The Analysis of the Global Change using Hurst Re Scaling
S.I.Outcalt : Emeritus Professor of Physical Geography, University of Michigan
Abstract: Three data sets used to document the case for anthropogenic global warming were analyzed using Hurst Rescaling. The analysis indicated that a more likely interpretation of the data is that the observed linear trend in global temperatures is an artifact of regime shifts. The dramatic “hockey stick” trace, which began in 1976 accompanied by a major transition in the Pacific Decadal Oscillation, ends at the onset of the 21st Century and might be better termed the modern warming regime. This regime was replaced by a pronounced cooling regime. These observations attenuate the demonic interpenetration of the linear trend in the historic global temperature data.
Introduction: Hurst Re Scaling or Integral Inflection Analysis is a simple operation which is used to detect regime transitions in serial data. Although it is seldom employed the technique of has been demonstrated to be extremely effective in the detection of regime shifts in serial data [Outcalt et.al.(1997), Runnalls and Oke (2006)]. The method is named in honor of H.E.Hurst, who used the extremes of the integral of deviations from the record mean of serial data to analyze persistence in time series. The method is based on the assumption that most natural data is composed of regimes ranging in scale for geologic epochs to turbulence. In this world view nature has a strongly fractal structure with serial regimes covering the entire range of space and time.
Implementation: Dplot software uses a variety of rapid operators to analyze serial data. A small group of operators are used in Hurst Re Scaling Analysis. These operators are the calculation of the integral trace or the cumulative deviations from the record mean, mean value subtraction, linear trend removal and normalization. The analysis begins with the subtraction of the record mean followed by integration. Inflections in the integral trace signal regime transitions. If several variables are used in the analysis they may be normalized and plotted on the same graph. Another informative integral trace can be produced by removing the linear trend before integration. This operation phase shifts the initial inflections but signals subsets of record that might be parsed and analyzed using simple integration after mean subtraction. Even in the case where the data is in deviations from the record mean initial mean subtraction ensures integral closure. Trend removal on integral traces before normalization insures that the normalized integral traces cover the entire range of zero to unity.
The Test Signal: Three sets GHCN, HadCRUT3 and NASA were used as test signals. These data signals are remarkably similar and are displayed as figure 1.
Figure 1. The three record used as a test signals.
Integration: Integral traces were calculated from the test signals. Two integrations were performed. The first integration was done after a second mean subtraction to assure integral closure and the second followed trend removal and mean subtraction. These traces are displayed as Figure 2.
Figure 2. The initial integration (open symbols) displayed strong inflections near the the major global climate transitions in 1936 and 1976, which were accompanied by major ocean circulation transitions. The integrals of departures from the linear trend (filled symbols) indicate a major transition in the last decade of the 20th Century.
Figure 2 suggests that the period from 1976 until the end of the record should be parsed for detailed analysis. The traces of the 1976-2008 segment of the record were integrated and normalized after mean subtraction. The traces resulting from these operations is displayed as Figure 3.
Figure 3. These traces indicate that the modern warming regime ended in 1997.
Figure 3 indicates that a major transition occurred at the onset of the 21st Century. The global thermal response to this transition is somewhat muted. An inspection of the data displayed as Figure 1 shows only slight downturns near the end of the record in 2008. However, ground temperature data collected by Janke(2011) and analyzed by the author indicates a major shift from a warming to cooling regime in the early years of the 21st Century. This ground temperature data is based on the mean annual temperatures calculated from probes at 1 m intervals in three 6 m boreholes along Trail Ridge Road in Rocky Mountain Park, Colorado. The annual mean temperatures were calculated from hourly observations and are therefore extremely robust. The data were collected in mountain tundra terrain above treeline along an east / west ridge. The data from these boreholes is displayed as Figure 4.
Figure 4. Mean annual temperature profiles from Trail Ridge. The temperature inflection in BH2 profile is an artifact of the 1976 onset of modern warming. The Terzaghi equation makes it possible to estimate the overlying inflection dates. The upper inflections in all three boreholes indicate a dramatic transition from a warming to cooling regime in the early years of the 21st Century.
Figure 4 indicates a dramatic shift in the climate at Trail Ridge. Linear extrapolation if BH2 profile below 4 m to the surface yields an extreme minimal estimate of a 2C surface temperature drop. As disturbance profiles are parabolic [Terzaghi (1970)] the actual drop in surface temperature over the first decade of the 21st Century is probably more than double the conservative estimate in the realm of 4-6 C.
