## Thursday, July 5, 2007

### LIES, DAMNED LIES, AND STATISTICS (Part 3)

All about the abuse of anecdotal math to falsify the truth and truthify falsehood.

This is the third part of my "presentation" on the topic of "Lies, ..." Click for Part 1, and Part 2.

In this part, we'll consider the relationship between correlation and causation.

EXAMPLE #1: Direction of Causation

You've heard the cynic claim:

The more police you see directing traffic, the bigger the traffic
jam!

The implication is: police *cause* the traffic delay. Of course, that's possible, but, more likely, the police were called to the scene because of the traffic delay. The delay was due to some other original cause.

Please consider the three situations depicted on the following chart:

ACCIDENT -- Cars stop or slow down to change lanes and snake around the accident scene. Police and ambulances and tow trucks are called to the scene. The police direct traffic around the accident while the victims are evacuated and the cars are towed away. Traffic resumes its normal pace, and the police leave.

Causation may be summarized as follows: ACCIDENT >CAUSES> Delay >CAUSES> Police.

RUSH HOUR -- Traffic predictably builds up around quitting time when many workers depart for home. Anticipating the traffic delay, police are dispatched to try to keep traffic moving as well as possible. Despite the police presence, traffic overwhems the available lanes and delays build up. Some time later rush hour ends, traffic resumes its normal pace, and the police depart.

No causative relation between the Delay and the Police. Causation is: RUSH HOUR >CAUSES> Police and RUSH HOUR >CAUSES> Delay.

ROADBLOCK -- A criminal has escaped and the Police set up a roadblock to try to catch him. Cars are stopped and searched and that causes Delays in traffic flow. At some point, the Police catch the convict and end the roadblock and traffic resumes.

Causation may be summarized as follows: ROADBLOCK by Police >CAUSES> Delay.

LESSON: Consider the time relationship between factors to determine the direction of causation.

EXAMPLE #2: CORRELATION, CAUSATION and "AN INCONVENIENT TRUTH"

OK, now we understand the time of occurance relationship between correlation and causation! Let's watch a video clip from Former VP Al Gore's infuential movie "An Inconvenient Truth." (If you have not seen the complete movie, I recommend it highly.)

In this video clip, Gore demonstrates the strong historical correlation between atmospheric carbon dioxide (CO2) and Global Warming of the surface of the Earth. He then makes some interesting claims about causation. On the basis of relatively recent and historically high CO2 levels due to human over-production of CO2, he predicts disasterous increases in Global Warming.

[DOUBLE-CLICK ON THE ARROW IN THE MIDDLE TO START THE VIDEO CLIP]

Let us consider the points made by Gore in this video clip:

1. CO2 is highly correlated to global temperature. Historically, high surface temperature periods have been accompanied by high levels of atmospheric CO2. [TRUE]

2. Current CO2 levels are rising above historical highs, almost certainly significantly caused by human over-production of CO2. [TRUE]

3. Therefore, global temperatures will rise way above historical highs within the next fifty years unless humans drastically reduce production of CO2. [AIN'T NECESSARILY SO! Correlation does not necessarily imply causation!]

According to the "Real Climate" website that Stu Denenberg put me onto, which, by the way accepts and strongly supports Gore's Global Warming thesis, the historical ice core record shows that rising CO2 levels come some 800 years after global temperature rises. See full text at: http://www.realclimate.org/index.php/archives/2004/12/co2-in-ice-cores
I have copied the text verbatim and have added emphasis to some key phrases.

At least three careful ice core studies have shown that CO2 starts to rise about 800 years (600-1000 years) after Antarctic temperature during glacial terminations. These terminations are pronounced warming periods that mark the ends of the ice ages that happen every 100,000 years or so.

Does this prove that CO2 doesn't cause global warming? The answer is no.

The reason has to do with the fact that the warmings take about 5000 years to be complete. The lag is only 800 years. All that the lag shows is that CO2 did not cause the first 800 years of warming, out of the 5000 year trend. The other 4200 years of warming could in fact have been caused by CO2, as far as we can tell from this ice core data.

