More on the 4C and Other Boundary Layers (From Other Blog)

Again with the high quality graphics, the Temperatures of Earth, (yes, I know there is a degree or so off here or there.)

Most understand the simple heat transfer barriers, insulation, gas to liquid contact, optics and radiant energy. RHC just defines all heat transfer in terms of time scales (changes in rates of change may be better). It is a simplification, probably not an ultimate solution, but a step in that direction.

I will be working on this from time to time to define simple RHC boundaries. One of the more interesting is the deep ocean 4C barrier. This is density barrier, above 4C sea water density varies with energy flow. Below the 4C barrier, temperature is relatively constant as heat flow is slow, tens of millinia and mirco Watts per meter squared. The effect is the appearance of near perfect conduction of heat, thermal equilibrium on a much longer time scale, that is a much tigher, denser, probability cloud, i,e, if it is easier to locate a packet of energy, its rate of change is less.



What is The 4C Thermal Boundary?


Selecting a frame of reference is more than just a choice of a point in space, it is a choice of space and time. The 4C boundary in the deep ocean is the point of maximum density of our saline ocean. From this boundary upward is the ocean atmopshere mixing layer. Heat is transfer is much greater speed than below the 4C layer. Below the 4C layer is the ocean crust mixing layer. Its heat transfer time scale is on the order of tens of millinia.

This is analogous to the tropopause, we the rate of heat transfer can be much greater than the rate of transfer of energy from the surface mixing layer to the tropopause.

Most studies of thermodynamic full cover thse issues with coefficients of heat transfer across a thermal barrier. Part of the description of the coefficient of heat transfer is the time restraints, but in normal applications, the time constraints can be simplified. In studying the Earth system, these time constrains are only negligable between one boundary per estimate. The relative impacts of the time constraints between two or more thermal boundariers has to be consider for correct estimates.

4C boundary time constant tens of millinia

upper ocean time constant roughly a millinium


This layer is from the 4C density boundary to the surface. There are several layers in this layer. The 100m layer, defined by shorter short wave radiant energy, green to ultraviolet, and the 10 meter layer defined by the longer short wave energy, yellow moving to near infrared, and the skin layers, millimeters to micro meters.

surface air mixing layer time constant roughly months


This is the most interesting boundary to me. Radiant heat from the surface of the oceans is limited by the coefficient of heat transfer from water to air. Changes in wind change the rate of flow. Changes in density change the flow. Changes in the composition of the gases change the flow. Once radiant energy is transferred, the photons enter a supercharge version of nature's pinball machine from Hell. Greenhouse gases can readily absorb photions but the much higher rate of collisional heat transfer to emission by relaxation is phenominal. Conductive heat transfer is more coherent in the direction of temperature drop while emissions are totally random. The absorption the collision de-excitation can enhance conductivity like crazy. The wavelength of the photon from one form of de-excitation can change in nanoseconds. Each of these relaxations that change wavelength can be less efficient than the last or more efficient than the next. This is thermal chaos! Going from near zero to light speed and back billions of times in fractions of seconds.

This is the main reason for my considering relativistic heat conduction and the possibility of variable light speed. While the speed of light may not vary, it would definitly appear to vary. It is like the doppler effect on steroids. Yeah, I think it is kind of exciting :)

The probability density approach is the only way to come close to solving this layer. Once that is estimated, the probability density changes with density of the media, ratio of the mixed gases and the rate of temperature decrease with density. This is where the Kimoto equation becomes a major tool to simplify the calculations. Using surface temperature, potential temperature and "effective" emissivity, a reasonable approximation may be possible. Approximation though, is all it will ever be. There is no equilibrium, just probability density.

The Latent Boundary Layer

This is one I was hoping could be lumped in with the troposphere. Unfortunately, the Latent Boundary layer is the point where latent energy from the surface is shifted upward to the point of average initiation of condensation. The relationship of theis layer to the average energy absorbed by CO2 is critical in gaining some understanding of the feedbacks, plural, of clouds and water as both liquid and solid. The atmospheric heat pipe I had discussed in a previous post. The balance of incoming solar, outgoing long wave and downwelling long is a complex relationship that determing if clouds are positive or negative feedbacks. This may be one of the more fun layers to attempt to describe.


