) despite hot surfaces.
Why this doesn’t explain the surface warming (or replace the greenhouse effect)
The pattern the chart shows is a consequence of the greenhouse effect, not an alternative explanation for it.
(part 2 below)
1. The 30 °C cap is real but not proof against CO₂
Tropical oceans rarely exceed ~30 °C due to convective self-regulation (the “thermostat” hypothesis from Ramanathan & Collins 1991 onward). But this thermostat operates within a greenhouse framework: higher CO₂ raises the effective emission altitude (colder emission → less OLR for given surface temp → warming needed to restore balance). The cap exists because of water vapor feedback and convection, but CO₂ still shifts the whole system warmer.
2. Global picture vs. selected tropical snapshot
The chart is only tropical warm-pool ocean on one day. Globally averaged OLR is still ~240 W/m² → 255 K effective temperature. Over clear subtropical oceans, deserts, or high latitudes, emission is closer to surface temperature. The cold bias over convective regions is balanced by warmer emission elsewhere. The article’s focus on oceans ignores that.
SummaryThe commenter/article observes a genuine phenomenon: in the deep tropics, outgoing radiation often originates from high, cold ice rather than the warm surface. But this happens because the atmosphere is opaque to IR (greenhouse effect), which traps heat, creates instability, drives convection, and lifts moisture to form those icy emitters. Relabeling it an “ice effect” and claiming it makes CO₂/back-radiation irrelevant is like saying a car’s radiator explains why the engine is hot while denying the fuel and combustion. The ice/cirrus emission is the visible symptom of the underlying greenhouse physics, not a replacement for it.
The real reason Earth is ~33 K (not exactly 50 °C, unless ignoring albedo) warmer than a bare SB calculation is greenhouse gases raising the average emission altitude to colder levels. The chart illustrates part of how that looks over convective oceans — it doesn’t disprove or supplant the standard explanation.
I appreciate you putting the first part to Grok and I am reasonably satisfied with the response.
However I know from point 5 that it is wrong because back radiation DOES NOT EXIST. You even know that now. So Grok needs to be educated on that fact.
You have not taking Grok through the basic logic I have detailed below and repeat here:
What its the average radiating temperature of Earth?
What is the average surface temperature?
It follows that most of Earth’s OLR comes from the atmosphere – do you agree?.
What molecules in the atmosphere are able to emit long wave radiation to space?
What form does water take at the radiating temperature?
Logically is is obvious that ice is the dominant OLR emitter to space. You should be able to get Grok to agree to that. If not, you are not trying.
So it is not the greenhouse gasses that contribute to Earth’s emittance rather it is ice. Then ask Grok to propose a better short handle descriptor of the ice effect.
The ice effect explains why the surface temperature cannot exceed 303K because the high altitude ice resulting from convective overshoot into the thin atmosphere is very small and has very slow descent.
This is MS Copilot view on the topic of ice:
At an effective emission temperature of 255 K, Earth’s thermal radiation peaks near 11–12 µm, right in the centre of the atmospheric infrared window. In this spectral region, water vapour absorbs only weakly, because its rotational–vibrational lines do not significantly overlap the window. By contrast, solid ice has a much larger absorption coefficient at these wavelengths, meaning that if ice crystals are present in the atmospheric column, they interact far more strongly with radiation near the Planck peak for 255 K.
Because the upper troposphere at 255 K is extremely dry, water vapour is largely absent, but ice crystals can persist due to their slow sedimentation rates. Even very small concentrations of ice can therefore provide a radiatively active medium at the wavelengths where Earth emits most strongly. In this specific spectral region, the absorption cross‑section of ice exceeds that of water vapour by orders of magnitude, making ice the more effective emitter when it is present.
This leads to the important conclusion that at the effective emission temperature of 255 K, and at the dominant emission wavelength near 11–12 µm, ice—not water vapour—is the stronger emitter to space. While water vapour dominates infrared absorption and emission in the warm, moist lower atmosphere, the radiative physics at the emission altitude are governed by the spectral window and the materials still present there. Under those conditions, ice becomes the dominant radiating substance in the relevant part of the spectrum.
It is no accident that Earth emits at 255K because most comes from ice and it is a high absorption band for ice. Ice rules the OLR and reflected short wave. Know ice and you know climate.
