A recent post at Dot Earth has brought out the usual auguments by those that disagree with human-induced climate change (Earth Scientists Express Rising Concern Over Warming). In addition to Dr. Ray Pierrehumbert (a contributor to RealClimate) and Marc Morano (staffer to Senator James Inhofe) being in what I assume to be a fight to the death, there is the typical “how do the warmers explain the fact that it hasn’t warmed in the past X years?” type of argument.

When confronted with the fact that by some metrics global temperatures have not risen in the past couple years, persons with a predisposed position with respect to anthropogenic climate change my claim that the warming of the globe has stopped. Of course, the time period over which this temperature trend is calculated is extremely important. (The folks at RealClimate had a post similar to this, but I can’t find it. Any help with a link would be greatly appreciated.) [Added 30 Jan 2008: Thanks to Hank Roberts who found this post at Stoat.]

First, let’s take an extremely short time period over which to calculate temperature trends - 5 years. In fact, if one looks just at the last five years of temperature data from HadCRU, the global tempeatures have not risen. It has actually fell, although the decrease is not statistically different than a zero trend. What’s enlightening is when the 5-year trend lines are plotted on the same graph as the temperatures.

Here, the black line is the actual temperature anomalies reported in the HadCRU data, and the little red lines are the individual trends calculated for all the years (minus the end points). In the subtitle I’ve included the number of years where the trend is positive, and the number of years where the trend is negative. Even though for this data there is clearly a positive trend in the data (from left to right), the number of positive 5-year trends is not much higher than negative trends.

How many years of data do we need to calculate a significant trend?

The word ’significant’ has a precise meaning in the world of statistics. For this post, I’m going to relax that definition - because it’s my site, that’s why. Instead of the usual statistically significant meaning, I’ll just use the word significant if the results show anything interesting.

Using the same methodology used previously, the percentage of positive X-year trends was calculated for all X in the range 2 to 157. The lower bound is contrained by the fact that 1-year trends are ill-defined - 2 points are needed to calculate a slope. The results can be seen below.

As can be seen, at small intervals, the number of years of positive trends is only slightly larger than 50%. As the number of years in determining the trend increases, the percentage increases rapidly to around 70% for 13 years. There is a slight decrease to 30, and then a general increase to 100%. I’ve chosen two length scales to show below; 13 years and 30 years.

Calculating temperature trends over a 13 year period gives interesting results. One thing that pops out at me is that since about 1910 there are very few red lines that have a negative slope. In the 1940s there are several consecutive years with a negative trend, but even through the 60s and 70s the trends generally stayed above zero. The number of positive trends vastly outnumbers the negative ones 100 to 45. And most of the negative trends occured from 1880 to 1910.

Finally, I looked at 30-year trends. This is because there is a dip in the percentage of positive slopes relative to values slightly higher and lower (see plot #2 in this post).

After seeing the graph the reason for the dip becomes obvious. The years 1880 to 1910 still show a negative trend, as do the years in the 1940s. There are still positive trends elsewhere, but the fact that the total number of years has decreased means that the percentage of negative slopes has increased.

Trends where more than 30 years were analyzed quickly rose to 100% positive slopes. This is naturally because the global temperature today is higher than it was in the late 19th century.

Conclusions

When reporting trends in global temperature (especially from the HadCRU dataset), very short timescales are meaningless. Only when trends are computed over at least a decade are the trends not influcenced by the random nature of the years weather. A time period of 13 years provides some clear advantages; it will effectively eliminate any signal due to ENSO, which has a period of 3-7 years; it will also eliminate the weather noise since, at least for this dataset, the global warming signal appears to be larger than the noise at time periods greater than about 10 years.

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