Andrew,

I think you can use a thought experiment to determine that reflected radiation will not lead to some sort of thermal runaway, your 2.a. Let’s say we have a plane blackbody surface (opaque by definition) that is being irradiated, has no other energy input and is at steady state at a particular temperature To. It will then emit and absorb σTo^4. If we now change the emissivity to 0.98, then the surface will emit less radiation, 0.98σTo^4 and reflect 2% of the incoming radiation and will absorb 98% of incoming radiation. Since we have postulated that steady state exists, then the temperature of the surface won’t change because it will still emit the same amount of energy that it absorbs. Emission plus reflection, however, is still equal to σTo^4.

This is also why a cavity with a small hole is a good approximation of a blackbody. The radiation flux in the cavity will be almost the same as for a blackbody even for an interior with a relatively high reflectivity, except for gains or losses through the hole.

Obviously things will be more complicated for a surface that’s irradiated by a solar spectrum and radiates to and absorbs radiation from an atmosphere that is not completely opaque, but the principle is the same.

]]>P = eoT^4 is the formula for the flux of radiation emitted by a gray-body. If the atmosphere and surface both behaved like gray-bodies, then the upward flux emitted by the surface would be eoTs^4 and the downward flux emitted by the atmosphere would be eoTa^4 and the net transfer of energy from the surface the atmosphere (which is called heat in thermodynamics) would be e_s*o*Ts^4 – e_a*o*Ta^4. (The emissivity of the surface e_s and the atmosphere e_a are different.)

By saying “if the atmosphere and surface behaved like gray-bodies”, we are proposing a MODEL for how our climate system behaves. Aside from the problem that temperature varies with latitude and altitude, a gray body is a lousy model for a semi-transparent atmosphere composed of gases that emit and absorb very differently at different wavelength (and negligibly at some wavelengths). So you need to be careful how far you trust this model. The model works great for some phenomena, but not others.

Many skeptics are confused about how radiation can travel from the colder atmosphere to the warmer surface, when the second law of thermodynamics says HEAT flows from hot to cold. They refuse to acknowledge that HEAT refers to the net flux in the case of radiation. Instead, they have proposed an absurd “alternative reality”, where both emitting surfaces and the radiation traveling between those surfaces somehow “know” what their temperatures and emissivities are and magically arrange for a one-way flux of photons from hotter to colder with an intensity of eσ(T1^4-T2^4). This formulation ignores the fact that two different emissivities are involved. Some believe that interference may be involved, but interference occurs only with coherent radiation from a single source. This alternative reality guarantees that heat will flow from the warmer surface to the colder atmosphere. This “alternative reality” is extremely appealing, because it allows skeptics to claim that the presence of more GHGs in the atmosphere doesn’t change the rate at which the surface radiates away the energy acquired by absorption sunlight.

Warning: As soon as I mention an increase in GHGs, we are encountering a situation where a gray-body model for the atmosphere can create confusion. Usually we think of emissivity as parameter that varies from one material to another, but doesn’t vary with the amount or thickness of the material. In the case of our atmosphere, increasing the amount of GHGs in the atmosphere increases the number of thermal infrared photons traveling from the atmosphere to the surface (a higher emissivity in a gray-body model) and decreases the number escaping to space from the atmosphere (a lower emissivity). This happens because photons are both emitted and absorbed at different altitudes with temperatures and densities. Technically, a gray-body model for a non-homogenous atmosphere has an “effective emissivity” based the temperature you assign it in your model and its GHG concentration. Some phenomena, like upward and downward fluxes of radiation, can only be fully understood by using radiation transfer calculations (Schwarzschild’s equation).

