Thursday, January 24, 2008

Symmetries in the Global Temperature Record -Introduction and Part I


This is the first of a number of posts on the global temperature record, climate cycles and natural and human-caused temperature changes. In the first several posts of the series I will show you some fascinating numerical patterns lurking within the apparent chaos of the global temperature record. You will see that these patterns are, like snowflakes, beautifully symmetric and, even more amazing, the same symmetric pattern is found within and across portions of the temperature record as well as across the entire time series to be analyzed. For those readers needing the hard numbers of probabilities to be impressed by these symmetries, a post will detail how astonishingly unlikely these numerical patterns could be present within the temperature record by chance.

The series will then move to the most astonishing finding of all - the timing of these symmetries corresponds with major long-term temperature movements in the temperature record. The correspondence of intricate and improbable symmeties with major long-term movements in the temperature record suggests that the symmetries themselves are fingerprints of natural temperature cycles in the temperature record.

While the evidence of natural temperature cycles will undoubtably cheer skeptics of anthropogenic global warming theory, I will show that the temperature record in fact contains clear evidence of human-induced warming. I will demonstrate, making use of a very simple assumption, that in fact significant and measureable human-induced warming took place during the global cooling period of the 1940's to mid-1970's and that this human-induced warming accelerated from the mid-1970's to the present. However, while the temperature record contains clear evidence of human-induced global warming, I will argue that this record offers little evidence of major feedback effects from increasing concentrations of greenhouse gases in the atmosphere.

Finally, I will offer a global temperature forecast for the 21st century based on the above findings. I will suggest that recent episodes of unusually cold weather in many parts of the globe are in fact evidence the earth is just entering a new cooling phase, a cooling phase that will last for the next 30 years. We may expect however that human-induced warming will roughly offset this cooling phase resulting in very little temperature change in the world over the next 30 years.

Fascinating Figures - Part I

If you are like most people, your impression of the time series chart of global temperatures is probably quite vague. You might have seen this chart one of the reports put out by the UN's Intergovernmental Panel on Climate Change (IPCC) or perhaps in Al Gore's movie (or book) "An Inconvenient Truth". Chances are, all that may come to mind for most readers is a squiggly line that climbs up and to the right. Chances are any chart that you may have seen focused on the general temperature trend and deemphasized more short-term temperature movements.

That's because everyone knows that short-term movements are just "noise" in the data needing to be tamed so that we can see the forest of reality rather than get lost in the trees of detail. I've reproduced below such a "noisy" chart of monthly global temperatures, (expressed as anomalies, or departures from long term averages) for the period from 1880 to 2007:

It sure looks "noisy", especially if you look closely at a small piece of the chart, say a period covering a decade or so. Over such a short period it's hard to see any real trend and you really need to step back a bit and look at the entire chart to see that the long-term trend is definitely up. But you can easily imagine why people replace all that "noise" with squiggly, thick lines so that we can focus on the underlying trend. Afterall, the trend is what's really important, since knowing the past trend will help us to understand the future trend.

Of course, this assumes that the cause of the upward trend is understood. If we do understand the cause of the trend, then subtracting out the effect of that cause leaves us with random, directionless movement. In the case of global temperature movement most scientists studying the earth's climate believe that humans have caused this upward temperature trend, or at least have been the cause of this trend over the past 50 years or so. Most of these scientists would argue that without human intervention the global temperature movement, at least over the past 50 years or so, would have been random and directionless. This is essentially the argument made in the IPCC's most recent report on the earth's climate.

I am going to show you that this thinking is incorrect. I will show you that the general temperature trends in the above chart, over its entire period from start to finish, are ordered and not random. I will show you that the evidence for this order lies in a series of intricate and interwoven numerical patterns found within the data itself. These patterns can be found in a recent release of the NOAA NCDC global temperature anomaly time series (the figures in this post were calculated from the time series released in December of 2007). These numerical patterns are revealed by taking first differences (that is, the month to month changes) of the time series for the 1880 to 2006 period and transforming the first differences into a binary format. Successive divisions of the time series reveal these increasingly complex and interwoven numerical patterns.

The analysis to uncover these patterns will use monthly data for the January 1880 to September 2006 period, a period containing 1521 data points whose first difference produces 1520 data points. The analysis will use three simple steps:

1. Calculate first differences, that is, the one-period change in the global temperature anomaly.

2. Transform the resulting first differences into a binary format with values greater than zero being given a value of 1 and values less than or equal to zero being given values of 0 (note that reversing the value labels produces the same results) . For the record, a single first difference value in the transformed time series was equal to zero.

3. Examine the resulting numerical pattern of binary values for various partitions of the transformed time series.

We begin with the resulting distribution of binary values for the full time series:
There are an equal number of 0 values and 1 values in the full time series.

Since there are an equal number of 0 values and 1 values in the full time series, a partition of the time series into two equal halves produces a symmetrical numerical pattern:

We next partition the time series into four quarters of 380 data points each. Note that there is now no guarantee of a symmetric outcome for this partition; however, a very interesting pattern does, nonetheless, emerge:

The first and third quarters have an equal number of 1's and 0's while an excess of 1's in the second quarter are balanced by an excess of 0's in the fourth quarter. The patterns get even more interesting as we increase the number of partitions in the time series. More to come in my next post . . . .

No comments: