August 19, 2007
Projected US temperatures in 2050 - U.S. and/or global warming?
What will US temperatures be in the year 2050?
Many have predicted that ongoing global warming, due in large part to human activity, will produce a US meltdown by the year 2050, with much of Florida under water, rampant tropical diseases such as malaria, and the US essentially going to Hell temperature-wise. What’s actually most likely to happen?
The Bottom Line
In 2050, the US temperature is projected to be essentially the same as it was in the period 1995-2005.
In other words, a yawner. Keep reading for the details.
Background
The US government publishes standardized temperatures for the US through the years, trying to compensate for heat effects of urbanization, etc. These temperatures are called “temperature anomalies” but we’ll call them “temperature differences“ - the word “anomalies“ has an implication of being unusual. These are some sort of average of temperature readings all across the continental US. The temperature differences are relative to the average for 1950-1980. That is, a temperature of 1 °C doesn‘t mean the average temperature was 1°Celsius; it means the temperature for that year was 1° Celsius hotter than the 1950-1980 average. These temperature differences can be found at the following web site:
http://data.giss.nasa.gov/gistemp/graphs/Fig.D.txt
Note: when going to this site, type it in exactly as shown. For example, fig.d.txt (lower case) gives an error message.
More information can be obtained by moving backward through the site; e.g.,
http://data.giss.nasa.gov/gistemp/graphs/
Note: The temperatures were recently updated because of a Y2K glitch, caught by an outsider, not by the government scientists who produced them. (Is anybody surprised?) It is not known how many additional errors are in their data and interpretations, because the source code and original data are not available to the public. But we’ll use these data as the best currently available.
AnalysisSuppose one wants to predict the temperature for some year. The absolutely simplest form of analysis imaginable is to do a linear regression of temperatures versus time
Y= a + b X, where Y is temperature and X is the year
with the year for which the temperature is being predicted set to X=0 in the regression equation. The intercept of the regression line is the temperature of the year of interest, and the slope is how rapidly the temperature is changing.
The regression analysis is equivalent to finding the best-fit straight line for a graph of temperature differences vs. year and then extrapolating the line to find the temperature for the year in which you’re interested. See Fig. D (“U.S. Temperature”) on the site
http://data.giss.nasa.gov/gistemp/graphs/
Here’s a simple example of such a regression calculation. Suppose in 1934 Al Gore’s grandfather had the temperature data available only for the years 1924-34, and decided to predict the temperature for 2004. The data would look like:
Actual ...........Year (for ..............Temperature
Year ..............regression) ..........(°Celsius)
1924 ...............-80......................... -0.74
1925 ...............-79 ...........................0.36
1926 ...............-78 ...........................0.04
1927 ................-77 ...........................0.15
1928 ...............-76 ............................0.07
1929 ...............-75 ...........................-0.58
1930 ..............-74 .............................0.16
1931 ...............-73 ............................1.08
1932 ...............-72 ...............................0
1933 ...............-71 ...........................0.68
1934 ...............-70 ...........................1.25
Put these numbers into an Excel spreadsheet, crank up the Tools\Data Analysis package, and regress “Temperature” against “Year (for regression),” and you get the following results - and lots more statistical information as well. Temperatures are given in both °Celsius and
°Fahrenheit, because a typical US citizen hasn‘t got a clue what a Celsius temperature is.
Predicted average US temperature difference in 2004: 9.1 °C (16.4 °F)
95% confidence interval: 1.2 °C to 17.1 °C (2.1 °F to 30.7 °F)
Slope (change in temperature per year): 0.12 °C/year (0.21 °F/year) - that is, the regression equation says the temperature increases 1 °F every 5 years
Significance level of F-statistic: 0.031 (without being too fancy about it, the significance level indicates a significant relationship at the 97% confidence level between temperature and year)
So Al Gore’s grandfather could have made a movie and gone out on the lecture circuit talking about how the US would be impossibly hot in the year 2004. The predicted temperature in 2004 would be about 9 °C (16 °F) hotter than the average during the 1924-1934 period (0.2 °C or 0.4 °F temperature difference) and perhaps as much as 17 °C (30 °F) hotter. A truly frightening possibility of a truly frightening calamity by 2004!! Back to reality: The actual 2004 US temperature difference was 0.44 °C (0.79 °F). OOPS!
This example was just to show how the regression process works - try it yourself to see if you get the same numbers. It’s obviously silly to extrapolate too far from the actual observations. For example, it would be downright stupid to extrapolate from the US temperatures in 2000-2006 to say the sky will be falling and Florida will disappear into the ocean by 2050. OOPS again! That’s what people do.
But let’s try a serious analysis. We want to predict temperatures in 2050, using temperatures through 2006; that is, 44 years in the future. So let’s see how good a job we can do at predicting temperatures 44 years in advance.