Tropopause time constant roughly microsecs


In the Tropopause, you have up welling infrared with downwelling infrared with incoming solar at wide angles and scattered/reflected solar from below. A lot of different fluxes from all directions. The spectral window is very clear for some wavelengths and opaque for others. This is the one spot in the atmosphere that a sandard radiative model could get totally lost. More ice, water vapor or water would play hell in getting a good number. All it takes is a few molecules combined to change the radiant spectrum of the small amounts of water. Measurement of the changes would be complicated becaue of the available angles of emission and absorption not inline with the instrumentation. Getting it close is quite a feat. This is were RHC can really come in handy. The complicate relationships of heat flux can be simplified to temperature, pressure, potential temperature, which is a function of temperature and pressure, to get an estimate of the "effective" emissivity*. That may sound complicated, but the change in temperature with altitude is a direct indication of the net flux. Change in the rate of change of temperature is an indication of the magnitude and sign of the net flux. So the temperature relationship between the mid-troposphere temperature and the lower stratosphere can give you and indication of the flux relationships in the tropopause.

Now that the weird energy changes and actual change in the speed of light are ruled out, the relative motion of the of the photons is the impedance to radiant flux, which changes with density. Near the tropopause the side windows are more open, which expalins the dramatic changes possible in the tropopause. So it will be much easier to explain why the change in rate of change has such an impact. Resistance to flow through the stratosphere changes slowly with respect to the side windows, allowing radiant flux relief, if you will, for larger changes in flux from the surface.

What does this mean for the mid-tropo/strat Watt-meter? That larger areas of the stratopshere will be needed to get the full signal of the change in flux from the surface.

* At the surface, emissivity of the surface times transmittance of atmosphere times the change in transmittance with respect to density. Roughly at this point in the calculations.

The confusing part is the "Effective" emissivity. In a straight line, electromagnetic radiation would follow all the classic rules. The mixture of wavelengths, energies and angles appears to be simplified as a single "effective" unit, with this special case of RHC. How accurately, I am still working on that. It looks pretty close and would be closer with two accurate estimates at two different denisities. The more points you get right, the more you can get right.

In any case, the change in the rate of change is very important.

The 100K Magnetic Flux Boundary

Yes! Ladies and Gents you have read correctly! At approximately 100K, the magnetic portion of the Electromagnetic spectrum regulates the amount of warming possible by the atmospheric effect. While still preliminary, this also appears in the conditions of Mars and Venus. We have a new boundary!

TOA time constant with space roughly nano seconds

As at the tropopause, but much simpler. With less banging around, the photons are more coherent. There is still some, "resistance" to flow so there will be a change in the rate of change of interaction entering relatively constant emissivity of space. Space still has a "resistance" so there is still entropy. So there is roughly an order of magnitude change in the rate of collisions between the stratosphere and space.

This is the concept of Relativistic Heat Conduction, as I see it, the change in the rate of change for all forms of energy is related to entropy, so all forms of energy flux share common transmission properties.

90% of DWLR is from the First 100 Meters. So?

Where does 90% of the CO2 forcing come from? Where does 90% of water vapor forcing come from? Where does 90% of the latent come from? 90% of the energy cooking my dinner came from the ground some where. My meatballs only care how much of that energy they are experiencing due to me turning on the burner. How hot is the burner, how far away is the heat, how conductive is the pot and what is the mass of the meatballs? 90% is meaningless without a reference, often several.

50% of the energy is where in the atmosphere? 50% of the energy due to CO2 is where in the atmosphere. How much will changing that 50% to 51% change the where 50% of the energy in the atmosphere is? How much will that change, change the surface temperature? How much will that surface temperature change impact the cooking time of my meatballs?

Why don't people ask the right questions?

Just for a though experiment, let's say the molecule for molecule, water vapor is just as potent a greenhouse gas as CO2. It's not, but this is my thought experiment. Then CO2 and H2O would have the same impact when they both had the same concentration. Where it that point in the atmosphere?

Okay, you don't like my thought experiment. So where is the impact of H2O equal to the impact of CO2? You pick the number.

Is that at the surface? 100 meters? 1000 meters? Does that make a difference? In thermodynamics it does. The change in forcing with respect to the surface needs to be considered if you what the answer at the surface.

Since water vapor impact is expected to change, where will it change with respect to the surface?

Power Series or Opposing Forces?

Power Series or Opposing Forces?

There are dozens of ways to solve problems. The atmospheric effect is not different. It is actually a simple problem. Feedbacks in the dynamic system are the problem which should be a little easier with the correct solution of the atmospheric effect. Being a big fan of keep is simple, I choose a simple frame of reference, the take small steps from a solid foundation toward a better solution of the more complex issues.

