By Philip Mulholland and Stephen Wilde
A fundamental concept at the heart of climate science is the contention that the solar energy that the disk of the Earth intercepts from the Sun’s irradiance must be diluted by a factor of 4. This is because the surface area of a globe is 4 times the interception area of the disk silhouette (Wilde and Mulholland, 2020a).
This geometric relationship of divide by 4 for the insolation energy creates the absurd paradox that the Sun shines directly onto the surface of the Earth at night. The correct assertion is that the solar energy power intensity is collected over the full surface area of a lit hemisphere (divide by 2) and that it is the thermal radiant exhaust flux that leaves from the full surface area of the globe (divide by 4).
In between these two geometric relationships of energy collection and departure back to space lies the Atmospheric Reservoir, the Earth’s gaseous coating within which all climate processes occur. The following table and figure adapted from the canonical model of Kiehl and Trenberth (1997) are used to illustrate a model in which the fundamental realities of a lit (day) and unlit (night) hemisphere are retained as the irreducible logical minimum geometric relationship for the energy budget of the Earth’s climate.
In the following figure the parameters have been adjusted by using hemisphere dependent thermal exhaust flux values of 200 W/m2 (day) and 270 W/m2 (night) based on a Dynamic Atmosphere Energy Transport model of the Earth’s Climate (Wilde and Mulholland, 2020b).
Key Features of the Diagram
- It demonstrates that the concept of the Atmospheric Reservoir can be made to work for a Lit Hemisphere (Divide by 2) Solar Irradiance.
- It shows how the Atmospheric Reservoir behaves as both a store and a transporter of energy.
- All captured fluxes are doubled by the process of infinite geometric recycling (the half lost; half retained process by which an infinite series of halves of halves sums to one).
- In the daytime the Troposphere expands as it stores potential energy with work done against gravity.
- Potential energy cannot be radiated away so the daytime loss at the Top of the Atmosphere (TOA) is reduced as the atmosphere expands.
- During the night the Troposphere contracts as it cools, this converts potential energy back into kinetic energy which accounts for the enhanced night-time loss of energy to space.
- The atmospheric reservoir gross value of 780 W/m2 is halved to the 390 W/m2 canonical value because the surface area of the emitting globe is twice that of the solar collection hemisphere.
- The daytime processes of thermals and evapo-transpiration are driven primarily by direct solar energy and so do not occur at night (lots of caveats here: if the surface is moist then the evaporation process can also occur at night e.g. land versus sea, moist tropical forest versus dry desert, weather systems advection etc).
- The Earth’s surface is a huge slow release storage radiator that emits its captured solar energy at night and in the winter.
- The bypass radiation occurs both during the day and at night at the same rate (40 W/m2) as in the canonical model because of the same surface area issue of collection versus emission as listed in point 7.
The Lungs of Gaia
One could liken the process of the daytime capture of solar energy that causes the atmosphere to expand, followed by the night-time contraction of the atmosphere as it cools – to the Earth ‘breathing’. The atmosphere being the lungs of our planet which expand and contract over the course of a 24-hour cycle, and in doing so varies the supply of potential energy back to the surface. This rhythmic process acts to maintain hydrostatic equilibrium for the atmosphere as a whole by matching thermal radiant energy out to space with high frequency radiant energy coming in from the sun.
References
Kiehl, J.T and K.E. Trenberth, 1997. Earth’s Annual Global Mean Energy Budget. Bulletin of the American Meteorological Society, Vol. 78 (2), 197-208
Wilde, S.P.R. and Mulholland, P., 2020a. An Analysis of the Earth’s Energy Budget. International Journal of Atmospheric and Oceanic Sciences. Vol. 4, No. 2, 2020, pp. 54-64. doi: 10.11648/j.ijaos.20200402.12
https://www.researchgate.net/publication/344539740_An_Analysis_of_the_Earth’s_Energy_Budget
Wilde, S.P.R. and Mulholland, P., 2020b. Return to Earth: A New Mathematical Model of the Earth’s Climate. International Journal of Atmospheric and Oceanic Sciences. Vol. 4, No. 2, 2020, pp. 36-53. doi: 10.11648/j.ijaos.20200402.11
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The diagram appears to be simplified in several ways. First, aerosol and Rayleigh scattering scatter light in all directions, including the forward (toward the ground). Aerosol scattering is highly complex and varies spatially as well as with light wavelength. Second, cloud reflections also vary and do not always reflect backward into space. Lastly, thermal radiation by the atmosphere is in all directions, it also does not all go upward into space.
