A More Accurate Multiplier

Guest Post by Willis Eschenbach

In my previous posts, yclept “Greenhouse Efficiency” and “The Multiplier”, I described a metric I’d developed to look at how successful the very poorly named “greenhouse effect” was at warming the surface. The metric was the upwelling surface longwave radiation (in watts per square meter, W/m2) divided by the solar power actually absorbed by the system (solar minus albedo reflections).

And of course, since radiation emitted by an object can be used to determine the temperature, this metric also measures how efficiently the incoming sunshine is converted to surface temperature.

Here’s how that metric has changed over time, as discussed in my two previous posts.

Figure 1. Greenhouse multiplier. The multiplier is calculated as upwelling longwave surface radiation divided by incoming solar radiation (after albedo reflections). A multiplier of 2 would mean that the surface would be radiating two W/m2 of energy for each one W/m2 of solar energy actually entering the system. This shows that the greenhouse has increased the incoming solar radiation by about two-thirds, as measured at the surface.

I got to thinking about that, and after a while I realized that that doesn’t tell the whole story. I realized that the answer was distorted because I hadn’t included advection.

Advection is the horizontal transport of heat. Generally, it’s in the form of moving ocean and atmosphere. It generally flows, as you might expect, from warm to cold—from the equator to the poles. Here’s a map showing the average transport, both export (red) and import (blue) of energy.

Figure 2. Advection (horizontal transport) of power from the tropics to the poles.

The issue with not including advection comes up especially in the polar regions. There, a large amount of the power input is from advection, and little is from sunlight. So it looks as thought the power in the sunlight is highly multiplied, but it’s not—the extra power is from advected atmosphere and ocean.

Since I wanted a measure of the total watts out divided by watts in, the true multiplier, I had to include the advected energy. Since the net energy advected is about zero, I didn’t expect it would change the overall average multiplier by much. But I did expect it to be more accurate on a gridcell-by-gridcell basis since it was no longer missing the advected energy.

And indeed, this was the result. Figure 3 shows the earlier calculations as in Figure 1 (blue), plus the calculation including the advected energy (red).

Figure 3. A comparison of the two metrics, which either include (red) or omit (blue) the advection.

Now, there are some interesting things about this figure.

First, as I’d hoped, regarding the standard deviation (SD) of the detrended results, it is smaller when we include the advected power. This means they cluster more tightly around the trend line. The SD of the original method (blue) is 0.0040, and of the method including advection (red), it’s 0.0026.

Including the advection also corrects the problems at the poles which import copious power, and the problems at the tropics, which export the same.

Figure 4. Average multiplier, both with (red) and without (blue) the advection. Average CERES data, Mar 2000 to Feb 2021

I love the surprises of science. The surprise in this one for me was that once we’ve included the effects of advection, the multiplier is pretty much equal from the North Pole down to the north tip of Antarctica.

Next, a small digression. Ramanathan pointed out that we can measure the poorly-named “greenhouse effect” directly. It is the amount of upwelling longwave power absorbed by the clouds, aerosols, and greenhouse gases in the atmosphere. Note that the power absorbed ends up back at the earth’s surface.

The size of the “greenhouse effect” is measured as the upwelling longwave at the surface minus the upwelling longwave at the top of the atmosphere (TOA). The difference between the two is the “greenhouse effect”, in watts per square meter.

Here’s the most surprising oddity. It turns out that when we include advection in our surface power changes, the new multiplier is exactly equal to one plus the greenhouse effect (measured as above) divided by available solar energy. Math in the footnotes.

And this lets us understand what is happening in Figure 2. The blue trend is the change in surface upwelling per unit of incoming energy. This is measured above in W/m2, but it can be converted using the Stefan-Boltzmann equation to the surface temperature. That multiplier has been decreasing.

The red trend is the trend of the change in total surface power, not just the radiation but the advection as well, per unit of incoming energy. That multiplier has been increasing as we’d expect given increasing levels of CO2.

Figure 5. Figure 2, shown again

And that is very interesting. It shows that overall, increasing greenhouse gases increase the amount of downwelling radiation per unit of incoming solar power. And in fact, they are increasing at the rate expected from the increasing concentration of CO2. But that’s not what is expected overall.

Figure 6. Changes in the efficiency of the “greenhouse effect”, as measured by the multiplier.

The first reason that the increase is less than expected is that there are other greenhouse gases besides CO2 (methane, N20, chlorofluorocarbons). So with those other gases, the increase in greenhouse efficiency as measured by the multiplier should have been more than it actually has been.

There is also the purported positive cloud feedback and the water vapor feedback. Like the effect of other greenhouse gases, these should also have increased the multiplier.

So it appears that there are unknown countervailing forces preventing a larger increase in greenhouse efficiency despite increases in a variety of greenhouse gases. However, the net of all of these is a slight increase in greenhouse efficiency.

But curiously, this is counterbalanced by a reduction (per unit of incoming solar power) in the amount of increase in surface temperatures, along with a corresponding increase in the advection.

And the net result of the two is that in Figure 2 the multiplier shown by the blue line (how efficiently the system multiplies the incoming energy into surface temperature) is trending down, despite the increasing efficiency of the “greenhouse effect” due to increasing GHGs as shown by the red line.

“Simple physics”?

I don’t think so.

w.

MATH: Here are the equations showing that

surface upwelling + advection / available solar

is equal to

one plus the greenhouse effect (as defined by Ramanathan) / available solar.

Where:

  • SOLAR = TOA incoming solar power
  • SWtoa = Upwelling (reflected) shortwave measured at the top of the atmosphere
  • LWtoa = Upwelling (emitted) longwave measured at the top of the atmosphere
  • LWsurfup = Upwelling longwave at the surface

Advection is measured as the amount of solar power (shortwave) entering the gridcell (SOLAR) minus the amount of radiated power leaving the gridcell to space (SWtoa + LWtoa). The difference must be advected, except for a very small fraction that raises or lowers the surface temperature and can be neglected at this level of analysis.

My Usual Note: When you comment PLEASE quote the exact words you’re discussing. I can defend my own ideas. I can’t defend someone else’s random claim about what they think I said.

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September 17, 2022 10:23 am

“upwelling surface longwave radiation” – as measured at the orbit. I would omit the word “surface”.

Prjindigo
Reply to  Curious George
September 17, 2022 5:06 pm

I find myself pondering at all this photonic and cosmic energy penetrating deep into our relativity whether anyone has considered deflection from refraction as a thermal input. With light’s infinite energy-to-mass ratio how many thousands or tens of thousands of years of endurance is being consumed in reaching the surface of the Earth then leaving again? Considering due to quantum effects we literally can only detect 49.99~% of the photons coming in but they ALL interact with the atmosphere what kind of result are we looking at in calculating the margin of error of these models?

Is all the upwelling longwave actually upwelling longwave?

The solar wind incidence directly at the silhouette of the planet adds about 24W/M^2 across that plane that has nothing to do with induction or electron saturation.

We’ve only recently discovered that the chemical signals “of life” from Venus are literally proton collision with its constituent atmosphere… imagine how infantile the “model” linear progressions currently used in “settled science” are…

Last edited 12 days ago by Prjindigo
David A
Reply to  Prjindigo
September 18, 2022 4:46 am

“The solar wind incidence directly at the silhouette of the planet adds about 24W/M^2 across that plane that has nothing to do with induction or electron saturation.”

Interesting. Do you have a reference? What is the residence time”
( How long does said energy stay within earth’s land, oceans and atmosphere.) How much does said energy input vary?

Last edited 12 days ago by David A
michael hart
September 17, 2022 10:24 am

yclept

noun
Forms of the preterit and past participle of clepe.

I went to the dictionary, and it brushed me off.

Oldseadog
Reply to  michael hart
September 17, 2022 10:58 am

yclept, adj., archaic or joc., called ( by the name of ), [Old English gecelopod , past participle of cleopan “call”, from Germanic]
Concise Oxford Dictionary Ninth Edition.

Dave Fair
Reply to  Oldseadog
September 17, 2022 6:33 pm

Its fun to use words with which nobody is familiar. “Niggardly” immediately comes to mind.

Matt Kiro
Reply to  Oldseadog
September 18, 2022 7:27 am

I inferred from its use in the sentence , yclept roughly equalled ‘called’

Meisha
Reply to  michael hart
September 17, 2022 11:03 am

yclept — “by the name of”

Steve Case
Reply to  michael hart
September 17, 2022 1:04 pm

Thank God it’s six letters long – which means
I won’t ever see it the daily wordle puzzle.

Disputin
Reply to  michael hart
September 17, 2022 1:59 pm

Didn’t you know that?

Streetcred
Reply to  michael hart
September 17, 2022 11:11 pm

yclept
[ɪˈklɛpt]
ADJECTIVE
archaic

  1. by the name of:
  2. “a lady yclept Eleanora”
Last edited 12 days ago by Streetcred
Streetcred
Reply to  Streetcred
September 17, 2022 11:12 pm

“archaic” ? I use it all the time ROTFLMAO.

Rud Istvan
September 17, 2022 10:51 am

Nicely done, WE.
Your last figure is most interesting. It implies that over the observational period net there were no positive feedbacks as the climate models presume. I have three thoughts about that new fact:

  1. The observational period is only a little more than two decades, much of which was two ‘pauses’ interrupted by one El Niño. So natural variation must be playing a significant role in the figure’s net finding. But we cannot say how much. See my previous posts on why models are wrong (running hot) for demonstrations of natural variability significance before 1975 and before 1945 (a ~25 year warming ending about 1945 that is indistinguishable from 1975-2000, which even the IPCC said in AR4 SPM WG1 could NOT be mostly anthropogenic since there simply was not enough change in CO2 level).
  2. The WVF must logically be something net positive since water vapor is a potent green house gas and there is more humidity with rising surface temperature. Observationally it must be less than half of climate models based on newish ARGO findings that ocean precipitation is about twice what is modeled—there simply is less water vapor available having whatever positive feedback.
  3. Point 2 implies the cloud feedback (even IPCC says all other feedbacks net to zero) must be something negative rather than positive as in the climate models (offsetting whatever positive WVF over the observational period). This is something that both AR4 and AR5 said there was the most model uncertainty about.

The figure’s three points together completely undercut not just CAGW, but any assertion of AGW eventually causing a future problem based on models.
A new and independent way to arrive at this conclusion than prior observational EBM studies getting an ECS about 1.6-1.7C, also showing AGW will not eventually cause a problem based on Schellnhuber’s arbitrary 2C threshold.

michael hart
Reply to  Rud Istvan
September 17, 2022 11:13 am

Schellnhuber’s arbitrary 2C threshold was of course plucked from where the sun don’t shine. Just like the economic models which used to say warming would be net beneficial until mid-century. Funny how that doesn’t get mentioned much.

That they then arbitrarily reduced it to 1.5C is indicative that they knew 2C was unlikely to be reached anytime soon, if ever (and much of that warming happened before CO2 could be blamed.)

Old Man Winter
Reply to  michael hart
September 17, 2022 12:56 pm

“As for tipping points, any or all of those flagged in the new
research could happen at some point below 1.5C, so we may have
crossed one or more already– only time will tell.”

Bill McGuire added the cherry on top!

https://wattsupwiththat.com/2022/09/12/the-guardian-downgrades-the-1-5c-global-warming-limit/

TallDave
Reply to  michael hart
September 20, 2022 7:40 am

and the existing warming — even that since 1979, when we launched satellites because of fears the glaciers were returning — is now A CRISIS

Last edited 10 days ago by TallDave
M Courtney
Reply to  Rud Istvan
September 17, 2022 1:02 pm

If cloud feedback is something negative then there would have been warmer days after 911 when the planes were grounded.
And there were.
So, I would suggest that uncertainty over the sign of the cloud feedback springs from non-empirical sources.

Prjindigo
Reply to  M Courtney
September 17, 2022 4:58 pm

sort of… there’s the particulate carbon to consider

David A
Reply to  Rud Istvan
September 17, 2022 11:34 pm

If LWIR is converted to cloud feedback ( See Willis’s diagram, (2.) “Extra energy evaporates a molecule of water” and consider that said GHE down-welling LWIR is 100 percent absorbed at the very surface “skin layer” where evaporation takes effect, and yes, a negative feedback is likely.
At “Climate Audit they have long talked about the need for an “engineering” type discussion of GHG dynamics. I think Willis is getting closer to that goal.

David A
Reply to  David A
September 17, 2022 11:35 pm

It takes a lot of energy to accelerate the hydrological cycle.

A C Osborn
Reply to  David A
September 18, 2022 1:49 am

Yes it does, so in figure 5 what is the ‘with advection’ trend between 2000 and 2015 and the trend from 2016 to date, which visually looks to be negative.
It is obvious that a “step change” took place when the 2015/16 El Nino occurred.
Where is the explanation of how GHGs, especially the continuous increase in CO2 can cause a “step change” in the amount of energy in the system.
How can an overall trend be legitimate when step changes are occurring without an explanation of how the items being trended caused the step change. The El Nino energy was not stored in the GHGs it was stored in the Oceans.

David A
Reply to  A C Osborn
September 18, 2022 5:17 am

Greenhouse liquid?

