Bob Wentworth Ph.D. (Applied Physics)
Recently, Stephen Wilde invited me to “have a go at deconstructing” the work he and Philip Mulholland have been doing to understand how climate functions. I was curious. So, I began looking at what Wilde and Mulholland (W&M) have written.
Today, I’d like to examine a building block concept which impacts their work, energy recycling.
It’s a topic that leads to seemingly endless confusion among people who doubt that long-wave-absorbing gases can warm planets. So, this topic is likely to be of interest beyond its relevance to W&M’s work.
This inquiry was stimulated by reading W&M’s 2020 paper, An Analysis of the Earth’s Energy Budget. W&M’s analysis is informed in part by the diagram below (my Figure 1, W&M Figure 4, originally from Oklahoma Climatological Survey).
This figure illustrates how a layer of the Earth’s atmosphere interacts with radiant energy.
Solar short-wave radiation, with a mean radiant flux, Fₛ(1-A)/4, is absorbed by the Earth’s surface. The Earth’s surface, at an effective radiative temperature, T₀, emits long-wave thermal radiation with a flux, σT₀⁴, in accordance with the Stephan-Boltzmann law. A fraction (1-f) of this surface-emitted long-wave radiation passes through the atmosphere and reaches space, while a fraction f is absorbed by the atmosphere.
A particular layer of the atmosphere is assumed to be at a temperature, T₁. This temperature is the temperature that equalizes the flows of energy entering and leaving that layer. According to the diagram, the layer will emit long-wave radiant energy equally in all directions, with a flux fσT₁⁴ being sent upward and an equal flux being sent downward.
It should be noted that this diagram is intended for general education, and oversimplifies some details that a serious climate modeler would take into account. In particular, I see the following simplifications:
- The diagram depicts the total absorbed mean solar irradiance, Fₛ(1-A)/4, being absorbed by the Earth’s surface. However, something like 27% of that is actually absorbed into the atmosphere (via clouds, water vapor, dust, and ozone).
- The long-wave flux emitted by the Earth’s surface actually has the form 𝜀₀σT₀⁴, where 𝜀₀ is the mean emissivity of the surface, which has been measured to be 0.94.
- How much long-wave radiation is emitted by a layer of the atmosphere depends on the thickness of that layer. Saying the radiant flux is fσT₁⁴ reflects a few implicit assumptions, namely that (a) the layer has sufficient optical depth that it absorbs most of the incident radiative at the wavelengths of interest and (b) the temperature doesn’t vary much across the layer. Serious modeling would involve formulas for the radiative properties of a thin layer of atmosphere, as well as accounting for convection, etc.
- The radiant flux emitted by an atmospheric layer is given as fσT₁⁴, but would more accurately be given by 𝜀σT₁⁴ where 𝜀 is the emissivity of the gas. It’s likely to be approximately true that 𝜀 ≈ f, but this may not be precisely the case. Additionally, the overall emissivity of a gas depends somewhat on temperature, so the radiated flux may not scale precisely as T₁⁴.
Yet, the purpose of the diagram is public education, not rigorous modeling. For that purpose, the diagram has its uses.
How do W&M apply this diagram? In part, they correctly note (p. 56) that some “of all captured flux is returned to the surface as back radiation and recycled.” (More precisely, they assume that “half” of the flux captured by the atmosphere is returned to the surface; that’s not quite right, but we’ll return to this point later.) They also note (p. 57) that “Because the intercepted energy flux is being recycled this feed-back loop is… endless … It has the mathematical form of a geometric series, and is a sum of the descending fractions…”
Let’s look at a diagram that illustrates the energy recycling process that W&M are talking about.
In this diagram, sunlight with power S is absorbed by the surface of the Earth. (For simplicity in sorting out the concepts, we’ll ignore the solar irradiation that is directly absorbed by the atmosphere.)
Because the surface of the Earth is assumed to be neither gaining or losing net energy (when averaged over a day or a year), the amount of power absorbed by the surface must lead to an equal amount of energy leaving the surface. The power leaves the surface via a combination of thermal radiation and convective transport of latent heat (water vapor) and sensible heat (hot air).
Suppose we assume that, for every unit of energy flux that leaves the surface, a fraction (1-β) is radiated into space, and the remaining fraction, β, is returned to the surface via long-wave back-radiation. (In steady-state, on average, the energy flux leaving the atmosphere must equal the energy flux entering the atmosphere. Hence, any energy flux that doesn’t reach space must be returned to the surface, for energy flux balance to hold.)
For each energy flux that reaches the surface, an equal energy flux leaves the surface and enters the atmosphere. A fraction (1-β) reaches space, and a fraction β is returned to the surface. The energy flux returned to the surface must lead to an equal flux leaving. This results in another cycle of some energy reaching space, and some being returned to the surface. In principle, this recycling continues forever, with ever smaller fluxes. Because each round of the cycle reduces the flux by a fixed proportion, the fluxes form a geometric series, making it easy to sum the infinite series. Computing these sums, one finds that the total power radiated into space is S, the same as the energy flux absorbed by the Earth. That’s as one would expect.
One finds that the total back-radiated energy flux, B, is given by B = β⋅S/(1-β).
Climate models don’t usually include a figure like Figure 2 above, in which each iteration of the energy recycling process is shown. Diagrams like Figure 2 are useful for instructional purposes, but aren’t as practical as other ways of depicting things.
Instead, climate models often offer a diagram of total energy fluxes, like the one below. This diagram shows the net result, after all the recycled energy flows have been added together.
This diagram shows solar flux, S, being absorbed by the surface. There is also an energy flux S/(1-β) leaving the surface (via thermal radiation and other heat transfer), and a back-radiation energy flux B = β⋅S/(1-β) from the atmosphere to the surface. The radiant energy flux leaving the top of the atmosphere is S, equaling the amount of solar irradiance that was absorbed by the Earth. The thickness of the lines qualitatively suggests the differing magnitudes of these energy fluxes.
For Earth, the data in Kiehl and Trenberth (1997), which is used as a reference by W&M, indicate a ratio of back-radiation to absorbed insolation, B/S = 1.38. This corresponds to a recycling fraction β = 0.58. (These calculations pretend all absorbed solar irradiance is absorbed by the surface.)
Sometimes people are incredulous at the idea that the back-ration flux, B, is greater than the absorbed insolation, S. Yet, this is what is measured to be true.
The energy recirculation diagram, Figure 2, should make clear how this can and does happen, without requiring that anything “fishy” be going on.
It might be reassuring to look at heat flow, instead of the usual energy balance diagram (like Figure 3 above) which mixes heat flows with radiant energy flows. Recall that heat flow is the net energy flow, so that a heat flow (unlike an energy flow) is only in one direction. Translating Figure 3 into an equivalent heat flow diagram yields the diagram below.
If one takes the combined energy flux away from the surface, S/(1-β), and subtracts the back-radiation flux, β⋅S/(1-β), one finds that the heat flux from the surface to the atmosphere is S, exactly the same as the heat flux absorbed from the Sun, and the heat flux radiated into space.
There is nothing contrary to energy conservation happening here. It all adds up.
To some people, it seems counter-intuitive to some that energy recirculation can result in recirculating energy fluxes higher than the initiating absorbed energy flux. But, this result, while perhaps surprising, is not wrong. The math is quite straightforward, as I think I’ve shown.
* * *
Of course, having back-radiation be greater than the absorbed insolation requires that the recycling fraction, β, be larger than ½.
W&M assume that the largest β can get is ½, in which case the back-radiation flux is B = S. They write (p. 55):
“The standard assumption is that for all energy fluxes intercepted by the atmosphere, half of the flux is directed upwards and lost to space, and half of all captured flux is returned to the surface as back radiation and recycled.”
It appears that W&M reach their conclusion that this is the “standard assumption” by examining Figure 1 (their Figure 4), and noting that an atmospheric layer radiates an equal amount upward and downward.
The conclusion that equal amounts are radiated upward and downward is correct—but only for a single layer of the atmosphere.
The atmosphere has more than one layer. To consider the behavior of the atmosphere as a whole, one needs to consider the aggregate effect of many layers interacting with one another.
To illustrate this, let’s look at a “toy model” of the atmosphere, consisting of N layers, each of which behaves like the atmospheric layer in Figure 1.
Sunlight with an average flux, S, is absorbed by the planetary surface.
The surface emits a total flux of long-wave radiation, σT₀⁴. For simplicity, we assume a fraction (1-f) of this thermal radiation has wavelengths that pass through the atmosphere unhindered, while a fraction f is at wavelengths which are totally absorbed by each layer of the atmosphere.
Each layer of the atmosphere has a distinct temperature, and radiates equally in both directions, with a radiant flux fσT⁴.
For simplicity, I assume that only radiative heat transfer is relevant. I assume that the radiant long-wave flux from space is negligible.
This model is not a realistic representation of Earth’s atmosphere. But, solving this problem is likely to be informative, nonetheless.
Using energy balance, we can solve for all the temperatures. This is done easily using a corresponding heat flow diagram.
Here’s how the calculation works. Feel free to skip these details. I denote the heat flux from the surface to the atmosphere, Q. Because the heat flowing to and away from the surface must balance, we know Q=S-(1-f)σT₀⁴. Energy balance also tells us that the heat flowing to and from each atmospheric layer matches, so that Q flows between each layer, and out of the final layer. Comparing the amount flowing out of the final layer in Figure 5 and 6 allows us to solve for the temperature of the last layer, Tₙ, in terms of Q. That allows one to solve for the temperature of each layer in turn, finally yielding a formula for T₀ in terms of Q. Combining this with the previous formula for Q allows us to eliminate Q and solve for T₀ in terms of S and N.
The layers of the atmosphere have T⁴ values which are spaced linearly between the value for the surface, T₀⁴, and zero (the assumed value for space). In this model, the atmosphere gets monotonically colder as one moves to higher layers.
Other key results include:
Q = S⋅f/[1+N(1-f)]
T₀⁴ = (S/σ)⋅(N+1)/[1+N(1-f)]
B/S = N⋅f/[1+N(1-f)]
Relating this model to the prior energy-recycling model, one finds that the energy recycling fraction associated with N atmospheric layers is:
β = N⋅f/(N+1)
For an atmosphere that is opaque to long-wave radiation (i.e., f=1), then a single layer (N=1) yields β=½ and B = S, as assumed by W&M. However, in general, for an atmosphere opaque to long-wave radiation, the energy recycling fraction is β = N/(N+1) and back-radiation flux is B = N⋅S.
As long as an atmosphere has more than one layer, it is entirely possible for the recycling fraction to be greater than ½, and for the back-radiation flux to be arbitrarily large, compared to the absorbed insolation.
How can we make intuitive sense of this result?
An atmosphere as a whole is not at a single temperature.
In our “toy model”, the top layer is much colder than the bottom layer. The radiant flux downward to the surface (the “back radiation”) is determined by the temperature of the bottom layer. The radiant flux upward to space is determined by the temperature of the top layer. Because of the temperature difference between the top and bottom layers, it is entirely natural that the atmosphere as a whole directs more radiation downward to the surface than it does upwards to space.
* * *
Thus, what W&M interpreted as “the standard assumption” that “for all energy fluxes intercepted by the atmosphere, half of the flux is directed upwards and lost to space, and half of all captured flux is returned to the surface as back radiation and recycled” is false.
It’s not “the standard assumption” with regard to the atmosphere as a whole. It’s a false assumption for the atmosphere as a whole, as demonstrated by our model of a multi-layer atmosphere.
The hypothesis that the atmosphere as a whole behaves this way is also contradicted by measurements. Those measurements show significantly more flux being directed downwards to the surface than is directed upwards and lost to space (by a factor of around 1.38).
* * *
Let’s use the results of our modeling to think through a few issues unrelated to W&M’s work.
Does the model violate the Second Law of Thermodynamics?
For an atmosphere opaque to long-wave radiation (f=1), my toy model of a multi-layer atmosphere predicts a surface temperature given by T₀⁴ = (S/σ)⋅(N+1). This has no upper limit, as the number of layers in the atmosphere increases.
It appears that the model is predicting that, with a sufficiently thick long-wave-absorbing atmosphere, a planet could achieve a surface temperature hotter than the Sun. That would be a violation of the Second Law of Thermodynamics. That can’t happen in reality. So, what is going on here?
The solution is very simple. If a planetary surface gets sufficiently hot, the surface will start to emit more and more of its thermal radiation as short-wave radiation. That short-wave radiation will pass through the atmosphere unhindered, just like the incoming solar radiation did. So, once a planet becomes hot enough to emit short-wave radiation, it can efficiently cool its surface.
As a result, a very thick long-wave absorbing atmosphere can never warm a planetary surface to be as warm as the Sun.
* * *
The other imagined violation of the Second Law that some people worry about relates to energy flowing from a cooler heat reservoir (the atmosphere) to a warmer heat reservoir (the surface of the planet).
But, the Second Law doesn’t say no energy can flow from cooler to warmer. It simply requires that the heat flow (i.e., the net energy flow), must be from warmer to cooler. As illustrated in the heat flow illustrations (Figure 4 and Figure 6), even with energy recirculation, heat always flows from warmer to cooler.
There is no violation of the Second Law.
Saturation
One of the naïve arguments against the possibility of increasing CO₂ having an effect on climate involves arguing that “CO₂ fully absorbs radiation after it travels a relatively short distance through the atmosphere, so how could adding more CO₂ make any difference?”
My toy model offers some insights regarding this issue.
In the model, each layer is assumed to absorb 100% of the longwave radiation within the fraction f of wavelengths that are absorbed. Yet, despite this, each added layer of atmosphere increases the surface temperature.
Whether or not the atmosphere absorbs long-wave radiation many times over is irrelevant to the potential of increasing greenhouse gases to lead to more warming.
However, there is a different type of “saturation” that does have an element of reality.
The energy recycling fraction in my multi-layer model of the atmosphere is given by β = N⋅f/(N+1). For large N, this become approximately β ≈ f⋅(1 − 1/N). So, as the total number of long-wave-opaque layers (or equivalently, the concentration of greenhouse gases) increases, additional layers do have smaller and smaller impacts on the energy recycling fraction.
This is vaguely like the assertion that the impact of increasing CO₂ levels is logarithmic, so that you need to keep doubling CO₂ levels to get comparable changes.
But, the mathematical form for this “saturation” effect isn’t quite the same. Where does our toy model go wrong?
The toy multi-layer model assumes that various wavelengths of long-wave radiation are either 100% transmitted or 100% absorbed. Yet, for real gases, there is a continuum in to the degree to which various wavelengths are absorbed.
One way of thinking about it is that the number of “opaque layers” in the atmosphere varies with wavelength. So, even if increasing gas concentrations has little impact on one wavelength, it might have a significant impact at another wavelength.
Another way of thinking about it is that, as you increase the concentration of long-wave absorbing gases, you effectively increase f, the fraction of wavelengths for which outbound long-wave radiation will be absorbed.
So, it makes sense that as you increase the concentration of long-wave-absorbing gases, the impact of additional increases declines, but in principle, there will still be an impact.
How many “layers” does Earth’s atmosphere have?
I calculated how an atmosphere with only radiative heat-transfer might affect surface temperature, as a function of how many “layers” the atmosphere has.
But, how do we decide how many layers there are in an atmosphere, for purposes of applying this model?
Recall that, in discussing Figure 1, I said that the formulas involved require one to assume that (a) the layer has sufficient optical depth that it absorbs most of the incident radiative at the wavelengths of interest and (b) the temperature doesn’t vary much across the layer.
This is a rough model, and there is no hard number one what constitutes absorbing “most” of incident radiation. But, an optical depth 2 would absorb 86% of incident radiation, so maybe that would be the minimum optical depth we’d want to associate with a layer?
For radiation with a wavelength of 15 microns, where CO₂ absorption peaks, the optical depth of Earth’s atmosphere may be around 100. So, that might suggest the use of as many as 50 layers in our toy model. But, at a wavelength of 14 or 16 microns, the optical depth is around 10, corresponding to no more than 5 layers. (However, if you divided the atmosphere into only 5 layers, the assumption that temperature doesn’t vary much across a layer would be unlikely to be valid.)
In general, optical depth varies strongly with wavelength. And, for many wavelengths, atmospheric temperature can be expected to vary over the distances needed for full absorption of those wavelengths.
The bottom line is that the toy model cannot be expected to model the behavior of the real atmosphere. (Let’s not forget that the toy model omits convection, which makes it even more likely that it could quantitatively describe the real atmosphere.)
Real climate models make use some of the ideas I’ve included in the toy model, but they fill in an enormous number of details that I’ve left out.
Conclusions
How things play out in a real atmosphere is, of course, vastly more complicated than can described quantitatively by models as simple as a what I’ve offered here.
Yet, a simple model like what I’ve shared here can help illustrate general mechanisms, and clarify some otherwise mystifying phenomenon. These simple models explain things like how back-radiation fluxes can be larger than the absorbed solar flux, and how more atmospheric radiation can reach the surface than reaches space.
I hope this has been helpful.
The layers are imaginary. They don’t exist. You’re essentially reverse engineering layers and emissivities from the surface temperature.
Of course the layers are imaginary. It’s a “toy model.”
I’ve shown, from first principles, how things would work if there were layers as described. The point is that, if you understand how things work in with the toy model, you’re likely to be better able to understand certain aspects of how related real systems work.
The assertion of “reverse engineering layers and emissivities from the surface temperature” seems surprising, given that the model doesn’t use emissivities at all and doesn’t reference any real surface temperature.
“seems surprising, given that the model doesn’t use emissivities at all and doesn’t reference any real surface temperature.”
Essentially same model as here:
https://www.realclimate.org/index.php/archives/2007/04/learning-from-a-simple-model/
Still reverse engineering. No?
