Climate Modeling using a Leaky Integrator

[Iceberg]

CB.

I will perform an example using the LI for both the toilet with a minimum flush and an average over time(probably tomorrow), I have NO objections to the LI model, its very useful, but it cannot model everything and somethings would be so complicated to model them accurately as to need a super maths prof to do, this is far greater than my limited intellect hence I don't know.

Again I said in my last sentence that if we have the measurements it's worth putting in the LI. I know it's far harder than anything you will find on the web but without those accurate output figures you won't be able to model it.

Finally I agree lets see what happens next. but I am allowed reservations, believe me I wouldn't have put the effort in trying to understand this just to dismiss it in a few hours.

[Iceberg]

As promised I am trying to put together an LI to model a Toilet, however I think I am still half asleep on a Sunday morning and might be missing something.

Th pic below is my main play worksheet, however when I try and increase the size of the leak to equal the quantity that exists in the system (i.e the simulation of pulling the chain) it doesn't empty out. ?

Now I could just frig the figures but I want to try and understand why isn't not emptying it like this. ?

Any help ?

[Admiral_Bobski]

As promised I am trying to put together an LI to model a Toilet, however I think I am still half asleep on a Sunday morning and might be missing something.

Th pic below is my main play worksheet, however when I try and increase the size of the leak to equal the quantity that exists in the system (i.e the simulation of pulling the chain) it doesn't empty out. ?

Now I could just frig the figures but I want to try and understand why isn't not emptying it like this. ?

Any help ?

o, the quantity of water leaking, is a constant. You have it spiking every sixth or seventh term. Try setting o to 0.18 throughout.

CB

[Iceberg]

Thanks CB, Wouldn't setting it to 0.18 all the way through will negate what I am trying to do....I think.

Does o always have to be a constant ?.

I am trying to empty out everything that had gone in before i.e 0.18 had gone in, if I set the leak to 0.18 then it should all go out in a single time. Although saying that I am might be setting the leak to 0.18 per an x, so only setting it once will only allow 0.18/x to leak out, this might be what your saying CB ?.

[LadyPakal]

You're trying to do this, right?

Edited February 22, 2009 by LadyPakal

[Iceberg]

Yes thanks LP, but I where you've got the 1 I want to have the sum of the input that has gone into the system, does that make sense ?. i.e the sum of the inputs goes out in one lump out.

Sorry trying to say this over this kind of forum isn't easy but I appreciate people taking the time to reply, all the more impressive for VP to have got the basics over.

[LadyPakal]

Because the numbers are multipliers, the 1 means all. If you add 0.5 there, you get half, 0.25 = quarter etc.

More detail, as a toilet fills, the amount of water going in (i) tends to have the same flow (altho' in real life it slows as it reaches full). The inlet is a constant diameter ( r). When you flush, the whole lot (o=1 or 100%) is let out of a hole (l) of constant size (it just has a valve across it when it is unused).

Edited February 22, 2009 by LadyPakal

[Iceberg]

Superb I understand now, thanks very much LP !!

[Admiral_Bobski]

Worth pointing out is that the water in the bottom of a toilet is your effective baseline. The reason there is water in the bottom of the toilet i because there is a u-bend - water gets trapped in the u-bend to the height of the pipe on the other side. Any extra water added to the toilet bowl increases the level of water, which then trickles down over the pipe at the back of the toilet, and the water level returns to its rest level (which is why a toilet never fills up no matter how much you tinkle!).

When you flush the toilet, more water is coming in than can escape down the pipe at the back, so - just like the leaky integrator - the level will rise until the input (the flush) decreases to a lower rate than the rate at which water is pushed out of the u-bend.

I've scanned in a hastily scribbled sketch to help illustrate this!

CB

[LadyPakal]

Yes, I was working with a simple 'total water content' model. All fluids within the bowl & cistern, with 'empty' the minimum fluids (post flush), and maximum, when the cistern was full. Also discounting any fluid or solids introduced via non-cistern means!

[VillagePlank]

Moving in an odd direction, here. The example of a toilet flush introduces a discrete nature whilst the LI is intended to be continuous over time. Anyway, can we all agree that temperature acts the way the LI does? That is the hotter it becomes the harder it is to make it hotter, and the colder it becomes the harder it is to make it colder?

[Iceberg]

Yes thanks I'll look at this in more detail.

Sorry VP, I did take it off topic a bit, but I think it's helpful to model something really simple before moving onto something more complicated. If anybody has anything else to model as an example I am all ears(eyes at any rate)

Yes your right YP.

[Admiral_Bobski]

Okay, I don't know if this is going to take the thread too far ahead too quickly, but I've found some figures we could try plugging in.