TallDave
Reply to  David A
September 20, 2022 7:51 am

yes, that was my argument against DWLWIR warming the surface skin — at least some of that additional energy has to go into phase-transitioning additional water, although I am generally open to the idea that warming the cold top of a blanket can also warm the person under the blanket

Last edited 10 days ago by TallDave
TimTheToolMan
Reply to  Rud Istvan
September 18, 2022 1:43 pm

Rud says “The WVF must logically be something net positive since water vapor is a potent green house gas and there is more humidity with rising surface temperature.”

Unless you’re defining WVF to only include radiative properties then this logic is flawed. Water vapour transports energy of latent heat of evaporation through the atmosphere to be radiated and that’s a negative feedback to surface warming. It’s not obvious which is the larger effect over time.

TallDave
Reply to  Rud Istvan
September 20, 2022 7:43 am

no positive feedbacks as the climate models presume.

well, remember, according to Monckton the IPCC has been assuming that all the feedbacks magically appeared after 1850, and had no effect on the original reference temperature

this seems to lend some weight to that argument

Last edited 10 days ago by TallDave
Robert W Turner
September 17, 2022 10:55 am

So it appears that there are unknown countervailing forces preventing a larger increase in greenhouse efficiency despite increases in a variety of greenhouse gases.”

Yeah the null hypothesis is wrong. The “greenhouse” multiplier being flat across latitudes despite vastly different concentrations of “greenhouse” gases is yet more solid evidence of that.

Greg
Reply to  Robert W Turner
September 18, 2022 1:36 pm

Vastly different ?? From memory it’s about 6ppmv more in Alert than it is in Antarctica. 6 in 400 is not vastly different.

Nicholas McGinley
Reply to  Greg
September 18, 2022 2:07 pm

Water vapor differs hugely from the poles to the equator.

Richard M
September 17, 2022 11:24 am

One very interesting result is the LOWESS smooth of greenhouse-efficiency follows the PDO index very closely. I suspect a trend of the PDO index would also show a rise. Could it be your data is thus affected by the timing of PDO changes? If so, the slight rise will disappear as the PDO becomes more negative.

PDO phases are generally described as a change in the locations of pressure systems which would likely affect advection.

Mike Maguire
Reply to  Richard M
September 18, 2022 12:08 pm

We are currently in a solidly negative -PDO regime which is a big factor in the long lived La Nina.

https://psl.noaa.gov/pdo/

https://www.marketforum.com/forum/topic/88653/#88659

Screenshot 2022-09-18 at 14-01-58 Pacific Decadal Oscillation (PDO) NOAA Physical Sciences Laboratory.png
Richard M
Reply to  Mike Maguire
September 19, 2022 11:49 am

The PDO index appears to be directly influenced by ENSO. Makes it difficult to use. It will generally be negative during La Nina events. Not sure which is the chicken and which is the egg.

However, whichever is the driver, the result appears to be similar. The greenhouse efficiency value moves up and down as the PDO index moves up and down.

Certainly a curiosity. It may mean that advection is increased or decreased. This could be affecting the results Willis is seeing.

TallDave
Reply to  Mike Maguire
September 20, 2022 7:54 am

it’s almost like it got warmer in the 1940s, and then colder in the 1970s, and then warmer in 1998

you know, like the graphs used to say back before 1999

Richard M
September 17, 2022 11:36 am

An often ignored aspect of CO2 radiation in the atmosphere is the latitudinal changes. With more CO2 you have more energy moving in all directions. This should move more energy from warmer (tropics) to colder (poles).

Since it takes less energy to warm colder objects, the same amount of energy spread across the planet more evenly will raise the average temperature. If you want to calculate a more accurate greenhouse-efficiency, you would need to factor in this difference.

Barry Malcolm
Reply to  Richard M
September 17, 2022 3:24 pm

Nice, you are thinking, good points.

David A
Reply to  Richard M
September 17, 2022 11:41 pm

Yes, and we already know most warming is at night, and beneficial; less frost damage.
It takes a lot of energy to accelerate the hydological cycle, and that decreases energy residence time, and assuming steady state input all T change is a result of energy residence time.

Reply to  Richard M
September 18, 2022 5:53 am

Since it takes less energy to warm colder objects,
=======
No. The specific heat of water is constant. It takes 1 calorie to heat 1 gram of water 1 C regardless of water temp.

Richard M
Reply to  ferdberple
September 18, 2022 8:13 am

True, but the greenhouse effect occurs in the atmosphere. Not talking water here. I should have been more precise.

Reply to  Richard M
September 18, 2022 10:37 am

The specific heat of air is still somewhat flat. That determines how much energy is required to heat a specidic amount of air thru a specific amount of temperature.

The SB equation deals with power. It telks us it takes less power to warm cold objects than hot objects but it does not tell us the equilibrium time.

It is this equilibrium time that determines how much energy is required to change temoerature for a given radiated power change..

Reply to  Willis Eschenbach
September 18, 2022 10:17 am

My definition is straight from any physics text.

You are confusing energy and power. It takes less power to warm cold object. Not less energy.

Steve Keppel-Jones
Reply to  ferdberple
September 19, 2022 8:37 am

Willis is always confusing energy and power. Ask him what units he thinks should be used to measure radiation (a form of energy, as he explained)… he can’t answer that question without shooting himself in one foot or the other, so instead he will just call you a pig and claim that he refrains from engaging in pig wrestling as a matter of principle. (The fact that he can’t tell the difference between physics and pig wrestling probably goes a long way towards explaining the atrocious state of his physics knowledge.)

leitmotif
Reply to  Steve Keppel-Jones
September 19, 2022 12:59 pm

Willis wouldn’t pig wrestle with me because I asked him for evidence for the warming effects of downwelling longwave radiation or back radiation.

It was solved by me being, still being, moderated.

Steve Keppel-Jones
Reply to  leitmotif
September 21, 2022 12:23 pm

Yup. He’s quite a character. As a physicist, he makes a good fisherman. Maybe he should just stick to the fishing!

leitmotif
Reply to  ferdberple
September 22, 2022 1:24 pm

Willis is confusing science with sophistry.

Reply to  Willis Eschenbach
September 18, 2022 10:55 am

The difference between power and energy is equilibrium time.

Energy = power x time

When you increase the radiated power warming an object, it will start to warm. As it warms it will radiate increasing power until it reaches equilibrium and incoming and outgoing radiation match..

The difference between the incomming and outgoing radiated power integrated over the equilibrium time tells you how much energy it took to raise the temperature.

All other energy is accounted for in the incoming and outgoing radiation, so the difference must be the actual energy required to warm the object.

Last edited 11 days ago by ferdberple
David A
Reply to  ferdberple
September 19, 2022 5:33 pm

So the residence time of the energy flowing to the object receiving it?
A black hill, and a snow covered hill receive the same input, yet the residence time of the input is longer in the black hill.

The Real Engineer, CEng etc.
Reply to  ferdberple
September 20, 2022 9:45 am

Now that will really mess things up!
Energy is measured in Joules, power is measured in Watts. An energy flow of one joule per second is a power of 1 Watt.

Lets look at this properly in the atmosphere, the power arriving from the sun is measured in watts per sq metre, and changes continuously depending on the angle of the sun and the Earths rotation. The temperature on the surface depends on how many joules are absorbed, and the the temperature rise is given by the specific heat of what is being heated.

Now lets look at the CO2 and water in the atmosphere. What happens to each as 1 joule of energy is added (at a frequency where they are actually absorbing, this is not specifically long or short wave it is exactly defined). Each will increase in temperature by some quantity, and then its molecules being excited will attempt to loose this energy to something colder, to resume the ground state depending on their nominal temperature (loosely speaking the temperature of everything around them). This ocours in all directions, not specifically up or down. Note this cannot be something hotter, and if nothing is colder the temperature will not change. This is why we say “heat rises”, the effect being convection.

Any heat on the surface will heat the atmosphere layer next to it, and convection will take over, moving the heat to the top of the atmosphere. This of course is exactly why “Greenhouses” work, they prevent the convection of heat from the surface upwards, and trap much of it.

The confusion we see above and very commonly is that radiation is seen as a mechanism which heat is transferred around the atmosphere, and some small amount is, but one cannot simply take some “energy” and assume that this can be transferred by any mechanism without the temperature difference being in the right direction. Heat energy always moves from hot to cold in all circumstances, it is simply attempting to unify the energy per unit volume to the same value.

Greenhouse proponents always fail to see this, they think that the wavelength controls the flow in some magic way, and that the heat energy can flow in any temperature direction. Imagine I could make heat move from cold to hot without doing any work (expending even more energy). To some very small extent I can in a heat pump, but the limits and power input required are very fully defined by thermodynamics, and depend on the Carnot cycle of pressure and temperature. Rising atmospheric heat actually suffers cooling due to falling pressure, but that is far too complex for “warming” modellers.

Sorry for the long post but we must get the basics right first, it is all in any good thermodynamics text book.

Greg
Reply to  Willis Eschenbach
September 18, 2022 1:44 pm

we add 1 kcalorie of constant heat flux to it,

Flux means flow. Heat flux is W/m2, not calories ( which is energy ).

Reply to  Greg
September 18, 2022 3:35 pm

Exactly.

leitmotif
Reply to  Greg
September 22, 2022 1:26 pm

Willis is such a darling, isn’t he?

Energy? Flux? What’s the difference?

Where I live, we just call it heaty stuff.

dk_
September 17, 2022 11:43 am

Thanks for repeating

very poorly named “greenhouse effect”

which I choose to take as acknowledgement of one of my pet peeves.

I had not considered advection as a factor before now, so thanks for that as well.

Wondering now if “unknown countervailing forces” to “positive cloud feedback and the water vapor feedback” may be partly in the effects of topology and water/air density with convection, and hinted at in your other hydrologic cycle observations. Wind and ocean current would seem to increase the diffusion of energy, and evaporation/precipitation events should decrease surface heating.

David A
Reply to  dk_
September 17, 2022 11:44 pm

Speaking of evaporation,,,, Interesting to see the possible effect of Hunga Tunga…
https://electroverse.co/greenlands-record-gains-major-stratospheric-cooling-event-over-southern-hemisphere/

Scroll past the Greenland information

Kevin kilty
September 17, 2022 12:05 pm

SW_{toa}/SOLAR is the albedo of the Earth. One minus it is not the same as solar absorptivity of the ground surface which is what will determine \sigma T_s^4 - \text{Advected heat}. The reason being foremost that some solar is reflected within the atmosphere before reaching the ground but also that the surface is not diffuse but has some specular quality to it as well.

I have no idea if the rather small trends shown indicate an efficiency of the greenhouse, or is some component in the uncertainties in all of the other factors involved over time?

Last edited 12 days ago by Kevin kilty
Kevin kilty
Reply to  Kevin kilty
September 17, 2022 2:48 pm

Excuse me \sigma T_s^4 + \text{Advected heat}

Gary Pearse
September 17, 2022 1:39 pm

“So it appears that there are unknown countervailing forces preventing a larger increase in greenhouse efficiency despite increases in a variety of greenhouse gases.”

Simple physics – I dont think so either. The Le Châtelier Principle (LCP) predicts what you have found. It is your countervailing force. LCP is well known to chemists and particularly to Chemical Engineers who manipulate it to produce higher quality chemical products at lower cost.

Simply stated, in any interacting system of multiple components (e.g. concentrations of chemicals in solution, different phases of a component, P, T and V, say, in equilibrium), a change in any one of the components induces changes in the other components in such a way as to resist shifting away from this equilibrium. A change caused by this perturbation of the system is therefore much smaller than expected!

I want to note here that it should be self evident that my example system doesn’t have to be in equilibrium for this resistance to be invoked. Chemists tend to include equilibrium in the statement of the principle because in chemistry they are much preoccupied with chemical equilibrium. In the more dynamic general statement of LCP, the system may be heading for equilibrium and perturbing the system, say, by raising T 10° causes the system to head for a new equilibrium – the one it would have had if you had waited for equilibrium before raising T 10°. I offer this note because climateers use “equilibrium” to argue LCP isn’t applicable to climate which isn’t in equilibrium.

Climate has dozens and dozens more components than my example and and can martial even greater resistance to changes. Add more CO2 to the atmosphere and we find that half of it has disappeared when we measure it. Simply heat the atmosphere and it expands which lowers its temperature somewhat. Some of the lost carbon dioxide has been sequestered in plants. Moreover, since photosynthesis is an endothermic reaction, the Greening removes heat from the atmosphere…..

Willis, calculate the countervailing force at play and you can make an LCP coeff = the difference between Expected and Actual ÷ by Expected. When T- anomaly forecasts made for 2005(?) turned out to give values 300% too high, I suggested an LCP coefficient of 0.33 needed to be incorporated into the models of the “physics”.

Kevin kilty
Reply to  Gary Pearse
September 17, 2022 2:51 pm

Le Chalier’s principle pertains to chemical systems. It would be interesting to formulate an argument that it also pertains to mechanical systems. I don’t know that it does.

RickWill
Reply to  Kevin kilty
September 17, 2022 6:56 pm

I expect the Chatelier Principle of equilibrium is a special case of the principle of least action, which can be applied to any system.

David A
Reply to  RickWill
September 17, 2022 11:48 pm

Negative feedback’s do, without doubt, tend to dominate.

Reply to  RickWill
September 18, 2022 6:52 am

the principle of least action, which can be applied to any system.
======
Very interesting point. The energy in and out of the climate system is a fixed “constant” solar energy.

