The AGW climate feedback discussion

[vanesch]

I am going to throw a big word out there I normally don't use and say that the whole idea of feedback is very abstract. There seems to be some substance missing.

Well, the thread is about feedback in climate. For that, one has to be clear about what is feedback. For some it might be elementary, for others, they might learn something. We start with the basics, I don't think it is a bad idea! I can help with the basics, I know less about the exact climate feedback systems. It's always a good idea to be clear about the fundamentals even though it may be trivial to some.

To tell you that it is not so trivial for climate science is the nice paper here that has already been discussed if I remember well:
http://earthweb.ess.washington.edu/roe/Publications/BakerRoe_Predictable_Jclim09.pdf

If one can publish a research paper in climate science about the formula A / (1 - A B), and its asymmetrical aspect in B (fig 1 in the paper), then that means it is worth discussing this, to come to full understanding, no ?

 

[Andre]

(1 - A B) Y = A X

so Y = { A / ( 1 - A B) } X

Thanks Vanesch, with that correction the total gain in the different simulation attempts dovetail nicely. So my orginal assessment about transient effects was rather overstated.

Again, the objective of these little demonstrations, were, firstly, showing that significant 'amplification' in attenuated - non-amplified processes, like climate, are unlikely, especially when the total feedback is a combination of positive and negative feedbacks. Hence one could sincerely wonder if the modeled climate feedback claims, so abundantly supplied by Xnn, are either the result of actually modelling the different feedback loops in detail or just dialing in guestimated parameters. This would be an especially valid question about the assessment of IPCC of the positive feedback amplification of the climate sensitivity of doubling CO2 from the Planck response of 1.1 to 1.2 degrees to some 2 -4.5 degrees and this little exercise was to substantiate that doubt.

Secondly, we have introduced persistency and anti-persistency as characteristics of positive and negative feedback response, the tendency to persist in or oppose to the direction of the process output in relation to the average value. And the question arises if it is possible to assess the type of effective feedback of a process on this feature alone. Of course this is rather complex, one has to deal with attractors, autocorrelation, cyclic forcings like diurnal and seasonal cycles, etc. but especially the typical time constant of the different feedbacks. So signal behavior has to be analyzed on many different time scales to assess persistency. Also, for statistical significance, a large sample is required. http://www.aai.ee/~olavi/ has addressed this issue and his researches of many different climate data series all end in the conclusion: anti persistency.

See http://www.aai.ee/~olavi/2001JD002024u.pdf, http://www.aai.ee/~olavi/cejpokfin.pdf and http://www.aai.ee/~olavi/E-Ac-Sci-07.pdf.

There are more as you can see from him home page but linking to those is illegal in these dark ages of global warming groupthink excess.

 

[vanesch]

Again, the objective of these little demonstrations, were, firstly, showing that significant 'amplification' in attenuated - non-amplified processes, like climate, are unlikely, especially when the total feedback is a combination of positive and negative feedbacks. Hence one could sincerely wonder if the modeled climate feedback claims, so abundantly supplied by Xnn, are either the result of actually modelling the different feedback loops in detail or just dialing in guestimated parameters.

That's where I would like to learn more too. But I don't see how an elementary verification of the concept of feedback allows one to conclude that the feedback in the climate system should be small: it all depends on which feedbacks and on their amplitude, right ?

I too would like to know how the feedbacks in climate models are implemented, where they come from, and how their amplitude is determined.

This would be an especially valid question about the assessment of IPCC of the positive feedback amplification of the climate sensitivity of doubling CO2 from the Planck response of 1.1 to 1.2 degrees to some 2 -4.5 degrees and this little exercise was to substantiate that doubt.

A nice review of these values would indeed be nice. Anyone ?

Secondly, we have introduced persistency and anti-persistency as characteristics of positive and negative feedback response, the tendency to persist in or oppose to the direction of the process output in relation to the average value. And the question arises if it is possible to assess the type of effective feedback of a process on this feature alone. Of course this is rather complex, one has to deal with attractors, autocorrelation, cyclic forcings like diurnal and seasonal cycles, etc. but especially the typical time constant of the different feedbacks.