Gosh, claims without citations … how scientific. Here’s an analysis of Copilot’s unsupported claims.
w.
===
Earth’s 255 K “effective emission temperature” comes from balancing absorbed solar radiation with globally averaged outgoing longwave radiation (OLR), not from any particular material’s absorption peak, and satellite spectra show that much of the emission near the Planck peak comes directly from the surface and lower troposphere through the 8–13 µm window, with strong contributions from water vapour and clouds; ice is important where present, especially in cirrus, but it does not “rule” OLR or uniquely set the 255 K effective temperature.
NASA Earth Observatory (Earth’s Energy Budget) https://earthobservatory.nasa.gov/features/EnergyBalance/page4.php
CERES Science Team, “Top-of-Atmosphere Radiation Budget” https://ceres.larc.nasa.gov/science-information/energy-budget/
Harries et al., Phil. Trans. R. Soc. A 2001 (DOI-linked abstract page) https://royalsocietypublishing.org/doi/10.1098/rsta.2000.0600
First, the claim that 255 K emission “peaks near 11–12 µm right in the centre of the atmospheric window” is spectrally imprecise, because a 255 K Planck curve peaks around 10.8 µm and the atmospheric window is usually defined roughly as 8–12 µm; within that band, satellite line‑by‑line spectra show substantial structure from water vapour continuum, ozone around 9.6 µm, and cloud/ice absorption, not a clean window where only ice matters. Measured TOA spectra (e.g., Nimbus, IRIS, AIRS, IASI) consistently show deep CO₂ and H₂O bands flanking a window region where radiances often correspond to warm lower‑tropospheric or surface temperatures over clear skies, contradicting the idea that emission at the Planck peak generally comes from high, cold ice.
NASA SORCE “Spectral Irradiance and Climate” page (Planck peak discussion) https://lasp.colorado.edu/home/sorce/data/tsi-total-solar-irradiance/
AIRS Level‑1B User Guide (examples of Earth’s IR spectra) https://gmao.gsfc.nasa.gov/pubs/docs/Susskind136.pdf
The statement that water vapour “absorbs only weakly” in the 8–12 µm window and is “largely absent” at 255 K emission altitudes overstates both points: modern spectroscopy and line‑by‑line calculations show that H₂O has weaker lines there than in its strong bands but still non‑negligible line and continuum absorption, and upper‑tropospheric humidity, while low, is not zero and plays a documented role in OLR and feedback. Line‑by‑line studies of OLR versus temperature find that water vapour remains the dominant greenhouse agent shaping the broadband OLR–temperature relationship between about 220–300 K, even though spectral windows stay relatively transparent compared with band centres; this contradicts the claim that H₂O is radiatively unimportant at emission levels.
Schwarz et al., PNAS 2018 “Earth’s outgoing longwave radiation linear due to H2O greenhouse effect” https://www.pnas.org/doi/10.1073/pnas.1721626115
Clough et al., JQSRT 2005 “Atmospheric radiative transfer modeling” (RRTM)
https://www.sciencedirect.com/science/article/pii/S002240730400243X
Regarding optical properties, laboratory and theoretical compilations show that bulk ice has relatively high emissivity in the thermal IR and non‑zero absorption across 8–12 µm, but the absorption coefficient of ice at 10–12 µm is not orders of magnitude greater than that of water vapour; rather, we are comparing a condensed‑phase solid (with high effective path length in a particle) to a dilute gas whose effect depends on column density and line strength. Warren and Brandt’s widely used optical constants indicate that ice is “moderately absorptive” in the thermal IR, and review articles note that snow and ice surfaces have emissivities of about 0.98–0.99 across thermal wavelengths, but that does not translate into ice systematically dominating emission at 11–12 µm throughout the atmospheric column.
Warren & Brandt, “Optical constants of ice from the ultraviolet to the microwave” JGR 2008 https://atmos.uw.edu/ice_optical_constants/Warren_and_Brandt_2008.pdf
Warren, “Optical properties of ice and snow” Phil. Trans. R. Soc. A 2019 https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6501920/
Part 2 below
Part 2.
