A Rose by any Other Name Would Still Be Non-Linear

Shakespeare was a pretty good communicator. I do a good job with my audience, fishermen. When it gets to academic communication, I need a Redneck to geek translator.

I say frame of reference is the first consideration in thermodynamics, the geeks think I am miss applying the meaning of frame of reference. WTF?

I say increasing the thermal conductivity of air changes the rate of heat flow, I get blank stares.

I say you have to recognize the boundary layers before you can formulate a solution and all I hear is chuckles.

That is the nature of a complex problem, some easy solutions appear masking the more complex relationships.

Radiant forcing is an easy solution. Different molecules respond to different wavelengths or photon energies producing an impact, obvious in the radiant transfer of energy. The not so obvious is the interactions of the change in energy flux or flow with other molecules and other methods of energy transfer. There are critical points where the interactions need to be understood.

Saturation is a critical point in radiant heat interaction. Since molecules are limited in the spectrum or range of photon energies they can absorb and emit, as they approach a saturation point, where all energy levels are occupied, reactions and interactions have to change. The changes depend on the environment where saturation occurs, temperature, pressure, composition of molecules, relative velocity of molecules and relative energies of molecules, to name a few.

Two that appear to be more important than considered are the relative velocities and energies. When a radiant spectrum range reaches saturation, it not long can change the relative velocities or energies with the addition of more absorbent molecules in that spectral window. For there to be a change in impact there has be be a change in one or more of the other variables, temperature, pressure or composition. Adding more of just the same molecule in the saturated spectrum produce interesting changes.

At perfect saturation, all the interactions are at a maximum. The average relative velocities and energies are maximized for maximum interaction with the condition it that environment. Adding more molecules in that radiant spectrum reduces the distance between the similar molecules which changes the average relative velocity and energy of the photon exchange. This increases the probability that the photons involved in the interaction can match the energy and wavelength of other molecules with a different radiant spectrum. This would cause a broadening of the overall radiant spectrum of the environment. This is the effect found useful in laser technology. Energized photons in a chamber designed to reflect photons above or below a desired wavelength bounce back and forth until their relative velocity and energies match that of another molecule in the desired emission spectrum.

For a CO2 laser, the peak energy wavelength is close to but not exactly equal a nitrogen spectral peak. With the right chamber dimensions and the right excitation, the relative velocities and energies of the two molecules match closely enough for the nitrogen molecule to emit the absorbed radiant energy at the wavelength the discharge mirror is tuned to release. Nitrogen lases.

Since most molecules have emission spectra inclusive of a number of wavelengths, without the tuning of the discharge mirror, other lasing wavelengths which can also be excited are contain in the lasing chamber. All of these other wavelengths are less energetic than the desired peak wave length. Contained in the chamber, they can either climb up, step by step toward the peak wavelength or down to a weak energy wavelength. Nitrogen is a good lasing gas, because its peak energy wavelength is relatively isolated from weaker wavelengths.

In a mixed gas environment, the number of weaker energy wavelength increases. Once the maximum energy wavelength is saturated, the probability of weaker wavelength excitation increases, effectively stepping down the peak absorption and spreading the energy more uniformly across the entire spectrum of the environment. Wavelengths, where there is an easier path to de-excite or emit the energy will allow photons to leave the local environment freeing that wavelength for excitation yet again.

If we continue to add molecules in an open environment, the molecules will diffuse uniformly through the environment within the limits of their physical properties based on temperature, pressure and the limits of gravitation and magnetic/electric field constraints. As the environment of the individual molecules change, the path of least resistance for emission changes. Spectral broadening in one environment leads to increased excitation in the weaker spectral energies increasing rate of photons finding an unoccupied transmission frequency/wavelength. Due to the force of gravity, free emission windows increase with the reduction of gravity which reduces the density of molecules and in our atmosphere, the average temperature/energy of the radiant spectrum. Increasing the concentration of one type of molecule increases the average height of the effective maximum radiant layer of that molecule's spectrum relative to the surface.

Below this average maximum energy layer, the average relative velocity and energy decreases. At lower energies, the conductive properties of the environment are enhanced. Some molecules, water vapor for example, have nearly constant thermal conductivity. Other molecules, carbon dioxide for example, have nonlinear thermal conductivities. Once radiantly saturated, the thermal conductivity of both of these molecules are enhanced. The enhancement is greatest from water vapor where the concentration of water vapor is the greatest. The enhancement of carbon dioxide is greatest where the concentration of water vapor is the least. Both molecules are in competition for the available energy.

So I find, that the change in forcing is equal to 5.35ln(Cfinal/Cinitial) a bit simplistic. I am rather surprised that so few seem to agree.

Defining a Chaotic System?

There is a lot of talk about the need for multidisciplinary approach to Climate. To me that is an obvious requirement, starting with just the definition of what the "Climate System" entails. Playing with the opposing forces and multi-disc models, I am finding there are quite a few energy boundary layers that cannot be dismissed as negligible.

To me, the Earth system begins with the dynamic energy in the core itself. The internal dynamo generates heat, a magnetic field and as a fluid, has some impact rotation/tilt of the planet itself.

Between the core are thermal/radiant boundaries, the 4C sea water density boundary, the surface/atmosphere boundary, the Atmospheric boundary layer which consider the latent boundary to be a part, the thermal/radiant boundary layer, the tropopause boundary and so on until the thermal/non-thermal radiant boundary layer and space, in just the vertical. This should be the system envelope.