The 4200 years of warming make up about 5/6 of the total warming. So CO2 could have caused the last 5/6 of the warming, but could not have caused the first 1/6 of the warming.

It comes as no surprise that other factors besides CO2 affect climate. Changes in the amount of summer sunshine, due to changes in the Earth's orbit around the sun that happen every 21,000 years, have long been known to affect the comings and goings of ice ages. Atlantic ocean circulation slowdowns are thought to warm Antarctica, also.

From studying all the available data (not just ice cores), the probable sequence of events at a termination goes something like this. Some (currently unknown) process causes Antarctica and the surrounding ocean to warm. This process also causes CO2 to start rising, about 800 years later. Then CO2 further warms the whole planet, because of its heat-trapping properties. This leads to even further CO2 release.

So CO2 during ice ages should be thought of as a "feedback", much like the feedback that results from putting a microphone too near to a loudspeaker.

In other words, CO2 does not initiate the warmings, but acts as an amplifier once they are underway. From model estimates, CO2 (along with other greenhouse gases CH4 and N2O) causes about half of the full glacial-to-interglacial warming.

So, in summary, the lag of CO2 behind temperature doesn't tell us much about global warming. [But it may give us a very interesting clue about why CO2 rises at the ends of ice ages. The 800-year lag is about the amount of time required to flush out the deep ocean through natural ocean currents. So CO2 might be stored in the deep ocean during ice ages, and then get released when the climate warms.]

I accept the factual statements above as true, but some of the reasoning seems a bit tortured to me. Levels of CO2 begin their increase about 800 years after Warming has begun its increase. The ice core data also shows that temperatures decrease a thousand years or more before CO2 begins to decrease. That implies the direction of causation is: SOMETHING ELSE >CAUSES> Warming >CAUSES> CO2 increase and Reduction of SOMETHING ELSE >CAUSES> Cooling >CAUSES> CO2 reduction.

Like the situation described above, where ACCIDENT >Causes> traffic Delay >CAUSES> Police to be dispatched, it appears clear that SOMETHING ELSE causes the Warming and then the Warming causes CO2 levels to rise. That makes sense. If you take an ice cold glass of soda and leave it at room temperature for an hour, the CO2 bubbles out as the soda warms. Similarly, but on a global scale, CO2 is disolved in the oceans and, as the Earth surface warms, more of the CO2 comes out into the atmosphere. When that SOMETHING ELSE gets reduced, Cooling causes CO2 levels to drop as more of the CO2 gas is re-absorbed into the oceans.

What might that SOMETHING ELSE be that causes Warming when present and Cooling when it goes away? It's the SOLAR RADIATION FROM THE SUN stupid!

Reread the fifth paragraph of the above quote. They say the Earth's orbit around the Sun varies on a cycle of 21,000 years and that is known to affect the comings and goings of ice ages. Right on!

But it is more complicated. According to http://www.homepage.montana.edu/~geol445/hyperglac/time1/milankov.htm there are three major cyclic components that affect the Earth's orbit around the Sun: (1) Eccentricity of ~100,000 years, (2) Axial Tilt of ~41,000 years, and (3) Precession (or "wobble") of ~23,000 years. These components do not affect the total amount of solar radiation reaching the Earth, but rather energy distribution between the polar and equatorial areas and seasonality. That, in turn, affects the build up and melting of polar ice. Based on the ice core data, the combination of these cycles triggers cooling and warming periods.

Energy radiation from the Sun varies on several cycles, the best known of which is called the "Sun spot cycle" and happens every eleven years. There are longer cycles of variability that extend to centuries and millenia.

Therefore, when the orbital and solar radiation cycles happen to coincide, which may occur around every 100,000 years, a Global Warming cycle is initiated. The Warming causes more CO2 to be driven out of the oceans and, over an 800 year period, CO2 levels rise and stay high until the solar radiation high point passes. At that point, Cooling begins and, a thousand years or more later, CO2 levels decrease as the more of the CO2 gas is again absorbed into the cooler oceans.

Reread paragraph eight of the above quote. They clearly say that "CO2 does not initiate the warmings, but acts as an amplifier once they are underway."