In the upper troposphere, cirrus ice crystals certainly interact strongly with radiation in and near the window region, and studies using 8–12 µm channels show that small ice particles can produce notable brightness temperature differences between, say, 8.3, 11, and 12 µm channels; however, these papers treat cirrus as one contributor among others and do not claim that ice dominates total OLR or uniquely sets an “emission temperature.” Radiative transfer calculations and satellite analyses of cirrus consistently find that thin cirrus modifies OLR by on the order of a few tenths to tens of W m⁻² locally, with global mean net effects of order 0.1–1 W m⁻², small compared with the global mean OLR of about 239 W m⁻² and with water‑vapour‑driven variations.
Liou & Takano, “The effects of small ice crystals on cirrus infrared radiative properties” NASA NTRS 1992 https://ntrs.nasa.gov/citations/19920067717
Yang et al., “Effects of ice crystal habit on thermal infrared radiative properties of cirrus clouds” JGR 2007 https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2006JD007899
Spang et al., “Radiative effect of thin cirrus clouds in the extratropical lowermost stratosphere” ACP 2024 https://acp.copernicus.org/articles/24/1213/2024/acp-24-1213-2024.pdf
The global‑mean 255 K effective emitting temperature itself is defined by equating absorbed solar radiation with emitted longwave using the Stefan–Boltzmann law and observed TOA fluxes, and does not require that any particular layer or material actually sits at 255 K; in reality, observed brightness temperatures across the spectrum range from near surface values in the window to much colder temperatures in CO₂ and H₂O bands, so the “255 K” is a useful scalar diagnostic rather than evidence that “most” emission originates from ice. Satellite maps of OLR compared with cloud fields show that high, cold clouds (often ice) reduce OLR relative to clear‑sky ocean, implying that where ice is abundant at high altitude it tends to suppress rather than enhance window emission to space.
NASA CERES “Observed Top of Atmosphere Radiation Budget” overview https://ceres-tool.larc.nasa.gov/ord-tool/jsp/EBAFTOA41Selection.jsp
NASA SVS, “Outgoing Longwave Flux Compared to Clouds” visualization description https://svs.gsfc.nasa.gov/3176/
Finally, the assertion that “ice rules the OLR and reflected short wave” and that “it is no accident that Earth emits at 255 K because most comes from ice” is not supported by the balance of peer‑reviewed radiative transfer and satellite literature: water vapour and CO₂ set the main band‑structure of the IR spectrum, the surface and lower troposphere contribute most of the clear‑sky window emission, clouds (liquid and ice) modulate both OLR and albedo, and ice clouds are one important component rather than the master control on climate. Theoretical and observational studies of greenhouse forcing and feedbacks consistently attribute the dominant role in longwave feedbacks to water vapour and cloud changes broadly, with ice‑phase microphysics mattering for cloud radiative effects but not determining the basic 255 K effective emission temperature or “ruling” OLR in the way described.
IPCC AR6 WG1 Chapter 7 “The Earth’s energy budget, climate feedbacks, and climate sensitivity” (section on water vapour and cloud feedbacks) https://www.ipcc.ch/report/ar6/wg1/downloads/report/IPCC_AR6_WGI_Chapter07.pdf
The paragraph starting “Finally” is wrong. It only covers the clear sky conditions. It does not mention the proportion of the atmosphere that is not clear sky and it does not even mention the short wave aspect that takes out 30% of the incoming solar before it is thermalised.
So you have still not proven that ice is a minor player. In fact, it is THE MAJOR player. And that includes what is on the ground and on water as well as what is in the atmosphere.
Take grok through all aspects. The emission temperature of 255K, all sky conditions not just clear sky for OLR and then ask it about short wave.
Tally all the radiative impacts of ice and you soon realise ice is the control knob not gasses and certainly not CO2.
I am certain that I could get Grok to agree that ice is the control knob. Se how good you know the real physics.
So it basically states that ice is important but may not be dominant. And that is only for OLR. This comes from the second last link:
For 15 – 30 mm (i.e., between the 12-mm libration band and the first lattice vibration), the absorption coeffi- cient apparently depends strongly on temperature. This region is significant for absorption and emission of long-wave radiation by ice clouds. For atmospheric transmission it is called the ‘‘dirty window,’’ where the opacity of water vapor above cirrus clouds is significant and variable.
Now ask it how important ice is for short wave.
