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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Indeed, I expect the MSM and the AGW folks to be in de Nile about consequences of a “Hurst Shuffe”.
P. Solar & Paul Vaughan
Thanks for your comments.
It is appreciated.
Glad you weighed in Steve. I was wondering if you’d tried this math before. Do you know if Lucia has also explored using Hurst rescaling?
Agreed. Exploring math challenges always swallow more time, as the intellectual puzzle unfolds, than one ever intended initially. I’ve never played with this series before, it’s like opening a hidden puzzle door. I’ll have to add it to my list of math to play with. Right now, I’m playing with lens formulas/physics. That is, refractive/reflective light using multiple elements and coatings comprising telescope optics.
Besides worrying about man’s GHG bank account, any insights on the use of Hurst rescaling on temperature data?
Doesnt this method make more sense then complex gcm’s?
Once we can accept the regimes, then measure and define their slopes; we can then move on to defining the regime change mechanism. Would seem to take a lot of the noise and churn out of models.
An interesting topic, which seems to be causing a lot of comment. I find it more than just interesting because I’ve been using somewhat related methods for about 18 years, I’d guess, specifically to examine climate time series for hints of discontinuities. My general conclusion is that climate data seem to be to a large extent periods of very little enduring change punctuated by short periods of very rapid change. These changes occur in both senses but over long periods have tended to be mainly increases. The notion that climate data have any simple relationship to the almost ubiquitous linear model when looked at over periods of many years is quite preposterous. Simple plotting of the cusum (relative to the period mean) over a hundred or so years, either as annual means or of “deseasonalised” values, instantly shows the folly of placing any trust in the analytical value of a linear fit (or “de-trending”) for such a period of time. Cusum plots instantly reveal the general behaviour of a series and suggest periods for speicial study, either because the are times of sudden change or because the can identify periods when change was effectively absent. Such periods are of course linear. If the linear fits that appear regularly in the literature (“scientific” and the blogosphere) also provided confidence intervals at some useful probability level those who believe in them would soon realise how little useful information they contain. When I compute a “trend”, linear or quadratic, I always display the confidence intervals for a mean value and a single future observation at a given value of the x variable, which are pairs of hyperbolae for linear models or more complex forms for higher order models. (The software I use does cannot compute approximate confidence intervals for non-linear models.) Note that there is an inherent assumption of a very approximately normal distribution for the underlying data – clearly not correct but I think adequate for the approximate nature of the science and observations.
I’ll look at the data from http://www.esrl.noaa.gov/psd/data/correlation/amon.us.long.data, which seem to be monthly values (as referred to by Vukcevic) in his reply to P.Solar to see what I can find.
Unfortunately I can’t post graphs due to lack of computer know-how.
Robin
S.I. Outcalt writes:
“Figure 3. These traces indicate that the modern warming regime ended in 1997.”
No, they do not. The U-shaped traces are an artifact of the method. You see the same “regime shifts” in random data analyzed the same way, as Tamino noticed.
Warming ended in 1997? Before the hottest months, years and decade in any of the global temperature records? That claim should have been a warning the analysis was wrong.
This makes a lot of sense. Since 9 of the 10 warmest years in the global temperature record have occured since 1997, this means that the earth is now cooling. If the next El Nino year brings a new global high temperature record, that must mean that the earlth is quickly cooling. In my region, we have had 1.2 inches of rain since May 1. Perhaps the corn is dying from too much water!
Several years ago, Demetris Koutsoyiannis, and his papers were mentioned on “Climate Audit”.
I think this paper gives a pretty clear description of the “Hurst” factor.
http://itia.ntua.gr/getfile/849/2/documents/2008EGU_HurstClimatePr.pdf
[snip. Labeling our host as being dishonest gets you snipped. My decision alone, Anthony had nothing to do with it. ~dbs, mod.]
James Sexton says:
July 3, 2012 at 9:35 pm
In fact, the global temps this year have been well below the temps of 2010.
