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« Upper Tribunal Decision | Main | Yorkshire goes unconventional »
Friday
Jun032016

What New Scientist wouldn't print

A couple of weeks back, New Scientist published an article trying to up the ante on climate sensitivity. 

One headline-making 2013 study had concluded that the immediate warming that would result froma doubling of CO2 in the atmosphere would be around 1.3°C - significantly less than most previous estimates. But this was before global temperatures shot past 1°C above pre-industrial levels last year, as predicted by New Scientist in July 2015. If the 2013 study was repeated using that value, it would give an estimate for the immediate warming of 1.6°C, says Piers Forster...

It also claimed that Forster and Lewis's 2013 paper had got its estimates of aerosol forcing wrong:

[Other studies] suggested that Forster's team underestimated how much warming has been masked by the cooling effect of other pollutants, such as sulphur aerosols, that we pump out alongside CO2. 

Quite why anyone would want to estimate TCR from a single year's temperature figure is anyone's guess. This observation prompted Nic Lewis to write a letter to the editor, which, needless to say, has not been published. So you can read it here.

Letter to the Editor concerning New Scientist article in the 28 May 2016  issue, Vol 230, No 3075, page 8: 'Earth's sensitive side'

The claim in your 28 May article 'Earth's sensitive side' that the strong warming over the last few years means we can now rule out low estimates of climate sensitivity is wrong. You quote Piers Forster, a co-author (along with myself) of one 2013 study that concluded near-term warming from a doubling of CO2 in the atmosphere would only be around 1.3°C. I have also been sole or lead author of three different studies published since then, all of which support that conclusion. One of those studies used the Intergovernmental Panel on Climate Change 2014 assessment report's estimates for the effects on the Earth's radiation balance of both warming agents such as CO2 and of cooling agents such as sulphur aerosols. I have extended these estimates to 2015 and recomputed the warming from a doubling of CO2. It is unchanged at 1.3 °C, averaging over 1995-2015 data. It remains 1.3 °C when using data just for the last ten, or five, years. Use of a shorter period gives a less reliable estimate; using a single year's temperature is unsound.

The suggestion that the team Forster and I were part of underestimated how much warming had been masked by the cooling effects of sulphur aerosols and other pollutants is mistaken. Our team's method is unaffected by the arguments on this point raised by the Shindell and Schmidt team studies referred to. The latter study anyway contained several errors.  The corrected version fixed two of the errors I had pointed out, and shows that near term warming from a doubling of CO2 is correctly estimated from the historical mix of warming and cooling agents, including sulphur aerosols. Moreover, the findings by the Storelvmo team relied on a relationship existing between solar radiation at the surface and sulphur emissions, but over their full data period that relationship is statistically insignificant. Furthermore, two recent studies (Stevens 2015 and Kirkby et al. 2016) conclude that sulphur aerosols have had less effect on radiation than previously thought, implying that estimates of the warming from a doubling of CO2 are actually too high.

 

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Reader Comments (123)

Any article whose headline include the phrase "worse than we thought" can be consigned straight to the bullshit pile without further consideration.

Not for nothing does the great Motls refer to that magazine as the "Nude Socialist".

Jun 6, 2016 at 8:20 AM | Unregistered CommenterAndrew Duffin

Andrew Duffin
I had not heard that re-titling.
Does it therefore follow that Scientific American could also be rebranded, perhaps as Trump's toilet paper?

Jun 6, 2016 at 8:40 AM | Unregistered CommenterAlan Kendall

As Nic Lewis correctly points out in his letter, the wind on aerosols is currently blowing in the opposite direction, towards the suggestion that anthropogenic sulphur aerosols have had less of a cooling influence overall, implying that sensitivity has been overestimated.
Using a year of rapid warming associated with the build up of surface heat in the Pacific, culminating in an exceptionally strong (but very short-lived) El Nino is pure alarmist opportunism. But then, what can you expect from a CAGW mouthpiece masquerading as a science news journal? The good times are almost over; they'll soon have to go back to reporting on boring old science, unless they can find some new hypothetical catastrophe with which to engage their readership.They did AIDS and the Ozone Hole back in the '80's. Warmism has filled in very nicely since then.

Jun 6, 2016 at 8:56 AM | Unregistered CommenterJaime Jessop

"Climate advocates are everywhere. They are pretty good in authoring text, but not very honest and intelligent.