That first graphic is simply chock FULL of … β⋅S
In fact on at least three separate levels of … β⋅S
Just when I thought there couldn’t be more … β⋅S
The math throws a few … fσTs in then goes T₀ T₀ T₀ T(n) along
10 out of 10 Bob, “…as simple as possible, but not simpler..” as was said by a famous person. Maybe a %100=%emitted+%reflected+%absorbed description in your bullet points would get you 11 out of 10.
And BTW Zoe is a Flat-Sky Geothermal believer not worthy of a response, future FYI
In some ways off-topic, but in others, not so much but Zoe, is anyone using your work on the Perdue-Ossoff election fraud in Georgia? Seems like the whole thing is starting to get legs as I predicted to a cynical friend of mine who thought nothing would come of it. I’ll go check out your site.
Indeed another pseudoscience illustration. A surface in a vacuum with imaginary layers above it, first principles based on pseudoscience only leads to GIGO.
I like how the reflectivity was dust and Ozone(O3) while O3 does exist in our atmosphere it’s more predominant in the stratosphere- what we know as the O3 layer, and with no mention of GHG’s. Brilliant! but, I digress you say this is the simpler version of “educational purposes” but, I study climate and have many of these “climate textbooks” you talk about and none of them are as convoluted as your post. you think you have validity because you use complicated math jargon that the masses would give up reading 1/2 way through and conclude ” look he must be right because… Math…” that was a garbled word salad of a post if anyone wants to know how this actually works there are 100s of other sources to explain it without the nonsense.
You may be right. Dunno. But do know you are unnecessarily complicating things like they also do. The GHG is simple at its core science. Incoming SWR warms, including oceans to photic depth. The warmed surface emits IR. Its cooling radiative IR emission to space is retarded by GHE. Nothing to do with ‘backradiation’, since any of that must be cooler than the surface it generated thanks to the well proven atmospheric lapse rate. Cooler never warms warmer.
The GHE is simply an absence of sufficient cooling. Any theory asserting any actual back radiation warming is false from first principles.
You clearly do no understand “first principles” or GHE.
“Cooler never warms warmer” is a false paraphrasing of the Second Law of Thermodynamics.
So, a cooler object doesn’t add energy to a warmer object per se. The flow of heat is always from warmer to cooler. However, the presence of a cooler object between a warm object and something even colder, will reduce the heat flux thus raising the temperature of the warmer object if the heat flux is to remain constant.
Rud, being an engineer (and lawyer) with a long and distinguished career, knows what he’s talking about. That said, I’ve seen that phrase used by people who patently have no clue. For that reason I find the phrase distressing.
There are two equivalent perspectives for viewing the situation of a “cooler object between a warm object (being heated by an ongoing source of heat) and something even colder”:
Because the “heat flux” is simply a name for the forward-radiated flux minus the back-radiated flux, these two perspectives are equivalent. One simply needs to be clear about which perspective one is using.
I worry that Rud appears to be calling the latter perspective “false from first principles,” when it’s simply an alternative way of looking at exactly the same thing that the first perspective describes.
I’m concerned that referring to the latter perspective as “false” unnecessarily contributes to confusion.
Indeed. As far as I can tell, Rud has never been a teacher.
There were certain things I learned not to say. If you confuse students, it can be very difficult to unconfuse them later. That particular phrase sounds like one of those things.
Sorry to disagree with you, but I agree with Rud. You are missing a couple of things in your analysis.
The first is that as pointed out, is that a cooler object can never “back radiate” (or reflect if you will) sufficient energy to make an object “hotter”. At best, it can only retard the loss of heat over time. In other words, Tactual at a specified time “t” will be higher than it would be without the retardation.
The second item you haven’t discussed is the ability of CO2 specifically to “raise” the temperature of the earth by 33 deg. I haven’t worked through the math, but be careful with your geometric series that you don’t end up “creating” energy. The atmosphere is not a source of energy, and especially not CO2. You jump the shark with the statement:
“Sometimes people are incredulous at the idea that the back-ration flux, B, is greater than the absorbed insolation, S. Yet, this is what is measured to be true.”
You just created an energy source out of nothing. We all wish that could happen, but it isn’t reality.
Actually, nobody is claiming that CO2 raises the temperature 33 C. The predominant greenhouse gas is water vapor.
The reason CO2 got dragged into it was because of what has to be seen as a whacko application of feedback theory.
That theory says that CO2 will cause a little bit of warming which will cause more water vapor which will cause even more warming. It’s been thoroughly been debunked.
If Rud took his engineering pre 1980’s, he would need to update his radiant heat transfer theory significantly with some quantum mechanical theory. This basically involves accepting that photons are emitted at discrete wavelengths, and photons aren’t classical “heat” until absorbed. There is nothing really wrong with the classical thermodynamics approach, but heating objects with discrete frequencies, as with lasers and microwaves, became difficult to describe correctly to students.
I took my engineering pre 1980s. Disappointingly, physics hasn’t progressed that much since then. The basics that Rud and I learned weren’t a lot different than what students now learn.
Yes, the assertion that “Cooler never warms warmer” is only valid for conduction. Photons emitted from a surface above absolute zero don’t know what the temperature is of the ‘target’ that they impinge on. However, what is important are the reflectivities and emissivities of the target at the equivalent wavelengths of the photons. I haven’t done a deep dive into this, but I do know that the optical properties of materials in the visible region of light have a poor correlation with the behavior in the IR and RF regions.
However, it would seem reasonable to me that if low-energy photons emitted from a cold source were to be absorbed by some other object, irrespective of its temperature, then the heat-energy content, and consequently the temperature, would increase. It would seem that the measurement of the cosmic background microwave radiation is proof that ‘warm’ antennas are capable of absorbing ‘cold’ photons.
Reflectance is independent of temperature. Not precisely, but the variation is in the 4th or 5th decimal. Not unlike the refractive index of air, which is considered to be 1, but in reality, will be different at different temperatures, again, around the 5th decimal. I use Johns Hopkins data for reflectance (available on NASA site). I use https://refractiveindex.info/ for information on specular reflection and refractive index, transmission, etc. I use the info. in fresnel equations to obtain reflectance data. It’s a perfect match to Johns Hopkins data, although at a lower resolution. I do like it when two methods yield the same result.
As an autodidact I am disappointed that people with Phds in physics , don’t have a clue about things.
I’ve followed your comments over several years and like the way you think.
Alexy
Thank you for the compliment.
Alexy,
And, thank you for the link.
Alexy,
Mineralogists who use polarized light microscopy for the characterization of minerals are quite familiar with dispersion of the refractive index (RI) with wavelength. One technique for determining the RI is to match it with that of a calibrated liquid. The liquid always has the temperature at which the calibration is valid. That is, at least the real part of the RI for transparent solids and liquids varies with temperature; the slope of the dispersion can be positive or negative, depending on the composition. It is not a lot; however, for very precise work, it has to be taken into account. Much less is known about how the imaginary part (extinction coefficient) of the RI for opaque substances varies with temperature. However, the extinction coefficient is more important than the real part for controlling reflectance in opaque substances that might be reasonable proxies for a Black Body. If I live long enough, I may get around to investigating it.
As you know, Fresnel’s equation allows one to calculate the reflectivity of solids and liquids from the complex RI. Obviously, the reflectivity will vary with temperature, but it is at least a 2nd-order phenomena, which I suspect can be either up or down in magnitude.
But, your point that the acceptance of photons from cold bodies is not significantly different from photons from warm bodies is valid, with one possible caveat — n and k tend to vary wildly around absorption features and slight changes in temperature may have profound effects on reflectivity at those wavelengths. I think that it is problematic to make generalizations across the EM spectrum and all temperatures. One needs to be specific with regard to wavelength and temperature.
https://en.wikipedia.org/wiki/Refractive_index
However you want to describe it, the radiant transfer of heat between two objects is a function of (T1^4 – T2^4). link In other words, a cooler object reduces the heat lost by the warmer object.
True. I said the same thing backwards, by simply observing that back radiation cannot heat the surface. My whole and only point was it retards cooling. Your last sentence agrees.
You and I agree because it’s well understood engineering. I have, however, often seen others misinterpret the statement that back radiation cannot heat the surface, which is why I shy away from that particular phrasing.
From my perspective it is easier and less ” confusing” to consider energy residence time. If you increase the residence time of energy within a system ( the earth surface and atmosphere) while input ( solar radiation ) remains constant, that system must warm, or at least have greater energy.
As to the GHE, simply determine the increase in residence time of LW radiation, and you would get the gross warming affect. (Except)
However and unfortunatey, statements like…
The power leaves the surface via a combination of thermal radiation and convective transport of latent heat (water vapor) and sensible heat (hot air).”
…completely forgets conduction from the surface, and so I think it is an unnecessary and perhaps erroneous statement.
Also conduction within the lower atmosphere dominates. Now, if there were no GHG in an equally dense atmosphere, the residence time of conducted surface energy would increase, ( having no means of escaping the non GHG atmosphere while within it) and and said atmosphere would have more conducted energy then a equally dense GHG atmosphere.
So, a GHG atmosphere has more LWIR energy ( due to the GHG increasing said LWIR energy residence time) then a non GHG atmosphere. Yet a non GHG atmosphere has more conducted energy, ( due to the lack of GHG molecules to radiate energy to space)
Now the LWIR surface flux to the atmosphere is said to be greater then the conductive flux to the atmosphere. Yet the residence time increase of conductive surface energy to the non GHG atmosphere involves a greater residence time increase.
Calculate the relative surface fluxs, LWIR and conduction, and their residence time change within the atmosphere, and you have an answer as to how much additional GHG adds or “subtracts” to
atmospheric energy.
Subtracts? Yes, take a non GHG atmosphere filled with conductive and convective energy, now add one GHG molecule at elevation. Does it cool or warm? Did the energy it sent to space come from contact with a non GHG atmospheric molecule filled with conducted energy? Then that GHG molecule was then cooling. Or, did it intercept surface LWIR, and send that energy back towards the surface, increasing residence time? That GHG molecule was warming.
“There are only two ways to change the energy of a system in a radiative balance, either a change in the input, or a change in the residence time of energy within the system.”
David’s law (-;
The corralary to “David’s Law” is that ” Assuming equal WSqM input, the only thing that affects the residence time of the energy within a system, is a change in the materials encountered, or a change in the input WL.
I don’t know the answers, yet I think the concept is correct.
Oh, don’t forget the oceans. A very long residence time there.
You’d need to detail what you mean by “residence time” a bit more clearly, before I can know if I agree with you. I feel suspicious of the term.
So, I worry that this may be an erroneous concept which does not properly link to temperature regulation—and I’d be curious to know more about what you’re thinking.
Possibly. I’d need to research that. I’ve generally heard that conduction in the atmosphere was negligible, compared to convection of sensible and latent heat.
If conduction is in fact significant, I regret not mentioning it.
I suppose it is conduction that gets heat from the surface to the air, to then be convected away. But, that often seems like an unimportant detail subsumed under the heading of “convective” heat transfer from the surface.
I need more unpacking of this “residency time” concept.
What I’m clear affects temperature is power fluxes.
I don’t yet have a clear sense that the idea of “residency time” relates to that in a useful way.
Thank you Bob, I will give more detailed response this evening.
Residence time in this case refers to how long solar insolation entering Earth’s atmosphere surface and oceans stays there, before exiting the atmosphere.
We ( the earth’s system) is very close to being in a radiative balance; what comes in, is close to what leaves. Again, the assertion…” Only two things can affect the energy content of a system in a radiative balance, either a change in the input, or a change in the residence time of energy within the system.”
We certainly agree that energy is never destroyed. The short answer is that when a GHG molecule delays LWIR surface energy radiating out of Earth’s atmosphere, it is increasing the residence time of that energy within the system. ( Land oceans atmosphere) As input is continues, total energy within the system must increase.
Hope that helps, deeper utilitarian understanding of residence time to follow.
“Residence time” is defined and rooted in first principles.
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 as energy is never destroyed.
Thus ” Only two things can affect the energy content of a system in a radiative balance, either a change in the input, or a change in the residence time of energy within the system.”
and it corralary…
” Only two things determine the residence time of energy within a system, the W/L or spectrum of the input and the materials encountered within the system.”
…are rooted in first principles.
“System definition”; Earth’s atmosphere, land and surface waters.
Practical application…
“GHGs increase the residence time of LWIR radiation from the surface, thus increasing total energy within the system, as input is continues.”
This is the simple straightforward hard to refute assertion. Thus established, it is not difficult to demonstrate that said energy is a form of heat, or vibrating molecules. No maths required.
Further practical application…
Assertion; All GHG and climate debates are based on the residence time of the energies involved and the materials encountered.
Does the Earth’s ( land oceans atmosphere) energy content increase or decrease in the Southern Hemisphere summer when the Earth is receiving plus 90 watts per sq’meter?
During the Southern Hemisphere Summer at Perihelion there is about plus 90 watts per sq meter entering the atmosphere, completely dwarfing the GHE, yet the atmosphere cools!
Why does it cool? Well we know that some energy residence time is reduced via expanded ice and snow reflection in the Land rich Northern hemisphere. ( Increased albedo)
Yet energy in the southern hemisphere is also lost to the atmosphere, for a time! The intense radiation penetrates the ocean, and that energy is lost to the atmosphere also, for a time.
Yet “this loss” is an increase in Earth’s energy content. Indeed the residence time of SWR entering the oceans can vary from micro seconds ( reflection) to centuries, penetrating up to 800 feet deep.
The disparate residence time of SW insolation entering the oceans is not known or clearly defined, so the answer to the question,
“Does the Earth’s ( land oceans atmosphere) energy content increase or decrease in the Southern Hemisphere summer when the Earth is receiving plus 90 watts per sq’meter?” … is not, AFAIK, currently known.
It is a curious thing to attempt to quantify the Earth’s energy content and flux from simply measuring atmospheric T, when , in fact, the oceans hold 1000 times the energy of the atmosphere, and we live on a water planet with the oceans having vastly greater energy residence time, vastly greater total energy input, and much greater residence time flux.
So, back to practical applications and the GHE based on residence time…
Assertion 1. – GHGs increase the residence time of LWIR surface radiation, but they decrease the residence time of surface conducted energy.
Let’s take the Sahara Deserts 3.5 million sq miles. Surface T reaches up to170 F. Earth’s total desert is about 19 million sq miles. That is a lot of conductive energy to the atmosphere. Of course there is a great deal more over the entire surface of the earth. This energy is radiating AND conducting.
Let’s follow the conducted energy in a non GHG atmosphere composed of mainly nitrogen and oxygen. Such molecules, being transparent to LWIR, can only heat via conduction from the surface.
In contact with the surface nitrogen and oxygen molecules
do of course have thermal capacity, and they gain and lose their heat with each other by molecular collisions and convection within the atmosphere.
They do heat, rise via convection, establish a lapse rate and thermal capacity based mainly on density and convection, yet they do NOT release their energy to space due to the nitrogen and oxygen not being GHGs. Over time they can only release their energy to space via, I hate to say it, back conducting said energy to the surface, which then radiates a portion of that energy to space. PH
The residence time of said conducted energy in a non GHG atmosphere is longer then in a GHG atmosphere. For instance, add one GHG molecule near the top of this nitrogen – oxygen atmosphere. As soon as that non GHG molecule conducts it’s energy to a GHG molecule, that energy may then be radiated toThe residence time of said conducted energy in a non GHG atmosphere is longer then in a GHG atmosphere. For instance, add one GHG molecule near the top of this nitrogen – oxygen atmosphere. As soon as that non GHG molecule conducts it’s energy to a GHG molecule, that energy may then be radiated to space, thus DECREASING the residence time of said energy. Thus this space, thus DECREASING the residence time of said energy. Thus this GHG molecule is now a cooling factor!
Sans the GHG molecules, this conducted heating process would continue, a slow heating of the atmosphere, the denser the atmosphere, the greater the heat capacity and residence time of said energy from the surface!
So, as far as conducted energy from the surface, non GHGs increase the residence time of the Earth’s surface conducted energy, and adding a GHGs to such an atmosphere shortens the residence time of said conducted energy.
Now at night it appears logical that a dense atmosphere full of non GHG molecules would provide back conductive energy to the surface. It would happen during the day of course, yet visualizing it at night is easier. So, although it may take longer for a non GHG atmosphere to reach its thermal capacity ( vs also warming from contact with GHGs) why would it not reach an equal energy content, having no means to cool itself except through contact with the surface?
So, assertion number 1 – “GHGs increase the residence time of LWIR surface radiation, but they decrease the residence time of surface conducted energy”
… is supported.
Thank you for your time, all the Best…
Bob, sorry the edit function failed. It timed out as I was editing, Arg!! Hopefully it still communicates.
I have reposted it here for communication….
Residence time” is defined and rooted in first principles.
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 as energy is never destroyed.
Thus ” Only two things can affect the energy content of a system in a radiative balance, either a change in the input, or a change in the residence time of energy within the system.”
and it corralary…
” Only two things determine the residence time of energy within a system, the W/L or spectrum of the input, and the materials encountered within the system.”
…are rooted in first principles.
“System definition”; (Earth’s atmosphere, and surface land and waters.) Leaving aside geothermal for now.
Practical applications…
The GHE simplified…
“GHGs increase the residence time of LWIR radiation from the surface, thus increasing total energy within the system, as input is continues.”
This is the simple straightforward hard to refute assertion. Thus established, it is not difficult to demonstrate that said energy is a form of heat, or vibrating molecules. No maths required.
Further practical application…
Assertion: Assuming input, all GHG and climate debates are based on the residence time of the energies involved and the materials encountered.
An example…
Does the Earth’s energy content increase or decrease in the Southern Hemisphere summer when the earth’s atmosphere is receiving plus 90 watts per sq’meter?
