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/