Jun 3, 2016 at 5:51 PM | Unregistered Commenterwert"

And to confirm everything you said UC, the very next comment after yours had me bringing my breakfast back up quicker than a Mann Made Global Warming (TM) subsidy!! :)

Jun 6, 2016 at 9:01 AM | Unregistered CommenterMailman

I finally got round to reading my two-week old rag yesterday, and fired off a letter to NS, which they doubtless won't publish either.

I'm afraid folks have lost sight of the 'Pea' - the NS article managed to say that a current estimate of ECS might be going up from 1.6 to 2 without mentioning that this compares to the IPCC's number of 3 (the last time they bothered to state a number), which is also the number in many climate models.

This is scandalously misleading, notwithstanding the fact that they have gotten their facts wrong, per Nic's response.

Jun 6, 2016 at 9:54 AM | Unregistered CommenterRERT

If ECS is recalibrated from 3 down to 1, could climate scientists be required to repay 2/3rds of their salaries over the last 20 years?

Obviously if ECS is nearer zero .......

Jun 6, 2016 at 11:59 AM | Unregistered Commentergolf charlie

Au contraire GC, give them sinecures in the WMO, UNEP and the IPCC.

Oh, sorry, that has already been the case for decades.

Jun 6, 2016 at 12:04 PM | Unregistered CommenterNCC 1701E

Martin A

NS have a Comment page for opinion articles.

If Mr Lewis could put together 1500 words making a reasonable case for low climate sensitivity, they might publish it.

Jun 6, 2016 at 12:27 PM | Unregistered CommenterEntropic man

golf Charlie. According to Delia, lobster thermageddon is not a culinary delicacy. It employs a kitchen blowtorch to convert the crustacean into superheated steam infused with long chain chitin molecules and is used alleviate the severe symptoms of climate change induced asthma. It has the additional advantage of being mildly hallucinogenic inducing a hatred of CO2. Legislation is being considered to forcibly administer it to the standout 3%, leading to universal climate harmony, peace and all things nice.

Thanks to you Charlie the secret's out and IPPC policy will now require "adjustment".

Jun 6, 2016 at 1:33 PM | Unregistered CommenterAlan Kendall

Entropic Man has given some constructive advice.

This is no guarantee that New Scientist will accept any constructive comment.

Jun 6, 2016 at 1:36 PM | Unregistered Commentergolf charlie

My own back of the envelope calculation suggests that NIC Lewis' transient climate response (TCR) of 1.3C/doubling is too low.

The LIA temperature decline stabilised around 13.8C in the latter 1800s and CO2 started rising around 1880.

Leaving aside the current El Nino the long term trend puts current temperatures around 14.8C and the post-1998 "pause" is disappearing back into the post 1970 trend.

Over the same period CO2 has increased from 280 ppm to 407ppm.

A 45% increase in CO2 has produced a transient climate response of 1C. This is equivalent to a TCR of 1*100/45= 2.2C/doubling. Since TCR is lower than equilibrium climate sensitivity, the current TCR also sets a lower boundary of 2.2C/doubling for ECS.

Jun 6, 2016 at 1:38 PM | Unregistered CommenterEntropic man

Entropic Man. Do you get much mail? I only ask because I worry you may run out of envelopes.

Jun 6, 2016 at 1:45 PM | Unregistered CommenterAlan Kendall

Entropic man (Jun 6, 2016 at 1:38 PM), are you aware that your calculation makes the implicit assumption that the change in temperature is driven solely by CO2 and therefore ignores any natural forcings that may also have been acting?

Jun 6, 2016 at 1:58 PM | Unregistered CommenterDave Salt

Alan Kendall, if only someone could find the scribbled on envelope, that was used to determine ECS so incorrectly in the first place, Computer Generated Climate Science might be closer to reality, and less unbelievable.

It may be that EM has replicated the original errors perfectly.

Jun 6, 2016 at 2:10 PM | Unregistered Commentergolf charlie

Dave Salt,

Not to mention the logarithmic effects of CO2. Meaning we've already had probably two thirds of any warming that might be caused by a doubling of CO2.

Jun 6, 2016 at 3:47 PM | Registered CommenterLaurie Childs

David Salt

Do you have evidence for alternative forcings? On the available evidence to date all the likely alternative forcings have been flat or slightly cooling since 1880.

Laurie childs

If we were seeing ten doublings the logarithmic effect might be significant,

Let's try a few doublings.