With opposing forces, the impact of any of these layers can be twice their singular value. For example, Arrhenius' greenhouse relationship appears to be an ideal relationship that would produce twice the impact. Based on the climatic conditions at the time of his paper and the region he lived, that is what he would have discovered attempting to explain the glacial/interglacial climate transitions, the ideal relationship. In the real world, only half of his expectations are realized globally, with regions near ideal conditions approaching his expectations.

This is one of the largest mistakes being made in climate science, comparing the real world to a ideal world. People lose sight of the subtle expecting the exceptional.

More Fun with Multi-Disc Radiant Models

More Fun with Three Disc Radiant Models



With the three disc models, I was attempting to simulate what that disc would sense. That disc is limited to energy bands or lines that can interact with the material of the disc. When I use a CO2 disc, I should use only the CO2 spectrum to determine what interactions that disc would have with the energy incident to its surface. I cheated and used a percentage of the spectrum based on the difference in temperature between the source of the energy and the sink, or disc receiving the energy. That is not a major cheat, it gives a ballpark which is all I was looking for at the time.

I can adjust my little model to get more information on just CO2, with just minor tweak, by making all the discs CO2 discs. That way a warmer disc would interact with all of the energy incident on its surface from a cooler disc and two equal temperature disc would not have any energy pass through. The two equal temperature discs with perfect absorption and return is fun to think about.

Disc 1 emits X towards disc 2 which returns x/2 to disc 1 which returns x/4 to disc 2 and so on. Since disc 1 started at X on the face toward disc 2, it effective emission due to interaction with disc 2 would approach 2X. Because of conservation of energy, the other side of disc 1 would approach 0 as the opposite face approached 2X. The same thing would happen at disc 2 since it started at the same temperature. We would end up with two discs emitting and receiving 2X on the common faces and emitting 0 on the opposite faces. There is no perfection, so this would be impossible, but where the discs would try to be headed.

Without some other source of CO2 friendly photons, nothing else would happen. If we inserted another CO2 disc between the two, all the faces would approach the same value of X. If the inserted disc had initial flux values of 2X, nothing would change with the other two discs which were in equilibrium at the perfect 2X flux prior to insertion. If we inserted a disc with X flux on each face, it would approach a higher value and the outer discs would have to find a new equilibrium. But what would happen on the other faces of the original discs?

Since the new disc had energy equal to half the total system energy, the outside faces of the original discs can emit a portion of that energy, so at perfection, the opposite faces could emit X each, or half of the addition 2X per face of the new inserted disc. That poses a small problem though. With three discs we have six faces, two at X and four at 2X. That would make a total of ten X when we started with eight X, two faces at 2X for the original disc and two faces at 2X for the inserted disc. So is this model wrong?

Not really, the Xs are energy flux or energy flow, which I am not allowing to flow. This model is similar to charging a capacitor which can only hold so much energy but can appear to have a greater potential energy. If I allow some of the energy in the model to flow for a short amount of time, the X value of all the faces would decrease proportionally. Since the disc in the middle has to interact emitting its energy with the outer discs, it would reach zero energy last by some fraction of a second.

If instead of letting energy flow, I inserted another disc at 2X per face, nothing would change, just the time required for the inside discs to lose their energy. If I inserted an infinite amount of discs at 2X per face, only the time to discharge would increase because more energy is stored.

This should be an example of saturation. The CO2 discs cannot manufacture energy, only delay its transfer. We have a stack of disc swapping photons with no net energy flow.

Now let’s imagine I take a stack of discs more massive than the stack above, capable of emitting X plus something and put it up to one of the faces. The more massive stack contains more energy, so there can be flow from it to the less massive stack of discs. The adjacent faces would approach 2X plus 2 something and the outside face of the less massive stack would approach X plus half of something. If the more massive stack could maintain its energy, the outer face of the less massive stack would emit X plus half of something as long as there was energy available.

This would be steady state energy transfer at saturation. As long as the more massive stack can maintain X plus something, the face between the more and less massive stacks can maintain the 2X plus twice something, while the opposite face of the less massive stack maintains emission of X plus half of something.
Adding more discs doesn’t change anything unless the space between the faces of the discs is not at 2X plus twice something. If the energy available at the face changes then the flux interaction at the faces change by twice that change, but that only applies to the CO2 portion of the change.

For example: 3.7Wm-2 of additional CO2 forcing would produce 7.4Wm-2 net effect. If the surface temperature were 288K it would increase to 289.3K or 1.3K increase in temperature. If the same forcing were at the Antarctic surface with -20C or 253K @ 232Wm-2, then the result would be 255K or 2 degrees of warming. Since the Antarctic is not warming significantly, odds are that any forcing due to CO2 change is not near the surface.

This estimate does not attempt to determine the impact of the change in temperature due to more CO2, but instead changes in forcing that are impacted by CO2 at saturation. So it may be useful for locating the effective radiant layer of CO2 to determine the feedback of water vapor on the altitude of the effect radiant layer. An atmospheric layer that shows nearly twice the flux change of another layer could hold clues to the magnitude of the CO2 impact.

I have no clue if this is actually measurable because it is not a true net flux, but it could be an indication of location of the radiant layer because local temperature should change even though there is no real energy transfer, just a backup or flux charging, if you will.

Note: This is just a musing post. The increase in Antarctic 600mb temperature by 0.7C per decade with no apparent impact on the surface got me wondering if that oddity may be of any use. I haven't checked it out and may never. Just in case anyone would like to, it may be worth a few minutes.

I know this is a simple model but that can be a good thing. Spectral broadening and a few other things change the basic relationship. An almost two times impact though is a lot easier to spot than a, “I have no clue”, impact. Since it really doesn’t matter where in the stack the hot disc is placed, the Antarctic troposphere might have an odd hot spot or two worth checking out.