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BornFromTheVoid

The LI Revisited (Climate Modelling Using a leaky integrator)

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So, James Delingpole (another Heartland Institute buddy, who could have guessed!?) is back repeating "its the sun wot did it"?

The very line

"The forcing from changes in total solar irradiance alone does not seem to account for these observations,"

Says the opposite of what wuwt and the telegraph are stating, and claims something like GCRs are necessary for TSI to have the claimed effect.

Anyway...

"TSI [total solar irradiance] and volcanic aerosols demonstrate a near-zero (–0.04 W m–2) change in the natural forcing compared to the anthropogenic AF increase of ~1.0 ± 0.3 W m–2"

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Then surely there has to be a worry about how impacted TSI is by Particulate Pollution and if current warming is driven by TSI(mainly) then what happens to global temps when we sort out a good percentage of that pollution??

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So, James Delingpole (another Heartland Institute buddy, who could have guessed!?) is back repeating "its the sun wot did it"?

The very line

"The forcing from changes in total solar irradiance alone does not seem to account for these observations,"

Says the opposite of what wuwt and the telegraph are stating, and claims something like GCRs are necessary for TSI to have the claimed effect.

Anyway...

"TSI [total solar irradiance] and volcanic aerosols demonstrate a near-zero (–0.04 W m–2) change in the natural forcing compared to the anthropogenic AF increase of ~1.0 ± 0.3 W m–2"

Might be worth reading about the IPCC AR5 leak straight from the horse's mouth:

http://www.stopgreensuicide.com/ and http://wattsupwiththat.com/2012/02/22/omitted-variable-fraud-vast-evidence-for-solar-climate-driver-rates-one-oblique-sentence-in-ar5/

There's something strangely familiar about what Rawls says (cough-Leaky Integrator-cough!)

=)

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Might be worth reading about the IPCC AR5 leak straight from the horse's mouth:

http://www.stopgreensuicide.com/ and http://wattsupwithth...entence-in-ar5/

There's something strangely familiar about what Rawls says (cough-Leaky Integrator-cough!)

=)

I'm having a read of Rawl's explanation , but when it starts off like this

So may we please see this "science" on the basis of which our existing energy infrastructure is to be ripped out in favor of non-existent "green" energy? The only reason for secrecy in the first place is to enhance the UN's political control over a scientific story line that is aimed explicitly at policy makers

I'm not going to expect much in the way of rational thought! Perhaps I'll be proven wrong...

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Ok, after a quick read of the section causing the blogosphere commotion... it would appear to be another case of taking something out of context and twisting it beyond recognition.

As far as I can tell, the line was setting the scene for the analysis they were about to do regarding GCRs and clouds. The full paragraph:

"Correlations Between Cosmic Rays and Properties of Aerosols and Clouds

Many empirical relationships have been reported between GCR or cosmogenic isotope archives and some aspects of the climate system (e.g., Bond et al., 2001; Dengel et al., 2009; Ram and Stolz, 1999). The forcing from changes in total solar irradiance alone does not seem to account for these observations, implying the existence of an amplifying mechanism such as the hypothesized GCR-cloud link. We focus here on observed relationships between GCR and aerosol and cloud properties. Such relationships have focused on decadal variations in GCR induced by the 11-year solar cycle, shorter variations associated with the quasi-periodic oscillation in solar activity centred on 1.68 years or sudden and large variations known as Forbush decrease events. It should be noted that GCR co-vary with other solar parameters such as solar and UV irradiance, which makes any attribution of cloud changes to GCR problematic (Laken et al., 2011)."

They then go on to summarise and evaluate a raft of studies, coming to the conclusion that:

"there is medium evidence and high agreement that the cosmic ray-ionization mechanism is too weak to influence global concentrations of CCN or their change over the last century or during a solar cycle in any climatically significant way. The lack of trend in the cosmic ray intensity over the last 50 years (Agee et al., 2012; McCracken and Beer, 2007) provides another strong argument against the hypothesis of a major contribution of cosmic rays to ongoing climate change."

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Ok, after a quick read of the section causing the blogosphere commotion... it would appear to be another case of taking something out of context and twisting it beyond recognition.

The conclusion is erroneous - it's a typical straw man. To paraphrase, "There is evidence the Sun is a bigger player than has been accepted, but TSI alone doesn't account for it. Perhaps GCRs are linked....yadda yadda yadda...but there's no evidence that GCRs have anything to do with global warming."

This leads to the conclusion that the Sun is not responsible, but the train of logic is incomprehensible (you might say "irrational").