AFAIK given a terrestrial grid cell the path of incoming radiation varies with the sun’s angles, and so the surface heating effect must vary by these angles and also the varying length of the atmosperic path.
But, the outgoing radiation from the surface goes in all directions irrespective of the time of year and time of day and so the lengths of the radiated atmospheric paths will not change.
Can anybody say whether the summing these effects is a feature of basic climate models?
Dr Spencer
The Stefan-Boltzmann-Law describes a „just in time“-relation (temperature=>specific radiation power) and does not allow any time-averages of both. Consequently, a S-B-Inversion (specific radiation power=>temperature) must not use a 24h-time-average of the specific radiation power to calculate a temperature-equivalent. A 24h-time-average destroys the S-B-T^4-relation because it calculates specific radiation power [W/m²] back from energy [(W/m²)*s=Joule/m²].
Citation from your article „A Simple “No Greenhouse Effect” Model of Day/Night Temperatures at Different Latitudes“:
“I hope this will help convince some who are still open-minded on this subject that even intense tropical sunshine cannot explain real-world tropical temperatures. The atmospheric greenhouse effect must also be included. The temperature (of anything) is not determined by the rate of energy input (say, the intensity of sunlight, or how fast your car engine burns gas); it is the result of a balance between energy gain and energy loss. The greenhouse effect reduces the rate of energy loss at the surface, thus causing higher temperatures then if it did not exist.”
1. The S-B-temperature-equivalent of the solar constant (1367W/m²) is about 120°C. That’s much more than the real-world tropical temperatures count. And because of the heat capacity of water the temperature on the night side of the earth drops only in temperature models to 0 Kelvin.
2. The greenhouse effect is said to account for 33°C. But how should any object get that 33°C warmer by less cooling? That object only cools slower down from its original temperature…
From “Atmospheres” by R. M. Goody 1972.
“Our theory (The Greenhouse Effect on Earth) is inadequate ( that the surface temperature should 45ºC warmer at 60ºC than the observed 15ºC ) because radiation is not the only process that carries heat upward from the ground and from the lower levels of the troposphere. Another process tending to hold down the temperature at the ground and to increase the temperature of the upper troposphere is known as convection.”
Convection doesn’t heat the upper troposphere because the expansion with height cools the rising without any loss of energy.
The significance of convection and the gas laws is entirely missing from all the models.
Convection upwards cools the surface and convection downwards warms the surface due to conversion of energy between potential and kinetic forms.
That delays the emission of solar radiation to space which warms the surface beneath a convecting atmosphere.
If radiative imbalances occur then the consequential distortion of the lapse rate slope alters the speed of convection in order to maintain stability for the system as a whole.
Thus there is no overall thermal effect from varying amounts of ghgs.
“If radiative imbalances occur then the consequential distortion of the lapse rate slope alters the speed of convection in order to maintain stability for the system as a whole.”
Agreed, except for:
“Thus there is no overall thermal effect from varying amounts of ghgs.”
Concentrating on water vapour as the main radiative gas and taking the effective temperature for Earth to be -18ºC. at 3km. altitude with a skin temperature of -60ºC at a tropopause at 12km. radiative transfer theory calculates that in the presence of water vapour the surface temperature should be 60ºC.
But the reality is that as the sun warms the surface, convection kicks in as soon as that resistance to radiative surface cooling (radiative imbalance) occurs to enable extra sensible and latent heating and a cooling of the surface to the observed 15ºC.
On a global scale the latent heat is moved polewards from the equatorial regions to be revealed in the downward dry air at the sub tropics.
At night the more humid the air, the less likely there will be a ground frost.
The ratio of sensible to latent heating is determined by the biosphere at the surface.
Sensible heating tends to be confined to the boundary layer, whereas above that the troposphere is warmed more by latent heat when clouds form, only to be revealed as such when dry air closes the loop on its descent.
https://www.britannica.com/science/climate-meteorology/Biosphere-controls-on-the-structure-of-the-atmosphere#ref967546
[[A fundamental concept at the heart of climate science is the contention that the solar energy that the disk of the Earth intercepts from the Sun’s irradiance must be diluted by a factor of 4. This is because the surface area of a globe is 4 times the interception area of the disk silhouette (Wilde and Mulholland, 2020a).
