Climate Modeling using a Leaky Integrator

[Iceberg]

I am not doubting you've shown it in Excel VP, I can see that......

But it's meaningless unless you can show what I've discussed, You've constantly said I don't understand but refuse to answer my concerns/questions.

Again I will keep it very simple are you saying that an increase in temperature will lead to less energy leaving the earth, without any other mechanism factored in ?. (again I will say that Yes I can see how an increase in CO2(GHG) will lead to less energy leaving the earth as it stays there for 200 odd years and directly reduces the leak !)

.

If I am wrong point out where I am wrong rather than keep saying I am being thick.

I think you've got so hung on what you've produced that you've lost the whole concept you've tried to look at.

[VillagePlank]

I am not doubting you've shown it in Excel VP, I can see that......

But it's meaningless unless you can show what I've discussed, You've constantly said I don't understand but refuse to answer my concerns/questions.

Again I will keep it very simple are you saying that an increase in temperature will lead to less energy leaving the earth, without any other mechanism factored in ?. (again I will say that Yes I can see how an increase in CO2(GHG) will lead to less energy leaving the earth as it stays there for 200 odd years and directly reduces the leak !)

.

If I am wrong point out where I am wrong rather than keep saying I am being thick.

I think you've got so hung on what you've produced that you've lost the whole concept you've tried to look at.

That's complete rubbish, and you know it. For instance you made a claim that the system exhibits 10 in, and 10 out behaviour. Patently not true - where's your retraction? Where's questions such "I don't understand why this isn't 10 in, 10 out" You've made suggestions that I think I've managed to create water out of thin air to fill up a bucket. Again, patently **NOT TRUE**

I've tried to explain from precise mathematics, and by metaphor, and yet still you persist!

Far from me being hung up some mathematical model I've using for years, I think it is you, who is seeing a dead elm tree in a forest of oaks. Why that is - well that's a question for yourself.

Edited February 18, 2009 by VillagePlank

[Iceberg]

The maths model is fine VP, but that doesn't mean it can be applied to everything in the real world. When Applied to CO2 or water vapour yes, but when applied to the input of the sun, NO.

my 10 in 10 out was an example. All things being equal the amount leaving the earth and entering the earth is equal, otherwise we would be dead after a few thousand years.

I've asked a very specific question and I will ask it again. Are you saying that an increase in the temperature of the earth caused by increased solar drive will by itself lead to a reduction in what leaves the earth.?

[VillagePlank]

The maths model is fine VP, but that doesn't mean it can be applied to everything in the real world. When Applied to CO2 or water vapour yes, but when applied to the input of the sun, NO.

You cannot know that that is the case. Period.

my 10 in 10 out was an example. All things being equal the amount leaving the earth and entering the earth is equal, otherwise we would be dead after a few thousand years.

No, Iceberg, it was an assertion about the invalidity of the model. A wrong one, too.

I've asked a very specific question and I will ask it again. Are you saying that an increase in the temperature of the earth caused by increased solar drive will by itself lead to a reduction in what leaves the earth.?

NO! More water lead to a FASTER rate of decrease. It's why it's known as a leaky integrator - when there is more water it creates more pressure around the leak meaning more water is forced out.

WILL YOU LOOK AT THE BLOODY GRAPH ON PAGE ONE, POST ONE. YOU WILL NOTE THAT WHEN THE INPUT IS SWITCHED OFF THE CURVE REDUCES STEEPLY AT FIRST AND THEN LESS STEEPLY AS THERE IS LESS QUANTITY.

I am SO SO glad I didn't make it semi-linear and push the inputs and outputs through a sigmoidal function ..... I have to admit that I beginning to think you are simply trolling ....

Edited February 18, 2009 by VillagePlank

[Iceberg]

Stop being obtuse, so the temperature of the earth directly effects the amount that goes out then ?. NO. It doesn't the amount in effects how much goes out, not how much is already there. Whether the current temperature of the earth is 10C or 11C doesn't effect how much goes out(unless you explain how on earth it does). I agree it can though WV etc but this isn't included, your model isn't about WV it's about temperature per se.

This is directly against CO2 where the amount already in the system does effect how much goes out.

[VillagePlank]

Stop being obtuse, so the temperature of the earth directly effects the amount that goes out then ?. NO. It doesn't the amount in effects how much goes out, not how much is already there. Whether the current temperature of the earth is 10C or 11C doesn't effect how much goes out(unless you explain how on earth it does). I agree it can though WV etc but this isn't included, your model isn't about WV it's about temperature per se.

This is directly against CO2 where the amount already in the system does effect how much goes out.

Let's go back a step, huh? Do you now understand about the rate of change changing depending on the quantity of water? I only ask because 20 minutes ago, you hadn't, and you seem to just make assertion after assertion and then simply move on.

