Saturday, August 22, 2015

More About Generating Hockey Sticks

A little more about generating hockey sticks from the world's history of CO2 emissions....

As Hüsler and Sornette discuss here, the world's CO2 emissions were superexponential, up until around the middle of the 20th century when the population growth rate peaked. Before that, a realistic-looking model for the amount of CO2 in the atmosphere over the last millennia is


where t is time, going from 0 to 1, and C(t) is the atmospheric CO2 concentration at time t. (More on the exponent 2/3rds below.) This means C=1 at the start time t=0, which you can rescale to 280 ppm if you want, but I'll keep the function simple to make the conclusion clearer.

Then the forcing from that CO2 in the atmosphere is



and the change in temperature, which is proportional to the change in forcing, is

   



(I've dropped proportionality constants.) This is simple enough. I've plotted these functions to the right.

Again, I'm not interest in an exact match, only getting a realistic shape for the C(t) curve. (You can rescale everything by adding constants and multiplying constants, if you really want to get a good match to the observed values.)

The curve C(t) is superexponential -- it's increasing faster than an exponential function. The green line is the exponential fit to the C(t) data points using linear regression, and it can't keep up with the C(t) curve.

The brown line is the resulting temperature change -- a hockey stick. It's a straightforward consequence of the world's path on CO2 emissions and the basic physics.

Thus, it would be surprising if any of the paleoclimate studies gave anything other than a hockey stick.

Of course, the real world is messy with natural flucuations and nonlinearities and the like, so a hockey stick isn't guaranteed by the data. But it seems to me a hockey stick is the best, first guess. (I think it was John Wheeler who said you should never start a calculation until you know the answer, and this, plus a good intuition for the actual numbers, is the kind of thing he had in mind. Though few of us are John Wheelers, and this kind of argument shows up for me usually only in retrospect.)

--

In their paper, Hüsler and Sornette construct a very simple economic model that gives this superexponential for atmospheric CO2. They make some basic and plausible assumptions -- about population growth, the labor force, about the amount of capital, and about the progress of technology, and get a set of coupled differential equations they solve. A simple case give the exponent 2/3rds I used above. You can tweak that too, if you want. See their paper for details.

C(t) is no longer increasing superexponentially. It can't do that forever, in a real, finite world -- as Hüsler and Sornette write, such an increase eventually leads to "regime change" -- a fundamental change in an input function like population. Perhaps that's what the peak population growth rate in the 1960s was.

On the other hand, climate feedbacks are coming into play, so the temperature increase is hardly over yet. Really, it's just getting started.

19 comments:

Jim Bouldin said...

"C(t) is no longer increasing superexponentially."

I think it is actually. It's up to about 0.5% per year now, and I know the long term average going back to the early 20th C is a little under 0.4%.

Gordon Fulks said...

David,

You are here mixing overly simplistic theory and manipulated reality. The Global Temperature need not rise with CO2, as you mistakenly call basic physics. And you certainly should not present Michel Mann's Hockey Stick as the ultimate proof, when you know that it has been falsified in many ways and is far from the only or best temperature reconstructions we have. If your simplistic view were correct, why would we need billion dollar Climate Models to project the future? We would not.

Mann replaced his tree ring data after 1900 with NOAA temperature records to make it look like a tremendous upswing and hide the tree ring decline after mid-century. The ice core temperature reconstructions that most scientists prefer show an upturn out of the Little Ice Age beginning about 1830 (long before significant CO2 emissions), and they show the Medieval Warm Period (and earlier warm periods) that you ignore (because they clearly had nothing to do with humans).

Even most climate alarmists agree that your simple minded explanation is far from reality. They know that our climate is driven by more than CO2, notably oceans, sun, and a hydrological cycle. How else can you explain the lack of net warming since the end of the Second World War, when human CO2 emissions took off? The Global Temperature went down for three decades, up for two, and has shown no trend for another two. Our climate today is very much like our climate was during the Dust Bowl of the 1930s, or perhaps a little LESS warm.

Aren't you completely missing the cyclical nature of our climate? And aren't you refusing to give up on Mann, because his Hockey Stick is all you have to support a primitive theory that has clearly failed?

In science, robust empirical data trumps theory every day of the week. You don't get to choose and manipulate the data that you like, just to support your view of the world. Honest data is what separates science from fiction. You should know that!


Gordon J. Fulks, PhD (Physics)
Corbett, Oregon USA

David Appell said...

You are wrong on several points, Gordon.

"The Global Temperature need not rise with CO2, as you mistakenly call basic physics."

Bullshit. There is no doubt that CO2 causes a planet to warm.

"And you certainly should not present Michel Mann's Hockey Stick as the ultimate proof..."

I did not -- I did the opposite, saying basic physics says there should have been hockey stick after the Industrial Revolution, and it's not surprising that so many studies have found such a graph in their reconstruction.

"...when you know that it has been falsified in many ways and is far from the only or best temperature reconstructions we have."

No, it has not. There are dozens of studies that find a hockey stick in paleoclimate data. See my recent post, "36 Hockey Sticks (And Counting)."

David Appell said...

Gordon Fulks wrote:'
"If your simplistic view were correct, why would we need billion dollar Climate Models to project the future?"

The hockey stick isn't a climate model -- this is a very common misconception. It is a reconstruction, and it ends around 1960 due to the so-called divergence problem.

"Mann replaced his tree ring data after 1900 with NOAA temperature records to make it look like a tremendous upswing and hide the tree ring decline after mid-century."

False. Mann et al used the 19th-20th century overlap between proxies and thermometer readings to calibrate the proxies.