For any increase in CO2 of all possible paths the climate might take, it must take the one requiring the least change. This goes back to some really fundamental physics.

So the question is, is an increase in global surface temperatures the least effort path?

That seems highly unlikely. The least effort would be just as likely to increase clouds or increasecwinds or all sorts of other changes.

Reply to  Kevin kilty
September 18, 2022 6:06 am

pertains to mechanical systems
™≥======!
Any dynamic system with negatice feedback follows Le Chalier’s principle.

Any dynamic system with positive feedback quickly destroys itselt and is no longer available or latches at the limits and is no longer dynamic.

A dynamic system with no feedback hurts my head. I see a unicorn.

another ian
September 17, 2022 1:59 pm

Willis

I’d be curious as to why the black/white line has that finger up into central Australia in Figure 2

RickWill
Reply to  another ian
September 17, 2022 4:30 pm

The response of land to sunlight is different to water. Basically land responds twice as fast and twice the temperature range as water for the same solar input because the water stores much more heat than the land:
https://1drv.ms/b/s!Aq1iAj8Yo7jNhG4gM4gmzW9MS07d

Then deep convection plays a role in the transport of energy from ocean to land. Trees and other land biomass are really important in this process because land that retains water behaves differently to dry land. Dry land heats very quickly and become mid level divergent zones so get little water from oceans. The Sahara is the best example but also central Australia. The Amazon is a good example of land that has retained water through its abundant biomass.

David A
Reply to  RickWill
September 18, 2022 5:07 am

 because the water stores much more heat than the land:”

Greenhouse Liquid??

Redge
Reply to  another ian
September 18, 2022 12:55 am

I think it’s the Ceres data telling Albanese his climate pledge is madness

arjan duiker
September 17, 2022 2:21 pm

Dear Willis, figure 2 tells SH gets 1,7 W/m2 more heat via advection than NH. How does this relate to your other analysis called ‘A balancing act’? I mean, is advection been taken into account in that analysis as well, or does it not play a role?

bill
September 17, 2022 3:06 pm

For me, the most interesting thing is that it’s another example of very large numbers being subtracted from each other and the consequent number being very small. It also as a consequence shows that the analysis is likely to be solid.
The net of 0.8W/M2 is also potentially wrong given there must be errors and being such a small residual the flux of energy in or out may be still unknown.

Very good analysis, are there measurement errors that we can calculate?

Clyde Spencer
Reply to  bill
September 17, 2022 8:55 pm

One can tell that it is climatology being discussed because there are no uncertainties associated with any of the numbers used.

RickWill
September 17, 2022 3:13 pm

A multiplier of 2 would mean that the surface would be radiating two W/m2 of energy for each one W/m2 of solar energy actually entering the system. This shows that the greenhouse has increased the incoming solar radiation by about two-thirds, as measured at the surface.

This is why climate phiisics is nonsense. The atmosphere does not have more energy at the bottom than the top. If there was no atmospheric absorption on the way in then the best it can be is the same bottom and top.

So what you have come up with now is that your last post was wrong. That is what I pointed out. Now you believe you are right – nope still wrong.

Your figure 2 should give you a clue. It shows land responds differently to sunlight than water. What happen if sunlight worked differently on land than water and the amount of sunlight over each surface was changing:
https://1drv.ms/b/s!Aq1iAj8Yo7jNhG4gM4gmzW9MS07d
In a nutshell, away from the tropics, the land temperature response to sunlight is twice and in half the time.

This is how solar intensity has/will change in April at 30N from 1000 years ago to the next 1000 years from J2000:
-1.000  405.746351
   -0.900  406.156246
   -0.800  406.568410
   -0.700  406.982423
   -0.600  407.397883
   -0.500  407.814408
   -0.400  408.231635
   -0.300  408.649215
   -0.200  409.066813
   -0.100  409.484100
    0.000  409.900750
    0.100  410.318143
    0.200  410.734184
    0.300  411.148357
    0.400  411.560133
    0.500  411.968970
    0.600  412.374329
    0.700  412.775676
    0.800  413.172498
    0.900  413.564305
    1.000  413.950642

These are not trivial changes and time constants for oceans are of this order.

This table was generated here:
http://vo.imcce.fr/insola/earth/online/earth/online/index.php

Last edited 12 days ago by RickWill
RickWill
September 17, 2022 3:44 pm

We know the Southern Ocean has declining solar intensity and the surface is cooling as a result. So to prove to yourself that your theoretical CO2 forcing is BS, you should do the calculation for each grid on the globe. Or just pick a few points across the globe to see how each “CO2 forcing” is varying over time.

Given that CO2 is well mixed, you should have the same result across the globe irrespective of latitude or surface composition.

RickWill
Reply to  RickWill
September 17, 2022 4:16 pm

You have shown the multiplier for different latitudes but you have not shown the change at different latitudes over time. And you have not separated land and water responses.

The CO2 forcing is supposed to be constant across the globe. Any long term downward temperature trend dispels the notion that CO2 is a player in the energy balance.

Hubert
September 17, 2022 3:53 pm

This multiplier factor can be obtained differently using the IR absorbtion factor X bv greenhouse gas and the part of IR re emetted to Space K :
multiplier = 1 / ( 1-X + K*X ). Where X = 0.9 and K = 0.56 , which could be adjusted …

Ad Huijser
September 17, 2022 4:09 pm

Dear Willis, Very nice analysis. I just used your CERES data published here recently (many thanks) to make the plot for both hemispheres, all- and clear sky as well. I didn’t use the deseasoned CERES data, but the moving annual total of the quotient GE/AS in your formula. The slope of 1.2*10^(-4) for the global fits indeed perfectly the 3.7 W/m2 2xCO2 forcing over the 2001-2021period, but the slopes for the NH and SH with 3.4 and -0.7 (10^(-4) units) respectively, don’t. For the clear sky situation, I find 3.3., 4.7 and 2.4 (10^(-4) units) for Global, NH and SH, respectively. So, I am wondering if that global all sky slope is coupled to CO2, or that is just a coincidence, or the variations I calculated, are simply within the bandwdith of uncertainties in the CERES data.
I think your observation is somehow related to some plots I made a couple of days ago from the sum of Sensible + Latent Heat vs the absorbed solar radiation from the same data. SH+LH is taken as (the balance of) the net radiation at the surface, just forgetting the less than 1 W/m2 absorbed by the oceans (see attachment). Although I expected somewhat close to this outcome, I was anyhow puzzled by the almost perfect slope of 1 over the entire range of the year, that shows that almost every extra watt/m2 of solar input dissipates through SH+LH, and not through net LW-radiation. That can only be true for a very stabilized climate system where the evaporation of water is the control mechanism. Any thoughts from your side?

SH+LH CERES.png
RickWill
Reply to  Ad Huijser
September 17, 2022 5:17 pm

So, I am wondering if that global all sky slope is coupled to CO2, or that is just a coincidence, or the variations I calculated, are simply within the bandwdith of uncertainties in the CERES data.

You have shown that CO2 is selective in what it warms, cools or doesn’t change. Or maybe that the idea that CO2 does anything is wrong and it is just orbital mechanics shifting the solar intensity predominantly from water in the SH to relatively more land in the NH.

Reply to  RickWill
September 18, 2022 5:40 am

Yep. Ja.
I subscribe to that idea.
Click on my name.

Reply to  HenryP
September 19, 2022 10:35 am

I meant the idea that CO2 could be doing something wrong. It does not. Its warming properties are nullified by its cooling properties. It is our dung in the air, so to speak, as it makes the earth greener and the plants more drought resistant.

Last edited 10 days ago by HenryP
September 17, 2022 4:16 pm

Next, a small digression. Ramanathan pointed out that we can measure the poorly-named “greenhouse effect” directly. It is the amount of upwelling longwave power absorbed by the clouds, aerosols, and greenhouse gases in the atmosphere. Note that the power absorbed ends up back at the earth’s surface.

The size of the “greenhouse effect” is measured as the upwelling longwave at the surface minus the upwelling longwave at the top of the atmosphere (TOA). The difference between the two is the “greenhouse effect”, in watts per square meter.

The first is not quite correct, the second is. Power absorbed by the atmosphere is only partially returned to the surface. Insulator, not reflector.

Reply to  Willis Eschenbach
September 17, 2022 8:35 pm

Sigh… SOME of the power is returned to the surface.

An energy packet (a “quantum”) is emitted from a surface molecule, in the form of a long wave photon.

That photon travels some distance – it may be absorbed by a molecule in the atmosphere – or it may actually just go “past” all of the atmosphere and go into space. (Obviously, the more molecules that can absorb it along the path, the more likely it will be absorbed. If we had a pure helium atmosphere, we’d lose every bit of solar heating every twenty four hours.)

Now, that absorbing atmospheric molecule will eventually get rid of the energy that it has absorbed, going back to the lowest energy state it can. Very near to the surface, that can happen through kinetic transfer with another molecule, and a very good chance that it will be a molecule of the surface. Thus starting the whole thing over again. But, higher up, there is either kinetic transfer to another atmospheric molecule – or, in many cases, the “absorber” simply emits another long wave photon. That photon could go straight up, straight down, or anything in between. (A kinetic transfer could also move the energy up, down, or anywhere, for that matter. Only slightly more likely downwards to a higher density.)

That molecule, the pass receiver, will do the same thing. That quantum, either through direct escape, or through transfers through multiple molecules, does eventually escape into space. Guaranteed. Actually, Vegas odds rule, since there is a somewhat higher chance that the energy emitted (whether through kinetics or radiation) will NOT be on a path that intersects the surface. The Earth is a spheroid.

The problem with the first assertion should be obvious. “It is the amount of upwelling longwave power absorbed by the clouds, aerosols, and greenhouse gases in the atmosphere. Note that the power absorbed ends up back at the earth’s surface.” No, the power absorbed will, guarandamnteed, EVENTUALLY go into space as longwave radiation. Just SLOWER than if there were no absorption.

This is why the second assertion IS correct. The upwelling longwave radiation at TOA is the sum of energy that directly escapes from the surface PLUS the energy that has been transferred between one or more atmospheric molecules before it reaches TOA. The “greenhouse” effect only slows that escape, sufficiently so that the surface only loses a few degrees at night by upwelling before its energy is replenished by the Sun. (On average, of course. A humid equatorial location might not lose a measurable amount over night at all, some nights – while a polar desert will lose an enormous amount, especially during the “long dark.”)

Sorry for the long-windedness (though only slightly). You pushed my “Pedant Button.” An unqualified assertion, lacking even a “most” or “majority of” qualification, is saying “all.” At least in the English as she be precisely spoke.

Robert W Turner
Reply to  Willis Eschenbach
September 18, 2022 6:15 am

Where is it going? Wind power.

Robert W Turner
Reply to  Willis Eschenbach
September 18, 2022 6:28 am

Not all of the energy in the atmosphere is in the form of heat. The atmosphere has enormous wind power.

It’s interesting to note that the wind power density is much lower in the tropics than it is in the Northern Hemisphere, which in turn is lower than in the Southern Hemisphere.

https://earth.nullschool.net/#current/wind/isobaric/1000hPa/overlay=wind_power_density/orthographic=-153.85,0.57,422/loc=73.005,-49.697

I’ve always likened the atmosphere to a thermal capacitor, but it is more like a thermal capacitor and flywheel all in one.

TimTheToolMan
Reply to  Willis Eschenbach
September 19, 2022 6:24 am

Willis writes “Power leaves the surface. It does not make it to space.”

Some of it obviously makes it to space. Radiation is both up and down and the radiation at the effective radiating level of the atmosphere tends to escape to space (by definition)

Its well known that CO2 is the molecule responsible for radiating much of the energy to space from higher in the atmosphere.

TimTheToolMan
Reply to  Willis Eschenbach
September 19, 2022 6:26 am

Willis writes “So where is it going?”

Specifically, it is leaving the atmosphere, radiating to space at the same rate shortwave radiation is entering it.

John in Oz
September 17, 2022 4:19 pm

Willis,

Thanks for all of your work, especially for us non-scientist types

Please explain: “radiating two W/m2 of energy for each one W/m2 of solar energy actually entering the system.”

How does one become two?

My understanding (admittedly poor) is (from Wiki and my bold):

In physics and chemistry, the law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be conserved over time.[1] This law, first proposed and tested by Émilie du Châtelet,[2][3] means that energy can neither be created nor destroyed;

leitmotif
Reply to  Willis Eschenbach
September 18, 2022 1:27 pm

The Steel Greenhouse“. 

The Steel Greenhouse is a perfect example of junk science.

It’s been debunked so many time it should get an award.

FLoT broken.
SLoT broken.

Doesn’t get any better.

leitmotif
Reply to  Willis Eschenbach
September 19, 2022 1:11 pm

And here is that very debunking.

https://climateofsophistry.com/2013/03/08/the-fraud-of-the-aghe-part-11-quantum-mechanics-the-sheer-stupidity-of-ghe-science-on-wuwt/

Enjoy Willis being debunked by a real scientist. Joe takes The Steel Greenhouse apart, line by line.

It’s so embarrassing.

Mods – are you going to do something about Willis calling me a fool? Thought not.

leitmotif
Reply to  leitmotif
September 19, 2022 1:46 pm

Here’s the best bit.