During the Southern Hemisphere
summer, at perihelion, there is about plus 90 watts per sq meter entering the atmosphere, completely dwarfing the GHE, yet the atmosphere cools!
Why does it cool? Well we know that some energy residence time is reduced via expanded ice and snow reflection in the land rich Northern hemisphere. (Increased albedo)
Yet energy in the southern hemisphere is also lost to the atmosphere, for a time! The intense radiation penetrates the ocean, and that energy is lost to the atmosphere also, for a time.
Yet “this loss” is an increase in Earth’s energy content. Indeed the residence time of SWR entering the oceans can vary from micro seconds (reflection) to centuries, penetrating up to 800 feet deep.
The disparate residence time of SW insolation entering the oceans is not known or clearly defined, so the answer to the question…
“Does the Earth’s energy content increase or decrease in the Southern Hemisphere summer when the Earth is receiving plus 90 watts per sq’meter?”
… is not, AFAIK, currently known. There are many additional factors of course.
It is a curious thing to attempt to quantify the Earth’s energy content and flux from simply measuring atmospheric T, when , in fact, the oceans hold 1000 times the energy of the atmosphere, and we live on a water planet with the oceans having vastly greater energy residence time, vastly greater total energy input, and much greater residence time flux.
So, back to practical applications and understanding residence time and the GHE…
Assertion 1. – GHGs increase the residence time of LWIR surface radiation, the GHE, but they DECREASE the residence time of surface “conducted” energy!
Let’s take the Sahara Deserts 3.5 million sq miles where surface T reaches up to170 F. Earth’s total desert is about Earth’s intotal desert is about 19 million sq miles. That is a lot of conductive energy to the atmosphere. Of course there is a great deal more over the entire surface of the earth. This energy is radiating AND conducting.
Let’s follow this conducted energy in a non GHG atmosphere composed of mainly nitrogen and oxygen. Such molecules, being transparent to LWIR, can only heat via conduction from the surface.
In contact with the surface, nitrogen and oxygen molecules do of course have thermal capacity, and they gain energy, and they gain and lose their heat with each other by molecular collisions and convection within the atmosphere.
They do heat, rise via convection, establish a lapse rate and thermal capacity based mainly on density and convection, yet they do NOT release their energy to space due to the nitrogen and oxygen not being GHGs. Over time they can only release their energy to space via, I hate to say it, “back conducting” said energy to the surface, which then radiates a portion of that energy to space.
Thus the residence time of said “conducted energy” in a non GHG atmosphere, is longer then in a GHG atmosphere. For instance, add one GHG molecule near the top of this nitrogen – oxygen atmosphere. As soon as that non GHG molecule conducts it’s energy to a GHG molecule, that energy may then be radiated to space, thus DECREASING the residence time of said energy. This GHG molecule is now a cooling factor!
Sans the GHG molecules, this conducted heating process would continue, a slow heating of the atmosphere, the denser the atmosphere, the greater the heat capacity and residence time of said energy from the surface!
So, as far as conducted energy from the surface, non GHGs increase the residence time of the Earth’s surface conducted energy, and adding a GHGs to such an atmosphere shortens the residence time of said conducted energy.
Now at night it appears logical that a dense atmosphere full of non GHG molecules would provide back conductive energy to the surface. It would happen during the day of course, yet visualizing it at night is easier. So, although it may take longer for a non GHG atmosphere to reach its thermal capacity ( vs also warming from surface radiative contact with GHGs) why would it not reach an an equal energy content, having no means to cool itself except through contact with the surface?
So, assertion number 1 – “GHGs increase the residence time of LWIR surface radiation, but they decrease the residence time of surface conducted energy”
… is supported.
There is lots more, yet…
David, Thanks for this wonderful, thought-provoking exposition. I’ve been longing to develop a clear framework for thinking about “energy residence time,” and thinking about what you’ve written has helped me gain enormous clarity.
I’d like to share some of what I’m now thinking:
In working through your examples, I think I’m mostly following you, but I’m a little uneasy about some language and distinctions.
I’d like to clarify what you are meaning when you say “back-conduction”, e.g., from the atmosphere to the surface.
First, I’d like to review that I think of there as being two perspectives for analyzing thermal systems: the “heat flow” perspective (in which we focus on net heat flow, which can occur only from hot to cold) and the “energy flow” perspective (in which energy can flow bi-directionally, with the “net” of that bi-directional flow being the heat flow).
When you say “back-conduction”, I imagine you could refer to one of two things (or both):
Or, you could mean something else? Or maybe you haven’t been using the term with a consistent meaning, in which case this unpacking might help?
I initially found the phrase “Earth’s surface conducted energy” very unclear. Were you talking about some process happening within the Earth’s surface? However, I now believe I understand that you are referring to energy in the atmosphere that it received via conduction (and likely subsequent convection) from the surface.
As you’ve talked further, I felt uneasy that you were talking about the residence time for “surface conducted energy”, as if it had a residence time distinct from that of all the other energy in the atmosphere.
My understanding is that one can talk about residence time for energy within a defined body of matter, but I feel uneasy about the prospect of distinguishing residence times based on how energy first entered that body of matter. Yes, there may be some implications to what subsystem of that body of matte the energy first takes up residence, but it would take some very careful reasoning to track the implications of that.
In the case of “surface conducted energy”, that energy is fairly quickly mixed widely via convection. So, I don’t see a rationale for distinguishing that energy as a special category, for purposes of looking at residence time.
Maybe you were trying to talk about the radiative vs non-radiative case, and this linguistic distinction crept in, inspired by that, without really being important?
When you compare the radiative atmosphere vs. the non-radiative atmosphere, I am uneasy that you seem to only consider the effect of radiation that exits to space, and the effect of radiation that exits the atmosphere to the Earth’s surface.
Radiation in both directions will tend to lower the residence time of energy in the atmosphere when the atmosphere is considered in isolation.
However, radiation from the atmosphere to the surface, increases the residence time of energy in the total system of surface+atmosphere, increasing the total energy content of the total system.
With regard to thinking about the energy content of the surface (see point #7 above):
With regard to thinking about the energy content of the atmosphere:
Bleah. It’s clear that I haven’t yet fully untangled how to reason about energy retention times.
Maybe we’ll be able to sort that out, but not within the scope of this comment.
Anyway, I’m not yet ready to accept the conclusion that a non-radiative atmosphere
would “reach an an equal energy content” relative to a radiative atmosphere.
It’s an interesting question, though, and I appreciate how much thought you’ve stimulated.
Although this comment hasn’t provided complete answers, I hope it might incrementally progress our thinking.
As I mentioned in my 9:21 pm comment above, whether it “retards cooling” or “back radiation heats” are two equivalent perspectives for viewing the same situation.
Perhaps, by mentioning the “retards cooling” perspective you’re trying to interrupt the objections of those who think greenhouse gas effects can’t be real?
If so, I’m not sure that the strategy helps, insofar as it seems to suggest you are questioning the veracity of other people who are saying things that are true but who are using a different perspective.
“…saying things that are true…”. This choice of words sums it up. THis is exactly what is wrong with science today. HIghly specialized individuals use their chosen epistemology and area of expertise to justify a certain hypothesis as truth. The epistemology starts with belief, leads to illusion of truth, resulting in justification. Perhaps this isn’t new. The conditional veracity of knowledge on a subject is bound by the individual’s own bias. Constructive discussion on alternative hypotheses are automatically deflected.
The point is that GHG’s do not “raise” the equilibrium temperature between the earth and the sun. If they did, it would require new, additional energy from somewhere.
Using averages and toys can lead one astray similar to using the Bohr atom model. It is easy to forget that SB characterizes the NET radiation between two bodies. However, the implicit assumption is that each body radiates energy based upon its equilibrium temperature with sources, not what other non-source bodies surround it.
A better solution is to apply integrals based on time to see what happens to the temperature. I assure you, retardation or back radiation, from a cooler body (the atmosphere) will not raise the equilibrium temperature achieved between the earth and the sun.
The idea that “new, additional energy from somewhere” is needed is a false inference.
If your argument were correct, then the Earth would need to be at the temperature determined by radiative equilibrium between the surface and the Sun, neglecting the atmosphere. This results in a temperature at least 33 K colder than what is observed.
Actually, SB doesn’t characterize the net radiation. It just characterizes the radiation from one body. The net radiation is determined by subtracting the radiation flows in the two directions.
The equilibrium temperature is certainly affected by the bodies that surround it.
How are you distinguishing between “sources” and “non-sources”? This seems to be an artificial, non-physical distinction.
Properly done, that should produce the same result.
Jim, if the Earth took up a sizeable percentage of the Sun’s view of -273 degree outer space, the Sun would actually get hotter to radiate its nuclear fusion powered heat, so GHG raising the Earth’s temperature do affect the Sun’s temperature. But only of the same magnitude as time running faster at the top story of an apartment building due to reduced gravity.
You say: “, whether it “retards cooling” or “back radiation heats” are two equivalent perspectives for viewing the same situation.”
I disagree. Slowing the rate of going from 50 down to 49 is totally different than going from 50 to 51.
The claim is CO2 is making us go from 50 to 51 not that is taking long to get to 49.
You’re simply offering evidence for the inadequacy of what happens when ambiguous verbal reasoning is used rather that writing out the math.
We’re using similar-sounding language that actually means something different.
Verbal reasoning is obscuring what both sides are actually saying. It leads you to misinterpret what others are saying, and reach a false conclusion.
I regret I don’t have the energy to unpack this right now.
If you have the energy for it, I unpack this verbal-reasoning-yields-erroneous-logic issue in a related context, in a critique of G&T‘s paper.
Mkelly says…
“I disagree. Slowing the rate of going from 50 down to 49 is totally different than going from 50 to 51.”
“The claim is CO2 is making us go from 50 to 51 not that is taking long to get to 49.”
Mkelly, in my view you are conflating one process, that is actually two. You are forgetting that the input into the system has not changed. ( Solar insolation)
So if you delay any part of the system from cooling as rapidly; energy that was exiting the atmosphere now stays a bit longer, and input (solar insolation) remains the same, net energy must increase.
the role of the lapse rate in a layer is critical. It’s why an increase in IR radiatively absorbing gas concentration produces a warming effect in a negative lapse rate layer (troposphere) and a cooling effect in a positive lapse layer (stratosphere).
Rather than the “absence of sufficient cooling”, I prefer “decrease in the rate of cooling”. But this just means the surface becomes warmer to rebalance the energy flows in and out. No one including the IPCC calculates the effect of CO2 by itself as enough to be harmful. The real problem with the alarmist position is the assumption of positive water vaper feedback. This has never been validated and in fact the data and common sense argues for a negative water feedback. Otherwise atmospheric warming, regardless of the initial cause, would always run away to much higher levels. As many skeptics have pointed out, actual warming is less than that predicted for CO2 alone most likely due to cloud formation and reflection of more incoming insolation.
Precisely. The lack of CO2 having any effect on the Earth’s temperature is shown by observation.
Launching one “defense” after another of the so-called “greenhouse effect” means nothing, because CO2 in and of itself clearly “drives” nothing. If it did, then the Earth’s temperature at 7,000ppm CO2 would have been the highest by far, and it was not; if it did, then an ice age at 4,000ppm would have been impossible – but it happened; if it did, then atmospheric CO2 changes would precede temperature changes, not follow them; if it did, then there would not be reverse correlation between atmospheric CO2 and temperature every time the (excuse me) REAL causes of temperature changes reversed from cooling to warming influences or vice-versa; if it did, then temperatures would not begin to rise with CO2 levels near their low point and falling, nor would temperatures begin to fall with CO2 levels near their high point and rising.
Citing whether has CO₂ lagged or lead temperature in the past always strikes me as completely missing the point, regarding how dynamical systems function.
Imagine two pendulums, A and B, connected by a spring.
If you kick pendulum A, A will start to swing back and forth, and B will start to swing too, in a way that lags. B lags A.
But, if you kick pendulum B, B will start to swing back and forth, and A will start to swing too, in a way that lags. A lags B.
Which lags and which leads is a function of the type of stimulus to the system.
Which variable has lead or lagged in the past tells you nothing about what stimuli are capable of affecting the system.
Einstein
The model shows how things could work if we could ignore everything except radiation.
Of course, radiation is the only way the Earth eventually loses energy to outer space.
Having said the above, I suspect the value of Β is wildly different than that presented above. I also suspect that it is not a constant.
A while back I calculated the surface temperature of the planet if the heat were perfectly distributed. If I remember correctly, it resulted in a surface temperature about 15 C below the accepted value for the average temperature. In other words, it reduced the necessary ‘greenhouse effect’ by half.
Yeah, exactly. I don’t know what question exactly it is that you’re answering Bob with what I assume is some fine work. The question that needs to be answered is what happens in the real world: ppm CO2 above 280, convection, clouds, faked data …. and the list goes on.
I suppose it doesn’t really matter as the answer from the climate liars is that Bob Wentworth is a “climate denier” either way, if you don’t fit their scientifically juvenile (or less) narrative.
It also doesn’t really matter if it’s possible to do it, as the empirical data shows what it is.
The section related to Figures 2 and 3 can include the effects of convection. It’s only the subsequent multi-layer atmosphere model that ignores everything except radiation.
The value of 𝜷 quoted is taken from measurements. I agree that it’s potentially not strictly a constant in practice, with regard to the real atmosphere.
Do you have a link for those measurements? Especially for CO2, direct measurements of its effects are a real bear because of the temperatures involved. One problem is that, in the lower atmosphere, it will lose energy by collisions with other molecules (mostly nitrogen which isn’t a greenhouse gas) whereas as we approach outer space it is more likely to re-radiate.
As I understand it, 𝜷 is an emergent property of the atmosphere as a whole. To calculate it, after the fact, all you need to know is the ratio of back-radiation flux, B, to absorbed solar irradiance, S. As I mentioned in the blog post, the data in Kiehl & Trenberth (1997) indicate a ratio of back-radiation to absorbed insolation, B/S = 1.38. This corresponds to a recycling fraction β = 0.58.
However, this “energy recycling” model is not intended by me to be the basis of serious quantitative work. (Maybe you could do serious modeling work using these ideas, maybe not. If you were going to do that, you’d need to go way beyond what I’ve offered.)
Primarily, it’s a framework for thinking conceptually about how long-wave-absorbing-and-radiating gases can lead to high back-radiation levels and warming of the surface.
If that is the simple model, WTF is the complex model like?
I do realize that while making arbitrary assumptions to simplify computing an effect are useful, one must not reify those assumptions.
Your definition appears to be based on a linear distribution of layers. It ignores gravity. As a result you miss the fact that downward radiation goes a much smaller distance than does upward radiation and the amount of radiation from each layer is determined by the mass of that layer.
Sometimes things cannot be oversimplified.
Couple of other problems that this simplification ignores.
1) The emissivity of the atmosphere is completely different than the surface.
2) As you move upward the temperature drops which causes more and more radiation to flow through the atmospheric window.
I’ve found these types of problems make this kind of model useless. That is why I prefer to look at the averages such as emission direction and path length. That gets you an even simpler model.
Another simplification is to make the surface skin different than the deep surface. What happens is very enlightening.
For a partially transparent layer, mass affects the amount of radiation. In the multi-layer toy model I offered, the layers are taken to be opaque to the wavelengths that they absorb. For an opaque layer, mass is irrelevant to how much radiation is emitted.
The toy model is actually indifferent to the distribution of layers, as long as they have the two properties of being (a) entirely opaque to the wavelengths they absorb and (b) uniform in temperature.
These conditions are not likely to be met anywhere in a real atmosphere. That’s why it’s a “toy model.” It’s something that is meant to illustrate certain aspects of the way physics works, without reproducing all the features of the more complex system we’re trying to understand.
Yes, that’s why, in the toy model, f is used as an approximation to the emissivity of the atmospheric layer, but the emissivity of the surface is taken to be 1.
As I said, the toy model is not intended to reflect all the physics in the real atmosphere. It’s intended to help understand certain simple ideas, to help one then think more clearly about more complicated systems.
There are different aspects of a complex system that one can gain insight into by considering different simplifications of the problem.
I find it’s useful to understand various simplified models and how they work, and then build back towards thinking about the more complex reality.
So much nonsense it is not worth the effort to read through it.
There is no “greenhouse effect” – it is a myth for true believers.
Earth’s surface temperature is quite simply the result of two surface temperature control processes; cloudburst that propels vast quantities of water high into the atmosphere above the level of freezing to create persistent cloud that regulates the maximum sea surface temperature to 30C and formation of sea ice at -2C to insulate the water surface below. The average surface temperature of 14C sits neatly at the mean of the two extremes because of the amount and distribution of the surface water.
The radiating temperature of Earth is simply the result of most OLR emittance being from an ice surface ranging from ground level up to an altitude of about 12km with a temperature range of 220K to 273K. The 255K typical radiating temperature being somewhere around the average. But the radiating temperature AND albedo are results of surface temperature control processes based on sea surface temperature not some delicate energy balance.
The tropical warm pools moving about from day-to-day and separated by vast distances all regulating to the same 30C:
https://earth.nullschool.net/#2021/04/13/1200Z/ocean/surface/currents/overlay=sea_surface_temp/orthographic=-294.50,2.86,369/loc=49.906,-3.937
Look at the moisture level well above freezing over a warm pool:
https://earth.nullschool.net/#2021/04/13/1200Z/wind/isobaric/250hPa/overlay=relative_humidity/orthographic=-297.42,-2.18,369/loc=49.474,-7.253
All that water will form reflective cirrus cloud as the water vapour is solidified by the OLR exitence.
Look at the CAPE being developed over the warm pools – recharging the energy source for the next cloudburst cycle:
https://earth.nullschool.net/#2021/04/13/1200Z/wind/isobaric/250hPa/overlay=cape/orthographic=-297.42,-2.18,369/loc=49.474,-7.253
These are things you need to understand to work out how the global surface temperature is controlled. You can see the processes in operation every day of the year as they have done for the last 10M years at least.