They are partially correct. Yes, like the ROADBLOCK situation, where Police >CAUSE> Delay, it is also possible for CO2 to cause (more) Warming when it gets into the atmosphere and acts as a greenhouse gas. However, since the ice core data show sustained high levels of CO2 for a thousand or more years after Cooling starts, it is clear the CO2 levels do not cause the Cooling either.

Therefore, the ice core data show the relationship between global temperatures and CO2 levels are more like the ACCIDENT scenario than the ROADBLOCK scenario. In their third paragraph, the "Real Climate" writers make much of the fact the 800 year delay is only a sixth of the 5000-year cycle. So, they say, during the other 4200 years CO2 could be the cause of the Warming. Well, if you look at the ACCIDENT scenario, the lag between the traffic Delay and the arrival of the Police is also much shorter than the total time it takes for the ambulances and tow trucks to evacuate the victims and clear the wrecks, but that still does not mean the Police are the cause of the Delay!

CONCLUSIONS

1) GLOBAL WARMING IS A REAL PROBLEM -- Am I claiming that Global Warming is not a problem? No, that is not my claim at all. I believe we are in a definite Global Warming cycle.

2) GLOBAL WARMING IS PARTLY DUE TO HUMAN-PRODUCED CO2 -- A significant amount of atmospheric CO2 and therefore greenhouse warming is caused by the historically unprecedented production of CO2 due to human civilization. That part of the equation is under human control and we may be able to do something about it with concerted action (but don't hold your breath waiting for that action, see item (6) below).

3) BUT, THE MAIN CAUSE IS THE SUN, STUPID! -- I believe the main cause of the current Global Warming cycle, as of all previous cycles according to the ice core data, is increased solar radiation and the distribution of the solar energy falling on the Earth, due to a combination of orbital cycles and Sun spot and other solar cycles. That part of the equation is out of our control.

4) GORE'S MOVIE HAS SOME MAJOR PROBLEMS -- My problem with the Gore movie is his implication that the ice core data, per se, is applicable to our current situation. As careful reading of the pro-Gore (but still honest :^) "Real Climate" website postings reveal, that is not true. Our current situation is totally unprecedented because human civilization, until the past few hundred years, has not been capable of producing enough greenhouse gas to be significant on the scale of solar radiation.

5) "POLITICAL CORRECTNESS" HAS AFFECTED SCIENTISTS -- The above "Real Climate" website quote was composed and posted a few years ago, before Gore's movie came out. That website has a more recent posting regarding the lag of CO2 behind temperature. While, to their credit, they still link to their older posting quoted above, and they are a bit critical of some of Gore's statements, the new posting shows signs of "political correctness" when it comes to Global Warming.

You can read their new posting by clicking here: http://www.realclimate.org/index.php/archives/2007/04/the-lag-between-temp-and-co2/

The headline says: "The lag between temperature and CO2. (Gore’s got it right.)" That is an indication they are on Gore's side.

However, to their credit, they also say the following about what Gore did and did not do in the video clip you just watched:

What Gore should have done is extrapolated the temperature curve according this the appropriate scaling -- with CO2 accounting for about 1/3 of the total change -- instead of letting the audience do it by eye. Had he done so, he would have drawn a line that went up only 1/3 of the distance implied by the simple correlation with CO2 shown by the ice core record.

The quoted paragraph is a complicated way of saying, correctly in my opinion, that Gore led his unsophisticated audience to believe Global Warming due to human-produced CO2 was about three times worse than the available scientific estimates justify.

6) WHAT PRACTICAL THINGS CAN WE DO ABOUT GLOBAL WARMING? -- Not a heck of a lot! The portion of Global Warming due to Human overproduction of CO2 is almost certainly below 50% and more likely less than 20%. Thus, even if we could cut global CO2 production in half, we might reduce the temperature increase by 25% at best. More likely, a 50% cut in global CO2 production would yield less than a 10% reduction in Global Warming. So, if the projected increase in average global temperature over the 50 to 100 years is 2.0 degrees, we could cut it down to "only" 1.5 to 1.8 degrees.