Very true. For more detail:
2012 in Perspective so far on Five Data Sets
2012 started off rather cold but has warmed up since then. So the present rank may not be the most meaningful number. Therefore I will also give the ranking by assuming the latest month’s anomaly will continue for the rest of the year.
With the UAH anomaly for May at 0.289, the average for the first five months of the year is (-0.089 -0.111 + 0.111 + 0.299 + 0.289)/5 = 0.0998. If the average stayed this way for the rest of the year, its ranking would be 12th. This compares with the anomaly in 2011 at 0.153 to rank it 9th for that year. 1998 was the warmest at 0.428. The highest ever monthly anomalies were in February and April of 1998 when it reached 0.66. If the May anomaly continued for the rest of the year, 2012 would end up 5th.
With the GISS anomaly for May at 0.65, the average for the first five months of the year is (0.34 + 0.41 + 0.47 + 0.55 + 0.65)/5 = 0.484. If the average stayed this way for the rest of the year, its ranking would be 10th. This compares with the anomaly in 2011 at 0.514 to rank it 9th for that year. 2010 was the warmest at 0.63. The highest ever monthly anomalies were in March of 2002 and January of 2007 when it reached 0.88. If the May anomaly continued for the rest of the year, 2012 would end up 4th.
With the Hadcrut3 anomaly for May at 0.474, the average for the first five months of the year is (0.217 + 0.194 + 0.305 + 0.482 + 0.474)/5 = 0.3344. This is about the same as the anomaly in 2011 which was at 0.34 to rank it 12th for that year. 1998 was the warmest at 0.548. The highest ever monthly anomaly was in February of 1998 when it reached 0.756. If the May anomaly continued for the rest of the year, 2012 would end up 9th.
With the sea surface anomaly for April at 0.292, the average for the first four months of the year is (0.203 + 0.230 + 0.242 + 0.292)/4 = 0.242. If the average stayed this way for the rest of the year, its ranking would be 14th. This compares with the anomaly in 2011 at 0.273 to rank it 12th for that year. 1998 was the warmest at 0.451. The highest ever monthly anomaly was in August of 1998 when it reached 0.555. If the April anomaly continued for the rest of the year, 2012 would end up 12th.
With the RSS anomaly for May at 0.233, the average for the first five months of the year is (-0.058 -0.121 + 0.074 + 0.333 + 0.233)/5 = 0.0922. If the average stayed this way for the rest of the year, its ranking would be 16th. This compares with the anomaly in 2011 at 0.147 to rank it 12th for that year. 1998 was the warmest at 0.55. The highest ever monthly anomaly was in April of 1998 when it reached 0.857. If the May anomaly continued for the rest of the year, 2012 would end up 11th.
So on all five of the above data sets, for their latest anomaly average, the 2012 average so far is close to that of 2011. If present trends continue, 2012 will be warmer than 2011, but a record is out of reach on all sets.
Somebody need to tell the world’s oceans about the regime change – their heating continues unabated (http://imageshack.us/photo/my-images/338/ohc02000mjune2012.jpg/). And then there’s land ice, the melting of which is accelerating (http://climatesignals.org/2010/10/greenland-ice-now-melting-twice-as-fast/). Oh, and I forgot sea ice – extent, area, and volume are steadily decreasing. Did I mention the thawing of the tundra? The entire climate system is warming, regime change notwithstanding.
Gneiss (July 4, 2012 at 2:41 pm) wrote:
“S.I. Outcalt writes:
“Figure 3. These traces indicate that the modern warming regime ended in 1997.”
No, they do not. The U-shaped traces are an artifact of the method. You see the same “regime shifts” in random data analyzed the same way, as Tamino noticed.
Warming ended in 1997? Before the hottest months, years and decade in any of the global temperature records? That claim should have been a warning the analysis was wrong.”
—–
The author’s analysis & interpretation are messed up. The utility of the article is to get people thinking more about methods. Tamino prefers a different method for locating changepoints. Assumptions of randomness are patently untenable. Regards.
@Robin Edwards (July 4, 2012 at 2:04 pm)
Inference model assumptions don’t hold.
vukcevic (July 4, 2012 at 12:31 pm) wrote:
“P. Solar & Paul Vaughan
Thanks for your comments.