Thank you for the effort but unless I have missed something you are simply trying to justify the radiative theory and in the process you completely ignore our description of the mechanical process which is the primary cause of the enhanced surface temperature and which then leads inevitably to the observed radiative outcome.
If it were the case that radiative recycling could raise the surface temperature on its own then no planet with any radiative material contained within its atmosphere could ever sustain that atmosphere for long because the upward pressure gradient would always exceed the downward force of gravity and the mass of the atmosphere would be incrementally lost to space.
The only solution that works in the real world is our mechanical convection based process.
From the available data for various planets in our solar system plus the moon Titan we find that our model predicts various features of those atmospheres without any need to refer to radiative fluxes.
Indeed, our model appears to reflect universal features of every location where there is convective overturning in a gaseous medium.
Any correct theory must be built up out of correct building blocks.
In at least some of what I’ve read of your work, the idea that energy is radiated out to space and back down towards the surface in equal amounts seems to be a basic building block. I’m pointing out that that that particular building block seems unjustified and incorrect.
As I understand it, until that issue is addressed, any subsequent conclusions in your work that builds on top of that assumption cannot be trusted.
I am curious if the work that you are referencing builds upon this “standard partition” assumption (i.e., fluxes into the atmosphere are transformed by energy recycling into equal fluxes up and down)?
That’s an interesting (and shockingly implausible) claim. I can’t imagine any physics that would justify such a claim. Where is this “upward pressure gradient” supposed to come from? Can you point me to the relevant math?
Look up the ‘upward pressure gradient force’.
It is the upward force provided by kinetic energy at the surface which keeps gases off the surface. The warmer the surface the higher the gases rise against gravity.
Yes, I get that there is a pressure gradient force which yields an upward acceleration a = (-1/𝞀)(dP/dz), and that if a > g then air will accelerate upward.
What I don’t get is why you imagine that “if radiative recycling could raise the surface temperature on its own” this would lead to a > g “always” so that “the mass of the atmosphere would be incrementally lost to space.”
That’s the assertion that I’m hoping you might be willing to explain.
You write “The warmer the surface the higher the gases rise against gravity.”
Yes, but, is it’s not an unbounded process. So, I’m afraid I’m not yet seeing the point you are trying to make.
Well, if you start with hydrostatic equilibrium and warm the surface a bit more then the whole atmosphere expands which puts the top slice out of equilibrium and it will be lost to space.
That reduces the mass of the atmosphere so less surface heat is required for equilibrium and the atmosphere expands further putting a further slice out of equilibrium and that repeats until the atmosphere is gone.
Forgive me, but that strikes me as a very odd belief. The atmosphere easily adjusts to a new hydrostatic equilibrium if you heat the atmosphere and it expands. Why do you imagine that the “top slice” would go out of equilibrium?
The atmosphere would expand upwards so that part of it would then be at a height where the upward pressure gradient force exceeds the downward force of gravity.
Conversely if one were to cool the surface below the point required for hydrostatic equilibrium then the atmosphere would contract and the lowest molecules would experience a force of gravity greater than the upward pressure gradient force and would fall to the ground.
Either way, one loses the atmosphere if the kinetic energy at the surface is not at the appropriate level to sustain hydrostatic equilibrium.
You are again relying on radiative physics where a new equilibrium can readily be obtained between radiative fluxes in and out because all the relevant components are free to vary proportionately.
That does not apply to the mechanical process of balancing an atmosphere against a fixed downward force. Since the downward force is fixed the upward force also has to remain fixed otherwise no equilibrium can be sustained.
What leads you to believe there is a height at which this would happen?
The pressure gradient is continuously adjusting itself, at every point in the atmosphere, to maintain hydrostatic equilibrium.
The only deviations from this are horizontal pressure gradients that produce winds, or vertical pressure gradients that produce convection upward or downward.
Convection, which stops well before the top of the atmosphere, doesn’t have the power to eject air from the atmosphere.
At the top of the atmosphere, any deviations from hydrostatic equilibrium are automatically corrected by restoring forces. This doesn’t rely on anything to do with radiative physics. It’s just that if the pressure is too high above, gas will drop to make lower layers denser and restore equilibrium; while if the pressure of gas above is too low, gas from below will move up, increasing the pressure above, restoring the equilibrium. That’s the way pressure and density work together.
The same logic applies at the bottom of the atmosphere. If you “cool the surface below the point required for hydrostatic equilibrium” you’ll get a downflow of air from above which will restore the equilibrium. Nothing ends up “falling to the ground.”
You seem to have the odd idea that pressure, density, and temperature aren’t able to easily adjust themselves to create a new equilibrium when a change occurs.
Furthermore, that aspect of the radiative theory is not a building block for our mechanism because our mechanism works with no need to refer to radiation at all. Did you actually read it all or just go off on one when you saw that point?
We only comment on it because it seems to us that the idea of surface heating from downward radiation to a level above that caused by the sun is flawed for the reason we stated.
Your set of calculations simply amounts to a perpetual energy machine.
I read it quite closely.
The way that you eliminate the need to refer to radiation is by making use of the assumption that a flux absorbed by the atmosphere leads, via energy recycling, to one equal flux going upward, and another equal flux going downward (only for some reason you assert that this latter flux is “stored” in the atmosphere).
You record these fluxes in your tables with the label “Infinite Recycled Limit.” The value of the “infinite recycled limit” is based on your summation of 1/2 + 1/4 + 1/8 +…. = 1. In other words, these numbers are all based on energy recycling, under the assumption that β=1/2.
These “Infinite Recycled Limit” fluxes are one of the key novel features of the paper.
So, as I understand it, this assumption affects all the conclusions in the entire paper.
Why would your calculations based on the “Infinite Recycled Limit” be valid and my calculations based on exactly the same mechanism amount to a “perpetual energy machine”?
Have you paid any attention at all to how energy recycling works?
It’s a storage mechanism, that doesn’t actually create any new energy. That energy just visits the surface repeatedly.
Look at the heat-flow versions of the diagrams. Energy conservation and the Second Law of Thermodynamics are honored throughout.
There is no storage in the radiative theory because it all happens at the speed of light. Blocking of one wavelength immediately results in more outgoing of a different wavelength.
There is storage in the mass transport scenario because the energy transfers between KE and P E and back again are slower than the speed of light.
Two entirely separate processes.
“Storage” is actually the wrong metaphor for radiative energy recycling. We need to find a better metaphor for what happens inside a resonant cavity, because it’s an important effect.
I agree that “storage” is more characteristic of mass flows. But storage mechanisms cannot bring a planet about its radiative equilibrium effective temperature (i.e., 33K colder than observations in the case of Earth).
I know you have models that claim otherwise. But, regrettably, those models are wrong.
I’m with Rick Will on this one. In this simple model adding more and more CO2 leads to a continual rise in temps. There is no role for the water cycle which is driven by latent heat and convection. I have always believed the focus on radiative heat transfer is because the math is fairly straightforward. Convective forces are the dominate form of heat transfer from the surface, why make you models that focus on radiation.
All serious climate models consider both radiation and convection. However, only radiative processes apply at the interface between the atmosphere and space, so it is essential to understand those radiative processes.
Convection cools the surface, relative to the atmosphere, but I’ve seen no plausible explanation of how it could explain planetary warming. As I’ve said, any serious model should include both radiation and convection.
There seems to be a widespread lack of understanding about how radiative processes work, which is why I’ve emphasized them in this blog post.
Bob,
Our model does consider both convection and radiation but implies that the radiation fluxes observed are simply a consequence of the atmospheric potential energy reservoir created by convection.
Thus changes in convection will always neutralise the thermal effect of radiative imbalances otherwise there can be no atmosphere.
Only thermal energy radiates away, potential energy does not. Thus the existence of a variable reservoir of potential energy is able to act as a throttle on the radiative flows through the system.
I have only seen one climate model based on the real physics of planet Earth. Simply stated:
Global Average Surface temperature = {30 + (-2)}/2 = 14C = 57F
This is the only model not based on the mythical “greenhouse effect”. Show me a “serious” climate model not based on parameterising clouds that are responsive to the surface temperature.
I have sent my analysis of the climate model performance in the Nino34 region to two climate prognosticating groups and their response is to say their model is middle of the road. Absolutely no explanation why their models cool the past or warm the present.
One of the assumption your small model makes is that conduction/convection is superfluous. That is not the case. Much of the absorbed radiation is lost through collisions. That transferred energy is converted from kinetic energy to potential energy via the lapse rate and convection. In other words, much of the earth’s radiation is lost to the system from the very start. Additionally, the emissivity of CO2 is pretty low and results in even less radiation. You also forget that SB has an A (surface area) along with emissivity. As you increase the number of layers, you also reduce the effective surface area of GHG’s that can radiate.
This is a pure total nonsense description of an energy amplifier.
It is not an amplifier but a storage mechanism. For example a high Q optical
cavity (i.e. two flat highly reflective mirrors) can have an internal intensity that
is almost a million times higher than the input intensity. The atmosphere is similar —
the energy coming in equals the energy leaving but there is still a lot of energy
stored in the atmosphere.
The atmospheric density/pressure gradient is the energy storage mechanism.
Nothing to do with flat mirrors.
Stop with the stupid irrelevant analogies.
Get back to REALITY for a change, Izzy-dumb.
What matters to determining temperatures is power flux. A cavity with “two flat mirrors” greatly increases the net power flux.
An atmospheric density/pressure gradient does not.
(I’m expect I’ll be downvoted for this, but that doesn’t make it untrue.)
”The atmosphere is similar —
the energy coming in equals the energy leaving but there is still a lot of energy
stored in the atmosphere.”
Just exactly how does the atmosphere store any more energy than it’s native quantity? For that matter, how does the atmosphere ”slow down” radiation by scattering that coming from below?
Conversion of KE to P E in rising air and the reverse in falling air.
It takes time, hence the slowdown in energy throughput.
CO2 is just another radiative pathway for surface cooling.
No evidence it “slows down” anything.
Sounds like β is just a measure of whatever temperature the atmosphere is at. Focusing exclusively on long-wave radiative transfer equations is interesting but it may be a classic case of not seeing the forest for the trees when it comes to understanding planetary atmospheres.
I read the whole thing. If GHG are increased, what happens to the IR radiation from the the sun? More GHG should block more IR from the sun from reaching earth’s surface? Just imagine GHG all the way to the sun….would that result in a colder earth?
GHG only block what is called long-wave radiation, with a wavelength longer than 4 microns. Less than 1 percent of energy from the Sun is in this wavelength range.
And yet GHGs block considerable insolation, particularly WV.
And that energy, if it was not intercepted and reached the surface, would have a longer residence time, particularly if it struck the oceans.
Not true. H20 is a GHG. Look what it absorbs in near IR directly from the sun. See those clouds up there? A lot of precipitated H2O available at altitude to absorb near IR.
Water vapor may be a GHG, but clouds are droplets of liquid water. So, clouds don’t technically constitute GHG, though they are related to a certain GHG.
That said, you’re right that water vapor does absorb solar irradiation to an extent that matters.
CO₂ doesn’t absorb radiation shorter than 4 microns.
CO2 below 4 microns is covered up by water vapor. Wikipedia says so.
Water droplets in clouds are opaque to infrared.
I see nothing about the IR path length. It is longer pointing up then down. Read about Chapman layers. 1/2 down 1/2 up is not how it works..
I also see nothing about the IR being thermalized in the atmosphere with the lapse rates setting the tempature profile driven by convection. Anything that does not address convection is useless.
Yes, from any given point in the atmosphere, IR path length is longer looking up than looking down.
How many times do I have to say that what I was offering is a “toy model”, not a representation of the real atmosphere.
The purpose of the model is not to address the totality of atmospheric physics. The purpose is to address some common misunderstandings about what radiative balance in the atmosphere can and can’t do.
To address certain conceptual issues, it’s not necessary to bring in the whole kitchen sink.
I have a hard time accepting that the recycling fraction is greater than 1/2 in practice. Maybe it can be in theory with our pretend layers.
I have heard that the back-radiation has been measured, but I’ve never seen the literature. Can you direct me to this?
Anecdotally, it does seem absurd to have a recycling fraction bigger than 0.5 because of some observations.
After an ice storm, a thin layer of stratus clouds prevents ice from melting off of trees for at least a week at temperatures between 28 and 31 degrees. I have seen this twice. A week, no melting from the trees. With all that radiation hitting the trees from every direction all the time they should warm up, but they don’t. Yet…
After and Ice storm, at a temperature under 20 degrees, a break in the clouds allows all the ice to melt from the trees in minutes. So, let me get this straight. The trees are constantly radiating heat in equilibrium with all the incoming long wave radiation plus refracted and scattered radiation from the clouds (a lot of light is getting scattered through the low, thin stratus deck). Then the sun comes out, shines directly on the trees instead of being scattered through… and tips this balance just a hair, and the ice immediately melts? The tree bark warms up several degrees in minutes? Melting ice takes a lot of joules. This happens too fast to be plausible.
On a day with little wind, summer or winter, exposed skin in the shade, even if it is just a tiny piece of shade like a small cumulus cloud briefly covering the sun, feels MUCH, MUCH, cooler than when the sun appears. Similarly, when working down in a cool well and the sun suddenly passes overhead and shines into the well, the temperature rapidly becomes overwhelming. A small cumulus cloud passing in front of the sun should make almost no difference in how you feel. After all, the long-wave radiation from the rest of the sky should be much larger than the direct radiation from the sun. Yet it isn’t. It is not even close. Not even close to close. As soon as the sun peeps from behind that little cloud, you feel it burning and heating your skin immediately. When you walk outside from the outhouse, you do not feel your skin burning and heating immediately from all the downwelling IR if the sun is behind a little cloud.
So, while I don’t see anything mathematically wrong with your many layers model, (or the single layer model for that matter), I just can’t accept that it is the correct model.
However, I do have an open mind. If I can see the tests that show that there is more radiation hitting the earth from the downwelling IR than from the direct sun I’ll rethink what my senses are telling me.
I just Googled some random samples. Here’s a really homey sort of report on measuring “downwelling infrared irradiance” where they even show you a picture of their equipment. At a specific location, it apparently varies from day to day, and over the course of each day. Here’s a more comprehensive report from another location.
What one can see from all this is that isn’t not remotely theoretical. You go outside, point some instruments at the sky, and measure it.
You offer examples of the Sun coming out from behind a cloud making a big difference in ice suddenly melting, or feeling dramatically warmer.
If you look at the charts of solar irradiance and atmospheric downwelling radiation in the second reference, e.g., Figure 3, you’ll notice that the downwelling radiation isn’t typically more powerful than the Sun, but it’s more spread out in time so it often offers more energy than the Sun over the course of an entire 24 hour period.
It looks like, during the daytime the two fluxes are often comparable. So, say the flux of the Sun is S and the flux from the atmosphere is also around S. Maybe the clouds were blocking 2/3 of the Sunlight, so you have a total flux of 1.3 S. Then the clouds pass, and suddenly you’re at a flux of 2 S. That’s a pretty big change.
And maybe if the flux ever dropped below 0.3 S you’d be freezing, so you’re just used to there always being a flux of at least 0.3 S, so you don’t count that in your evaluation of whether it’s warm or cold.
I’m not sure exactly how it works. But, take a look at the charts, and see if maybe you can make sense of your experience.
“you’ll notice that the downwelling radiation isn’t typically more powerful than the Sun, but it’s more spread out in time so it often offers more energy than the Sun over the course of an entire 24 hour period”
But that is exactly the point of downwelling IR raising the temperature of the earth. To do so the downwelling IR must be greater than the upwelling IR. Adding more energy “back” only retards the loss of heat, it doesn’t “push” heat back up the gradient. IOW, the earth continues to cool.
The text of mine that you quote doesn’t say anything at all about upwelling IR. So, the point you’re making is separate to what I was talking about.
You’re right that you can think of downwelling IR (which is always less than upwelling IR) as “adding more energy back” in a way that “retards the loss of heat.” And, no, it doesn’t “push heat back up the gradient.”
However, the consequences of retarding the loss of heat, when heat is flowing in at a steady rate, is a temperature increase.
The difficulty of losing heat may be quantified as thermal resistance, R. There is a law that the temperature drop ∆T across a system with thermal resistance R with heat flux 𝚽 flowing through it is given by ∆T = 𝚽⋅R.
Sunlight being absorbed by the Earth’s surface supplies, on average, a heat flux 𝚽 to the surface. Because energy flows balance, an equal heat flux 𝚽 must flow from the surface to space through the atmosphere. The difference between the temperature of the surface and the temperature of space is given by ∆T = 𝚽⋅R.
When you increase the thermal resistance of the atmosphere (slow the loss of heat), this leads to the temperature of the surface being higher.
If the Earth’s surface had a pre-determined temperature and no ongoing source of heating, and was simply waiting to cool to the temperature of space, then yes, increasing thermal resistance would simply slow the rate at which the temperature decreases.
But, that’s not the situation we’re in.
When an active heat source is present, increasing thermal resistance increases temperature.
Thermal resistance is just like resistance in an electrical circuit. Power is expended and does raise the temperature of the substance providing the resistance. Its value is kelvin/watt. But again, it is not a source of energy that is added to the original source. In the case of the earth/atmosphere this means air temperature will rise, but not the temperature of the source, i.e. the earth’s surface.
Quote:”Sometimes people are incredulous at the idea that the back-ration flux, B, is greater than the absorbed insolation, S. Yet, this is what is measured to be true“”
That has got to be THE crunch point.
How was that measurement made
Who made it
When did they make it.