The Stefan-Boltzman equation is required since radiant energy is involved, though in the lower atmosphere it is not. Different methods can arrive at the same answer.

Since the Average surface temperature is 288K and the average outgoing energy flux at the top of the atmosphere is 238Wm-2, the S-B relationship makes perfect sense for a beginning. Using F=5.67e-8(T^4) and T=(F/5.67e-8)^0.25 you simple get temperature @ flux values for the surface and TOA.

288K and 390Wm-2 Surface and 238Wm-2 and 254.5K at the TOA, is the simple relationship between the surface and the True TOA. This has nothing to do with a tropopause, it has nothing to do with a no greenhouse gas Earth. Thinking it is more is a problem,

So on one of the blog, a commenter mentioned using power series to determine what a change in surface flux would cause. There is nothing wrong with that approach. There may be something wrong with the hypothetical question of the change being felt at the surface.

If we take 238Wm-2 outgoing flux and divided that by the surface outgoing flux we have 238/390 or 0.61. This is the emissivity of the atmosphere of the Earth. So one can consider that 1-.61 or 0.39 is the atmospheric resistance, feedback, whatever term you like. I happen to call it the “Effective” Emissivity or the portion of the surface emissions that has an effect on or is affected by the atmosphere. The Effective emissivity includes all thermal flux interactions with the atmosphere, interactions I know and interactions I may not know.

Since an impact of change from the surface will impact the atmosphere which will in turn impact the surface, at some point stabilizing. This is good application for a power series as I understand it.

So if the surface were at 254.5K and 20K was suddenly added to the surface temperature, we would need to use the flux values, which are non-linear with respect to temperature, to determine the stable resulting temperature.
238Wm-2 @ 254.5 K is already known, with 20 more degrees the flux at 274.5 would need to be determined by S-B which is 263.8Wm-2 @ 274.5K

So, the difference in the flux would be 263.8-238=25.8 added to the atmospheric flux, of that 39% would be returned or 10.1Wm-2, requiring 0.39*10.1 or 3.94, with 0.39*3.94=1.54 etc. etc,

This solution is simply 25.8/(1-.61) or 25.8/.39 = 66.15 meaning the stable surface flux would be 238 + 66.15 = 304 Wm-2. The 66.15Wm-2 would be a portion of the atmospheric effect IF, the 0.39 return was linear. Just for grins, let us pretend it is not. Let’s say something crazy like the effective emissivity in the lower troposphere where higher, say 0.75, effective emissivity.

Then let’s say we added 20Kto the temperature at some point in the lower atmosphere. Just for a guess, the 274.5 but this time in the atmosphere, We have the same flux as before, 25.8Wm-2 only 0.25 instead of 0.39, yielding 25.8/(1-.75)=25.8/.25 = 103Wm-2 at some point in the lower atmosphere.

That 103Wm-2 plus the 66 Wm-2 =169Wm-2, which is pretty close to 390Wm-2 surface minus 238Wm-2 TOA or 152W atmospheric effect, not too bad for a guess, had I guess 0.7 instead of 0.75, the value , , 25.8/.3=86, would exactly equal 152W/m-2, the ideal atmospheric effect as seen at the TOA. That added 20K in the atmosphere is radiated in both up and down. Before we had the surface increase from 238 to 274.5K @ 304Wm-2, adding the 86Wm-2 from the atmosphere would yield 390Wm-2 at the surface.

This is my visualization of the Atmospheric Effects, with the 20 degrees at the surface being most of the surface temperature increase and radiant gases in the atmosphere creating a balancing effect in the atmosphere. It only requires one more element.

That element is the lapse rate, including latent heat, which transfers heat directly from the surface where condensation begins to release that hidden heat. This depresses the 274.5K atmospheric value by approximate 20K to 255K as appears to have been estimated by Arrhenius, with one small issue, the latent component of the lapse rate.

There are several ways to estimate the temperature of the average layer of radiant impact, of the source of down welling long wave radiation, The simplest being the average mass level of the atmosphere or the average energy level of the combined lapse rate, conductive, latent and radiant. That would where ½ of the energy transferred from the surface to the atmosphere can be approximated.

A simple estimate based on observation would be the average altitude of low cloud bottoms or the average layer where condensation begins. This altitude is approximately 4000 meters.

Of course, one would have to assume that the return value even after applying power series can never be greater than the input value or perpetual motion would be involved.