Willis adds the shell around the sphere and then states “The inwards radiation warms the surface of the planet, until it is radiating at 470 W/m2“. He didn’t show how this happens, he didn’t explain why, and he didn’t do any math to support it – he just arbitrarily doubled the output radiation and hence the temperature (according to the Stefan-Boltzmann Law) of the planet. He just did it, arbitrarily.

Let’s look at his following statement where conservation of energy and equilibrium applies after he’s arbitrarily doubled the output from the interior: “The shell is receiving 470 W/m2 from the planet, and it is radiating the same amount, half inwards back to the planet [235 W/m2] and half outwards to outer space [235 W/m2]”. This is his condition of equilibrium. But wait a minute, the planet was intrinsically radiating 235 W/m2 at the start; if this was striking the shell, then his conservation of energy and equilibrium condition should have been that the shell emits half of this outward and half inward, i.e. 117.5 W/m2 either direction. However, what he actually did was just say that the shell emits twice as much energy as it receives, i.e. a full 235 W/m2 either way, so that the interior shell now has double the energy output. So, Willis just arbitrarily doubled the amount of energy available, so that he could add half of it back to the original 235 W/m2 in order to double it. Just arbitrarily doubled out of nowhere. Just made up bullshit.

And then what is strange, is that Willis stops this energy doubling process for no reason! If at the beginning, a 235 W/m2 output comes back to double itself to 470 W/m2, increasing its own temperature, then why doesn’t the 470 W/m2 output double again from itself coming back to increase itself yet again? Why should this process stop if the same conditions which caused this to occur in the first place still exist? 

Looks pretty dodgy to me. 🙂

Tim Gorman
Reply to  leitmotif
September 19, 2022 2:28 pm

And then what is strange, is that Willis stops this energy doubling process for no reason! If at the beginning, a 235 W/m2 output comes back to double itself to 470 W/m2, increasing its own temperature, then why doesn’t the 470 W/m2 output double again from itself coming back to increase itself yet again? Why should this process stop if the same conditions which caused this to occur in the first place still exist? “

This is the part that has always eluded me as well. Back radiation can only replace heat that has already been lost. It can’t add since there is nothing on fire in the atmosphere to create heat.

leitmotif
Reply to  Tim Gorman
September 20, 2022 12:54 pm

Willis was taken apart all those years ago by astrophysicist Joseph Postma but Willis is in denial that he is a sophist.

No matter how many shells you add the energy cannot increase and the FLoT cannot be broken while breaking the SLoT.

I compare WE to a zealot.

leitmotif
Reply to  Willis Eschenbach
September 22, 2022 2:39 pm

Willis, do you think commenters should get modified for disagreeing with you?

Reply to  John in Oz
September 17, 2022 8:51 pm

Simple way to look at it is as energy being recycled – not created.

Surface absorbs 1 W/m2 of energy from the Sun. Emits that 1 W/m2 of energy. Atmosphere absorbs that 1 W/m2 of energy. Emits that 1 W/m2 of energy back to the surface. Surface emits that 1 W/m2 again. Now, it has emitted 2 W/m2 of energy total, but no energy has been created (or destroyed), just passed back and forth like two people playing catch.

(More complicated than this, of course. The “multiplier” is actually the limit value of a diminishing continued fraction. Some of the energy escapes to space on every “throw.” See my semi-rant at Willis above…)

Peta of Newark
Reply to  writing observer
September 18, 2022 1:55 am

Thank you, you describe what is effectively a ‘Standing Wave’

= something that looks big and energetic yet no energy is flowing in either direction….

e.g. Revisit your school playground..
2 girls facing each other and swinging a long rope between them.
Someone, you, near the middle, skipping that rope as it revolves.
Face one of the girls and you see the rope rotating, seemingly a ‘wave of energy’ coming straight at you.
Aw wow you think. lots of energy coming from girl#1

Turn to face the other girl, you see the same thing but coming from the opposite direction =
Aw wow, look at all that energy coming from girl#2
In which case, why do the girls at each end of the rope stand there, all nonchalant, like nothing is happening. Why does all that energy have no effect upon them. Or, how much energy/work are they putting into that rope?
They are nonchalant because no energy is flowing from one girl to the other.

Now where did the energy, you so clearly see, go?
As it happens and a little while ago, some intelligent peeps asked that exact same question, name of Sadi Carnot (1796–1832) and Rudolf Clausius (1822–1888)

Because despite Willis’ repeated exhortations that he understands and obeys the 2nd Law, whenever he does say that, his very next words entirely trash it.
And from this distance, within this medium, it’s impossible to sort it out.
Willis himself repeatedly slams the door.

Start here to get your head around Entropy (and the 2nd Law)
https://fs.blog/entropy/

Even then, it’s not easy as one of the figures there demonstrates (screenshot as attached)
Because in that figure you may see on the left a block of ice and on the right a cloud of steam.
Yet bizarrely, the cloud of steam has less Entropy (is more ‘ordered’) than the block of ice.
Now where did the energy go? How do you get that message across?

It’s not easy. What is easy though in these modern times and this modern media, is just to close your mind, your eyes & ears and float on in your own Magical World. To slam down/cancel the conversation.

OK:
Entropy and the 2nd Law determine absolutely that heat energy only flows from hot to cold. Only. There is No Net Flow. None. Only Goes In One Direction. Ever. Always.

Next:
Radiation is NOT a variation on Conduction or Convection
The 2nd Law is not an amendment to, nor is it conditional upon, the 1st Law.
Both laws apply independently and absolutely, at all places, at all times and at all temperatures.

So:
Due to the well observed Lapse Rate, there is Only One Thing In The Entire Sky that can inject energy (cause a temp rise) in the Earth’s actual surface.

There is only one thing anywhere in the sky hotter than the surface and that one thing is The Sun.
Nothing else can add heat energy to what the surface itself already contains.
Do Not Confuse The Surface with the place thermometers are typically put.

Else otherwise and based on this perfect junk haha science

  • RIP Entropy
  • RIP The 2nd Law
  • RIP Everybody

The GHGE is itself, The Biggest Denial Of Science there could ever be.

(I’ve just figured it. Earth will, due to Entropy, Rest In Eternal Peace and so will everything onboard.
Is the Green House Gas Effect some crazy and unhinged attempt at reversing time or especially, to make ourselves immortal.
Considering the hubris endlessly demonstrated around here and ‘most everywhere, I’d not be the least bit surprised)

Ice Steam Entropy Fail.PNG
RickWill
Reply to  John in Oz
September 18, 2022 1:18 am

means that energy can neither be created nor destroyed;

None of the prior laws of physics apply in climate phiisics. These people write their own laws so the atmosphere can do wonderful things like create energy from nothing.

They have this concept of photons zipping about in all directions completely oblivious to the electromagnetic field the energy transfer occurs and Einsteins space time continuum.

They sort of get some idea about the gravity field interacting such that remote matter communicates in the space time continuum but deny that happens with the electromagnetic field.

mkelly
Reply to  John in Oz
September 18, 2022 6:36 am

John accept the physics and chemistry first law statement. Energy can neither be created or destroyed.

leitmotif
Reply to  mkelly
September 18, 2022 1:33 pm

The Steel Greenhouse has proved you wrong time after time, mkelly.

I know for a fact because I was in that Steel Greenhouse for 10 years. The shell kept getting closer and closer to me, as the hypothesis was adjusted, so that in the end my nose was touching the shell.

I don’t really want to talk about it. 🙁

Nicholas McGinley
Reply to  leitmotif
September 18, 2022 5:51 pm

“… so that in the end my nose was touching the shell.”

Well, that explains it.
I have been a long time wondering how it (your nose) got so bent out of shape.
I hear they are doing amazing things with rhinoplasty these days…

leitmotif
Reply to  John in Oz
September 20, 2022 3:48 pm

How does one become two?

By employing BS science like The Steel Greenhouse. See my comment below where I show evidence of debunking The Steel Greenhouse.

It explains everything.

Swenson
September 17, 2022 4:42 pm

All well and good, but the Earth has cooled since its creation. Nothing at all managed to stop it.

Continuous sunlight, atmosphere, CO2, radiogenic heat – cumulative effect zero.

No GHE. No warming, apart from more than seven billion humans producing and using energy about as fast as they can, all of which eventually flees the Earth to space.

Thermometers respond to this ephemeral increased heat, as they were designed to do.

No mystery at all.

David L. Hagen
September 17, 2022 6:43 pm

Willis My compliments on your breakthrough.
Re: “Including the advection also corrects the problems at the poles which import copious outpower, and the problems at the tropics, which export the same.
I am used to hearing about solar radiation downwards to the tropics and long wave radiation outwards from the poles. So I needed to rethink about your net flows and advection. May I suggest clarifying by expanding your discussion of both advection (and radiation.) E.g.
“Including the advection also corrects the problems of net energy flows in at the north and south poles which import copious net power from the tropics by horizontal advection (while outwardly radiating longwave radiation). It also corrects problems at the tropics, which export that copius net power by horizontal advection north and south (while receiving inward solar radiation).”

David L. Hagen
September 17, 2022 6:59 pm

Willis Your Standard Deviation (SD) of 0.0026 divided by a mean of about 1.67 gives a remarkable 0.16% relative standard deviation for your new metric at a given year. It will be interesting to see how much variations in clouds with incoming solar radiation and cosmic flux, and the solar cycle will vary that small slope shown (versus the variation from the Medieval Warm Period to Little Ice Age back to the Modern Warm Period. (vis Lüning, S. and Lengsfeld, P., 2022. How Reliable Are Global Temperature Reconstructions of the Common Era?. Earth3(1), pp.401-408. Earth | Free Full-Text | How Reliable Are Global Temperature Reconstructions of the Common Era? | HTML (mdpi.com))

angech
Reply to  David L. Hagen
September 17, 2022 8:48 pm

“PLEASE quote the exact words you’re discussing”
I am very happy you include this with all your comments.
You are correct in that people who do not wish to think when they engage change from the ( obvious) argument at hand to the one that they think they can win instead.
Difficult to do as it reduces the economy of words when the correct argument is being used.

I particularly like the advection concept as it helps explain why the night side of the earth stays warm when the sun seems to have gone.
“Advection is the horizontal transport of heat. Generally, it’s in the form of moving ocean and atmosphere.”
I use a different concept of the infra red radiating horizontally (adverting) from the warm side to the poles and the cold side, but whatever).
Your model does explain why more heat or energy, continues to go to space from the colder regions , even though not directly irradiated and even though the net energy flux in and out is zero.

I take exception to the comment on your first graph that the incoming solar radiation can be increased (or decreased) by GHG by about 2/3 as measured at the surface.
The GHG do not turn up the amount of solar radiation produced by the sun.
I would prefer you to add that the amount of radiation received at the earths surface is 2/3 greater than the directly received incoming solar radiation.

It is quibbling but correct thermodynamically and also allows a clearer concept of the forces at work.

“Figure 1. Greenhouse multiplier. The multiplier is calculated as upwelling longwave surface radiation divided by incoming solar radiation (after albedo reflections). This shows that the greenhouse has increased the incoming solar radiation by about two-thirds, as measured at the surface.”

“A tiny bit of extra energy delta q enters the system”
OK.

You are trying to find a relationship between the amount of energy measured as emitted from the earth surface and the amount of energy that reaches the earths surface from the sun.
A quandary as the amount estimated to reach the surface directly is a lot less than what the earth seems to be emitting in return.

The explanation is that the earth is covered in an atmospheric layer of GHG of increasing concentration such that the layer closest to the earths nominal surface is in constant balance with the surface hence the amount of energy going into the earth’s surface is almost double.

Half is the incoming solar energy, half is the IR which was emitted to the lowest GHG layer and is in balance with both the layer above it ands the earths surface with an energy concentration dictated by the GHG volume and concentration.

Why is the multiplier only 2/3 instead off 100%?
The horizontal loss is going laterally to the poles and other side of the earth so a true schematic would have to have a grid with some energy being lost laterally .
How much?
1/3.

Easy to say but is it correct?

September 17, 2022 7:09 pm

@Willis 

About 50 years ago I received Training on the B&W Once Through Steam Generators (OTSG) used at the B&W Nuclear Power Plants. These steam generators provided more than ten degrees of super heat to the steam they generated. This was caused by the fact that the feedwater was sprayed on the bare steam generator tubes. The tubes in the SG went from the bottom to the top, rather than in a U type shape as in the majority of the other SGs. Thus more than a third of the tubes were out of the water and exposed in a that allowed the FW to be sprayed on the tubes helping to transfer more heat to the steam. The one thing I remember was that these effect depended upon the concept of Constant Enthalpy – a thermodynamic quantity equivalent to the total heat content of a system. It is equal to the internal energy of the system plus the product of pressure and volume. It has been more 50 years since I have read my thermodynamic books (or seen them)m but the process you are explaining seem exactly the same. I see very little difference.

Constructive Criticism accepted.

mkelly
Reply to  Rich Lentz
September 18, 2022 12:03 pm

This is why saunas are hotter after you throw water on the stove or rocks.

Wim Röst
September 17, 2022 9:58 pm

Willis: “there are other greenhouse gases besides CO2 (methane, N20, chlorofluorocarbons). So with those other gases, the increase in greenhouse efficiency as measured by the multiplier should have been more than it actually has been.”
 
