Conclusion: Penn are global warming deniers! And the temperature of the earth is primarily a result of cooling through the adiabatic blanket together with a smaller component of direct cooling. The effect of IR interactive gases like H20 & CO2 is to change the ratio of these two.
After my last article: A scientist’s guide to greenhouse warming
I was reading a few articles:
- Hockey Schtick: Derivation of the entire 33°C greenhouse effect without radiative forcing from greenhouse gases
- Unified Theory of Climate Revisited
- Unified Theory of Climate
- A new Lunar thermal model based on Finite Element Analysis of regolith physical properties
When I finally came to this diagram on the Penn. After looking at it I decided to write down some thoughts as they occurred (so they haven’t been checked and may well be wrong).
Looking at the above, it contained very similar flows for the atmosphere as a whole compared to those I had shown for a single molecule atmosphere in A scientist’s guide to greenhouse warming however the the final value was different.
εσTE4 – σTS4
– [σTS4 – εσTE4 ]
Where I had (using their terminology):
εSσTS4 – εS εEσTE4
The first obvious difference is that they have no emissivity constant for the earth and must assume it to be equal to 1. This gives:
εSσTS4 – εS σTE4
But this still doesn’t match. Searching their diagram to find the cause, I first rearranged the energy flows so that rather than comparing rather vague flows which seemed e.g. to just go into the spaces between the earth and and their atmosphere I measured the flows at all the key points going into the earth and atmosphere, and there it was the missing flow of IR through the atmosphere:
No I see this missing term representing radiation that flows from the earth through the atmosphere it is clear that they are using a model that means all radiation from the earth is absorbed by the atmosphere. Their atmosphere is a perfect blackbody in the IR spectrum. In other words it is being modelled as:
- 100% transparent to incoming radiation
- 100% opaque to IR from the earth
But hang on! If the atmosphere is 100% opaque to incoming radiation, then there is no need for the lower half of this model. Because it is opaque to radiation from below, we only need the heat flows from the “one layer atmosphere” into and out of space giving the equation:
(1-A) S/4 = εEσTE4
Now, the warming effect is purely a consequence of the emissivity of the atmosphere and it’s temperature.
Is temperature an input or output
Perhaps the biggest difference between this model and my own is conceptual. This model implies the atmosphere is a perfect insulator and that no heat flows into or out of it except through radiation. As such the temperature of the atmosphere is solely determined by the radiative balance. In contrast, my “atmosphere” was a single molecule of CO2 whose temperature was determined by the ambient temperature of the non-radiative interactive gases around it. As such my model assumed that heat flow into or out of the atmosphere maintained the IR interactive molecules at the normal temperature of that portion of the atmosphere. I suppose that means I was assuming perfect heat conduction.
But where is the CO2?
Based on this model, there is only one place where the CO2 can affect the equation: that the emissivity changes as gases are added. But how can this be? Emissivity is effectively the split between absorbed and non-absorbed radiation. A gas doesn’t reflect radiation, it can’t stop radiation except by absorbing it and the higher the absorption, the higher the emissivity. So, saying that no radiation from the earth gets through the gaseous atmosphere means the emissivity must be 1. A real atmosphere can only selectively absorb some parts of the spectrum and allow the rest of the radiation to continue past.
But if we follow their logic ε=1, the radiation exiting the earth is purely a function of the temperature at the top of the atmosphere. This in effect means that the temperature at the surface is purely and simply a function of the physical characteristics of the atmosphere of which adiabatic heating of the atmosphere caused by its compression is the most significant feature. So, CO2 has no effect on this Penn model.
The Penn model of the atmosphere as being 100% opaque cannot support the idea of CO2 warming!
Conclusion: Penn are global warming deniers!!!!
But is this model actually used in the atmospheric models? If it is, then none (or very little) of the radiation from the earth will reach space. Below is a typical model from a climate alarmist website:
The key figures are toward the right where “surface radiation” heads upward. 350/m2 heads into what looks like cloud – which I assume means “into the atmosphere” where it is stopped dead as if it hit a brick wall. In contrast 40w/m2 travels through the atmosphere without stopping. This means the diagram suggests an emissivity of the atmosphere of 350/(40+350) = 0.89. And it is this 40w/m2 which is all that can change as a result of adding CO2, because radiation that has already been stopped cannot be stopped again and it will behave as per the opaque atmosphere in Fig 4 and obey the equation:
(1-A) S/4 = εσTE4 + (1-ε)σTS4
[ε ~= 0.9]
And from various sites the suggested figure for adiabatic warming from the surface tot he top of the atmosphere is:
TS = TE + 33C
So this appears to be the general equation that would govern the earth’s temperature:
(1-A) S/4 = εσ(TS-33)4 + (1-ε)σTS4
Which seems to give the surface temperature as mainly the result of adiabatic warming (90%?) and then an additional 10% of direct cooling. And if this is right the effect of “greenhouse gases” is to change the relative quantity of cooling through the adiabatic “blanket” and direct cooling via IR.
I will mull over this but please add any thoughts?
A more realistic atmosphere is a semi-transparent one which I used in reconciling skydragons and mainstream skeptics . Here I suggested that the temperature of the IR gases was set by the adiabatic lapse rate and that IR emissions and absorption happened through the atmosphere. However, that is not to say that certain parts may be more important or perhaps (like cloud?) dominant.
But with the importance of water vapour I am tending to favour a slightly different idea as I hope is shown in the following diagram:
Here I’m now focussing on the troposphere (the lowest level of atmosphere encompassing most of the main movement of air and most of the cloud layer). This layer has several important features:
- High pressure, so a dense atmosphere which contains 80% of all the mass of the atmosphere
- High levels of water vapour and condensed water (aka clouds) which means it contains 99% of all water vapour which is the dominant IR interactive gas (aka greenhouse gas)
- A convective cycle actively moving heat around which will maintain the temperature profile and means this layer is not a “perfect insulator” as the Penn model required.
- A layer of clouds which are strongly IR interactive and so act as an effective IR radiator sitting near the top of this region.
So this should mean LARGELY:
- Heat is delivered to the top of this region by convection (?is it enough?)
- The temperature profile is determined by adiabatic lapse
- The Temperature flow is determined by the top of this region
Where it is completely different from standard models:
- The atmosphere moves.
- It includes adiabatic lapse