[Iceberg]

Let's go back a step, huh? Do you now understand about the rate of change changing depending on the quantity of water? I only ask because 20 minutes ago, you hadn't, and you seem to just make assertion after assertion and then simply move on.

Not true VP, I have always said that CO2 meets this perfectly, temperature doesn't.

I have made the same comments time and time again to both your goodself and CB, there is no mechanism for solar change i.e sunspots to meet this model, ergo it cannot be modeled in the way.

[VillagePlank]

Iceberg, you asserted that the model implied the creation of energy. I presume that you made this notion on the exact opposite of what the model actually does. Can I take it as read and assume that you retract the premise that the leaky integrator implies energy creation? It's an important step in my view

Oh, and radiation emitted is equal to temperature raised to the fourth power t^4, but we will get to that point in a while (that being the assertion that higher temperatures do increase emmisivity)

Edited February 18, 2009 by pottyprof

[Iceberg]

Surely the model works both ways though ?. That is if you can get negative water. (but perhapes water isn't the best example).

And this is a genuine question if the leaky integrator is applied to CO2 then it can work both ways. i.e a negative enforcing memory and a postive enforcing memory.

[VillagePlank]

I've just edited my last post, could you answer the first bit, please? We can leave the Stefan-Boltzmann law bit till later. I really want to move on through these objections as fast as we can.

Edited February 18, 2009 by VillagePlank

[Iceberg]

My premise was that if higher temperatures do not effect the leak per se then there must be energy creation.

But if you say that higher temperatures do effect the leak, then I would evidence of that as I don't believe that's the case.

Under that then yes I retract the energy creation comment. (I wasn't saying that the leaky integrator must mean energy creation but the way you were using it implied this due to the lack of mechanism.)

[Admiral_Bobski]

I don't want to interrupt the flow of the debate, and I would very much like to see the responses to VP's questions, but if I may quickly interject.

I will say this one last time - this exercise is demonstrating a principle. That is all it is doing. It is far too simplistic, at this point, to be directly applied to the real world. There is a whole bunch of other factors that need to be considered.

To assess this proposal fairly we all need to play devil's advocate and assume that CO2 is irrelevant. We need to determine whether or not it is possible to recreate an accumulation of heat without invoking CO2 - if it is not possible then CO2 must be involved: QED.

It is far too easy to dismiss this idea on the basis that temperatures in Jan 08 were at the 69-90 baseline, therefore all the extra heat is lost. We need to consider the accumulation of energy throughout the entire Earth system - which this model implicitly does - rather than taking just the combined atmospheric and air temperatures. Melting ice, for example, will use up more energy than simply reading ocean temperatures might imply. All energy needs to be considered.

Let's assess rather than dismiss, eh?

<_<

CB

[VillagePlank]

But if you say that higher temperatures do effect the leak, then I would [need] evidence of that as I don't believe that's the case.

Well, you need to tell Mr Stefan, and Mr Boltzmann, because their law says that the higher the temperature the higher the rate of energy loss (for perfect black bodies)

Now, assuming that, at some level, the Stefan-Boltzmann law applies to the Earth (it does), and assuming that atmopsheric temperature is some function of the emmisivity of the Earth (in part it is), then I'm afraid, the leaky integrator seems, to me, to be modelling, in a very basic way, some of the dynamics of the atmosphere.

In fact the rate of change of water loss from the LI looks very much like the rate of change of radiative loss from the SB law.

Perhaps a merry coincidence.

Edited February 18, 2009 by VillagePlank

[matt_henson]

You know what the most disheartening thing is?

That I can produce a relationship between sunspots and rising temperatures, and not one - yes, not one, of the proponents of CO2 here on NetWeather has anything to say about it. Also, what's disheartening, is that this uses the simplest of simplest of calculus and people seem to be having such a difficult time in understanding the concepts. I can assure you that the mathematics underpinning the CO2 hypothesis are much much much more complex.

It leads to some very difficult questions that, I suspect,some people will have to start asking themselves.

Very disappointing indeed; and, it remains, that there is a simple relationship between sunspot data and rising temperatures.

You are going to wonder why a complete stranger has joined this thread for his first post but hey you have to start somewhere

I really appreciated this post simply because it catchs the true issue which is that many people fail to grasp simple mathematical concepts and yet argue painfully aggresively way against on matters they don't even understand.

VP I like your leaky integrator concept I am will no doubt quiz you as time goes on other concepts, not sure what I let myself in for by joining netweather but I will no doubt enjoy the ride...

[Chris Knight]

I think Iceberg mentioned that there are no mechanisms by which small variations in Solar input could be stored to give a lag effect.

