Stuff for CM92.HTML

Hurst and Spectral analysis
New datasets will be added to this site as soon as they will be available

cm92.html;  cm93.html;   cm94.html;   dm42.html (The whole story in English)   cm95 site (Italian Precip)

References: (not available on the net)

  • Koutsoyiannis, 2002 ; Koutsoyiannis, 2003; Koutsoyiannis, 2006 ; Mureika's 2015 WUWT article (Persistence).
  • Koutsoyiannis, 2019 Koutsoyiannis D.: Time’s arrow in stochastic characterization and simulation of atmospheric and hydrological processes , Hydrological Sciences Journal , 64, 1013-1037, 2019.
  • ===> Koutsoyiannis & Kundzewicz, 2020 Koutsoyiannis D., Kundzewicz Z.W.: Atmospheric Temperature and CO2: Hen-Or-Egg Causality? (Version 1) , Sci, 2-72, 1-27, 2020. doi:10.3390/sci2030072
  • Ludescher et al., 2020 Josef Ludescher, Armin Bunde, Ulf Büntgen, Hans Joachim Schellnhuber: Setting the tree‑ring record straight , Clim.Dyn. , 2020.
  • Ruzmaikin et al., 2006 Alexander Ruzmaikin, Joan Feynman and Yuk L. Yun Is solar variability reflected in the Nile River? , JGR, III, D21114, 2006. Also, at ResearchGate:
  • Alvarez-Ramirez et al.,2008. Jose Alvarez-Ramirez, Juan C. Echeverria, Eduardo Rodriguez: Performance of a high-dimensional R/S method for Hurst exponent estimation, Physica A, 387, 6452-6462, 2008. (Scheme for R/S computing. Added on Dec 10, 2020)
    ===>Added Mar 17, 2022:
  • Papalexiou et al., 2020 Simon Michael Papalexiou, Chandra Rupa Rajulapati, Martyn P. Clark, Flavio Lehner: Robustness of CMIP6 Historical Global Mean Temperature Simulations: Trends, Long-Term Persistence, Autocorrelation, and Distributional Shape , Earth's Future, 8:10, e2020EF001667, 2020, See also S.I. at DOI.