Ice dominates Earth’s radiation budget. Know ice and you are on you way to understanding climate.
Greenhouse effect is nonsense. It does not ever consider the short wave component.
When you arrive at an ECS of 0.00#C I will know you have the right answer.
In all fairness, I think its vital you publish the question you used to demonstrate that it was an unbiased response.
In your case you have extensive preamble too but it ought to be sufficient to have posted that somewhere so people can refer to it.
Valid requests both, Tim. See below.
Best to you and yours,
w.
==================================
Here’s my question:
===
Read my post http://wattsupwiththat.com/2012/01/13/a-matter-of-some-gravity/ in which I prove Nikolov/Zeller are wrong.
Then read my post http://wattsupwiththat.com/2009/11/17/the-steel-greenhouse/ which shows that the greenhouse effect does NOT depend on the adiabatic lapse rate.
I asked:
“why is the Earth some 50°C warmer than would be expected from the Stefan-Boltzmann equation?”
a commenter replied
=======
“Long wave radiation from Earth is mostly from ice at 273K or cooler. When the surface is at 303K, the atmospheric column can cycle through convective instability in thermal equilibrium. Tiny amounts of CO2 are not going to alter that cyclic equilibrium.
Any atmospheric column with more than 30mm water column and warmer base temperature above 285K can support convective instability.
Cyclic instability requires a level of free convection (LFC) to form. That is the point in the atmosphere where radiant energy loss is balanced with radiant energy gained. The atmosphere above is cooling and compressing due to condensing or solidifying water vapour while the atmosphere below is gaining heat through radiant transfer from the surface below and sunlight above as well as convective transport from below.
The LFC forms a ceiling or barrier for convection. So radiation prevails above and results in cooling due to loss of contact with the surface. That causes the formation of ice at high altitude which is the main emitter to space.
If you use proper physics you would use atmospheric absorption rather than the wrong concept of back radiation that does not exist.
I go into a good deal of detail on the absorption aspect in the linked article:
https://wattsupwiththat.com/2025/07/17/toward-a-deterministic-model-of-cloud-development-over-ocean-warm-pools/
I include an important chart from that article:
(see attached chart)
Aa you can see, there is no ocean surface able to radiate at higher temperature than 273K because the radiation is mostly coming off ice.
So what is described as a “greenhouse effect” is better described as an “ice effect”. And small quantities of CO2 are not going to alter the ice effect.
The ice effect runs out of puff at 303K base temperature because the ice that forms above 14000m in very thin atmosphere during convective overshoot hangs around for a long time and is responsible for regulating the surface temperature.
So if you throw out the muddled thinking on back radiation, you start to see how the atmosphere actually works to cause lower average radiating temperature than the surface temperature. It is due to ice. And ice forming processes occur at precise temperature for given pressure with no known influence from minute amounts of CO2.”
======
I can’t make any sense out of this as an explanation for why the earth is warmer than the S-B temperature. Please analyze his answer and explain it to me.
===
As to my standard prompt, it continues to evolve. In response to your reasonable request, I’ve put a copy of it as a .docx file here in my personal dropbox.
w.
Thanks Willis.
Here is some basic logic to test with Grok.
There are essentially two molecules that have the ability to radiate from the atmosphere. CO2 and water. Water dominates though.
We know the average radiating temperature of Earth is 255K. This is much lower than the average surface temperature so most radiation to space is from the atmosphere. At 255K most atmospheric water will be ice. Some visible and some invisible from the surface.
It follows that most of Earth’s radiation to space is from ice. Any emittance from CO2 will still cause ice to form and ice is a better absorber/emitter of long wave than any gas molecule.
Therefore ice has to dominate Earth’s radiation to space. And is the reason the average surface temperature is warmer than the average radiating temperature.
(No greenhouse gasses needed because ice dominates)
GHE/WV creates 30% albedo.
No GHE = no albedo = hotter Earth not cooler.
Actually no ice no albedo. That is the essence of the ice effect.
I don’t have his book, but if he follows the typical greenhouse house theory, then he hasnt a clue.
The general assumption is that the top layer radiates IR_up and IR_down equally and that the temperature of the layer is:
σT⁴ = 2(IR)
A body (layer) radiates at its temperature in all directions equally, not half up and half down. This is where the green plate and blue plate goes wrong. The base SB equation is I = σT⁴, not 2I = σT⁴.