We’ll try predicting the temperature difference in 2004 using temperature data from 1880-1960. The reason for choosing 2004 is that it’s the last year we can look at the 5-year average for 2002-2006 as what we’re really trying to predict. There are enough year-to-year variations that it’s better to predict the 2004 temperature difference, and see how closely the predicted temperature compares with the 2002-2006 5-year average, not just with 2004 itself - although we can also make that comparison.
So we take the 1880-1960 data, set 1960 as year -44, 1959 as year -45, etc., and do the regression with the intercept being the predicted temperature difference for 2004. Here’s what we find:
Predicted average US temperature difference in 2004: 0.66 °C (1.18 °F)
95% confidence interval: 0.30 °C to 1.01 °C (0.55 °F to 1.82 °F)
Significance level of F-statistic: 0.0003 (significant at the 99.97% confidence level)
The actual temperature differences in 2002-2006:
2002 0.53 °C (0.95 °F)
2003 0.50 °C (0.90 °F)
2004 0.44 °C (0.79 °F)
2005 0.69 °C (1.24 °F)
2006 1.13 °C (2.03 °F)
And the actual 5-year average for 2002-2006: 0.66 °C (1.18 °F)
Obviously, the agreement to within 0.01° between the predicted 2004 temperature difference and the average of the 5 years around 2004 is sensationally good. In fact, much, much better than one would reasonably expect. And the agreement between the predicted and actual 2004 temperatures (within about 0.2 °C or 0.4 °F) isn’t shabby.
Now that the model for the temperature estimation has been validated way beyond any reasonable expectations, let’s address the multi-trillion-dollar question: What will the US temperature be in 2050?
What we’ll do is to take all the data we have (1880-2006), and do the linear regression for the 2050 temperature. (In the regression, 2006 is year -44, 2005 is year -45, down to 1880 is year -170). Here’s the result:
Predicted average US temperature difference in 2050 (the intercept): 0.58 °C (1.06 °F)
95% confidence interval: 0.35 °C to 0.82 °C (0.64 °F to 1.48 °F)
Change in temperature per year (the slope): 0.0048 °C/year (0.0087 °F/year) - the regression predicts the temperature will increase 1 °C about every 200 years or 1 °F every 115 years.
Significance level of F-statistic: 0.00001
Let’s compare this result to some recent temperatures. The average temperature in the period 1995-2005 was 0.53 °C ( 0.95 °F).
In other words, the linear regression predicts that the US temperature difference in 2050 (0.58 °C or 1.06 °F) will be essentially the same as it was in the years 1995-2005 (0.53 °C or 0.95 °F). A bit warmer than the average since 1880, but not exactly a big deal.
A few quibbles, caveats, etc.1. There are as many ways of fitting data to equations as there are statisticians. The easiest way to begin is with the simple linear equation. That’s always the first place to start, and most of the time does about as well as much fancier equations. Although, of course, there are data for which a linear equation either doesn’t work or can be improved upon.
Anybody can use any equation, and see if that equation produces a significantly better fit than the simple linear equation. There are straightforward statistical tests to see if a fancier equation improves the fit. We’ve tried a few without much success, but anybody is welcome to try any other equation.
2. Whether it will be successful to do a straight-line extrapolation of previous temperatures for 44 years into the future is an open question. The extrapolation worked sensationally successfully 44 years in the “future” to 2004. What will happen going forward to 2050 is unknown. Perhaps a gigantic meteor will hit the Earth, even more gigantic volcanoes will erupt, or the cataclysmic tipping point events predicted by the global warming crowd will come to pass. Who knows?
3. The prediction here is only for US temperatures. Somebody might want to try the equivalent exercise for temperatures in other parts of the world.
4. The advantage of the linear extrapolation of temperatures is that the data and analysis are completely transparent - anybody can reproduce the calculation or look up the data. But ask any climatologist who has a climate model to show you the source code - lots of luck getting it. It’s a closely-held secret whether or not the code contains a line
IF ((T2050 - T2006) < 2.5) THEN (((T2050 - T2006) = 2.5) AND CALL AL GORE)
In modern science, data are considered proprietary trade secrets, even when the data are gathered on government contracts and grants.
The general rule is that you should take with a very large grain of salt any projection showing major effects on temperature due to human activity when the projection is done by somebody whose grant funding depends on getting results showing that human activity causes temperature changes. Too many scientists are more than happy to sing for their suppers whatever tune strikes the fancy of the person paying for the supper.
5. And a question to which we’ve never heard a very good answer: What will be the temperature effect of injecting, say, 1,000 kg of carbon dioxide into the atmosphere? 0.0000001 °C or 0.0000000000001 °C or what? Does anybody have an answer and, more important, will they let other people check their calculations?
That's all for now.