It's well known that many proxies -- especially at high latitudes -- stop being good proxies around 1960-70. See

"On the ‘Divergence Problem’ in Northern Forests: A review of the tree-ring evidence and possible causes," Rosanne D'Arrigo et al, Global and Planetary Change
Volume 60, Issues 3–4, February 2008, Pages 289–305.
http://www.sciencedirect.com/science/article/pii/S0921818107000495

David Appell said...

Gordon Fulks wrote:
"The ice core temperature reconstructions that most scientists prefer show an upturn out of the Little Ice Age beginning about 1830 (long before significant CO2 emissions), and they show the Medieval Warm Period (and earlier warm periods) that you ignore (because they clearly had nothing to do with humans)."

Prove it. That means citations and links to papers and data. You have provided none.

"Even most climate alarmists agree that your simple minded explanation is far from reality. They know that our climate is driven by more than CO2, notably oceans, sun, and a hydrological cycle."

CO2 is a forcing. Solar forcing has been very small. THe others are feedbacks. Surprised you don't know the difference.

David Appell said...

Gordon Fulks wrote:
"How else can you explain the lack of net warming since the end of the Second World War, when human CO2 emissions took off?"

This is the kind of bad science you are notorious for -- it indicated a serious lack of knowledge of the data.

GISTEMP shows 0.9 C of warming since 1945.

David Appell said...

Gordon Fulks wrote:
"How else can you explain the lack of net warming since the end of the Second World War, when human CO2 emissions took off?"

This claim is shocking. It shows you have no idea what the data and science says.

No one at all familiar with the data and the science would say there has been a lack of net warming since 1945. No one.

It's just staggering ignorance.

David Appell said...

Gordon Fulks wrote:
"The Global Temperature went down for three decades, up for two, and has shown no trend for another two. Our climate today is very much like our climate was during the Dust Bowl of the 1930s, or perhaps a little LESS warm."

You are wrong on so many things, it's getting tiring to correct you.

It's thought that aerosols (air pollution) lead to a slight cooling from 1945-1975.

Since then there has been much warming -- higher at times, lower at others, due to natural variability. Sometimes NV adds to AGW, and sometimes it subtracts from it.

It is entirely wrong there has been no trend in the last 2 decades. You seem to have entirely missed Karl et al Science (2015).

As a result of Karl et al's closer look at the data, GISTEMP shows +0.29 C of warming over the last 20 years.

David Appell said...

Gordon Fulks wrote:
"Our climate today is very much like our climate was during the Dust Bowl of the 1930s, or perhaps a little LESS warm."

Again, just wrong. GISTEMP shows 0.8 C of warming since 1935.

David Appell said...

"Aren't you completely missing the cyclical nature of our climate?"

What cycles? The PDO, AMO, solar cycles? Everyone knows about them. Ocean and other cycles shift heat around, they don't create heat. The amount of climate variation from the solar cycle is very low, ~ 0.1 K.

David Appell said...

Gordon Fulks wrote:
"And aren't you refusing to give up on Mann, because his Hockey Stick is all you have to support a primitive theory that has clearly failed?"

Unless you start proving your assertions, any future comments won't be allowed here.

Mann et al are right. Dozens of studies also find a hockey stick. As I've shown, it is hardly surprising that they do.

Clearly failed? How??

David Appell said...

Gordon Fulks wrote:
"In science, robust empirical data trumps theory every day of the week. You don't get to choose and manipulate the data that you like, just to support your view of the world. Honest data is what separates science from fiction. You should know that!"

I manipulated nothing. You will have to apologize for that.

Of the two of us, I'm the ONLY ONE presenting empirical data. You have presented none here -- none at all. As is typical.

So don't get all fucking high and mighty about the principles of science, when you are forever resident in their gutter.

David Appell said...

Gordon Fulks:

Your recent comment will not appear here until you prove your assertion that I manipulated data, as you claimed above, or until you withdraw that claim and apologize.

david clark said...

Hi David.
You said "It is a reconstruction, and it ends around 1960 due to the so-called divergence problem. "
ME --- Doesn't the "divergence problem" prove that the proxies that Mann used are not really temperature proxies. IOW, if they failed to match temperature after 1960, why do we think they match temperature before the 1800s?

As to you demanding proof from Gordon, when are you going to provide proof that man's CO2 is causing dangerous global warming?

David Appell said...

"if they failed to match temperature after 1960, why do we think they match temperature before the 1800s?"

Because studies show they do. See the D'Arrigo et al paper I cited above.


David Appell said...

As I've told you several times, Karlock, your second question is ill-posed.

Again, just stay in front of your keyboard and crank up your A/C and you'll be fine. It's the world's poor who will keep dying in heat waves.

david clark said...

ME --- "if they failed to match temperature after 1960, why do we think they match temperature before the 1800s?"

David Appell said---"Because studies show they do. See the D'Arrigo et al paper I cited above."

ME --- Fascinating paper - it lists several possible causes for tree rings being crappy indicators of climate after 1960. ALL OF WHICH COULD HAVE OCCURRED AT ANY TIME IN HISTORY and thus your citation is further evidence that tree rings are worthless along with Mann's hockeystick.

david clark said...

David Appell said... Again, just stay in front of your keyboard and crank up your A/C and you'll be fine. It's the world's poor who will keep dying in heat waves.
ME -- Why don't you care about the thousands of the world's poor who have already died from "climate solutions" (biofuels increasing the cost of food)?
Why don't you mention that the millions who will die from expensive energy and more expensive food?

David Appell said...

david clark:

Who exactly will die from more expensive energy?

But, yes, food will be getting more expensive as droughts (like California's) become longer and deeper, and as higher temperatures continue to decrease crop yields. It's a significant problem.

BTW, dendrochronology is a very interesting subject. You should go read some of it to see how scientists have been able to use tree rings as environmental proxies. Malcolm Hughes has a great book about it.