The change in direct forcing for the first doubling since 1880 is 5.35ln(560/280) = 3.71W/M^2.

Two doublings to 1120ppm would produce 5.35ln(1120/280) = 7.42W/M^2. If the change were linear you would also expect 7.42W.

Three doubling to 2240ppm would produce 5.35ln(2240/280) = 11.12W/M^2. The linear equivalent would be 11.13W.

After three doublings the difference between the linear increase and the natural logarithmic increase is less than 1%.

To put that into perspective, using the mid-range IPCC figures three CO2 doublings would produce 9C warming. The reduction due to using a logarithmic rather than a linear calculation is less than 0.1C.

Jun 6, 2016 at 6:24 PM | Unregistered CommenterEntropic man

Great to see that Mickey Mouse is back with the maths again. I suppose he must have done his studies while waiting for Pluto to return with the ball one day.

Jun 6, 2016 at 6:39 PM | Unregistered Commenterdiogenes

EM, do you have an alternative explanation for Mann's Hockey Stick being so completely wrong about it's predictions/projections? Or even why all the computer models are always so wrong, and on the high side?

It seems you are ignoring a wonderful opportunity to upstage some of the highest paid climate scientists in the world.

Jun 6, 2016 at 6:59 PM | Unregistered Commentergolf charlie

Alan Kendall

Are you OK?

I realise that you are trying to establish yourself as a BH insider, but turning from a geologist into a golf charlie clone may be taking it too far.

I had hoped for a critique of my calculation from you, rather than sarcasm.

Jun 6, 2016 at 7:38 PM | Unregistered CommenterEntropic man

EM. Thank you for your concern, but yes I'm OK.

I doubt very much that I ever will be a BH insider, I'm too left wing for many of the regulars and am constantly rubbing them up the wrong way to be fully acceptable.

I enjoy very much trying to match wits with golf Charlie but so often am completely outclassed. On a few occasions I feel I've just about matched him (maybe wishful thinking).

No you weren't expecting a critique from me. Be honest. I have never commented on your numerical calculations. I leave that to others better equipped than I. But I did immediately spot the flaw that Dave Salt (1.51pm) mentioned.

You commonly talk about your back of the envelope calculations and this time it suddenly occurred to me what would you use if you ran out of envelopes. My post was not meant to cause hurt; I even thought it might raise the slightest of smiles from you. I'm sorry if it didn't.

Alan

Jun 6, 2016 at 8:29 PM | Unregistered CommenterAlan Kendall

Entropic man (Jun 6, 2016 at 6:24 PM) said "Do you have evidence for alternative forcings?".

Are you saying that the Earth's temperature history is driven entirely by CO2 and has nothing to do with natural variations that are an emergent property of an extremely complex system... or more direct factors like solar activity or recovery from the last ice age, which was probably triggered/driven by orbital factors (e.g. Milankovitch cycles)?

Seriously EM, for someone who claims to understand the Scientific Method you seem to have forgotten that it's up to the person who proposes the hypothesis to prove its correctness with empirical evidence.

What you are doing is inverting the Null Hypothesis (i.e. that there is no relationship between two measured phenomena) to try and force your view, which is the basic flaw at the heart of all CAGW 'science'.

Jun 6, 2016 at 8:57 PM | Unregistered CommenterDave Salt

EM, I don't claim to be a climate scientist. Why do you choose to lash out at me for pointing out the simple fact that reiterating someone elses errors, doesn't reduce their magnitude, or make them go away.

Thank you for confirming that 97% of Climate Scientists are wrong, simply because they keep arriving at the same conclusions.

You could of course attempt to address some of the more mathematical and scientific points raised above, but you are not going to find the answers at Skeptical Skience, because they can't see the problems either.

Jun 6, 2016 at 10:01 PM | Unregistered Commentergolf charlie

Alan Kendall

Not offended, but worried.

You might want to understand the psychology underlying your current behaviour.

David Salt

Yes, I am saying that there is a causal link between increasing CO2 and increasing temperatures and that none of the other possible causes is sufficient.

Detection and attribution, inference to the best explaination is how you choose between the null and alternative hypotheses.

You can detect the temperature increase in the troposphere, at the land and ocean surface, and in the ocean heat content. You can detect secondary effects such as sea level rise and ice melt. You can also measure increased CO2 and demonstrate from isotope changes and accounting that it comes from fossil fuels.

