What is a model?

[Peter Ellis]

For Andrew B.

...
Quite so.  An exponential trend is a simplistic, naive mathematical model with no direct connection to the many many years of accumulated scientific knowledge of Earth's climate system.  Which is why I'm so baffled that you prefer it.

Again distorting what I wrote...

1) Trendline fitting is a mathematical/statistical tool. As the name implies, it extracts a trend from noisy data. No, it's not a climate model, and the exponential function is not a climate model either.

I never said it was a climate model, I said it was a mathematical model. In extrapolating an exponential trend, you are using a mathematical formula to model what you think will happen to the climate.  It is therefore a model. Maths is modelling.  I can't put it more plainly.

A sine wave is a model of the behaviour of a pendulum.  Linear acceleration is a model of how an apple falls under gravity - a model which breaks down when air resistance is significant, or when the distances involved are large enough that the gravitational field varies. Newtonian gravitation is a better model, but one which also breaks down when considering air resistance.

Both models also break down when you extrapolate inappropriately: for example in the real world the acceleration will stop when the apple hits the ground. Extrapolation from simplistic models will always be wrong, the only question is how wrong.  The more factors you leave out of your model, the more likely you are to be wrong.

Your exponential trend-fitting leaves out... pretty much everything.

To put it another way: what do you think will happen when the ice reaches zero?  Will it continue to decline at an exponential rate and go into negative territory?  Rhetorical question: of course it won't.  So you implicitly must acknowledge that the exponential trend model will break down at some point.  Why do you think that is necessarily at the point when ice is zero, and not before?

2) A climate model: see the Wikipedia definition which, while not perfect, is good enough. Let's stick to it and not try to redefine the meaning of the term.

We can both play the definition game:

model  (mŏd'l)   
A systematic description of an object or phenomenon that shares important characteristics with the object or phenomenon. Scientific models can be material, visual, mathematical, or computational and are often used in the construction of scientific theories. See also hypothesis, theory.

The American Heritage® Science Dictionary
Copyright © 2002. Published by Houghton Mifflin. All rights reserved.

You could also look at the Wikipedia page about scientific modelling.
https://en.wikipedia.org/wiki/Scientific_modelling

One form of scientific modelling - the type you are using - is when you attempt to describe aspects of a given phenomenon via a system of equations.  That is what you are doing with your exponential extrapolation. It remains a model even if you are incapable of grasping the fact that it's a model.

3) "Which is why I'm so baffled that you prefer it." I have no idea whatsoever what you could mean by that. But if you want to further explain your point of view, may I suggest you start a new thread?

You are asserting that PIOMAS modelling is materially wrong and that an exponential progression of melt is more likely.  i.e. that the future evolution of Arctic sea ice is better MODELLED by an exponential trend than by the more complex outputs of PIOMAS. You have produced no evidence or reasoned argumentation to support your view other than some hand-waving "feels like this" mumbo-jumbo. I am baffled why you are doing this.

[Jim Williams]

A model is a small imitation of the original.  Models always lack at least some of the fine details in the original -- otherwise they are called replicas.

[TerryM]

A model is a small imitation of the original.  Models always lack at least some of the fine details in the original -- otherwise they are called replicas.

The few models that I've met in person all appeared, to my jaded eye, to possess very fine details indeed.


Terry

[Pmt111500]

A model is a small imitation of the original.  Models always lack at least some of the fine details in the original -- otherwise they are called replicas.

The few models that I've met in person all appeared, to my jaded eye, to possess very fine details indeed.


Terry

But what you see of the details are mostly external, my guess is there's f.e. a mechanisn called anorexia nervosa that possibly influences the externally observable attributes. Possibly there are also the so called genes at play here.

[TerryM]

PTM
Models with playful genes play into my fantasies.


Way OT
My Bad
Terry

[Jim Williams]

A model is a small imitation of the original.  Models always lack at least some of the fine details in the original -- otherwise they are called replicas.

The few models that I've met in person all appeared, to my jaded eye, to possess very fine details indeed.


Terry

And they've all been pretty much identical...