Conclusion: This short analysis indicates that an alternate model of climate change based on serial regime transitions rather than anthropogenic global warming is consistent with the results of the Hurst Re Scaling analysis.
References:
Janke,J.R.(2011) personal communication.
Outcalt,S.I., Hinkel, K.M.,Meyer,E . and Brazel,A.J.(1997) The application of Hurst rescaling to serial geophysical data. Geographical Analysis 29, 72-87.
Runnalls,K.E. and Oke,T.R.(2006) A technique to detect micro-climatic inhomogeneities in historical records of screen-level air temperature. Journal of Climate 19: 959-978.
Terzaghi,K (1970) Permafrost, J. Boston. Soc. Civil Eng. 39(1): 319-368
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Tom Curtis,
Oh, quit sniveling about “censorship”. They don’t censor here. If you call the site owner ‘dishonest’, do you really expect kid glove treatment from the moderators? And you’re “abused”? Grow up, crybaby.
Tom Curtis’ censored comment started out with “Contrary to Gneiss…”
But in my contrary way let me try to pass along his main point anyway, in gentler terms. Basically, Outcalt’s post is transparently wrong, as anyone who thought about his arithmetic has figured out by now. Why the post was written and published without noticing that is a fair question. How Outcalt and Anthony respond now will shed light on the answers.
[REPLY: Anthony publishes lots of stuff, not all of which he agrees with. It is simply “interesting”. WUWT commenters are fully capable of critiqueing the work and have done so. Anthony is not a co-author on this article and is not required to justify or explain anything, especially to anonymous individuals using anonymous proxy servers. Check site policy regarding that. -REP]
@Gneiss (July 4, 2012 at 9:07 pm)
Did you not notice that I said the analysis was done wrong & misinterpreted?
One point where you are wrong is on randomness. You’re not thinking deeply enough about fundamentals underpinning inference. Specifically you are not being careful enough with stat inference model assumption integrity.
Regards.
With respect to figure 3, perhaps I am misinterpreting the analysis here, but I believe that any monotonically increasing time series, analyzed in this fashion, will produce an integrated sum with a decreasing, linear regime followed by a faster-than-linear increasing regime. Let’s take a mean-subtracted time series y(t) – . The cumulative sum is the integral of these terms. It is dominated by the integral of the negative term at short times and by the integral of the positive term at long times. If y(t) is linear, the latter part of the integrated time series will be quadratic, if y(t) is exponential, the latter part of the integrated time series will be exponential, etc. However, growth rates are small relative to the absolute level of the signal and the timescale in this 1975-now plot. The linear->transition->faster-than-linear behavior is obvious for the longer time series in the open symbols in Fig. 2. You can also look at any other data set that’s more or less described by exponential growth (population, some country’s GDP, stock market indices) and see the same thing.
Editing the above post because brackets in comments do not work here:
With respect to figure 3, perhaps I am misinterpreting the analysis here, but I believe that any monotonically increasing time series, analyzed in this fashion, will produce an integrated sum with a decreasing, linear regime followed by a faster-than-linear increasing regime. Let’s take a mean-subtracted time series y(t) – mean(y). The cumulative sum is the integral of these terms. It is dominated by the integral of the negative term at short times and by the integral of the positive term at long times. If y(t) is linear, the latter part of the integrated time series will be quadratic, if y(t) is exponential, the latter part of the integrated time series will be exponential, etc. However, growth rates are small relative to the absolute level of the signal and the timescale in this 1975-now plot. The linear->transition->faster-than-linear behavior is obvious for the longer time series in the open symbols in Fig. 2. You can also look at any other data set that’s more or less described by exponential growth (population, some country’s GDP, stock market indices) and see the same thing.
Moderator REP: I did ask a question about the science in this post. Yet you snipped it.
I asked Anthony Watts, or anyone else for that matter, to define and explain the following critical finding in the abstract of this “paper” by Outcalt:
“This regime was replaced by a pronounced cooling regime. These observations attenuate the demonic interpenetration of the linear trend in the historic global temperature data.”
I tried to learn what WUWT is telling us. I googled the term demonic interpenetration, and got some strange results; in some cases the term “demonic analogy of interpenetration” is used.