    Koutsoyiannis', 2003 paper.
    Please note that eq.(5) refers to an "aggregated process", what our processes may not be; so use the H-value only as a simple approach to the value the Hurst exponent really owns. Koutsoyiannis does not make use of this method, so caution is needed in too sharp statements about the H value!
    acf(1)=H(2H-1) or eq.(5) when lag=1.
    Please note that the auto-correlation function acf assumes values only between 0 and 1, so if acf(1) has negative value the computed H exponent is given as NaN (not a number).
    We can consider the negative acf value as a fluctation around zero and assign zero-value to it: in such a case the Hurst exponent is 0.5 and identifies a not-autocorrelated series which can be managed with normal statistics.
    Plots, Figures        
    NOAA Yearly 2017 (pdf) (png) and MEM Spectrum
    NOAA Yearly Diff (pdf) (png) and MEM Spectrum 2017
    NOAA Yearly ACF (pdf) (png) Hobs=0.975; Hdiff=0.52017
    NOAA17 Comp (txt) Spectral Comparison
    Victoria Obs (pdf) (png) and LOMB Spectrum
    Victoria Diff (pdf) (png) and LOMB Spectrum
    Victoria Deriv (pdf) (png) and LOMB Spectrum
    Victoria ACF (pdf) (png) Ho=0.962; Hd=0.638; Hder=0.781
    Victoria Comp (txt) Spectral Comparison
    NOAA monthly 1712 Obs (pdf) (png) and MEM Spectrum
    NOAA monthly 1712 Diff (pdf) (png) and MEM Spectrum
    NOAA monthly ACF both (pdf) (png) Ho=0.983 ; Hd=0.5
    NOAA Monthly Comp (txt) Spectral Comparison
    NILE Obs (pdf) (png) 622-1469 CE
    NILE Diff (pdf) (png)
    NILE ACF (pdf) (png) Ho=0.833; Hdiff=0.5
    Nile Comp (txt) Spectral Comparison
    TPW-HC4 Obs (pdf) (png) 1988-2017 CE
    TPW Obs (pdf) (png)
    TPW Diff (pdf) (png)
    TPW ACF (pdf) (png) Hobs=0.968; Hdiff=0.5
    TPW Comp (txt) Spectral Comparison
    OHC Obs (pdf) (png) 0-700m
    OHC Diff (pdf) (png) 0-700m
    OHC ACF (pdf) (png) Hobs=0.970; Hdiff=0.468
    OHC Comp (txt) Spectral Comparison
    Dendro Obs (pdf) (png) russ243
    Dendro Diff (pdf) (png) russ243
    Dendro ACF (pdf) (png) Hobs=0.809; Hdiff=0.467
    Dendro Comp (txt) Spectral Comparison
    Kinder Obs (pdf) (png) Kinderlinskaya Holocene
    Kinder Diff (pdf) (png) Kinder.. cave
    Kinder ACF (pdf) (png) Hobs=0.995; Hdiff=0.484
    Kinder Comp (txt) Spectral Comparison
    Stockholm Obs (pdf) (png) Longest Tide Gauge in the World
    Stockholm Deriv (pdf) (png) 1774-2000
    Stockholm ACF (pdf) (png) Hobs=0.950; Hder=0.523
    Stockholm Comp (txt) Spectral Comparison
    Stock psmsl Obs (pdf) (png) PSMSL Stockholm1889-2016
    Stock psmsl Diff (pdf) (png) 1889-2016
    Stock psmsl ACF (pdf) (png) Hobs=0.947; Hder=0.531
    Stock psmsl Comp (txt) Spectral Comparison
    CSIRO Sea Level (pdf) (png) 1880-2009
    CSIRO Sea Level Der (pdf) (png) linear fit 1880-2009
    Csiro ACF (pdf) (png)
    Csiro Comp (txt) Spectral Comparison
    ---- -------------
    NOAA Yearly 2017 .datObservedEarth+Ocean
    NOAA Yearly 2017 ACF .outHobs=0.975
    NOAA Yearly MEM .outSpectrum
    NOAA Yearly 2017 Diff .outDifferences
    NOAA Yearly 2017 Diff ACF .outHdiff=0.5
    NOAA Yearly Diff MEM .outSpectrum
    Lake Victoria Level .txt1896-2005
    Victoria Level LOMB .outLOMB spectrum
    Victoria Level ACF .outH=0.962
    Victoria diff (out)
    Victoria ACF diff (out) H=0.638
    Victoria LOMB diff (out)
    Victoria deriv (out)
    Victoria ACF deriv (out) H=0.781
    Victoria LOMB deriv (out)
    NOAA o1712 (dat)
    NOAA o1712 ACF (out) H=0.983
    NOAA o1712 MEM (out)
    NOAA h1712 (out)
    NOAA h1712 ACF (out) H=0.5
    NOAA h1712 MEM (out)
    NILE Obs (txt)
    NILE Obs ACF (out) Hobs=0.833
    NILE Obs MEM (txt)
    NILE Diff (txt)
    NILE Diff ACF (out) Hdiff=0.5
    NILE Diff MEM (out)
    TPW Obs (txt)
    TPW Obs ACF (out) Hobs=0.968
    TPW Obs MEM (out)
    TPW Diff (out)
    TPW Diff ACF (out) Hdiff=0.5
    TPW Diff MEM (out)
    OHC Obs (dat)
    OHC Obs ACF (out) Hdiff=0.970
    OHC Obs MEM (out)
    OHC Obs (dat)
    OHC Diff (txt)
    OHC Diff ACF (out) Hdiff=0.469
    OHC Diff MEM (out)
    Dendro Obs (out)
    Dendro Obs ACF (out) Hobs=0.809
    Dendro Obs MEM (out)
    Dendro Diff (txt)
    Dendro Diff ACF (out) Hdiff=0.467
    Dendro Diff MEM (out)
    Kinder Obs (txt)
    Kinder Obs ACF (out) Hobs=0.995
    Kinder Obs LOMB (out)
    Kinder Diff (txt)
    Kinder Diff ACF (out) Hdiff=0.484
    Kinder Diff LOMB (out)
    Stockholm Obs (txt) 1774-2000
    Stockholm Obs ACF (out) Hobs=0.950
    Stockholm Obs LOMB (out)
    Stockholm Deriv (txt)
    Stockholm Deriv ACF (out) Hder=0.523
    Stockholm Deriv LOMB (out)
    Stock psmsl Obs (txt) PSMSL1889-2016
    Stock psmsl Obs ACF (out) Hobs=0.947
    Stock psmsl Obs MEM (out)
    Stock psmsl Diff (out)
    Stock psmsl Diff ACF (out) Hder=0.531
    CSIRO SeaLevel .txt1880-2009
    CSIRO MEM .out1880-2009
    CSIRO Der .out1880-2009
    CSIRO Der MEM .out1880-2009
    CSIRO ACF .txt1880-2009H=0.989
    CSIRO Der ACF .txt1880-2009H=0.671

    victoria.bon, orig-17.bon, diff-17.bon, o1712.bon, h1712.bon, noaa-17-acf.bon,
    tot-acf.bon, fcorr.bon, acorr.bon,
    nile.bon, hnile.bon, acf-nile.bon,
    tpw-hc4.bon, tpw.bon, tpwh.bon, tpw-acf.bon,
    ohco.bon, ohch.bon, ohc-acf.bon,
    mmo.bon, mmh.bon, mm-acf.bon,
    kinder.bon, kinderh.bon, kinder-acf.bon,
    stock-yr.bon, stock-yrh.bon, stock-yr-acf.bon,
    stock-anno.bon, stock-anno-acf.bon, stock-anno-mem.bon, stock-annoh-mem.bon,
    level.bon, level-der.bon,

    Page Written: February 5, 2018,        Last Updated: