Climate Modeling using a Leaky Integrator

[Admiral_Bobski]

I've been a bit dim, haven't I?! I'm starting to see where I've been going wrong with this "just plug in those figures" stuff...

Oopsie. There's a moral to this story: when you're up to your neck in stuff, never try to apply yourself to something else that's any more basic than shoelace-tying!!

I'll be back later...

CB

[VillagePlank]

I'm going to leave this for a week.

FYI I posted some stuff that was particularly rude, and I am lucky not to be banned. If you need direction into how the leaky integrator works in the real world, look into Plancks law, and go pre Lorentz, and use Maxwell's equations.

Back in a week.

[Admiral_Bobski]

I'm going to leave this for a week.

FYI I posted some stuff that was particularly rude, and I am lucky not to be banned. If you need direction into how the leaky integrator works in the real world, look into Plancks law, and go pre Lorentz, and use Maxwell's equations.

Back in a week.

Well, you've given us all plenty of food for thought. I know that I'm going to be doing a lot of mulling and fiddling with the LI over the next week. Perhaps we'll have something interesting for you when you get back!

Looking forward to your input when you return

Take it easy,

CB

[VillagePlank]

Week's up.

Any more thoughts, anyone, before I push on further with this stuff?

Next two steps are big(ish) ones .... so thinking hats on please

[Admiral_Bobski]

Week's up.

Any more thoughts, anyone, before I push on further with this stuff?

Next two steps are big(ish) ones .... so thinking hats on please

I've been playing around with some data in the LI this week, but I haven't been able to put in as much work on it as I'd hoped

I haven't any questions or problems so far, so by all means, continue with your next big steps

CB

[pottyprof]

Bump - Just to bring this back to the top area of the forum

[VillagePlank]

OK, then.

Let's move (slightly) from the abtract to the concrete. Where I have made an assumption I will highlight it in bold.

Here's the first assumption: there is some relation between sunspot count and the temperature observed on Earth such that if the sunspot count increases at some point in the future as a causal effect, the temperature of the Earth will increase

So, on that assumption, let's add some sunspot figures .... I can't for the life of me remember where I got this file from (so if any one knows where this file originates, please can you mark it here)

sunspots.txt

We are talking about climate, so I've averaged the monthly means into annual means by uploading the raw data into a database engine, and querying to retrieve the average:

select [Year],
		(
			cast(jan as real) +
			cast(feb as real) +
			cast(mar as real) +
			cast(apr as real) +
			cast(may as real) +
			cast(june as real) +
			cast(july as real) +
			cast(aug as real) +
			cast(sep as real) +
			cast(oct as real) +
			cast(nov as real) +
			cast(dec as real)
		) /12.0
from _sunspots where [year]<2008

(I know that SQL has an AVG function - before anyone points it out) Note I am omitting data before 2008 because 2008 has a missing month. Here's the result:

avsunspots.txt

We can, now, add this data into our LI. You need to extend the previous exercise by some 260 rows. You can change the t element to now represent the year, and you can change the i element to the average sunspot count for the year. Here's what my one looked like ...

And, of course, you can draw a chart of the result ...

[VillagePlank]

Fortunately, thanks to Chris Knight, we can also add some volcanic forcing to this model. (the data is on post 26)

Here's what the datasheet looks like on mine once I've added the data:

A couple of points worth noting.

• v is the raw volcanic data, and v' is v multiplied by some constant (in this sheet the constant appear below the v' header
  
• Previous incarnations have opted for a starting height of zero. I've chosen about half of the initial value, which seems reasonable, to start the height off - appears under the header h
  

And, of course, you're going to want to see the chart ...

Feel free to play with the constants i, and o, the starting point of h, and the volcano modifier that gives v'

:lol:

And just for illustration ...

Using the above data if you chart (h-40)/5 instead of h directly, and you put a 4th order polynomial on top of it 'to help the eye' then the chart looks like this ...

[VillagePlank]

If anyone has access to more modern data (post 1995) particularly volcanic forcing, can you post a link, please.

[VillagePlank]

Here's the chart if you use the sunspot count up until end 2007 (but don't put any volcanic forcing in post 1995)

It appears to me that there is some sort of linear latency (of about four years) Does anyone know of any effect where as energy implied by the sunspot count takes 4 years to affect the earth?

[VillagePlank]

I've think I've made a mistake, guys.

I added volcanic forcing by taking v' from previous h. Effectively, saying, that the greater the forcing from volcanic activity the less the effect of more temperature in the system.