WR: Main greenhouse gas water vapor (H2O) can be added. Water vapor absorbs [part of] solar energy during its transport through the atmosphere to the surface and, like clouds, diminishes the quantity of solar energy that reaches the surface. Both factors (water vapor and clouds) resulting from evaporation (as stimulated by surface temperatures) diminish direct surface warming by solar. Solar is the principal energy source.
 
In fact, extra downwelling radiation coincides with less solar reaching the surface. Water vapor and related processes are actively reducing solar while enhancing downwelling radiation. The whole is well-balancing surface temperatures.
 
A higher surface temperature enhances evaporation, convection, and the formation of clouds (all H2O) and so the quantity of downwelling radiation is enhanced. But at the same time H2O is diminishing the primary source of surface energy as soon as surface temperatures (for whatever reason) rise. The fact that downwelling longwave radiation rises is interesting, but because downwelling radiation is not a primary source for surface energy, this is ‘but an interesting fact’. Not a reason to change our society’s energy system, because already less solar will reach the surface.
 
Hot Early Greenhouse Earth did not permit any solar to reach the surface (by high water vapor, high CO2, and by a thick layer of clouds). A cooling Earth started permitting solar to reach the surface, effectively diminishing and finally even ending surface cooling. It is solar energy that keeps the surface, warm, while atmospheric H2O cools and regulates the quantity of solar that may reach the surface. In turn, surface temperatures regulate the quantity of atmospheric water vapor. It is this system that sets and stabilizes surface temperatures at the actual level.  

Hans Erren
September 18, 2022 2:33 am

Willis, there are more people living on the 0 meridian than on the 180 meridian, please add Atlantic centered maps to your posts so that Africa and Europe are not split in half or poorly readable.

HAS
Reply to  Hans Erren
September 18, 2022 2:57 am

But the interesting stuff is happening in the Pacific.

Hans Erren
Reply to  HAS
September 18, 2022 3:47 am

I don’t live in the Pacific

Captain climate
September 18, 2022 4:44 am

Excellent writing. Have these very graspable concepts been published in any peer-reviewed forum?

AZeeman
Reply to  Captain climate
September 18, 2022 9:23 am

Good luck finding peers to Mr. Eschenbach to review his work. How many current climate scientists are able or even willing to do his level or type of research. It would be career suicide.
His strength lies in his independence of the climate cabal. Also, judging by the intellectual level of the comments, his research is being extensively reviewed. Finally, the ultimate peer, Nature, always has the final say.

leitmotif
Reply to  AZeeman
September 18, 2022 1:35 pm

Don’t forget WE is also wrong.

September 18, 2022 6:23 am

This is measured above in W/m2, but it can be converted using the Stefan-Boltzmann equation to the surface temperature.
≠=========
Don’t agree. As others have also noted because SB is a power function and avg T is linear, you can only get a unique answer in one direction. From T to w/m2. In the reverse direction many different values of avg(T) will yield the same w/m2 depending upon variance across the temperature grid.

Simply solving the S-B equation in the reverse direction implies zero variance in T across the planet, which is clearly not the case.

The exception would be to solve the S-B equation in reverse at each grid square, but even that assumes zero variance within each square.

Last edited 12 days ago by ferdberple
September 18, 2022 7:15 am

Because much of the data has already been averaged, the true variance of the underlying data is hidden. Given the problems in converting W/M2 to avg(T) due to vatiance it is quite possible much of the radiation budget is suspect.

The S-B equation solved in reverse does not yield avg(T) as one might expect. It yields max(T) or max(avg(T)) depending on the data..

Last edited 12 days ago by ferdberple
September 18, 2022 7:35 am

RickWill
Reply to
Kevin kilty
September 17, 2022 6:56 pm
I expect the Chatelier Principle of equilibrium is a special case of the principle of least action, which can be applied to any system.
======
Rick I think you have hit upon sonething that has so far been overlooked.

Thernodynamics is also governed by the same principle. Surface warming is only 1 of many courses of action available with increased CO2. It should be possible to calculate what action the climate system will take. Has this been done?

RickWill
Reply to  ferdberple
September 18, 2022 4:07 pm

It should be possible to calculate what action the climate system will take. Has this been done?

The climate system is a complex box to analyse from the inside. Increasing atmospheric CO2 is just one of the many changes changes occurring and I cannot see any prospect of it making a difference to the changes already occurring due to orbital changes, distribution of land and water and changes in biomass mostly due to CO2 enhancing growth.

There is a concept that was conceived by the late, great NASA/GISS physicist Michael Mishchenko based on first principle; meaning solving Maxwell’s equations for Earth’s energy budget. It is set out in a 2016 paper. This taken from the abstract:

Our derivation is based on an absolute minimum of theoretical assumptions, is free of outdated notions of phenomenological radiometry, and naturally leads to the conceptual formulation of an instrument called the double hemispherical cavity radiometer (DHCR). The practical measurement of the planetary energy budget would require flying a constellation of several dozen planet-orbiting satellites hosting identical well-calibrated DHCRs.

The idea here is that they work outside the climate box. Measure energy flux, either in or out, simultaneously over enough locations beyond the atmosphere and frequently enough to build a complete picture.

Although this would give insight into the energy budget, it still does not give any real insight to what is happening on and under the surface.

The oceans are warming as to be expected when the water cycle slows down while the peak solar intensity moves northward. More ocean is reaching the 30C temperature limit.

So observing more heat being retained in the climate system is not due to CO2. It is due to changing solar intensity relative to land and water.

September 18, 2022 7:52 am

Proof S-B not reliable in reverse. Had a psychedelic v-dub van with same problem.

Assume a 2 grid square earth. Use a simplified S-B. W/m2 = t^4

Earth 1. t1=2, t2=2, avg t=2
W/m2 = 32

Earth 2. t1=0, t2=2.38, avg t=1.19
W/m2 = 32

Same w/m2, different average T. Which one is correct? What happens when you split squares even finer?

Last edited 12 days ago by ferdberple
mkelly
Reply to  ferdberple
September 18, 2022 11:53 am

Quoting from my heat transfer book, “..,the S-B law of thermal radiation…”. It is only valid for thermal radiation. Thermal radiation is a result of temperature difference. So until temperatures are shown in all the charts above it is all hocum.

leitmotif
Reply to  mkelly
September 18, 2022 1:37 pm

Is S-B good for gases?

mkelly
Reply to  leitmotif
September 19, 2022 6:53 am

There is a section dealing with gases. So with the caveats in the book the answer is yes. However, when I put forth the emissivity of CO2 that is in the .004 region people object or don’t grasp the significance.

September 18, 2022 8:19 am

Willis, while the trend is amall I think your data shows something very important.

See RickWill
Reply to
Kevin kilty
September 17, 2022 

Principle of least action.

What i see in fig 5 is that principle in action. Down welling efficiency is not increasing as expected. Rather advection is increasing.

September 18, 2022 10:12 am

the net energy advected is about zero
=========
This may not be so simple. The temperature variance is reduced which will reduce total outgoing radiation. The planet must warm on average to restore the radiative balance.

Thus a change in advecrion changes average temperature if outgoing radiation is to remain unchanged. This is independent of the GHG effect and thus greenhouse effect must be smaller than assumed.

mkelly
Reply to  ferdberple
September 18, 2022 11:57 am

There would be no advection in the scenario used. All the earth receives 240 W/m^2. The entire earth then would have same temp. No advection would take place.

Reply to  mkelly
September 18, 2022 3:22 pm

You are in fact correct mathematically because a variance of zero implies the surface and air are all the same temperature.

David A
Reply to  ferdberple
September 18, 2022 8:12 pm

The problem with averages…

Nelson
September 18, 2022 12:40 pm

An interesting series of posts Willis!

Here is where I get confused. The GHE tells me that water vapor heats the earth’s surface.

Your emerging phenomena (thunderstorms) are cooling mechanisms, which are driven by water vapor and convection. ( I’m not sure you can separate the two). Do you see a contradiction here?

Why is the floor of the Grand Cayon 10 degrees hotter than the rim when it gets 70% less solar than the rim?

I always scratch my head when I see energy budget graphs that don’t net out LWIR. The latent heat number typically shown is a net number.

I never read the Steel Shell post until today. I scrolled through the huge number of comments wondering if someone had asked what I was wondering about. They did. What happens if we shrink the steel shell to the surface? My intuition is that it would radiate at 235, the same as the surface. What if you let the size of the shell expand, what happens? It seems to me that your 470 surface equilibrium because of back radiation would happen for an arbitrarily small increase in the shell size. This seems strange to me. What happens as the size of the steel shell goes to infinity?

I always thought that 2 objects of the same temperature exchange no net radiation. In effect, a standing wave is created where no energy is exchanged.

Given where things stand in society, arguing against the forced energy transition because there is no runaway warming using the alarmist’s data and theory is likely the right approach. I have always been bothered by the inconsistency between the gas laws and the GHE. Given that Prof Happer has forgotten more than I will ever know and he believes in the GHE makes me think that I am missing something.

While it is far from settled, it is interesting that new questions have been raised about the Big Bang as data from the James Webb comes in.

A thought experiment. If the molecular weight of the atmosphere was increased by 1% would it make a difference to surface temperatures if the increase came from homonuclear diatomics (O2 and N2) verse Polyatomics (H2O, CO2, etc)

RickWill
Reply to  Nelson
September 18, 2022 4:38 pm

A thought experiment. If the molecular weight of the atmosphere was increased by 1% would it make a difference to surface temperatures 

The mass of the atmosphere alters the surface temperature. As does the buoyancy of water vapour in the atmosphere.

The most important atmospheric process is its ability to form a level of free convection. Without that, Earth would be a snowball. Everything would be ice. Formation of an LFC guarantees convective instability, which guarantees clear skies occur over oceans.

An LFC can reliably form above a surface at 15C. That is the point where you will observe clouds shift from dull and listless to more lively and some popping.

Below 15C it is possible for the atmosphere to remain fully saturated because it does not partition. Above 15C, saturation only occurs at the point of convective instability; often referred to as cloudburst. And is temporary. The thick cumulonimbus cloud gives way to high altitude cirrus cloud that persists for longer as a function of surface temperature. That cloud persistence regulates the sunlight to the surface.

The attached shows the relative humidity for ocean 1×1 degree grids for March 2022. The key observation is that no surface warmer than 15C every remains saturated. The super saturated locations are more likely the result of monthly averages and air movements than being perpetually saturated. Also the RH above 27C is likely lower than reality because satellites have difficulty penetrating thick cloud. And cloud persistence increases dramatically above 27C.

The surface limit of 30C is due to the LFC getting very close to the altitude of freezing because clouds forming above freezing are highly reflective and if the LFC is near freezing than higher reflective clouds persist for most of the recharge cycle.

It is possible to determine the altitude of the LFC based on the buoyancy of water vapour in the atmosphere. Any factor that alters the water buoyancy relative to the altitude of freezing in the atmosphere will alter the surface temperature. With current atmospheric mass, the surface can only reach 30C before the shutters prevent further surface heat input.

RH.png
Greg
September 18, 2022 1:11 pm

yclept, handy scrabble word. WTF ?

Philip Mulholland
Reply to  Greg
September 19, 2022 12:39 am

yclept – Forms of the preterit and past participle of clepe.

yclept – From Middle English yclept, ycleped, iclept [and other forms] (i-, y- (prefix forming past participles)[1] + clepen (“to say, speak, utter; to call, shout; to name; to address; to appeal to, beg, pray; to ask, request; to appear; to send for, summon; to convene; to call forth, induce; to lay claim”)

Still present in Scots – a Clipe is a Snitch.

FOR THOSE of you who remember your schooldays, you might recall the unwritten and unofficial (yet somehow global) school laws which meant you were never to tell tales or ‘grass up your mates’, no matter how severe the playground crime.

@Wills Please just your call your work an essay.

leitmotif
September 18, 2022 1:46 pm

ycleptyou cannot let eschenbach proselytize thermodynamics

jo darr
September 18, 2022 2:27 pm

at first I thought you were saying that the energy out was greater than the energy in. I now understand that you are saying the rate of radiant flux out is greater than the rate of radiant flux in

September 18, 2022 4:33 pm

Willis wrote:”Eventually it will reach a temperature where radiative heat loss out = heat in, and it won’t warm at all.”
≠====!!!!!!
Willis if the energy required to heat an object was not relatively constant, there would be no property “specific heat”. The value would be meaningless because it would vary widely with temperature.

in your example you have neglected to consider that equilibrium time is not just “eventually”. Equilibrium time must vary such that specific heat remains relatively constant. More power, less time, same energy. Less power, more time, same energy.

David A
Reply to  ferdberple
September 18, 2022 8:19 pm

There are only two ways to change the energy content of a system, ( in this case the earth land oceans and atmosphere) in a radiative balance, either a change in input, or a change in the the residence time of the energy within the system.

Tim Gorman
Reply to  David A
September 19, 2022 7:47 am

A combination of both would be a third way.

David A
Reply to  Tim Gorman
September 19, 2022 5:46 pm

Indeed, change the w/l of the input, and you change the residence time. Change the materials encountered, and you change the residence time.

There us no reason both cannot happen at the same time. Every argument as to earth’s GMT, is a residence time and or a input solar debate. CO2 increases residence time of some solar, yet high CO2 can also expedite or release energy to space that a non GHG would keep in the atmosphere.

