Digital Diatribes

A presentation of data on climate and other stuff

Happy Valentine’s Day! Here’s a Global Temperature Analysis!

Posted by The Diatribe Guy on February 14, 2008

Just for fun (yes, for actuaries this really is actually fun…) I put together a data analysis based on this table of global temperature anomalies from NASA.

A warning: this post may bore some to tears. For those who enjoy taking a look at data and trying to come up with a story, you may find it interesting. At the very least, I hope to point out why it’s so difficult to really assess this whole global warming thing, in particular as it pertains to forecasting.

I looked at the data, assuming that I could order all the data points with relevance (i.e. that an anomaly in December is comparable in relevance to an anomaly in June). I figured, even if not entirely appropriate, that the trend lines would compensate for this over time.

One thing I did for the sake of curiosity was determine the longest period within the subset of data for which a trend line could be fitted that had a negative slope (thus, an apparent cooling trend line). The longest such period would use January 1921 as the first data point. A trend line can be fitted over 673 months (56 years, one month) through January 1977. This would imply that any time up until that point, if one would have used 1921 as a starting point in their analysis, the determination would be that the world is cooling. Other, shorter, periods have also suggested cooling, and have proved over the course of the entire data set to not be long-term trends.

The next thing I looked at was the impact of the starting point, using data through today, on the result. I hear a lot of “well, if you look at the last 20 years, or 30 years, or 40 years… All starting points are arbitrary, and depending on what you choose, it provides a different answer.

Here are the results of that:
Period / slope (1.00 in slope = .01 Celsius per month) / Implied Change per decade (Cel)
All Periods start with the month of January, and end January 2008

1880 – 2008 / .0504 / .0604
1890 – 2008 / .0565 / .0678
1900 – 2008 / .0576 / .0692
1910 – 2008 / .0593 / .0711
1920 – 2008 / .0602 / .0722
1930 – 2008 / .0658 / .0790
1940 – 2008 / .0822 / .0987
1950 – 2008 / .1128 / .1354
1960 – 2008 / .1432 / .1718
1970 – 2008 / .1675 / .2010
1975 – 2008 / .1739 / .2087
1980 – 2008 / .1552 / .1898
1985 – 2008 / .1922 / .2306
1990 – 2008 / .2091 / .2510
1991 – 2008 / .2448 / .2937
1992 – 2008 / .2803 / .3364
1993 – 2008 / .2564 / .3077
1994 – 2008 / .2229 / .2675
1995 – 2008 / .2014 / .2417
1996 – 2008 / .2142 / .2571
1997 – 2008 / .1890 / .2268
1998 – 2008 / .1430 / .1716
1999 – 2008 / .2582 / .3098
2000 – 2008 / .2355 / .2826
2001 – 2008 / .1069 / .1283
2002 – 2008 / .0127 / .0152
2003 – 2008 / .0673 / .0808
2004 – 2008 / .0972 / .1167
2005 – 2008 / -.3113 / -.3735

I would argue that the long-term trend (long-term meaning, reasonably what can be anticipated in our lifetime) is about .06 degrees Celsius increase per decade, or about 0.6 degrees Celsius in the next Century. I would also argue that one can make nearly any case they want, from extreme warming (using 1992 – 2008) to actual cooling (2005-2008). The shorter the time period, the more tenuous the position. Obviously the cooling period can’t be looked upon as anything but a potential indication of a reversal of the trend, without the statistical significance of the longer term trends.

Likewise, I don’t see any credible reason to start the time period any time after 1880 for predictions about the next 100 years. It may be proper to talk about the next few years using more short-term data. Unless there is reason to believe the data is deficient, we should use all of it for the long-term trend. Even along the trend line, there have been periods of increase and decrease, spikes and valleys, and to argue that the most recent increase is to be extrapolated out any more than a short time period seems to poorly recognize that these short-term trends exist in the data.