I think it is a bad idea to do black box modelling. We want to understand the climate system dynamics by using explicit physical modelling, not by fitting parametrisable general model classes on existing data, or by trying to extract some general properties from time series analysis. That's something you can do if the complexity of the underlying system is hopelessly beyond comprehension AND if you know that the time series you're analysing are entirely representative for the evolution you want to draw from it. However, this is in fact nothing else but a sophisticated way of "curve fitting and interpolation". You can do that if you need a dynamical model that needs to be used in conditions that are very near to the conditions of where you fitted the data. But you cannot hope to get out of such a thing any general dynamics that is universally valid.

I've been doing such kinds of things for work when I was young. It works rather well in "interpolation" mode and is hopeless in "extrapolation" mode. The reason is that there are myriads of classes of dynamical models which can all agree on the fitted region, and behave wildly differently when outside of that region.

As we want to explore a situation that we don't know much about, namely a quick increase in greenhouse gasses in the atmosphere, there's not much hope of getting the right dynamics out of just a black box curve fitter when such rise was not the case. There's much more hope to learn something by doing "white box" modelling, that is to say, implement physically understood relationships - even if they are rough and simplified - into a simulator and see what it does. It's also much more instructive to do so.

 

[Integral]

This is a simulation of environmental feedback called http://itg1.meteor.wisc.edu/wxwise/radiation/daisyworld.html" . The environment consists of and input luminosity and 2 species of daises one black the other white, The temperature range in which each species can exist is different but overlapping. The black daisies germinate at a low temperature but because they are black absorb heat and raise the temperature. At some higher temperature white daisies germinate. They reflect light tending to lower the temperature. The simulation runs until a equilibrium is reached.

 

[Integral]

That's where I would like to learn more too. But I don't see how an elementary verification of the concept of feedback allows one to conclude that the feedback in the climate system should be small: it all depends on which feedbacks and on their amplitude, right ?

I want to emphasise this statement. For all the pretty graphs there simply no way we can extent this analysis beyond what it is, a simple example of the effects of feedback. It is not a climate model and we should not attempt to draw conclusions about the climate from it.

I too would like to know how the feedbacks in climate models are implemented, where they come from, and how their amplitude is determined.



A nice review of these values would indeed be nice. Anyone ?




I think it is a bad idea to do black box modelling. We want to understand the climate system dynamics by using explicit physical modelling, not by fitting parametrisable general model classes on existing data, or by trying to extract some general properties from time series analysis. That's something you can do if the complexity of the underlying system is hopelessly beyond comprehension AND if you know that the time series you're analysing are entirely representative for the evolution you want to draw from it. However, this is in fact nothing else but a sophisticated way of "curve fitting and interpolation". You can do that if you need a dynamical model that needs to be used in conditions that are very near to the conditions of where you fitted the data. But you cannot hope to get out of such a thing any general dynamics that is universally valid.

I've been doing such kinds of things for work when I was young. It works rather well in "interpolation" mode and is hopeless in "extrapolation" mode. The reason is that there are myriads of classes of dynamical models which can all agree on the fitted region, and behave wildly differently when outside of that region.

As we want to explore a situation that we don't know much about, namely a quick increase in greenhouse gasses in the atmosphere, there's not much hope of getting the right dynamics out of just a black box curve fitter when such rise was not the case. There's much more hope to learn something by doing "white box" modelling, that is to say, implement physically understood relationships - even if they are rough and simplified - into a simulator and see what it does. It's also much more instructive to do so.

I have assumed that the climate modelers were doing what you call "white box" modelling. Am I wrong? For all the noise they make about the complexity of the models they had better be!

 

[Xnn]

A good white box model would have to include different time constants for all the different feedbacks. The simple model presented above does not do that.
Instead, it assumes that all feedback is realized during the next time step.