[gerontocrat]

It has to be said that increasing complexity and sophistication does not automatically produce a better result than, for example, Lovelock's "Daisyworld". Indeed, much of the questioning on ASIF is about the importance of parameters not included, or perhaps insufficiently included in the models.

You lot can dance on the head of a pin regarding a legalistic definition of a model. But what really matters is surely the validity of the  parameters in or not in the models that form the bedrock of the next IPCC negotiations. 2022 is surely the last chance saloon.

[oren]

It has to be said that increasing complexity and sophistication does not automatically produce a better result.

And indeed, the impetus behind this thread was the use of an exponential extrapolation to forecast Sept sea ice, while the use of the simpler linear function is more widely accepted for the job (and rightly so, imho).

[Jim Williams]

It has to be said that increasing complexity and sophistication does not automatically produce a better result.

And indeed, the impetus behind this thread was the use of an exponential extrapolation to forecast Sept sea ice, while the use of the simpler linear function is more widely accepted for the job (and rightly so, imho).

There's no reason to prefer either.  The driving changes have been built in over centuries, and each force has its own peculiar timeline for manifesting.  Changes in bottom water temperature might take millennia to produce a resulting change in atmospheric circulation.  I am more inclined to believe the people who tell me our current climate changes are due to the invention of agriculture than to those who tell me last week's CO2 is to blame.  (Though I do personally think it was the Industrial Revolution.)

[CognitiveBias]

The model should include an increasing increase in export (exponential?).  There is the Lebedev/Bilello exponent in the other direction as ice volume grows more quickly over thinner ice.  Does thinner more mobile ice also melt out more quickly?  Of course that trend is offset by the FDD shift, which is applied again in an exponential process.

 The question is which processes are driving?  I would say we are in transition to an exponential regime driven by export and mobility with thin dispersed ice transporting into warm water.

Time will tell...  maybe the next 4-5 months.

[AndrewB]

...
And indeed, the impetus behind this thread was the use of an exponential extrapolation to forecast Sept sea ice, while the use of the simpler linear function is more widely accepted for the job (and rightly so, imho).

Oren, sorry to say that, but that phrase is nonsense.

First, you can fit different trendlines on to noisy data, according to different functions. There is no "right" or "wrong" trendline and the data couldn't care less about what trendline you fit to it.

Remember, trendline fitting is a mathematical tool used by statisticians and scientists to remove noise from the data, in order to evidence a trend.

Let's go back to the chart with the different trendlines for PIOMAS (the first chart below).

The different trendlines are a characteristic of the data, and not the result of anybody trying to prove anything or demonstrate anything or reach a predetermined conclusion. There is no "more widely accepted" trendline either, although the linear trendline was more often used in the past simply because it was easier to plot, but in our age of widely available computing devices you just plug in the data and your PC/smartphone instantly draws your chart with all the various trendlines for you.

Now, about forecasting, yes I did use the Wipneus chart with the exponential trendline (second chart below) to forecast 2017 Minimum PIOMAS (in blue).
The shock!
The horror!
Why didn't I use the "more widely accepted" linear trendline!
Or the Gompertz trendline, that has such a nice name?

As I wrote before, for September 2017 it wouldn't make much of a difference, would it? ALL the trendlines indicate more or less nearly the same value for September 2017, showing that September 2017 will  probably be a new record low for minimum yearly PIOMASS. When I pointed this out, I also pointed out that December 2016, and January, February and March 2017 were all record month lows. PIOMAS end March-early April stands approx. 2,000km3 below 2016, and 2,500km3 below end March-early April 2012 which holds the record low for September/yearly minimum PIOMAS.

I also pointed out in various posts that the exponential trendline crosses the X axis around 2022. Again:

The shock!
The horror!
I am using the exponential trendline "model" to reach a predetermined conclusion!

Please, this is completely absurd. 

The data is what it is and the various trendlines as plotted are entirely determined by the data, not because I want to reach the conclusion that the demise of Arctic sea ice is right around the corner.

Again repeating myself: choose whatever trendline you like best, it changes nothing of the reality of what is happening.

