## Willis TOA

February 12, 2022 3:08 pm

I love TOA posts.
The topic has been raised by Willis on a number of occasions
and shows that most other people have fixed ideas and not many clues.
[This applies to me as well].

The first point is definition.
Where Is The Top Of The Atmosphere.
Cannot be answered without a definition of what is the TOA.
I note the proviso.
QUOTE THE EXACT WORDS
So just what is the TOA?
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angech
angech
February 12, 2022 3:20 pm

Willis includes a definition in his topic today.

(TOA) radiation at the top of the atmosphere . This is the TOA balance between incoming sunlight (after some of the sunlight is reflected back to space) and outgoing longwave radiation (OLR) from the surface and the atmosphere.

The definition needs a number of important details added or clarified.
For instance is there a TOA on the dark side?
After all there is no incoming sunlight there.
Is the TOA a mathematical abstraction for the whole of the planet?
It is usually taken this way.
Is the TOA variable over the whole of the planet?
Yes.
The TOA locally is higher when the amount of incident sunlight is higher.
How does one address the fact that there is not an easily definable TOA on the darkside?. Do we take the lit side and average it with the dark side?
Yes.
And No.
The TOA can be considered as an averagefor the whole planet, treating it as a black-body [absorbed radiation] or as a grey body utilising albedo effect on the whole incident radiation.
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angech
angech
February 12, 2022 3:33 pm

Where Is The Top Of The Atmosphere.
Where is the TOA ?

A lot of different answers which is why I would appreciate an exact definition of which one we are discussing.

One answer is that we consider the amount of sunlight incident on a disc the circumference of the earth at a distance of one solar unit from the sun on a plane parallel to the centre of the earth.
The top of the atmosphere is then defined as the average distance to that spherical surface that energy would radiate from if that surface was at the blackbody temperature fot that energy received by the disc.

Phew..

I doubt anyone can come up with a much better more exact definition although it has flaws.

Any takers?

A key flaw neglected by all is that the earth, having an atmosphere actually receives more energy that hits the atmosphere but missed the disc of the earth as that energy is absorbed by the atmosphere at the periphery but would miss the earth if there was no atmosphere.
The whole absorbing area is a disc of which the earth centre is only a major part.
I hope Willis factors this in.
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angech
angech
February 12, 2022 3:46 pm

There are two deeply conflicting ideas at play here.

One is the idea that an imbalance must exist because

• In order to restore the balance so that incoming solar radiation equals outgoing longwave radiation (OLR), the surface perforce must, has to, is required to warm up until there’s enough additional upwelling longwave to restore the balance.

The other that physics absolutely dictates that the outgoing energy must equal the in-going energy.

There are time frames involved that suggest this is not so.
Physical observations that suggest this is not so
Leading to this statement that seems to make absolute sense.

• The amount of atmospheric CO2 and other greenhouse gases (methane, CFCs, etc.) is increasing. • This absorbs more upwelling longwave radiation, which leads to unbalanced radiation at the top of the atmosphere (TOA). This is the TOA balance between incoming sunlight (after some of the sunlight is reflected back to space) and outgoing longwave radiation (OLR) from the surface and the atmosphere.

However, boring everyone to tears,
The two ideas as stated are fundamentally incompatible.
Hence we ignore the very physics everything is based on
To go with a concept of plausible imbalance.
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angech
angech
February 12, 2022 3:54 pm

The two definitely coexist but are incompatible as we view physics on our intuition and observation.
One concept I have toyed with is that what we see on our time scale is not what is actually happening in the true time space continuum.
Just as the sun and the earth are travel ling in straight paths through time space but we see one orbiting around the other.
The explanation for this phenomenon is that distance and time warp.
If the time is the same the distance is different. If the distance is the same the time is different depending on frame of reference.

I could and have argued that what we see as a build up of energy is really just our perception and the reality is that the energy entering and leaving the system actually has to balance.

Crappy argument but the best example I could give for a possible divergence.
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angech
angech
February 12, 2022 4:06 pm

If not, what are we left with?

The definition of a TOA which is physically real rules out the very accumulation of energy that we see in the atmosphere.

Again physics V observation.

I point out that if a TOA exists, at the TOA , by any definition, the energy in always equals the energy going out.

Must. Should. Could. Does.

If not, do not call it a TOA..

To illustrate.
Shine a light on an object and turn it off and describe to yourself the energy flow.

I defy anybody to show how the energy stays in or on the object.
How after it is shone and turned off the object can legally retain any of that energy.
This is talking pure physics of energy and objects, and not solar batteries or internal energies, nuclear energies etc.

Again any takings arguing physics?
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angech
angech
February 12, 2022 4:26 pm

Hence as energy cannot be stored how can we talk about an energy imbalance?
There are three possible states?
Energy coming in.
Energy going out.
Energy going out coming back in and going out again.