Feedbacks include:

Water Vapor
Lapse Rate
Cloud Cover
Surface Albedo (sea ice)
Surface Albedo (seasonal snow cover)
Surface Albedo (Vegetation)
Surface Albedo (Land Ice)
Surface Albedo (water level)
CO2 emission rates

Each of these have their own magnitude and time constant.

 

[vanesch]

I already quoted this in another thread, but this seems to be a good read about what's in actual climate models:
http://www.iop.org/activity/policy/Publications/file_4147.pdf

I scanned through it, I'm now reading it in more detail. Very good stuff!

 

[Xnn]

Here's another interesting article on climate models which includes a
brief discussion on feedbacks and transient rates:

http://www.iac.ethz.ch/people/knuttir/papers/knutti08natgeo.pdf

 

[Bored Wombat]

This is a simulation of environmental feedback called http://itg1.meteor.wisc.edu/wxwise/radiation/daisyworld.html" . The environment consists of and input luminosity and 2 species of daises one black the other white, The temperature range in which each species can exist is different but overlapping. The black daisies germinate at a low temperature but because they are black absorb heat and raise the temperature. At some higher temperature white daisies germinate. They reflect light tending to lower the temperature. The simulation runs until a equilibrium is reached.

Big tipping point between luminosity .93 and .94

 

[vanesch]

I did some playing on my own, but as it pertains more to "chaotic systems" than to "feedback" I put it in the thread there.

 

[Andre]

This is a simulation of environmental feedback called http://itg1.meteor.wisc.edu/wxwise/radiation/daisyworld.html" . The environment consists of and input luminosity and 2 species of daises one black the other white, The temperature range in which each species can exist is different but overlapping. The black daisies germinate at a low temperature but because they are black absorb heat and raise the temperature. At some higher temperature white daisies germinate. They reflect light tending to lower the temperature. The simulation runs until a equilibrium is reached.

Thanks, time to resume this thread.

This is a typical controlling/stabilizing effect of negative feedback. Too cold? then there is the black daisy absorbing - low reflectivity - warm feedback. Too warm? then is the white daisy - reflecting - cold feedback. Sign of the feedback opposite to the output.

So what looks like a tipping point to WB is in reality the start of the stable process, steered by negative feedback.

 

[Andre]

I think it is a bad idea to do black box modelling. We want to understand the climate system dynamics by using explicit physical modelling, not by fitting parametrisable general model classes on existing data, or by trying to extract some general properties from time series analysis. That's something you can do if the complexity of the underlying system is hopelessly beyond comprehension AND if you know that the time series you're analysing are entirely representative for the evolution you want to draw from it. However, this is in fact nothing else but a sophisticated way of "curve fitting and interpolation". You can do that if you need a dynamical model that needs to be used in conditions that are very near to the conditions of where you fitted the data. But you cannot hope to get out of such a thing any general dynamics that is universally valid.

I've been doing such kinds of things for work when I was young. It works rather well in "interpolation" mode and is hopeless in "extrapolation" mode. The reason is that there are myriads of classes of dynamical models which can all agree on the fitted region, and behave wildly differently when outside of that region.

As we want to explore a situation that we don't know much about, namely a quick increase in greenhouse gasses in the atmosphere, there's not much hope of getting the right dynamics out of just a black box curve fitter when such rise was not the case. There's much more hope to learn something by doing "white box" modelling, that is to say, implement physically understood relationships - even if they are rough and simplified - into a simulator and see what it does. It's also much more instructive to do so.

But if it works well for intrapolation, would that mean that Karners observation about a predominant negative feedback / stability is valid within the restraints of the extremes?

I would not be too sure that we understand the climate well enough to for white box modelling, how to fit in changes in the not-understood forcings like the http://www.birdpop.org/Media/ENSONAO.pdf .

Maybe that the role of the mobile polar highs with pioneer research of late Marcel Leroux has distinctive effect on the variation in minimum winter temperatures that appear to have some effect on the global temperature variations. Currently the USA appears to be experiencing what that means. As far as I know the MPH are not included in the models let alone its behavior.

