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Climate Modeling using a Leaky Integrator


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#341 Captain_Bobski

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Posted 19 September 2009 - 17:17

View Postparmenides3, on 19 September 2009 - 16:01 , said:

C-Bob:

As I said on another thread, I am leaning towards the idea that the mechanism that is being sought is nothing more than the long-established greenhouse effect - no need to change the basic principles there. The change to AGW theory would be that the greenhouse effect is not significantly altered by small changes in CO2 concentration - rather, the greenhouse effect's basic ability to retain heat, and how it reacts to changes in incoming energy, is sufficient to explain global warming in conjunction with the sun's varying output.

we need to be much clearer about this; 'greenhouse effect' is no more than a (dodgy) name used to provide a convenient analogy to the global climate system. You seem to be suggesting that the system's record of temperature change might be disconnected from the CO2 content - to a greater or lesser degree - if it can be shown that 'heat memory' from the Sun is in some way the cause of changes to the temperature record. But why would this phenomenon suddenly come into being since the 1950's, and not before?

If the system is retaining more heat than it used to, and the rate of retention is increasing, there must be some physical cause. Thermometers measure current conditions (+/- some short-term hysteresis); other than that, there is no 'memory' in the measurement tools, surely?

:yahoo: P

Hi P3,

I shall skip the hysteresis bit, since VP has answered it already and knows far more about it than I do! So, in response to that quoted above...

In this sense I am referring to the "greenhouse effect" as the effect by which the atmosphere helps to maintain a comfortable temperature for life on Earth. It blocks a certain amount of incoming energy, thereby preventing the daytime temperature from soaring to around 120C. It also blocks a certain amount of outgoing energy, thereby preventing the nighttime temperature from plummeting to around -230C. (These figures are the night- and daytime temperatures of the Moon - since the Earth doesn't stay illuminated on one side for as long as the Moon then these extremes may not be reached in the event of there being no atmosphere, but it illustrates the point.)

So, if you like, the greenhouse effect is the term used for the atmosphere's ability to even out the Earth's surface temperature.

We know that the greenhouse effect stops all the energy (heat) from rushing away from the Earth all at once by, if you like, cushioning the release of energy. (There's more to it than that, of course, because the ground absorbs radiation, the oceans absorb radiation and every object on the Earth absorb radiation, in addition to the atmospheric absorption.)

The Stefan-Boltzmann law tells us that as something heats up it radiates more energy, but its temperature at equilibrium will increase as well (since the emissivity does not increase quite as rapidly as the absorptivity).

So, my thinking which led to this Leaky Integrator idea is that if solar activity remains above a certain level then the absorptivity of the Earth increases a bit more than its emissivity, meaning that the Earth will warm even if the Sun's output remains constant until it reaches its new equilibrium.

As I say, the Sun's average output over the past 60 years or so has been higher than any other 60-year period since records began.

As I have said before (though you may have missed it since you've been away, P3) the temperature increase over the last 100 years or so would require the Earth to retain no more than an extra 1/1000th of a degree Celsius every month, which is not a great deal. Temperatures can still give us peaks and troughs as they always would, but those peaks and troughs would all be 1/1000th of a degree per month higher than they would otherwise have been, giving an increasing temperature trend.

CB

EDIT - I'm just about to start a Leaky Integrator Discussion thread, so that we don't clutter up this pinned thread with discussion that will take it off-course.
:yahoo:

Edited by Captain_Bobski, 19 September 2009 - 17:19 .

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#342 parmenides3

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Posted 27 September 2009 - 10:21

'As I have said before (though you may have missed it since you've been away, P3) the temperature increase over the last 100 years or so would require the Earth to retain no more than an extra 1/1000th of a degree Celsius every month, which is not a great deal.'

If the System retains 'extra' heat, this suggests that something has changed, either to the system, or the external forces working on it.

But consider a tropical desert at night, or a temperate location through the seasons; to what extent do these places exhibit hysteresis?

If I recall rightly, for example, temperatures in the UK respond to our relationship to the Sun with an approximate six-week lag (variable), so that we get our warmest months after the period of greatest insolation, and vice versa.

Where the global surface temperature may well exhibit hysteresis is in the case of our old friend the Arctic, sea ice and sea surface temperature. This has to do with the way in which the measurements works today compared to 30 years ago. The reason why the lower Arctic waters show such a high anomaly is at least partly because, 30 years ago, areas which were perennially ice-covered are no longer; therefore there is a large anomaly recorded. It is also important to understand how much of the long-term global trend is affected by these anomalies (though also important to recognise that models account for the phenomenon to some degree).