I’m gonna put words into folks’ mouths by saying that its ‘measured’ by using Stefan’s formula…
OK Lets do it
So we get, Radiation Power = 390 Watts per square metre
But that is BS
The emissivity of an Oxygen Nitrogen mix is about 0.02
The emissivity of CO2 at the temps involved is 0.00 (zero)
A small amount of water vapour is involved, lets say 1% and it has emissivity of 0.99
Thus, the Oxygen Nitrogen are emitting 7.8 Watts
The 1% water is emitting the figure above divided by 100 (390/100) = 3.9 watts
Perfectly nada comes from CO2 at temps bellow 33 Celsius
So now we get a radiation power of (7.8 + 3.9) = 11.7 Watts per square metre
And most important, it is coming from a cold object. Lapse Rate says exactly as much.
That 11.7 Watts can not be absorbed by The Surface – dirt/rock/water/sand/plants/anything
It would trash the whole idea of Entropy if it was absorbed
It would mean a spontaneously warming universe instead of a cooling one
And there-in lies The Real Problems with all these climate calculations
This essay nicely demonstrates that The Human Animal cannot pass off untruths.
The authors actually know they are talking BS, without ‘knowing’
They do it by skating (quickly) over what they find to be trivial or difficult-to-grasp things.
Most especially, “emissivity” and the relentless confusion of the 3 main types of energy transport mechanism
IOW: Perfect Contemporary Climate Science
i.e. Magically conceived and confused garbage
Indeed. Part of the confusion is the notion from Climate Science© that all Watts are created equal. Typically the Watts in these energy balance cartoons refer to energy content of radiation at an average wavelength of visible light. That is reasonable for shortwave solar radiation, but obviously overstates wattage from longwave IR.
Emissivity only applies to solids and liquids. A gas’s ‘temperature’ is actually the velocity of the molecule, relative to something. There is no reason for a gas molecule to absorb/emit differently merely because it is travelling at 100k/hr more or less. You’ve got some fancy calculations there but they are meaningless if you don’t get the basics right. Just because you have some fancy colouring pencils doesn’t mean you know how to draw.
Gases have emissivities and people can and do measure them. Here’s an example of this sort of data.
There are also very fancy calculations based on Einstein’s theory of radiation which derive the theoretical relationship of spontaneous emissions of gases (see equation 49).to Planck’s radiation law for solids and liquids.
Gas molecules aren’t just flying around, they are also colliding with one another. And when they do, some of their kinetic energy is transferred to vibrational modes (e.g., where the molecules flex back and forth). The hotter a gas is, the more molecules are vibrating. Those vibrational modes are what are involved in the absorption and emission of longwave radiation.
This is an area where I’ve done the work to “learn to draw.”
”Gas molecules aren’t just flying around, they are also colliding with one another”
But that does not change regardless of any added energy at the same pressure due to reduction of molar density (expansion) right? So how does extra co2 slow down radiation to space? No one has every explained this to me.
When CO₂ absorbs radiation, it vibrates more. The energy of this vibration is typically transferred to other molecules (most often N₂ or O₂). Every bit of radiation absorbed by a CO₂ molecule contributes to warming the air overall. That warmer air makes all the CO₂ molecules in the air vibrate just a little bit more. That’s what it means for the gas to be at a higher temperature.
At all times, vibrating CO₂ molecules occasionally spontaneously emit radiation. Some of that is emitted back towards the direction of the ground.
There are two ways of thinking about radiative energy transmission.
You can look at it at the level of radiative heat flow. In that case, the flux of radiative heat flow between bits of matter at temperatures T₁ and T₂ is given by 𝚽 = σ(𝜀₁T₁⁴ – 𝜀₂T₂⁴) where 𝜀₁ and 𝜀₂ are the emissivities of the two bits of matter. As you can see, the term related to the second bit of matter reduces the value of 𝚽, the flux of heat leaving object 1. That’s what we mean when we say the second bit of matter “slows” heat leaving the first object.
But, you can also look at this at another level, the level of radiation going back and forth between the two bits of matter. The radiation leaving the first object to go to the second bit of matter has a flux σ𝜀₁T₁⁴. The radiation leaving the second bit of matter to go back to first object has a flux σ𝜀₂T₂⁴.
In the second way of looking at things, there is radiation flowing away from the surface, and there is radiation flowing back to it (the infamous “back radiation”).
But, in the other way of looking at things, there is just heat flowing away from the surface, with a flux 𝚽 = σ(𝜀₁T₁⁴ – 𝜀₂T₂⁴). And this flux is smaller (the surface is cooling slower) when the temperature T₂ is larger (or when there is more CO₂, but I’ve oversimplified by leaving out factors that express how much CO₂ there is).
So, CO₂ “slows” radiation from leaving the surface and getting to space in the sense that it absorbs some of the outbound radiation and sends some back to the surface. This can be thought of either as back-radiation, or simply as the outward heat flux being reduced.
Does that help explain what is meant by CO₂ “slowing” down radiation on its way to space?
”Does that help explain what is meant by CO₂ “slowing” down radiation on its way to space?”
Not really. How long does it take for a photon to reach space from the ground at night given that it travels at the speed of light regardless of any gasses intercepting it or how much it may bounce around before getting there?.
Ah, the imprecision of language.
Talking of “slowing down” is colloquial rather than literal.
What is really meant is that magnitude of the net radiant heat flux flowing from the surface to space is reduced.
The phrase doesn’t actually have anything to do with a literal velocity.
The pdf you linked to:
I have a feeling that it is a misnomer to call it emittance. There is absolutely no wavelength mentioned. I would be interested to see the apparatus used to determine the tables. It seems to me (from the sparse informastion on the pdf), that it is just a function of the specific heat of the gasses at different temperatures and pressures.
The paper you referred to refers to the spontaneous emmission of radiation of IR active gasses. That is hardly news. We are fully aware that IR active gasses absorb and emit particular wavelength of radiation. That is NOT emissivity.
‘When a gas is in thermodynamic equilibrium with its environment it can be described by an average temperature . Like any matter at a given temperature, which is in unison with its surrounding, it is also a source of gray or blackbody radiation as part of the environmental thermal bath. At the same time, this gas is interacting with its own radiation, causing some kind of self-excitation of the molecules which finally results in a population of the molecular states, given by Boltzmann’s distribution.’
Suddenly, through weasel words , we have gasses being gray bodies. You’ve gotta be sh!t!n me.
Um, you do realize that emissivity usually doesn’t involve specifying a wavelength? (Only “spectral emissivity” involves specifying a wavelength.)
It’s simply a matter of 𝜀 = (total radiative flux emitted by matter at temperature T)/(total radiative flux emitted by black-body at temperature T).
(“Emittance” is the emissivity associated with some volume of gas.)
This has nothing to do with specific heat. You put a volume of gas in a chamber and measure how much radiation comes out of it, subtracting off any radiation from the container. Here’s an example of a lecture on working with such information.
Yes. A gas at a given temperature spontaneously emits a certain amount of radiant power. You can relate this to the amount of radiant power emitted by a black body. The ratio is called emissivity.
How is this not emissivity?
Are you upset because gases don’t emit a black body spectrum?Here is one explanation of how the term “emissivity” can be properly applied to matter that is not a Planck radiator. Most matter is “gray body” and does not strictly emit a Planck black body spectrum.
Having a revulsion to the idea of a volume of gas acting as a gray body does not make the idea wrong.
Reality is not required to conform to your mis-impressions of it.
In your first link;
Running hot gasses through a pipe and the pipe heating up is not an indication of gray body radiation, it’s called conduction. The second link you sent me is not news to me and something I have always claimed. How on earth do you consider that link to support your argument?
I feel it’s pointless discussing this with you. I will briefly glance at some of your future posts and will try to avoid making comments (addressed to you).
I am sure you will appreciate this kind gesture from me.
Bob, I appreciate your comment. But if you say any serious model combines both convective and radiative forces, then your toy model is unserious. You can’t have it both ways.
Climate is a difficult general equilibrium problem and lots of time and effort is spent on unserious mathematical models. Yours is an example. My last formal math class was “The Theory of Partial Differential Equations.” This was back in the late 1980s. We looked at the Navier Stokes smoothness issues. I quickly learned that I had nothing to contribute. So I started to look at the data.
You can not explain what we have observed with your approach. By that I mean, how do you explain the climate that the Vikings experienced in the 10th century when they colonized Greenland. Radiative forces do not provide an explanation for what we observed. This is the problem I have with climate science today. It does not provide an understanding of the data. This is the reason that so much date is “massaged”. If you believe that radiative forces dominate the surface temperature, please explain what we observe from the Greenland ice core data. Also, thank you for your efforts. I would hate to think that we live in a world where everyone agreed on everything.
It’s “unserious” in the sense that I am not doing climate modeling.
It’s serious in that it’s useful for trying to help clarify some basic principles of physics that people commonly misunderstand.
I’d like to explain something about where I’m coming from when I post blog posts or comments.
I am not interested in taking any position on the merits or faults of claims about what is happening to the global climate and why.
The only thing I am interested in is advocating is for correct understandings of physics.
I read way too many arguments that deny the reality of basic physics.
Maybe you’re right that there are other phenomena that are important, or even dominant, in determining global temperatures. If you’ve got correct physics that says that, that’s fine with me.
What I’m not fine with are claims that contradict basic physics. The assertion that radiative warming of planets by greenhouse gases is entirely “bogus” or a “violation of the Second Law of Thermodynamics” is one such type of claim. That’s simply not true.
I’m not taking a position on how big or small the effect of greenhouse gases is compared to other things. There’s still room to possibly be right about various beliefs about climate in general.
But, I draw the line at accepting nonsense positions that deny aspects of science that are easily proven a thousand different ways, if people were willing to pay attention.
The toy model I offered is enough to clarify the faults in the logic of positions that some people express. That’s all that I’m trying to do.
In the same way a story about Santa Clause or the three little pigs does.
Maybe try Mills and Boon instead ! Its fantasy, too. !
“What I’m not fine with are claims that contradict basic physics. The assertion that radiative warming of planets by greenhouse gases is entirely “bogus” or a “violation of the Second Law of Thermodynamics” is one such type of claim. That’s simply not true.”
Yet your statement is taken by warmists and echoed by saying “See even physicists agree that GHG’s can warm the earth by back radiation.”
You address the issue correctly in your post above that says,
“But, in the other way of looking at things, there is just heat flowing away from the surface, with a flux 𝚽 = σ(𝜀₁T₁⁴ – 𝜀₂T₂⁴). And this flux is smaller (the surface is cooling slower) when the temperature T₂ is larger (or when there is more CO₂, but I’ve oversimplified by leaving out factors that express how much CO₂ there is).”
𝚽 will always be positive until T₂ equals or exceeds T₁. (Assuming 𝜀 and A are also equivalent)
You simply can’t keep adding more and more flux by adding more and more layers. You are creating energy at some point in the process. That is what the warmists are doing.
I’d like fairness for the “warmists.” That’s not what they are doing.
From a heat flow perspective, adding more and more layers increases the thermal resistance of the atmosphere. Thermal resistance R is related to heat flux 𝚽 and temperature difference ∆T by ∆T = 𝚽⋅R. When thermal resistance increases, then:
The Earth is in scenario #2. There is a fixed flux of heat supplied to the surface by the Sun which must escape to space through the atmosphere. The temperature difference between the surface and space, ∆T, is determined by the thermal resistance of the atmosphere, R.
“Warmists” are simply asserting that adding more “layers” increases the thermal resistance, R.
Yet a thermal resistance, just like an electrical resistance (or impedance) does not add energy to the system. It is not a source, it can not raise the power available. An impedance creates a “resistance” to current flow. There is a gradient across it, from the source to the load.
What you seem to be analoging is a transmission line with reflections creating standing waves. Standing waves can cause measurements of current and voltage to appear that they are creating additional power, but due to phase differences, that is not the case. A source transmitter only provides a given power level and reflections can not increase that power.
That is one reason that linear math, averaging, and regression can mislead one as to what is happening. Power has a time component that should not be ignored in the calculations.
Yup. That’s exactly similar, mathematically, to what radiative energy recycling does (within the “heat-flow perspective”).
It doesn’t actually add heat to the system. But, it reduces the net flux of heat out of the system.
* * *
People get confused because there are two perspectives for understanding such systems, the heat flow perspective and the radiation perspective.
Also, a shout out to Zoe. No one who has spent a night in a cave in WVA and then dressed up in the cave for the Greenbriar buffet on Sunday can believe that geothermal plays no role. It just makes no sense.
For what it’s worth, I’ve spent times in caves in WVA, and fondly remember my experience of OTR… (about 30 years ago)
Nice write up to try and explain a small fraction of what is going on in the real atmosphere.
What drives me crazy is this explanation and most others I have seen seem to start with the equivalent of “Imagine the Earth is a cube”.
The Earth’ interactions with incoming solar radiation (light) is far more complex then your simple model can address. It is these other complexities that always make me believe that researchers (in general) are far more confident in their understanding than is called for. The Earth’s climate system is simply not behaving in the manner the models predict, which is why their “Climate Sensitivity to a Doubling of CO2” keeps dropping over time.
In the real world, the Earth is not heated evenly, even within a local region. Hillsides create shadows, so the air masses above the sunlit part and the shadowed part become unstable, and convection occurs. In the real world water vapor is constantly trapping heat (water to water vapor) and through convection carrying great amounts of heat upwards to be released for away from the ground. In the real world the Earth is not flat, but a spheroid with constantly moving winds, so solar radiation is trapped more or less by the atmosphere depending on the angle of incidence and the number and types of clouds present.
I do not find your explanation of how CO2 could help to recycle energy to the surface difficult to follow at all – I simply think its a mistake to try to describe our climate system using a small piece completely out of context with the rest of the system. Your “toy model” is completely worthless for prediction because it is a piece of the puzzle ripped out of a larger system. When you try to embed it back into the system, the behavior becomes impossible to predict because we simply do not understand the complex system. You can model it all you want – it is a waste of time without a decent understanding of how all the parts interacts. I am not even convinced we know of all the parts.
I believe you are suffering from “confirmation bias” – you strongly believe what you say and so you look no further – why bother since you already understand it. You might even be completely right about that little piece of he puzzle, but if you do not keep leaving room for doubt, you become blind. I believe most climate researchers have become blind.
“Imagine the Earth is a cube”
No need to imagine … we have it on good authority –
“Up to 30,000 delegates are expected to attend Cop26 in November, from all corners of the world”
https://www.climatechangenews.com/2021/03/12/covid-proofing-cop26-test-solidarity-climate-weekly/
Even on gods authority –
Ezekiel 7:2 “An end! The end has come on the four corners of the earth.”
https://www.biblegateway.com/passage/?search=Ezekiel%207:1-3&version=CSB
Isaiah11:12 “And he shall set up an ensign for the nations, and shall assemble the outcasts of Israel, and gather together the dispersed of Judah from the four corners of the earth.”
https://www.kingjamesbibleonline.org/Isaiah-11-12/
four corners + four corners = 8 corners … So it must be a cube !!
Describing a complex system is built out of the building blocks of understanding aspects of basic physics.
I am not trying to predict the behavior of the overall climate system.
I have simply noticed that some people are using faulty building blocks in their own attempts to understand the complete climate system.
They routinely make claims about how physics works that can be shown to be wrong if one considers my “toy model” and how it works.
My interest in writing and talking about this is the remote hope that someone might notice they’ve been thinking about a building block of their logic in a way that wasn’t quite right and needs to be rethought.
I have no stake in what conclusion they ultimately come to about climate.
I just want to take a stand for at least building your understandings out of bits that are individually true, rather than including ideas that are easily shown to be wrong, if you’re willing to pay attention.
Confirmation bias seems unlikely in my case because I’m not taking any position on the larger issues. I just want a discussion that isn’t quite so routinely drenched in fundamental misunderstandings of physics.
There is still an issue, which has been claimed to be fabricated by a few climate deniers and it is if the reradiation flux from the atmosphere is really 345 W/m2. The accuracy of this value is not an issue in this case but if this radiation flux is a real thing. Here is a link to an article, which describes the ground-based network of measurement stations called Baseline Surface Radiation Network (BSRN). This network with 59 stations is hosted at the Alfred Wegener Institute (AWI) in Bremerhaven, Germany since 1992. Link: https://www.research-collection.ethz.ch/bitstream/handle/20.500.11850/286337/essd-10-1491-2018.pdf?sequence=2&isAllowed=y
Here is a link to an article published in 2008, where major flux values of the Earth’s energy balance are calculated utilizing the BSRN network: https://journals.ametsoc.org/doi/full/10.1175/2008JCLI2097.1. According to this study, the reradiation flux values have been 338.6 W/m2 and the surface emitted flux value 398.8 W/m2. These values can be found in Table 1 in the end of the article. The latter value is close to the black surface radiation value of 15…16 °C.
But I have noticed that even this concrete evidence is not enough for real “climate deniers”. They continue by claiming that LW radiation cannot be measured….
You do realize that using the values you have, the earth will not have a higher temperature than the equilibrium temperature between the earth and the sun, right? The net flux will still be away from the earth.
I do not understand your point. The net energy from the sun is 240 W/m2 corresponding to -18 C, but the brutto energy to the surface is 510 W/m2. The radiation balance temperature is according to 395 W/m2 about 16.3 C and it is also the observed surface temperature.
“According to this study, the reradiation flux values have been 338.6 W/m2 and the surface emitted flux value 398.8 W/m2. “
The earth/sun is in equilibrium with the earth radiating 240. 510 – 240 = 270. That would be 270 watts/m2 from where? Remember, at equilibrium, for every watt from the sun absorbed by the earth, the earth is simultaneously radiating 240 watts. You wouldn’t have equilibrium otherwise. So where does the 270 watts/m2 come from?