Increased/decreased temperatures and variations in the amount of OLR are only part of the outcome of expenditure of climatic energy. They are both relatively short term effects, but handle the bulk, but not all of the energy balance.

Water itself has 2 phase transitions from ice to liquid water, and from liquid to gaseous phase. Latent heat is stored in the molecules of water at each of these phase transitions, and released when the transitions are reversed. These can be short or long term energy transactions. The latent heat changes occur without temperature change.

Oceans do take part in the energy balance, in kinetic, thermal and transport roles, and for the ENSO zone, above a critical surface temperature of 27.5 deg C interact violently with the atmosphere to initiate "deep convection" events, triggering violent storms, releasing large amounts of energy into the atmosphere. At the poles, formation of ice during the winter prevents loss of heat to space from oceans, which immediately below the ice are much warmer than the upper ice surface.

There is potential energy stored when precipitation leads to increase in thickness of ice caps and glaciers, which can do work (releasing heat) centuries, or millennia later as the mass of water returns to sea level. Similarly when water is trapped in aquifers, there may be long term delays before the mass of water descends to sea level. Continental landmasses sink under the weight of ice during glaciations, and slowly rise again after the ice has melted.

I haven't mentioned seasonal changes, but some will have already got the point.

As long as there are temperature differences, convective air movements, rotational forces on the earth, and fluid motion of atmosphere and oceans, there will be pressure differences leading to zonality, vorticity and winds. Continental shape and relief due to orogeny will focus and organise wind patterns. The winds in turn move the surface of the oceans.

When winds affect the rate of rotation of the earth, causing tiny changes in the length of day, the potential kinetic rotational energy of the earth changes. These changes can have multidecadal time scales to return to the earlier state, and can indeed be cumulative. Tidal friction by sun and moon counteract these changes, and that friction releases heat into ocean, atmosphere and landmasses.

There is also energy sequestered by the biosphere, in the form of biomass, which may hold on to the energy for up to several millennia, and even beyond the lifetime of the organism, which in turn may become part of the geosphere. Examples are of course fossil fuels, oolitic limestones and other sedimentary rocks, which may be recycled to the atmosphere and oceans after many millions of years. Some people seem to think that this may be a problem.

VP, (nice work BTW ) if you ever want to reduce the abstraction of your model slightly, instead of sunspots, you could use the Total Solar Irradiation (TSI) figures published on Leif Svalgaard's site. Leif's own reconstruction goes from 1700-present.

The longest ENSO related record I can find is Here -the CRU SOI back to 1866.

Gary Sharp's Chronology of Climate related events uses Quinn's (1992) historical ENSO events dated back to before 1700, either as warm (El Nino) or cool (La Nina) events, but not their intensity.

Edited February 19, 2009 by Chris Knight

[Methuselah]

To assess this proposal fairly we all need to play devil's advocate and assume that CO2 is irrelevant. We need to determine whether or not it is possible to recreate an accumulation of heat without invoking CO2 - if it is not possible then CO2 must be involved: QED.

Yes. That does make perfect sense to me, I think? VP is building up a model bit-by-bit; piecemeal being one way to 'know' which individual piece contributes what to the system, I think? And CO2 will have its turn?

Well, you need to tell Mr Stefan, and Mr Boltzmann, because their law says that the higher the temperature the higher the rate of energy loss (for perfect black bodies)

Now, assuming that, at some level, the Stefan-Boltzmann law applies to the Earth (it does), and assuming that atmopsheric temperature is some function of the emmisivity of the Earth (in part it is), then I'm afraid, the leaky integrator seems, to me, to be modelling, in a very basic way, some of the dynamics of the atmosphere.

In fact the rate of change of water loss from the LI looks very much like the rate of change of radiative loss from the SB law.

Perhaps a merry coincidence.

That all looks good to me, VP...Only time will tell.

[Iceberg]

Morning VP and all.

Stefan Boltzmann is one of the basic building blocks of GHG theory.

I would suggest a return to basic principles though.

(BTW I spent a few hours last night trying to familiarise myself with some of these issues using the web, I found quite a few skeptics using almost the same model your using to prove that AGW doesn't exist, going back 10 years or so. However it never really gained traction.)

I think this is worth going into in detail as it under pins and hinges your entire theory.

[VillagePlank]

I would suggest a return to basic principles though.

(BTW I spent a few hours last night trying to familiarise myself with some of these issues using the web, I found quite a few skeptics using almost the same model your using to prove that AGW doesn't exist, going back 10 years or so. However it never really gained traction.)

Agreed - I am planning to write up a walkthrough of the LI to aid understanding; attributing it's various behaviours, as you say, can be left for now.