Theoretically we could cut CO2 production in half, but I strongly doubt we will. My wife and I share one car, a hybrid gas-electric Prius. We get actual 45-55 MPG, which is about double the gas mileage for the average car, implying a 50% cut in emissions. To achieve 55 MPG, I have to drive extraordinarily carefully, with slow accellerations and extreme anticipation of traffic light changes to avoid most braking. My antics are probably driving other motorists crazy. Also, much of our gasoline savings were cancelled out by the initial higher cost of the Prius compared to similar standard cars as well as the costs we face when the batteries wear out or the fancy gas-saving electronics fail. My wife and I use our electric golf cart for much of our local travel and I also use my bicycle for 40-50 miles per week. We have the luxury of doing all this because we are retired. How many Americans and others living in industrialized countries will follow our example? Not many!

Even as gasoline prices hit \$3 and even \$4 in some places, we Americans increased our usage! That is an indication "we have money to burn" and gasoline prices are too low rather than too high. I favor a punitive "carbon" tax on non-renewable energy. It would start at \$1 per gallon of gasoline (or the equivalent in coal energy, etc.) and go up \$1 per year until usage levels began to decline. I think it will take a \$10/gallon increase, so that will give Americans ten years to adjust their usage patterns. John Kerry proposed such a tax a decade ago but had to abandon it because it has no political traction whatsoever. What are the chances the "carbon" tax will get passed in our lifetime? You are correct, the changes are about ten degrees below absolute zero. Tis a pity!

China and India and other formerly less-developed countries have modernized their economic systems and will soon be consuming energy at levels rivaling our own. They will not stop their industrialization.

7) EVEN THE "GOOD NEWS" IS BAD! -- Is there any way we might see a reduction of 50% in human-generated CO2? Well, globalization might help put social pressures on excessive human breeding. Reproduction is below replacement rates in some industrialized countries. Population growth in those countries is mainly due to immigration. As the social effects of globalization spread to more and more countries, worldwide reproduction may fall to below replacement levels. Over time, we might reach a 50% reduction in population. But, would that translate into 50% less CO2 or would the people just ramp up their use of energy? What do you think?

A major genetic engineering disaster that killed a billion people would result in a rapid population drop. Or, even worse, a localized nuclear war would not only rapidly reduce population, but also cause a mini "nuclear winter" as high-altitude debris from the nuclear explosions reduced the transparency of the atmosphere to incoming solar radiation. I don't think any of us would wish for these types of disasters.

Those of us who look favorably on the "Gaia Hypothesis" that the Earth has some sort of Global Consciousness might be comforted by the thought that Global Warming is "Gaia's plan" to warm the Earth in preparation for the coming chill of "nuclear winter." As nuclear weapons spread to more and more countries and terrorist groups, nuclear war seems all-but-inevitable. Ah, how I wish I could muster a higher level of religious belief!

LESSON: Situations change and statistics that correctly described the past may not apply to the present.

Ira Glickstein

The above is the third part of my "presentation" on the topic of "Lies, ..." Click for Part 1, Part 2, and Part 4.

Ira Glickstein said...

According to yesterday's New York Times, "Counting on Failure, Energy Chairman Floats Carbon Tax". http://www.nytimes.com/2007/07/07/washington/07carbon.html?ei=5090&en=2360b6693500bdb8&ex=1341460800&partner=rssuserland&emc=rss&pagewanted=print

As I noted in the Topic that started this thread, I favor a steep tax as the best way to tame energy usage and human-produced CO2, but I doubt it will ever become law. I've reproduced the complete text of the NYTimes story. Here is why a carbon tax has no political traction at all:

**********************
July 7, 2007
Counting on Failure, Energy Chairman Floats Carbon Tax
By EDMUND L. ANDREWS
WASHINGTON, July 6 — A powerful House Democrat said on Friday that he planned to propose a steep new “carbon tax” that would raise the cost of burning oil, gas and coal, in a move that could shake up the political debate on global warming.