Tim Gorman
Reply to  David A
September 20, 2022 4:50 am

A complicated system which I don’t think is adequately addressed by an snapshot of averages.

Reply to  Tim Gorman
September 20, 2022 12:45 pm

don’t think is adequately addressed by an snapshot of averages.
==========
Dont understand why anyone would down vote that statement.

Averages are like DC power. But the solar heating cycles, like AC piwer.

AC and DC behave very differently.
Nowhere is this addressed.

Tim Gorman
Reply to  ferdberple
September 21, 2022 3:58 am

The daily temperature curve is a DC signal with a psuedo-sinusoidal signal superimposed (sine wave during the day and an exponential decay during the night). The average temperature is not (Tmax + Tmin)/2. The rms (power) value is not (Tmax+Tmin)/2.

The daily temperature curve is related to a whole host of factors that are ignored by trying to use average values of any of these factors. The fact that Tmax doesn’t occur at the point of time when the sun is directly overhead is proof of that.

It’s my opinion that using average flux values is misleading. What should be used are the integrals of the flux values over time. This would take into account the cyclical nature and time offsets of many of these factors.

There are trolls on here that always downvote me just because I keep on pointing out the obvious problems with climate science methods today. Ce le vie!

September 18, 2022 7:29 pm

Willis wrote:

“So if we have a container of 1kg of water sitting on a table and we add 1 kcalorie of constant heat flux to it, it will never stop getting hotter?”
========
There are 0 kcals in heat flux, so the question is a nonsense.

Plot radiation in and out over time. This is kcals. The area between the curves is the energy absorbed/released to heat or cool the object.

From observation this energy is relatively independent of the temperature of the object – which surprises many, apparently.
.

Last edited 11 days ago by ferdberple
September 18, 2022 11:23 pm

I am going to try this one more time, about the 1st and 2nd Laws. 1st Law! The amount of energy that existed before an energy transfer is the same as the amount that exists after an energy transfer. 2nd Law! Heat flows from warm things to cooler things and never ever the other way.

I will not discuss the Mass Defect of a Nuclear Reaction here, 9000 kg/sec as happens in the Sun, of which we on Planet Earth receive 1/2-Billionth

Now we must define “Warming.” This word means that the temperature of an object increases, or else the two laws above are meaningless. Note that this does not include Cooling More Slowly!!!

So, concerning the Sun and the Sky, we all feel the heat from Father Sol, but none of us ever feel Warmed by the Sky.

You tell me. Discern and Discuss.

Once again, you should try some schooling. This is not intuitive but verified by your utility bill.

September 18, 2022 11:44 pm

And there has been much discussion here about what happens when radiation from a cool object, such as the atmosphere of the Earth, reaches a slightly warmer object, such as dirt or water at the surface of the Earth. Since there is rarely money involved in such a puny transfer, I had to look it up. Radiation from a cooler object reaching a warmer is simply reflected. You can say that the photons do not know at what temperature they were radiated, but they do, cannot warm a warmer object.

Give this up Willis, do not beat a dead horse.

angech
Reply to  Michael Moon
September 19, 2022 12:40 am

Michael Moon
And there has been much discussion here about what happens when radiation from a cool object, such as the atmosphere of the Earth, reaches a slightly warmer object, such as dirt or water at the surface of the Earth.
“Radiation from a cooler object reaching a warmer is simply reflected.”

Cannot stop people putting up bad science but can complain about it.
Michael.
You obviously recognise some of the many flaws in your argument else you would not have to resort to tricks to overcome them.
Here the trick is to claim reflection as a mechanism to deny the fact that warm objects do receive EM radiation.
But only for “ warmer” objects.

consider a mirror receiving radiation that it can reflect, hot or cold, The mirror will reflect it whatever temperature it is because it is a mirror, not because of its innate heat.

consider the effect of the action you claim.
The temperature of the object you claim is hot and therefore reflecting colder energy as well as emitting warmer energy itself now causes your thermometer a problem .
It become hotter to you even though it has “reflected”, your words, some energy so now the thermometer must read two energy inputs and tell you your warm object is even warmer!

I get the idea that a hot object must cool and a warm object must heat up.
I get the idea that you can summate the two energy flows in opposite directions and claim there is only one energy flow observed.
But just because the second is true does not make the first false.
In actual fact each warm object is actually radiating energy in all directions.
Every point around them has an energy level which is the combined temperature of the two warm objects.
There can be no physical scientific reason to say that this energy equation suddenly ceases to exist at the surface of a warmer object.

Enjoy your day.

leitmotif
Reply to  angech
September 19, 2022 4:08 am

angech the sophist.

angech
Reply to  leitmotif
September 19, 2022 9:29 pm

Thank you.

leitmotif
Reply to  angech
September 20, 2022 12:47 pm

Or would you prefer Willis Cheerleader?

Do you really believe the nonsense you post? Cold heats hot?

angech
Reply to  leitmotif
September 21, 2022 5:19 pm

Leitmotif
Cold heats hot is nonsense?
True

Definitions matter , do they not?

Cold is the absence of energy.
Hot is having energy.
When two objects both have energy they are no longer cold.
Both will transfer energy to a cold object ( one lacking any energy).

Now if both warm objects will heat up a cold object they must both radiate energy to a cold body

So both objects must radiate energy at each other as well.

If yo bothered to make each a heat source but one hotter than the other.
Note, neither is cold, they both have energy.

And you care to do the maths.
Not that you have shown any such care to date.
You will find that both warm objects will be warmer than their original temperatures.

The less warm body heats the warmer body and vice versa.

A cold body is only one at absolute zero.
All warm bodies have energy which they have to radiate and receive, absorb and remit.

mkelly
Reply to  angech
September 19, 2022 6:41 am

Objects at energy level 1 can’t absorb photons at energy level zero.

There are only 3 things that can happen to a photon once it encounters a surface. Those are absorption, transmission, or reflection. Reflection seems a reasonable answer. There is no way of telling a reflected photon from an emitted one.

Please do an S-B equation to show your work. Especially when you multiply by zero and still get warming somewhere.

leitmotif
Reply to  Willis Eschenbach
September 19, 2022 1:28 pm

That’s not the S-B equation, Willis. That’s your back radiation S-B equation.

The S-B equation is about the  power radiated from a black body in terms of its temperature into a sink at zero Kelvin.

Sophists like you invented the second black body.

Even Wiki disagrees with you.

https://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_law

Nelson
Reply to  Willis Eschenbach
September 20, 2022 5:02 am

Here is where I find it confusing. The net rate heat transfer, q, is positive if T1 is greater than T2. How does T1 increase without a net energy flow increase? I don’t think anyone believes a warm object magically reflects photons. Heck, I’m not even sure the photon is a useful concept. I think what is in question is how to interpret the 33 degrees that iscalled the GHE.

I think what we can all agree on is that NASA is failing at its job of informing on greenhouse gases. This is directly from their website

Greenhouse gases include carbon dioxide, methane, nitrous oxides, and water vapor. (Water vapor, which responds physically or chemically to changes in temperature, is called a “feedback.”) Scientists have determined that carbon dioxide’s warming effect helps stabilize Earth’s atmosphere. Remove carbon dioxide, and the terrestrial greenhouse effect would collapse. Without carbon dioxide, Earth’s surface would be some 33°C (59°F) cooler.

Reply to  Willis Eschenbach
September 20, 2022 1:56 pm

q = s A(T1^4 – T2^4)

This seems problematic

For example, if we increase the size of shell 2 to infinity, it will not affect shell 1 regardless of temperature.

That was the trivial example.

Last edited 9 days ago by ferdberple
Reply to  Willis Eschenbach
September 20, 2022 2:19 pm

how on earth is a photon going to determine the temperature of whatever it hits
===========
Quantum physics. The photon energy must match the electron orbital energies. Fractional interactions are not permitted.

Reply to  ferdberple
September 20, 2022 5:11 pm

Thinking more on this it may be more gasses that are limited in the absorbtion frequencies. Been more than 50 years since I studied this.

angech
Reply to  mkelly
September 21, 2022 5:36 pm

“Objects at energy level 1 can’t absorb photons at energy level zero”

What the heck is an object at energy level 1?
Why can it not accept a photon?
How can a photon not have energy?
What is a surface in regard to a photon?
How does reflection work anyway?
Since it breaks the rules of physics it is actually not reasonable.

In regard to warming somewhere I could point to the example of a magnifying glass that causes extreme heating in a concentrated area yet the energy input to that general area from the sun does not have to vary one iota.
Is the surface temperature at that spot a true temperature?
Yes.
What that is to indicate to you is that the temperature of a specific layer of air can vary immensely depending on its GHG load.
Yet the energy in and out of that region remains as constant as the heat source it has due to SB.
Does that help?

Tim Gorman
Reply to  angech
September 19, 2022 1:47 pm

What gets reflected merely replaces what was lost in the first place. The mirror isn’t on fire thus creating energy to radiate. The only thing CO2 can do is slow down cooling. If the nighttime earth was cooling down to t1 before the 1900’s, CO2 might only allow it to cool down to t1+ Δ today. Thus we would see the Tmin go up which would cause Tavg to go up as well. That same CO2 acts as a partial shield to the daytime sun’s energy thus keeping Tmax during the day from going up because of an increased Tmin.

Which really does describe what we are seeing today. The true fraud is the lie being pushed that the earth is going to turn into a cinder if something isn’t done.

To me the earth is like an old steam engine. Insulate the boiler and the minimum steam pressure won’t go down as fast and will stay at a higher level but it won’t affect the max pressure much if at all. You can only increase max pressure with a larger fire. And since nothing in the earth’s biosphere is on fire the only fire is from the sun. Unless the sun’s fire goes up the max temp on the earth won’t go up. The only real question is whether a higher minimum pressure in the steam engine (i.e. higher Tmin) is a problem!

angech
Reply to  Tim Gorman
September 21, 2022 5:01 pm

Tim Gorman
” The mirror isn’t on fire thus creating energy to radiate”
Wise words.

Philip Mulholland
September 19, 2022 12:53 am

Wills,

Self evidently the solid surface of the zonally rotating Earth cannot translate energy from the equator to the poles. All of this meridional energy transport is done by the mobile fluids of the water in the oceans and the air in the atmosphere.
Climatology is based on the mass-motion physics of fluids in the presence of a gravity field, these are the domains of Oceanography and Meteorology and not domain of Radiative Physics.
Please see our latest essay here:
The Application of the Dynamic Atmosphere Energy Transport Climate Model (DAET) to Earth’s semi-opaque troposphere

Reply to  Philip Mulholland
September 19, 2022 6:56 am

Philip, while difficult to read on my phone I believe you are making many of the same points as I have questioned.

The radiative greenhouse affect takes energy that would normally be radiated to space and returns it to the surface, warming the planet.

However, once you consider the earth is not a flat disk you realize that there are non radiative processes that do the same thing. Warm the surface with energy that would othwise escape to space.

These other processes are not accounted for in the radiative model which means that the radiative greenhouse effect must be smaller than calculated.

The process of discover is slow. To me the atmospheric lapse rate has not been give proper recognition in the role is plays in determining surface temperatures.

It is too much of a coincidence that 500mb altitude is also effective emissions height. This locks insolation to surface temp via lapse rate and atmospheric height.

Last edited 11 days ago by ferdberple
Philip Mulholland
Reply to  ferdberple
September 19, 2022 11:54 am

while difficult to read on my phone

Ferd, The tables are loaded as image files into Word. I will go back to ascii and try to fix that.

Reply to  Philip Mulholland
September 19, 2022 12:15 pm

I always have trouble reading pdf’s from my phone.

What is needed is a free pdf reader that has browser like display capability.

The fixed format pdf eventually gets too small as the screen size shrinks.

There is likely a reader out there that does it.

Last edited 10 days ago by ferdberple
Reply to  Philip Mulholland
September 19, 2022 1:15 pm

Hi Philip

I just switched to adobe android liquid mode and so far looks good. I’m using a download from your original link

Thanks

Reply to  ferdberple
September 19, 2022 1:18 pm

If you are going to switch tables I would recommend an additional link to allow quick testing.

angech
Reply to  ferdberple
September 19, 2022 9:27 pm

ferdberple
Philip, while difficult to read on my phone I believe you are making many of the same points as I have questioned.
“The radiative greenhouse affect takes energy that would normally be radiated to space and returns it to the surface, warming the planet.”
Ferd,
At any one time the body is radiating to space the energy incoming to it.
There is no normally here as there is GHG here.
The surface is irretrievably changed.
With the GHG present the pathway in and out is such that the same amount of energy is always being radiated out of the whole body overall.

angech
Reply to  angech
September 19, 2022 9:33 pm

The proof of that being without that fact SB does not work.
The fact that we attribute temperature to retained energy rather than energy passing through seems logical on the surface but practically has to be wrong somehow.

Reply to  angech
September 20, 2022 1:41 pm

that the same amount of energy is always being radiated out of the whole body overall.
========
Agreed. The problem is that earth is radiating from 5+ km effective altitude. Solar heating is AC not DC. We live in a layered, moving, moist heat conductive mass 5km under the effective surface.

After many simplifying assumptions climate sciences arrives at the correct answer to 1 part in 600 precision. Having known the answer in advance.

Philip Mulholland
Reply to  ferdberple
September 20, 2022 4:23 pm

We live in a layered, moving, moist heat conductive mass 5km under the effective surface.