Can you post links to those who've used a LI before, please: I've spent quite a while looking, and I haven't been able to find anything particularly relevant with reference to a climate analogue using a LI (of course, they might not have called it a leaky integrator which is why I haven't been able to find it)

I think this is worth going into in detail as it under pins and hinges your entire theory.

It's nowhere near a theory yet. Just playing with numbers and seeing what fits where. It's interesting simply because it is, in and of itself.

Edited February 19, 2009 by VillagePlank

[matt_henson]

Agreed - I am planning to write up a walkthrough of the LI to aid understanding; attributing it's various behaviours, as you say, can be left for now.

Can you post links to those who've used a LI before, please: I've spent quite a while looking, and I haven't been able to find anything particularly relevant with reference to a climate analogue using a LI (of course, they might not have called it a leaky integrator which is why I haven't been able to find it)

It's nowhere near a theory yet. Just playing with numbers and seeing what fits where. It's interesting simply because it is, in and of itself.

How would you propose to place the LI concept in to simple model?

Presumably if you started with a 100x100x100 3D matrix with layers to represent the air-sea interface and the air-land interace and a "volume" of storage in the "sea" you could start map a model in excel to test the concept

Edited February 19, 2009 by matt_henson

[VillagePlank]

Presumably if you started with a 100x100x100 3D matrix with layers to represent the air-sea interface and the air-land interace and a "volume" of storage in the "sea" you could start map a model in excel to test the concept

It's a bigger abstraction than that holding the entire earth as a single entity; but, yes, in principle, one could have a many LI's and join them up together to see what happened, and change the constants for each part of each LI to denote albedo, emmisivity, etc etc, and indeed, modifying the input based on season, angle of insolation and so on ...

This has just occured to me - the bucket is presumed to be infinite in size, that is you can pour as much water in it as you want to and it will never 'fill' It'd be interesting to limit to range of water that the bucket can hold ie a minimum, and a maximum.

Looks like I'm going to be busy

Edited February 19, 2009 by VillagePlank

[VillagePlank]

Right, sorry about the poor graphics, and changes in terms ....

Here is a graphical representation of the leaky integrator:

For now, so let's avoid climate for just one bit, this is all about filling up a bucket with water, as an analogue to other natural systems. The soma membrane sitting on all of your neurons is one just natural system where this model works well.

Here's what the terms represent:

r=diameter of incoming pipe

i=flow of incoming water

h=height of water in bucket

o=quantity of water leaking

l=size of leak

In this model we are interested in looking at the height of the water, h, so we must calculate the rate of change for each time period, t, and add it to the height, h.

The rate of change for h in each time period t is given by dh/dt=-olh+ri

Up until now, I treated the size of l, the size of the leak, as constant of 1, so until now it has been omitted, leaving dh/dt=-oh+ri, which is analagous to the equation on the first post of the first page. I have also treated o, and r as constants, too (see the values for a and b previously)

(Any errors of omissions - please do not PM me, post them here, so everyone can see - also any questions; the chances are that others have exactly the same questions but haven't, for a variety of reasons, asked them)

EDIT: I'll leave for it a couple of hours and then I'll post some walk-through mathematics, so we can delve into the details, more

Edited February 19, 2009 by VillagePlank

[Iceberg]

I agree with that.

http://books.google.co.uk/books?id=dkD69N_...9&ct=result

Above is a book P128 in particular which talks about applying Stefan and Bloltzmann to the earth's surface, I know it's slightly further on, but when you get to it I'd be interested to hear how you've applied the law.

Everything else I've read also states that it should only ever be used for black bodies, hence the interest in how you've applied it.

I am sure it's connected but the below picture is an abstract from another book where they work out Net and emitted radiation of a leaf at a varied temperature and altitude.

Also my understand is that even if you can apply the Stefan law to none black bodies using a reduced figure of 0.5 instead of 1 you still have the problem that is only comes into effect when the body and it's surroundings are in perfect temperature equilibrium.

Sorry as I said I know this is for further on, but didn't want to forgot about it.

[VillagePlank]

... snip ...

Briefly, we can talk about the SB law later, but I didn't include the SB law - it, or better put, something like the SB law emerges, from LI model. I have not applied it. We'll leave this for now, otherwise we'll get stuck like this for another day.

How did you get on with, what I think, is a clearer picture of the LI? Do you have any further questions?

Edited February 19, 2009 by VillagePlank

[Iceberg]

whats d ? For Clarity.

[VillagePlank]

whats d ? For Clarity.

It stands for delta, which means change.

So, very briefly, dh/dt means the change of height with the change of time, which in turn means the rate of change of height with time. It is a singular quantity (being that of the other side of the equation) and should not be read d*h divided by d*t.

Edited February 19, 2009 by VillagePlank