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Climate Modeling using a Leaky Integrator


VillagePlank

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Posted
  • Location: A small planet somewhere in the vicinity of Guildford, Surrey
  • Location: A small planet somewhere in the vicinity of Guildford, Surrey
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 ...

First of all I would like to say a big Thank You to VP for all of his work yesterday on explaining the basics of Leaky Integrators. This discussion wouldn't be going anywhere without all of your invaluable input from the beginning, and your LI Masterclass has given us all the basic grounding we need to take this discussion even further, so many thanks indeed. :lol:

To move on to your questions...

The first thing to appreciate, from a standpoint of physics, is that the Sun's energy is delivered in photons, and these photons have specific energies (the energy of a photon is directly related to the wavelength of the electromagnetic radiation it is imparting).

When the Sun's activity increases, the energy contained within each photon remains the same. What changes is the number of photons being emitted. (If the energy of the photons increased then the wavelength of the light would change, which of course does not happen!)

So, when Solar activity is higher you have more photons flying around that are willing to part with some of their energy. How much energy a photon will part with is dependent largely upon how much energy is contained in the particle it hits.

Quantum theory tells us that the energy in a photon is composed of discrete packets (quantum actually means "packet"). In simple terms, a photon contains a whole number of these packets, and can only give up whole numbers of packets. So if a photon has 10 packets of energy is can only give another particle 1 packet, 2 packets, 3 packets and so on - it can't give up 1.5 or 2.3 packets of energy.

Similarly, a particle can only take in a whole packet of energy from a photon. The more energy that particle has the more packets it requires to take in as a minimum. To put it another (simplified) way, and using some arbitrary numbers, if a particle has energy 1 then it can take on board 1 packet of energy. Now that it has an energy of 2 it can only take a minimum of 2 packets of energy to increase its total energy to 4 - its energy level cannot take on a value of 3. (Note that a particle with energy 1 can take on 3 packets from the outset to jump straight to energy 4, but it cannot take on 2 packets because it is not allowed an energy of 3.)

If you followed that (please let me know if you didn't so I can go into greater detail) then you will see that increasing the number of incoming photons increases the chance of a photon-particle collision, but the more energy the particles have the harder it becomes for them to increase their energy. This is what is meant by "saturation point" in this respect - there comes a point where the incoming photons do not have enough energy to increase a particle's energy by a whole number of packets, so it can not become any more energetic.

Again, I can go through this in far greater detail if need be, but that's as brief as I can make it for now (it's still too early in the morning!).

To move on, the more energy a particle has, the unhappier it is. Particles generally like to be in the lowest-energy state in which they can exist. So if a particle has a lot of energy it loves to get rid of it, as quickly as possible. It will only be able to get rid of that energy in the reverse form of the way in which it took it in, so if it took 1 packet of energy, then 2, then 4 and then 8, it will only be able to get rid of 8 packets to begin with, then 4, then 2 and then 1.

Although it might seem that it would be easier to get rid of the extra energy the more it gets rid of (since it needs to get rid of a full 8 packets at first, but it only needs to get rid of 4 packets the next time), it doesn't quite work this way. The more energy the particle relinquishes, the more stable that particle becomes. The more stable the particle is, the happier that particle is with the amount of energy it contains, so it takes longer for it to work up the enthusiasm to give up the extra energy.

So, from a quantum perspective, it is harder to heat an object the hotter it becomes, and it is harder to cool something the cooler it becomes.

Did anyone follow all of that?

:lol:

CB

Edited by Captain_Bobski
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Posted
  • Location: Beccles, Suffolk.
  • Weather Preferences: Thunder, snow, heat, sunshine...
  • Location: Beccles, Suffolk.
First of all I would like to say a big Thank You to VP for all of his work yesterday on explaining the basics of Leaky Integrators. This discussion wouldn't be going anywhere without all of your invaluable input from the beginning, and your LI Masterclass has given us all the basic grounding we need to take this discussion even further, so many thanks indeed. :lol:

Did anyone follow all of that?