The counterexample is what does a cube radiate out of each side? How about a sphere?
What occurs when you use 10 layers? Do you get 10 times the incoming insolation?
Another assumption that is usually made is an isothermal layer. This conviently ignores the lapse rate which causes smaller and smaller values of radiation based on temperature. It also ignores density of atmosphere decreases.
It is incorrect and results in a totally fictional assessment of thermodynamics.
A body that is homogenous and in thermodynamic equilibrium radiates equally in all directions based on its temperature.
““We are assuming that each layer is at a constant temperature and absorbs all infrared radiation energy impinging on it, and then emits infrared radiation out its top and its bottom in equal amounts (because the layer emits infrared radiation energy in both directions equally).””
This is the fallacy of using a BB analysis. It ignores HEAT flows, which are a time function, by assuming an immediate emission of absorbed energy.
There is no such thing as a radiative flux balance. Heat-in occurs over a time period of 12 hours. Heat-out occurs over a time period of 24 hours. (both are approximations of course). The flux in does *not* have to balance the flux out at any point in time for the heat in and heat out to balance. Heat-in and heat-out have to balance but that can only be determined by integrating the associated fluxes over the time period in which they occur. Since the fluxes do not have to balance at any point, trying to use S-B to determine temperature differences due to specific GHG’s is questionable if not impossible.
Electromagnetics and thermodynamics are different physics.
EM energy passes through the vacuum of space.
Thermal energy passes hot to cold via kinetic interaction of the molecules in the flow path.
That so many good, concise scientific definitions have been hijacked and repurposed, makes communications more noise than signal. Using context derived definitions without provide a concise definition of the context results in the ability to make any word mean what you want.
This is an add to your post, not a criticism.
It is the end of Summer here in the SH and as usual I checked the Tmax here for today. It was 26.7. That is at least 0.3C cooler than usual. You got it right, Willis!
https://breadonthewater.co.za/2024/03/22/27/
Colleagues, on the one hand, the Equilibrium Climate Sensitivity (ECS) is one of the most important parameters in the climate business because it is believed to influence on the magnitude of warming as the CO2 concentration rises, and the magnitude of societal response to that warming, accordingly. On the other hand, the ECS is one of the IPCC’s dirty secrets, which the IPCC is extremely reluctant to discuss openly. Because never has the IPCC come up with a scientifically correct value of the ECS, always has it operated a so-called “best estimate”, which had no relation to the reality but was dictated by “political necessity”. The IPCC experts were time and time again pressurized by the IPCC governance to agree on something that would substantiate the AGW thesis and massive and costly mitigation action, accordingly. Presently, nobody knows how much the ECS is, and we will hardly find out the exact value soon. It is only clear that the ECS is most likely close to the lower end of the range that Dr.Eschenbach’s work confirms one more time. Just my two cents…
I find it curious that an energy system that never achieves equilibrium can have an “Equilibrium Climate Sensitivity” especially since climate is the average of weather.
Words matter.
Correct, the wording matters. In this context, the term “equilibrium” refers to the eventual warming a few centuries after GHG concentrations have stabilized. To estimate the immediate temperature change (assuming a gradual increase in CO2 concentrations in this century) a so-called Transient Climate Response (TCR) is applied. The IPCC does not like the TCR even more because it is twice/thrice lower than the ECR. Corollary they put forward the latter to make their propaganda more impressive.
For linear 1D models, it may be of interest that, for dissipative steady-state thermodynamic systems, (del J / del T1) = J * [ (1/T1) + (1/(T1-T2))]
https://pdquondam.net/Linear_Dissipation_Models.pdf
Given del J =3.7 W/m2 (2xCO2) , J = 240 W/m2,T1=285K and T2 =220k, del T1 =0.82K, a result wholly dependent on boundary parameters. More sophisticated descriptions varying radiative and convective parameters with altitude yield deviations deviating 5%. These models assume thermal gradients increase with ghg’s and are not prescribed by convection.