Lets hear from the WUWT regulars. What does this important conclusion actually mean?
[REPLY: I’m not going to bandy words with you or edit out the bits that violate policy. Violate policy and the whole thing will get snipped. You don’t like policy? Be as upset as you wish. -REP]
Moderator: According to the moderation policy, “Most people wouldn’t be rude, loud, or insulting in somebody’s home or office, I ask for the same level of civility and courtesy here.” With this policy in mind, please consider the following comment:
“Smokey says:
July 5, 2012 at 4:21 am
Tom Curtis,
Oh, quit sniveling about “censorship”. They don’t censor here. If you call the site owner ‘dishonest’, do you really expect kid glove treatment from the moderators? And you’re “abused”? Grow up, crybaby.
[REPLY: There is nothing incorrect or wrong about Smokey’s comment. It is not rude to comment on someone’s rude behavior. -REP]
Paul Vaughan writes,
“Did you not notice that I said the analysis was done wrong & misinterpreted?”
Yes, that’s pretty vague. The analysis turns out to be meaningless, but earlier you defended it. And did you not notice that I said Tamino’s objection was not due to his preferring a different method for locating change points, as you claimed in your next sentence? Tamino’s objection was due to Outcalt’s method not being a method for locating change points at all.
“You’re not thinking deeply enough about fundamentals underpinning inference. Specifically you are not being careful enough with stat inference model assumption integrity.”
Specifically where did I say something wrong about stat inference model assumption integrity? Feel free to propose your own test for how cumulative-sum-of-deviation plots can be used to tell a true regime shift from the U-shape with squiggles that will always result when you apply Outcalt’s method to a straight trend with noise. Then show that your method works, as Tamino has very clearly and simply shown that Outcalt’s approach does not.
@Gneiss – A good test of this method is to take a data series that (1) increases in the long run, (2) has little noise compared to the temperature record and (3) changes trend for periods of several years. One such time series is the annual average of the Dow Jones Industrial Average. If this is a reasonable method of visually detecting changes in trend, you should obviously be able to pick out the rapid growth rate during the 90s followed by the multi-year decline of the tech bubble.
Over at the “other site”, arch stanton clearly mis-interpreted Dr. Outcalt’s key finding in this paper,
But never fear WUWT regulars, I was there to defend this site’s integrity:
arch stanton | July 5, 2012 at 4:15 pm | Reply
Clearly, “demonic interpretation” is a legal term, even if “dist” isn’t. (but don’t use it in regards to Smokey)…
Zinfan94 | July 5, 2012 at 5:02 pm | Reply
arch, please be more careful with your terminology.
A “demonic interpretation” would mean that the demons have caused a misinterpretation of the data. OTOH, a “demonic interpenetration” indicates that demons have actually changed the system creating the data, or changed the data measurement system. And according to sources, the process they use involves the demonic interpenetration of human spirits, causing the humans to act under the influence of the demons.
In short, in the Outcalt theory publicized by Anthony Watts, demons invading human spirits cause the system changes that result in the linear trend of rising temperatures.
And you know what? For once, they just might be right!
With regard to “demonic interpenetration”, the suggestion is that using a linear trend to interpret the historical temperature record is a demonic activity. IMO no other interpretation makes sense. Of course, that is not at all abusive of the people who do in fact apply a linear trend to the record.
The power of holding two contradictory beliefs in one’s mind simultaneously, and accepting both of them… To tell deliberate lies while genuinely believing in them, to forget any fact that has become inconvenient, and then, when it becomes necessary again, to draw it back from oblivion for just as long as it is needed, to deny the existence of objective reality and all the while to take account of the reality which one denies – all this is indispensably necessary. Even in using the word doublethink it is necessary to exercise doublethink. For by using the word one admits that one is tampering with reality; by a fresh act of doublethink one erases this knowledge; and so on indefinitely, with the lie always one leap ahead of the truth.
Gneiss (July 5, 2012 at 8:15 am)
“The analysis turns out to be meaningless, but earlier you defended it.”
I’ve not defended this particular analysis. I’ve defended the direction of attention towards data exploration & methods (as opposed to tabloid-style politics, for obvious contrast).
The useful content at WUWT often comes out in comments, not articles. Integrity of an article is not necessary to generate deeply insightful comments. The occasion to learn & the stimulation to further explore is what matters most.
