Leaky Integrator Discussion

[Roger J Smith]

Here is the link to the sunspot thread:

[VillagePlank]

Thus absorptivity does not increase more than emissivity as energy in a system increases, because emissivity increases as a fourth power

The critical part is that as an object acquires energy it is more difficult to acquire more energy, and as an object loses energy is becomes more difficult to lose energy. Graph of this effect, over time, is on PDF in main LI thread.

[VillagePlank]

Diessoli has kindly, and correctly, pointed out that eq5 in the PDF document is in error (different units of measure) There are even more howlers in there if you care to look for them Of course, there is an assumption that the PDF is some sort of finished polished assertion. That is not true, I've made it clear that it's not true, I've made it clear there are errors in it.

I should add that the SB law is not required for the LI; it was a thought, early-on, and it's there to demonstrate that hysteresivity exists in all dynamical systems. In fact that hysteresivity exists in dynamical systems is so self-evident there should be a law for it.

EDIT: for clarity eq5 does not use correct units of measure, so is false. Even more so, and yet to be pointed out, is that even if it were true, it only works from absolute zero, not, say, room temperature.

EDIT2: eq5 should use j* on the left hand side, instead of T. The resulting graph is still the same, and it still demonstrates hysteresivity.

Edited December 12, 2009 by VillagePlank

[VillagePlank]

This has gone in a very interesting direction with all sorts of stuff that I know little about.

Therefore, I want to make it clear, as I already have, here, that the LI is a mathematical exercise and attributes no physical process as it's cause (or even attempts to)

Frankly, I just don't know enough about it. I should have cut out the SB law from the PDF.

[Admiral_Bobski]

If the SB law is not directly relevant to the LI then I agree that we should drop it. We may find, further on down the line, that it will come into play. In the meantime I shall do some more reading up on it and see if I can find anything that ties it in to what we're doing here.

The good news is that my earlier description of a potential physical process that would explain what is happening is still valid (I think). It may not describe the process of hysteresis - in fact it obviously doesn't if hysteresis occurs at the subatomic level, as saperlo says (and I'm sure he is right) - but it does describe the basic processes of absorption and emission at the atomic level.

The even better news for you, VP, is that this process is irrelevant to the mathematical work you are doing at present. The maths would remain the same regardless of the physical process taking place.

Is there anything you are fuzzy on that is impeding your progress, and if so then can I help at all? Remember: there's no such thing as a stupid question - only stupid answers.

CB

[saperlo]

Apologies to all if I’m covering stuff that’s old hat – I have read back over previous discussion now and am better acquainted with the thread (although maybe not enough, so thanks to all – esp. VP and Cap Bob - for your patience!)

Myself, I’m very much in the “yet be proven” camp on AGW, and it’s great to see it being investigated and discussed without all the usual emotive stuff.

VP regarding possible drivers for your hysteresis thesis, have you considered

1. Tilt/wobble of the earth wrt the sun (nutation), which is cyclical every 18 years approx. Coupled with the variables of solar activity will certainly vary the exposure of the earth to the sun’s radiation, in an extended and complex cyclical pattern (implications of which may be years away being understood)

2. Decreasing salinity of oceans due to sea level rise – fresh water has a lower specific heat capacity than salt water and the oceans are a massive heat sink - as the sea becomes more dilute it releases this heat progressively. Even a small change will liberate a lot of energy

3. Variation in Pacific algal blooms which follow solar cycles

[Admiral_Bobski]

Apologies to all if I'm covering stuff that's old hat – I have read back over previous discussion now and am better acquainted with the thread (although maybe not enough, so thanks to all – esp. VP and Cap Bob - for your patience!)

Myself, I'm very much in the "yet be proven" camp on AGW, and it's great to see it being investigated and discussed without all the usual emotive stuff.