The proposal came from Representative John D. Dingell of Michigan, chairman of the House Energy and Commerce Committee, and it runs directly counter to the view of most Democrats that any tax on energy would be a politically disastrous approach to slowing global warming.

But Mr. Dingell, in an interview to be broadcast Sunday on C-Span, suggested that his goal was to show that Americans are not willing to face the real cost of reducing carbon dioxide emissions. His message appeared to be that Democratic leaders were setting unrealistic legislative goals.

“I sincerely doubt that the American people will be willing to pay what this is really going to cost them,” said Mr. Dingell, whose committee will be drafting a broad bill on climate change this fall.

“I will be introducing in the next little bit a carbon tax bill, just to sort of see how people think about this,” he continued. “When you see the criticism I get, I think you’ll see the answer to your question.”

The idea behind a carbon tax is to provide an incentive to reduce the use of fossil fuels like oil and coal, which are loaded with carbon, and increase the use of cleaner, renewable fuels like solar power, wind and fuels made from plants and plant waste.

Many economists like the idea of a carbon tax, saying that it would be simple to administer and could profoundly affect energy choices.

But most Democrats are staunchly opposed, saying that a tax would raise the costs of travel, commuting and heating and cooling homes, and that it would be wildly unpopular at a time when voters are already angry about high energy costs. Republicans, they said, would seize on any such proposal as proof that Democrats were bent on raising taxes and increasing the size of government.

Indeed, many Democrats still cringe at the memory of President Bill Clinton’s trying to pass a broad “B.T.U. tax” in 1993 on most forms of energy. The measure passed the House but not the Senate, and more than a few Democrats believe the effort was one reason they lost their majority in the House in 1994.

Now, House and Senate Democrats are writing bills that would require factories and power plants to reduce emissions of heat-trapping gases through a so-called cap-and-trade system of mandatory requirements and tradeable pollution credits.

Most of the proposals would impose mandatory limits on the amount of carbon dioxide that companies would be allowed to produce each year, and those limits would become steadily more rigorous over time. A factory or a power plant that is already below the limit could sell its unused allocations to companies that were over the limit.

The United States already uses a cap-and-trade system to limit emissions of sulfur dioxide and other pollutants that cause acid rain.

The European Union has adopted a system to reduce greenhouse gas emissions, though the system has come under considerable criticism for letting companies game the rules and for failing to reduce emissions in line with European goals.

Kendrick said...

Regarding the statement, "Correlation does not necessarily imply causation," I prefer to state it as: Correlation is a necessary, but not sufficient condition for causality. It sounds picky, but the word "imply" is overloaded -- it has a common English meaning and it has a formal logical meaning (defined by a truth table) and we definitely don't need any more ambiguity between the relationship between correlation and causation :)

Great points throughout though, especially on global change. When I watched An Inconvenient Truth, I thought of the same thing while Gore was showing the "hockey stick" chart with CO2 and temperature. CO2 and temperature are obviously related, but not necessarily through a cause-and-effect relationship.

I think this is another case where systems thinking hasn't quite made it to the general public yet. Instead of thinking about CO2 and temperature, one has to think of the atmosphere a complex system (really, a subsystem of the Earth) that is full of interacting variables. Establishing the relationship between two variables in the system is merely a hint of what really is happening in the system.

I agree with you though, although Gore's presentation was somewhat flawed, the true science behind what he was trying to convey is pretty valid. Beyond that, I think Gore is trying to bring attention to the scope of the problem, and call people to take action.

A few years ago, I watched a lecture by Gene Takle, a professor of meteorology at Iowa State University. He made an interesting point that I hadn't heard before. Regardless of the exact causes, assume the correlation between CO2 and temperature will hold. Because of the 50+ year lag in the correlation of CO2 and temperature, even if we stop 100% of CO2 production today (which is impossible because CO2 production is a part of nature), the next 50+ years will be very rough for us (and all the species on Earth) and the only strategy we have at the moment is adaptation. Plus, the effects of any mitigation strategy we take today won't be visible for another 50+ years. We've done the damage and the next generation has to live with it. However, that does not mean that we shouldn't keep trying to resolve the problem for subsequent generations.