[[This geometric relationship of divide by 4 for the insolation energy creates the absurd paradox that the Sun shines directly onto the surface of the Earth at night. The correct assertion is that the solar energy power intensity is collected over the full surface area of a lit hemisphere (divide by 2) and that it is the thermal radiant exhaust flux that leaves from the full surface area of the globe (divide by 4).]]
While it is true that the infamous leftist-run U.N. IPCC has tried to bolster their fake physics CO2 15 micron -80C global warming hoax by miscalculating the potential warming from the Sun, this entails more than just dividing the Earth’s surface area by 4 and turning it into a flat disk. They also divide the Sun’s power by 4, and no surprise, the Sun can’t keep the Earth from freezing.
Like with the 15 micron problem, the IPCC just can’t face the fact that the Sun is a Planck (blackbody) radiator, like the Earth’s surface, and is subject to an ironclad law of Nature. The Planck power-wavelength curves are all parameterized on the temperature, and to cut the curve by a factor of four switches it to a new lower temperature. This of course makes the Sun weaker, solving their problem by carnival-level sleight of hand. In truth, the Sun is quite capable of keeping the Earth from freezing without assistance from fake CO2 radiation heating. The Sun shines on a hemisphere at a time, and bears down on a given spot for several hours, heating it up, while the atmosphere slows down the cooling process. Every time the temperature reaches 100F in Arizona, you know they’re pushing a sick hoax. The only proper calculation method is a computer program that slowly rotates the Earth while calculating the opposing processes of heating and cooling and keeping score. Where in all the billions spent on IPCC did they create such a program and release the source code for all to check their work? Never. Instead, they churn out boatloads of fake global temperature data from a Seinfeld restaurant in Manhattan 🙂
https://www.quora.com/What-are-the-most-important-principles-you-can-apply-to-save-the-Earth-from-global-warming/answer/Tracy-Zeron
The exact amount the Sun’s temperature is reduced when the power is reduced by a factor of f is
(1/f) * (4th root of f). When f=4, the reduction is 35%, brrr!
http://www.historyscoper.com/howmuchisthesuncontributingtoglobalwarming.html
“The only proper calculation method is a computer program that slowly rotates the Earth while calculating the opposing processes of heating and cooling and keeping score. ”
TL Winslow
I have been thinking about this on similar lines.
The key point is to decouple the lit hemisphere collection process from the full globe emission processes and place the atmospheric reservoir in between as the “keeping score” vector process that it so clearly is.
To Phil Mulholland
“The key point is to decouple the lit hemisphere collection process from the full globe emission processes and place the atmospheric reservoir in between as the “keeping score” vector process that it so clearly is.”
I hope this includes the varying lengths of the sun’s-rays through the atmosphere, and also the changing albedo of the clouds as they are illuminated from the sides …. particularly the tropical daily cu-nim formations (per Willis)…. etc.
“I hope this includes the varying lengths of the sun’s-rays through the atmosphere, and also the changing albedo of the clouds as they are illuminated from the sides”
TonyN,
Yes, that complexity must be located inside the black box of the atmospheric reservoir.
In our model we apply the concept of the illumination divisor to account for the quantity of energy captured by the model globe at the Top of the Atmosphere (TOA). This concept is also used in the standard model which applies the concept of the Vacuum Planet equation from Astronomy, which is the ratio of the surface area of the intercepted disk silhouette to the surface area of the emitting globe, and has a ratio value of 4. So, the point at issue here is illumination intensity and its value due to geometric effects before the energy has even entered the atmosphere.
In our model as applied here we use the ratio of the surface area of the intercepting disk silhouette to the surface area of the illuminated hemisphere, which is a value of 2. This power intensity dilution factor at the TOA is applied before any atmospheric processes are invoked (albedo, atmospheric absorption travel path etc.).
If you wish to study the average annual illumination of the 3 main atmospheric cells (Hadley, Ferrel and Polar) then the illumination divisor for each is calculated as the ratio of their global surface area to the area of the disk silhouette that illuminates each cell.
