All about the abuse of anecdotal math to falsify the truth and truthify falsehood.
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
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:
- CO2 is highly correlated to global temperature. Historically, high surface temperature periods have been accompanied by high levels of atmospheric CO2. [TRUE]
- Current CO2 levels are rising above historical highs, almost certainly significantly caused by human over-production of CO2. [TRUE]
- 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!
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.