For attribution you can measure the candidate forcings, such as solar insolation, aerosols, orbital mechanics, volcanoes and CO2. Separately or collectively most of these have not changed much and cannot explain the observed warming. If anything their collective effect should be slow cooling.

The exception is increasing CO2. Courtesy of the USAF, the radiation physics of CO2 in the laboratory and in the atmosphere is well understood. Increased CO2 would be expected to produce decreased outgoing radiation in the 13-17 micrometre range, increased downwelling radiation at the same wavelengths, stratospheric cooling and an increase in the altitude at which CO2 radiates to space. Their effect is to create an imbalance in Earth's energy budget leading to increasing temperature. All of these have been observed.

This is all consistent with the alternative hypothesis that there is a causal link between global warming and increasing CO2 and falsifies the null hypothesis that there is no causal link.

If you want to propose another cause, then detection and attribution applies to you too. You must be able to show that whatever alternative hypothesis you put forward shows effects that can be detected and physics which attributes the observed effects to your cause.

Jun 6, 2016 at 10:24 PM | Unregistered CommenterEntropic man

EM doesn't explain the high value for the alleged water vapour feedback, when increased water vapour results in increased albedo because of cloud formation, resulting in a negative feedback.

Jun 6, 2016 at 10:42 PM | Unregistered Commenterrotationalfinestructure

Rotational consistencies

Do your homework.

Increased water vapour increases cloud cover at low altitudes and high altitudes.

Increased low altitude cloud increases albedo and has a cooling effect. Increased high cloud decreases radiation to space and has a warming effect. The combined effect is neutral.

Jun 6, 2016 at 11:13 PM | Unregistered CommenterEntropic man

EM, I love to go cloudbathing on a lovely cloudy day, but when the sun is shining, like today, I have to put on an extra jumper.
When you say "neutral" I think the words you are looking for are "too complicated to explain".

Jun 6, 2016 at 11:39 PM | Unregistered Commenterrotationalfinestructure

EM says that sea level rise is a detectable secondary effect of CO2 increase. 14000 years ago, sea level was 140 meters lower than today. One meter per century on average for the past 14000 years compares well with current sea level rise. Could the current sea level changes not be caused by the continuing winding down of the Milankovich Cycles?

Jun 6, 2016 at 11:55 PM | Unregistered Commenterrotationalfinestructure

EM suggests that a logarithmic relationship between CO2 and temperature is more or less the same as a linear relationship.
If climate sensitivity were 3 degrees per doubling of CO2 then at 560 ppm CO2, temperature would be 3 degrees more than at 280 ppm, and at 1120 ppm it would be 6 degrees more than at 280 ppm. (two doublings).
If there were a linear relationship, 3 degrees per 280 ppm increase, then at 560 ppm CO2 the temperature would be 3 degrees more, but at 1120 ppm it would be 9 degrees more than at 280 ppm. (3 x 280).
That seems a significant difference to me.
The calculated temperature is only the same at those two points, 280 ppm and 560 ppm.

Sorry I didn't have an envelope to calculate it on the back of.

Jun 7, 2016 at 12:44 AM | Unregistered Commenterrotationalfinestructure

EM
Using natural logarithms:
ln(280) = 5.634
ln(407) = 6.009
ln(407)-ln(280) = 0.375
ln(560) = 6.328
ln(560)-ln(280) = 0.694
0.694/0.375 = 1.85
1 degree C times 1.85 = 1.85 degrees C

Using base 10 logarithms
log(280) = 2.447
log(407) = 2.610
log(407)-log(280) = 0.163
log(560) = 2.748
log(560)-log(280) = 0.301
0.301/0.163 = 1.85

Your back of envelope calculation result of 2.2C is way out.

Jun 7, 2016 at 1:35 AM | Unregistered Commenterrotationalfinestructure

Jun 6, 2016 at 11:13 PM | Unregistered CommenterEntropic man

"Increased low altitude cloud increases albedo and has a cooling effect. Increased high cloud decreases radiation to space and has a warming effect. The combined effect is neutral."

If the Earth today became permanently 100% covered by high cloud would the Earth warm or cool?

Jun 7, 2016 at 1:47 AM | Unregistered CommenterRob Burton

Could David Salt kindly explain how he expects an " emergent property of an extremely complex system" to contravene the laws of thermodynamics and radiative equilibrium ?

Jun 7, 2016 at 6:00 AM | Unregistered CommenterRussell

Rotationalfinestructure (11.39pm)
Ah, but (in warmer climes) AT NIGHT I might go out sleeveless when the sky is cloud-covered, but on a starry night might freeze and need a jacket.