 

[vanesch]

Thanks, time to resume this thread.

This is a typical controlling/stabilizing effect of negative feedback. Too cold? then there is the black daisy absorbing - low reflectivity - warm feedback. Too warm? then is the white daisy - reflecting - cold feedback. Sign of the feedback opposite to the output.

So what looks like a tipping point to WB is in reality the start of the stable process, steered by negative feedback.

Indeed. However, the model, simple as it is, is much richer than just "negative feedback". In fact, you get another tipping point around 1.7

If you look at the temperature as a function of "luminosity", then you see that for most values of luminosity, the system controls itself such that temperature is something like 25C.
(do this for several values between 0.94 and 1.70). So there is strong negative feedback here to get temperature to the desired value (more or less): if it is too cold, more black daisies, if it is too hot, more white daisies. Note that there is even "over steering": close to 1.7, the temperature lowers below 20C.
However, a small variation, from 0.94 to 0.92 is sufficient to make temperature drop from this 25 degrees to 0 degrees ; in the same way, a small variation from 1.69 to 1.71, where temperature goes from 20 C to 45 C.

So we see in this simulation that we have a more or less "stable" population occupying 2/3 of the land, of an adapted mix of white and black to keep temperature more or less constant, within two boundaries (0.94 and 1.7), and a total collapse of this system by a tiny change over these boundaries.

 

[vanesch]

I would not be too sure that we understand the climate well enough to for white box modelling, how to fit in changes in the not-understood forcings like the http://www.birdpop.org/Media/ENSONAO.pdf .

The point is that you don't want to "fit that in". You would like to "get it out" from the dynamics of the system itself. If all individual physical local processes are well enough described, the dynamics should "by itself" show this behaviour. It would be a good thing that GCM could reproduce these things (without them being "put in by hand"). It would increase the confidence that one is closing in on the full climate dynamics.

To me, it would be the only way to really be confident in climate predictions: that we just put into a model (essentially an augmented weather simulator as we use it for weather forecasting) all physically relevant information (without any "fitting the data", but just physical modelling), and be able to 1) compute rather accurately current and near-past climate and 2) compute things like these oscillations. Once all that is accurately coming out of the model (without having it put in by hand), I would start to be rather confident that eventual future evolutions would be well-described too.

 

[vanesch]

But if it works well for intrapolation, would that mean that Karners observation about a predominant negative feedback / stability is valid within the restraints of the extremes?

The point is that you don't KNOW if a black-box dynamical model is "having negative feedback" or not. Remember that feedback is the chopping-up of a certain dynamical model into separated chunks (which might be physically motivated), to obtain an overall dynamics. However, by doing black-box modeling, you ONLY fit the general overall dynamics. You don't know if "for real" it is internally chopped up in pieces, that are connected into a feedback loop. That's something you can only do by physical modeling.

Of course, you can FIT an arbitrary feedback model with free parameters onto some data. But nothing tells you that an even rather good fit has any structure that ressembles the "true" structure. The dynamics will reproduce more or less well similar signals as those used to fit it.

My dynamics professor told us: "give me any dynamical model with 12 free parameters and I fit you an elephant ; add a 13th parameter, and I make its trump swing!"

But that doesn't mean that the model is the correct model of an elephant!

 

[Xnn]

Have been toying around with Excel to build a simple model of Earth's climate.
It's physics based with temperature dictated by the Stephan Boltzmann law.
Albedo is based on the fraction of water and ice present.
The model was calibrated to match approximate global temperature corresponding to ice age/interglacial with 180/270 ppm CO2.

Add a little CO2 and emissitivity falls and temp goes up.
Increased temp results in melting a little bit of ice.
The ice doesn't melt immediately to equilibrium, but enough so that albedo goes down a little bit.
In other words, there is a simple feedback mechanism with time delay.

After a couple time steps of rising CO2 levels, levels are held constant.
Problem is that what happens is run away global warming.

So, there has to be some negative feedback mechanism for stablity.
During the Ice age/Interglacial, we know that solar irradiance and CO2 levels fell
and that these kept temperatures from getting too high. However, without those forcings, what is left?