I'm going to have to think about that one, because, to my eyes, the graph looks OK, but I don't think that that effect is the accepted effect of volcanic activity.

Hrumph.

[Chris Knight]

Here's the chart if you use the sunspot count up until end 2007 (but don't put any volcanic forcing in post 1995)

It appears to me that there is some sort of linear latency (of about four years) Does anyone know of any effect where as energy implied by the sunspot count takes 4 years to affect the earth?

What about the change in the earth's angular momentum, equivalent to -Δlength of day? This is made up of effects of mountain torque (winds), changes of distribution of mass - ocean, cryosphere, atmosphere and lithosphere, and lunisolar precessional torque (effects of tides from all bodies in the solar system). The figure of a mean change of 2 thousandths of a second a day per year doesn't sound a lot, but it does mean we gain a (leap) second about every 500 days, and the earth has a lot of angular momentum in total.

This equates to the effects of all the heat that does not go into radiation out to space, apart from that stored say in the oceans, either as heat, or as change in total global biomass. It can be thought of as heat transduced to kinetic energy, stored as potential mechanical energy. It can be released as heat through friction by the tides in both shallow and deep oceans. Now whether the actual heat amounts are significant is doubtful, but the associated changes (i.e. oscillations) in ocean currents, upwelling and winds are certainly becoming more important, the more is known about them.

On the graph below, a negative slope represents a slowing down, a positive slope represents an increase in angular momentum. Negative represents more friction, positive less, I think. Effects would certainly represent a latent period between energy input and output. Omega is in prads/s.

There is some interest in the role of the earths angular momentum as a climate forcing/feedback, by the Russians, particularly Nikolay Sidorenkov, who has a book out soon, and Leonid Klyashtorin, an oceanographer.

The data above can be found at IERS (International Earth Rotation Service) or here:

LODomega.txt

[SleepyJean]

This is an interesting thread, some actual science in action. Cool. It is really good that you are going through from a basic principal and trying to figure out how everything fits in and just seeing where it takes you, whether it proves AGW or disproves it. That is a great way to do things.

I think I understand the basic principle. It's a bit like a storage heater, with it's input knob and output knob. You can adjust both the input and the output and have different results in terms of how warm your living room is. So the solar activity is the input (as that is the only place we get energy into the system from) and the other variables like volcanic activity and co2 etc effect the output (how warm the living room actually feels).

As to your question,"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? "

Thinking back to science lessons at school, I remember measuring the temperature of a beaker of water at one minute intervals from boiling point. The heat loss, as far as I can recall, was faster at first then slowed down. So the answer to (ii) is definitely yes. I can't specifically remember an equivalent experiment for (i) but my hind-brain is telling me that this too is true (I have one of those brains that retains information without necessarily reminding itself of where the info came from). So I am with you so far, I think.

Sorry to go over the basics again, I have just read the whole thread (skipping the parts with silly squabbles) and just wanted to make sure I had it. As a fence-sitter, this is going to be fascinating.

SJ

[VillagePlank]

Keeping with the (faulty?) volcanic stuff, I decided to do a correlation test (pearson) The result 0.823 - I'm not sure how to interpret this - anyone? I presume it means it correlates reasonably well. Although, I'm sure that such a test depends on the type of variable in question.

Here's the chart with the Hadley observed series overlaid after messing around with some of the mutlipliers, constants, and scale variables ...

Here's the data series:

[VillagePlank]

Two questions:

• What happened (or didn't happen) between c.1910 and c.1950 to cause the Hadley series to have that big jump
  
• Is the method of including volcanic forcings acceptable (is serendipitdy playing a hand here - for instance do volcanoes push out huge amount of GHGs that increase the climate forcing, even though the weather forcing is undeniably negative?)
  

Any help gratefully received ....

[VillagePlank]

What about the change in the earth's angular momentum, equivalent to -Δlength of day?

[snip]

I would say that, perhaps, this might be (part of) a mechanism that demonstrates the LI's ability to 'hold on' to energy rather than radiating it back to space instantly.

[Chris Knight]

Two questions:

What happened (or didn't happen) between c.1910 and c.1950 to cause the Hadley series to have that big jump

Is the method of including volcanic forcings acceptable

Any help gratefully received ....

Those naughty Germans, twice.

A great depression.

A greater dependence on oil (petrol and diesel) for transport, on Land and Sea, with a lot of methane and petrochemical gases (mostly potent GGS) released (remember "gushers") as oilfields were found and oilwells were drilled.

Increase in population leading to increase of requirement for irrigation in drought stricken corn belts.