I have experienced really cold nights in northern Western Australia when daytime temperatures were horrendously hot. Those with me reported rimefrost, but I cannot vouch for it. By the time I got there it had all, allegedly, melted away.

Jun 7, 2016 at 7:16 AM | Unregistered CommenterAlan Kendall

I hear that logarithms are to be renamed "denierithms" because 97% of "climate scientists" don't know how to calculate using logarithms.

Jun 7, 2016 at 8:30 AM | Unregistered Commenterrotationalfinestructure

Climate Scientists continue to deny making mistakes, despite the overwhelming evidence.

Climate Scientists expect others to find, identify and correct these mistakes for free, whilst they continue to get paid to lecture others about their wrongdoings.

Cut off the supply of money, and like a carbonated drink left in the sun, Climate Science will simply, and harmlessly fizzle out.

Jun 7, 2016 at 9:17 AM | Unregistered Commentergolf charlie

It is an article of faith for the geekarati that Arrhenius worked out 97% climate science on the back of a fag packet in a Stockholm pole dancing club 100 years ago. It was only in 2006 that John Cook using modern envelopes firmly established that it was much worse than we thought.

Since then, Skeptical Science has been a Mecca for those who wish to sneer at the capitalist denialsphere using real school maffs. That includes Guardian journalists desperate to find their own complexity denying Fox News type source that even they and their liberal arts acolytes can understand.


Complexity deniers rool o.k.

Jun 7, 2016 at 11:49 AM | Unregistered Commenteresmiff

esmiff

Envelopes have a lot to answer for.
Those used for climate calculations need to be embossed by stamps declaring them IPCC property and thus free from FOI.
On no account should envelopes be sent to a little town in Northern Ireland.

Jun 7, 2016 at 12:32 PM | Unregistered CommenterAlan Kendall

Alan Kendall

You may have ended climate FOI applications in one short sentence.


Many years ago, a Guardian article on the robustness and accuracy of climate models was roundly ridiculed by mathematically literate readers on the basis that modelling the earth's climate was not something computers were capable of doing, even if data and understanding were much more complete. This was before ideological entrenchment,


Prediction being like asking your new Everest tour guide the best time to leave for Tibet.

Tibet ???

Jun 7, 2016 at 2:15 PM | Unregistered Commenteresmiff

esmiff. On first reading I misread part of your last post "That was before ideological ENTRENCHMENT" as " That was before ideological ENRICHMENT". Then I realized both versions applied.

Jun 7, 2016 at 3:06 PM | Unregistered CommenterAlan Kendall

Rotational fine structure

Are you sure you read my post properly.

The calculated figures for forcing are 3.71W after one doubling, 7.42W after two doublings and 1.13W after three doublings. All three are increases relative to the value for 280ppm.

They were calculated using the formula ∆f = 5.35ln(C/Co)

If the increase were linear the three values would have been 3.71W, 7.42W and 11.13W. You have to go into the third decimal place to see any difference.

Your 1.35AM calculation assumes that ln(x/y)=lnx-lny. Would one of the mathematicians here care to comment?

Jun 7, 2016 at 4:18 PM | Unregistered CommenterEntropic man

esmiff

Most Everest climbers start on the Nepal side. There are also routes from Tibet

Jun 7, 2016 at 4:27 PM | Unregistered CommenterEntropic man

Alan Kendall & esmiff

would climate science be improved if they used bigger envelopes, or do they struggle to fill the back of one small one with all of their factually accurate, evidence based conclusions?

Jun 7, 2016 at 4:29 PM | Unregistered Commentergolf charlie

Entropic man (Jun 6, 2016 at 10:24 PM), let me remind you that my comment simply pointed out your BoE analysis was based upon the implicit assumption that *ALL* of the temperature rise in that period was due solely to a rise in CO2. Had you said that your analysis merely placed an upper bound upon sensitivity, I would not have commented because this would have been the correct way to present the hypothesis.

Instead, you reel-off a set of statements that seem to try and deflect the reader from the essence of my comment and make me look like I’m denying that CO2 has any impact on climate. This is a pity because, having measured the spectral properties of CO2 in the lab many decades ago as a physics undergraduate, I’m well aware that CO2 has the potential to cause warming. My issue is that I see no scientific evidence that this warming will have catastrophic consequences and therefore require draconian measures to prevent it. Nevertheless, as many believe ‘sensitivity’ is a good metric to judge these potential impacts, an accurate assessment would obviously be very useful.