Ferd,
That is really good. (I may steal it).

Consider this:
As 71% of the planet’s surface is covered by ocean water with a basal temperature of 4 Celsius then where is the global warming?

I have now reloaded in to the Word document all of the image files from Excel as ASCII (Sizing Excel tables in Word is a real pain but the learning was useful).

I spotted a few more typos and fixed these in this 19 Sept PDF version on Research Gate.
How does it look now?
(p.s. I don’t own a surveillance ‘phone so I can’t this check myself).

angech
Reply to  Philip Mulholland
September 20, 2022 6:20 pm

Philip Mulholland

Reply to 
ferdberple

We live in a layered, moving, moist heat conductive mass 5km under the effective surface.

That is really good.

I agree

Reply to  Philip Mulholland
September 19, 2022 2:28 pm

Hi Philip,

Did a quick read of your paper. It bothers me a lot that climate science makes a whole series of simplifying assumptions in their models, ignore variance and arrive at the right answer. 15C. So I would not be concerned to hit 15C.

For me, in a planet with an atmisphere, energy cannot tell if it is moved via radiation, conduction, convection, advection, etc, etc, etc.

So why is climate science hung up on back radiation. All this does is take energy that would escape to space and return it to the surface. The same can be shown for any process that moves energy. Gotta run.

Philip Mulholland
Reply to  ferdberple
September 19, 2022 3:14 pm

Ferd
I changed the tables to ascii, but the process fell over at Table 10 on page 15.
So, for public viewing I have switched back to the first file I loaded on to Research Gate.

For me, in a planet with an atmisphere, energy cannot tell if it is moved via radiation, conduction, convection, advection, etc, etc, etc.

So why is climate science hung up on back radiation

Our key message is Figure 3 on page 11. The back-radiation loop of the standard radiative physics model is actually our adiabatic mass motion convection loop (aka the Hadley Cell) of meteorology.

TallDave
September 20, 2022 7:22 am

The surprise in this one for me was that once we’ve included the effects of advection, the multiplier is pretty much equal from the North Pole down to the north tip of Antarctica.

thus helping explain why we’ve been in an Ice Age since the all-important Antarctic isolation

But curiously, this is counterbalanced by a reduction (per unit of incoming solar power) in the amount of increase in surface temperatures, along with a corresponding increase in the advection.

makes sense that advection would increase, another thermostat like tropical thunderstorm frequency

Last edited 10 days ago by TallDave
Reply to  TallDave
September 20, 2022 1:16 pm

makes sense that advection would increase, another thermostat like tropical thunderstorm frequency
============
I woulg go further and say that it is the global thermostat, by controlling temperature variance.

The non-linearity between temperature and radiation means that for any given radiative balance you can change the average temperature without changing the radiation. All you need do is change the variance in temperature. And this variance is controlled by advection, not by CO2

I demonstrated the math behind this earlier in the post. I belive this is likely what Willis has discovered in his multiplier and what Philip has discovered in his model.

September 20, 2022 2:37 pm

q = s A(T1^4 – T2^4)
==============
This is an interesting equation. Say we doubled the size of shell 2. Offhand that would give us 8 times the radiative surface. Now leave the temperature of shell 2 unchanged. This means shell 2 now has 8 times the radiative flux acting on shell 1. That is clearly going to change the effect on shell 1.

So I call BS on this formula except in the trivial case where shell 1 and 2 are the same size which violates the requirement that shell 2 enclose shell 1.

September 20, 2022 2:45 pm

q = s A(T1^4 – T2^4)
==============
Further, now expand shell 2 to infinity, and set the temperature of shell 2 to any value greater than 0. Say 3.4K

Now select any size for shell 1 less than infinity. The flux from shell 2 acting on shell 1 must be infinite, therefore if we live in an infinite universe the planet earth would have burned up unless the universe is expanding faster than the speed of light.

If the speed of expansion is limited to rhe speed of light then our universe is not infinite. There must be a region outside our universe or the formula is wrong.

leitmotif
September 20, 2022 5:02 pm

WUWT cannot be considered an AGW sceptical website while Willis Eschenbach continues to post bullshit articles on the effects of atmospheric back radiation on surface warming.

No evidence. No credibility. No honesty. No humility. Just sheer arrogance.

The Steel Greenhouse is just The Steel Craphouse.

A joke representation of how our planet is heated and how it cools.

Dump this WE guy.

Only kidding. You should just dump me instead. Problem solved. That’s what WUT normally do anyway..

Reply to  leitmotif
September 20, 2022 5:04 pm

You have been working to get my attention. You got it now. Happy?

leitmotif
Reply to  Charles Rotter
September 20, 2022 5:47 pm

Charles Rotter, do your worst.

I am a committed anti-CAGW voice. I am also a committed anti-lukewarmist voice.

Shut me up if you desire a smooth running WUWT..

Do it. I dare you.

I double dare you.

Cowards like you are easily exposed.

Willis Eschenbach is a sophist. End of.

Give me evidence for the surface warming properties of atmospheric CO2.

You cannot can you, Charles, can you?

Just ban me, instead.

Easy way out.

Reply to  leitmotif
September 20, 2022 5:57 pm
angech
Reply to  leitmotif
September 20, 2022 6:40 pm

leitmotif “Just throw me in the briar”patch!

“Give me evidence for the surface warming properties of atmospheric CO2.”
“I am a committed anti-CAGW voice”.
or is it
“I am a committed anti-surface warming properties of atmospheric CO2.voice”.

CO2 does not, of itself, warm things.
It is not a power source per se.
So, sadly, technically speaking, you are correct.

However, the presence of CO2 in at atmosphere irradiated by an energy source enables said atmosphere to run at a different temperature to an atmosphere sans CO2.

This is also a property of other gases irradiated by energy at their spectral “absorption” settings.
Nothing to do with them being a heat source

You either believe that such reactions are possible, or you don’t.
Closing your eyes to this fact, but accepting the rest of science, is a problem.

leitmotif
September 20, 2022 6:23 pm

Is WUWT a respectable climate change website as long as it adheres to cancel culture?

I say this as I have been told by Charles Rotter that I have been brought to his attention over a comment made by me about the sophist Willis Eschenbach. You know, the guy who believes that atmospheric back radiation from ghgs heats the planet, Yeah, I know, bullshit but ….

While griff, loydo and simon are allowed to express their CAGW beliefs on WUWT, I am not allowed to express my views on lukewarmism and the ECS.

Funny old game, climate change.

Reply to  leitmotif
September 20, 2022 7:08 pm

Yes, yes. It was that ONE comment.

leitmotif
Reply to  Charles Rotter
September 22, 2022 3:17 pm

Charles. Are you a CO2 sceptic or a lukewarmist?

Your choice.

September 20, 2022 8:19 pm

The back-radiation loop of the standard radiative physics model is actually our adiabatic mass motion convection loop (aka the Hadley Cell) of meteorology.
==========
I have no problem with the back radiation concept in a vacuum. However I think it is a nonsense in earth’s atmosphere.

The bulk of energy tranfer from the surface to 500 mb is done by convection because the lower atmosphere is opaque to outgoing IR radiation. This is well documented.

Well if the lower atmosphere is opaque to outgiing IR then it most certainly is also opaque to incoming IR back radiation.

This means that the so called greenhouse effect is not and cannot be a radiative effect. It must be due to something else.

The obvious candidate is the cold dry air carried to altitude by convection. As this air descends it will warm at a rate of about 9.8K/km, returning the work done by the ascending air back to the surface in the form of thermal energy.

This can also combine with surface air carried from warm to cold as well as ocean currents all under the label advection. This xonrrols the variance in temperatures, allowing average temperatures to change without any radiative change at TOA.

There is no need for back radiation to explain this. And in fact as has been documenred elsewhere, the lower atmosphere will not allow significant amount of IR to pass in either direction. As such back radiation cannot be the cause of the greenhouse effect.

This has nothing to do with compressive heating and other pooly constructed arguments against this most obvious process.

Last edited 9 days ago by ferdberple
angech
Reply to  ferdberple
September 20, 2022 11:53 pm

ferdberple

[The back-radiation loop of the standard radiative physics model is actually our adiabatic mass motion convection loop (aka the Hadley Cell) of meteorology.}
==========
” I have no problem with the back radiation concept in a vacuum.”

Ferd, An amusing but vacuous dodge presumably meant because a vacuum cannot initiate back radiation.

“However I think it is a nonsense in earth’s atmosphere.”

Amazing how some scientists think that GHG molecules actually absorb and radiate energy , including backwards against all rational thought processes and observations.

“The bulk of energy transfer from the surface to 500 mb is done by convection because the lower atmosphere is opaque to outgoing IR radiation.”

Human eyes do not see infra red which is how energy transfers from the earth’s surface to space.
Yet if you put your hand 4 inches above a bitumen road surface you can feel the IR radiating through the non opaque atmosphere quite easily.
Another example is your TV remote control where the IR message goes quite easily through meters of the lower atmosphere to reach and control the set.

The exact situation is that in the very lowest atmosphere a large amount of most IR is able to be absorbed in a distance of meters from the surface.
That IR, as you know is remitted into the next layer up [and sideways and back down] a few more meters and as the layers rise the air concentration and GHG decrease meaning the upwards portion can travel longer distances before being reabsorbed.
Eventually it reaches a layer where the radiation can be lost to space without intervention bt GHG.
There is no opaqueness, as you claim, or the energy is not stopped from traveling from warmer to cooler larger layers of atmosphere upwards.
Only if not remitted would there be opacity.

As for convection, piffle.
True, you can do convection diagrams til the cows come home.
Hadley cells, trade winds currents whatever.
All they do is provide a convenient explanation for why the energy going to space, or the next higher layer is coming from that part of the air mass.
Or as Willis puts it helps to explain why the heat loss per grid varies while overall staying the same.
Remember the molecules are constantly loosing energy to space and back radiating at the same time as they are receiving more energy from space and less from the ground.
As Zelazny would say the masses of hot rising air, the molecules, are ephemeral.
The real heat loss is IR constantly going on radiating to space through whatever is in the way and absolutely uninfluenced by it.
N.B
For every hot air mass rising a cool mass is coming down around it resulting in zero change of energy at the overall TOA.

“Well if the lower atmosphere is opaque to outgoing IR then it most certainly is also opaque to incoming IR back radiation.”

As pointed out your concept of opaqueness is wrong.

“This means that the so called greenhouse effect is not and cannot be a radiative effect”.

Yet it is a radiative effect, all the way to space, constantly, opaqueness be damned.
.
“There is no need for back radiation to explain this. And in fact as has been documenred elsewhere, the lower atmosphere will not allow significant amount of IR to pass in either direction. As such back radiation cannot be the cause of the greenhouse effect.”

The flaw in your argument is overlooking the IR radiation to space which could never occur if the IR from the SW on the surface was trapped by opaque atmosphere.
Itwould lead to an inevitable super heated earth and no outward radiation.

Tim Gorman
Reply to  angech
September 21, 2022 7:54 am

The exact situation is that in the very lowest atmosphere a large amount of most IR is able to be absorbed in a distance of meters from the surface.

That IR, as you know is remitted into the next layer up [and sideways and back down] a few more meters and as the layers rise the air concentration and GHG decrease meaning the upwards portion can travel longer distances before being reabsorbed.
Eventually it reaches a layer where the radiation can be lost to space without intervention bt GHG.
There is no opaqueness, as you claim, or the energy is not stopped from traveling from warmer to cooler larger layers of atmosphere upwards.”

The layer *is* opaque. Otherwise there would be no convection upwards. All the radiation would just escape straight to space. You are conjoining two separate processes – absorption and convection.

angech
Reply to  Tim Gorman
September 21, 2022 5:55 pm

Tim,
“The layer *is* opaque. Otherwise there would be no convection upwards. All the radiation would just escape straight to space. You are conjoining two separate processes – absorption and convection.”

The layer is a term used to describe the distance that those IR frequencies which can be absorbed would be completely absorbed in.
Not a series of opaque blankets that IR can never travel through.
In essence there is no opacity.
At all times the number of IR photons being absorbed and emitted is equal.
It is only when one gets to the last layer, the TOA that the IR goes out and does not return.

Convection is a description of the behaviour of loose surface molecules while the process of IR radiation occurs.
If they were all bound tight on the surface you would talk of vibrations of the solid molecules and how one composition was more vibratory than another.
Basically matter moves when energy is passing through it but the energy does not care where the matter is, just how to get in and out

Tim Gorman
Reply to  angech
September 22, 2022 5:06 am

At all times the number of IR photons being absorbed and emitted is equal.”

Absorption implies opacity of some kind. Perhaps not total but at least significant.

Like I said, you can’t conflate absorption and convection. They are different processes.

angech
Reply to  Tim Gorman
September 23, 2022 3:37 am

Tim
Absorption implies opacity of some kind. Perhaps not total but at least significant.

Stopping at stage one of a two stage process does not help clear the air either.

The concept here is not the temporary pause if indeed one exists.
The concept is the energy flow, not which particular photon carries it.

If the energy is not retained or stored then the energy is clearly seen.

The mechanism of reemission which accompanies “absorption” means that there is no loss of transmission hence no opaqueness.

Unless you want to contest the notion that energy is continually passing through the atmosphere back to space,
with or without the assistance of an atmosphere.