It is appreciated.”
—-
My pleasure vukcevic. I fully support P. Solar’s eminently sensible suggestions. Feel welcome to request my assistance with any of P. Solar’s suggestions either publicly or privately at any time. Implementation is not difficult. Best Regards.
If you run a cumulative sum (the correct name for this analysis technique) on a zero centered linear trend with noise, you will see a parabolic curve with a bend near the middle. Regardless of noise level, regardless of the steepness of the trend, even regardless of the length of the data set – you get a parabola bending somewhere near the middle of that trend (near where it crosses zero), with some variations as per the noise. Not regime changes at all – just the outcome of cumulative sums on a centered trend plus noise.
Tamino has described this in his latest post (http://tamino.wordpress.com/2012/07/04/sum-fun/), and multiple folks have chimed in with their own random noise/linear trend graphs reproducing Outcalt’s graphs. Whether you care to look or not, this is a horrible piece of analysis on Outcalt’s part. Cumulative sums can be tricky, and the appropriate care was not taken here.
Owen says:
July 4, 2012 at 7:01 pm
Somebody need to tell the world’s oceans about the regime change – their heating continues unabated
You show a positive slope for 0-2000 m from 2005 on. However the sea surface shows a negative slope from 2005 on as shown below. How do you reconcile the difference?
http://www.woodfortrees.org/plot/hadsst2gl/from:2005/plot/hadsst2gl/from:2005/trend
The slope from 2005 is -0.00672523 per year.
Furthermore, if the heat is going into the deep ocean somehow instead of warming the surface, then what are we worried about? As long as the sea surface is cooling, then hurricanes cannot get worse since there is less energy for them. As well, since the surface temperatures are not increasing, why should we care if the deep ocean gets 0.1 C warmer?
Paul Vaughan writes,
“Tamino prefers a different method for locating changepoints.”
That is true, but that’s not Tamino’s objection. The far larger problem is that Outcalt’s method is no method at all for this purpose. It will find a U-shape parabola inflected in the middle (i.e., the mid-90s) for any line with a positive slope. It will find an inverted-U inflected in the middle for any line with a negative slope. If you take a line with a positive slope and add noise, that makes a lumpy U exactly like Outcalt’s key figure above. So that lumpy U is not evidence of a regime shift in 1997, it is simply an artifact.
“Assumptions of randomness are patently untenable.”
No one assumed randomness. What statistics can do is test whether imagined patterns are different from random. Outcalt’s extraordinary claim that “the modern warming regime ended in 1997” fails this test in a very basic way.
Gneiss says:
July 4, 2012 at 2:41 pm
Warming ended in 1997?
Excellent point! Here are the specific ranks for 1997 according to five different data sets: GISS-13th, Hadcrut3-11th, RSS-14th, UAH- 20th, Hadsst2-10th.
However it is possible to draw graphs from 1997 for three of the data sets showing essentially zero slope for over 15 years as per the details below. Just focus on #4, #5 and #6 below.
Can it be said the warming ended because we can get slopes of 0 from 1997 on?
On all data sets, the different times for a slope that is flat for all practical purposes range from 10 years and 8 months to 15 years and 7 months. Following is the longest period of time (above 10 years) where each of the data sets is more or less flat. (For any positive slope, the exponent is no larger than 10^-5, except UAH which was 0.00103655 per year or 0.10/century, so while it is not significant, it could be questioned whether it can be considered to be flat.)