So, is the sea ice reducing at 8% per decade because of warming oceans, or are the oceans showing warming because the sea ice is reduced? The two are obviously demonstrating the same overall pattern - one of warming - but establishing cause and effect is less obvious.

So, a suggestion here might be that the leaky integrator model could work quite effectively in relation to the Arctic Ice; think of single-year and multi-year ice as the 'new' and 'carried over' elements of the system. For a year like 2007 to happen, there has to be a loss of multi-year ice as well as the expected seasonal variation in the single year ice. This is, in part, what happened on 07; because of the currents, the winds and the Summer synoptics, multi year ice was pushed out of the 'bowl' of the Arctic Ocean, via the Fram Strait, out into the warmer Greenland Sea, whence it melted.

If the system is 'in balance', then, over time and allowing for variability, the proportion of multi-year and single year ice remains broadly similar. This is because the steady build-up of the hysteretic element is countered by the occasional 'burst' of the system, leaking what has been gained out into the oceans surrounding.

Is this suggesting anything?...
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#343 Captain_Bobski

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Posted 27 September 2009 - 10:29

View Postparmenides3, on 27 September 2009 - 10:21 , said:

'As I have said before (though you may have missed it since you've been away, P3) the temperature increase over the last 100 years or so would require the Earth to retain no more than an extra 1/1000th of a degree Celsius every month, which is not a great deal.'

If the System retains 'extra' heat, this suggests that something has changed, either to the system, or the external forces working on it.

I can't say too much at the moment, but I think it's worth pointing out that in the Earth Climate system something is always changing - that is the nature of dynamic equilibrium.

More later...

:mellow:

CB

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#344 parmenides3

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Posted 27 September 2009 - 10:35

View PostCaptain_Bobski, on 27 September 2009 - 10:29 , said:

I can't say too much at the moment, but I think it's worth pointing out that in the Earth Climate system something is always changing - that is the nature of dynamic equilibrium.

More later...

:mellow:

CB

Yes. Here we need to find something which is/has changed which has led to an observed trend; a long-term positive forcing which did not previously exist. :D P
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#345 Captain_Bobski

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Posted 27 September 2009 - 10:42

View Postparmenides3, on 27 September 2009 - 10:35 , said:

Yes. Here we need to find something which is/has changed which has led to an observed trend; a long-term positive forcing which did not previously exist. Posted Image P


Why does it need to have not existed previously...?

:mellow:

CB

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#346 parmenides3

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Posted 27 September 2009 - 10:54

View PostCaptain_Bobski, on 27 September 2009 - 10:42 , said:

Why does it need to have not existed previously...?

:mellow:

CB

Well, it can have existed, perhaps at a relatively stable level, for a long time, but then an increase or decrease over an extended period would have to come in to alter the response of the system to said forcing. Volcanoes are an interesting short-term example; Pinatubo changed several elements of the system, resulting in short term fluctuations which would not have other happened. There is also a degree of hysteresis in the system response, but, once it stopped erupting, the system was eventually allowed to restabilise at close to its previous state. We have to find a mechanism to account for the persistent trend.

Actually, we have found a lot of mechanisms, with various degrees of influence; the question still remains which mechanisms matter, and which if any we (humans) can do anything about.

Without the change to the system, your solar hysteresis idea would suggest that, over time, the earth would warm indefinitely (I think) :D P
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#347 Captain_Bobski

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Posted 27 September 2009 - 10:57

View Postparmenides3, on 27 September 2009 - 10:54 , said:

Well, it can have existed, perhaps at a relatively stable level, for a long time, but then an increase or decrease over an extended period would have to come in to alter the response of the system to said forcing. Volcanoes are an interesting short-term example; Pinatubo changed several elements of the system, resulting in short term fluctuations which would not have other happened. There is also a degree of hysteresis in the system response, but, once it stopped erupting, the system was eventually allowed to restabilise at close to its previous state. We have to find a mechanism to account for the persistent trend.

Actually, we have found a lot of mechanisms, with various degrees of influence; the question still remains which mechanisms matter, and which if any we (humans) can do anything about.

Without the change to the system, your solar hysteresis idea would suggest that, over time, the earth would warm indefinitely (I think) Posted Image P


Not indefinitely, because the Sun goes through periods of high and low activity. That's kind of the crux of the matter.

