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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 - PowerPoint PPT Presentation
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Inhomogeneities in temperature records deceive long-range
dependence estimators
Victor VenemaOlivier 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
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
Autocorrelation function – SRD vs. LRD
Long range dependence (LRD) 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
Example long range dependence
Demetris Koutsoyiannis, The Hurst phenomenon and fractional Gaussian noise made easy, Hydrological Sciences, 47(4) August 2002.
Uncertainty in trend estimate
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
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
FARIMA - power spectrum
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
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.
DFA spectrum
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
H-estimates: raw vs. homogenised
Simulation experiment
LRD regional climate data Added noise to obtain station data Added inhomogeneities Caussinus-Mestre to correct Compared H before and after
FARIMA simulation experiment: original vs. perturbed
FARIMA simulation experiment: original vs. perturbed
DFA simulation experiment: original vs. perturbed
DFA simulation experiment: original vs. homogenised
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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