1. UAH: since October 2001 or 10 years, 8 months (goes to May)
2. GISS: since May 2001 or 11 years, 1 month (goes to May)
3. Combination of the above 4: since October 2000 or 11 years, 6 months (goes to March)
4. HadCrut3: since January 1997 or 15 years, 3 months (goes to March)
5. Sea surface temperatures: since January 1997 or 15 years, 4 months (goes to April)
6. RSS: since November 1996 or 15 years, 7 months (goes to May)
7. Hadcrut4: since December 2000 or 11 years, 6 months (goes to May using GISS. See below.)
See the graph below to show it all for #1 to #6.
http://www.woodfortrees.org/plot/hadcrut3gl/from:1997/trend/plot/gistemp/from:2001.33/trend/plot/rss/from:1996.83/trend/plot/wti/from:2000.75/trend/plot/hadsst2gl/from:1997/trend/plot/uah/from:2001.75/trend
For #7: Hadcrut4 only goes to December 2010 so what I did was get the slope of GISS from December 2000 to the end of December 2010. Then I got the slope of GISS from December 2000 to the present. The DIFFERENCE in slope was that the slope was 0.0046 lower for the total period. The positive slope for Hadcrut4 was 0.0041 from December 2000. So IF Hadcrut4 were totally up to date, and IF it then were to trend like GISS, I conclude it would show no slope for at least 11 years and 6 months going back to December 2000. (By the way, doing the same thing with Hadcrut3 gives the same end result, but GISS comes out much sooner each month.) See:
http://www.woodfortrees.org/plot/hadcrut4gl/from:2000/to/plot/hadcrut4gl/from:2000.9/trend/plot/gistemp/from:2000/plot/gistemp/from:2000.9/to:2011/trend/plot/gistemp/from:2000.9/trend
KR,
you may want to look closer at this paper and an explanation of Hurst coefficients, limitations of noise analysis and how steeply this curve gets indicating a regime change and not just noise creating a parabolic curve. As far as Tamino is concerned, he knows how to apply statistics but he has a habit of overstating the finality of his analyses a particular technique and his results. Clearly the “trend” is not some linear concave up occurrence to be correlated with so called GHG forcings.
Regarding p values and statistical significance, there are numerous limitations to looking at probability of committing a type I or type II error and in such a complex and chaotic system it is better to look at occurrences and relationships using Hurst between time periods.
http://www.stats.ox.ac.uk/~snijders/Encycl_isb203057.pdf
jcbmack: Please explain why any linear rising trend with white noise gives the same basic result as Outcalt. Doesn’t this demonstrate that once again this site has published a post with conclusions that are totally nonsense?
jcbmack – One of the basic, and critical, techniques I use in evaluating an analysis method is to test with an assortment of synthetic data; to see if what goes in comes out in the analysis. Outcault’s work fails this test, as any trending series with random noise produces curves just like the ones he shows, even though there are no regime changes in that synthetic data! Let me restate that for clarity – given synthetic data of known characteristics, Outcault’s analysis method indicates aspects that are not present, that are false conclusions, bad analysis.
In addition, his work is using cumulative sums, not the Hurst exponent (which is used to analyze autocorrelation, not regime shifts), as discussed in http://tamino.wordpress.com/2012/07/04/sum-fun/, which I would suggest you read. Outcault has (perhaps inadvertently?) mislabeled his technique.
Again – the opening post makes conclusions not justified by the analysis.
Moderator: Did you snip the Tom Curtis comment [SNIP: the Tom Curtis comment was snipped for exactly the reason moderator dbs said it was. Insult your host or impugn his integrity, your friendly moderators will snip the comment. Complain about moderation policy, and that, too, will be snipped. Abuse fellow commenters and you will be snipped. Demand that Anthony justify posting an article…. get the picture? Discuss the science or not as you please, but demeaning, snarky comments will be snipped. -REP]
@ferdberple (July 4, 2012 at 5:39 am)
“…Here is a simple proof that says otherwise:
Radiation in = radiation out …”
Are you serious?
You do know the difference between the emission spectrum of a black body with an effective temperature of 5780 K and the emission spectrum of a black body with an average temperature of 288 K? And you do know the absorption spectrum of CO2? Yes? No? And you do know that your blatant over-simplification shows that you don’t know what you are talking about? Yes? No?
Sorry if you are being sarcastic, because I could not tell.
Except of course, if you are a proponent of climate science and are abused by the fake skeptics that frequent this site, you will not find their abuse snipped. But long live the hypocritical censorship at WUWT