Going back to my original comment, I’ll add weight to it by providing this quote from SPM-4 of the IPCC WGI AR5…
“It is extremely likely that more than half of the observed increase in global average surface temperature from 1951 to 2010 was caused by the anthropogenic increase in greenhouse gas concentrations and other anthropogenic forcings together. The best estimate of the human induced contribution to warming is similar to the observed warming over this period.”

Like me, the IPCC are not denying that CO2, along with other anthropogenic emissions, has an impact on temperatures. However, like me, they are saying that the evidence to date suggests that these were only partially responsible for that rise. Yes the words “…more than half…” could be used to suggest that 100% is still possible but if this is what they believed I would have expected them to have used a much higher boundary like three-quarters or nine-tenths.

Of course, the obvious response to this is that the IPCC were talking about a different period and that non-anthropogenic CO2 could be one of the primary forcings responsible for the rest of the temperature rise, which may be true but is hardly conclusive to your hypothesis. However, based upon past interactions with you, I’m sure you’ll disagree with me and then continue to brand me a ‘denier’ without any credible justification… just like Russell has.

Jun 7, 2016 at 4:54 PM | Unregistered CommenterDave Salt

97% of Climate Science's calculations for ECS are worse than previously thought possible.

Would a pause in global warming be possible with a lower ECS, without resorting to data adjustments, and unprecedented fudge factors? 97% of climate scientists dare not find out.

Jun 7, 2016 at 5:51 PM | Unregistered Commentergolf charlie

Entropic man


'Most Everest climbers start on the Nepal side'

That's probably why he said 'Tibet' ?

Well spotted.

Jun 7, 2016 at 7:09 PM | Unregistered Commenteresmiff

"...why anyone would want to estimate TCR from a single year's temperature..." It's not a temperature. It's a meaningless statistic. I still maintain an average of temperatures tells us nothing about what temperatures are doing. If I throw out an average, no one could tell me what the high or low was - and you can actually have cooler temps with higher averages than those with days that got hotter.

Jun 7, 2016 at 9:09 PM | Unregistered Commenter4TimesAYear

David Salt

the implicit assumption that *ALL* of the temperature rise in that period was due solely to a rise in CO2.

It is not an assumption. None of the other measured parameters which might force increasing temperatures are doing so.

The evidence indicates that Increased CO2 is the only driver presently forcing temperatures up and that the observed change in CO2 and its associated feedbacks are sufficient to explain the observed warming.

Jun 7, 2016 at 11:52 PM | Unregistered CommenterEntropic man

David Salt

You need to understand some IPCCspeak.T hey are extremely cautious in their phrasing.

"Extremely likely" means 95% statistical confidence. The statement may be rephrased as "The probability that human influence caused less than 50% of the oberved warming is smaller than 5%.

In practice the non-CO2 parameters together should be producing slow cooling. The effect of CO2 has been to overcome this cooling and then produce warming. It might be said that increasing CO2 has produced more than 100% of the observed warming. (golf charlie and co should have great fun with that)

Jun 8, 2016 at 12:10 AM | Unregistered CommenterEntropic man

EM, so if it is all down to CO2, did CO2 stop rising and cause the pause?

Or did something else stop happening?

Jun 8, 2016 at 1:04 AM | Unregistered Commentergolf charlie

EM, perhaps you could give everybody some fun by working out what percentage of global warming is not due to CO2, and why all calculations by 97% of climate scientists for ECS are wrong.

I don't claim to be a maths or science expert, but your sums don't match reality. That you claim expertise, but won't address your own mistakes does place you in the top 97% of 97% of climate scientists.

Jun 8, 2016 at 7:43 AM | Unregistered Commentergolf charlie

Your 1.35AM calculation assumes that ln(x/y)=lnx-lny. Would one of the mathematicians here care to comment?
Jun 7, 2016 at 4:18 PM | Unregistered CommenterEntropic man


EM - What are you on about? It is not an "assumption" that ln(1/y) = - ln(y).

It's a basic *fact* that ln(y^a) = a . ln(y). In this case, a = -1.

O-level schoolkids used to learn that in their first (OK, their second) lesson on using logarithms. What were you up to during those lessons?

Jun 8, 2016 at 8:05 AM | Unregistered CommenterMartin A

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