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Strawman? Where? They're talking about cloud cover here...

Something along the lines of

  • There are theories suggesting that changes in GCRs reaching Earth, caused by solar variations, influence cloud cover
  • This is suggested because the variations in TSI are too small to explain the cloud cover changes observed
  • Here, we will look at the literature to see if that if there is a strong case for GCRs having a significant effect on global cloud cover...
  • ....
  • The literature says no.

Simples.

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So in other words they are disregarding any chance that the sun has any significant effect because the only mechanism they will countenance is this GCR-cloud link?

And so, because the GCR-cloud link is apparently tenuous....this means that the sun has no effect on climate...?

And that's not a straw man?

okay......

But I've had this debate and this discussion before, when the AR4 was released, and I'm not going to start it all over again. It is completely pointless. I was merely interested in Rawls' comments on the two links I posted because they were so reminiscent of the Leaky Integrator theory ("hypothesis" would be perhaps more accurate) that VP and I worked on a while back.

Basically, I'm pretty convinced by the Leaky Integrator, which puts the lion's share of the "blame" for 20th Century warming at the Sun's feet - which, to me, makes a great deal of sense, for all the reasons I gave back when VP and I were working on it. We got shot down by a bunch of people who weren't interested in thinking about alternative hypotheses because "CO2 must be responsible". How could two people without "Climate Science" credentials possibly claim to have found a valid alternative to the hallowed IPCC?

=)

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That particular section that we were discussing, which the quote was wrongly taken from and twisted in order to make the silly claims, was entitled,

Clouds and Aerosols [subsection =] Correlations Between Cosmic Rays and Properties of Aerosols and Clouds

The other effects of the sun are discussed elsewhere in the report, which a few moments spent looking at it rather than working entirely of the reports of "sceptics" would have shown.

As for what the claims made by the heroic report leaker himself, half of it is nonsense. He claims dozens of papers support his view, posts links to half a dozen, most of which either don't support his view or have nothing to do with it. He ignores countless studies that prove much of the warming is human induced, makes false claims about the IPCC and continues on with his rant.

He gets away with making false claims because most people won't bother to read the links he's provided and even better, they won't understand them. Most sceptics will simply trust his calims because hey, he's another gallant sceptic fighting the good fight!

I can't say much about the leaky integrator, as I wasn't around or at least posting much when ye worked on that. Without a plausible physical mechanism for the hysteresis, I have doubts about it's validity. But I'd be more than willing to discuss it further and learn more about it.

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I confess that I haven't read the papers to which he linked, and nor have I yet taken the time to read the AR5 - I read through the links that I posted and was immediately struck by the similarities between what he was suggesting and the LI hypothesis that VP and I conceived over 2 years ago, and that seemed like a pertinent reason to post up the links.

Further investigation into Rawls shows that he is a staunch Republican who is very anti-AGW, which begs the question of why he was involved in the review of the AR5 in the first place. I'm not sure I agree with many of his views, despite me tending towards conservatism and anti-AGW sentiment myself! But, just because someone is an extremist of one sort or another does not necessarily invalidate their opinions. As I say, I was struck by the similarities between his arguments and the LI.

With regards the LI, I reject the assertion that the lack of a plausible physical mechanism invalidates the hypothesis. Furthermore, we know that the atmosphere exhibits hysteresis - from a very basic and obvious standpoint, the atmosphere prevents Earth's temperature from plummeting to -100C or more at night - it is clearly capable of retaining heat! When we discussed the LI I posited some possible mechanisms, though I think some of it was more confusing (and perhaps nonsensical) than it needed to be. The bottom line is that the atmosphere "leaks" heat at a variable rate, determined by the amount of heat it receives, as specified by the Stefan-Boltzmann law.

Regardless, from a purely statistical standpoint, the correlation between solar activity (as proxied by sunspot activity) and global temperatures is uncanny, if one assumes that the Earth exhibits hysteresis (which, as I say, it clearly does). The absence of a known mechanism does not negate the fact that this correlation exists. The correlation alone is enough to warrant further investigation - after all, AGW theory is largely a statistical analysis, and is based primarily on the fact that temperatures correlate roughly with CO2 levels (though, ironically, this correlation is to a far smaller degree than the sunspot-proxy-with-hysteresis correlation).