 

[Andre]

Have been toying around with Excel to build a simple model of Earth's climate.
It's physics based with temperature dictated by the Stephan Boltzmann law.
Albedo is based on the fraction of water and ice present.
The model was calibrated to match approximate global temperature corresponding to ice age/interglacial with 180/270 ppm CO2.

Add a little CO2 and emissitivity falls and temp goes up.
Increased temp results in melting a little bit of ice.
The ice doesn't melt immediately to equilibrium, but enough so that albedo goes down a little bit.
In other words, there is a simple feedback mechanism with time delay.

After a couple time steps of rising CO2 levels, levels are held constant.
Problem is that what happens is run away global warming.

So, there has to be some negative feedback mechanism for stablity.
During the Ice age/Interglacial, we know that solar irradiance and CO2 levels fell
and that these kept temperatures from getting too high. However, without those forcings, what is left?

Surely that ice albedo is possible positive feedback loop. Two elements.

1: it happens on the areas with the least insolation at higher lattitudes during the time of minimum insoltation, say spring. Not getting very warm then.

2: It is directy testable: a winter with much snow cover should -statistically significant- be followed by a cold late spring/summer and vice versa, due to that feedback

I'll get back on that dominant negative feedback factor

 

[Andre]

... Once all that is accurately coming out of the model (without having it put in by hand), I would start to be rather confident that eventual future evolutions would be well-described too.

Surely, you're not redefining the scientific method? I'd say that a model can be a good tool to shape hypotheses into detailed quantitative prediction, which has to be verified by testing it eventually to the reality. And even then you can have 100 white swans but if the 101th is black then your all-swans-are-white-hypothesis is falsified (I know the example does not work in Australia - swap white and black)

Also it seems that other specialists like Freeman Dyson or Henk Tennekes have a different view on the skill of models.

Anyway, the thread was about feedback, not models, and I don't think that the discussion about the skill of Karners observations changes from anti-persistent to persistent in this discussion. So if his work suggest anything is that no traces can be found of a dominant positive feedback mechanism, able to push the climate sensitivity for doubling CO2 from the Planck response of 1.1 to 1.2 degrees to some 2 -4.5 degrees.

 

[Andre]

Anyway, the most overlooked feedback factor in my opinion is the latent heat / evaporation. We had a lenghty and difficult discussion about that in this thread in which we dispute whether or not an increased temperature with more of less constant relative humidity would or would not require an additional increase in evaporation rate. If so then the required energy for that would be in the same order of magnitude that the increased greenhouse effect would supply.

But you can't use that energy both for additioal heating and for more evaporation. Hence if the evaporation rate would increase, it would act as a negative feedback, transporting more latent heat to higher levels of the atmosphere where it can be radiated out more easily.

But what goes up must come down and more evaporation also means necesarily an increase in precipitation when dynamic equilibrium is reached and that is testable, see my last post in that thread linking to http://www.sciencemag.org/cgi/content/abstract/317/5835/233, showing that the observed increase of precipitation is roughly consistent with my assumptions (7% per degree kelvin).

However more studies that suggest various increase rates in precipitation:

http://www.agu.org/pubs/crossref/2009/2009GL040218.shtml

We find that the top 10% bin of precipitation intensity increases by about 95% for each degree Kelvin (K) increase in global mean temperature, while 30%–60% bins decrease by about 20% K−1. The global average precipitation intensity increases by about 23% K−1, substantially greater than the increase of about 7% K−1 in atmospheric water-holding capacity estimated by the Clausius-Clapeyron equation.

need to study that,

But also:

http://www.nasa.gov/centers/goddard/news/topstory/2007/rainfall_increase.html

"When we look at the whole planet over almost three decades, the total amount of rain falling has changed very little. But in the tropics, where nearly two-thirds of all rain falls, there has been an increase of 5 percent,"

 

[Xnn]

Actually, my little model runs away in both directions.

Add a little cooling, water freezes to ice and then by albedo changes it runs away to total ice.
Add a little warming, ice melts and albedo runs it away to about 38C. The 38C is just an artifact of how it was tuned.

Albedo changes from Ice/water always re-enforce the initiating forcing (i.e. positive feedback).

Would think that clouds might be a negative feedback at the extremes of warming/cooling.
That is at extreme warming, clouds build up enough to rise albedo.
At extreme cooling, clouds clear enough to counteract the falling albedo.

Problem is that clouds, with some uncertainty, are considered to be net positive feedbacks by conventional climate science. What is supposed to stop run-away global warming in the real world is increased precipitation. From increased weathering this sequesters CO2 and introduces cooling. At the other end of the spectrum, what stops run-away global cooling are volcano's. However, falling CO2 also inhibits plant growth and the lack of plants may halt CO2 levels from falling too much as well.

 

[billiards]

What about the one where all the permafrost melts and loads of greenhouse gases currently trapped are set free?

Or the one where due to increased heat waves we get more forest fires, which then kills a whole load of trees and releases a mass of carbon? (which not only increases greenhouse in the short term but also weakens the planet's ability to capture CO2)

 

[Bored Wombat]

So what looks like a tipping point to WB is in reality the start of the stable process, steered by negative feedback.

Isn't that what a tipping point is? The point between the start of one stable process and the start of a dramatically different one?

 

[vanesch]

Surely, you're not redefining the scientific method? I'd say that a model can be a good tool to shape hypotheses into detailed quantitative prediction, which has to be verified by testing it eventually to the reality.

It's not science, it's engineering. The science was the part where the theory came from on which the model is based. If you do calculations of trajectories of satellites, you also take it on that Newton's laws are valid, and you don't "falsify" the calculated trajectory by sending different satellites and comparing with your calculation. You verify that there aren't bugs in your program, and you are confident that the calculation is going to be right.

Of course, that's a tad too easy, I agree, because you have to make approximations when you do so. You have to decide what's important and what's not if you're modeling things physically. So indeed, it would be better to be able to do some "test casing".

But if you have only one single system (earth's climate), and you don't have a long time (say a few million years of reliable data), then the best you can do is to set up your physical model as best as you can, and take that as the best guess you can make.

Also, you can test subsystems of your calculation. If the main engine is a weather forecast engine that has been tested for several tens of years, this means you master the short-term response well. You can also try to test several other parts, if you have historical data concerning them. And then you have to hope you put it all together correctly.

That's how people build the first atomic bomb too. If you do something totally new, you don't always have the luxury of "prototyping". So you have no choice but to trust your calculations. It's always partly a guess - that you didn't make silly mistakes (but that can be solved by having different independent working groups doing the same thing) - but more importantly that you didn't overlook an important aspect that you thought you could neglect, or that you made a fundamental error somewhere.

Anyway, the thread was about feedback, not models, and I don't think that the discussion about the skill of Karners observations changes from anti-persistent to persistent in this discussion. So if his work suggest anything is that no traces can be found of a dominant positive feedback mechanism, able to push the climate sensitivity for doubling CO2 from the Planck response of 1.1 to 1.2 degrees to some 2 -4.5 degrees.

Feedback is inherently coupled to models. Feedback is a modeling concept. It means constructing a model with a "main" part and a "feedback" part.

You cannot find any "traces of feedback" in pure time series. You don't know if it is inherent dynamics or if the system is structured as a feedback system. What you can do is to try to find/fit a model of the overall system but you never know if that was obtained by a feedback loop or not.

I'll try to explain that later.

 

[vanesch]

To come back to the feedback concept:

In time series analysis and modelling, you have two kinds of linear system descriptions:
"finite impulse response" (FIR) systems, and "infinite impulse response" (IIR) systems.

In fact, one can model almost any (linear) time series systems dynamics both with IIR and FIR systems. Often, IIR systems are more computing-resource-efficient than FIR, but on the other hand, they are a bit harder to "tune".