Everyone with a technical education learns the physics of the macroscopic world: Newtonian mechanics and the laws of thermodynamics. Most are told that the physics of the microscopic world of atoms, molecules and photons – quantum mechanics – is radically different. Few learn statistical mechanics, a difficult branch of physics and chemistry that explains how large numbers of molecules and photons following the laws of quantum mechanics produce macroscopic phenomena such as temperature, pressure, entropy, and heat flow from hotter to colder. The laws of thermodynamics don’t control the behavior of individual molecules and photons – those laws are a CONSEQUENCE of large numbers of molecules and photons obeying the laws of quantum mechanics. The laws of quantum mechanics say that a single photon can be emitted from a GHG molecule in the atmosphere and absorbed by the surface. The concept of temperature is only defined for a large groups of molecules. Heat flows from a large warmer GROUP of molecules on the surface to a large colder GROUP of molecules in the atmosphere, but individual photons are traveling both ways between individual molecules in both groups. Since warmer groups emit more photons than colder groups (and absorptivity equals emissivity) heat flows in the correct direction.

]]>Andrew,

1. There’s a simple formula for emission of thermal radiation from a surface:

εσT^{4}

It’s in all the textbooks. The temperature of the atmosphere isn’t relevant.

2. Very low. It depends on the material. Emissivity is wavelength and direction dependent. Absorptivity is equal to emissivity for the same wavelength and direction.

You can see the graphs of different surface types – the emissivity is very close to 1 across the wavelengths of interest. This means the reflectivity is very close to zero.

2a. It’s hard to explain to people who’ve never done heat transfer equations how to do heat transfer equations.

Try reading Heat Transfer Basics – Part Zero – a few examples of heat transfer, simple stuff but often misunderstood.

There’s an online heat transfer textbook that’s free – Lienhard & Lienhard -Heat Transfer Textbook, 3rd edition, MIT. I downloaded it ages ago.

It’s not for everyone – textbooks usually aren’t. But without understanding what’s in the textbook all kinds of crazy ideas can seem sensible.

]]>If All the “Back Radiation” Was Reflected..

In this section, it is discussed what would happen if all the radiation was reflected by the surface then we explore what would happen. I have a few questions:

1) Why do we use σT^4 to estimate up radiation to the atmosphere, the atmosphere is not at 0K, so should we use P=eσA(T1^4-T2^4)?

2) What % of the back radiation is actually reflected? 100% (unlikely as argued), 0%? somewhere in between?

2.a – If we accept that a certain percentage of the back radiation is reflected upwards; have we created a run-away process whereby this reflected radiation is in turn absorbed by the atmosphere and reradiated back down, only for a percentage to be reflected by the surface again ad-infinitum. When does this stop? Do we have to sum the infinite series to determine the up radiation?

]]>Mark and NK: If you go to the Modtran website, you will find that no plausible change in stratosphere ozone will have any effect on DLR.

NK, I didn’t understand much about this paper. In Figure 1 and 2, the changes in reflected SWR and LWR are -0.10 and -0.021W/m2/yr. (Negative values for heat lost by the climate system to space.) If these are SWR and LWR feedbacks to warming over the past four decades (roughly 0.02 K/yr), dividing gives SWR and LWR feedback parameters of -5 and -1 W/m2/K! That would make ECS about 0.5 K/doubling, so something may be wrong.

Looking at the amount of noise in the LWR channel, the slope could easily +/-50%, so this data is not inconsistent with the conventional view that LWR feedback is about -2 W/m2/K (-3.2 W/m2K from Planck feedback plus +1.1 W/m2/K from WV+LR plus weakly positive cloud LWR feedback). LWR has increased from about 237.5 in 1980 to 238.3 W/m2 in 2017 with a STD of about 2.5 W/m2.

If SWR feedback is positive the slope of the reflected SWR vs. time plot in Figure 1 would have to be negative, not positive. SWR feedback is conventionally believed to be about +0.5 to +1.0 W/m2/K. This is way off. However, the spike is reflected SWR is about right (3-4 W/m2) for Pinatubo in 1993 and smaller for El Chichon in 1982. Reflected SWR has grown from about 103 W/m2 in 1980 to 107 W/m2 in 2017 with the value in any 2 hour period varying by +/-5 W/m2.

