Climate Modeling using a Leaky Integrator

[Admiral_Bobski]

I am not sure how to copy and post text so i have had to do this the long way.

WBZ-tv in Boston ran a short video interview with harvard astrophysicist Dr Willie Soon back on the 14.04.09 discussing the plausible scenarios of a dimmer sun on the Earth's climate.

A reduced energy imput from a dimmer sun will result in less heating of the oceans surface which would lead to less evaporation from the oceans surface. This would result in less water vapor which is by far the Earth's major greenhouse gas.

Less water vapor would result in viewer high cirrus clouds which trap more heat than they reflect.

Reduced energy imput from the sun would equal less energy to bring water vapor high into the atmosphere so more would collect a few kilometers from the surface resulting in more low clouds.

Low clouds are much more effective at reflecting sunlight which would produce a net cooling effect.

Dr Soon also spoke at the International conference on climate change which was held in New York in early March.

I stand corrected

CB

[VillagePlank]

Moderator(s) and I have decided that this thread is going to be truncated so it is more of a tutorial, than, a free for all. I hope you all approve? I'm sure there will be a general thread associated, too, so discussions to continue there.

The big process thingy is due soon, so hopefully, that will revitalise the whole LI thing.

(EDIT: the big process thingy is about using a process to select the data from the data itself - generally using fourier analysis etc etc. I'm working on it, but it's difficult to make clear what the hell is going on - sorry guys!)

Edited May 31, 2009 by VillagePlank

[AtlanticFlamethrower]

Thank you Captain_Bobski and especially VillagePlank for this wonderful thread.

I don't understand elementary calculus so please pitch replies at a level I can understand

Can you combine a Leaky Integrator model with other calculus models? Or are calculus models always self-standing?

For example, there are sources of non-solar heating entering the Earths climate system: geothermal. Impact, minimal, so no need to add that to the model.

However, more relevant: what if solar heating of the oceans releases more CO2 and CO2 does have a warming effect, namely it makes the hole in the bucket smaller. Can you model this easily in the same model? Does that question make sense?

BTW: I just came up with a new model to explain internet discussion threads! It's called the "squeaky interrogator". In a discussion thread the amount of understanding leaking from it is proportional to the level of understanding that the thread has reached!

[VillagePlank]

Thank you Captain_Bobski and especially VillagePlank for this wonderful thread.

I don't understand elementary calculus so please pitch replies at a level I can understand

Can you combine a Leaky Integrator model with other calculus models? Or are calculus models always self-standing?

For example, there are sources of non-solar heating entering the Earths climate system: geothermal. Impact, minimal, so no need to add that to the model.

However, more relevant: what if solar heating of the oceans releases more CO2 and CO2 does have a warming effect, namely it makes the hole in the bucket smaller. Can you model this easily in the same model? Does that question make sense?

Hi AFT,

The basic idea of the LI is that it models change, and, particularly, latency of change over time. It started out as simply an assertion, but the correlations started to add up, in my opinion, quite substantially. The model, in fact is remarkably simply, and I've tried to show how it can be replicated in Excel. The conclustions, of course, are not anywhere near as simple.

The key point is the lack of recourse to CO2 forcing, to get something that correlates at over 90%. What does this mean? Has there been some sort of fundamental error? Is this something people should be considering?

I don't know, and, to be honest, I've concentrated, on work and at home since my last post, here. I think that there is mileage in it, and I just haven't had the time to complete it.

Sorry,

VP

[AtlanticFlamethrower]

Well, there's very little reward for your efforts here in any case. You have been generous enough to take it as far as you have. The little demonstration clearly shows you do not need CO2 forcing to model recent climate change to a very high degree of correlation.

There was no reason whatsoever for scientists to have made such a huge deal about CO2 over the last two decades. They could have easily suggested a solar based LI model for the same funding they had.

Of course, your LI model is only correlation and so, on that basis alone, is no status higher than the CO2 driven model which is based on correlation (that is if we assume CO2 does increase warming, and most skeptics agree temperature increases proportionally as CO2 increases on a logarithmic scale, 1 °C per doubling).

If only the two models could be combined?

[VillagePlank]

Right, I've got my thinking cap on, not going to lose my rag with anyone, so over the coming weeks it should be all guns blazing. I still think that there is mileage to go with this one. If you google "Leaky Integrator", then this page is 5th in the list! If the moderators have a spare moment, could they post page read/download stats?