And yet nobody seems to be interested in pursuing this correlation, while the lesser correlation has been investigated to the nth degree, which I find frustrating. I also find it frustrating that so many people are not even interested in this correlation - I was absolutely blown away when VP posted the first graph. I had postulated this idea that maybe the increased solar activity was above and beyond what the Earth could "cope" with, that maybe there is some kind of lag in Earth's ability to process the incoming and outgoing thermal radiation, and it was because of this increase that temperatures were on the rise, rather than because of an increase in Earth's capacity to retain it via CO2. VP suggested this concept of hysteresis to me (which was something I was not overly familiar with) and told me about the Leaky Integrator. Using this basic equation he took the sunspot activity as a proxy and processed it, and out popped this uncanny graph. It wasn't perfect, but it was interesting enough to explore further.

As a result, we played around with other factors that looked like they might be relevant - volcanic activity (which has a known cooling effect), ENSO (which alters the amount of heat in the atmosphere via the oceans), and albedo (which affects the amount of insolation reflected back into space). Interestingly - and excitingly, to me - every additional factor we incorporated into the equation refined the graph, bringing it closer and closer to the observed temperature record.

We didn't jig the equation. We didn't tweak any data. We started with the basic Leaky Integrator equation and we took real-world figures from respectable sources (records of major volcanic eruptions came from, I think, USGS; ENSO data came from NOAA; for albedo we used ice coverage as a proxy, also taken, if memory serves, from NOAA). VP would be able to give you a better idea of what went into the equation - there were a couple of assumptions, but these assumptions manifested themselves as constants, as I recall.

Anyway, it seems implausible to me that this hypothesis, which is very simple and requires the minimum of input data, can be complete nonsense. The correlation alone is surely enough to pique the curiosity of the scientifically-inclined? How can such a simple premise, with such limited data, produce such an astonishingly similar result to our measured temperature record?

=)

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I never said the lack of a plausible physical mechanism invalidates it, just that I'd have doubts without there being one.

Hysteresis is certainly observable on many different scale, I have no arguments whatsoever with that. Where my problem would lie, is with the mechanism for the storage and release of heat from solar variability on multi-decadal scales.

Once more, I certainly do not question that the sun plays a large role in our climate on variable time-scales, neither does the climate science community either. Nobody in their right mind would reject that idea. The only thing where people differ is on the magnitude, timing and knock-on effects of solar activity. Which is why numerous peer reviewed studies are reviewed for things like the IPCC report, and not just the ones that support a particular view point.

I would disagree with you that the CO2 temperature relationship is a purely statistical one. CO2 (and others) are known greenhouse gasses. They are part of the Earths hysteresis system, without them, it would be quite a deal colder than it is now! When we see that the surface of the Earth is warming while the stratosphere has been cooling, that is another sign that CO2 is at play.

If you want to look at where the purely statistical relationship lies, it's much more with solar activity. Despite that, it's been an area that has generated large amounts of research, past and on going, it has not been ignored.

Anywho, how do you mean you didn't jig the equation? Surely ye based the different forcings such as solar, ENSO etc., on figures that would best fit the observed temperature trend? You can't just put the raw index figure into an equation like that, what adjustments and weighting did ye assign to the different factors and what was yer reasoning behind them?

Like I said earlier, I wasn't involved the this area much during the LI phase, but while it does sound interesting, I'd need a lot more info to take it seriously as what you've said so far hasn't left me filled with confidence for it!

Perhaps it's time to re-open the LI thread? If it's still about?

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There are 2 threads regarding the LI. Both are archived but we can open a further one if anyone want's to discuss it.

Part 1

Part 2

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I never said the lack of a plausible physical mechanism invalidates it, just that I'd have doubts without there being one.

If you doubt it then you doubt its validity, hence the lack of a plausible physical mechanism would render it invalid top you.

Hysteresis is certainly observable on many different scale, I have no arguments whatsoever with that. Where my problem would lie, is with the mechanism for the storage and release of heat from solar variability on multi-decadal scales.

I don't understand this. You accept that there is hysteresis, but that it can only occur on short timescales? That makes absolutely zero sense to me.

I would disagree with you that the CO2 temperature relationship is a purely statistical one. CO2 (and others) are known greenhouse gasses. They are part of the Earths hysteresis system, without them, it would be quite a deal colder than it is now! When we see that the surface of the Earth is warming while the stratosphere has been cooling, that is another sign that CO2 is at play.

I never claimed that the CO2-temperature relationship was purely statistical. I used the terms "primarily" and "largely" statistical, but never "purely". A greenhouse gas in a pure laboratory environment might be proven to act in a certain way, but when in the real world, with a huge and complicated set of checks and balances and other mechanisms in play, is the effect of the greenhouse gas necessarily going to be identical to the laboratory?

