The LI Revisited (Climate Modelling Using a leaky integrator)

[VillagePlank]

It's nothing to do with independence of variables, it's the fact that you're using a proxy for long-term temperature change to try and predict long-term temperature change - explaining one variable in terms of itself. A good fit isn't surprising. It's like trying to model the changing height of the British population over time by using trouser length as an input. Sure it agrees well, but it's not going to tell you anything about what happens in 50 years' time.

It's everything to do with independence of variables. Since they aren't independent, they exhibit the effect you are describing. I do see where you are coming from, but exactly the same criticisms can be levelled at any climate modelling exercise simply because it is dynamical and is self referring. I agree that the selection of variables is, perhaps, poor, and others have already pointed this out. Perhaps it's beneficial to point out that sunspots on their own can be attributed, using the LI as the filter, to the temperature record in terms of a least squares regression against both sets of data, and with signifcant statistical results. I will have to do it all over again, to give you the figures. Other variables were added to try and mimic the noise, not the overall behaviour.

Edited January 13, 2013 by Boar Wrinklestorm

[Admiral_Bobski]

I'd just like to chip in here and say, up front, that I have very little desire to pursue the LI any further. I immersed myself in it 3 years ago, researched my butt off, read papers, gathered datasets and so on and so forth - BW did even more than I did, a fact for which I am very grateful and also extremely sorry about - but I really no longer have the enthusiasm for the subject.

To be frank, I think we struck gold with the idea and I was extremely disappointed and upset that very few others shared my enthusiasm (there are many people who say, "oh, I wish, I wish, I wish AGW weren't true!" but actually have no desire to explore alternative hypotheses).

I really don't want to be dragged down into the mire, and I would be devastated if my recent rekindling of the subject were to drag BW back into it out of a sense of duty.

On the other hand, and as I said in a previous post, I am happy to restate some of the thoughts we had at the time, or try to elaborate upon those thoughts. I saw a post in which the LI was sorely misrepresented and I didn't want it going down in Netweather history as some crackpot idea that was complete nonsense, on the basis of a few ill-informed posts by other members.

My only regret is that we didn't go so far as to run the model into the future by 30 years, just so that we could perform a comparison every 10 years - that would have been interesting. The prediction up to 2015 is a curiosity that has held up pretty well for 3 years, but the cooling it predicts is on the basis of assumptions (the presumed datasets) that no longer hold true. I don't feel the idea can be rubbished if temperatures do not plummet in the next 2 years (though, on the other hand, if temperatures do plummet then that would be remarkably interesting).

So, in conclusion, ask me questions and I'll do my best to answer them. If BW wants to get back into the thick of it and start producing models again then I'll be happy to get back into it, but if he has no desire for it then that's absolutely fine by me. I don't want to drag others in after me, especially after the grief that we got last time.

[Admiral_Bobski]

It's nothing to do with independence of variables, it's the fact that you're using a proxy for long-term temperature change to try and predict long-term temperature change - explaining one variable in terms of itself. A good fit isn't surprising. It's like trying to model the changing height of the British population over time by using trouser length as an input. Sure it agrees well, but it's not going to tell you anything about what happens in 50 years' time.

I think this is an important point you've brought up here. The LI is not really a predictive theory - it operates on the basis that the inputs at any given moment in time carry over to the next moment in time. It is an explanatory model: it explains why temperatures behave the way they do, retrospectively. The only way to use it for prediction would be to know for a fact what the Sun is going to do in the future, what ENSO is going to do, what the planet's albedo will be, what volcanoes are going to erupt. SInce these inputs are not easily predictable, the output cannot be predictive as such.

So the LI shows that hysteresis can explain temperature change. Prediction is irrelevant. The difference between the LI and your analogy of leg-length is that in your proposal, all we are doing is plotting raw data and then drawing a conclusion, like the old bar graphs we did in school. With the LI, the data are undergoing a process which produces results which are then plotted - the graph is not a plot of raw data, it is data that have undergone a function. The raw data don't explain anything.

Does the LI's predictive limitations invalidate it as a model of climate? Not at all. This would only be the case if climate was inherently predictable, and we know for a fact that it is not. This being the case, AGW theory - a theory that purports to be able to predict future climate - seems even less credible to me than it did before.

[Gray-Wolf]

I'd imagine (and I do a lot of that!) that the worry with AGW was that we did not fully understand the complexities of the initial climate inertia and so 'tweaked' models to get agreement with observations for the hind-casts.

Were this indeed the case then the projection of those models will fall woefully short of the reality we find ourselves in with this 'extra energy' appearing in amounts that the models did not account for. Impacts would , of course, snowball thereafter.

When you look at sea levels the last time global GHG's were at a similar level you get to see just what type of 'warming' event would be needed to see the situation 'normalised'? Sadly 'normalising' sea levels just reanimates another swathe of hibernating carbon cycle and so around we go again.

