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Inhomogeneities in temperature records deceive long-range dependence estimators

Inhomogeneities in temperature records deceive long-range dependence estimators. Victor Venema Olivier Mestre Henning W. Rust Presentation is based on: Henning Rust, Olivier Mestre, and Victor Venema. Fewer jumps, less memory: homogenized temperature records and long memory

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Inhomogeneities in temperature records deceive long-range dependence estimators

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  1. Inhomogeneities in temperature records deceive long-range dependence estimators Victor Venema Olivier Mestre Henning W. Rust Presentation is based on: Henning Rust, Olivier Mestre, and Victor Venema. Fewer jumps, less memory: homogenized temperature records and long memory Submitted to JGR-Atmospheres

  2. Content • Long range dependence (LRD) • What it is? • Short range dependence • Why is it important • Estimating long range dependence • FARIMA modelling, Fourier analysis • Detrended Fluctuation Analysis (DFA) • The influence of inhomogeneities on LRD • Comparison of raw and homogenised data • Homogenisation produces no artefacts • Validation on artificial data

  3. Autocorrelation function – SRD vs. LRD

  4. Autocorrelation function LRD:  () =  () -α(2-2H),  0.5 < H < 1 Short range dependence (SRD)  () <  ()  e-,  Spectral density LRD: S()  ||-, ||0  = 2H - 1 0 <  < 1 d = H - 0.5 Long range dependence (LRD)

  5. Example long range dependence Demetris Koutsoyiannis, The Hurst phenomenon and fractional Gaussian noise made easy, Hydrological Sciences, 47(4) August 2002.

  6. Uncertainty in trend estimate

  7. Inhomogeneous data and trends • LRD may lead to a higher false alarm rate (FAR) in homogenisation algorithms • Depends on physical cause of LRD • Inhomogeneities can be mistaken for a climate change signal • Inhomogeneities lead to overestimates of LRD • Artificially increase estimates of natural variability • Artificially increase the uncertainty of trend estimates

  8. Inhomogeneous data and LRD • Most people working on LRD do not report whether their data was homogenised • Literature search: 24 articles • 18 gave no information on quality • Two articles: high quality data or selected homogeneous stations • One article partially inhomogeneous • Two articles partially homogenised • One article homogenised

  9. FARIMA - power spectrum

  10. DFA algorithm • Cumulative sum or profile: • Xt is divided in samples of length L • For every sample a linear trend is estimated and subtracted • F(L) is variance of the remaining anomaly

  11. DFA example for one scale Peng C-K, Hausdorff JM, Goldberger AL. Fractal mechanisms in neural control: Human heartbeat and gait dynamics in health and disease. In: Walleczek J, ed. Nonlinear Dynamics, Self-Organization, and Biomedicine. Cambridge: Cambridge University Press, 1999.

  12. DFA spectrum

  13. Problems with DFA • H depends on subjective scaling range • No criterion for goodness of fit for DFA spectrum • Heuristic: no error estimate for H • Not robust against non-stationarities

  14. H-estimates: raw vs. homogenised

  15. Simulation experiment • LRD regional climate data • Added noise to obtain station data • Added inhomogeneities • Caussinus-Mestre to correct • Compared H before and after

  16. FARIMA simulation experiment: original vs. perturbed

  17. FARIMA simulation experiment: original vs. perturbed

  18. DFA simulation experiment: original vs. perturbed

  19. DFA simulation experiment: original vs. homogenised

  20. Conclusions • Inhomogeneities increase estimates of LRD • Studies on LRD should report on homogeneity • As well as other studies on slow cycles, low-frequency variability, etc. • LRD increases uncertainty of trend estimates • As well as other parameters related on slow cycles, low-frequency variability, etc. • DFA is not robust against inhomogeneities • Manuscript: http://www.meteo.uni-bonn.de/ venema/articles/

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