Well, FIR systems don't contain feedback, and IIR do.

In fact, the definitions are easy:

If x(i) is the input time series (i is an integer indicating "sample number" and represents "time" in most cases) and y(j) is the output time series, then a FIR system is defined by:

y(j) = a0 x(j) + a1 x(j-1) + a2 x(j-2) + ... an x(j-n)

where n is the "order" of the system.

In other words, the output at sample number j is a weighted sum of the n last input samples, and the weighting coefficients are fixed constants which determine the "dynamics" of the system.

For a IIR system, we have:

y(j) = a0 x(j) + a1 x(j-1) + a2 x(j-2) + ... an x(j-n)
- b1 y(j-1) - b2 y(j-2) - ... bm y(j-m).

So an IRR system is a FIR system plus feedback, that is, the output at a certain sample number is composed of, as in the case of a FIR system, a weighted sum of past input samples, but now also a weighted sum of past outputs.

Well, you can approximate any IIR system with a FIR system (of much higher order).

You can't do so exactly, but you can do so within any limit of accuracy. The price to pay is that you will have a very high-order FIR system in some cases to approximate well a rather small-order IIR system.

It is only in the case of unstable IIR systems that you can't build a reliable, long-term FIR system (although you can STILL build a FIR system that approximates the beginning of the divergence). A FIR system can never become unstable. An IIR system can, and that's what makes working with IIR systems somewhat nastier. They are more powerful models, but they are nastier to work with, exactly because of questions of instability.

Andre's simulation was nothing else but an elementary IIR system, something of the kind:

y(j) = G x(j) + F y(j-1)

(so a0=G was the "gain" and b1=-F was the "feedback")

But you can approximate this by a FIR system, by finite substitution:

y(j) = G x(j) + G^2 F x(j-1) + G^3 F^2 x(j-2) + G^4 F^3 x(j-3) + ... + G^(n+1)F^n x(j-n)

In this last system, there is no explicit feedback (the output is not computed using previous outputs).

Note that we see a trace of the feedback loop gain GF :

y(j) = G { x(j) + (GF) x(j-1) + (GF)^2 x(j-2) + ... + (GF)^n x(j-n) }

If GF is smaller than 1 in absolute value, then these coefficients diminish in absolute value as a power series. Hence, the last terms become very small, and truncation is justified. So our FIR system is then a good approximation for the original IIR system.

That's exactly the condition that is necessary for the IIR system to be stable.

And now I come to my original point: if I'm just given time series x and y (inputs and outputs) of the system I'm supposed to model, then I can try to fit a FIR system to it, or I can try to fit an IIR system to it. Now, depending on the quality of the data, that fit will be of good or bad quality. But if the fit is in both cases of good quality, then both system models will reproduce well the behavior of the system, at least for similar signals as the data had.
This is for the very simple case of a *linear* system and one input and output signal.

 

[Andre]

What about the one where all the permafrost melts and loads of greenhouse gases currently trapped are set free?

Or the one where due to increased heat waves we get more forest fires, which then kills a whole load of trees and releases a mass of carbon? (which not only increases greenhouse in the short term but also weakens the planet's ability to capture CO2)

Why would these effects be strong enough to steer climate. Once there was little or no permafrost, when the trees grew at the Arctic coast, http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WPN-45BCR6K-M&_user=10&_rdoc=1&_fmt=&_orig=search&_sort=d&_docanchor=&view=c&_searchStrId=1133189953&_rerunOrigin=google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=0e829aa6f1e183a5e99a5a7d50e8d656, this was close to biggest methane hydrate decompositon event in the Nordic sea (http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V9Y-4FG2XBV-1&_user=10&_coverDate=01%2F01%2F2005&_alid=1133192856&_rdoc=1&_fmt=high&_orig=search&_cdi=5911&_sort=r&_docanchor=&view=c&_ct=27&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=1e072f80837a7092144b4a463d2c4036.

So already in the Holocene, Earth has seen pretty extreme conditions and it only has got colder since then.

More later, I'm maxed out.