:)

CB

Yes indeed. Thank you VP...And, in answer to your Q, CB - I think I may have a quantum brain: it's tunneling out through my skull whilst I'm trying to understand all this stuff. :lol:

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Posted
  • Location: A small planet somewhere in the vicinity of Guildford, Surrey
  • Location: A small planet somewhere in the vicinity of Guildford, Surrey
Yes indeed. Thank you VP...And, in answer to your Q, CB - I think I may have a quantum brain: it's tunneling out through my skull whilst I'm trying to understand all this stuff. :lol:

I haven't read up on the intricate details of quantum brains, though I have witnessed my own brain tunneling through skulls, walls and even interstellar space on more than one occasion! :)

Seriously though, I can go back through that stuff in the last post a bit slower, and in more detail (perhaps in a separate thread) if you would like. Let me know.

:)

CB

EDIT - thanks, LadyP. Sometimes it's hard for me to tell whether I'm spouting gibberish or not! :lol:

Edited by Captain_Bobski
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Posted
  • Location: South Yorkshire
  • Location: South Yorkshire
though I have witnessed my own brain tunneling through skulls, walls and even interstellar space on more than one occasion! :)

Hey CBob and Pete T,didn't know it was magic mushroom season already!

"Water cannot be raised above 100C no matter how you try" (Iceberg). Only true at 'normal' atmospheric pressure Ice! That's why you can't make a decent cuppa at the top of Mount Everest unless you have a pressure vessel - the damn water won't get hot enough. Similarly,a pressure cooker works by raising the boiling point of water,hence faster cooking. Um,anyway...

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Posted
  • Location: A small planet somewhere in the vicinity of Guildford, Surrey
  • Location: A small planet somewhere in the vicinity of Guildford, Surrey
Hey CBob and Pete T,didn't know it was magic mushroom season already!

"Water cannot be raised above 100C no matter how you try" (Iceberg). Only true at 'normal' atmospheric pressure Ice! That's why you can't make a decent cuppa at the top of Mount Everest unless you have a pressure vessel - the damn water won't get hot enough. Similarly,a pressure cooker works by raising the boiling point of water,hence faster cooking. Um,anyway...

With quantum mechanics it's always magic mushroom season!

Good point about pressure, although everything has a heating point above which it is no longer the thing it was to begin with (for example water will eventually break apart into separate hydrogen and oxygen, and eventually even atoms will break apart if subjected to enough energy - which is, of course, what happens in particle accelerators, hence their more casual name of "atom smashers"!).

:)

CB

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Posted
  • Location: Rochester, Kent
  • Location: Rochester, Kent
"Water cannot be raised above 100C no matter how you try" (Iceberg). Only true at 'normal' atmospheric pressure Ice! That's why you can't make a decent cuppa at the top of Mount Everest unless you have a pressure vessel - the damn water won't get hot enough.

I think we can presume at this early stage that the leaky integrator assumes the properties of an isopiestic and isochoric system. For now, anyway :)

Edited by VillagePlank
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Posted
  • Location: A small planet somewhere in the vicinity of Guildford, Surrey
  • Location: A small planet somewhere in the vicinity of Guildford, Surrey

Does anyone have anything further to add with regards to VP's questions?

CB

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Posted
  • Location: Rochester, Kent
  • Location: Rochester, Kent

Perhaps a little rephrase to focus ....

All other things being equal ...

If you add a constant amount of heat to a system over time does the rate at which the temperature increases reduce as the temperature gets higher? If you withdraw the mechanism for adding heat, so no heat is being added to the system does the temperature drop quite fast at first, but, as it cools, it slows down?

This is precisely the properties that the leaky integrator show, so, to progress, we need to demonstrate that temperature can, and does, act that way.

I've just been to the local book shop and bought "The Fundamentals of Thermodynamics" Looks like I'm in for an exciting evening :) Also bought a reference on QM because of CB, too. :)

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Posted
  • Location: South Yorkshire
  • Location: South Yorkshire
I think we can presume at this early stage that the leaky integrator assumes the properties of an isopiestic and isochoric system. For now, anyway :)

Ok but pressure and volume are never static in the 'real world',whatever that is!

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Posted
  • Location: A small planet somewhere in the vicinity of Guildford, Surrey
  • Location: A small planet somewhere in the vicinity of Guildford, Surrey
Also bought a reference on QM because of CB, too. :)

Sorry about that, VP! :)

CB

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Posted
  • Location: Rochester, Kent
  • Location: Rochester, Kent
Sorry about that, VP! :)

CB

You owe me £45 (£44.99) worth of beer, now :)

Ok but pressure and volume are never static in the 'real world',whatever that is!