Note: the (excellent) charts below are by Wipneus, more high-quality visualizations on his website https://sites.google.com/site/arctischepinguin/home

[ktonine]

...
And indeed, the impetus behind this thread was the use of an exponential extrapolation to forecast Sept sea ice, while the use of the simpler linear function is more widely accepted for the job (and rightly so, imho).

Oren, sorry to say that, but that phrase is nonsense.

As Oren points out, using an exponential trend to forecast is nonsense.  What is the predicted value for 2050?  -3mkm^2?    That's nonsense.  It's nothing more than curve fitting and ignores the physics of the actual situation.

[CognitiveBias]

...
And indeed, the impetus behind this thread was the use of an exponential extrapolation to forecast Sept sea ice, while the use of the simpler linear function is more widely accepted for the job (and rightly so, imho).

Oren, sorry to say that, but that phrase is nonsense.

As Oren points out, using an exponential trend to forecast is nonsense.  What is the predicted value for 2050?  -3mkm^2?    That's nonsense.  It's nothing more than curve fitting and ignores the physics of the actual situation.

Obviously there is a physical limit of 0 ice.  That does (edit) NOT(/edit) invalidate the path to 0.   

[oren]

TBH, a linear trend-fitting forecast crosses zero too, not just the exponential one. Both are inherently limited by using only historical data.
A forecast based on historical curve-fitting is (indeed) a model, albeit a very simplistic one. Sometimes such empirical models have better predictive value than full physical simulations when the system is too complex and the data is not sufficient, although the physical models will provide more explanations and enable "what if" simulations.
And when using a very simplistic empirical model disconnected from the actual physical processes, it is best to stick to as few variables as possible unless the empirical evidence strongly says otherwise. Therefore Occam's Razor gets me to the "linear" "model" when looking at arctic sea ice.
(And yes I do expect a record low PIOMAS volume this year, but that's a different thread)

[AndrewB]

TBH, a linear trend-fitting forecast crosses zero too, not just the exponential one.

The horror!
The shock!
Forecasting negative ice volumes! 

Both are inherently limited by using only historical data.

Yes, unfortunately we don't have the data for the future, only for the past. That is indeed a serious "limitation" of trendlines. 

A forecast based on historical curve-fitting is (indeed) a model, albeit a very simplistic one. Sometimes such empirical models have better predictive value than full physical simulations when the system is too complex and the data is not sufficient, although the physical models will provide more explanations and enable "what if" simulations.
And when using a very simplistic empirical model disconnected from the actual physical processes, it is best to stick to as few variables as possible unless the empirical evidence strongly says otherwise. Therefore Occam's Razor gets me to the "linear" "model" when looking at arctic sea ice.
(And yes I do expect a record low PIOMAS volume this year, but that's a different thread)

And here is the good news: it's not a beauty contest, so you can have both the linear and the exponential trendlines plotted on the same chart, and you are not forced to choose between them! 

[Steven]

Here's an animation showing how the exponential extrapolation of the PIOMAS annual minimum has changed since the start of this century.  The first frame of the animation fits data up to September 2000,  the second frame up to 2005,  the third frame up to 2010,  and the final frame up to 2016.  Note that the extrapolated date of ice-free Arctic has shifted forward by about a decade:



And here's a similar animation for Gompertz:  http://i.imgur.com/044XwCT.gif

Anyway, I think this kind of simplistic extrapolations (exponential, Gompertz etc.) are meaningless.

[CognitiveBias]

Steven,

  It would be interesting to see how the linear extrapolation performs during the same time frames.  While the exponential extended from about 2011 to 2022, the linear looks to have pulled in from ~2050 to about 2030.  I'm betting on more of an exponential finish than a linear one.

[Random_Weather]

Anyway, I think this kind of simplistic extrapolations (exponential, Gompertz etc.) are meaningless.