Their back radiation is a magical energy amplifier, it increases its own energy and its own temperature,
Magic is only physics you don’t understand.
Agree with your math.
It should be rather easy to verify you model with experiments. Has that been done ?
It’s basically a homework problem that commonly occurs in thermodynamics courses. It’s so basic that I doubt anyone has bothered to re-verify it in the last 50 years.
The math, though, it identical to the math that is used in all sorts of practical thermodynamic calculations, affecting real systems. So, the math is verifying on a practical basis almost daily.
But at this point, it’s so established that it’s considered engineering, not science, so there is little reason you’d find a verification of things like this in a scientific publication.
This is the point I made earlier. Using “averages” hides info and inaccurately describes much of what is going on. To do this properly requires the use of integrals over time. Too many folks are trying to describe a continuous function in time without involving time at all by using average this or that. To have an accurate view of what is happening really requires a solution that involves time and trig functions to determine the instantaneous values at any point in time during a day.
Yes, rigorous climate modeling involves looking at variations over time and space and taking those into account.
You can do simpler calculations that smooth over these effects, and those calculations are suggestive, but you always need to check those simple calculations by seeing how much things change when you take temporal and spatial variations into account.
I am fully aware that it is basic. You write that there is no need to “re-verify”. Has anyone “verified” it 50 years ago ? I doubt it.
I thought that “experiment” was the king of physics.
Your model says that if I have a box with an IR- radiator in – put 10 glass plates at top of box (as a lid) without any separation – wait till equilibrium is reached – then separate the plates – the temperature should increase in the box according to your model.
Will it really do that ?
Thermodynamics has been well-understood (by those who understand it) for well over a hundred years. If you do a correct calculation, it tends to work out. Particularly for a simple system.
Inside the box there needs to be a heat source inputting a continuous flux of thermal power, warming that IR-radiator.
Your question amounts to: will the thermal resistance of ten pieces of glass be less when the the pieces of glass are stacked together (resulting in a lower temperature) and more when they are separated (resulting in a higher temperature)?
This setup doesn’t just involve radiative heat transfer, but also conduction and convection.
Still, the answer must be “yes.”
The conductive thermal resistance (within the pieces of glass) is the same in the two scenarios.
Heat transmission between the pieces of glass when the pieces are separated is likely dominated by convection rather than radiation.
Yet, what is important is that the conductive heat transmission when the pieces of glass are in contact is more efficient than the convective+radiative heat transport that transfers heat between pieces when they are separated.
The net effect is that thermal resistance is increased when the pieces of glass are separated. Therefor, for an equal heat flux to escape the system, there must be a large temperature change across the “lid” of the box when the glass pieces are separated. The temperature inside the box will rise in this case.
So, this version of the experiment isn’t specifically about radiation. But, yes, this experiment could be done fairly easily, and the separated pieces of glass would be expected to yield a higher temperature in the box.
I am of course talking about a set up vacuum. I do understand that there is a difference between radiation and convection.
I have spent some year in research, Theoretical Physics, solid state, thermodynamics.
What I am saying is that you verify a theory by experiments – not by stating that it is “trivial”, “basic”, “homework” or “well understood”.
I do not understand why you object so strongly to experiments.
I do agree that your calculations are very basic. I am not convinced that it really catches all details of radiation physics.
I personally think that a few simple experiments should be more convincing than your model.
Fascinating. Problem is, it doesnt happen.
How do you know it doesn’t happen? Have you tried the experiment?
Interesting enough. I am not well versed in thermodynamics, (just enough to pretend I know better than my betters, the mark of ignorance) but can someone reconcile these two statements?
1) Each layer of the atmosphere has a distinct temperature, and radiates equally in both directions,
2)Because of the temperature difference between the top and bottom layers, it is entirely natural that the atmosphere as a whole directs more radiation downward to the surface than it does upwards to space.
Heat radiates from hot to cold, no? So the warmer bottom should radiate more towards the colder top than the even warmerer bottomer, no?
Asking for a friend, I already know everything.
Back radiation is magical radiation, its -80c black body heating potential is keeping us all, all warm and toastie.
The idea that there is “-80c black body heating” involved is a product of severely muddled thinking. I unpack that meme here.
When thinking about radiative heat transfer it is essential to keep in mind that there are two distinct perspectives one can think about: (A) the heat transfer perspective, or (B) the radiant energy perspective.
The difference is that: the radiant energy perspective involves thinking about radiation going back and forth, while the heat transfer perspective involves thinking about heat going only one direction. These perspectives are related because the heat flow is defined as the difference between the two radiation flows.
Both are valid perspectives, but if you don’t keep it straight which one you are talking about, you’ll get confused and come to nonsensical conclusions.
Heat flows only one direction. Radiation flows in both directions.
In your question, you appear to mixing up the two perspectives. You seem to be thinking about how much heat should be flowing, and in what direction, then trying to apply your conclusions about this to radiation (with in part of the other perspective).
Radiant heat flows from hot to cold. Radiation and its energy flows in both directions, but the flow from hot to cold will be larger than the flow from cold to hot.
Does this help at all?
I find your reply informative, but I am not sure you taught me what you set out to. I shall directly attend to informing myself better on the subject, as my initial mindmodel makes clear that it is the imbalance in effective radiation, adjusted for Planck, that causes the heat transfer. But that is not the issue, I was referring to passages that seemed contradictory, taken to their absurdest consequences. The first asserts a temperature gradient in one direction, the other posits a radiation imbalance in the other direction. I shall meditate…in 3D.
Thanks for clarifying what you perceived as contradictory.
<– A — [ warm —- B_heat=(A-C) —-> cool] — C –>
A diagram (see above) might help. The temperature gradient is inside the atmosphere. Within the atmosphere, heat flows as expected from warm to cold (flux B_heat in the diagram).
Exiting the atmosphere, the radiation flux (A) exiting downward is larger than radiation flux (C) exiting upward.
It’s entirely self-consistent.
“Radiant heat flows from hot to cold. Radiation and its energy flows in both directions, but the flow from hot to cold will be larger than the flow from cold to hot.”
This really confirms paranoid goy‘s question doesn’t it?
“Heat radiates from hot to cold, no? So the warmer bottom should radiate more towards the colder top than the even warmerer bottomer, no?”
The warmer bottom should radiate more to the top than the the top radiates down. The end result is more going to space than coming back down.
This is a very good explanation. This statement caught my attention
When you consider conduction as a diffusion of molecular KE, or the diffusion of phonons through material, then the whole transport picture is not so different between radiation and other modes like conduction. Statistical fluctuations might cause a cool molecule occasionally to transfer some of its KE to a hotter molecule…
You are only looking at one form of heat transfer, when you add conductive, convective and latent you have such a confused mess it is impossible to model.
These are the two most popular claims of those people denying the GH effect (GHE): 1) Cooler never warms warmer. 2) Any theory asserting any actual back radiation warming is false from first principles.
I describe two ventilation systems of my house in a cold climate with electric heating elements. The first system was a ventilation unit with two fans: one transfers air in and another sucks the air out. The temperature of the incoming air was the same as the outside air. It was inconvenient during the wintertime. In my present ventilation unit, I have also an integrated heat transfer unit. This unit recovers about 80 % of the energy flowing out by warming the incoming air. The incoming air temperature is still below the inside room temperature. Anyway, the electric bill is now about 20 % lower than before. The cooler can never warm warmer?? In my house, it does all the time.
The claim that reradiation can not warm up Earth’s surface, is a typical strawman argument. The GHE is a fact and I do not claim that the reradiation of 345 W/m2 from the atmosphere can keep the surface temperature at 15 °C which can then emit radiation of 395 W/m2. What I say is that the direct solar radiation of 165 W/m2 plus reradiation 345 W/m2, totally 510 W/m2 can easily keep the surface temperature at 15 °C and emit radiation of 395 W/m plus create sensible heat flux of 24 W/2m plus latent heat flux 91 W/m2 which are totally 510 W/m2.
The IPCC’s GH effect definition is against the physical law and the correct definition is here:
https://www.climatexam.com/single-post/the-six-definitions-of-the-greenhouse-effect
Try again. You have at least two systems here. The sun/earth and the earth/atmosphere. The earth radiates based upon the equilibrium temperature established between it and the sun, which is the only source in the system by the way. The atmosphere will radiate energy based upon the equilibrium temperature established between it and the earth. The earth becomes the source in this calculation. Please note, at equilibrium, as a watt is received from the sun, the earth simultaneously radiates a watt regardless of what the atmosphere is doing. As the earth is radiating that watt outward toward the atmosphere, GHG gases are simultaneously “back radiating” something less. That means more leaving the earth than it is getting back.
Redo your calculations and show us how this is wrong.
It is fundamentally erroneous to treat these as two separate systems, as if the Sun and Earth surface alone set the equilibrium temperature of the surface (if that’s what you’re saying).
(Treating the Sun and the Earth surface as an isolated system that determines the surface temperature would result in a surface temperature at least 33 K cooler than what is observed.)
It is a single system, involving the Sun, Earth surface, and atmosphere, and temperatures are determined by equilibrium within that integrated system.
No sir. If, as everyone seems to think, the atmosphere is transparent to the sun’s radiation, then the earth/sun can be treated as a single system. The sun will heat the earth to whatever equilibrium temperature is appropriate especially concerning albedo. This ends up as ALL the energy input there is to the entire system.
Consequently, it is also ALL the energy that can enter the earth/atmosphere system. In this system the earth is the single source of energy and it radiates energy based upon the equilibrium temperature maintained by the sun.
Now in order to heat this system to as you say 255 K + 33 K, the earth must now radiate at 288 K. To accomplish that feat, there are two options.
1) the energy from CO2 is added to the energy arriving from the sun, or
2) the energy from CO2 must be greater than the energy the earth is radiating at 255 K.
The problem with either option is this. There is more energy in the system than you started with. A nice trick if you could do that. Just think what kind of fuel mileage increase you could get from an ICE automobile.
What is the problem? First, using linear algebra averages of time-varying and space-varying natural phenomena can really lead you astray. I have been slowly working my way through Planck’s treatise on heat and radiation. The man was a genius. I haven’t used vector calculus in a long, long time. Basically since learning how to solve Maxwell’s equations in college. He treats it like simple arithmetic!
People seem to forget that when the earth radiates, it cools momentarily. Radiation being absorbed from CO2 must do more than just replace that radiation in order for the earth to warm.
Quote: “No sir. If, as everyone seems to think, the atmosphere is transparent to the sun’s radiation, then the earth/sun can be treated as a single system.”
Sir, It looks like that you have not even basic knowledge about the Earth’s energy balance. The atmosphere is not transparent to the sun’s radiation but 75 W/m2 has been absorbed by the atmosphere. There is no point to continue because the basic things are so different.
You might want to think about resistors. What determines the temperature of an electrical resistor?
It’s the power time the thermal resistance between it and the ultimate sink for its heat.
A system including only the power source and the resistor in no way determines the temperature of the resistor.
The Sun is the Earth’s power source, but it does not determine its temperature.
* * *
With the way you’re thinking about things, you will be unable to correctly predict the behavior any thermodynamic system involving three or more radiating bodies.
Sorry, I’m too tired to spell out the physics in more detail right now.
I strongly encourage you to pick up a thermodynamics book and engage in solving any of the problems related to thermal radiation.
The model is useful in illustrating a theoretical resistance to the speed of radiation through a radiative gas. But reality transforms that into a cooling of the surface.
The daily solar pulse of upward surface IR faces a resistance to direct exit to space through mainly water vapour. The temperature gradient of this medium (influenced by gravity) through which this radiation has to travel every day is determined by a skin temperature of minus 60ºC where radiative equilibrium with space occurs at around 12 km altitude.
This stratospheric temperature is fairly uniform around the globe due to all the thermodynamic processes within oceans and the atmosphere moving warmth polewards.
In theory to maintain this skin temperature through a motionless atmosphere the radiation would need to be from a surface at a temperature of plus 60ºC.
In reality during the daytime radiative resistance at the surface or lack of higher up destabilises the atmosphere by increasing the lapse rate for convection to begin and reduce the theoretical to actual 15ºC.
The only time the “greenhouse effect” acts as a “blanket” is at night when the more humid the atmosphere the less likely there will be a ground frost.
I’m generally aligned with your narrative, apart from one quibble and one question.
The tropopause is at around 12 km altitude, but I feel uneasy about your characterization that this is “where radiative equilibrium with space occurs.”
It depends what is meant by these words. Yes, there is an equilibrium there, in the sense that the tropopause is where warming from insolation absorbed at higher altitudes balances heat radiant heat loss, creating a temperature inversion and putting an end to convection.
However, I would put the fundamental point of “radiative equilibrium with space” somewhat higher in the atmosphere.
If one looks at the spectrum of outgoing longwave radiation (OLR), one sees that the temperature associated with the 15 micron CO₂ emission line is higher than the temperature at the tropopause. This indicates that radiative equilibrium with space occurs further up in the stratosphere, where the temperature is higher than at the tropopause.
You’re right that the dry adiabatic lapse rate of 9.8 °C/km predicts too large a temperature difference between the surface and the tropopause, and the lower moist adiabatic lapse rate of around 5 °C/km (which accounts for convection of latent heat) accounts for the observed temperature difference.
I’m not sure what is meant by this.
Thanks.
“Nighttime radiation cooling is very dependent on atmospheric water vapor conditions from cloud cover and ambient relative humidity. Low humidity areas like desserts and high elevation locations can generate large temperature drops: “… temperature differences as large as 400C have been measured for thermally insulated approximate black bodies in the Altacama dessert in Chile” (Eriksson and Granqvist).”
https://asterism.org/wp-content/uploads/2019/03/tut37-Radiative-Cooling.pdf
Has anyone measured night time cooling as a function of humidity?
The above paper [https://asterism.org/wp-content/uploads/2019/03/tut37-Radiative-Cooling.pdf] looks at cloud cover.
Night time cooling as a function of humidity would be a direct measurement of the GHG effect, and could be used to calculate the effects of CO2.
Is there some reason this hasn’t been done?
Angstrom on radiation from the humid atmosphere.
http://adsabs.harvard.edu/pdf/1916PPCAS…5…78A
Also re.dry adiabatic.
As I understand it, this not the reason for the theoretical 60ºC average pulse of heating at the surface. It would be from a radiative resistance to the real power of sunlight at the surface through a motionless humid atmosphere to create a tendency for a super adiabatic lapse which automatically creates instability for convection to occur.So it never actually happens.
Bob,
We have set emissivity to value one for the simple reason that it maximises the requirement for an atmospheric greenhouse effect.
In their 1997 paper K&T comment as follows:
From this statement we can be absolutely certain that the following fluxes as shown in Figure 7 are surface cooling effects:
Thermals 24 W/m^2,
Evapo-transpiration 78 W/m^2
and that in the absence of these mass fluxes the radiating surface in the K&T model would be held at a higher global average surface temperature.
What we have attempted to demonstrate is that even in the K&T analysis there is a mass motion flux and working on the principle that what goes up must come down it follows that at least some of the 324 w/m^2 Back Radiation flux in figure 7 must in fact be mass motion recirculation of thermal flux.
Bob,
There is a clear and critical distinction between diabatic (gross Earth model) and adiabatic (internal system model) processes.
I get that you see a critical distinction, but it is not yet at all clear to me.
I’m aware that adiabatic generally refers to a reversible thermodynamic process without heat gain or loss, and without a change in entropy. A diabatic process is one that’s not that.
However, I am not following how you are using these terms in the current context.
The distinctions “gross Earth model” vs. “internal system model” are intriguing. But, again I don’t know what you mean.
Would you be willing and able to unpack these for me?
This and your follow-up comment seem to relate to my follow-up blog post, not this one. It might make more sense to discuss these issues in the comment threads for that blog post.
Most of the energy “absorbed” by various so-called greenhouse gasses (GHGs) is NOT re-radiated (scattered) in all directions. It is transmitted by conduction (direct collision) almost immediately to increase the latent heat of neighboring air molecules, only a tiny portion of which are capable of re-radiating. Furthermore, all the radiating done by CO2 molecules in the air cannot be apportioned to simply equating to 100% absorption of ground based IR, but must be apportioned from two sources, the amount directly re-radiated PLUS the amount generated from conduction (direct collisions) with faster moving molecules of air that excite the symmetrical vibration of the so-called GHGs that were not previously excited. Furthermore, when convection has caused the warmed air to rise, and raised the elevation at which this re-radiation occurs, the down-welling portion of air that CAN radiate downward, now has a much thicker atmosphere to penetrate for that re-radiated energy to strike the ground. And we haven’t even begun to discuss the additionally confounding energy transfers de to evaporation and condensation which are also carried by gasses rising due to convection. Layers…. HAH! I spit on your layers.
Much of what you describe names things that happen, but you’re making it seem unnecessarily complicated. (Some of your terminology is off too. Gas molecular collisions aren’t generally referred to as “conduction”; that’s just part of how energy is thermalized in a gas. And “latent heat” is specifically about water vapor.)
The bottom line covering most of what you say is: radiation absorbed by CO₂ warms the mixed gas that contains the CO₂. A mixed gas containing CO₂ that is slightly warmer will radiate slightly more.
As for convection, yes, that does change where the atmosphere will have what temperature, which affects the dynamics of longwave radiation in some ways. A detailed climate model needs to account for that.
I don’t mean to be tiresome, and I understand that my use of the term ‘conduction’ in this argument might be considered unconventional. Nevertheless, thermalization of a mass, even a mass of air by direct collision IS exactly the definition of conduction. I’m sticking with it. I don’t know, but I think maybe you’re hinting somehow that conduction only occurs at the boundary layers between solid or liquid surface of the Earth, and the gas layer of the atmosphere. If so, no one should think that.