VP regarding possible drivers for your hysteresis thesis, have you considered

1. Tilt/wobble of the earth wrt the sun (nutation), which is cyclical every 18 years approx. Coupled with the variables of solar activity will certainly vary the exposure of the earth to the sun's radiation, in an extended and complex cyclical pattern (implications of which may be years away being understood)

2. Decreasing salinity of oceans due to sea level rise – fresh water has a lower specific heat capacity than salt water and the oceans are a massive heat sink - as the sea becomes more dilute it releases this heat progressively. Even a small change will liberate a lot of energy

3. Variation in Pacific algal blooms which follow solar cycles

Hi saperlo

And thank you for contributing!

We haven't looked too closely at specific drivers yet (or perhaps it would be better to call them processes, as we are considering the Sun to be the main actual driver). With regards to axial tilt, the major variations in insolation due to Earth's tilt and distance from the Sun - the Milankovitch Cycles - operate over timescales much longer than the 150-or-so years that we've been focusing on so far, so we haven't incorporated them. When we (hopefully) extend the LI back over the last 11,000 years they may become more of a factor. (We have sunpot proxy data going back 11,000 years, so we're hoping to go back at least that far.)

The Milankovitch cycles are: Orbital Eccentricity, with a period of between 100,000 and 413,000 years (depending on which component of the variation you are looking at); Axial Tilt, with a period of roughly 16,000 years; Axial Precession, with a period of around 26,000 years; Apsidal Precession, with a period of around 23,000 years (on average); and Orbital Inclination, with a period of around 70,000 years.

In terms of our time range of about 11,000 years, it is the axial tilt, axial precession and apsidal precession that might have some relevence to global temperatures.

CB

[Guest diessoli]

Hi CB,

I have some objections:

Since SB incorporates the Planck constant, it must hold true down to the atomic scale (since the Planck constant is a quantum-mechanical constant). This means that the LI concept must also hold true down to the atomic scale.

The SBL describes the behaviour of black (and grey) bodies and is not valid on an atom level. As you point out further down, atom absorb and emit energy in discrete amounts which means they cannot be black bodies (which emit and absorb all wavelengths).

What SB tells us is that the absorptivity of a body increases at a slightly faster rate than its emissivity does.

Black bodies absorb and emit exactly the same amount of energy. In grey bodies there is a constant linear factor between absoprion and emission.

The SBL does not tell us anything about how absortion or emission properties of a body changes, it only tells us that a black bodie's radiation depends on it's temperature alone.

D.

[Gray-Wolf]

But are we not providing the drivers for excess e energy within the system which ,in the past, may have forced variance in the system but today only bring the 'extra energy' to be trapped by the excess GHG's we have blanketed the planet in?

Are we not exploring how we can actually accelerate the slow process of heat capture by highlighting processes that place a surplus into the system?

You know my fears are grounded not only in what 'we' are doing but also in the massive works that Mother N is always capable of doing?

We tend to focus on massive volcanic eruptions as a very real cooling mechanisms but now we are exploring the very things that may help fuel the warming by promoting 'natural,cyclical warming' which now surely stands to be trapped (in some part) by our meddling in the atmospheric 'mix'?

Thanks saperio for the input of the 'SB' laws... it was all too black and white for me

[Admiral_Bobski]

Hi CB,

I have some objections:

The SBL describes the behaviour of black (and grey) bodies and is not valid on an atom level. As you point out further down, atom absorb and emit energy in discrete amounts which means they cannot be black bodies (which emit and absorb all wavelengths).

Black bodies absorb and emit exactly the same amount of energy. In grey bodies there is a constant linear factor between absoprion and emission.

The SBL does not tell us anything about how absortion or emission properties of a body changes, it only tells us that a black bodie's radiation depends on it's temperature alone.

D.

Hi D,

Yes, I'm starting to suspect I've got some things a bit confused here. This "absorptivity increasing slightly faster than emissivity" thing does not appear to be SB Law-related at all, and yet I'm sure I've read something to that effect while we've been doing the LI. I'm going to have to go back through the thread and see if I can retrace my steps and figure out where I got that from.