If you want to look at where the purely statistical relationship lies, it's much more with solar activity. Despite that, it's been an area that has generated large amounts of research, past and on going, it has not been ignored.

I know there's been lots of research. I've even read some of it. In fact, some of that research is what I referred to in an earlier post when I said that some conclusions do not follow on logically from the preceding paper. It seems as though the scientific community is too scared to suggest that CO2-driven global warming might not be wholly accurate. I'll probably be pilloried for that statement, but it's true.

Anywho, how do you mean you didn't jig the equation? Surely ye based the different forcings such as solar, ENSO etc., on figures that would best fit the observed temperature trend? You can't just put the raw index figure into an equation like that, what adjustments and weighting did ye assign to the different factors and what was yer reasoning behind them?

You would be surprised how little was done to the raw figures. No real adjustments were made, to the best of my knowledge (VP actually ran the data, though I did do some preliminary stuff with the basic equation which was literally just plugging numbers in, no adjustment necessary). The closest we came to "weighting" data was, I believe, attributing numbers to the volcanic data on the basis of the VEI number - to clarify, we took every magnitude 4 eruption as a number 4, every magnitude 3 as a number 3 and so on, which did mean that we were effectively using ballpark figures. Even the albedo was proxied by using ice coverage data and pretty much just plugging it in to the equation.

Like I said earlier, I wasn't involved the this area much during the LI phase, but while it does sound interesting, I'd need a lot more info to take it seriously as what you've said so far hasn't left me filled with confidence for it!

Perhaps it's time to re-open the LI thread? If it's still about?

So you have no confidence in it? What about the visible similarity of the output of the LI with observed temperature data? Are you suggesting that we falsified the output? That we tweaked it to make it fit? You're welcome to take a look at the LI thread - you'll find that there may be a few bitter comments from various contributors (including me), but if you can overlook that then you might get something out of it.

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If you doubt it then you doubt its validity, hence the lack of a plausible physical mechanism would render it invalid top you.

What?

I don't understand this. You accept that there is hysteresis, but that it can only occur on short timescales? That makes absolutely zero sense to me.

I'm just looking for a mechanism that can store and release heat on the timescales needed, that's all.

I never claimed that the CO2-temperature relationship was purely statistical. I used the terms "primarily" and "largely" statistical, but never "purely". A greenhouse gas in a pure laboratory environment might be proven to act in a certain way, but when in the real world, with a huge and complicated set of checks and balances and other mechanisms in play, is the effect of the greenhouse gas necessarily going to be identical to the laboratory?

Ah, now your just arguing for the sake of arguing! Like I said, plenty more evidence for how CO2 is influencing our climate. The fact that it also hold up in the lab, is just more evidence. Every way you question the CO2 temperature relationship can also be applied to the solar one, and more!

I know there's been lots of research. I've even read some of it. In fact, some of that research is what I referred to in an earlier post when I said that some conclusions do not follow on logically from the preceding paper. It seems as though the scientific community is too scared to suggest that CO2-driven global warming might not be wholly accurate. I'll probably be pilloried for that statement, but it's true.

That's not how it is though, just your opinion. It demonstrates a lack of knowledge on how climate research works in the real world too I'm afraid.

You would be surprised how little was done to the raw figures. No real adjustments were made, to the best of my knowledge (VP actually ran the data, though I did do some preliminary stuff with the basic equation which was literally just plugging numbers in, no adjustment necessary). The closest we came to "weighting" data was, I believe, attributing numbers to the volcanic data on the basis of the VEI number - to clarify, we took every magnitude 4 eruption as a number 4, every magnitude 3 as a number 3 and so on, which did mean that we were effectively using ballpark figures. Even the albedo was proxied by using ice coverage data and pretty much just plugging it in to the equation.

I'm afraid that makes little sense to me. Don't know how raw index values can simply be fed into that without a weighting.

So you have no confidence in it? What about the visible similarity of the output of the LI with observed temperature data? Are you suggesting that we falsified the output? That we tweaked it to make it fit? You're welcome to take a look at the LI thread - you'll find that there may be a few bitter comments from various contributors (including me), but if you can overlook that then you might get something out of it.

I read though both threads (well most of them) last night. A fascinating concept, but needs more grounding in the real world. You could just as easily take a number of random features, say for example, the size of the papal army, the number of pirates and the price of wheat, stick them into a model and get a good correlation with temperature. Does that mean we should take it seriously because the correlation is there? I think not (an exaggerated example, please don't be offendedsmile.png ), especially when they ignore increasing greenhouse gas induced warming, a process that is as widely accepted among climate scientists as evolution is amongst biologists!