It sounds scary, but I sometimes worry about human existence. I know I will live my lifespan out, but I'm not so sure about the people after me. Humans are resourceful, we can build things to help us adjust to temperature. However, we depend heavily on the other life in our biosphere to live and evolutionary change is an extremely slow process in the range of thousands of years. If the climate isn't suitable to raise livestock or grow crops, major famine will result. If resources grow thin, we will return to more primal battles for resources (and your nuclear scenario becomes more likely). The issue really goes beyond just the climate (which is why I refer to it as global change). Earth is one big interrelated system -- if the climate changes, the changes aren't isolated to the atmosphere, we'll see effects in other places we have yet to realize. However, I am glad that sustainability is now an important theme in life and in design -- it just makes more intuitive sense from a systems perspective too. If we want the system to work, we have to study the things we are taking out of it and putting back into it and not just assume that the system is large enough to handle "small" changes -- I think we all realize that the human footprint is nothing but small.

Finally, as for developing countries that are just beginning their energy consumption era, my recent travels abroad showed me that people in developing Asia really emulate American culture (our strongest export). I feel that if we can set a good example and make sustainability a fashionable lifestyle, the world will follow. Despite the recent focus on consumerism in our culture, everybody wants a nice place to live for themselves and their families -- and from what I've seen in Asia, they are on the brink of realizing that too as their cities and citizens are suffocating in pollution and heat.

Ira Glickstein said...

Kendrick:

Great to "see" you again (Kendrick is a former System Engineering student in the online course I teach at the University of Maryland -- we've never met in person.)

Excellent Comment. You added a new element to the possible response to Global Warming and that is adaptation.

If temperatures rise as much as predicted, low-lying, highly populated portions of the Earth's surface will become uninhabitable. We need to rethink how we've handled flooding in the past. Floodwalls and dams are not the correct answer!

For example, when another city like New Orleans gets flooded, I think governments at all levels have an obligation to rescue those affected and feed and house them until they can get back on their feet. Of course they should also receive insurance payments for the value of what they lost. However, I think it is wrong to rebuild in areas that are below high water level. Those areas should be made into parks and golf courses and, if environmentally acceptable, used for agriculture.

If someone wants to rebuild in such an area it should be on the condition that governments have no obligation to rescue them again. That seems hard-hearted, but we need to adjust our perceptions to prepare for future flooding.

A friend of mine wrote "Mississippi Father of Waters" (Norah Deakin Davis, 1982, available used on Amazon). She makes the point that floodwalls that protect local areas also serve to channel the waters downstream where they do more damage. We need to step back and let Mother Nature have her way (and, regardless of what we do, she will, in the end :^)

We need to adapt to the new climate realities "voluntarily" and with planing and thought -or- we will be dragged into compliance against our wills with much loss of life and property.

Ira Glickstein

Stu Denenberg said...

http://uk.reuters.com/article/scienceNews/idUKL101501320070710?pageNumber=2

the above link is entitled: " Solar variations not behind global warming: study". What do you think?

Stu

Ira Glickstein said...

My Dear Friend Stu:

A couple days after I posted the Topic that said "It's the SUN, STUPID" you post the news report saying: "Solar variations not behind global warming ..."!

Trying to embarrass me? :^)

OOPS! Did I get it wrong?

Sorry, I did not get it wrong!

The recent news report is about the eleven-year Sun-spot cycle apparently having little or no effect on the steady increase in surface temperature over the past twenty years.

My "Its the Sun stupid" claim is about much longer-term variations in the Earth's orbit around the Sun. I wrote: "These components do not affect the total amount of solar radiation reaching the Earth, but rather energy distribution between the polar and equatorial areas and seasonality."

Thus, I am not claiming these changes in the Sun's energy striking the Earth are due to changes in total amount of radiation, but rather how much of that radiation falls on the polar regions vs the equatorial regions.