My commentary about Tamino’s preference for other methods was based on articles he has written in the past. From your comments I infer that he has now posted commentary on this WUWT thread. I will take a look.
Gneiss, I have taken a look at Tamino’s “Sum Fun”. Nothing has arisen in that thread that wasn’t already obvious. Outcalt fooled few, if any, at either site, but we all had occasion to delve into data exploration & methods (which is a welcome, refreshing change from politics, which I almost always skip). Many commenters at Tamino’s appear to falsely assume uniform composition of the WUWT readership. We are actually a very diverse bunch, associated only in the loosest sense. Nature is beautiful & fascinating. Politics? Not so much… Cheers to All.
KR and others: The idea of random noise/white noise is over stated. So called noise is mostly part of the signal.For so called global climate mean temps, you cannot just dismiss data as noise. P values for statistical significance is not nearly as useful as the public is lead to believe.
For example see here: http://wmbriggs.com/blog/?p=4024
Also of interest this 1997 date closely coincides with data showing global warming went flat after 1998.
There is also significant data on climate regime shifts that coincide for the year 1997 among other years. Looking it up is easy.
The real issue here is the completely falsifying of the Hockey Stick, with terrible statistics like where data is smoothed and then re-input for more analysis instead of independent non-smoothed data being used for comparison. for example see here:
http://wmbriggs.com/blog/?p=195
Then there is the misrepresentation of heat flow, internal energy states, the greenhouse effect and temperature as described here:
http://www.biocab.org/Heat.html
and here:
fect
http://slayingtheskydragon.com/en/blog/192-that-bogus-greenhouse-gas-whatchamacallit-efffect
Now while more statistical studies looking at these results maybe warranted, the fact that you can create parabola with so called “noise” does not excuse smoothing data and using that smoothed data as an input where it should not be.
Oh and the humor of such commentary from here: http://wottsupwiththat.com/ on my comment to Anthony and the same quoting from Tamino is not lost to me. For one there is a parabola shape there to be sure and of course Anthony may or may not agree with the paper by Outcalt, however, the paper uses a valid method and arrives at a scientifically defensible conclusion. Picking at lack of noise adjustments or questions about p values does not eliminate this paper from due consideration. And it is also true not everyone here who blogs at wattupwiththat buys into it either, but it is still superior to Tamino’s analysis and Mann’s reconstructions.
Another point of irony is that I ended up being what many would term a “denialist” byt studying the science and defending it among many blogs, this one included. As I saw how the pro AGW blogs were censoring and deleting many well written and evidenced counter arguments and even arguing with me when I would not say the sky was falling, I looked deeper into the data and statistical analysis. Outcalt uses a parsimonious form of analysis with greater accuracy than what has been seen from the mainstream climate establishment. I stand by my remarks that Hurst is a good choice and this will go over Tamino’s head. Interestingly enough over at “Open Mind” many posters are claiming Anthony would not publish their posts, but none of my responses to Tamino’s quote was allowed until the relatively innocuous comment of mine was allowed: “still overhead”.
In this effect, then whether Anthony has a different view or not, Tamino attempted to shoot down the paper without proper consideration. Interestingly enough this paper coincides well with long term paleo-climate temperature records in terms of the curves which also form, eeek gasp… parabolas!
jcbmack – You appear to be discussing something other than my comment. The test of an analysis method against a known signal, synthetic data (which can include noise), resulting in conclusions that do not match the known signal indicates a bad analysis method. No more, no less.
P-values, time periods too short for any statistical significance, and the “Slaying the Dragon” nonsense (which Watts and Fred Singer have both noted is not even worth discussing) are red herrings in this discussion. Outcault’s test produces false conclusions from synthetic data, and can be expected to do the same with observations. It’s a bad method.
KR I addressed your comment. There is plenty of data showing regime shifts and weather patterns and climate shifts indicating support for Outcalt’s paper. Furthermore the hockey stick has 0 validity. The method of Outcalt is a good one. The only thing that maybe good is another analysis by Outcalt with a longer time period. Briggs is a good statistician to read though he does not consider the hockey stick fraud but full of un- admitted errors. If you were to look at research on climate regime shifts and there are plenty to choose from you will find either a cooling from 1997 or a natural warming signal from 1997-1998 and then a drop off in global temps. We each have our own minds, so it should not surprise you if we do not all agree with each other within the skeptical community.