A guest post by Basil Copeland
[NOTE: After seeing some other analyses posted in comments by Basil, I’ve invited him to post his work here. I hope you will enjoy it as much as I have so far – Anthony]
Everybody talks about the weather, but rarely has a scientific debate engaged the public as have concerns about climate change and and anthropogenic global warming. It is a scientific issue or debate that everyone can have an “informed” opinion about just by going outside, or by thinking about how climate has changed in their lifetime. If they cannot understand the physics of GCM’s (global climate models) they can read a thermometer and opine whether it is getting colder or warmer “than it used to be.” Few scientific issues or debates are as reducible to an everyday metric — a thermometer reading — as the debate over global warming.
The experts merely fan the fires when they issue press releases about how this year or that is the warmest since whenever, or that the earth’s temperature is rising at X degrees per decade and is likely to continue to rise Y to Z degrees for the rest of the century. The truth is that taking the earth’s temperature is no easy task. Some would argue that it is not even possible to speak of a global temperature as such, e.g. that climate is regional, not global. Others, such as the host of this blog, have drawn attention to serious questions about the accuracy of the station records on which estimates of global average temperatures are frequently based. Then there are the stat geeks, like myself, who understand how hard it is to accurately or meaningfully measure the “average” of anything! It begs reciting the old saw about a statistician being someone who can stand around with one foot in a bucket of boiling water, and the other foot in a bucket of ice water, and say that “on the average” they feel fine.
But despite all the legitimate reasons to question the usefulness of global average temperature metrics as measures of climate change or global warming, we’re not likely to stop using them any time soon. So we should at least use them the best we can, especially when it comes to divining trends in the data, and even more so when it comes to extrapolating such trends. In a series of recent blogs, our host has drawn attention to the dramatic drop in global average temperature from January 2007 to January 2008, and more recently to what appear to be essentially flat trends in global average temperature metrics over the past decade. Not surprisingly, a vigorous discussion has ensued about how reliable or meaningful it is to base inferences on a period as short as ten years, not to mention a one year drop like we saw from January 2007 to January 2008. While there are legitimate questions one might raise regarding the choice of any period to try to discern a trend in global average temperature, there is no a priori reason why a period of 10 years could not yield meaningful insights. It all depends on the “skill” with which we look at the data.
I’m going to suggest that we begin by looking at an even shorter period of time: 2002:01 through 2008:01. Before I explain why, I need to explain how we will be looking at the data. Rather than the familiar plot of monthly temperature anomalies, I want to call attention to the seasonal difference in monthly anomalies. That, in a sense, is how this all started, when our host called attention to the sharp drop from January 2007 to January 2008. That 12 month difference is a “seasonal difference,” when looking at monthly data. The average of 12 monthly seasonal differences is an estimate of the annual “trend” in the data. To illustrate, consider the following series of monthly seasonal differences:
0.077, 0.056, 0.116, 0.036, -0.067, -0.03, -0.119, -0.007, -0.121, -0.176, -0.334, -0.595
These are the 12 monthly seasonal differences for the HadCRUT anomalies from February 2007 through January 2008. During that 12 month span of time, the average monthly seasonal difference was -0.097, and this is an estimate of the annual “trend” in the anomaly for this 12 month period.
With that by way of introduction, take a look now at Figure 1. This figure plots cumulative seasonal differences going back in time from the most recent month, January 2008, for each of the four global average temperature metrics under consideration.
While they vary in the details, they all turn negative around the end of 2001 or the beginning of 2002. At the point where the series cross the x-axis, the cumulative seasonal difference from that point until January 2008 is zero. Since the “trend” over any period of time is simply the sum of the seasonal differences divided by the number of seasonal differences, that’s just another way of saying that since near the end of 2001, there has been no “net” global warming or cooling, i.e. the “trend” has been basically flat, or near zero. Yet another way to put it is that over that period of time, negative and positive seasonal differences have worked to cancel the other other out, resulting in little or no change in global average temperature.
But Figure 1 tells us more than just that. Whenever the cumulative monthly seasonal difference is below zero, the average monthly seasonal difference over that time frame is negative, and the annual trend is negative also. For most of the time since 2001, the cumulative seasonal difference has been negative, indicating that the average seasonal difference, and hence “trend,” has been negative.
This is shown, in somewhat different fashion, in Figure 2. In the most recent 12 months, the trends vary from -5.04% to -9.70%. They diminish as we go back in time toward 2001, but are mostly negative until then, with the exception of positive trends at 36 months for GISS and UAH_MSU.
Finally, in Figure 3, we have the more familiar anomalies plotted, but just for the period 2001:01 through 2008:01. The basic picture is the same. At the end of the period the anomalies are below where they were at the beginning of the period, indicating an overall decline in the anomalies over this period of time. Interestingly, the UAH_MSUn series dips below the x-axis four times during this period. When we consider that the metrics have all been normalized to a zero anomaly around their 1979:01 to 2008:01 means, that indicates that within the last six years, the UAH_MSU series has returned to, and dipped below, the 1979:01 to 2008:01 mean anomaly four times. All of the metrics have dipped below their 29 year mean twice in the last six years, and are well below the mean at the end, in January 2008.
Figure 3 – click for larger image
However you look at the data, since 2001 the “trend” in all four metrics has been either flat, or negative. There has been no “global warming” since 2001, and if anything, there has been “global cooling.” But is it “statistically significant?” I imagine that one could fit some simple trend lines through the data in Figure 3 and show that the trend is negative. I would also imagine that given the variability in the data, the trends might not be “statistically significant.” But since statistical significance is often measured by reference to zero, that would be just another way of saying that there has been no statistically significant warming since 2001.
But that may not be the most insightful way to look at the data, or frame the issue. Prior to 2001 we have a much longer series of data in which there has likely been a positive trend, or “global warming.” What can we say, if anything, about how the period since 2001 compares to the period before it? Rather than test whether the trends since 2001 are significantly different than zero, why not test whether the trends since 2001 are significantly different than the trends in the 23 years that proceeded 2002? We will look at that intriguing possibility in Part II.