Yep, given that the state can be modelled by a function, f(p,v,t) (which sets up the relations p,v, and t) then we can see the standard equation of dp/dt*dt/dv=dp/dv, and solve accordingly - so we can possibly solve pressure by assuming a constant volume, or volume assuming a constant pressure, from the LI temperature (the water height)

That, though, seems to be an age away, and would only be useful should we deem the LI to be a useful model of temperature.

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Posted
  • Location: A small planet somewhere in the vicinity of Guildford, Surrey
  • Location: A small planet somewhere in the vicinity of Guildford, Surrey
You owe me £45 (£44.99) worth of beer, now :)

I'll e-mail you a copy of a photo of a cheque :)

CB

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Posted
  • Location: Dorset
  • Location: Dorset

Before applying it to the leaky integrator we need to remember that the input is tuned off at night time (or at least vastly reduced), also the amout of input is very seasonal at the poles, that temperature through out the globe isn't distributed evenly (i.e temperature doesn't tend to transfer from one hemisphere to the other very well).

Finally that if you increase what comes in you need to increase what goes out, but an interesting question if you have more solar input do you have the same proportional increase in the output all things being equal ?.

The seasonal component I think is pretty critical. As we know in the UK an awful lot of cooling occurs does this negate, use up the memory contained built up in the system ?

Finally does the earth cool down faster or slower than it heats up ?.

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Posted
  • Location: Rochester, Kent
  • Location: Rochester, Kent
Before applying it to the leaky integrator we need to remember that the input is tuned off at night time (or at least vastly reduced), also the amout of input is very seasonal at the poles, that temperature through out the globe isn't distributed evenly (i.e temperature doesn't tend to transfer from one hemisphere to the other very well).

Finally that if you increase what comes in you need to increase what goes out, but an interesting question if you have more solar input do you have the same proportional increase in the output all things being equal ?.

The seasonal component I think is pretty critical. As we know in the UK an awful lot of cooling occurs does this negate, use up the memory contained built up in the system ?

I think we should ignore the seasonal component for the minute - of course, also implied by your post is angle of insolation etc etc; if the LI matches the 'mean' then, perhaps, we might be onto something. That, for now, is a target small enough to hit without making it any smaller.

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Posted
  • Location: A small planet somewhere in the vicinity of Guildford, Surrey
  • Location: A small planet somewhere in the vicinity of Guildford, Surrey
Before applying it to the leaky integrator we need to remember that the input is tuned off at night time (or at least vastly reduced),

We should also ignore the daytime/nighttime issue (for now, at least), since one side of the Earth is always facing the Sun, regardless of the time of day. I suggested in an earlier post that we should consider the oceans as being like a spitroast, and this analogy can be extended to the entire Earth, of course, if we're going to be talking about long-term averages.

CB

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Posted
  • Location: A small planet somewhere in the vicinity of Guildford, Surrey
  • Location: A small planet somewhere in the vicinity of Guildford, Surrey

Further to my last post (and digressing from the thread's topic slightly), and for comparative purposes, if the Earth were the size of a common household oven and the Sun were a rotating heating element, the element would rotate at about 5 rpm, or once every 12 seconds. This is roughly comparable with the speed of the rotating dish in an average microwave oven!

B)

CB

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Posted
  • Location: Dorset
  • Location: Dorset

The difference though CB, is that in a Microwave most of the heat which is gained isn't all lost again, by the time the plate has rotated.

The leaky integrator replies upon memory of what's gone on before, if every night you suddenly open up the leak to let out 99% of everything that built up previously, This figure could be anything from 80 to 120% depending on the time of year, your going to have very different results.

I understand that over a 24 period it evens out but I am not sure the leaky integrator works well with averages. Over a 24 hr period you still press the reset switch for 99% of the heat.

A good example is that if you roll up VP's previous example into 4 pieces of data instead of 40 and average out the input and output you get very different results.

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Posted
  • Location: A small planet somewhere in the vicinity of Guildford, Surrey
  • Location: A small planet somewhere in the vicinity of Guildford, Surrey
The difference though CB, is that in a Microwave most of the heat which is gained isn't all lost again, by the time the plate has rotated.