[Admiral_Bobski]

I haven't forgotten about this thread - honest! I don't want people to think I've abandoned the idea. I'm just not entirely sure where to go next with it.

Any thoughts on what to do next, VP?

CB

[VillagePlank]

I want to put it more a firm theoretical ground, and frame it on a more logical analysis.

Sounds like a nightmare, but essentially this means conducting (and writing up for those who don't know how to do it) Fourier Analysis, and perhaps, Wavelet analysis, in order to select the 'things' to put into the LI. Preliminaries show the 11 year sunspot cycle is very obvious, and there are few other things. If we do that, then my reasoning is, start with the pronounced cycles, and then gradually identify and include other cycles in descending order and see where we go.

That way the selection of data is driven by the data itself and not by 'arbitrary' selection, and this should tighten up the case somewhat.

Currently I am writing a quick guide to Fourier Analysis - conceptually it's not that difficult - and am wondering whether to put in the mathematics, or simply to leave it as a conceptual guide.

[VillagePlank]

I have posted links on other websites to provoke some hyper-criticisms. Hopefully, that'll help to add to the direction to take.

Edited August 16, 2009 by VillagePlank

[VillagePlank]

I want to put it more a firm theoretical ground, and frame it on a more logical analysis.

Sounds like a nightmare, but essentially this means conducting (and writing up for those who don't know how to do it) Fourier Analysis, and perhaps, Wavelet analysis, in order to select the 'things' to put into the LI. Preliminaries show the 11 year sunspot cycle is very obvious, and there are few other things. If we do that, then my reasoning is, start with the pronounced cycles, and then gradually identify and include other cycles in descending order and see where we go.

That way the selection of data is driven by the data itself and not by 'arbitrary' selection, and this should tighten up the case somewhat.

Currently I am writing a quick guide to Fourier Analysis - conceptually it's not that difficult - and am wondering whether to put in the mathematics, or simply to leave it as a conceptual guide.

Of course, this only works for external climate forcings, but doesn't work for internal climate forcings, like volcanic activity, which are, for all intents and purposes, random events. Ice cover might be cyclical, so hopefully we'll see that.

[VillagePlank]

The leaky integrator has been linked to climate, before: book

From that, a better theoretical basis for the LI model might be Torricelli's Law which is specific formulation (from that wiki) of Bernoulli's Principle although, of course, these are about fluid dynamics and not thermodynamics.

Might be time to do the hard work and link it formally.

Yikes.

Edited August 16, 2009 by VillagePlank

[BARRY]

The leaky integrator has been linked to climate, before: book

From that, a better theoretical basis for the LI model might be is Torricelli's Law which is specific formulation (from that wiki) of Bernoulli's Principle although, of course, this is about fluid dynamics and not thermodynamics.

Might be time to do the hard work and link it formally.

Yikes.

thanks VP now i understand what your getting at.

[Methuselah]

The leaky integrator has been linked to climate, before: book

From that, a better theoretical basis for the LI model might be Torricelli's Law which is specific formulation (from that wiki) of Bernoulli's Principle although, of course, these are about fluid dynamics and not thermodynamics.

Might be time to do the hard work and link it formally.

Yikes.

Thanks VP...It's while since I've used any of those equations...

[VillagePlank]

thanks VP now i understand what your getting at.

Yeah - I wish I had found that book reference about twelve months ago; better late than never, I guess. I suppose that it adds extra weight to the LI hypothesis that others have been thinking along the same lines.

Good job CB asked the question all that time ago ... we mustn't forget that it was CB's enquiry into latency effects that started this whole thing off!

Edited August 16, 2009 by VillagePlank

[Admiral_Bobski]

Yeah - I wish I had found that book reference about twelve months ago; better late than never, I guess. I suppose that it adds extra weight to the LI hypothesis that others have been thinking along the same lines.

Good job CB asked the question all that time ago ... we mustn't forget that it was CB's enquiry into latency effects that started this whole thing off!

That was a great find, VP! How on Earth did you come across that?! There's a lot of stuff in that book to read and digest - it might be prudent for everyone interested in the LI to give it a good read through (which I shall hopefully be doing a bit later on today).

Thanks for the shout-out, too. Of course, we wouldn't be anywhere near this point if you, VP, hadn't defined the process and put so much time and effort into explaining it and working on it, and for that I thank you.

I must away now to appease my children (only 3 more weeks of hols left - yay!), but I'll get reading later on.