:mellow:

CB

(Sorry for the brevity of my response - lots to do!)

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#348 Boar Wrinklestorm

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Posted 07 December 2009 - 11:23

As I've started to rewrite this thing - for the umpteenth time - I thought it would be good to show what the beginnings of one of the very first drafts looked like.

Unfortunately, there are spelling/grammar and other errors in it, but it should be OK to get the gist. For reference, this sort of stuff will appear in the final paper, but a couple of the ideas in this lot have turned out to be sufficiently large to become research subjects in their own right without any reference to climate.

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

Attached File  li3.pdf   92.71K   98 downloads

I am deeply indebted to Captain Bobski for endless encouragement and for first determining the idea that hysteresis (it wasn't called that back then) might be a critical player in climate.

#349 Captain_Bobski

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Posted 07 December 2009 - 11:31

View PostVillagePlank, on 07 December 2009 - 11:23 , said:

As I've started to rewrite this thing - for the umpteenth time - I thought it would be good to show what the beginnings of one of the very first drafts looked like.

Unfortunately, there are spelling/grammar and other errors in it, but it should be OK to get the gist. For reference, this sort of stuff will appear in the final paper, but a couple of the ideas in this lot have turned out to be sufficiently large to become research subjects in their own right without any reference to climate.

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

Attachment li3.pdf

I am deeply indebted to Captain Bobski for endless encouragement and for first determining the idea that hysteresis (it wasn't called that back then) might be a critical player in climate.


Posted Image Thank you, VP. And, at the risk of making this into some kind of love-in (!), I am deeply indebted to you for taking the idea and running with it. When I first proposed the concept I had no idea that it would lead to anything of any interest (though I had hoped!). I wasn't sure that I was barking up the right tree. In fact I wasn't sure that the tree was in the right forest, or even whether or not it was actually a tree!

Back on-topic, though, I would encourage everyone with any interest in the idea to read VP's document - he has done, as usual, an excellent job of simply explaining a concept that can be quite complicated. Any comments, questions or suggestions would be greatly appreciated.

:yahoo:

CB

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#350 Boar Wrinklestorm

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Posted 07 December 2009 - 12:12

I should note - this is a 'cut and paste' edit to protect the work. As a consequence I've managed to leave in some references that, ahem, are not referenced!

(They are all a good read, though :yahoo: )

Edited by VillagePlank, 07 December 2009 - 12:13 .


#351 Solar Sausage

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Posted 07 December 2009 - 12:59

Many thanks for all the effort, VP...Can I just ask one question, though: is the diameter of the pipe really relevant? Is it not just the 'influx' (Q?) into the 'bucket' that is important???

Am I shooting myself in the head? :yahoo: :lol:
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#352 Boar Wrinklestorm

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Posted 07 December 2009 - 14:33

View PostPete Tattum, on 07 December 2009 - 12:59 , said:

Many thanks for all the effort, VP...Can I just ask one question, though: is the diameter of the pipe really relevant? Is it not just the 'influx' (Q?) into the 'bucket' that is important???

Am I shooting myself in ther head? :) :)

It may or may not be. The idea is take first principles, dynamical systems, and reason through to the LI via the Stefan-Boltzmann law. I have a proof (not confirmed) that dynamical systems must necessarily exhibit hysteresis, and the rest stems from there.

The LI is an abstraction of those ideas so we can play more. Whether or not it is needed is yet to be ascertained.

#353 Solar Sausage

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Posted 07 December 2009 - 14:45

View PostVillagePlank, on 07 December 2009 - 11:23 , said:

As I've started to rewrite this thing - for the umpteenth time - I thought it would be good to show what the beginnings of one of the very first drafts looked like.

Unfortunately, there are spelling/grammar and other errors in it, but it should be OK to get the gist. For reference, this sort of stuff will appear in the final paper, but a couple of the ideas in this lot have turned out to be sufficiently large to become research subjects in their own right without any reference to climate.

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

Attachment li3.pdf

I am deeply indebted to Captain Bobski for endless encouragement and for first determining the idea that hysteresis (it wasn't called that back then) might be a critical player in climate.

Oops! :)

I should have read the above before I PM'd you, VP!! :) That'll teach me! :) :)
Pete

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Non cogito ergo non sum!

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#354 Boar Wrinklestorm

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Posted 07 December 2009 - 16:40

No probs' Pete. There's quite a bit to go through, anyway.