 

[Bill Illis]

Actually, my little model runs away in both directions.

Add a little cooling, water freezes to ice and then by albedo changes it runs away to total ice.
Add a little warming, ice melts and albedo runs it away to about 38C. The 38C is just an artifact of how it was tuned.

Albedo changes from Ice/water always re-enforce the initiating forcing (i.e. positive feedback).

Would think that clouds might be a negative feedback at the extremes of warming/cooling.
That is at extreme warming, clouds build up enough to rise albedo.
At extreme cooling, clouds clear enough to counteract the falling albedo.

Problem is that clouds, with some uncertainty, are considered to be net positive feedbacks by conventional climate science. What is supposed to stop run-away global warming in the real world is increased precipitation. From increased weathering this sequesters CO2 and introduces cooling. At the other end of the spectrum, what stops run-away global cooling are volcano's. However, falling CO2 also inhibits plant growth and the lack of plants may halt CO2 levels from falling too much as well.

Xnn, you can constrain your runaway Albedo values to:

- about 0.245 (the lowest level possible in our current atmosphere corresponding to an Earth with no ice, high sea levels and small continental areas concentrated toward the equator, basically clouds will keep it higher than this level) ; to,

- about 0.550 (the highest possible value corresponding to Snowball Earth where all the continents are locked together at one or both of the Poles and ice covers most of the Earth).

The climate history indicates we have come very close to both levels in the past 650 million years.

 

[Skyhunter]

Anyway, the most overlooked feedback factor in my opinion is the latent heat / evaporation. We had a lenghty and difficult discussion about that in this thread in which we dispute whether or not an increased temperature with more of less constant relative humidity would or would not require an additional increase in evaporation rate. If so then the required energy for that would be in the same order of magnitude that the increased greenhouse effect would supply.

Please see the thread you linked for an explanation of why your opinion is wrong.

Your premise that it requires 80 W/m² to support evaporation is over stated by a factor of 1000.

It only requires .08 W/m² to evaporate 1/2 a million cubic kilometers of water per year.

I see what I did. I forgot to convert to grams.

Irregardless, it is still accounted for, witness the IPCC diagram.

 

[Andre]

okay let's try again.

The anual evaporation is 440.10³ km³ per year = 440,000 km³

the Earth surface is 148,300,000 sq km land + 361,800,000 sq km water = 510,100,000 sq km

So the average evaporation for the complete surface = 440,000 km³/510,100,000 km² = 0,000863 km/year = 0.863 meters/year

This is a cube of 0,863 m³ per square meter, which is 863,000 cubic centimeters or grams water per year

So per second per square meter the evaporation is 863000 grams/(365*24*3600)=0.027 gram per square meter per second.

one gram of water requires http://www.usatoday.com/weather/wlatent.htm hence 0.028 gram requires 68.4 joule per second per square meter or 68.4 watt per square meter. Indeed I was off by some 10 watt but as far as I can see not by a factor 1000.

 

[Sorry!]

one gram of water requires http://www.usatoday.com/weather/wlatent.htm hence 0.028 gram requires 68.4 joule per second per square meter or 68.4 watt per square meter. Indeed I was off by some 10 watt but as far as I can see not by a factor 1000.

where did you get that value. one gram of water requiring 2500 joules for evaporation.EDIT: Nvm see where you saw it lol.

it's just that I seen values around 540 cal/g... so about 2260 joules which would bring the value down to what 63?

I am pretty sure there are a lot more factors thuough which effect this value... like pressure, temperature, density etc. etc. it's been awhile since I've taken my physics course though, lol.

 

[Xnn]

The IPCC pegs evapotranspiration at 78 Watts/m^2.
See FAQ 1.1 Figure 1:

http://www.ipcc.ch/pdf/assessment-report/ar4/wg1/ar4-wg1-chapter1.pdf

Anyhow, this very important mechanism tranports energy within the Earth's atmosphere, its precise value is not a classic feedback.

Feedbacks need to fall into 2 categories:

Albedo
Emissivity