CB

[VillagePlank]

Over on WUWT a discussion has moved onto hysteresis, so I posted a comment and a link to this thread. Hopefully, we'll get some input from them too. Discussion is here I posted a link on the tip-off page on that site.

I've also emailed RealClimate with a link and (very) brief overview, so it'll be interesting to see what those fine fellows have to say. Hopefully, we'll get some good criticisms from them, too.

Essentially, the cat is out of the bag.

That was a great find, VP! How on Earth did you come across that?! There's a lot of stuff in that book to read and digest - it might be prudent for everyone interested in the LI to give it a good read through (which I shall hopefully be doing a bit later on today).

Yeah - a bit disappointing that it's not an entirely original idea, being that it's in print elsewhere (I should have guessed, really. Dynamic equilibria is the starting point for all non-linear systems in a huge swathe of fields, not limited to neural nets (which is where I found out about it)) but none-the-less, nice to know we're not completely barking mad, or indeed barking at the moon, or barking up the wrong tree.

Still slightly suspicious, because it takes little more than an hour to get the data and integrate it - so why has no-one else gone this far? Actually, suspicious is the wrong word - more like 'worried' that somewhere we have made a fundamental error ...

Edited August 16, 2009 by VillagePlank

[VillagePlank]

Sunspots are caused by magnetic activity inside the sun, which then, points to a path to the hypothesis that you and Roger have supposed. If you can cross correlate this activity, throughout the solar system, then you might have a general theory that might be able to predict weather and climate - which, to my mind, is a very powerful, and motivating notion.

Here's a link that, I think, Roger, and BFTP might find very interesting ....

[VillagePlank]

Here's the Fourier stuff.

I will start applying it, as outlined above, at some point this week. You should be able to ignore most of the maths and glean what it is that the Fourier Transform does from this.

DFT.pdf

[Admiral_Bobski]

Here's the Fourier stuff.

I will start applying it, as outlined above, at some point this week. You should be able to ignore most of the maths and glean what it is that the Fourier Transform does from this.

Thank you VP - an excellent inroduction

So, basically a Fourier Transform should be able to break the observed temperature trend (in our case) into a set of waveforms, with each separate waveform being the effect on temperature of a separate cause (the original temperature graph being the sum of these separate waveforms).

Then it would be a case of ascribing each waveform to a known (or, perhaps, an unknown) climatological phenomenon.

Is that right?

<_<

CB

[VillagePlank]

Thank you VP - an excellent inroduction

So, basically a Fourier Transform should be able to break the observed temperature trend (in our case) into a set of waveforms, with each separate waveform being the effect on temperature of a separate cause (the original temperature graph being the sum of these separate waveforms).

Then it would be a case of ascribing each waveform to a known (or, perhaps, an unknown) climatological phenomenon.

Is that right?

<_<

CB

Spot on. The largest amplitude that appears in a Fourier Analysis, of, say, the Hadley Series is the sunspot trend - which is how I connected your initial query into a framework for including hysteresis into a climate model by selecting sunspots. So, based on the method given earlier, the sunspot data will always be the first to be included into the LI model.

I am having a few difficulties with source-code at the moment, which is why it's not complete, yet. You can do an analysis in Excel - but I find it a little awkward, myself (it uses the imaginary number line (and I don't want us to go down that route with the LI) and not a rational one) but not OpenOffice so I'm writing the source code to do this. Will publish that at some point this week, hopefully, and then the results should start piling in.

[Methuselah]

Thanks for going to all that trouble, VP...It must be fifteen years' since I ever used those formulae.

[VillagePlank]

Thanks for going to all that trouble, VP...It must be fifteen years' since I ever used those formulae.

I'm not so sure it's error free, so please let me know if anyone finds any problems with this.

[Methuselah]

I'm not so sure it's error free, so please let me know if anyone finds any problems with this.

I doubt I'm sufficiently qualified, VP? But, I'll let you know if I see anything.

[VillagePlank]

I doubt I'm sufficiently qualified, VP?

I doubt any of us are!

[AtlanticFlamethrower]

VP, absolutely keep going. this thread has inspired me to think up other instances where you can use the leaky integrator model, such as life expectancy.

Life is not like a box of chocolates, but a leaky bucket...

Keep up the good work. It's a fresh new perspective.

I also now think I understand why you can't combine the models - neither model assumes a non-linear system, rather they both are modeled with linear differential equations, whereby the initial linear bias is then adjusted according to variables, feedbacks and such like.