Gray-Wolf, I think you still haven't quite grasped the idea behind this investigation. The leaky integrator's process is one that comes out of the equation - all we have to do is figure out what inputs are required and the LI does the rest. The output of the LI is our equivalent of global temperature.

What we are trying to do is to see which inputs are required to give an output that looks like reality. So far we have a pretty good correlation with reality (0.91) and we've only had to input sunspots, ENSO, volcanic activity and albedo (these latter two using proxies).

The idea is to refine the output by successively adding inputs (which is called a perturbative method). So far there has been no need to add CO2! We've managed to get a remarkably promising output without the supposed effects of CO2, which begs the question (if the LI should stand up to scrutiny, of course) are the supposed effects of CO2 actually real effects?

CB

[Roger J Smith]

I am beginning to catch on to the actual concepts of the LI after going back and forth a couple of times. I have some comments and suggestions. In general, I think you're onto something very promising with this, but I think you would agree the concept is only correlating with temperature over decadal time scales. Perhaps some other variables would force it to perform on year-to-year time scales. But bear with me, there are several points to follow:

(.a.) I am not sure why you start the LI as high as you do in the graph correlating the LI (sunspots and volcanic) with CET (which I note are annual values). In 1749, the solar activity had just returned to "regular active" service as of 1718. Would it not be more in keeping with the lag concept to start it at 30 instead of 50. Then you might also get a better fir with CET which are generally below your index curve in the first half century?

(.b.) You could easily extend your LI back as far as the MWP or 290 AD by using Schove's values that I show in the linked thread. You could estimate annual values by assuming that all peaks have similar profiles to modern peaks. The strongest peaks like 1372, 1382 could be modelled like 1947 1957. Runs of moderate peaks could be modelled like 1893 1905 1917, etc. If you wanted a list of annual sunspot value estimates for any period extending back from 1749, I would be happy to provide one (no work involved, already have it on file). While not as reliable as the modern data, it's all we could possibly have at this point. By the way, I had a look at the MWP and it was sustained through 2-3 centuries of rather average looking solar activity, while the 14th century that turned colder was a period of high solar activity. This is why I am somewhat suspicious that sunspot number is not as robust a climate predictor as the modern period might suggest. But perhaps it's all in the lags and leaks.

(.c.) Volcanic activity in that earlier period would have to rate as a general unknown. C'est la vie. How much did you find that adding volcanic dust estimates to the sunspot count resulted in better fit? I would say the only really strong cases are 1816-19 and 1884-88.

(.d.) Now for the possibly revolutionary step that might bring inter-annual variability into play. What about adding two lunar components to this LI index, with a much shorter lag function involved. I would propose that you try running your model with these two cycles added, starting from 1749 as follows ...

(.d-1.) a cycle of 18.6 years in duration, to account for declination, setting the amplitude at about 30% of total CET annual variability, and the peaks at year eight of the cycle, which would equate to placing the first peak in 1753 (more specifically 1753.6), therefore the last one in 1995.4. Note, there is no lag in this index as applied, but I believe there is a built-in three year lag from optimal zonal flow at year five of the declination cycle, that is five years after maximum declination. The lag is zero years for central North America, two years for the western Atlantic, and three years for the UK (from my research).

(.d-2.) a cycle of 4.43 years in duration, to account for lunar perigee, setting the amplitude at about 20% of CET annual variability, and the first peak set for 1748.0 (or 1752.4) ... you would have to be careful to make this precise or it would wander off the schedule (4.4 years would not be precise enough). This factor would account for the greater tidal pull north and south with perigee at southern and northern dec max. We are currently just past a northern perigee peak in this (from 1748.0 you would get a peak at 2009.4).

Just a general note here, your LI charts begin at 1749.5 and not 1749.0 in this scheme, the meaning of 1749.5 is mid-year so any annual average has the value 1749.5.

I would love to see how the LI model responds to these two variables, and then if it shows further improvement, we could add a Jupiter modulation of 11.86 years. If you want to go for that one too, I would need to give you a code as the signal is not a sine wave, these lunar signals can be approximated with sine waves to make it easier. You can spice up (d-2) by running a second-harmonic offset at 2.2 years (i.e. half the amplitude, giving smaller peaks every 2.2 years between the strong peaks).

