onsdag 20 februari 2013

Illuminating Model of Global Energy Balance

The radiative heat transfer from the Earth surface to outer space via the atmosphere can for resonant frequencies of the atmosphere be illustrated in a simple water flow model for two connected containers,  with container 2 representing the Earth surface with the water level H_2 representing temperature, and container 1 representing the atmosphere of height/temperature H_1 < H_2 with an outlet representing outer space.

If the channel connecting 2 with 1 has the same dimension as the outlet of 1 and the channel flow Q is proportional to level difference, we have by conservation of water, normalizing the constant of proportionality to one:
  • Q = H_2 - H_ 1 
  • Q = H_1
and thus Q = 0.5 x H_2. We compare with the situation with container 2 directly pouring into outer space (no atmosphere) which would give the double outlet flow  2 Q = H_2, as illustrated on top right. This would correspond to non-resonant frequencies for which the atmosphere is transparent.

Introducing 1 (atmosphere) between 2 (Earth surface) and outer space thus reduces the flow with a factor 2, the reduction coming from requiring the water to pass two channels instead of one. 

The model exhibits the following fundamental aspects of heat transfer in the Earth-atmosphere system: 
  • One water flow from high (2)  to low level (1): One-way heat transfer from warm Earth surface to colder atmosphere: No "back radiation".
  • 1 as passive mediator between 2 and outer space reduces the flow: Decrease of outgoing long wave radiation OLR for resonant frequencies of the atmosphere. No decrease for non-resonant frequencies.
  • 1 is a passive mediator in the sense that whatever it absorbs from 2 is emitted into outer space. 
The total reduction of OLR or "radiative forcing" caused by radiation through the atmosphere, is then determined by the denseness of the resonant frequencies of the atmosphere. The trace gas CO2 has a very sparse spectrum which gives small "radiative forcing" (small emissivity), as shown in previous posts.  

  1. Warming effect of the atmosphere, acting as a passive intermediate "blanket" between the Earth surface and pure space, for resonant frequencies. 
  2. Non-warming effect for non-resonant frequencies.
  3. Total warming effect dependent on denseness of resonant frequencies.
  4. One-flow of heat energy from warm to cold.
  5. Not two-way flow of heat energy carried by "photons" traveling back and forth.
For a new approach to radiative heat transfer connecting to this post, see Computational Blackbody Radiation.

CO2 alarmism is based on the hypothesis that the spectrum of the atmosphere with CO2 as a trace gas is dense in the entire wave number band 600 - 800, with a suggested "radiative forcing" of 3.7 W/m2 upon doubling of the concentration from preindustrial level to 600 ppm.

But the spectrum of CO2 as atmospheric trace gas is not dense but very sparse except in the narrow band 667 - 669, and thus the basis of "radiative forcing" of 3.7 W/m2 appears to be grossly incorrect, probably a factor 10 too big. Without this "radiative forcing" of 3.7 W/m2 CO2 alarmism collapses.

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