A Follow Up to the March 2008 Temperature Analysis
Posted by The Diatribe Guy on March 26, 2008
I have continued to refine the analysis I have been doing on the GISS global temperature anomaly data to see what I can glean out of the trends in the data. Previously, I ran a trend of anomalies on rolling 120-month periods, and then determined that the trend of the slopes was downward. The conclusion is that the trend line overall was still positive, but declining in magnitude (i.e. warming rates are slowing). Warming rates cycle up and down over time, and the current trend in declining rates is true of the last 6+ years of anomalies. That entry is here.
Well, while it is interesting to review, there are the following deficiencies to the analysis that should be looked at and addressed.
Proposed Deficiency #1: Looking at only one basis for trend. Is 120-month averages predictive? And should I be using a trend line on the calculated slopes that always begins with the most recent peak or trough? In this entry, I show the results of looking at moving averages of anomalies for 60-month, 180-month, 240-month, 300-month, and 360-month slopes in the trend of anomalies. Also, instead of using the convention of looking at the trend in slopes since the last peak or trough, I instead calculate 12-month rolling average “trend of the trend” points and then further evaluate the successive differences in those values to ultimately arrive at the future anomalies. I will explain the process in more detail later.
Proposed Deficieny #2: Anomalies are not adjusted for ENSO or other outside impacts. While I agree that temperature is affected by a number of contributing factors, and that some of these factors are deemed to have a larger impact than other factors, I have purposely left the data unadjusted. The purpose of the rolling trend lines is to see current trend changes for short-term predictions. I am not making 30-year forecasts with the analysis. Trending will flatten these error terms out (granted, it will reduce the fit – that is understood) and using the rolling average helps to smooth out these differences. But the main reason why I do not adjust these things is because such adjustments are subjective. Is ENSO driven by natural cycles that should not be smoothed? And not all ENSO events are of the same magnitude, so how much of a temperature anomaly can scientifically be known to be attributable to such events? What about other random events, such as volcanic eruptions? No, I have decided to simply use the data as it is. The actuary in me understands the need for adjusting “bad” data and outliers, and this is certainly a consideration the reader must account for during review of the information.
Proposed Deficiency #3: Lack of historical testing of the predictive model. Guilty as charged. Keep in mind that I have a job and a family, and this is a hobby. This is a work in progress. I am happy to have introduced more trending criteria to observe. As time goes on, I will start to retrospectively test the different trend periods to assess predictive value. So, for now, it is admitted that this seems like a logical approach in concept, but it is yet to be determined which trend period employed (if not another period) provides the best fit to historical data. As I develop that, I will provide updates accordingly.
Here is the general approach employed, with any noted exceptions:
1) Slopes were calculated based on raw anomaly data for rolling time periods. The time periods analyzed were 60, 120, 180, 240, 300, and 360 month intervals.
2) The slope of the slopes in (1) was calculated on a rolling 12-point basis. The only exception to this was the 240-month trends, for reasons which will be explained later.
3) The difference in successive slope calculations from (2) were calculated for the last few data points.
4) The next successive data difference point was judgmentally selected based on the trend or average of the difference points in (3). Consideration was given to whether or not there appeared to be a constant increase or decrease, a declining rate of increase or decrease, a declining rate of increase or decrease, or random fluctuation about an average level.
5) Once the next future difference point was selected (in this case, for March 2008) then the n-month slope was determined through an iterative process such that the n-month slope produces the next 12-month trend calculation that, in turn, determines the next difference point. (In many cases, the difference wasn’t explicitly selected, but a reasonable range was targeted as values of the n-month slope were entered. It made the iterative process easier with minimal impact on final results.)
6) Once the next slope point is determined, for the time being, the remaining successive points are those produced by the trend line using the trend of the trend adjustments. A more robust approach could be obtained if there was high confidence in future difference points. This is an element of future consideration.
7) Once the remaining n-point slope values are determined, the required trend-line anomalies are determined through another iterative process.
Exception: the only case in which the 12-month trends produced unreasonable results was in the 300-month scenario. In this case, the trend period was extended back one month at a time until a reasonable result could be obtained. By “reasonable,” I mean that the difference calculation produced by the change in the trend line produces a 300-month slope level that is in line with previous levels. It does not require a continuing of a trend, just not a large, nonsensical swing. For example, if previous 300-month slope calculations are .1852, .1843, .1836, .1830, and the next level indicated by the approach above requires a slope of .1918, then it is clearly out of line. The next calculation should probably be around 0.184, but at the very least even if a reversal is indicated, it should not be such a large step, which in turn indicates an unreasonable anomaly required. So, in this case, judgment was employed to extend the trend period of the slope to 16 data points, which produced reasonable results.
