What is a Watt???

[Derek]

Hi All,
Elsewhere I have been following discussions in regards of whether it is correct or not to divide solar input received at the top of the atmosphere by 2 or 4.
I think this is an absolutely central issue, that must be understood.

On this thread so far, the casual reader can not have failed to notice the "pain" I have suffered in trying to understand what a W/m2 actually is.
My confusion is because of the way W/m2 is used in the K&T plots.
I hope that may have become apparent to at least some whilst reading the thread.

I shall try to explain what has been confusing me in regards to the way W/m2 has been used in K&T.

As far as physics is concerned, W/m2 is a power figure, derived from a Watt AND
as such it is a timeless figure. ie, it must apply across all time scales.
This later point has, I think, been missed by many.

So, when using W/m2 figures the physics of what is being described must be taken into account in determining what maths can be used.
ie, the physics determines the maths.

If W/m2 is used in a way that is not physically correct, then it is the maths determining the physics, which will not work in reality.
The maths may be wonderful, but if it ain't physical, it is worthless maths.

My maths is particularly weak, I have no issue admitting that, but, I do remember vividly one maths lesson.
My maths teacher at school went purple with rage trying to explain to a classroom of not particularly interested teenage boys,
with regards to algebra, that you can not compare lions and zebras..
They have to be the same, you must use a common denominator.
With regard to W/m2, the only "common denominator" is that the figure must describe the physics in such a way as to be a timeless figure.
Otherwise comparison is not correct or possible.

The sun permanently illuminates half of the sphere that is planet earth.
So, as a hemisphere is twice the area of a disc, then dividing the power of solar input received by 2 over a lit hemisphere is correct.
The physics of dividing solar P received by 2 for planet earth is found in reality.

If however we divide solar P received by 4 then we have to assume that the planet has rotated fully once, or "x" number of times, (or the planet is disc shaped...)
because the solar input has been spread over the entire sphere's surface.
(A sphere has 4 times the area of a disc, and twice that of a hemisphere.)
This has introduced a time element to W/m2, in this case 24 hours, or multiples thereof.
P/2 = lion.
P/4 = zebra.

When P/2 and P/4 are used we are not using the same "thing", infact according to the definition of what a W/m2 actually is,
then because P/4 introduces a time element to a timeless figure, then,
whatever the figure is, it is not a W/m2.

The K&T plots start off with 342 W/m2 solar input, which is a P/4 figure.
From there on in, almost all the figures used in the plots are of different time scales,
some are timeless, as they should be, figures, some are not.
We are comparing lions, zebras, monkeys, giraffes, and goodness knows what other animals all together on one plot.

My maths teacher would probably of exploded, if he had ever looked at a K&T plot.....

When physically incorrect figures are used, or net figures are used, then the physics are mangled and any resemblance to reality is lost completely.
Maths does not determine the physics,
maths can ONLY describe the physics when applied in the correct physical manner to a given situation.

In K&t, and computer climate models the maths determines (mangles) the physics...

Net figures are a major problem also because, there could be, let us say,
16 arrows / reasons in one direction, and 6 or 7 arrows / reasons in the other direction.
Using a net figure would just mangle the physics, and any relationships within the physics.
Furthermore the net arrows will probably give the wrong impression of how it might change due to other factors changing.

In short, there are so many ways that the physics have to be described correctly by the maths, that,
the "sum" overall is probably impossible.
On thing is for certain though, calculating physics determined by maths is not the right way to go about things,
infact, it is a crassly stupid approach doomed to failure.
The best example of which is dividing solar input power to planet earth by 4.