One hint about the nature the problem is that the data taken every 2 hours was transformed to induce stationarity. This process must have removed the seasonal 8 W/m2 increase in LWR associated with summer in the NH. There are regular seasonal changes in reflected SWR due to the 7% increase in SWR arriving in NH winter in the due to the elliptical nature of the Earth’s orbit and snow cover in the NH winter.

The other thing worth remembering is MERRA is a re-analysis product – changing sources of observations proceeded through a climate model to produce a best fit to all of the data. There are questions about Paltridge’s paper about re-analysis data showing humidity in the upper troposphere falling with time. It would be nice if this data were “right”, but I’m not expecting it to be.

]]>Mark writes: You have just given the “top of atmosphere” explanation again, with which I am familiar. Nullius repeated this above. I quite like that one. It took me a couple of weeks of mulling before I spotted the obvious flaws. So at least it[‘s a bit of an intellectual challenge!”

A lot of words have been written above, so the “obvious flaws” you spotted aren’t clear to me. Could you please be kind enough to copy and paste the key passages above describing those flaws in a reply?

What is clear is that, if the rate of radiative cooling to space across the TOA slows and the rate of incoming SWR remains, then the law of conservation of energy demands that it warm somewhere below the TOA until incoming and outgoing radiation are again in balance.

Mark also wrote: PS, you don’t need to take a Schwarzschild Equation out of context and fudge the variable to prove that upper atmosphere emits less radiation than the surface. It’s a lot colder up there (because of the gravity induced lapse rate), so of course it emits less.

I didn’t take Schwarzschild’s Equation out of context – I am applying it to the real context, our atmosphere is it really is today. While Schwarzschild’s Equation is used to calculate radiative fluxes between grid cells in an AOGCM, it can not predict temperature anywhere that convection also transfers a significant amount of heat – in other word in the troposphere. Temperature is an INPUT used in the B(lambda,T) term to calculate how radiation changes in intensity. The other input is the density of GHG(s) – n. The OUTPUT from Schwarzschild’s Equation is a CHANGE in radiative flux, not any prediction about temperature – such as why it is colder in the upper atmosphere.

As you correctly note, it is colder in the upper troposphere. This is mostly, but not solely, because the atmosphere is unstable to buoyancy-driven vertical convection, where the local lapse rate exceeds a moist adiabatic [gravity-dependent] lapse rate. However, as in noted in my first comment, temperature is never the result of a single mechanism of heat flux – it is the net result of all mechanisms. The word “adiabatic” in “moist adiabatic lapse rate means with no gain or lost of heat (for example, by radiation), which isn’t the case in the troposphere. What we observe on the average is close to a moist adiabatic lapse rate because heat transfer by convection is often significantly faster than by radiation.

Furthermore, at wavelengths in the atmospheric window (ca 800-1000 cm-1), the coldness of the upper troposphere has no effect on outgoing radiation, which has the same intensity as it did leaving the surface.

]]>NK, good find. The extra DSR is probably because of ozone depletion.

]]>Well lets make the target object no bigger than that small area of the focus spot of radiation. Then the target object is hotter than the source, not necessary the sun. As SoD says, transfer from cold to hot is not outlawed . He calls outlawing that is “imaginary”. Therefore temperature higher at the target than the source from focused radiation is not outlawed. What do you think.

]]>Dinero,

Sorry, it doesn’t work that way. For example, you can’t achieve a higher temperature than the sun’s visible surface by simply focusing sunlight on an object. Period. The part you missed is that the object focused on radiates in all directions while only a small fraction of the area being radiated to has a higher temperature.

]]>It may be around 0,8 W/m2. And DSR (shortwave radiation) has increased much more, about 3,6 W/m2. As seen from figures in a paper : Analyzing changes in the complexity of climate in the last four decades using MERRA-2 radiation data. Alfonso Delgado-Bonal et al 2020.

All the change of DLR can be attributed to change of DSR and perhaps some surface warming, which is attributed to change of clouds. A conclusion that can be drawn is that change of CO2 has no effect on back-radiation, in the real world. Or can it be another explanation?

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