Future testing: In retrospectively analyzing model predictability, not only should tests be run on which n-month calculation provides the best predictive value, but also the x-month trend of the slope should be addressed. Due to the requirement that there be judgmental selections and iterative calculation, such testing is tedious, which helps explain why it hasn’t yet been done. Analysis on differences should also be reviewed to see if there is a predictable selection method that can be incorporated on a basis further into the future than the next successive month so that predictability of future months is improved.
Are the trend-line anomalies predictive?
Yes and no. Clearly, one of the ideas with this analysis is to better understand the trends in the data. By looking at n-month slopes, and then x-point trends of the slopes, and then trends in the differences of those slopes, the retrospective analysis should best represent the different cyclic trends that appear in the data, to the extent that they are consistent. Once these optimum values are determined, the model can more and more be considered a predictive outlook of future anomalies by month.
Until then, it is more an analysis of interest in comparing the required trend anomaly to the actual emerging anomaly. Here’s what the result does mean: if the actual anomaly is lower than the required trend anomaly, then this means that – at least based on the results of that month – the rate of warming is decelerating more than previously determined (or if the trend line were positive, not accelerating as much as previously determined). Hitting the trend line says that the current rate of warming or cooling is continuing. Coming in above the trend line says that the current rate of warming is not decelerating as fast as expected (or if a positive slope, is accelerating). At the very least, looking at the results indicated by the n-month anomaly slopes tells us whether or not it is reasonable to use that trend line when discussing current temperature trends. As we will see, it becomes clear that the 30-year trend line produces the least reasonable short-term results, and by induction if it produces the worst short-term results. And while it doesn’t necessarily follow that this means it’s a poor long-term fit, it is also clear that with the anticipated future change to the 30 year slope given short-term expected anomalies, the future 30-year slope will be changing to a large enough extent that we can reasonably assume that it also has poor long-term predictive value.
The Results. (I will not delve too much into the calculations. The process has been explained.)
60-month slope ending February 2008: 0.028397
Projected 60-month slope ending March 2008: –0.040000
Monthly selected change in 60-month slope: –0.022013
120-month slope ending February 2008: 0.147469
Projected 120-month slope ending March 2008: 0.150000
Monthly selected change in 120-month slope: –0.005827
180-month slope ending February 2008: 0.247959
Projected 180-month slope ending March 2008: 0.239000
Monthly selected change in 180-month slope: –0.006670
240-month slope ending February 2008: 0.192246
Projected 240-month slope ending March 2008: 0.192786
Monthly selected change in 240-month slope: 0.000100
300-month slope ending February 2008: 0.182990
Projected 300-month slope ending March 2008: 0.183000
Monthly selected change in 300-month slope: 0.000019
360-month slope ending February 2008: 0.163443
Projected 360-month slope ending March 2008: 0.163100
Monthly selected change in 360-month slope: 0.000458
Table of Results – Required Anomalies to maintain indicated trend:
Month 60 120 180 240 300 360
March 32.7 59.8 25.7 49.5 72.8 140.1
April 59.0 38.5 47.2 58.3 54.6 68.1
May 46.5 29.7 46.5 46.4 42.8 74.3
June 68.3 23.8 54.8 48.4 60.8 94.9
July 64.8 16.7 47.1 64.5 68.2 76.3
August 42.4 30.7 56.5 60.7 41.2 111.8
September 47.4 57.5 70.0 55.8 39.2 83.4
October 42.5 47.4 57.6 58.0 66.4 93.9
November 58.0 51.3 70.3 97.5 60.6 87.3
December 39.2 35.0 71.0 74.0 72.8 90.8
Annual Avg 46.9 37.7 50.7 56.3 53.5 81.9
The Annual Average includes the known anomalies of 31 in each of January and February. The coldest of the results, using the 120-month slope changes (round to 38), would be the coldest year since 1994, but the 17th warmest year since 1880. Using the 60-month slope changes (47) would be the 10th warmest. Believe it or not, this would still be consistent with a cooling trend, so hearing “tenth warmest” as an argument for warming would be one of those situations where the saying “there are lies, damn lies, and statistics” comes into play. Use of the 180-month, 240-month, and 300-month slope changes (51, 54, 56) indicate 2008 would be the 9th warmest year on record. Using the 360-month slope changes provides the bizarre trend line that tells us that 2008 will be the warmest on record. This includes a whopping 140.1 anomaly required in March, which just seems very unlikely based on what I’ve seen of the weekly anomaly estimates.