I've taken some shots at Australian climate skeptic David Evans in a previous diary about one of his odd theories. But I do have to give Evans his props in one regard: unlike some others in the skeptic community, he has the guts to put his money where his mouth is. Evans is darn sure that the IPCC is wrong about how hot it's going to get, and he has laid a series of bets with Brian Schmidt, who blogs under the nom-de-net Eli Rabett (caution: bunny puns fill the Rabett's blog), on the five-year average GISS global surface temperature in the years 2019, 2024, and 2029.
What Evans apparently doesn't realize is that because of the thermal inertia of the oceans, within narrow bounds we can already predict what global temperatures will be in 2019, 2024, and 2029. And David Evans is going to lose his shirt.
Terms of the wager
As explained here, The Rabett is betting that global surface temperatures will rise at .17°C per decade (or faster) from 2005, while Evans is betting that the rise will be .13°C per decade or less. If the actual rise falls between .17 and .13, it's a push. The bet will be evaluated on five year averages, which should prevent any unusual volcanic activity or El Niño events from skewing things too much. This primary bet is for $1000 payable when GISS annual temperatures are published for the years 2019, 2024, and 2029.
In addition, Evans is taking 2-to-1 odds wagers that the rate of temperature will be .09°C per decade or less, while the Rabett is giving 2-to-1 that warming will be .11°C or greater. These bets are a push if it falls between .09 and .11°C per decade. If Evans wins one of these bets, Schmidt pays $2000, while Evans pays only $1000 if he loses. These three odds bets are also evaluated in the same three years under the same terms. Thus for all six bets, Evans is risking $6000 while the Rabett is risking $9000.
In summary, if the rate of rise is .17°C per decade or more, Schmidt wins both bets for $2000; if the rate falls between .17 and .13, Schmidt wins one bet and the other is a push, for a net of $1000; if the rate is between .13 and .11, each man wins one and loses one, no money changes hands; if the rate is between .11 and .09, Evans wins one bet and the other is a push, for $1000 to Evans; and if the rate is below .09, Evans wins both bets for $3000.
A very simple climate model
Here's a very simple, one-variable model of global surface temperature, compared to actual global surface temperature:
You can see that the model (red line) tracks global temperature (blue line) quite well; the blue line swings around quite a bit, especially in the early years, but it never gets too far from the model. So, how did we draw that red line? What's the magic single variable?
It's the logarithm of CO2, lagged by 14 years and scaled appropriately. In other words, this year's temperature is well predicted by the logarithm of CO2 from 14 years ago. Using logarithms is needed because according to the Beer-Lambert Law, absorption of infrared by CO2 increases according to the logarithm of CO2 (rather than arithmetically, just using straight parts-per-million). The 14-year lag was determined empirically; that's the lag needed to maximize the correlation between ln(CO2) and temperature. Physically, it represents the time it takes for a pulse of CO2 added to the atmosphere to warm the mixed layer of the upper ocean. It's a measure of thermal inertia. (If you look at the correlation of monthly, rather than annual, temperatures, the correlation maximizes at 174 months, or 14.5 years exactly.)
Now let's modify that a bit, by using 5-year averages, which is what the Evans-Schmidt bet is based on:
It looks nearly the same, but there is one subtle difference: now the correlation maximizes at a 17-year lag instead of 14 years. The reason for that is because a five-year average ending in 2005 encompasses the years 2001, 2002, 2003, 2004, and 2005, and the average time of that 5-year span is 2003.5. So when we count back 14.5 years from 2003.5, that's a 17-year lag to the year 2005, when the 5-year span ends. It's the same 14.5 year lag, plus half the 5-year span.
The point of all this is that when we use 5-year averages, we can use already known CO2 levels from the past to tell, with fairly good accuracy, expected global temperatures up to seventeen years in advance. That's warming "in the pipeline" from our past CO2 emissions that we cannot stop.
We can see how that works by graphing 17-year lagged ln(CO2) against 5-year average temperatures, getting an almost perfectly straight line, as in the graph below. Here, we restrict the data to 1950 and later, when correlations are tighter and errors are smaller.
The black line is the regression line: it's where we expect temperatures to be, based on lagged CO2 alone. The blue dots are actual CO2 and temperature data from the past. The diamonds reflect where temps would have to be to pay off the various bets; pink diamonds are where Schmidt is betting, and green diamonds are where Evans is betting. We can put those diamonds on the graph because we already know what the lagged CO2 values will be in 2019, 2024, and 2029.
[Side note: you can also use the slope of the regression line to determine climate sensitivity, roughly defined as the temperature rise you get from doubling CO2. Just multiply the slope (451 in this case) by ln(2) and you get 313. Since GISS temps are given in hundredths of a degree, that's 3.13°C of warming from every doubling of CO2, right in the middle of the IPCC's predicted range of 1.5 to 4.5°C per doubling.]
Wager Predictions
The blue dots don't fall exactly on the regression line, but they're pretty close; the difference between a blue dot and the black line is called "error" in statistics. The standard deviation of the errors is 4 (which is .04°C, because GISS temperature anomalies are expressed in hundredths of a degree). If those errors were distributed normally, we would be able to tell the exact odds of each of the six bets being won by either Evans or Schmidt. In this case, the errors are not normally distributed because of "autocorrelation". You can see autocorrelation in the graph by noting that the blue dots tend to stay above or below the black line in clumps or groups, instead of bouncing above and below the line individually.
What we can do, however, is ignore autocorrelation and compute what the expected outcomes would be if the errors were distributed normally. The results we get won't be highly accurate, but they will be roughly in the ballpark.
For the 2019 bets, the regression line passes between the two pink diamonds. If actual temperatures fall there, the main bet is a push, occurring about half the time. The rest of the time Schmidt and Evans have about an equal chance of winning the main bet, with Evans' chances very slightly higher (25% to 23%). The odds bet is won by Schmidt 91% of the time and by Evans less than 2% of the time. Total expected value of both bets in 2019 is $861 in Schmidt's favor.
For the 2024 bets, the odds swing more strongly in Schmidt's favor. (This is because their chosen winning criteria all have slopes less than the regression line. Thus the criteria fall farther and farther from the regression line as time goes on.) For the main 2024 bet, Schmidt has a 57% chance of winning, while Evans' chances are less than 2%. (The rest of the time the bet is a push). For the odds bet, Schmidt's chances are about 99.9% to win, while Evans' chances are only one in 29,000. Total expected value in 2024 is $1552 for Schmidt.
For 2029, the main bet chances are 81% for Schmidt, and only .05% for Evans. The odds bet is predictably worse, with Schmidt virtually certain to win and Evans' chances only 1 in 140 million. Total expected value in 2029 is $1808 for Schmidt.
Total expected value for all bets in all years is $4221 for Schmidt, but if each individual bet obtains its most likely outcome, Schmidt would win $1000 in 2019 and $2000 in each of the other years, for a total of $5000 out of a maximum $6000.
Sooner or later, David Evans is going to lose his shirt.