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Then there is no point in discussing this further. You are against the idea in principle, you fail to grasp any point I am making. Your assertion that throwing in any random information would correlate with temperatures is complete nonsense. The fact that you can't grasp how raw data can be usable is slightly worrying. I've demonstrated a lack of knowledge of how climate research works? Really? So, does climate research work by writing a scientific paper and then drawing conclusions that aren't rational or legitimate so that it supports AGW? If so then all the pieces start to fall into place.

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Sorry CB. We don't seem to be getting each other. Just trying to ask some questions and get some answers to clarify the LI concept. Honestly didn't mean to offend. I do actually find the LI idea interesting, just looking for some of the possible physical mechanisms first.

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I'm just looking for a mechanism that can store and release heat on the timescales needed, that's all.

The oceans will do the trick for you. Not forgetting Newton's Cooling Law which guarentees hysteresis. Nice to see Cap'n Bob' around again, but if anyone thinks I am going to go through what we both did last time, they can forget it.

On the LI thread we made predictions and hindcasts. We extrapolated the formula, and weightings back though time, and hindcasted the Little Ice Age, we also carried forward in time, and, as far as I can ever see, the forecast it made was the only forecast at the time that predicted a slow down in the rate of temperature increase since the turn of the century and it was still posting positive anomalies, so global temperatures would still be increasing. The problem with the forecast is that I assumed a static sea-ice level, not the horror story that is developing the Arctic, so the slow down rate would be mitigated by this, to, I think, pretty much exactly what has happened with the global temperature series. We even found a flaw in the HadCru series - we couldn't get the temperature series to match, until TWS pointed out a paper that showed the error of measurement of the period in question - so the analysis predicted a fault with the global temperature series.

It's all on the LI thread - even how to do it yourself (so no hidden factors, or assumptions) I don't want to get involved in it; I promised my wife that I would leave it alone after blowing £10k on papers, journals, books and materials and spending two years living it inside and out, online, and elsewhere.

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These boards used to get quite heated at times! Anyway, that's enough of that, if someone else wants to carry it on, please feel free: like pocket bullets, you know you have to fold, sometimes, even if you are reasonably certain the others hold off-suit 8,2. I might even look in from time to time.

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I'd love to see your efforts get the recognition they derseve B.W. (and C.Bob). I'm sure there is plenty of room in the climate shift to accomodate?

As for 'the oceans' They have been ex[posed to a slow upward temp rise for at least 150yrs now so surely there 'forcing is now only just coming to the fore? (deep ocean heat returning to the surface etc?)

With some areas of the planet warming much faster than others there is also the issue with the shelf seas in those regions acting on a short term 'seasonal' way (but offsetting past heat transport into those regions backing up heat further south??)

I told you's guys at the time that such close scrutiny made me dizzy.....big pictures and constant revision I can handle but close,crisp focus????

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As for 'the oceans' They have been ex[posed to a slow upward temp rise for at least 150yrs now so surely there 'forcing is now only just coming to the fore? (deep ocean heat returning to the surface etc?)

The underlying forcing trend, if I recall correctly (it's quite possible that I am wrong) required is approx 0.015C/Yr. That could easily be accomodated by long deep currents transport heat deep in the ocean and don't resurface for many many years.

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I'm sure there is plenty of room in the climate shift to accomodate?

Unusually for a 'sceptic' theory at the time, the LI required the observations to be identical to that of the AGW community. There was no denying; I think that got under some people's noses a bit. I never liked the label sceptic nor denyer; we simply wanted to create a simple climate model and find out at what point we needed to add CO2 to the model. We never had to.

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The oceans will do the trick for you. Not forgetting Newton's Cooling Law which guarentees hysteresis. Nice to see Cap'n Bob' around again, but if anyone thinks I am going to go through what we both did last time, they can forget it.

On the LI thread we made predictions and hindcasts. We extrapolated the formula, and weightings back though time, and hindcasted the Little Ice Age, we also carried forward in time, and, as far as I can ever see, the forecast it made was the only forecast at the time that predicted a slow down in the rate of temperature increase since the turn of the century and it was still posting positive anomalies, so global temperatures would still be increasing. The problem with the forecast is that I assumed a static sea-ice level, not the horror story that is developing the Arctic, so the slow down rate would be mitigated by this, to, I think, pretty much exactly what has happened with the global temperature series. We even found a flaw in the HadCru series - we couldn't get the temperature series to match, until TWS pointed out a paper that showed the error of measurement of the period in question - so the analysis predicted a fault with the global temperature series.