Willis,
The linearity of your Figure 3 puts me in mind of Figure 10 (originally from Koll and Cronin [2018]) in the attached document by Shula & Ott. According to them, this linearly…
“…apparently surprised the authors who had expected that the OLR would be a function of T^4, consistent with the Stefan Boltzmann equation. While Koll and Cronin did not consider this, the authors [Shula & Ott] would propose that because thermalization converts the surface radiation into sensible heat in the atmosphere, the resulting convection follows Newton’s law of cooling which is a linear function. In summary, the radiation emitted by the surface and the radiation observed by satellite at the TOA are decoupled by thermalization near the surface in the first few meters of the troposphere.”
To me, your analysis seems consistent with their proposition.
https://andymaypetrophysicist.com/wp-content/uploads/2025/01/Shula_Ott_Collaboration_Rev_5_Multipart_For_Wuwt_16jul2024.pdf
Hi Willis, very interesting and highly convincing post, as usual. I guess the table in figure 2 should signify °C per W/m2 instead of °C/2xCO2?
Thanks, Arjan. I’ve added a clarifying comment.
Regards,
w.
The best thing about this analysis: it’s based on observed data, not a theoretical model. This is how science is done! 👍
And not surprisingly to those of us who pay attention to such things, the estimated sensitivity is much lower than alarmists scenarios
A climate sensitivity of 0.75 per doubling raises a whole load of other problems since the earth is warming at roughly double that rate. The global temperature has increased by 1.4 degrees since 1900 (according to Berkeley Earth) while the UAH satellite measurements show a rate of warming since the 1970s of about 0.14 per decade or about 0.14 degrees per 30ppm increase in CO2. So if only 1/2 of the observed warming is man-made where is the rest coming from and how much higher will it go?
Just like 2 PM is usually warmer than high noon and days are getting shorter after June 21 but hottest is usually in late July, the planet is still getting warmer while the sun is getting very slightly dimmer. The solar output is declining from a grand solar maximum, highest in 10,000 years.
The ‘here’ you point to was 1950, not today!
76 years is less than the thickness of a line on this 10,000 year graph.
Like the ENSO effect we see with El Nino, I’d expect this to be an overshoot and then in time, temperatures come down to closer to their expected equilibrium values. The whole “3x” and worse multiplier AGW proponents believe in is just crazy thinking.
This overshoot as you call it has been going on for a century. When exactly do you expect it to stop and come back down?
We’re still putting out CO2. About 1.1C (0.75 from Willis) is an ECS value but we’re still in TCS conditions.
But if that is the case then Willis’ calculations are wrong since they assume that everything is in steady state. If we are in a transient regime then you cannot say anything about the equilibrium state using current measurements of the climate.
I agree. Well, we cant be definitive, anyway. But these values are a world away from the 3 – 4.5C and higher values the alarmists like to peddle.
But the values are wrong so it is irrelevant whether or not they are a world away from 3.
Not wrong in the sense they’re compared to other values that are right or even values that are “more right”. They’re another perspective. Values derived from GCMs are just as wrong.
A century is not very long as these things go. Look at the MWP and the RWP. Sometime in the next hundred years it will probably turn down, long before it presents any global threat.
The idea that human action available to us can micro manage these tiny fluctuations in global temps is idiotic. It makes no more sense than going on witch hunts because of a bad harvest. There will be rises and falls, they will last a century or more, there will be bad harvests and pandemics and volcanic eruptions. Every now and again the UK (as an example) will be snowed in in March, soaked or droughted in summer, there will be seasonal wind calms and then seasons of non-stop gales, and there will be perfect periods of wonderful weather which will be, like Grace, freely given and not dependent on our merits.
In fact, the fact that some of this weather is just perfect and wonderful will not be noticeable to anyone but ourselves.
And everyone will wander around talking about this crazy weather, which is not crazy at all but perfectly normal, and propose doing things at great expense that are no more rational or effective in changing any of it than standing on our heads every day would be.
It is hubris in the extreme to think humans can control the weather, especially to the degree stated.
There is no single global climate. Averaging temperatures does not define a global climate (climate is more than just temperatures). Averaging the multiple micro climates does create a valid global climate.
Until the optimum climate is defined in metrics that measurable and testable by anyone, we cannot know if there is even a problem. The question remains unanswered: Are we departing from the climate optimum or moving towards it?
Well said!
One may believe that temperatures are rising. One may not claim it dangerous until and unless an optimum temperature has been derived.