I would encourage you to retro-fit the LI model to 1659 at the very least to give full overlap with the CET.

If these additions gave good results, then we could start analyzing the errors on an annual scale to see if other periodicities showed up, such as the mean 7.1-year El Nino signal.

Take your time, I've been at this for 29.5 years, about the same time it has taken Saturn to do one orbit around the Sun. PS, I want a third of the Nobel prize money if you upgrade, publish and win.

Edited December 13, 2009 by Roger J Smith

[Guest diessoli]

OK.

I have no read through the 21 pages of the pinned thread. I've not tried to follow each argument and counter argument, but to understand the gist of your idea.

Of course, there is an assumption that the PDF is some sort of finished polished assertion. That is not true, I've made it clear that it's not true, I've made it clear there are errors in it.

Yes, you have made clear that it's only a draft. But you also asked for criticism

Here you go, and as always constructive criticism is always helpful.

which I thought I provide by pointing out an error. What's the point in asking people to criticize your work and then, when they do, complain about it, saying that you told them there where errors?

Anyway.

[...] it's there to demonstrate that hysteresivity exists in all dynamical systems. In fact that hysteresivity exists in dynamical systems is so self-evident there should be a law for it.

Not all dynamical systems exhibit hysteresis. An N-body system does not, to give just one example.

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?

You might be overfitting.

The data sets you fit (sunspots, volcanic forcing, ...) have enough variability to fit the temperature curve nicely. The more noisy data you add, the better your fit is likely to become.

I could not find your XLS file with all the data sets and parameters, or I would have made some changes to demonstrate what I mean. Would you mind posting it?

But try and fit your model to only a part of the data(e.g. the first half) and see how well it describes the part not used for fitting.

You can also try and replace one of your data sets with, say, stock market prices.

added:

I've started to gather the data and do the regression. But looking through the thread again, I can't find what model you have been using in the end.

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.

For what it's worth:

Robinson uses the leaky bucket to illustrate the climate system, a better metaphor than the "greenhouse" image, if you like.

An illustration of a zero-dimensional climate model with negative feedback. You will find that one of the first things he points out is that the equivalent of the rate of loss of water is determined by the greenhouse gases in the atmosphere.

D.

Edited December 13, 2009 by diessoli

[SleepyJean]

So that's where that stands. I keep looking for a reason for this weakening, which seems to be fairly constant going back into the less reliable records of Schove. The conventional explanation is not really much more than a description, the Sun stays regular for long intervals, then the magnetic fields weaken and its cycles weaken. But there is quite a difference between the weakness of the Maunder and the Dalton. The un-named later weak period is a half-cycle removed and may represent a secondary feature pointing to a 90-year long cycle.

I'm going off to look for the thread on solar variation that I posted.

Comets? Combinations of comets? Meteors/Asteroids (never did quite sort out which was which). These are things which have irregular shaped orbits which could perhaps interfere with the effects of the more regular-shaped planetary orbits and relationships, but of course it is difficult to trace records of comets as they can have such a long orbit. Just a thought, however, and may reflect my lack of understanding more than my understanding of your theory.

[VillagePlank]

Yes, you have made clear that it's only a draft. But you also asked for criticism which I thought I provide by pointing out an error. What's the point in asking people to criticize your work and then, when they do, complain about it, saying that you told them there where errors?

Anyway.

I wasn't complaining. I wanted to make it clear that this was something written a long time ago containing a multitude of errors. I appreciate the time and effort you've put in. Constructive criticism, of the sort you are kindly donating, is the only way to push this from a hobbyist idea, into something that might be much more interesting. The point of interest (ie time for me to start buying books and to start learning more) occured when the correlation of r=0.91 occured. It is, still, very much so a work in progress.

Not all dynamical systems exhibit hysteresis. An N-body system does not, to give just one example.