The leaky integrator replies upon memory of what's gone on before, if every night you suddenly open up the leak to let out 99% of everything that built up previously, This figure could be anything from 80 to 120% depending on the time of year, your going to have very different results.

I understand that over a 24 period it evens out but I am not sure the leaky integrator works well with averages. Over a 24 hr period you still press the reset switch for 99% of the heat.

A good example is that if you roll up VP's previous example into 4 pieces of data instead of 40 and average out the input and output you get very different results.

If you check back at the very first post on this thread you'll see how a variable input (sine wave) leads to an oscillating "temperature".

If, as you say, you were to "press the reset switch for 99% of the heat" then what happens to the remaining 1%?

If the figure can be anywhere between 80% and 120% depending on the time of year, you have to take into account the fact that when it's 80% in one part of the world it is 120% in another part of the world, and vice versa.

When talking about globally averaged temperature over decades (as we are), the rotation of the Earth is not directly relevant. The LI is roughly modelling the entire Earth, not just England.

More to the point, though, we are attempting to build up a model from first principles here, which means we need to take it a step at a time. If seasonal variations and transitions from night to day do make a difference then I am sure we will eventually get to that.

Right now we just need to know whether temperature does, in fact, behave the way the LI models it. Do you have any thoughts on this?

:lol:

CB

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Posted
  • Location: Dorset
  • Location: Dorset

In answer to your question I am really not sure CB. I think the simply answer is yes, But when you compare temperature straight to Solar input the lag isn't really very big and I think the simple answer to this is that when you run the LI above a range of 12 hrs and don't take seasonal variability into account you miss the important emptying of the bucket(or at least the very large discharge).

Um... I am thinking how best to say this, maybe a Toilet, the toilet builds up slowly as water enters into it, you then flush the toilet and it all goes out again. Now if you ignoring the flushing which empties it down to a base point again regardless of how much is in there i.e it will flush down and leave 5 cm at the bottom regardless. Then the LI won't model this accurately, particularly if you average out the toilet and say that there is normally 20cm of water in it.

Does that make any sense or is it a very poor example..... :lol:

Edited by Iceberg
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Posted
  • Location: A small planet somewhere in the vicinity of Guildford, Surrey
  • Location: A small planet somewhere in the vicinity of Guildford, Surrey
In answer to your question I am really not sure CB. I think the simply answer is yes, But when you compare temperature straight to Solar input the lag isn't really very big and I think the simple answer to this is that when you run the LI above a range of 12 hrs and don't take seasonal variability into account you miss the important emptying of the bucket(or at least the very large discharge).

Um... I am thinking how best to say this, maybe a Toilet, the toilet builds up slowly as water enters into it, you then flush the toilet and it all goes out again. Now if you ignoring the flushing which empties it down to a base point again regardless of how much is in there i.e it will flush down and leave 5 cm at the bottom regardless. Then the LI won't model this accurately, particularly if you average out the toilet and say that there is normally 20cm of water in it.

Does that make any sense or is it a very poor example..... :lol:

I understand what you're saying, Iceberg, I just think you're missing the bigger picture - the Sun is always illuminating part of the Earth. You seem to be focusing on one part of the Earth's surface - like London, for example - and seeing that it gets illuminated for roughly 12 hours and then is dark for roughly 12 hours. But when London isn't illuminated, somewhere else is illuminated that was previously dark.

I am not denying that there is an oscillation of input over areas of the Earth's surface, and I appreciate your reservations, but I don't agree with your conclusion. You say that a direct comparison between temperature and solar input shows that the lag really isn't very big. What do you mean by this? Is it that the Sun warms the Earth during the day and the Earth cools at night, without solar input? Granted that these immediate effects do not suffer lag, but I think it's not really looking at the bigger picture.

:)

CB

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Posted
  • Location: Dorset
  • Location: Dorset

um... No I do understand what your saying but the LI relies upon memory, unless you think that the extra heat that the LI builds up travels around the earth with the sun then any residual memory *could* be removed from the system. But if you modelled this using the LI it would still have the memory there.

A good example might be sunspots.

If you say that a particular year has a high amout of sunspots and then model it. When if you dig a little deeper the sunspots occured in a period between Feb and April, but between Aug and Dec they completely died away, then any extra heat the sunspots put into the system would have completely left the system during the cold period. However modelled over a year your would extra energy into the LI model which would be wrong. This is a different point to the toilet one but still valid.