The next thing I did was to run the slope on a rolling 120 month time period, starting with January 1880 as the first data point of the first slope calculation. The first 120 month trend line has a slope of -.0922 and the slope in subsequent months decreases until its MIN of -.2077 in December 1881 (references here are to the initial data point of the 120 month period). The 120 month slope starts to increase until it reaches a maximum of 0.3858 in January 1891. Following is the remainder of the MINS and MAXES:

First Data Point of 120 Months / Slope (1 = .01 C) for Max or Min value
August 1899 / -.2238
November 1906 / .2920
May 1909 / -.0466
December 1916 / .3166
December 1925 / -.0105
January 1929 / .2201
April 1941 / -.2418
January 1954 / .1478
March 1957 / -.2487
January 1964 / .2363
March 1967 / -.0544
December 1973 / .3903
December 1979 / .0058
October 1981 / .2835
January 1987 / -.0127
June 1992 / .3970

That is the most recent Max/Min. Since then, some of the 120 month trend points:

October 1993 / .2943
June 1994 / .2436
July 1997 / .1966
August 1997 / .1791
September 1997 / .1760
October 1997 / .1679
November 1997 / .1659
December 1997 / .1650
January 1998 / .1598
February 1998 / .1443 (last date with 120 data points)

So, it looks like the 10-year trends fluctuate up and down quite a bit. It would appear that we are currently in a time period where the rate of warming is decelerating. This is not the same as saying we will eventually be cooling, but it does not correspond with certain claims I’ve heard that the warming rates are only getting worse.

January 2008 had a temperature anomaly of 31 (0.31 degrees Celsius higher than the period they relate temperatures to, which is 1951-1980). This is the lowest anomaly since December of 2000.

In order for the 10 year trend starting with the March 1998 data point to be less than .1443, the temperature anomaly in February 2008 will need to be 23 or less. An anomaly of 23 would be the lowest since October 2000 (22).

An online actuarial acquaintance has an interest in this and is much more sold on global warming as a reality than I am (from the anthropogenic viewpoint). For fun, he put together a little model that considers solar irradiance, some historical events impacting weather (volcanoes, el nino, etc.) and suggests that the temperature anomaly for 2008 will be 0.60 degrees above the baseline of 14 degrees Celsius. Using a completely different approach, I predicted an anomaly of 0.51 degrees.

We have two different views of what our numbers mean. He believes his is a continuation of an increasing trend line, accounting for an assumed irradiation level and La Nina. I, on the other hand, simply looked at the decreasing value of a rolling 120-month slope, and assumed the trend would continue. The built-in assumption with this approach is that a lot of outside influences are cyclical in nature and the information is, in aggregate, incorporated into the trend. Throw in the idea that many influences are outright unpredictable (volcanic activity, for example), and you have my explanation for simply using a trend line. Plus, I’m too lazy to refine it any further… Anyway, I was actually conservative in the projections, based on the decelerating slopes of the trend line. My projections only slightly reduce the slope of the 120-month line. Actual deceleration observed over the last number of data points is more rapid than my assumptions. This would mean that my prediction is actually what I would consider the high side of the projected anomaly for 2008. In my estimation, the likelihood of error is far greater in overestimating the anomaly than underestimating it.

The decelerating trend is not saying we have entered a cooling phase, although it doesn’t say we haven’t. We still may be in a warming phase, but it is at a slower pace than recent. The most recent data actually indicate that we may have reached the peak and are, in fact, reversing into a cooling phase. But there are not enough data points to credibly state this, and only more data points could make that case, which we will just have to wait for. But the 120-month trend average shows an obvious deceleration, nonetheles, and I think a reasonable case can be made that, at minimum, warming trends are not accelerating.

That all said, my predicted anomalies by month, using data through December 2007:

January 67
February 23
March 54
April 52
May 44
June 38
July 31
August 46
September 73
October 63
November 67
December 51

It would still make it a warm year, while at the same time continuing to reduce the slope of the moving 10-year trend line. Again, I believe if I am wrong it will be because we have a colder year than I am predicting. January came in well below the initial estimate (an anomaly of 31), and we’ll see if that trend continues. February’s a pretty aggressive estimate compared to recent history – it would be the smallest anomaly in any month in nearly 8 years. Based on my region’s temperatures this month, it seems plausible, but I haven’t paid too close attention to worldwide weather in the last two weeks, so who knows? The month-to-month variations really make it unlikely that my predicted anomalies will be accurate on a month-by-month basis, but for the overall 12 month period I think it will bear itself out. Stay tuned for updates.

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