I should be more specific. A dynamical system is one where some previous quantity is mapped into some future quantity. To go further than this definition requires the use of topology. I have a book on order from Amazon. Therefore, a more accurate definition is that any real (the number, not existential) dynamical system, by definition, must demonstrate hysteresis apart from the special case where the constant modifier = 1. I am working on a proof by mathemtical induction. I will carry on with the topology argument once I understand more about it (ie got the book, and read it)

In terms of the N-body system (something I know little about) surely there is some value that is carried over to the next time iteration? Perhaps I should refine further and specify a difference between continuous and discrete evolution functions?

You might be overfitting.

The data sets you fit (sunspots, volcanic forcing, ...) have enough variability to fit the temperature curve nicely. The more noisy data you add, the better your fit is likely to become.

I could not find your XLS file with all the data sets and parameters, or I would have made some changes to demonstrate what I mean. Would you mind posting it?

But try and fit your model to only a part of the data(e.g. the first half) and see how well it describes the part not used for fitting.

You can also try and replace one of your data sets with, say, stock market prices.

added:

I've started to gather the data and do the regression. But looking through the thread again, I can't find what model you have been using in the end.

Yes, the constants, and parameters, whilst easy enough to to simply copy off the thread have not been published- nor has the model that ties it all together. You should be able to reproduce the results uisng the run-through. I have to keep something back, as I am sure you understand. For interest, it uses gradient descent techniques, and it treats algebraic expressions as a hierarchy (but that may go). This approach may well be wrong; so, I need to generate random datasets and pass them through the techniques to test for quality and confidence.. I think I might have mentioned this somewhere before. I'm sure I've made it clear that it either succeeds or fails on this point (ie that we can be confident that the correlation exists above the 1.96sd confidence level (>95%))

I can't post XLS documents without originating details held within the document itself. ie It will have my name on it. I suppose I can set up a nonsense profile and create it there ...

For what it's worth:

Robinson uses the leaky bucket to illustrate the climate system, a better metaphor than the "greenhouse" image, if you like.

An illustration of a zero-dimensional climate model with negative feedback. You will find that one of the first things he points out is that the equivalent of the rate of loss of water is determined by the greenhouse gases in the atmosphere.

I have been in touch with Robinson and we have exchanged emails. He is, I am sure he wouldn't mind me saying, interested in the formal (finished) write up.

Edited December 13, 2009 by VillagePlank

[VillagePlank]

As a quick update, I am not so sure that the term hysteresis is in and of itself the correct term. In natural English, where that term has been used, it is used to denote 'something left over' and it is not restricted to positive numbers either, in terms of this discussion, something can be be negatively left over. I have avoided the term 'lag' because of it's association with, ahem, more vehement sceptics, I can't use remainder since it causes namespace problems with number systems ... I am very open to suggestions ...

It might be worthwhile treating the term 'hysteresis' as a borrowed term at this point for lack of another.

Edited December 13, 2009 by VillagePlank

[VillagePlank]

Take your time, I've been at this for 29.5 years, about the same time it has taken Saturn to do one orbit around the Sun. PS, I want a third of the Nobel prize money if you upgrade, publish and win.

Thanks for your input Roger. As far as I can see the LI doesn't really work on anything apart from decadel timescales, although I haven't expended any real effort in trying, to be honest - even the ENSO parameters are averaged out. I suppose this is to be expected since the primary solar cycle (c. 11 years) is around a decade, and the premise is that 'something' from the last solar cycle or last few solar cycles is 'left-over' which, obviously, creates warming during, but especially after, very active solar periods. It could well be that the sun is driven from planetary factors, and that's certainly, in my view, something worth looking at.

Diessoli makes a good point in that if the data is sufficiently spread then it should be, at least in theory, possible to make good fits regardless of the data used.

