Dan Pengburn has been commented several times, so I think that he deserves a post of his own.

anom(Y) = calculated temperature anomaly in year Y

N(i) = average daily Brussels International sunspot number in year i

Y = number of years that have passed since 1700 (or any other year where the net summation is approximately zero such as 1856, 1902, 1910, 1938, or 1943)

T(i) = agt (average global temperature) of year i in °K,

ESST(c,Y) = ESST (Effective Sea Surface Temperature) in year Y calculated using an ESST range (magnitude) of c

CO2(Y) = ppmv CO2 in year Y

CO2start = ppmv CO2 in 1880

Dang, his equation is just too big to fit the image.

However we could simplify his equation and tidy it up a bit.

In the first summation, N(i) will always be positive, since N(i) >= 0 (you cannot have negative sunspots).

It is also dimensionless. For dimensional analysis Dan has to change this to degrees, but doesn’t say how it does.

In the second term, 6.52×10^{-9}T^{4} is quoted.

Dan did not state how this was derived, or cited. Is it based on science, or has Dan just made it up?

It is vaguely reminiscent of the Stefan Boltzmann law, but he is certainly not using the Stefan–Boltzmann constant (which is more than 10 times larger than Dans). Besides which the the Stefan Boltzmann equation is in units of Watts per square metre. We need to derive the anomaly in degrees Kelvin, so somehow Dan needs to define his constant.

Using Dan’s value at 288K, term 2 results in ~ 45. So (according to Dan) we should be warming whenever the “average daily Brussels International sunspot number” is more than 45 then we should result in warming (e.g. 2000), and a lower number should mean cooling (e.g. 2007).

Check any of your favourite datasets and see if how many years agree with Dan’s figures. I don’t know how many that you might find in agreement with Dan’s, since I gave up looking after seeing 2000 and 2007.

But there are more terms – perhaps we need to look at them to see if this makes more sense further along.

(Or maybe not. :))

ESST(c,Y) = ESST (Effective Sea Surface Temperature) in year Y calculated using an ESST range (magnitude) of c

I haven’t got a clue what this means, since Dan does not say how he derives it. But I don’t think it means the Sea Surface Temperature. Perhaps he meant the anomaly?

The last term does makes sense – that CO_{2} will warm logarithmically.

Then we have Dan has four “coefficients”, **a**, **b**, **c** and **d**.

Usually are coefficients are constants without dimensions (e.g. π). I know that some engineering terms use coefficients with units, but if they are they quoted in units. Since Dan doesn’t explain the units for his terms the equation , there is a real problem with a, b & d when looking at dimensional analysis (I can’t comment on c since I don’t understand the term). Possibly he meant that a and d were in units of K and b was in K^{-1} it might make more sense – but he didn’t say this.

But wait – Dan earlier stated that the coefficients are “to be determined” (i.e. not known).

They are not coefficients or even constants – he selects his terms according to the year (and even offers different versions for the same year).

His “coefficients” are variables! He even it states that the “coefficients” are adjusted to get the “best fit” of R^{2}.

If I’m reading this correctly, then there is no supporting science of his coefficients. His “coefficients” are nothing more than pattern matching.

Since the coefficients were determined using all available data, some reviewers asserted that the equation may have no predictive ability in spite of it being formulated from relevant physical

phenomena anda known lawof thermodynamics.

(My emphasis)

Of course I would expect Dan as an engineer would understand “a known law of thermodynamics”. In fact I would expect him to know at least three of them.

Which one has he selected? It would help.

Dan has however predicted the temperature for the next 25 years or so (and, surprisingly enough, we see that it will be cooling).

He is assuming that the sunspot variability over the next years is the same as the pattern between 1915 to 1941 – which is fair enough, since that he knows that it is a guess.

If sunspots do resemble then Dan predicts a cooling of about of between 0.2 K and 0.4 K (depending on his variable “coefficients”, despite that he has no idea what almost all his terms are unknown).

The beauty of it is that his own graph shows **substantial warming** between 1915 to 1941.

Shot in the foot? I think so.

Finally, Dan “shows” that the temperature has been declining between 2005 and 2011 (despite that the 2011 isn’t yet known yet).

He draws a straight line between 2005 and 2011(using UAH).

This is just sloppy. If Dan knows how to calculate R^{2} then he is perfectly capable of working out an OLS trend.

Over to you, Dan.

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