The average amount of incoming solar radiation is 1366 W/m².

The IPCC say that the Earth retains between 0.6 and 2.4 W/m² of this.

NASA's CERES, Terra and Aqua satellites have found this figure to be 1.4 W/m², which is right around mid-range of the IPCC estimate.

So, if we take solar irradiance data and put that in as our "water in", and we take a figure of 1364.6 as our "water out" then we could start to assess the validity of the model.

Now all I've got to do is find the solar irradiance data...! I know it can be found from the beginning of the satellite era to present, but does anyone know if there is any proxy data that extends back further?

Any thoughts?

CB

EDIT - here's a link to the Scafetta & West 2006 paper (in pdf) which discusses TSI proxies:

http://www.fel.duke.edu/~scafetta/pdf/2006GL027142.pdf

Another interesting article (though it's from the Science and Public Policy Institute, so draw your own conclusions!):

http://scienceandpublicpolicy.org/sppi_rep...sis_series.html

And here's some actual reconstructed data - it's a bit sparse, though, with up to 10-year gaps between records:

ftp://ftp.ncdc.noaa.gov/pub/data/paleo/cl..._irradiance.txt

Edited February 23, 2009 by Captain_Bobski

[LadyPakal]

This may, or may not, be useful.

http://www.aer.com/scienceResearch/rc/rc.html

A figure towards the bottom: 'The annual mean global energy balance for the earth-atmosphere system'

[Methuselah]

Moving in an odd direction, here. The example of a toilet flush introduces a discrete nature whilst the LI is intended to be continuous over time. Anyway, can we all agree that temperature acts the way the LI does? That is the hotter it becomes the harder it is to make it hotter, and the colder it becomes the harder it is to make it colder?

Yes. I think we can?

[Chris Knight]

Okay, I don't know if this is going to take the thread too far ahead too quickly, but I've found some figures we could try plugging in.

The average amount of incoming solar radiation is 1366 W/m².

The IPCC say that the Earth retains between 0.6 and 2.4 W/m² of this.

NASA's CERES, Terra and Aqua satellites have found this figure to be 1.4 W/m², which is right around mid-range of the IPCC estimate.

So, if we take solar irradiance data and put that in as our "water in", and we take a figure of 1364.6 as our "water out" then we could start to assess the validity of the model.

Now all I've got to do is find the solar irradiance data...! I know it can be found from the beginning of the satellite era to present, but does anyone know if there is any proxy data that extends back further?

Any thoughts?

CB

EDIT - here's a link to the Scafetta & West 2006 paper (in pdf) which discusses TSI proxies:

http://www.fel.duke.edu/~scafetta/pdf/2006GL027142.pdf

Another interesting article (though it's from the Science and Public Policy Institute, so draw your own conclusions!):

http://scienceandpublicpolicy.org/sppi_rep...sis_series.html

And here's some actual reconstructed data - it's a bit sparse, though, with up to 10-year gaps between records:

ftp://ftp.ncdc.noaa.gov/pub/data/paleo/cl..._irradiance.txt

These bolded sources are mean figures, presumably taken over several years.

see post #95 for link to total solar irradiance figures:

VP, (nice work BTW smile.gif ) 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.

Edited February 23, 2009 by Chris Knight

[Admiral_Bobski]

These bolded sources are mean figures, presumably taken over several years.

see post #95 for link to total solar irradiance figures:

Thanks for that Chris - I have no idea how I missed that one Perhaps I should wake up before reading these threads!

Yes, the Earth retention figures are means, but I figured that they would be as good a starting point as any to gauge the working premise of the model proposed here.

CB

[VillagePlank]

Yes, the Earth retention figures are means, but I figured that they would be as good a starting point as any to gauge the working premise of the model proposed here.

Not sure that holds, to be honest, CB.

The premise here, I think, is that the differences from the mean can add or subtract together over time to produce a warming climate, or a cooling climate.

[Devonian]

Someone may have said this, but average radiation is indeed ~1366w/m2 but the Earth is round so effectively average radiation is ~341w/m2. See this.

Edited February 23, 2009 by Devonian

[Chris Knight]

Someone may have said this, but average radiation is indeed ~1366w/m2 but the Earth is round so effectively average radiation is ~341w/m2. See this.

Which article does not explain why 1366 is reduced to a quarter of its value ~ 341.

1366W/m² is the approximate amount of energy a flat disk the size of the earth facing the sun would receive on average if it orbited the sun in place of the earth. The earth is not flat, but a globe, and it revolves around an axis that is slightly tilted from the vertical plane of the orbit. For global averages, it is irrelevant that the globe rotates or not.