So, a pair of equatorial Hadley cells located between 30S and 30N that cover 50.00% of the Earth’s surface area cut a zone from the disk silhouette between 30S and 30N that is 60.90% of the disk silhouette illumination area. This relationship produces an average annual illumination intensity ratio of 0.60899 for the Hadley cell. (or its reciprocal of 1.6420 as a power intensity divisor).
Similarly, a pair of mid-latitude Ferrel cells located between 30 degrees and the (Ant)Arctic polar circles cover 41.75% of the Earth’s surface area and cut a zone from the disk silhouette between latitude 30 degrees and each hemisphere’s polar circle that is 36.29% of the solar beam disk silhouette illumination area. This relationship produces an average annual illumination intensity ratio of 0.43462 for the Ferrel cell. (or its reciprocal of 2.3008 as a power intensity divisor).
Finally, the pair of Polar cells located beyond the (Ant)Arctic polar circles cover 8.25% of the Earth’s surface area and cut a zone from the disk silhouette that is just 2.81% of the solar beam disk silhouette illumination area. This relationship produces an average annual illumination intensity ratio of 0.17025 for the Polar cell. (or its reciprocal of 5.8738 as a power intensity divisor). (using illustrative precision).
The value of using this approach is that it proportions the illumination power intensity as an annual average for each atmospheric cell in toto. Please note that although we are often able to look directly at the setting Sun as it sinks below the horizon, the diminution in the intensity of the sunlight at the surface is due solely to atmospheric absorption. If you were standing on the surface of the Moon watching the sunset at the end of the fortnight long lunar day then you would be blinded because even though the horizon grazing angle of the setting sun is zero, there is no diminution in the solar beam intensity in the Moon’s vacuum. So too for the Earth at the TOA the power intensity of the solar irradiance normal to the beam is a constant value and is independent of the location of the intercepting grid cell, whether it be at the pole of rotation or on the equatorial terminator. (N.B. this is at the TOA!)
TL:
You say: ” The only proper calculation method is a computer program that slowly rotates the Earth while calculating the opposing processes of heating and cooling and keeping score.”
This is exactly what EVERY computer climate model has done for decades now, and if you had even a cursory knowledge of the subject, you would understand that. (I am certainly not claiming they do it perfectly, they all do what you want.)
In the most basic description of any model, they will state the size of the elements they divide the earth’s surface into (e.g. 1 degree by 1 degree) and the size of the time interval (e.g. 15 minutes). In operation, for each time interval, for every single surface element (and multiple vertical slices for each surface element), they “calculat[e] the opposing processes of heating and cooling and keep[] score.”
I have looked at the source code for one of the models and confirmed this fundamental point. Again, I am not claiming it is done perfectly, or even accurately enough to reach any conclusions, but it IS done.
Do not make the mistake so many do of assuming that a highly simplified conceptual illustration for laymen is actually what is calculated in practice.
[[This is exactly what EVERY computer climate model has done for decades now, and if you had even a cursory knowledge of the subject, you would understand that.]]
Duh, they all have subroutines adding in the fake physics CO2 back radiation, causing them to wildly overpredict temperatures out in the future based on ever-increasing CO2 levels.
Yes, the models are one thing, their popular explanations are another. The weak Sun hoax is for the consumption of the public to make them think that without CO2 the Sun alone couldn’t keep the Earth from freezing, making CO2 global warming seem proved without further ado.
[[I have looked at the source code for one of the models and confirmed this fundamental point. Again, I am not claiming it is done perfectly, or even accurately enough to reach any conclusions, but it IS done. ]]
Do they really predict that without CO2 back radiation the Earth would always be freezing? It’s not about conclusions but about basic modeling. Of course real models can’t get accurate initial info. for all the cells, plus many physical processes happen inside cells so they can’t be modeled but only included in parametric form. Clouds are big problem. But I don’t want a weather prediction model just a basic climate model that disproves the CO2 warming hoax.
We must take climate modeling away from all CO2 warming hoaxers and refound climate science sans CO2 back radiation.
https://www.quora.com/Are-The-Global-warming-climate-change-theory-models-oversimplified-and-or-corrupted-by-data-that-is-not-accurately-representative-of-reality-the-main-reason-for-their-dismal-track-record-on-their-predictions-could/answer/TL-Winslow
Overly complicated analysis for what is in reality a simple geometrical & time concept.