My main point is that the energy that moved away from the solid or liquid surface as 15um IR is REMOVED from the radiation ‘budget’ altogether, and is moved into the thermal ‘budget’ where most of the mass is O2 and N2 and convection rules the day, and massive amounts of energy, now in the form of latent heat, lifts itself away from the surface of the Earth by rising up and carrying the added potential energy of evaporated water with it. Quantum mechanically, I suppose it’s a very difficult exercise to predict what the surface temperature will be because of a few extra parts per million of CO2. But when we model for simplicity, we can clearly presume the null hypothesis to be that any difference will be damn close to zero. Because the extra CO2 just means that the existing energy of the surface will be more efficiently thermalized in a slightly narrower band above the surface, at which point, the warmer air rises up and away from the surface, just as it did before those extra molecules were added. No new energy is added into mix, because that’s all from the sun heating the surface during the daylight. The energy that warmed via IR, absorption and conduction was not trapped in CO2 molecules trading 15um IR energy with each other for all time.
Back radiation budget exercises IMO, turn CO2 scattered light into a sort of perpetual motion machine that both HEAT the N2 and O2 mass of the atmosphere, and yet still miraculously bounce back and re-warm the surface as IR radiation. NO! You can’t use it to do both things, you silly alarmists (this comment isn’t directed at Bob W.).
I don’t have any deep objection to your using the term “conduction” in the way that you do.
There is not a separate “radiation budget” and “thermal budget.” They are (almost) always inextricably linked. There is thermal energy, and sometimes that resides in matter, and sometimes it is transported by radiation.
A mixed gas at any finite temperature can transport heat via convection (of sensible or latent heat) and can also absorb or radiate longwave radiation.
If the concentration of greenhouse gases is low, the mixed gas will be weakly couple to longwave radiation, and if the concentration is high, the mixed gas will be more strongly coupled to longwave radiation.
That macro way of looking at the situation seems to capture all one needs to know, without worrying too much about what happens at the molecular level.
And, for simplicity, we could assume the world is at absolute zero. But, that wouldn’t get us far towards understanding reality.
Your “null hypothesis” is a speculation seemingly based only on intuition. One needs to run the numbers to know how big an effect there is likely to be.
That’s not all that it means.
How CO₂ affects the air near the surface is one of the least interesting things about its impact. Its impact is systemic and emergent.
One way of describing its impact is this. Increasing the concentration of CO₂ raises the altitude at which the atmosphere becomes transparent to radiation in the 14-16 micron band.
The temperature of gas at this altitude will (with some complications) be in radiative equilibrium with space, at some temperature Tx.
If you increase the concentration of CO₂, you increase the altitude where the atmosphere is at temperature Tx. Given a tendency of the atmosphere to have a generally increasing temperature with decreasing altitude, with a certain lapse rate, raising the altitude where temperature Tx occurs can lead to temperatures at all lower altitudes increasing, to maintain the same temperature profile.
This is just one example of a way in which the impact of increasing CO₂ concentrations need not have anything to do with its effect on near-surface air.
I get it. You really want to be sure that energy is being conserved. What you think you’re hearing sets off alarms, sounding like someone isn’t paying attention to energy conservation. You want no part of that.
Makes sense.
I wonder if you can look at the situation from other people’s perspective.
Some people pay extremely close attention to details. They’ve been very careful with the rigor of their analysis. Energy is clearly being conserved, and the Second Law of Thermodynamics is clearly be honored.
Yet other people keep showing up, saying “That doesn’t look right! You’re cheating! That’s obviously wrong!”
And many are never, ever, are willing to actually look at the details. Nor do they offer an alternative analysis of their own that rigorously and correctly attends to all the relevant details.
They simply refuse to believe that things can work in the way they interpret things being described. Yet, often, they’re consistently misunderstanding something that was said.
This creates a tragic impasse. Yuck.
If you’re willing to talk through the details, I’m happy to do that, to unpack the particular moment in the analysis where you think something incorrect is being said. Then we could unpack that. Maybe one, or both of us, might learn something.
* * *
In my energy-recycling diagrams, Figures 2, 3, and 4, energy conservation and the Second Law of Thermodynamics are both honored.
Energy fluxes from the surface to the atmosphere can be carried by convection or radiation. It doesn’t matter. Either process contributes to warming of the mixed-gas atmosphere. Some fraction of that warming leads to longwave radiation being emitted, which cools the air.
So, energy isn’t doing double-duty there. It’s either thermal energy in the air, or it’s radiation, but it’s never both.
Nice work, Bob. Here are a couple of comments:
1) My calculus students always hated infinite series. They wondered if anything real actually involved an infinite series. Here is a good example of something that does.
2) Any time a person tries to explain radiation transfer, the explanation becomes long winded and people stop paying attention. It is an irony, therefore, that to fully understand the Greenhouse effect one has to understand radiant transfer — we resort instead to very simple explanations.
3) In engineering terminology the Earth is a re-radiating panel with a special coating on it to make it warmer. It wasn’t designed this way, but it’s how things turned out. In this sense the Earth is like a solar panel intended to make warm water.
Infinite series is the reason I washed out of a ChE PhD program, and left with my MS!
I got most things the first time. I remember in calculus when infinite series did not compute, and that thought “when will I see infinite series again?”.
Answer was in the 4th semester of Grad School “Advanced ChE Mathematics”. It was a whole semester of solutions involving infinite series! I scored 16/100 on one off the tests!
Your simple model (and apparently W&M’s) ignores reflection of both the incident SW radiation and the recycled LW radiation.
Neither model ignores reflection of the incident short-wave radiation. It’s just not included as an explicit term, because it doesn’t need to be. What I call S is the absorbed solar flux, i.e., the portion of sunlight that is not reflected back to space.
As for longwave… the emissivity of the Earth’s surface is 0.94. That indicates that the surface reflects, on average, 6 percent of recycled longwave radiation. It’s true that my simple model does not take that into account.
That’s one more aspect of it being a “toy model”, which includes only certain aspects of the real physics. It’s one of many simplifications.
ScarletMacaw
Jesus what a trivial reaction…
J.-P. D.
Bob, you said:
Strictly speaking, the long-wave fraction that is potentially re-absorbed by the surface is only 1/2 of the total for a flat Earth with an infinite extent. Because the surface is curved, some of the ‘downward’ radiation will be tangent to the surface of the Earth and escape to space (minus any atmospheric absorption). The higher the radiating layer, the larger the fraction of the downward radiation that will escape to space.
This isn’t critical to your argument, but it does make things a little more realistic if one acknowledges that the downward fraction is an upper-bound. It also demonstrates that the correct calculations require an integration that takes into consideration the altitude of the various hypothetical layers. That is, the assumption of the sum of the infinite series is too high and the equilibrium point is different than assumed.
Clyde Spencer
Maybe you think, before writing, a bit about the fact that the highest altitude for CO2’s activity isn’t 2000 km above surface, but… merely 50 km.
And that therefore, the incidence angle of backradiation reaching Earth is near 180 °, and hence the amount of backradiation around Earth, thus reaching outer space, is absolutely negligible.
Thanks for doing the simple trig math at home 🙂
J.-P. D.
Yes, the cone of depression is only about 1/2 a degree. We can quibble about the meaning and justification of calling a small angle “absolutely negligible.” It is calculable and is about one part in 360. Would you be upset if you had to spend one day a year in prison? Would you complain if your paycheck was 1/360th smaller than what the company had promised to pay you?
I offered a refinement to the statement of the problem where I acknowledged “This isn’t critical to your argument, …”
Maybe next time you should do “the simple trig math at home” before commenting.
Bob Wentworth
Thanks for your excellent contribution, especially for your patient, qualified replies to many opponents.
I’ll have to spend lots of more time into it.
You head post reminds me an article written in 2011 by two French scientists, Jean-Louis Dufresne and Jacques Treiner:
https://www.researchgate.net/publication/275205925_L'effet_de_serre_atmospherique_plus_subtil_qu'on_ne_le_croit
Unfortunately, it has been written in French, and Adobe is doing its best to prevent us from easily transferring parts of PDF documents into Google Translate’s windows, for example.
A simplified resumee exists in pasteable HTML form however:
https://www.centrale-energie.fr/spip/spip.php?article151
Merci beaucoup
J.-P. D.
Merci.
I appreciate the reference. I haven’t taken the time to try to translate, but it does appear that it covers some similar territory, and more.
🙂
Bob
Job
Take an imaginary Earth model with no CO2 produced r H2O in its atmosphere say only nitrogen.Compared to real, this would still be heated by solar radiation. Without radiative gases to cool it, what temperature would it reach?
Seems to me that you have to include nitrogen and oxygen as able to conduct and lose heat. Geoff S
Without any greenhouse gases, the atmosphere would have very little capacity to cool the surface.
I recently realized, that without greenhouse gases there wouldn’t be any convection. (Greenhouse gases provide the elevated “heat sink” needed to provide a “thermal driving head” to power natural convection.)
So, the surface could transmit heat to the atmosphere only via conduction.
But, without greenhouse gases, the atmosphere would have no means of cooling itself. (It couldn’t radiate any power to space.)
So, an atmosphere without greenhouse gases would have only minor effects on the temperature of the surface, compared to the temperature it would experience in a vacuum.
Probably the most important effect it would have would derive from the way that atmospheric pressure increases the thermal conductivity of dirt.
The devil is in the details, not the higher order vague toy models.
A) CO₂ is not homogenous throughout the atmosphere.
The higher the elevation, the lower the content of CO₂. CO₂ has been known to pool and suffocate humans and wildlife. Without winds and storms to keep mixing the lower atmosphere, oxygen based life would be difficult.
B) CO₂ longwave radiative interactivity is miniscule.
C) CO₂ emissions suggest the molecules have reached a temperature where emissivity is possible.
None of this affects your toy models or atmospheric layers. It does affect any claims that atmospheric CO₂ prevents or reduces longwave radiation to space.
As long as one realizes that H₂O is the main driver for all of the longwave radiation absorption and emissions as depicted.
There are some serious problems with this model. For one, the “f” factor in Figure 5 is NOT a constant. Assuming that IR photons at a wavelength that can be absorbed by CO2 or water vapor are emitted at an intensity Io from the earth’s surface, the fraction of these photons absorbed is proportional to an absorbance coefficient times the number of molecules of GHG per cubic meter.
Even if the mole fraction Yc of CO2 in the atmosphere is assumed constant, the number of CO2 molecules per cubic meter is proportional to YcP/RT, where P is atmospheric pressure and T is absolute temperature. It is well known that atmospheric pressure decreases with altitude z, and at the adiabatic lapse rate, T(z) = To * [P(z)/Po]^[(k-1)/k], where k is the ratio of specific heats Cp/Cv of air, and To and Po are the temperature and pressure of air at the surface.
Since k for air is about 1.4, the absolute temperature at altitude proportional to absolute pressure to the 0.29 power, and the ratio YcP/RT decreases proportional to absolute pressure to the 0.71 power. This means that, for a GHG at a constant mole fraction throughout the atmosphere, more IR radiation is absorbed close to the surface of the earth than at higher altitudes, and “f” decreases with altitude.
Unlike CO2, water vapor (a far stronger IR absorber than CO2) is not evenly distributed in the atmosphere–it is at higher concentrations near the surface, but at low concentrations above any cloud layer. Absorption by water vapor in the lower part of the atmosphere can “screen out” IR radiation (at wavelengths absorbed by water vapor) so that it never encounters a CO2 molecule, which minimizes the relative effect of CO2. Over a tropical ocean, water vapor concentrations can be greater than 10,000 ppm (1 mol%), or more than 25 times CO2 concentrations at the surface.
Another problem is to determine how absorption of IR radiation by GHG molecules can warm the atmosphere. If a GHG molecule (CO2 or H2O) absorbs a photon of IR radiation, an electron is raised to a higher energy state, and one of two things can happen. If the molecule re-emits another photon of the same energy in a random direction, on average almost half the photons will radiate toward the earth, and the rest will radiate toward space, but the net kinetic and rotational energy of the GHG molecule is not changed, and on the macro scale, there is no change in temperature.
However, if a GHG molecule absorbs an IR photon, then collides with another molecule (such as N2 or O2, the most common molecules in air), it can transfer its additional kinetic energy to the other molecule, and NOT re-emit a photon. On a macro scale, this would increase the temperature of the layer in which the GHG molecule is located, and decrease the total flux of IR radiation to space, without any “back radiation” toward earth.
This effect would also result in the outward-bound heat flux Q decreasing with altitude.
Also, since the nitrogen and oxygen molecules in the atmosphere do not absorb nor emit IR radiation, the factor “f” has to be proportional to absorption coefficient times YcP/RT (plus a similar factor for water vapor), integrated over the part of the spectrum where CO2 and water vapor absorb IR radiation. Depending on where this range of wavelengths (or wave numbers) occurs on the Planck function, this may not be proportional to T^4.
In summary, the effect of additional CO2 on warming the atmosphere is based on the part of IR radiation that is not absorbed by water vapor, that is absorbed by CO2 molecules and not re-emitted, and that is not absorbed by CO2 molecules lower in the atmosphere.
It’s true that optical depth varies with altitude, so that for layers to have roughly similar effect, you’d need to use thicker layers at higher altitudes. The factor f is only partly about optical depth, it’s also about what wavelengths do and don’t absorb. Still, it’s true that f will vary somewhat.
Most of the details you name are addressed by the caveat “It’s a toy model, not intended to reproduce all the intricacies of the atmosphere.”
No. The relevant 15 micron CO₂ absorption band involves a transition to a molecular flexing vibrational state. No electron excitation is involved. Typically, the vibrating CO₂ molecule collides with another molecule in the mixed gas before it re-radiates. But collisions in the mixed gas are constantly leading to some CO₂ molecules vibrating, and being capable of radiating.
When a vibrating CO₂ molecule radiates, it stops vibrating, and this incrementally cools the mixed gas.
You’re looking at the details too finely, in a way that introduces errors in the description and the conclusions.
The bottom line is that if a mixed gas containing greenhouse gases absorbs a photon of radiation, it incrementally warms the gas. A warm mixed gas is always spontaneously radiating in all directions, and it radiates slightly more when it is slightly warmer. Radiating a photon incrementally cools the mixed gas.
Well, what you describe only has this effect because systemic errors in the description create this outcome.
In equilibrium, it cannot be that the average, net outward-bound heat flux Q changes with altitude (summing over all modes of heat transport), except to the extent that some insolation is absorbed in the atmosphere. (This atmospheric absorption means that the average, net outward-bound heat flux Q must increase somewhat with altitude.)
Well, in the toy model, the layers are assumed to be sufficiently optically thick that the incremental absorption per unit length no longer matters.
But, ultimately, “f” and “N” are a little too simplistic to capture all the details of the radiative physics.
Agreed. Atmospheric radiation scaling as T⁴ is a crude over-simplification.
Not actually true.
Consider the results of my N-layer toy model. In that model, every layer is assumed to be entirely opaque to the wavelengths that are absorbed. So, for layers 2 through N, all the longwave radiation from the surface that could be absorbed has already been absorbed. Yet, layers 2 through N still contribute to warming of the surface.
Today’s scientists have substituted mathematics for experiment, and they wander off through equation after equation, and eventually build a structure which has no relation to reality. N.Tesla couldn’t be more right.
[[A particular layer of the atmosphere is assumed to be at a temperature, T₁. This temperature is the temperature that equalizes the flows of energy entering and leaving that layer. According to the diagram, the layer will emit long-wave radiant energy equally in all directions, with a flux fσT₁⁴ being sent upward and an equal flux being sent downward.]]
This paragraph along with the whole nonsense diatribe is pure dodo climate science.
You can immediately throw it in the trash when you see imaginary atmospheric layers with T^4 arrows coming out of them up and down. This is total ignorance, because gases don’t emit black body radiation, only photon by photon radiation at specific wavelengths based on absorption and reemission. A black body must be solid or liquid, and its number one power is the ability to absorb and emit radiation at all wavelengths. In the Earth-Sun climate system, only the Sun and the Earth are black bodies. The atmosphere doesn’t qualify. Their total power output over all wavelengths comes nowhere close to anything times T^4, and indeed doesn’t depend on T, only the incident photons.
End of this dodo line of reasoning.
I already blocked Wentworth on Quora after finding him pushing every IPCC hoax and then denying any connection with them while coming back over and over palming himself off as an expert. It didn’t take long to find out that his understanding of radiative physics is nil, especially when he failed to even mention key laws until I taught him.
Who am I? Go ahead and check me out. Do you believe that Wentworth has any credibility? Would you like to learn real climate science that destroys every IPCC lie? The only place to go is my free Climate Science 101 course that I spent years perfecting to cover every key physical law methodically and answer all objections. Until you master it you’ll always be a climate science dodo, open to IPCC-twisted brain manure dumps like this one.
http://www.historyscoper.com/climatescience101.html
For anyone interested, I’ve written a fairly popular deconstruction of one of TL Winslow’s main ideas.
Not a deconstruction, an exposition of rank ignorance, like the insane claim that gases emit T^4 radiation.
No matter how many times I disprove his nonsense, it bounces off.
[[Notice that the radiation emitted by CO₂ is still centered around a wavelength of 15 μm. However, for CO₂ at 0ºC the total radiance emitted is 4.4 times as large as it is for CO₂ at -80ºC. Surely, radiation from CO₂ at 0ºC will have more warming effect than radiation from CO₂ at -80ºC given this more than four-fold increase in power!]]
Duh, -80C is -80C. Power is irrelevant. And what is 0C CO2? That’s a gas, not a solid. Atmospheric CO2 only reemits 15 micron photons absorbed from the surface, and has no total radiance as such unless you’re considering the entire air column. Is he trying to treat gas as solid again, claiming that CO2 spontaneously emits radiation based on its temperature? ROTFL.
