Climate Modeling using a Leaky Integrator

[VillagePlank]

Right, time for a quick run through .....

We are going to add some input into the system, and, then, we are going to arbitrarily chop that input off. Here's the data ...

All of the terms are explained in the previous. Two points to note, though, please ignore the radix (decimal point) before the title terms. It's there to stop Open Office automatically capitalising the damn things, and also the zero under .h is the starting point for the height (so we are starting here with an empty bucket)

You can run through this yourself by solving dh/dt=-olh+ri by simple substitution (all of the terms are there) and then adding the result of that to the previous t's h value. EDIT: I decided to add a little bit more, here. Effectively, you need to calculate -olh+ri. The h you use in solving this is the immediately previous h. You then add the result of this to the immediately previous h to get a new h for this t.

Here's the graph of the height produced by this data. Note that, and borrowing from terms used by our audio scientist friends, the attack slows down as h gets larger, and the decay slows down as h gets smaller. An important point - the rate of change of h is related to h itself.

I urge anyone struggling with this to open Excel, or Open Office, and give this a go yourself. If I can be so bold .... it really does add to understanding stepping through each t.

Again, any questions, please don't PM me, post them here in open fora, so they can be discussed or answered for all to see.

EDIT: I've just noticed that I've truncated the last few data records on the data sheet. I'll leave it as an exercise for the reader, unless you all scream blue murder

Edited February 19, 2009 by VillagePlank

[LadyPakal]

All done in Excel and looks exactly like yours. I must admit I find this all quite interesting.

[Iceberg]

Yep done as well

Taking out cell references it looks something like this near the start

=SUM((-0.05*1*0.117)+(0.03*2))

I get the height relationship as well. and that when you remove the flow of incoming water (i) it reduces the height of water, (although the height of water stays above it's initial level still for a long time, hence the memory component.

Essentially the flow of incoming exceeded the flow of outgoing and it took a while for it to get rid of the extra water...

[VillagePlank]

If we, then, change the o constant to 0.08 (it exaggerates the effect on a smaller workspace), extend the series to t=60, and, at your leisure add in another bulk of inputs - I have put 2 from t=16 in i for a little bit, we can get a dataset that looks something like this:

For some reason it is still chopping of the last few rows. Sorry about that.

This gives a chart that looks something like this:

This leads directly to and answers the question that CB had asked - is there some way where a quantity could be additive over time without exceeding any special limits. Here we have only added the same amount of water to the bucket as the first time but the height of water in the bucket has risen solely because of the input in relation to time.

In English, the system hasn't expelled all of it's water - not enough time has elapsed, so, of course, the water level will rise.

Edited February 19, 2009 by VillagePlank

[Iceberg]

Yep.

Can we play with the size of the leak l i.e the leak increases as well in proportion to the amount of h. ?

Or does this make is nolonger a correct model ?.

[VillagePlank]

Can we play with the size of the leak l i.e the leak increases as well in proportion to the amount of h. ?

Or does this make is no longer a correct model ?.

You can do what you want to - there are plenty of variables to play with - just be very careful when extrapolating conclusions

EDIT: and don't forget to add to the model equation if you change it so we can all keep up! Not that I think you're going to need to - I presume you want to play with the constants? There's some neat tricks to produce saw tooth waves etc ...

Did you (or anyone else) find these series of posts helpful, btw?

Edited February 19, 2009 by VillagePlank

[laserguy]

Did you (or anyone else) find these series of posts helpful, btw?

Excellent VP,really. Not been up long (working nights) so still catching up. Just occured to me though,that maybe you should approach the grant people for a,um,grant in order to facilitate research to overthrow the CO2/AGW theory,or whatever one wants to call it. Don't think you'd get very far! Erm,sorry PP.

[VillagePlank]

I think that that's going to be the lot for today

Hopefully, quite a bit of ground covered, so that we can all sing from the same hymn sheet from hereon in. Nice one to all who have followed the walkthroughs - I've never been that good at explaining stuff!!

Edited February 19, 2009 by VillagePlank

[LadyPakal]

You do yourself a disservice - it's all been very clear to me to far... let's see if I can keep up tomorrow!

[VillagePlank]

You do yourself a disservice

Not at all - have you read the last few pages? Evidence of failure to inform absolutely!!! Good job I'm not a teacher, I'd feel compelled to sack myself.