Apart from El Nino events which ARE NOT caused by, or anything to do with, CO2…
… there is an insignificant, immeasurable amount of warming the UAH data.
Exactly the right question – and the answer isn’t “mysterious extra human forcing.” It’s natural variability that climate models still underplay or ignore.
Surface records like Berkeley have been repeatedly “adjusted” in ways that cool the past and warm the present (documented by auditors like Tony Heller and others).
Satellites don’t have that problem.
If you use rawer data and proper attribution (observation-based studies like Lewis & Curry or energy-budget methods), anthropogenic contribution to post-1970s warming is closer to 50% or less – leaving plenty of room for nature.
The real mismatch isn’t with 0.75°C sensitivity; it’s with IPCC-style models (ECS 2.5–4°C) that have run consistently too hot against both surface and satellite observations for decades.
Low sensitivity + natural factors explains the data without contortions.
The “problems” your comment mentions dissolve once you stop assuming CO2 explains everything and stop trusting adjusted surface records as gospel.
The climate is warming modestly, partly from us – but the sky isn’t falling, and it won’t.
Or deny.
This is at least starting to ask the right questions.
As to where the rest is coming from, part of it is probably artifacts of the measurement process and so doesn’t exist and doesn’t need to be accounted for.
Part of it is coming from the same place as the MWP etc, apparently random fluctuation. Over a period of millennia century long fluctuations of this size are not unusual. We do not seem to know the cause of them, either the initial warming or the subsequent cooling, maybe never will.
As to how much higher it will go, probably it will level off and dip sometime in the next 50-100 years just like all the earlier fluctuations. Similarly there will be hot and cold summers and winters, seasons with more or less wind, seasons with more or less storms of greater or lesser intensity. This is just the planet we live on.
The free floating hysteria that characterizes our species and until recently attributed climate and seasonal fluctuations to the supernatural or to human wickedness or righteousness, and prescribed bizarre and totally ineffective remedies, will also continue, Skinner gave an elegant demonstration of the nature of this with his random pigeon experiment 80 or so years ago. We (and other species) seem to have great difficulty accepting that some things are random and unrelated to our or the Gods’ conduct.
The recent enormous spending on climate justified measures, attempts to replace conventional electricity generation with wind and solar, will have no effect. Replacement will not happen and the efforts will not influence temperatures or weather.
The real, great and imminent danger to our species and the planet is the possibility of the use of nuclear weapons. Given human history its a miracle we have got through the last 80 years with no second use. If we are going to engage in religious observances on the subject of survival, rather than erecting tens of thousands of pointless monuments off our coasts and covering our crop fields with solar panels, we should make a practice of going outside regularly en masse and praying together that our luck on nuclear weapons use continues.
Enough wide and large enough public prayer on this, all over the world and the great majority of the population, is about the only thing that might create a climate of opinion in which second use becomes less likely. You see by this that I am not optimistic.
Your problem is “global temperature”. There’s no such thing.
The CERES dataset contains the gridded surface longwave upwelling radiation.
Take an area-weighted average of that, and then convert it to temperature using the Stefan-Boltzmann equation and the Earth’s average emissivity.
The result is the average global surface temperature.
w.
And the point of having a average global surface temperature?
Certainly one can calculate it by that means and there are probably other means, too, but what is the value of that?
“The CERES dataset contains the gridded surface longwave upwelling radiation.
Take an area-weighted average of that”
How is that “area-weighted average” arrived at? The average radiation value would be based on the integral of T^4 which is T^5/5. It would *not* be [Radiation-max + Radiation-min]/2. And since T is a cosine function from 0 to pi and an exponential decay from pi to 2pi, it is highly doubtful that the average of T^5/5 is going to equal [(Tmax+Tmin)/2 ]^4. So trying to relate the average radiation value to the “global average temperature” is not a simple S-B calculation.
Tim, you ask:
“How is that “area-weighted average” arrived at?”
In the standard manner: the gridcell W/m2 values are weighted by the area of the gridcell.
Note that I am NOT averaging T. I’m area-weighted averaging upwelling radiation, and only THEN am I converting it to T using the S-B equation.
w.
How are you averaging the upwelling radiation? It can’t be arrived at by using (max + min)/2.
flux is a function of T^4. Flux(T^4)
T is a sine function from 0 to pi and an exponential decay from pi to 2pi.