The current version pushes all raw data through the sigmoid function precisely to avoid such problems. Since the sigmoid function squashes extremities, and can restrain all input values between zero and one, it introduces semi-linearity to the system, and each component added can therefore be assigned equal weight. It also avoids having to filter data looking for values outside the main extremities (st-dev >2) and interpolating them which is a valid method, but avoidable at this juncture - avoidable meaning it introduces more complexity (and more software writing - need to write the least-squares routine (actually it is written, but is not of sufficient quality))

Edited December 13, 2009 by VillagePlank

[Admiral_Bobski]

So the quickest way to test diessoli's assertion is to go back to our first run - the basic LI with just sunspot data - and then, instead of adding ENSO, volcanoes and albedo, throw in three sets of white noise (or even just one set, to begin with)?

Unfortunately my computer crashed a few months back and I have lost the LI Excel sheet I had been working with, so I shall have to start from scratch, but I could try this out if anyone wants me to.

So far we have had a few objections to specifics of terminology (whether the LI describes actual hysteresis), the application of datasets (whether white noise datasets will yield the same results - which is at least testable), and to omissions of data (like leaving out CO2), but can anyone think of a broader reason why the LI can't be correct? Is there any objection to using the LI as a way of introducing climate-system lags?

CB

[VillagePlank]

So the quickest way to test diessoli's assertion ...

My plan to verify or otherwise the LI is something like this ...

y_t=f(x,y_t-1)

where y, and x are vectors, and we need to test the validity of f(x,y_t-1) such that the observed dataset, z_t changes well with y_t

So, we need to generate lots of random numbers divide them into sets with the same cardinality as y, and x, push them through f(x,y_t-1) such that we can derive r by comparing z with y. We need to continue to do this until the median of r converges upon the mean of r to some prearranged difference (maybe 2.2% or less - so a positive difference means it is right-skewed (bad) and a negative difference means it is left-skewed (good)) with at least 20 seperate runs - so we don't accept such a convergence until the 20th run is completed; after that the numbers talk for themselves, as it were.

Then, we need to calculate how many standard deviations away from the mean the LI correlation is. If it exceeds, ie is greater than the mean by 1.96 standard deviations, then we have confidence in the LI. Is this too strong a threshold?

Until that moment it's an interesting idea. Does anyone object to testing the LI in this manner? Indeed, is this enough to show confidence?

We might well have to drop both ENSO, and sea-ice because they are known (I think) to be directly, and proportionally related to the sun, so it interferes with degrees of freedom calculations that require each dataset to be independent (as far as I understand it) Recall that the hypothesis is that the sun, with variable 'lag', proportional to some quantity already in the system, can account for the modern warming. And, since this is, erm, a little against the grain, then chi-squared tests are an absolute must.

EDIT: Ignore the x for now, if you can, so basic function should read: y_t=f(y_t-1). x is meant to mean the input vector for the datasets. I'm not so sure my maths notation is entirely correct :blush:

Edited December 13, 2009 by VillagePlank

[VillagePlank]

Unfortunately my computer crashed a few months back and I have lost the LI Excel sheet I had been working with, so I shall have to start from scratch, but I could try this out if anyone wants me to.

Unfortunately (see me last posting) a spreadsheet, unless you want to spend weeks generating millions of numbers, is now out of the question. Indeed, the generation of random numbers is a contentious issue in it's own right ... I think we're at the stage, now, where we need to use software, written for the job, to move forward.

I am currently in the process of writing the requirements for such software - even the tools for the job require quality assurance, now.

Edited December 13, 2009 by VillagePlank

[Admiral_Bobski]

Unfortunately (see me last posting) a spreadsheet, unless you want to spend weeks generating millions of numbers, is now out of the question. Indeed, the generation of random numbers is a contentious issue in it's own right ... I think we're at the stage, now, where we need to use software, written for the job, to move forward.

I am currently in the process of writing the requirements for such software - even the tools for the job require quality assurance, now.

Bum! Well let me know if there's anything I can do.

CB

[Gray-Wolf]

Comets? Combinations of comets? Meteors/Asteroids (never did quite sort out which was which). These are things which have irregular shaped orbits which could perhaps interfere with the effects of the more regular-shaped planetary orbits and relationships, but of course it is difficult to trace records of comets as they can have such a long orbit. Just a thought, however, and may reflect my lack of understanding more than my understanding of your theory.

