BPSDB

Following from Dan Pangburn: Dan commented on this, helpfully providing links to several pdfs showing where he derived his constant.

So I took a look at them.

Dan uses the First Law of Thermodynamics.

That’s a start: Energy(in) – Energy(out) = Energy(retained).

Let’s take a look at Energy(Out). A single term: **X·T ^{4}**, where

**X**is Dan’s constant.

Dan helpfully provides a link to Wikipedia’s A very simple model. This shows

**(1-a)S = 4εσT ^{4}**

where

**S**is the solar constant – the incoming solar radiation per unit area—about 1367 W·m^{−2}**a**is the Earth’s average albedo, measured to be 0.3**σ**is the Stefan-Boltzmann constant—approximately 5.67×10^{−8}J·K^{−4}·m^{−2}·s^{−1}**ε**is the effective emissivity of earth, about 0.612

Dividing both sides by **(1-a)S**, we get 1 = **Y·T ^{4}** where

**Y = 4εσ/(1-a)S**.

Plugging in the terms into **Y**, we get

**Y** = (4 x 0.612 x 5.67×10−8)/(0.7 x 1367) K^{−4}

= 1.45·10^{-10} K^{−4}

(or 1·10^{-10} K^{−4} to 1 s.f. – we can’t justify more than one significant figure)

**Y** can’t really be a constant, though, since 1 = **Y·T ^{4}**. If

**T**increases then

**Y**must decrease (and vice versa). Perhaps we should rewrite it as

**Y**1. But for small

_{i}·T_{i}^{4}=**ΔT Y**will not change by much.

So far, so good.

Dan derives his constant in the same way, but then multiplies an additional term (the average sunspot count).

Quoting from his pdf on page 6:

The average sunspot number since 1700 is about 50, the energy radiated from the planet is about 342*0.7 = 239.4 (for the units used) and the earth’s effective emissivity is about 0.61 (http://en.wikipedia.org/wiki/Global_climate_model). Thus, as a place to start, X should be about 50/239.4 times the Stephan-Boltzmann constant times 0.61.

50/239.4*5.67E-8 *0.61 = 7.2E-9

Which then he “refines”, continuing:

With this plugged into the equation, a plausible graph is produced with a dramatic change observed to take place in about 1940. In EXCEL, 7.2E-9 was placed in a cell and the cell (value for X) called by the equation which produced a graph. The graph was observed as the value for X was varied. X was adjusted until the net energy from 1700 to about 1940 exhibited a fairly level trend. This occurs when X is 6.519E-9 (unbeknownst to me at the time, cell formatting rounded it to 6.52E-9).If an average sunspot number of 6.52/7.2*50 = 45.28 had been used, no adjustment would have been needed.

This is, of course, nonsense.

But we will follow this for now to see where it goes.

If we now multiply **Y** by Dan’s sunspot average count, we get

45.28**Y** = 45.28 x 1.45·10^{-10} K^{−4}

= 6.56·10^{-9} K^{−4}.

This is pretty close to Dan’s value (the difference is probably due to slightly different values of the terms **S** & **ε**, which I had used from the model).

To all intents and purposes **X** = 45.28**Y**.

Now go back to Dan’s term **X·T ^{4}**, the output energy.

Replacing **X** with 45.28**Y**, and remembering that **Y·T ^{4}** = 1 (so that

**Y**=

**T**), we get

^{-4}**X·T ^{4}** = 45.28·

**T**.

^{-4}·T^{4}Gosh! The Temperature terms cancel, the Stefan-Boltzmann equation vanishes, and the energy we are left with is ….

45.28 Sunspots ….

Solar & Heliospheric Observatory

*We give our consent every moment that we do not resist.*

# Comment Policy

–

It is worth knowing and abiding by whether you comment on this blog or not.

- The “Mostly” Open Thread” is for general climate discussion that is not relevant to a particular post. Spam and abuse rules still apply;
- The “Challenging the Core Science” Comment Thread is for comments that purport to challenge the core science of anthropogenic climate change.
- The “Spam” Comment Thread is for comments posted by people who think that they can ignore site policy.

:

on November 13, 2011 at 1:27 pm |BenHow many brain cells did you have to kill to wade your way all the way through that?

My brain thanks you for your sacrifice.

—-

on November 13, 2011 at 5:10 pm |adeladyI think you may be due for some kind of award.

It never occurred to me that anyone would actually read those things – let alone carefully enough to pinpoint the exact point where it all falls apart.

on November 14, 2011 at 10:06 am |Ian ForresterPierett said:

Nice to see Pierett at last admitting that he is absolutely ignorant of science Only a fool, or a dyed in the wool AGW denier, would actually think (I know that is impossible for these types) that what Pangburn says is in any way related to real science and maths.

on November 14, 2011 at 10:14 am |BenThat’s hilarious! I glanced at Pierett’s comment and figured it was heuristically generated spam.

Following the forestry blog link, I found a post touting the fact that he

commentsat Huffington Post and Discover Magazine. I guess that makes me a “regular contributor to Scientific American.”on November 14, 2011 at 11:38 am |frank -- Decoding SwiftHackBUT THE R SQUARED!!!! CAN’T SOMEONE THINK OF THE R SQUARED!!!!!🙂

But even there Pangburn is full of fail. As I said in that other thread,

R² is useful for correlating estimates of two different variables, not estimates of the same variable (temperature).Of course, Pangburn will ignore all that, since in his own mind he’s authoring his very own

Principia.And a side note: Pierett says:

Sounds like there’s the expectation that “local businessmen” are mathematical idiots.

(But given the 2008 financial crisis, maybe that expectation isn’t too far off…)

— frank

on November 17, 2011 at 10:20 am |frank -- Decoding SwiftHackDan:

I stand corrected on that point. But you do know this, don’t you:

So your

LOOK AT THE HIGH R SQUARED!!!!talking point still doesn’t hold.— frank

on February 1, 2012 at 2:03 pm |citizenschallengeExcuse me for piping in again, but the above is left dangling. . .

Could someone please offer a short bullet point summation of the mistakes in Dan’s formula and reasoning – I appreciate that a number of flaws have been highlighted here and there, but a list would be nice.

thank you

Peter M.

~ ~ ~ ~ ~ ~ ~

Also, if someone could shed light on how a Google of the title to Dan’s article gets wallpapered over seven pages of results, that would be interesting too.

on May 27, 2012 at 4:38 pm |pendantryI don’t mind admitting that you lost me somewhere in the middle of the first equation.

I do think that I understand the final point: energy isn’t measured in sunspots. If I have got the right end of the stick, somewhere inside I’m waiting for an allusion to babel fish, and the final and clinching proof of the non-existence of god.

on March 1, 2015 at 9:21 am |EvelynWell, the Sun cannot be considered guilty of producing the global warming today, but our polluting activities can.

So, before trying to explain that climate change is only in the mind of some people who have an interest in getting government money for research, I say that we better look in our yard, and try to learn a few tricks about stopping climate change in our area.

http://www.alternative-energies.net/a-few-solutions-to-fight-climate-change-in-2015/