Summary
A generalized time series decomposition technique is applied to monthly total precipitation data from a German station network of 132 time series covering 1901–2000. The decomposition technique shows that observed time series can be interpreted as a realization of a Gumbel distributed random variable with time-dependent location parameter and time-dependent scale parameter. It provides a full analytical description of the series in terms of the probability density function (PDF) for every time step of the observation period. Consequently, probability assessments of extreme values are possible for any threshold at any time.
Most of the year, an increase in the probability of exceeding the 95th percentile and a decrease in the probability of falling under the 5th percentile can be detected at several stations in the southern part of Germany. In the western part, we observe the same phenomenon in the summer months, but these changes go along with smaller magnitudes. However, climate is getting more extreme in that region in winter: Probability for both exceeding the 95th percentile and for falling under the 5th percentile is increasing. In the eastern part of Germany, increases in the probability of occurrence of relatively low precipitation in winter as well as decreases in both probabilities (>95th percentile, <5th percentile) in summer and autumn prevail.
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References
DJ Dupuis CA Field (1998) ArticleTitleRobust estimation of extremes Can J Stat 26 199–216
DR Easterling JL Evans PYa Groisman TR Karl KE Kunkel P Ambenje (2000) ArticleTitleObserved variability and trends in extreme climate events Bull Amer Meteor Soc 81 417–425 Occurrence Handle10.1175/1520-0477(2000)081<0417:OVATIE>2.3.CO;2
J Grieser S Trömel C-D Schönwiese (2002) ArticleTitleStatistical time series decomposition into significant components and application to European temperature Theor Appl Climatol 71 171–183 Occurrence Handle10.1007/s007040200003
EJ Gumbel (1958) Statistics of extremes Columbia University Press New York 375
PJ Huber (1981) Robust statistics Wiley Series in Probability and Mathematical Statistics New York 328
IPCC (2001) Climate Change 2001: The Scientific Basis. Contribution of Working Group 1 to the Third Assessment Report of the Intergovernmental Panel on Climate Change [Houghton JT, Ding Y, Griggs DJ, Noguer M, van der Linden PJ, Dai X, Maskell K, Johnson CA (eds)]. Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA, 881 pp
RW Katz BG Brown (1992) ArticleTitleExtreme events in a changing climate: Variability is more important than averages Clim Change 21 289–302 Occurrence Handle10.1007/BF00139728
MR Leadbetter G Lindgren H Rootzen (1983) Extremes and related properties of random sequences and process Springer Berlin 336
S Mallat (1999) A wavelet tour of signal processing Academic Press New York 620
L Mearns RW Katz SH Schneider (1984) ArticleTitleExtreme high-temperature events: Changes in their probabilities with changes in mean temperature J Climate Appl Meteor 23 1601–1613 Occurrence Handle10.1175/1520-0450(1984)023<1601:EHTECI>2.0.CO;2
WH Press SA Teukolsky WT Vetterling BP Flannery (1992) Numerical Recipes in Fortran 77 Cambridge University Press Cambridge 933
Rapp J, Schönwiese C-D (1996) Atlas der Niederschlags- und Temperaturtrends in Deutschland 1891–1990. Frankfurter geowissenschaftliche Arbeiten, Serie B, Band 5, 253 pp
Schlittgen R, Streitberg BHJ (1999) Zeitreihenanalyse. Oldenburg, 571 pp
C-D Schönwiese J Rapp (1997) Climate trend atlas of Europe based on observations 1891–1990 Kluwer Academic Publishers Dordrecht 228
K Schrader T Hettmansperger (1980) ArticleTitleRobust analysis of variance upon a likelihood ratio criterion Biometrika 67 93–101 Occurrence Handle10.2307/2335321
HV Storch FW Zwiers (1999) Statistical analysis in climate research Cambridge University Press Cambridge 484
Trömel S (2004) Statistische Modellierung monatlicher Niederschlagszeitreihen. University Frankfurt a.M., doctorate thesis, 236 pp (also Report No. 2, Inst. Atmosphere and Environment, Univ. Frankfurt, 2005)
S Trömel C-D Schönwiese (2005) ArticleTitleA generalized method of time series decomposition into significant components including probability assessments of extreme events and application to observational German precipitation data Meteorol Z 14 417–427 Occurrence Handle10.1127/0941-2948/2005/0039
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Trömel, S., Schönwiese, CD. Probability change of extreme precipitation observed from 1901 to 2000 in Germany. Theor. Appl. Climatol. 87, 29–39 (2007). https://doi.org/10.1007/s00704-005-0230-4
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DOI: https://doi.org/10.1007/s00704-005-0230-4