Well it seems we are now of the opinion that not just the oceans came from off world but the majority of the atmosphere too!!!

Maybe a few comet tails heavy in CO2 ?

Or the odd Tunguska body?

As you say ,hard to plot out unless we have a regular swarm every so often..........2012?

[Guest diessoli]

So the quickest way to test diessoli's assertion is to go back to our first run - the basic LI with just sunspot data - and then, instead of adding ENSO, volcanoes and albedo, throw in three sets of white noise (or even just one set, to begin with)?

A simple thing to do is to divide the data into two distinct samples (e.g. 1850 - 1950 and 1951 to 2008)

Then you determine your best fit parameters for the first sample (your training set) and calculate the error.

Apply the model with the same parameters to the second sample and calculate the error.

If the errors are too different, this indicates a problem with your model (like over-fitting).

OTOH even if model seems to perform well it's not guaranteed to be correct. You need to do more rigorous testing.

D.

[Gray-Wolf]

V.P. ,if I've yanked your chain it was unintentional.Your colours are nailed to the mast as your model is fixed and you appear content with the results you are producing as you tweak it further.

I am interested in Meto's predictions (and their model) as this does have the increasing GHG forcing in it.I do favour their 10 year outlook (half of the years warmer than our current 'hottest').

I do not think their model will then trend flat of reduce.

[Guest diessoli]

Yes, the constants, and parameters, whilst easy enough to to simply copy off the thread have not been published- nor has the model that ties it all together. You should be able to reproduce the results uisng the run-through. I have to keep something back, as I am sure you understand. For interest, it uses gradient descent techniques, and it treats algebraic expressions as a hierarchy (but that may go). This approach may well be wrong; so, I need to generate random datasets and pass them through the techniques to test for quality and confidence.. I think I might have mentioned this somewhere before. I'm sure I've made it clear that it either succeeds or fails on this point (ie that we can be confident that the correlation exists above the 1.96sd confidence level (>95%))

Just a quick question then, to make sure I am not barking up the wrong tree.

The model you are using is the discrete form of the LI i.e. something like

T(t) = (1 - a * DT) * T(t-1) + { b * S(t-1) + c * V(t-1) [ + d * X(t-1) ...] } * DT

with :

T = temperature

S = sun spot number

V = some sort of volcanic forcing

X = some other forcing

DT = time difference here one year

a,b,c,d = some constants (negative or positive depending on the forcing)

and all time depend quantities are global and annual averages, so the difference between t and t+1 is one year.

You then use some form of multi-variate regression to determine a,b,c,d,...

For the optimal parameters you calculate a temperature series and check the difference from the actual temperatures.

Is that about right?

D.

[Admiral_Bobski]

V.P. ,if I've yanked your chain it was unintentional.Your colours are nailed to the mast as your model is fixed and you appear content with the results you are producing as you tweak it further.

I am interested in Meto's predictions (and their model) as this does have the increasing GHG forcing in it.I do favour their 10 year outlook (half of the years warmer than our current 'hottest').

I do not think their model will then trend flat of reduce.

You still seem to be failing to grasp the concept of the LI. The whole point is to see whether or not GHG forcing is even required to explain global temperature trends.

Your preference for the MetO model appears to be that they have not "overlooked" GHG forcing. Well, the LI (as yet) doesn't even need GHG forcing. Don't you find that interesting?

You favour the MetO 10-year outlook, but it is not that dissimilar to the LI's outlook. But, rather than discuss the merits and shortcomings of the LI, you prefer to dismiss it as wrong because it doesn't fit in with your presumptions.

Do you actually know what science is?

CB

EDIT - A quick PS to Diessoli: thank you for your inputs so far Unfortunately I shall have to let VP field the maths questions, as I am only too happy to admit that the maths side of things is not my forte!

Edited December 14, 2009 by Captain_Bobski