Edited February 19, 2009 by VillagePlank

[VillagePlank]

Quick idea to the moderators - can we have two threads, please? I know it's a bit of work and all that, but it might be useful to have my last three technical posts as the 'current definitive model' state thread, and another one where people can band ideas around? Ideas (from everyone) are always good, and I don't want to subdue them ... but I also dont want to clutter the definitions and the walkthroughs ...

I am sure as we move towards the end of next week that supposition, hysteria, disappointment etc etc are all going to go loopy

Edited February 19, 2009 by VillagePlank

[Iceberg]

You have explained it well VP, I still don't think it applies to global temps at least not significantly but lets leave that for tomorrow !.

The more complicated stuff of SB to come yet......

Thanks for your time and effort.

[VillagePlank]

You have explained it well VP, I still don't think it applies to global temps at least not significantly but lets leave that for tomorrow !.

Well, hopefully, we've got the building blocks to move forward and debate on rational grounds, now. It's still going to go forward slowly, I think, but that is an inevitable consequence of posting on a public forum. A lesson I have learnt the last two days!!

I must say again, Iceberg, sorry for some of my posts yesterday

[LadyPakal]

Not at all - have you read the last few pages? Evidence of failure to inform absolutely!!! Good job I'm not a teacher, I'd feel compelled to sack myself.

I inderstood your explanations from the last few days so it can't have been that bad!

[Chris Knight]

You can do what you want to - there are plenty of variables to play with - just be very careful when extrapolating conclusions

EDIT: and don't forget to add to the model equation if you change it so we can all keep up! Not that I think you're going to need to - I presume you want to play with the constants? There's some neat tricks to produce saw tooth waves etc ...

Did you (or anyone else) find these series of posts helpful, btw?

Thanks VP, for all your work, building a simple model is always helpful. It is all very clear so far.

Just so some of us don't go too far adrift, could we have your version of .xls files at crucial junctures, in the same way that JACKONE has kindly supplied Arctic Ice 2009 files in that thread on this forum.

[VillagePlank]

Thanks VP, for all your work, building a simple model is always helpful. It is all very clear so far.

Just so some of us don't go too far adrift, could we have your version of .xls files at crucial junctures, in the same way that JACKONE has kindly supplied Arctic Ice 2009 files in that thread on this forum.

Unfortunately, I've already tried to provide the 'goodies' to some so they can play without any of the effort of really understanding the model.

It doesn't work, it doesn't foster any understanding, and we all get really annoyed with each other really quickly.

Information, from me, will always be free, but you'll only get the core information, and how to process it, and, by default, the same results .... sometimes. That, in my opinion, is science and understanding. I guess a lot of people won't see it that way, which, I think, is disappointing.

So with mucho sadness, I'm afraid you will need to work through this on your own (or, naughtily, ponce it off someone else who has done it apart from me!)

Sorry.

Edited February 19, 2009 by VillagePlank

[VillagePlank]

Tomorrow, then, is the big day!

That is the day when every vociferous interest - including me, dev, roo, ice, cb, and others, start the debate whether or not this model is ever applicable to the real world.

Those who don't subscribe (that is, fail to put forward their ideas) will be noted by their absence. Really noted.

EVERYONE claims open mindedness - let's play it through, then. The basics are there to work through, and, I trust, you are all interested in working through them? At this stage, in my honest opinion, and I've used this model for years, CO2 is just as much a player as the sun - the question being quantity.

So let us all get together, as a team, where we can all work on something productive - even if the outcome turns out to be entirely negative - which will, probably, turn out to be a very productive thing.

EDIT: please do the walkthrough first, though

Edited February 20, 2009 by VillagePlank

[Methuselah]

Yes VP. Brilliant work...I really do wish that I'd subscribed a lot sooner.

[VillagePlank]

Rightyo, guys.

Two points to make today (and to debate)

Does temperature act in this way .... more specifically ....

(i) Is it harder to heat heat something the hotter it becomes?

(ii) Is it harder to cool something the colder it becomes?

Over to you guys ...

Edited February 20, 2009 by VillagePlank

[Devonian]

Tomorrow, then, is the big day!

That is the day when every vociferous interest - including me, dev, roo, ice, cb, and others, start the debate whether or not this model is ever applicable to the real world.

Those who don't subscribe (that is, fail to put forward their ideas) will be noted by their absence. Really noted.