[Admiral_Bobski]

Look at it this way - some energy from the Sun has gone into the melting of the ice and now, in your words, that energy is "free". It has taken some time for the ice to melt, so the incident energy has come into the system, performed a "task" (the task of melting sea ice) and then been "freed up". That means that energy has been trapped in the system, which means that there has been a lag between the energy coming in and its being freed up into the atmospheric system. Is this not just one of many ways in which there is a lag in the climate system?

It's been a long time since I did science at school but hasn't that energy been used to melt the ice to water and therefore it cannot be "freed up" into the atmospheric system unless the water refreezes.

Absolutely right, Pete. The point being that there is energy "stored" in the liquid water that can be released further down the line when the water refreezes. I apologise for not making that clear.

I'd imagine (and I do a lot of that!) that the worry with AGW was that we did not fully understand the complexities of the initial climate inertia and so 'tweaked' models to get agreement with observations for the hind-casts.

Were this indeed the case then the projection of those models will fall woefully short of the reality we find ourselves in with this 'extra energy' appearing in amounts that the models did not account for. Impacts would , of course, snowball thereafter.

When you look at sea levels the last time global GHG's were at a similar level you get to see just what type of 'warming' event would be needed to see the situation 'normalised'? Sadly 'normalising' sea levels just reanimates another swathe of hibernating carbon cycle and so around we go again.

I'm sorry - I don't quite get what you're saying...?

[songster]

It is an explanatory model: it explains why temperatures behave the way they do, retrospectively.

You're missing my point. One of your input variables (ice extent) is inherently a proxy measure for the output variable (temperature). So what you end up doing is explaining that temperature = temperature, which doesn't explain <i>why</i> anything at all.

[Admiral_Bobski]

You're missing my point. One of your input variables (ice extent) is inherently a proxy measure for the output variable (temperature). So what you end up doing is explaining that temperature = temperature, which doesn't explain <i>why</i> anything at all.

Ice extent is a proxy for albedo in this model. We can take it out if it makes you feel better, but your point is irrelevant.

[songster]

Ice extent is a proxy for albedo in this model. We can take it out if it makes you feel better, but your point is irrelevant.

You want to use it as a proxy for albedo, but (like it or not), it is also a proxy for temperature, because ice melts when it gets hotter. Agreed that it would be a useful exercise to take it out and see how much it affects the overall fit. It would be good to do this for all the variables: sunspots included.

[songster]

Going back to the initial thread, a further question.

How are you dealing with model initialisation? From the very first post here, we see that it takes quite a long time for the model to "settle down" after initialisation.

Looking at the second graph on the page, it takes at least 10 cycles to settle down to a steady state, even when forced with a completely steady oscillation. That's simply an artefact based from the fact that you're (arbitrarily) starting with an empty bucket. Obviously the time taken to get to the steady state will depend on the size of the leak relative to the filling rate (i.e. the time constant of the resulting exponential).

How have you accounted for this when running the LI model with sunspot data? If you haven't accounted for the arbitrary choice of starting conditions, then the upward rising trend you see could be artefactual, due to initialising the integration at zero. One sensible way to account for it would be to take an average size/length of sunspot cycle and run the LI for a few hundred years using this as a perfectly steady input cycle. Once the LI reaches equilibrium, then you can start integrating over the actual sunspot data, to see how changes in sunspot activity lead to changes in temperature.

If you didn't do this, then your model is confounding two things: (1) how changes in in sunspot activity lead to changes in temperature, and (2) the effect of switching on the Sun at time t=0.

[songster]

We *didn't* make any adjustments or tweaks to the model per se, in that we didn't add anything beyond the basic setup of the LI equation.

.. but what you call "setup" of the LI equation" involves adjusting and tweaking parameters! Or, as BW put it in 2009, "fiddle mucking around with constants, multipliers etc"

http://forum.netweat...00#entry1517881

At a basic minimum, you have the starting height, the rate of influx, the rate of the leak, the degree to which ice extent affects the leak rate, the degree to which volcanic activity affects the leak rate, and how long the effect of a given volcano persists for. That's six adjustable parameters! They're even listed on the output graphs, such as this one.

http://forum.netweat...attach_id=81512

See that list of r, o, i', v' and e'? Those are your adjustments and tweaks! (And you forgot to mention the arbitrary starting value, which I think you were calling h).

In fact, it's even more ad hoc than that, since there was also a "Hadley correction" (i.e. tripling the rate of the leak for 6 years) with no justification at all other than making the curves match. Given that this model is fundamentally about energy balance, can you suggest a mechanism which would cause the Earth to triple the rate at which it loses energy into space?

Edited January 13, 2013 by songster

[Paul]

Ok, re-opening this - but please can we keep it respectful....