The confusion is strong in this one..
@ur momisugly Philip Mulholland
Your calculation in “Return to Earth: A New Mathematical Model of the Earth’s Climate” for the irradiation on the hemisphere is not correct.
The static model is based on a central solar point. In the case of temperature distribution on a non-rotating spherical surface (hemisphere) with validity of Lambert’s law of cosines and Stefan-Boltzmann’s law, isothermal concentric circular bands form around the central solar point T0, where T0 = [(1-A)*S/(ε*σ)]^0.25. If the central solar point T0 is defined as the energy pole, then the temperature at the thermal latitude β after: T(β) = T0*cos(β)^0.25.
The average temperature value of the circular area results in T(β,avg) = 306K, where this corresponds to an average energy flux density of j = ε*σ*T(β,avg)^4 = 0.96*5.67*10^-8*306^4 = 478 W/m^2. This value of 478 W/m^2 applies only to the circular area, but not to the hemisphere.
Circle surface averaging is not the same as sphere surface averaging of a hemisphere. You can see this (example: edge darkening of the sun) by averaging the area of the regions of a circle and a hemisphere with |x| ≤ 1/2*r. For the area of the circle the result is π/3 + √(3)/2]*r^2, which makes up about 61% of the total circular area. For a hemispherical surface results in π*r^2, which is exactly 50% of the total surface of the hemisphere. In fact the pole regions are overweighted and the equatorial regions are underweighted in the circular averaging.
One have to calculate with a weighting factor of π/[π/3 + √(3)/2], in order to calculate a circle area averaging on a hemisphere. This would result in an energy flux density for the hemisphere of 472.27 [W/m^2] * π/[π/3 + √(3)/2] = 775.5 W/m^2.
How does that make any difference to the point at issue ?
It doesn’t its just obfuscation .. see how all the normal gate-keeper luke-warmer skid-”marks” are nowhere to be seen.
Dr roy with his fisher price cold warms hot physics tried to hold the line for the luke-warmers, but soon fecked off when he knew he would be embarrassed by the grown-ups in the room…..
I dont think any of the other luke-warmer phuckwitz the marks etc etc showed their faces.
Gary,
Thanks for chipping in.
Speaking personally as a mere geoscientist I found the exercise useful and now have a new line of enquiry vis-a-vis CERES.
Lets face it Phil i mean no offense at all,, none at all……what took so long.
How can it take 30yrs .. what happened to ”the science” the marxist march through the institutions that’s what happened, then the infiltration of the true skeptic’s the ones that were always right but became the equivalent of carnival barkers, they were banned from here if they stood their ground in the early years.
I mean no disrespect to anthony or willis i like both now they have grown on me, and come along way down the rabbit hole, i sense they both doubt now the co2 rghe in ways, and both have been around long enough here to have read dozens of articles like this, but dr roy how can you respect that plum, he must know the RGHE is bullshit, but he still pushes it not wanting to rock the boat, and too many years invested in his bullshit its all true its just not as bad as we thought line, ……… but it is all ”real” honest…..
The most fundamental part of AGW is the RGHE and its been protected all these years from within the skeptical side, alot of people have a decade or more defending it so they won’t eat humble pie on it, they are in it for life, and its just disgusting to me because a focused attack on that RGHE hypothesis would have destroyed ”the science” 25 yrs ago, and ive been doing the global warming rounds since the dial up days reading the debates, since before cookie and his crew of degenerates popped into existence.
I always knew the defenders of it in debate were the bullshitters as they were always the ones that started running smart with the mouth, insult and sophistry, see the debates started for me reading them in educational fora, you know college sites/forums, and clever kids arguing the physics of it.
That was until the sites got their warnings about being blacklisted unless they banned any GW stuff that didnt obey the progressive narrative, and the ”scene” changed and went more bloggish..
Gary,
None taken.
I started this work in earnest in Jan 2019 when I first wrote to Stephen and we began our collaboration.
I am pleased to say that the Research Gate stats for our paper have gone up significantly thanks to this thread and once again I must thank Anthony for allowing us to publish here on WUWT.
Balance is important.
Upsetting the balance could tip us into warming or cooling.
Setting up arbitrary warming by including the imbalance is very important to understand.
The question is, where is the basis for that imbalance? Its not there!
It was not there before!