EVERYONE claims open mindedness - let's play it through, then. The basics are there to work through, and, I trust, you are all interested in working through them? At this stage, in my honest opinion, and I've used this model for years, CO2 is just as much a player as the sun - the question being quantity.

So let us all get together, as a team, where we can all work on something productive - even if the outcome turns out to be entirely negative - which will, probably, turn out to be a very productive thing.

EDIT: please do the walkthrough first, though

VP, I think it's not right to set those who choose not to contribute as negative. I'm not contributing for several reasons. What you are doing doesn't (yet?), to me, make sense compared with how I understand the world, the atmosphere. I also am inclined to wait and see what your answer is - just like people like to read completed scientific papers not stand over the shoulder as it's written. That does not mean my absence should be pejoratively 'really noted'. Besides, this kind of maths is not my strong point, and I'm not sure I think this whole ACC business is this way complex - I think it's pretty simple really (but that's a debate I wont spill into this thread).

I'll keep reading, when you come up with a conclusion I can see what I think of it based upon what I think is the conclusion is.

Edited February 20, 2009 by Devonian

[VillagePlank]

I'll keep reading, when you come up with a conclusion I can see what I think of it based upon what I think is the conclusion is.

The point is that everyone gets involved to reach a conclusion whatever it might be! The chances are no conclusion will ever ever be reached (we do not have the resources to get there)

IMO you should get involved - your understanding of the atmosphere and how it works could be invaluable.

Besides, this kind of maths is not my strong point

This "kind of maths" is the basis for (nearly) all science

EDIT: and I need people who subscribe wholly to the CO2 hypothesis to help eliminate bias.

Edited February 20, 2009 by VillagePlank

[Methuselah]

Rightyo, guys.

Two points to make today (and to debate)

Does temperature act in this way .... more specifically ....

(i) Is it harder to heat heat something the hotter it becomes?

(ii) Is it harder to cool something the colder it becomes?

Over to you guys ...

Well, you can't cool anything past absolute zero because that would require a negative entropy change?

AS for heating: For entropy to rise, heat must travel from hotter to cooler bodies; therefore, to prevent both bodies stabilizing at the same temperature, the hotter object (heat source) must itself be made hotter...2nd law of thermodynamics??

So, the workload must increase nonlinearly for both situations??

I haven't included phase changes in the like...

Thanks for the Qs VP...Even if I'm wrong (my brain is rusty!), the thinking was well worth it!

[Hiya]

Rightyo, guys.

Two points to make today (and to debate)

Does temperature act in this way .... more specifically ....

(i) Is it harder to heat heat something the hotter it becomes?

(ii) Is it harder to cool something the colder it becomes?

Over to you guys ...

What do you mean by harder?

Also it depends on what the something is and the source of heat.

[Chris Knight]

Rightyo, guys.

Two points to make today (and to debate)

Does temperature act in this way .... more specifically ....

(i) Is it harder to heat heat something the hotter it becomes?

(ii) Is it harder to cool something the colder it becomes?

Over to you guys ...

Assuming an environment that is neither hotter than the situation in (i), nor colder than the situation in (ii):

(i) yes, more energy needs to be added than is already trying to escape from the heated body, the hotter it becomes.

(ii) yes, more energy needs to be removed than is trying to flow back from the environment into the cooled body, the cooler it becomes.

Air conditioners and central heating systems both consume more energy, the harder they work.

0°K is an absolute limit, there is no upper temperature limit AFAIK

[Iceberg]

This might help.

"Specific heat capacity, also known simply as specific heat, is the measure of the heat energy required to increase the temperature of a unit quantity of a substance by a certain temperature interval. The term originated primarily through the work of Scottish physicist Joseph Black who conducted various heat measurements and used the phrase "capacity for heat".[1] More heat energy is required to increase the temperature of a substance with high specific heat capacity than one with low specific heat capacity. For instance, eight times the heat energy is required to increase the temperature of an ingot of magnesium as is required for a lead ingot of the same mass"

The hardness of heating will depend upon a great many things including the temperature that the object is already. As well as the type of object your talking about, as well as how much heat the object can absorb before it reaches the maximum about of heat it can hold and the energy is then emited out. i.e Water cannot be raised above 100C no matter how you try, you can change it's form, but even you continue to blast 300C at the water it will stay at 100C.