It's all on the LI thread - even how to do it yourself (so no hidden factors, or assumptions) I don't want to get involved in it; I promised my wife that I would leave it alone after blowing £10k on papers, journals, books and materials and spending two years living it inside and out, online, and elsewhere.

Pity I missed out on the discussions, I think I would have enjoyed them. Could have passed the idea along to a few lecturers and researchers, see what kind of feedback they might have. With the ocean heat content still rapidly rising, how does that fit in the the LI concept?

C-Bob didn't seem to answer my question but perhaps you can (if your not hibernating in the hole already!)? What kind of weighting did you apply to the different forcings, solar/enso etc, and how did you come up with the weighting?

I appreciate any answers you can give.

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Pity I missed out on the discussions, I think I would have enjoyed them. Could have passed the idea along to a few lecturers and researchers, see what kind of feedback they might have. With the ocean heat content still rapidly rising, how does that fit in the the LI concept?

C-Bob didn't seem to answer my question but perhaps you can (if your not hibernating in the hole already!)? What kind of weighting did you apply to the different forcings, solar/enso etc, and how did you come up with the weighting?

I appreciate any answers you can give.

I used a gradient descent algorithm to derive the weightings, and treated the parameters as a system of equations on the basis that climate is deterministic, and will shown as such if we ever slay Laplace's demon, it is the emergent behaviour of climate that is chaotic. I never published the math, well, frankly, because it would have put a lot of people of seeing all these alien sort of symbols flying around everywhere. I also used custom software which wot I wrote to do the job. I alluded to the techniques throughout, however, but only one person ever asked, but he seemed like a PhD student, so I told him/her, to, ahem, sod off.

The system of equations are simple. Assuming we are looking at sunspots (s), sea-ice (i), volcanic (v), and enso(e), and we know plenty of equations for the system (the entire dataset can be fed the equations, in fact - but then that'd be overfitting!) we might say (note: I didn't say!) 255s - 123456i - 5v + 123e = temp. I tried both Guassian decomposition, and LU decomposition to try and solve the system, but it never worked properly (those algorithms seemed to be numerically unstable - it could've been my code, I guess!)

The reasoning behind this approach is simple. Given that no climate parameter is transcendental (perhaps an assumption) and that the composition of a global temperature series is normally analysed by some form of weighted parameter analysis which derives the most important signals within the series, it should be possible to do the inverse.

Problems: statistical analysis of the results were problematic because degrees of freedom, which are assumed to be independent, aren't - this is also a problem for just about every other climate body on the planet; and one that I've never seen resolved. For instance, Solar forcing melts ice, enso includes solar forcing, sun-earth distance may be a factor in volcanic eruptions etc etc etc etc. Of course, if one excludes the sun from the analysis, pseudo-proof of your work is much much simpler! I find it endless amusing that climate scientists tend to require criticims of their field by experts, but they seem quite happy to write some of the most appalling software on the planet; most of the time, I am surprised it even compiles. Scientists should not be writing computer software.

Using novel algorithms that are undoing a consensus is extraordinary, so the proof of it's correctness must be extraordinary, too (I wrote the software in SPARK, btw, so I could prove it was correct, which is eons ahead of current agencies that use MathLab, Fortran etc etc) For instance, the code in most climate models use a datatype called IEEE Float, which, whilst immensely useful, cannot even represent 1/10th inside a computer. This is a much more serious problem than you might imagine, see here, for more details.

And, you'll note, most people who read this post, have now gone to sleep. You'll also note that some things were purposefully held back since I was eventually hoping to publish.

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Cheers for that Boar! Between reading up on some of the things you mentioned and writing a literature review, it may take a few days for me to give a decent reply.

Saying that, if you were able to kinda stitch together what you have done up to this point, I could pass it around and look for feedback from a few that are significantly more knowledgeable in this area than I.

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I wouldn't bother now. I don't think I've even got the software or my notes left. I might revisit it should the consensus fall to bits laugh.png

On a more serious note, I took the work that I did incredibly seriously, and whilst I am less bitter and twisted about the treatment Cap'n Bobski and I received at the hands of the more enlightened members of this board, it still feels a little raw even this far out; so, I feel, I would be unable to sensibly accept honest critical appraisals of my work.

You are welcome to replicate my approach, or for anyone else to do so - it's public, now, but I won't be helping. Sorry.

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