Correct, its just fitting the past without any skill in future, because its none physics based fitting :-) But people always think its real :-)

[AndrewB]

Here's an animation showing how the exponential extrapolation of the PIOMAS annual minimum has changed since the start of this century.  The first frame of the animation fits data up to September 2000,  the second frame up to 2005,  the third frame up to 2010,  and the final frame up to 2016.  Note that the extrapolated date of ice-free Arctic has shifted forward by about a decade:

Steven, thanks for the excellent animation. And indeed, the exponential trendline is intrinsically sensitive to data at its extremity (the "latest" data). That's what your animation shows, isn't it? Try for example changing a data point midway and see what happens.
So if you make a forecast based on extrapolation of an exponential trend line far into the future, and a new data point comes along that is many standard deviations away from the calculated trendline, then your updated trendline changes and your previous forecast is less likely to be correct. You are forced to make a new forecast that is a lot different than the previous one.
"That is a feature, not a bug".
 
This is what happened in 2012 (many standard deviations below trendline) and then reversed in 2013 (many standard deviations above trendline).

Anyway, I think this kind of simplistic extrapolations (exponential, Gompertz etc.) are meaningless.

That is your opinion and you are free to think what you want of forecasting based on trendlines (exponential, Gompertz, linear, etc).

Most scientists and statisticians think trendlines are just another tool in their toolbox to analyze reality and deduce some valid information from noisy data. And they may be "simplistic" to you, but they are the result of centuries of thinking by very bright mathematicians.
But I am sure that like Isaac Newton, you are aware that you are standing on the "shoulders of giants". Or not?

[dnem]

In a population ecology class we were learning increasingly complex models that captured increasingly complex behavior.  To reveal the inadequacy of a simple model we were asked to calculate the population at some given time in the future which revealed a negative value for population.  "Aaaah, a fate worst than death" our professor quipped.

I tend to think both simple curve fitting to to PIOMAS data (linear, exp., gompertz,...) and more complex physical models are all unable to predict with any useful likelihood the end-game dynamics of arctic sea ice.  Since at least 2007 we have seen the ability of one season's weather to completely overwhelm any trend described by any mathematic function.  This high seasonal variability is only likely to increase IMO.

Also this:
https://cup.columbia.edu/book/useless-arithmetic/9780231132138
Useless Arithmetic
Why Environmental Scientists Can't Predict the Future
Orrin H. Pilkey and Linda Pilkey-Jarvis
Columbia University Press

[AndrewB]

In a population ecology class we were learning increasingly complex models that captured increasingly complex behavior.  To reveal the inadequacy of a simple model we were asked to calculate the population at some given time in the future which revealed a negative value for population.  "Aaaah, a fate worst than death" our professor quipped.
...

Well, at least your professor had a sense of humor. But what he really meant is that the simple model was showing the population going to zero sometime before the date for which you had calculated a negative population. That in no way demonstrates the inadequacy of a simpler model vs a more complex one.

Here is what George Box thought about simple models:

"Since all models are wrong the scientist cannot obtain a "correct" one by excessive elaboration. On the contrary following William of Occam he should seek an economical description of natural phenomena. Just as the ability to devise simple but evocative models is the signature of the great scientist so overelaboration and overparameterization is often the mark of mediocrity."

and

"Now it would be very remarkable if any system existing in the real world could be exactly represented by any simple model. However, cunningly chosen parsimonious models often do provide remarkably useful approximations. For example, the law PV = RT relating pressure P, volume V and temperature T of an "ideal" gas via a constant R is not exactly true for any real gas, but it frequently provides a useful approximation and furthermore its structure is informative since it springs from a physical view of the behavior of gas molecules.

For such a model there is no need to ask the question "Is the model true?". If "truth" is to be the "whole truth" the answer must be "No". The only question of interest is "Is the model illuminating and useful?"."

(from: https://en.wikipedia.org/wiki/All_models_are_wrong)

This is to be weighed against the famous quote attributed to Einstein that:

"Everything should be made as simple as possible, but not simpler."

http://quoteinvestigator.com/2011/05/13/einstein-simple/

Etc. That is essentially an epistemological discussion.

[oren]

Well at least we can agree that extrapolations are indeed (very simple) models, which brings this thread to a kind of conclusion

[DrTskoul]

Well at least we can agree that extrapolations are indeed (very simple) models, which brings this thread to a kind of conclusion

Amen...