At all stages they are equal
At the TOA specifically the actual amount of radiation out is the full amount the earth receives in

I could try to say that energy in equals energy out at all levels,not just at the TOA .
The reason the earth’s surface is hotter than the TOA is that the light and short wave that gets through is converted to IR at the surface [did not touch the atmosphere on the way through] and being back radiated heats the surface up much more than the atmosphere.
The thicker GHG atmosphere at the surface heats up the surface and itself until that outgoing energy reaches the level at which it is not blocked from going out.
No energy imbalance.
Everything is in balance.
Just the radiating surfaces are hotter which they have to be with that degree of radiation passing through
Not absorbed, Not stored.
R Ellison put it beautifully. The delay in that energy getting back out to space is microscopically small.
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angech
angech
February 12, 2022 4:36 pm

The upshot of this is that there is no
• In order to restore the balance so that incoming solar radiation equals outgoing longwave radiation (OLR), the surface perforce must, has to, is required to warm up until there’s enough additional upwelling longwave to restore the balance.

The surface appears to warm up with radiation because we measure the temperature by measuring radiation, usually infra red.
What are we measuring?
The molecule has cooled down because that radiation has left it.
As we measure that it is it is warm no longer.

So sure it is hotter when more sun comes in.
When there is more water and CO2 GHG causing more back radiation on the way out from the light that reached the surface unimpeded.
But no storage.
There is no retention.
No imbalance.
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angech
angech
February 12, 2022 5:10 pm

As a final comment, sorry Willis, for taking up so much space, consider the so called TOA measurements showing the so called but impossible imbalances.

Firstly they can be positive or negative, always.
Which means they are variations in the ability of the measuring instruments, not real.

There are two types of measurement, counting Earth shine estimations which agree poorly with Ceres particularly the last few years.
Satellites can and should take in most of the radiation from the earth.
Of course this means they would assess a TOA greater than what they claim to measure as they would get the radiation that hits the atmosphere outside of the disc of the earth, but who cares about a 3-10% discrepancy or adjustment due to this.
Does anyone know how this particular adjustment is done or do they even bother?

Roy Spencer has categorically asserted that the satellites make large errors in assessing IR in regions with cloud cover.
Large errors.
Anyone care to corroborate this?
Anyway the Satellites offer the best assessment even though they are 10% or more out.

“TOA fluxes based on ADMs from the Earth Radiation Budget Experiment (ERBE) applied to the same CERES radiance measurements show a 10% relative increase with viewing zenith angle in the SW and a 3.5% (9 W/sq m) decrease with viewing zenith angle in the LW.”

To sum up,

Energy imbalance as a concept allows de novo creation of energy in the atmosphere [storage of energy] which then allows GHG propnents to claim extra warming can continue to occur when physically all the energy that comes in [and there is a heck of a lot over 8 minutes from the sun] has gone 8 minutes later
We merelt observe. like with a thermometer how much energy is in our local area.
The world warms up and cools down through 15- 30C range every day.
No batteries store it at night or during the day.

## Fermat

Fermat’s theorem solved correctly and simply.
Paper written on 28/12/2021.
By Dr H W. Lee. Mb, Bs

Fermat made a conjecture that no two positive numbers greater than 2
could be raised to a power greater than 2 and yet add together to form a third positive number to the same power.
This is trivially true due to the fact that when any two such numbers are added it creates an extra factor of 2 in the resultant third number.
which means that any reduction in the number by the power cannot be a positive complete number.
The easiest way to show this is to take two simple cubes such as 8 and 27 or a and b.
There is always a gap between the first and second cubes in any sum
The resultant addition is always the first cube added to itself plus the gap between the first and second cubes.
Therefore any cube has to equal the first cube doubled plus the gap between the first and second cubes.

Since both the gap b-a and and the first cube a are cubes
this can be written in 2 ways
2a^3 +b ^3
or 2b^3 +a^3
When a and b are two different numbers they add up to 2 different sums.

If the numbers do add up to a third number it would have to be the same either way.
Since it is not, neither answer can be correct
so two cubes cannot equal a third numerical cube.

Further every a and b as a gap does form a cube with two cubes.
But only when those cubes are half of a real cube.
Hence 2[1/2 a^3] +b^3 = c^3 but only when the 1/2 cubes add to form a real cube.
Similarly 2[1/ b^3] + a^3 = c^3 but only when the gap is a half gap or cube
In other words for every gap b-a there is a cube c^3 which = 1/2 a^3
where two such cubes can form a cube but only if they themselves first add to a cube.

So when the cube is doubled it always has a factor of the square root of two as a cube and
therefore cannot form a cube with a numerical cube root when added to a cube with a numerical cube root.
When swapped around the same logic applies to the gap as a cube.
If it is a cube b^3 [ eg 19] then it will form a doubled cube 2b^3 that has to add to a cube a [8] to form a numeric cube and again,
as a doubled cube it cannot make a rational numeric cube root capable of adding to the gpa which is now the cube 8.