Here is the full paragraph I wrote:

******************************
But it is more complicated. According to http://www.homepage.montana.edu/~geol445/hyperglac/time1/milankov.htm there are three major cyclic components that affect the Earth's orbit around the Sun: (1) Eccentricity of ~100,000 years, (2) Axial Tilt of ~41,000 years, and (3) Precession (or "wobble") of ~23,000 years. These components do not affect the total amount of solar radiation reaching the Earth, but rather energy distribution between the polar and equatorial areas and seasonality. That, in turn, affects the build up and melting of polar ice. Based on the ice core data, the combination of these cycles triggers cooling and warming periods.
*******************************

So, I am not claiming the cyclic changes in the Earth's orbit around the Sun change the total amount of solar radiation on the total Earth. However, as the source I link to says, the *distribution* of that Sun energy does change on the ~100,000, ~41,000, and ~23,000 year cycles.

If the energy is concentrated in the equatorial regions (vs being shifted to the polar regions) that affects the rate of build up or melting of the polar ice caps, and also affects ocean currents critical to the balance of temperatures on the Earth.

As you know, the axis of the Earth tilts around 23 degrees with respect to the plane of our orbit around the Sun. As a result, the north polar region and northern hemisphere get relatively more solar energy during our summer and relatively less solar energy during our winter than do the south polar region and southern hemisphere. That is why we have seasonality, see: http://en.wikipedia.org/wiki/Axial_tilt.

That tilt slowly changes on a cycle of around 41,000 years. If the tilt were to change to zero degrees, there would be no seasons. However, that is not the case! It only changes about 2.4 degrees, so the change in seasonality is slight, but still significant in terms of melting and build up of polar ice and the strength of ocean currents.

The other components of the long-term changes in the Earth's orbit are more difficult to picture, but, taken together, they seem to match up with the comings and goings of ice ages in the ice core data.

"Real Climate" website says the following which I also quoted verbatim in my posting:

*********************************
It comes as no surprise that other factors besides CO2 affect climate. Changes in the amount of summer sunshine, due to changes in the Earth's orbit around the sun that happen every 21,000 years, have long been known to affect the comings and goings of ice ages. Atlantic ocean circulation slowdowns are thought to warm Antarctica, also.

*********************************

"Real Climate" says 21,000 years and the other reference says 23,000 years but they are both talking about the precession. That, plus the 100,000 and 41,000 year orbital cycles could, together, have the effects indicated in the "Real Climate" material where they say "...known to affect the comings and goings of ice ages."

The eleven-year Sun spot cycle does affect the total amount of solar radiation striking the Earth, but on such a short cycle it probably has no direct impact on the 800 year lag of CO2 behind average surface temperature. On the other hand, Sun-spot peaks and valleys may be the trigger that, taken together with the much longer cycles, flips us over the "tipping point" into a Global Warming cycle around every 100,000 years or so.

To get an idea of the "tipping point" concept, imagine a ship anchored in a harbor. Due to an approaching storm, the crew has been evacuated. The rough seas and strong, gusting winds cause the ship to pitch and roll. Oops, it is rolling perilously close to the point at which it may tip over onto its starboard side! What is this? The third mate was sleeping in his bunk and missed the evacuation order. Just as the ship is about to tip over (or not) he awakes, and sneezes! If he sneezes to port, the ship will tip over and sink. If he sneezes to starboard, the ship will right itself. You might say he is the "cause" of the ship being lost (or not). Of course, the real cause is the storm and resultant waves and wind. However, his sneeze could be the trigger.

The item released yesterday that you have pointed me to is simply saying the eleven-year Sun spot cycle is not at a high right now and it has gone up and down, as it always does, on that eleven year cycle, yet surface temperature has steadily increased during the past twenty years. So, they are rejecting a claim I never made!

To repeat my claims: (1) We are in a definite Global Warming trend now, (2) Human production of CO2, at levels unprecedented prior to the past hundred years or so, have a significant effect on that warming cycle (perhaps 20-50%) BUT (3) Other long-cycle (thousands of years) effects, such as the three orbital variations and Solar cycles of tens of thousands of years, are responsible for the remainder of the current warming cycle. The sum of all these cycles, plus human CO2 production, may tip us into another of those 100,000 year major Global Warming cycles (or not).

Ira Glickstein