The Toilet example is that an average could again lead to a build up under the LI system, but in real life it it kept going back down the 5cm there would be no continualed build up only warmer and cooler years.

I think part of this could be negated by using the average temperature across the equator, but that would induce more problems.

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Posted
  • Location: A small planet somewhere in the vicinity of Guildford, Surrey
  • Location: A small planet somewhere in the vicinity of Guildford, Surrey
um... No I do understand what your saying but the LI relies upon memory, unless you think that the extra heat that the LI builds up travels around the earth with the sun then any residual memory *could* be removed from the system. But if you modelled this using the LI it would still have the memory there.

A good example might be sunspots.

If you say that a particular year has a high amout of sunspots and then model it. When if you dig a little deeper the sunspots occured in a period between Feb and April, but between Aug and Dec they completely died away, then any extra heat the sunspots put into the system would have completely left the system during the cold period.

But would it? That's the question we're asking here.

You yourself said that for example, say at night-time, 99% of the energy acquired throughtout the day was released. What happens the next day when you have 100% input on top of the 1% of energy that was remaining from the day before?

It does seem rather that you are attempting to torpedo this idea before we have all had a chance to work through the model from first principles. You keep on trying to over-complicate the model at this early stage when all of your objections will be addressed when we reach the appropriate point.

The question was, "does temperature behave the way a leaky integrator models it?" We can move on to another question once this one has been resolved.

:lol:

CB

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Posted
  • Location: Dorset
  • Location: Dorset

CB using statements like I am trying to torpedo something isn't going to be very constructive.

I've said very clearly "In answer to your question I am really not sure CB. I think the simply answer is yes". In other words I am not sure I am floating ideas that *could* effect it not that will, because quite simply I don't know.

I think I've raised some very valid observations about lag, about using averages, about the loo principle which to be fair your not answering.

To simplify it totally then I have said yes. It will depend on all the factors we mentioned about heat on the other pages, but would this say anything about applying LI to global temperature then I don't know I have my reservations about the points I've mentioned.

If you've got the figures for how much energy the earth losses on a daily basis, what the average temperature in the globe is and how much energy has entered then we can put together a simple LI over time.

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Posted
  • Location: A small planet somewhere in the vicinity of Guildford, Surrey
  • Location: A small planet somewhere in the vicinity of Guildford, Surrey
CB using statements like I am trying to torpedo something isn't going to be very constructive.

I've said very clearly "In answer to your question I am really not sure CB. I think the simply answer is yes". In other words I am not sure I am floating ideas that *could* effect it not that will, because quite simply I don't know.

I think I've raised some very valid observations about lag, about using averages, about the loo principle which to be fair your not answering.

To simplify it totally then I have said yes. It will depend on all the factors we mentioned about heat on the other pages, but would this say anything about applying LI to global temperature then I don't know I have my reservations about the points I've mentioned.

If you've got the figures for how much energy the earth losses on a daily basis, what the average temperature in the globe is and how much energy has entered then we can put together a simple LI over time.

I'm sorry, Iceberg, but it really does seem that you are offering up objections to the whole model rather than trying to constructively work through it a step at a time.

You say you are not sure about the way temperature acts in the real world. What do you think of the suggestions that have been put forward, such as the quantum mechanical description of energy gain and loss at the atomic level?

I have answered your questions about lag by pointing out that they are flawed (by virtue of the fact that they look at isolated points and not the whole Earth). Your toilet example is also flawed - the LI models changes over time. If you were to take the average height of water in the toilet over time you would find that the toilet spends far more time static than itspends being flushed. If you take an average of the two extremes you might find an average height of 20cm, rather than the minimum of 5cm, but if you averaged it out over time you would find an average around, perhaps, 5.1cm.

As for the exact figures of energy input and energy output in the real world, I am trying to ascertain that information, though it is rather harder than simply looking up a couple of numbers on the web.

As I have said seveal times, we are trying to build this model from first principles. So let's work through it a step at a time. VP certainly knows what he's talking about, so I shall leave it up to him to decide what the next step should be, assuming we are all agreed that temperature in the real world does act like a leaky integrator.

CB

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