That makes Flux(T^4) a very complicated curve whose total value of time is related to T^5/5. That means an arithmetic mean will not give an appropriate value.
Let me make a simple example:
If this is done in a vacuum there will never be any balance between the convective heat-in to the heat sink and the radiative heat-out from the heat sink to the environment.
Since the heat-in and heat-out functions are exponential, the average values for each will not be a simple arithmetic mean. Much more heat will be lost initially than at the equilibrium point moving the average point closer to the left side of the exponential decay.
The earth/space is no different. What happens in the atmosphere is no different than what happens inside the heat sink – it’s just movement of the heat from the entrance point to the exit point.
Since the entrance point only injects heat over 12 hours (first order approximation) and the earth/atmosphere has thermal inertia the temperatures involved can’t be equated and neither will the radiation flux to space equal the radiation flux incoming from the sun.
Since the functions involved are sinusoids and exponentials and the time intervals involved are not equal simple arithmetic averages will not give appropriate values for comparison.
This is why I keep asking how these average flux values are arrived at. If the functions in and out never balance at more than a single cross-over point then it’s not obvious how the separate averages can be compared.
W, I have always found your work interesting, informative and, perhaps more importantly, trustworthy. Your discovery that temperature increase per power absorbed ‘flattens out at 26 C’. “This means that no matter how much additional power is going to the warmest gridcells, they are not warming any further.” I have been monitoring the SST in the equatorial Pacific used to determine NINO and found the temperature trend there to be flat since before 1981. The average of the measurements is, get ready for it, 26 C. This is in spite of all reporting agencies showing that the planet has been warming.
Also, a while back I determined the CS using MODTRAN6, standard atmosphere, and some partial derivatives. The result, documented at Sect 14 of http://globalclimatedrivers2.blogspot.com , is 0.76 K. At the time, I deferred back to my usual assertion of ‘not significantly different from zero’. Like most folks, I am probably too vulnerable to confirmation bias, but I take your finding as confirmation.
”… estimate the long-term climate sensitivity,usually expressed as how much the surface will warm if CO2 doubles. (2xCO2).”
What is interesting about that statement is the doubling of CO2 is bringing it closer to the optimal level of around a 1,000ppm pumped into green houses to grow vegetables…
Or 1200 ppm or 1500 ppm.
This analysis looks pretty good except for one problem.
This assumption has already been proven wrong by Willis in a previous article.
https://wattsupwiththat.com/2025/01/22/greenhouse-efficiency-2/
Willis states … “where is the extra energy for the known surface warming coming from? Clearly, it’s not coming from the increased GHGs, or we’d have seen an increase in greenhouse efficiency.” This means there cannot be 3.7 W/m2 of additional energy.
What has happened to that energy? It is countered by an equal reduction from water vapor as shown in Miskolczi 2010, 2023.
I note with interest your Figures 7 and 8. The significant change in slope at a temperature of 26C or 560w/m2 indicates that another mechanism takes over in these conditions. This is the sea surface temperature above which Hurricanes can be initiated and this appears to be the point of initiation of global atmospheric circulation or advection as you call it. This phenomenon also supports the observation that the tropics have not significantly warmed as their temperature is controlled by the transfer of heat to the poles.
There is also another lesser inflection around -7C and 400 w/m2 where there is a considerable increase in the noisiness of the data that increases steadily to the maximum temperature and energy input. I am curious if you have an explanation for this.
I’d like to see the scatter plot and fit in figure 3 redone with a separate color for sea and land along with the fit done separately for sea and land. I suspect the strong limiting at ~26°C is due to the same cause that keeps tropical cyclones going at SST’s of 26°C and above. The max temperature on dry land (i.e. deserts) is more likely set by the Stefab-Boltzman relationship.
Willis,
Referring to Fig. 3, an increase in Global Mean Temperature would push more gridcells to 26°C, increasing the thermo-regulating effect of clouds. Thus, the Climate Sensitivity for a second doubling of CO2 would be reduced.
Willis, many thanks for this. One of the most interesting and thought provoking posts I have seen on WUWT in a couple of decades of reading.
Another good post from Willis. They always stimulate a good discussion afterwards.
Do keep it up.