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.
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