At any one time, half of the globe is in darkness, so that even a spot on the equator could only receive the maximum of 683 W/m² on average, and points on the globe nearer the poles receive respectively less irradiation as the sun appears lower in the sky, thus getting less incident energy.

There is some geometrical proof, but the outcome is that 1/4 of the incident radiation is the mean for the whole globe.

But, dawn eats into nighttime, and dusk eats into nighttime, so there's always a little bit more energy coming in than the maths says. The Salami Slicers can add that to the integration. :o

Edited February 23, 2009 by Chris Knight

[Admiral_Bobski]

Someone may have said this, but average radiation is indeed ~1366w/m2 but the Earth is round so effectively average radiation is ~341w/m2. See this.

Yes, the effective radiation at any one time is generally given to be about 340 W/m².

However, even if this is the case, Earth still retains around 1.4 W/m² (this is the net difference between incoming and outgoing radiation).

I stayed with the 1366 W/m² figure because TSI data is recorded as, well, the Total Solar Irradiance, not the effective solar irradiance. It doesn't affect the outcome.

VP - If we were to input actual TSI figures (including proxy data, obviously) which vary around a mean of 1366 W/m² could we not set our "outward flow" to remain static at 1364.5 W/m² and see what happens?

What the IPCC (and NASA) are saying is that the Earth is currently retaining around 1.4 W/m², but as more CO2 builds up that figure is increasing, as Earth retains a greater proportion of the heat.

I'm suggesting that rather than taking that figure as a mean let's take it as a solid unwavering figure against the average TSI. In this case, Earth would always emit 1364.5 W/m² regardless of the amount put in.

If that makes no sense then I'll try to clarify later. Must have coffee!

:o

CB

[Chris Knight]

Yes, the effective radiation at any one time is generally given to be about 340 W/m².

However, even if this is the case, Earth still retains around 1.4 W/m² (this is the net difference between incoming and outgoing radiation).

I stayed with the 1366 W/m² figure because TSI data is recorded as, well, the Total Solar Irradiance, not the effective solar irradiance. It doesn't affect the outcome.

VP - If we were to input actual TSI figures (including proxy data, obviously) which vary around a mean of 1366 W/m² could we not set our "outward flow" to remain static at 1364.5 W/m² and see what happens?

What the IPCC (and NASA) are saying is that the Earth is currently retaining around 1.4 W/m², but as more CO2 builds up that figure is increasing, as Earth retains a greater proportion of the heat.

I'm suggesting that rather than taking that figure as a mean let's take it as a solid unwavering figure against the average TSI. In this case, Earth would always emit 1364.5 W/m² regardless of the amount put in.

If that makes no sense then I'll try to clarify later. Must have coffee!

:o

CB

I think it means that the input figures for TSI, instead of Top Of Atmosphere figures of ~1366, should be divided by 4 to give the figures of mean irradiation at the earth's surface, as the 1.4W/m² relates to the global surface too, doesn't it?

[Methuselah]

For what it's worth, I have a thought experiment too:

What would happen if instantaneously the input of water was doubled? Or, likewise, the leakage volume was instantaneously halved?

This is started to keep me awake at night now, VP. But it's a damned good heuristic (sp?) IMO! :lol:

[Admiral_Bobski]

I think it means that the input figures for TSI, instead of Top Of Atmosphere figures of ~1366, should be divided by 4 to give the figures of mean irradiation at the earth's surface, as the 1.4W/m² relates to the global surface too, doesn't it?

You're right, of course. I figured it would be easier to just use the raw TSI data, but there's no reason we can't just throw in a division by 4, is there? It shouldn't make a big difference, but it will make a bit of a difference. :lol:

So if we, for now, assume the emissivity of the Earth to be 341.5 W/m² (1366/4) minus the average of 1.4 W/m² then we have a figure of 340.1 W/m².

If we then take the raw TSI data, divide each figure by 4 (giving us a range of between around 340-342.5 W/m², which is a quarter of the TSI range of 1360-1370 W/m²) then we can see what comes out of the LI?

(EDIT - We can tell straight away that any input of more than 340 W/m² is going to lead to an accumulation of heat...hmmm..... I think I'll go and check a few figures out first...!)

Does that sound good to anyone?

:lol:

CB

Edited February 24, 2009 by Captain_Bobski

[grab my graupel]

The discussion seems to be getting a bit personal in here again. Can we try to keep it

friendly in here and leave the personal attacks out of the posts; otherwise, they will be

removed or edited.

Please note the 'code of conduct' before posting in this area

Brian