He then claims that 15 micron radiation isn’t at -80C by regraphing Planck’s Radiation Law in terms of power/Hz instead of power/micron. He never ‘gets’ that it’s not power vs. Hz. vs. power vs. micron. The power/Hz curve is basically the slope of the power/micron curve, so of course its peak is way different, but Nature still puts most of its dry ice photons around 15 microns, and atmospheric CO2 still can only absorb and emit 15 micron photons one at a time, not in a T^4 Planck power-wavelength curve that has warming power.
Why did WUWT allow this charlatan to publish a whole article full of crackpot physics that licks IPCC butt? I hope there’s a good answer.
My opinions as a thermo-mechanical engineer is that you can’t neglect the main heat exchange mechanisms just because they are more complicate to understand than simple radiation between gray surfaces. Extract too much information from this toy model without the main mechanism of heat transfer in the troposphere at your own peril of remaining ignorant.
It is true that toy models are useful to further understandings of physics, but not every toy model furthers the understanding of atmospheric thermodynamics of planet Earth.
If you were honest you wold at least try to put a number on the amount of heat that is transported by convection to the cloud tops (caused mainly by raising vapor) in relation to the radiative fluxes. Of course this factor is not homogeneous changing greatly by latitud.
This purely radiative model is only accurate near the poles where there is (almost) no incoming radiation. In the tropics, where most of the incoming heat is absorbed the dominant mechanism is convection that transfers heat upwards into upper layers of the atmosphere and pole-wards.
The tropics are the key regions of earth atmosphere and the toy model does’t cut it there.
Radiation and convection are both very important heat transport mechanisms in the atmosphere.
I emphasized radiation in this post because that is one of the most widely misunderstood aspects of the Earth’s thermodynamic system.
You can’t build a correct understanding of the Earth’s thermodynamics if you understanding of the radiation piece is broken.
Yes, you ultimately need to consider it all.
* * *
By the way, I just recently came to understand that, in the absence of greenhouse gases, there wouldn’t be convection either. (Radiation by greenhouse gases provides the elevated heat sink needed to generate the “thermal head” needed to power natural convection.)
For what it’s worth, for Figures 2, 3, and 4 of my essay, convective effects are included.
But, as I’ve said, I was trying to improve understanding about what radiative energy recycling effects can and cannot do, not model the actual atmosphere.
The thermodynamics of the stratosphere are just as important as the thermodynamics of the troposphere in Earth’s thermoregulation.
And in the stratosphere, radiative effects are dominant.
This supposed back radiation mechanism that increases its own energy and increases its own temperature is a mathematical psychobabble describing an over unity perpetual machine like energy amplifier that catches back its own emitted radiation and ads it up to itself.
It is no different than eating a thousand calories lunch, then vomiting it, then eating it again, and then claiming you are getting fatter because you doubled you calories intake.
Good exercise of ideological mathematics with no connection to physical reality. How is that no one of us, poor thermal engineers, are able to design devices that take advantage from this stunning, 1st-Law-breaking, radiant energy recycling principle ? If this is science, how deep low has it fallen
These principles are very much used in engineering:
It only looks like there is “1st-Law-breaking” if you’re unwilling or unable to pay attention to details.
Just because something isn’t familiar to your way of thinking doesn’t making not real.
mmm…isn’t familiar to my of way of thinking ?
Please show us any solar panel that uses, say, 10 layers of separated glasses in order to recycle the long wave radiation and increase, by a factor of 1.5 (or whatever) its watts output. That would seem straightforward, if such ideological math would reflect real physics.
Or : how is that you don’t feel your face warming when standing in front of the mirror ? Your face radiates approximately 500 W/m2 and your mirror reflects it back to you. The wall around the mirror only provides 400 W/m2 (assuming it has a temperature of 18°C).
You should well feel that difference, when moving from wall to mirror !
With a 2 m2 mirror you would have a nice “recycling” heater, warming you with (500-400)*2 = 200 W, a nice gift coming from…yourself. Move yourself closer to the mirror…and feel the heat !
You are misunderstanding what is being claimed.
A barrier that passes shortwave but impedes longwave radiation leads to a temperature increase. This is relevant when building a “solar panel” of the sort designed to heat water.
A barrier that passes shortwave but impedes longwave radiation does not increase the power that can be extracted from the system.
Thanks for the interesting question.
First, let’s check if a mirror reflects thermal radiation. Most mirrors are made with aluminum coating the back side of a sheet of glass. Aluminum does reflect longwave radiation. Common glass is transparent to longwave radiation. So, I accept the premise that a mirror should reflect thermal radiation.
So, what happens if you stand in front of a mirror? If you stand 1 meter from a mirror, the effect is essentially the same as another person standing 2 meters away from you. I don’t know about you, but I can’t feel the warmth of another person’s body from that distance.
However, I just tried putting my face about 1 cm from a mirror, and I did feel warmth.
Then I tried other surfaces. Putting my face next to a white wall, I also felt some warmth. However, putting my face next to a dark brown piece of furniture, I felt no warmth. I infer that the white paint had significant ability to reflect longwave radiation, but the furniture did not.
In the normal geometries for using a mirror, the inverse-square law applies. Not much of your face’s thermal radiation is reflected back to it by a flat mirror unless you are very close to the mirror.
The predictions concerning a barrier impeding longwave radiation leading to noticeable warming generally apply to situations where that barrier covers all or most of the paths for longwave radiation to escape. That’s never going to be the case for a flat mirror on one side of you, even if it is held quite close.
However, a “space blanket” is an example of a barrier impeding longwave radiation which is typically used in a way that blocks most paths for longwave radiation to escape. “Space blankets” are specifically used to warm people, and, to a degree, they are effective in achieving this purpose. (Their effectiveness is reduced to the degree that they still allow convective air flow. And more layers of space blanket can be more effective, if one gets the air flow down enough that a better radiant barrier matters.)
In a more obscure and personal example, my father once worked on a project that involved a small plutonium heat source driving a Sterling cycle heat engine. The plutonium heat source was wrapped in many thin layers of radiant barrier. This provided very effective insulation, and led to a large temperature difference to drive the heat engine.
1) By increasing temperature, you are also increasing internal energy (U=m*Cp*DT), aren’t you ? Thermodynamics 101. If you increase energy, there is more energy that you can extract from the system.
2) Be honest with yourself. No, you don’t feel any warmer when close to the mirror. Go very close and you should feel it. You don’t. The mirror doesn’t heat you by radiating back your own heat. Try this experiment with two light-bulbs : two identical bulbs, except for the glass. One crystal clear, the other frosted. Frosted glass “traps” some of the light, heat, energy, inside. Crystal clear glass doesn’t. What is the effect of trapping this light ? Based on your theory, you would expect the filament to become hotter, so you should see it by the color temperature changing. It’doesnt change. The filament does not increase its temperature.
3) The problem with your belief is that you treat radiation like if it was convection or conduction. It isn’t. And blankets do not make you warmer by radiation (https://phzoe.com/2020/04/08/do-blankets-warm-you/).
4) I have not enough data to comment on the Plutonium heat source, but if what you claim is true, it seems likely that you are seeing the effects of convection/conduction, rather than radiation.
There is more energy that you could extract, transiently, but it’s not sustainable. The amount of energy that you could sustainably extract doesn’t automatically increase just because you increase the internal energy.
Suppose, for any type of conserved quantity (energy, mass, etc.) you have a flow rate 𝚽 into a system and an equal flow rate out of the system. The quantity of the conserved quantity that accumulates inside the system can be characterized as U = 𝚽⋅𝜏 where U is the quantity of that which is conserved, and 𝜏 is the mean time the stuff resides in the system. You can increase the amount of stuff by increasing that residence time. But, you can still sustainably only get stuff out of the system with a flow rate 𝚽.
As an example, consider a river that flows into a lake and then out again. How much water can you sustainable withdraw from the lake? You could take water out at a rate exceeding the flow rate for a little while, but that wouldn’t be a steady-state condition, and wouldn’t be sustainable. If you want a sustainable flow of energy, you cannot take water out of the lake at a faster rate than whatever is flowing in.
The rate at which you can remove water is limited by the flow rate in. But, that flow rate does not limit how much water can be accumulated in a lake (aside from issues of evaporation).
Do you believe that this is true for water?
It is mathematically identical to consider a flow of energy as it is to consider a flow of water. Energy flux into a system determines the rate one could sustainably withdraw, yet internal energy/temperature is not inherently determined by that energy flux alone. If you do something to increase the residence time of the energy in the system, you can increase internal energy/temperature. (That’s what’s going on with the “energy recycling” described in this blog post.)
I double-checked. Still happens the same way I reported.
The wattage of a filament is determined by its resistance. You can increase resistance either by making the filament longer or thinner. These have different implications regarding how much energy per unit area the filament radiates. This allows a manufacturer to tune the color temperature, independent of wattage.
I don’t accept the premise that one can obtain light bulbs that are truly identical except that one uses frosted glass and one doesn’t. The designs may look similar. But, the manufacturer can easily tune the filament design of the two bulbs to make the color temperatures equal, despite different thermal dynamics in the two cases.
In many ways, it is similar. They all convey heat across a temperature difference in a way that increases heat flux as the temperature difference increases:
Conduction: 𝚽 = ∆T⋅R where R is thermal resistance.
Convection: 𝚽 = h⋅(∆T)ᵇ where h is a heat transfer coefficient and b is a scaling parameter.
Radiation: 𝚽 = 𝜀𝜎F⋅((T₀ + ∆T)⁴ – T₀⁴) ≈ 4𝜀𝜎F⋅∆T [which needs to be tweaked if the materials are dissimilar]
The mathematics of heat flow is not dramatically different for these different modes of heat transfer.
What convinces you that they must be treated as totally different?
Go back to U = 𝚽⋅𝜏, as mentioned above. For a given energy flow rate, you can make something warmer by increasing the residence time of the energy. This is a general truth, and it doesn’t matter which heat flow mechanism you’re considering. (The link you reference is applying faulty logic.)
“Space blankets” are used as emergency blankets because they are effective at keeping people warmer. If it was just about convection, they could just use a film of plastic without bothering to make it reflective. They don’t. They make them reflective, because it increases their warming power.
Again, if it was about “the effects of convection/conduction” then there would be no reason for the designers to bother using reflective materials in the layers. Yet, they did use reflective materials.
Your posts keep becoming longer and longer, but I think you are missing the main point : empirical tests show your theory is wrong.
Mathematics is not bound by the laws of physics.
The two GE lamps I’m referring to are identical – according to the data sheet. The filaments are identical (type CC-8). The wattage are identical (200W). The color temperature are identical (2900K). The only difference is the light provided by the soft white glass that is lower (3405 lumen vs 3780 of the crystal clear) due to glass absortion. Yet filament temperature does not change by 1 degree.
“Backradiation” alone – if at all exists – isn’t able to heat-up the emitting source. I leave that to theorethical physicists to explain why. It should not be that difficult. Radiation is inherently different than other heat exhange mechanisms.
You can do the experiment using GE lamps models 16069 and 15585. I can send you the product datasheets if you need them.
It sounds like things seem pretty clear to you, and it would be nice if I wasn’t seemingly so dense and unable to see things the way that you do.
That sounds frustrating.
I’m doing my best to understand.
It’s frustrating to me as well, that you haven’t been able to see my perspective.
I’d like to figure out why we are seeing things differently, so that maybe we can achieve some sort of shared reality.
Towards that end, I appreciate you offering a concrete example.
It was fun to work through the math for the relevant physics. The prediction is that the filament in the frosted bulb should be 0.49K warmer than the filament in the clear bulb.
Since the manufacturer reports color temperature only to the nearest degree (and I suspect the actual precision is coarser than that), this prediction is consistent with the available data.
The light bulb example does not support the assertion that “empirical tests show your theory is wrong.”
* * *
If you’re certain that radiative heat-trapping cannot lead to warming, I’m guessing that’s pretty frustrating to hear.
Maybe you could find a different example that would support your hypothesis?
I’ve sometimes been convinced I was wrong. I publicly announced that I was wrong about an analysis of mine in a recent blog post.
I’m willing to be convinced, based on the evidence. Are you?
That’s true for mathematics in general. But, the laws of physics have been codified in mathematical form. The mathematical formulation of the laws of thermodynamics has been tested empirically for over 150 years and have never, even once, been found to be wrong.
This is equally true for radiative heat transfer as for other portions of thermodynamics.
(Sometimes erroneous calculations have been done, but that’s different than the math or physics themselves being wrong.)
As a theoretical physicist, I regret to tell you that you seem to be mistaken in your belief (that “‘Backradiation’ alone… isn’t able to heat-up the emitting source”), based on everything I understand about physics.
As for doubts about whether backradiation “at all exists,” it’s not rocket science to measure it. Here’s one paper that shows (see Figure 3) the data for atmospheric downwelling longwave radiation as a function of time of day and month of year, based on measurements done in Oklahoma.
The light bulb example led me to some physics that I hadn’t previously thought about. That relates to the importance of the “view factor” in radiative heat transfer.
In the case of a light bulb, the radiation emitted by the filament is 100% “viewed” by the glass bulb. But, for the radiation emitted by the interior of the glass bulb, only 0.37% reaches the filament (based on an analysis of the manufacturer’s specifications for the particular bulbs in question).
It is this difference in “view factor” that leads to the frosted glass bulb being not very efficient in warming the filament.
A light bulb and the Earth are different in this regard. The “view factor” between the atmosphere and the surface of the Earth is essentially the same (100%) in both directions. This geometric difference means that atmospheric heat trapping is relatively more efficient at warming the surface, while heat trapping by a frosted light bulb is relatively less efficient at warming the filament.
Good point, I agree with your conclusion that due to areas/view factors ratio, the “back radiation” filament heating (if existed) would be almost meaningless anyways. However here are a couple of experiments that arrive to the same result in a much more cogent way :
The error of your theory is that your found “mathematically compliant” solution is “unstable”. From 1st LOT dU=mCpDt=Q+W, steady state (equilibrium) means dU=0 => dT=0. Since obviously W=0 (no work being done) then this involves Q=0 i.e. the two “plates” tend to an equilibrium condition with zero heat exchange (Q=0) between the two, just like when you put in contact two pieces at different temperature. The colder body, will tend to increase its temperature until it becomes equal to that of the hotter heated body.
I’ll take the parts of your comment one at a time, since there is some work involved in digesting each part.
Here’s a slightly better site with the same Greenplate experiment report. (The other site has some broken graphics, in my browser.)
I wish that people “debunking” a theory would take the time to figure out what the theory they are trying to disprove actually predicts.
The theory predicts that, in the 10-minute run of the experiment, Arrangement 6 should produce a higher temperature than Arrangement 5 by a little less than a degree. That appears to be entirely consistent with the measured results.
My spreadsheet simulation of the experiment shows that the temperature of the second plate strongly lags the temperature of first plate. As a result, it takes around an hour to get to the stage where the second plate is adding 25℃ to the temperature of the first plate.
The experimenter ran the experiment for too short a period. As a result, the falsification is false.
The “experiment on back-radiation” demonstrates painfully confused thinking.
There doesn’t seem to be anything particularly surprising in the experimental results. Yet the author has the odd idea that somehow he has disproved mainstream understandings of the impact of back-radiation.
He writes:
These words are a nonsequitur because the author falsely equates “back-radiation results in the surface being warmer than it would otherwise be” or “back-radiation is absorbed by the surface” with “thermal radiation from the atmosphere is larger than thermal radiation from the surface.”
The latter is not what anyone claims to be true. So, falsifying this proves nothing.
He also writes:
Again, this is a nonsequitur, asserting that back-radiation “warming up the surface” has an implication that it doesn’t have, then declaring victory when that falsely-attributed prediction is falsified.
* * *
All the author has proved is that he doesn’t understand what is meant by the idea of back-radiation contributing to the surface being warmer than it would otherwise be.
I assume you’re talking about the “green plate” experiment?
Let’s pretend it’s a 1-dimensional problem, pretending the heat lamp is a little more all-encompassing of the front of Plate 1 than it actually is.
Then, the two cases in the experiment have heat flow that looks like this:
CASE A:
[Heat source] == Q ==> [Plate 1] == Q ==> [Heat sink]
CASE B:
[Heat source] == Q ==> [Plate 1] == Q ==> [Plate 2] == Q ==> [Heat sink]
The heat source is the heat lamp. The heat sink is the environment surrounding the apparatus.
Yes, the total dQ for Plate 1 is zero, but this is a result of a +dQ from the heat source and -dQ leaving Plate 1.
In Case B, there is a net heat flow from Plate 1 to Plate 2.
In Case A, the heat flow out of Plate 1 is σ(T1⁴ – Te⁴).
In Case B, the heat flow out of Plate 1 is σ(T1⁴ – T2⁴).
Because T2 > Te, it is necessary for T1 to be larger in Case B than in Case A in order to achieve the same heat flow.
QED.
In the depicted scenario, that can’t happen, because then Plate 1 would not be able to get rid of its heat through Plate 2.
As I’m guessing you will have gathered, from my perspective, each of the “experiments that arrive to the same result” were deeply flawed, and didn’t justify the conclusions they arrived at.
Where does that leave us?
I come back to the observation that reflective membranes are used as “emergency blankets” and as an integral part of building insulation.
As well as the fact that radiative heat transfer has been understood for nearly 200 years and the principles of analyzing radiating systems are extremely well-established and well-tested.
But, I suppose “your mileage may vary.”
Thoughts?
It seems what is of most interest is what the thermal profile of the atmosphere is at the “top of the atmosphere”, by which I mean the level at which most of the long wave radiation emitted upward escapes without being re-absorbed. Since there are many different greenhouse gases that level will vary by the wavelengths of interest but CO2 is one of the highest significant absorbers for longwave radiation so that is worth focusing on.