Increase in black carbon pollution in populated centres, increase in urbanization.

The rise of Communism.

Aviation.

Reduction in dependence on animals for transport and agricultural energy.

1950s reduced dependence on coal for domestic heating as the realisation of the danger of atmospheric pollution led to various clean air acts. Electrification of former gas lighting - streets, domestic.

[Thundery wintry showers]

0.823 is quite a high correlation coefficient but its statistical significance depends on the number of values that are being correlated. It is interesting that the volcanic component shows no relationship at all with the warming of the 1910-1940 period but a significant correlation arises post-1950.

[VillagePlank]

Those naughty Germans, twice.

The war years would have (did have?) meant a huge rise in manufacturing output ...... good call Chris!

0.823 is quite a high correlation coefficient but its statistical significance depends on the number of values that are being correlated. It is interesting that the volcanic component shows no relationship at all with the warming of the 1910-1940 period but a significant correlation arises post-1950.

Yup - I am looking at the chi significance test, now, and will post it once I understand what it means etc etc etc. And, of course, all of the normal warnings about correlation ....

[Chris Knight]

Two questions:

• What happened (or didn't happen) between c.1910 and c.1950 to cause the Hadley series to have that big jump
  
• Is the method of including volcanic forcings acceptable (is serendipitdy playing a hand here - for instance do volcanoes push out huge amount of GHGs that increase the climate forcing, even though the weather forcing is undeniably negative?)
  

Any help gratefully received ....

It could just be the volcano data from Mann et al 1998 (remember who this Mann is!). It is also possible that the degree of activity was underestimated.

It may not mean that the early half of the 20th century was unusually short of volcanic forcing as the graph of the data below indicates, it may be for various socioeconomic reasons, attention was directed elsewhere, and volcanoes went unreported. If real, that period was distinctly unusual. Not one southern hemisphere eruption below the tropics was recorded.

However, there were a few eruptions from the period which left (SO2) traces in the polar ice:

Ksudach, Kamchatka, Russia NH 1907

Novarupta-Katmai, Alaska NH 1912

Agrigan, Marianas USA(?) T 1917

Kelut, Indonesia T 1919

Cerro Azul (Quizapu), Ecuador T 1932

Rabaul, Indonesia (?) T 1937

Hekla, Iceland NH 1947

Bezymianny, Kamchatka NH 1956

(?) NH 1960

VP, If the LI algorithm is doing what it should, if there are volcanoes it should depress the slope, if there is no volcanic activity over a period of time, then perhaps the clarity of the atmosphere would act as a positive forcing, and therefore should increase the slope.

[VillagePlank]

VP, If the LI algorithm is doing what it should, if there are volcanoes it should depress the slope, if there is no volcanic activity over a period of time, then perhaps the clarity of the atmosphere would act as a positive forcing, and therefore should increase the slope.

The algorithm's fine; it's my use of it that's wonky! I'll amend and repost charts, later.

[VillagePlank]

Here's the chart with volcanism properly put in (it's deducted at the of the dh/dt sum) I've played around with constants, scales, and factors again, so I've included the data sheet.

Pearson score is down to 0.779

The period 1918-1950 is the tricky piece.

If you close the 'leak' to half between 1918 and 1945, and then open the leak to four times the amount between 1946 and 1950, this is what the chart looks like (so change l to 0.5, and then subsequently change l to 4)

I'm the first one to admit that the data has been 'hand-carved' in (so this chart is more than suspect ), but such a little change to move the Pearson score to 0.877 seems to mean, to me, that something happened during that time that affected our climate signifcantly and it weren't volcanoes nor sunspots.

[Red Raven]

Were the dust storms in the US in the 30's large enough to have any effect? Did other areas of the world suffer greater drought that caused an increase in particulate release. Deforestation and fires could have the same effect - maybe.

[Admiral_Bobski]

Hi VP!

Nice to see you and this thread back online

Just a thought - 1975-2005 (ish) has been El Nino dominated. 1945-175 (ish) was La Nina dominated. 1915-1945 (ish) was El Nino dominated.

So can we pop in some ENSO data and see if that jiggles the line around to make it fit better?

:o

CB

[Thundery wintry showers]

Another question:

The leaky integrator graph shows a sharp rise shortly after 1950, while the Hadley record shows a steady rise over the last 30 years, this results in a large area of differential between around 1950 and 1975.

Any ideas as to the reasons for this? I note with interest that the problem is largely nullified by tampering with the "leak" in the leaky integrator.