That seems to be the implication.
IR cannot get off the ground without convection,
because of opacity of the air but somehow when it gets high enough it suddenly looses its previous property of absorption with retention.

If you wish to support others arguments on opacity grounds while knowing full well that radiation has to continue unblocked be my guest.

Tim Gorman
Reply to  angech
September 23, 2022 7:29 am

Stopping at stage one of a two stage process does not help clear the air either.”

There *is* more than one process. Conflating them doesn’t provide any clarity.

If CO2 prevents heat from escaping out then it also prevents heat from getting in. You can’t have it both ways.

I said: “Absorption implies opacity of some kind. Perhaps not total but at least significant.”

Don’t imply I said total opacity. I didn’t. Stop putting words in my mouth.

angech
Reply to  Tim Gorman
September 24, 2022 1:00 am

Tim
“If CO2 prevents heat from escaping out then it also prevents heat from getting in. You can’t have it both ways”.
What?
Heat [energy from the sun] can get in by SW and then be interacted with by C02 on the way out as IR LW.

Heat does not restrict itself as to its means of getting in and out.
As an aside the Solar input has a lot of IR in it absorbed in the first layer in [last layer out] that never gets to the surface.

“I said: “Absorption implies opacity of some kind. Perhaps not total but at least significant.”
“Don’t imply I said total opacity.
I didn’t. Stop putting words in my mouth.”

“The layer *is* opaque.”

Tim Gorman
Reply to  angech
September 24, 2022 4:51 am

The sun’s spectrum includes a lot of IR, much of which is absorbed by water vapor before every reaching the surface and CO2 absorbs some of it as well.

Have you ever “felt” the heat on your face and arms while standing out in the sun? What do you suppose causes that? SW or LWIR?

September 20, 2022 8:54 pm

I do think WUWT was more interesting when there was a wider discussion of the alternative hypothesis.

Arguing the lukewarm position that climate science is correct in their methods, but in error over magnitude is self-defeating.

No scientist living today or in the past knows the correct answer because we do not know how much climate varies naturally.

As such, so long as the math can be demonstrated then no hypothesis should be off the table.

There is plenty of evidence that climate science gets the math wrong but the answer right, which suggests the methods are wrong.. Which means the lukewarm methods are wrong as well.

This hurts WUWT make a convincing case.

Last edited 9 days ago by ferdberple
September 20, 2022 9:47 pm

Philip I downloaded your latest and everything seemed good under adobe reader for android liquid mode. Screen in portrait mode. Tables colors and image all worked. Could expand/contract for readability. Tables with least columns easiest to read.

September 20, 2022 11:29 pm

Willis wrote
“Folks, there are a lot of untrue claims going on out here on the web.”
Willis wrote:
“My Usual Note: When you comment PLEASE quote the exact words you’re discussing”
===========
When you point a finger at other people you are pointing 3 fingers back at yourself.

September 21, 2022 12:22 am

Philip reading your model, some ideas came to mind.

Didnt like doubling the atmospheric window

The moist air lapse rate of 8 seems high. 6.5 is what is most often quoted.

You add the radiation from the 2 halves and apply S-B, effectively spinning the planet to get temp.

15C is based on gridding surface temps I believe. So apply S-B to each half to get 2 grid temps then average.

First frost warning so this snowbird is off to florida for some global warming. offline mostly.

Philip Mulholland
Reply to  ferdberple
September 21, 2022 3:53 am

Didnt like doubling the atmospheric window

OK I will check the logic for that.

Philip Mulholland
Reply to  Philip Mulholland
September 21, 2022 4:08 am

Ferd,

I reduced the Atmospheric Window in the Adiabatic DAET Opacity model to 40 W/m2 (post feedbacks) and the GAT rises to 22.1 Celsius with an Atmospheric Window sacrifice of 3.01% (as opposed to my preferred 6.4% sacrifice)

The key point is that with a single lit hemisphere the input solar power flux gets doubled, (divide original solar input by 2 and not by 4 is the rule for this model) so the output atmospheric window flux (post feedbacks) must also be doubled.
Have a look again at my Figure 3.

Philip Mulholland
Reply to  ferdberple
September 21, 2022 4:15 am

15C is based on gridding surface temps I believe. So apply S-B to each half to get 2 grid temps then average.

No. This is the critical mistake that I made, and I got caned by the Physicists for making it. The Diabatic Model fully matches the Vacuum Planet Equation only when I average Flux and not Temperature.
Have a look at Figure 2 and also Table 5.

Philip Mulholland
Reply to  ferdberple
September 21, 2022 4:19 am

You add the radiation from the 2 halves and apply S-B, effectively spinning the planet to get temp.

Yes, and our planet is not tidally locked Noonworld, it has a diurnal spin!
Nice touch that isn’t it 😉

Philip Mulholland
Reply to  ferdberple
September 21, 2022 4:22 am

The moist air lapse rate of 8 seems high. 6.5 is what is most often quoted

That is fine to alter, the model fluxes are unaffected by the lapse rate.
Can be adjusted to an acceptable value.

September 21, 2022 8:40 am

The Diabatic Model fully matches the Vacuum Planet Equation only when I average Flux and not Temperature.
========
Philip the S-B law when solved in the reverse direction gives you the upper limit on temperature, not the actual temperature.

The reason is that VPE assumes a 1/4 flat disk with zero variance. I have demonstrated the math numerous times.

Maximum temp works for GHG theory because it is sufficient to show max temp -18+33 would not be possible without ghg.

Your model does not have zero variance. So what temperature are you trying to match? A maximum or gridded average?

Another approach would be to solve min/max/avg in your model then try and narrow the limits.

Last edited 9 days ago by ferdberple
Philip Mulholland
Reply to  ferdberple
September 21, 2022 11:54 am

The reason is that VPE assumes a 1/4 flat disk with zero variance. I have demonstrated the math numerous times.

Ferd,
You have lost me here. Please provide a link to show this work you are referring to.

Reply to  Philip Mulholland
September 21, 2022 5:54 pm

Philip

Search WUWT for the holder inequality.

What it shows is that avg(T) < avg (T^4).

So, we know GISS and others have built their temperaturs as avg(T) by sampling surface temps and get 15C as the answer.

And we know that using avg(T^4)
climate scientists get an average temp of 15C.

And we know from the holder inequality that these results cannot be equal, that avg(T) < avg (T^4), so at least one and possibly both calculations of 15C are wrong.

For exanple
avg (2,2),=2
Avg (1,3)=2

Avg(2^4,2^4)=16
Avg(1^4,3^4)=41

The holder inequality shows that S-B Law is not reversible unless you know the variance.

Therefore your hot cold model is fundamentally different than a disk of uniform temperarure, because you have non zero variance..

Last edited 8 days ago by ferdberple
Philip Mulholland
Reply to  ferdberple
September 21, 2022 10:28 pm

Ferd,

Therefore your hot cold model is fundamentally different than a disk of uniform temperarure, because you have non zero variance.

This is where I lose track of your thoughts.
Above you also state this

The reason is that VPE assumes a 1/4 flat disk with zero variance. 

The VPE is NOT modelling a flat disk!

Please tell me that you do recognise that the VPE is modelling the illuminated surface of a sphere with surface area 4Pir^2 and that the power intercepted from the solar beam has a cross-sectional area of Pir^2 so the power dilution (intercept to surface distribution) will be 1/4.
The does not make the relationship into a flat disk.

Ferd,
Please let me be blunt. In our work we are presenting a re-design of the standard concept by changing the power dilution factor from 1/4 – total instantaneous surface illumination of the whole globe, to 1/2 – accurate representation of the real single hemisphere illumination.

Consequently, we must follow all of the rest of the standard logic. I cannot match your understanding of Hölder’s inequality and so need to stop here.

Thank you for raising the issue of lapse rate I have corrected 8 K/km MELR to 6.5 K/km MELR in the tables where necessary and added this comment to our text.

5.3      Lapse Rate Choice and Application.

Throughout this study we have used two lapse rates for the purpose of illustrating the results generated by each modelling scenario. These are the Dry Adiabatic Lapse (DALR) rate of 9.8 K/km and the Moist Environmental Lapse Rate (MELR) of 6.5 K/km. In the first phase of the analysis our modelling concept of a transparent nitrogen atmosphere that does not contain a condensing volatile requires us to use the DALR for both surfaces of our model (Tables 4, 7 and 8).

The incorporation of opacity and the atmospheric window into the model permits us to use the MELR for the lit side hemisphere’s environment of ascending air and the DALR for the dark side hemisphere’s environment of descending air. (Tables 10 and 12). For the study of the Habitable Zone, we deem it appropriate to use the MELR for both sides of the model of the Hot Earth (Table 14) because in this boiling ocean scenario the planet’s atmosphere will be saturated with water vapour. While for the Frozen Earth model the low temperature planetary atmosphere will contain no water vapour and therefore the DALR should be applied to both sides of the model (Table 16).

It should be noted that the choice of lapse rate does not impact on either the functional properties or the results of the DAET model and it is not a control variable. While the DALR is a fixed environmental property relating to planetary gravity and the specific heat of the atmospheric gas mixture, the MELR has considerable flexibility of application. It is this variability of the MELR that provides the feedback response which balances the two climatic processes of atmospheric heating and cooling in response to radiative forcings.

 

Philip Mulholland
Reply to  Philip Mulholland
September 22, 2022 2:18 am

I cannot match your understanding of Hölder’s inequality and so need to stop here.

Ferd,
A good night’s sleep and I wake with a new thought. You say:

The holder inequality shows that S-B Law is not reversible unless you know the variance.

I am going to assume that by variance you mean variation and so I will pick up from there. As I stated above the purpose of our work is to match the logic flow of the prior authors’ work. We have demonstrated that their work creates a single surface flux value of 390 W/m^2 and we have achieved this value with our DAET model by averaging surface flux, thereby matching them.

Once you move into the realm of averaging surface temperature (which is where I think that you are) then the issue of power flux variation over the surface of the lit hemisphere from zenith to terminator becomes paramount and we move into the complex realm spherical geometry.

Please note that when dealing with the averaging of surface temperature we approach this issue from the domain of meteorology and not that of radiative physics. Here is our technique of how we achieve this:

“We discuss how with knowledge of three simple meteorological parameters of tropopause elevation, tropopause temperature and lapse rate for each atmospheric cell, combined with the measurement of the area of that cell, the average global surface temperature can be calculated”.

Return to Earth: A New Mathematical Model of the Earth’s Climate

Philip Mulholland
Reply to  Philip Mulholland
September 22, 2022 3:26 am

So why does climate science with its flat surface toy model ignore spherical geometry? Because the planetary disk can NEVER intercept more power from the irradiance of the solar beam than the cross-sectional planar surface equivalent area of its disk shadow silhouette.

Philip Mulholland
Reply to  Philip Mulholland
September 26, 2022 5:09 am

Ferd,
A final comment on flat surface models and spherical geometry.
Note that in all of this climate modelling everyone uses the Bond Albedo.
The Bond Albedo is a spherical filter that incorporates all of the geometric effects of the illumination of the lit hemisphere by the incident solar beam into its computation. Consequently the need to apply Hölder’s inequality is avoided.

Last edited 4 days ago by Philip Mulholland
leitmotif
September 22, 2022 3:48 pm

This comment by Joseph Postma, astrophysicist, must have been really disturbing for Willis.

Get rid of the sphere, it is the shell itself which is its own power source. The shell itself produces the power inside its own material. There’s no sphere inside the hollow cavity of the shell. The power production is 240W, the surface area of the shell is 1m^2, and the shell is negligible thickness. What’s the temperature of the shell? What is its surface flux?

Mike Edwards
September 23, 2022 8:08 am

“The difference must be advected, except for a very small fraction that raises or lowers the surface temperature and can be neglected at this level of analysis.”

Is that really true for portions of the earth’s surface that have ice that melts and refreezes each year?

Using the CERES data, there is a calculation of the total amount of SW radiation absorbed by the surface in the Arctic here:

https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2021GL095813

  • numbers in the range 1800 – 5800 MJm-2 are shown

Meanwhile melting a mass of ice 1 meter thick takes about 333MJm-2. So quite a chunk of the absorbed radiation goes to melting ice in these regions – being returned when the ice refreezes, of course. The concentration of both melting and refreezing into relatively short periods should give a noticeable effect.

September 23, 2022 1:54 pm

I am going to assume that by variance you mean variation
=======//
No. I means statistical variance. The power of the difference about the mean.

Calculate average temperature using simple averages and s-b for 3 cases of a 2 hemisphere earth with temps:

15C, 15C
10C, 20C
0C , 30C

These all have the same avg but different variance. Does this average also hold true using S-B?

If you average radiation does S-B give you 15C in all 3 cases? The holder inequality says it won’t.

If not how do you resolve gridded avg temps like GISS and astronomer’s temp of earth?

Last edited 6 days ago by ferdberple
Tim Gorman
Reply to  ferdberple
September 23, 2022 2:00 pm

I don’t think you will ever get an answer. There should be a variance provided along with all of the climate science results but there never is. What does the Global Average Temp mean if you don’t have a variance to go along with it?

Peter Ibach
September 28, 2022 4:40 pm

Isn’t this an empirical confirmation of Javier’s hypothesis, that meridional transport is having a primar climatic influence?