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Stochastic Models and Spectra of Climatic and Related Time Series

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Time Series Analysis in Climatology and Related Sciences

Part of the book series: Progress in Geophysics ((PRGEO))

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Abstract

Research activities at all stages of analysis constitute preliminary steps for the most important task—time series forecasting. One of such stages includes efforts to understand statistical properties of the processes that are being studied including probability density functions, spectral densities, and the degree of statistical predictability. Climate is often regarded as a Markov process with a small parameter, which means a slowly and monotonically decreasing spectral density without any oscillations and/or quasi-periodic phenomena. Many climatic time series and indices including AO and AAO, NAO, PDO, AMO, and PNA behave in agreement with that Markov model or even with white noise. The climate indices related to ENSO behave in a different manner: their spectra are nonmonotonic and contain a smooth maximum at about 0.2 cpy. Yet, none of them contains regular oscillations and their predictability stays low. The annual surface temperature for 1920–2018 averaged over large parts of the globe generally does not follow the Markov model, and its predictability is relatively high. Some other oscillatory processes are studied as well, including a version of AAO and MJO—a bivariate random process whose scalar components are shown to possess some statistical predictability.

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References

  • Anstey J, Shepherd T (2014) High-latitude influence of the quasi-biennial oscillation. Q J Roy Meteor Soc 140:1–21

    Article  Google Scholar 

  • Artamonov J, Fedirko A, Skripaleva E (2016) Climatic variability of transport in the upper layer of the antarctic circumpolar current from hydrological and satellite data. Izv AN Fiz Atmos Ok 52:1051–1063

    Google Scholar 

  • Baldwin M, Gray L, Dunkerton T et al (2001) Quasi-biennial oscillation. Rev Geophys 29:179–329

    Article  Google Scholar 

  • Dobrovolski S (2000) Stochastic climate theory. Models and applications. Springer, Berlin

    Book  Google Scholar 

  • Frankingnoul C, Hasselmann K (1977) Stochastic climate models. Part II. Applications to sea surface temperature anomalies and thermocline variability. Tellus 29:359–370

    Google Scholar 

  • Gong D, Wang S (1999) Definition of Antarctic oscillation index. Geophys Res Lett 26:459–462

    Article  Google Scholar 

  • Hasselmann K (1976) Stochastic climate models. Part I. Theory Tellus 28:473–485

    Google Scholar 

  • Holton J, Lindzen R (1972) An updated theory for the Quasi-Biennial Cycle of the tropical stratosphere. J Atmos Sci 29:1076–1080

    Article  Google Scholar 

  • Naujokat B (1986) An update of the observed Quasi-Biennial Oscillation of the stratospheric winds over the tropics. JAS 43:1873–1877

    Google Scholar 

  • Pohl B, Faucereau N et al (2010) Relationships between the Antarctic Oscillation, the Madden-Julian Oscillation, and ENSO, and consequences for rainfall analysis. J. Climate 23:238–255

    Article  Google Scholar 

  • Privalsky V (1976) Estimating the spectral densities of large-scale processes. Izv. Atmos Ocean Phys 12:979–982

    Google Scholar 

  • Privalsky V (1977) The statistical predictability of the large-scale hydrometeorological processes. Izv. Atmos Ocean Phys 13:261–265

    Google Scholar 

  • Privalsky V (1983) Statistical predictability and spectra of air temperature over the northern hemisphere. Tellus 35A:51–59

    Article  Google Scholar 

  • Privalsky V, Yushkov V (2018) Getting it right matters: climate spectra and their estimation. Pure Appl Geoph 175:3085–3096

    Google Scholar 

  • Thomson R, Emery J (2014) Data analysis methods in physical oceanography, 3rd edn. Elsevier, Amsterdam

    Google Scholar 

  • Zhang C (2005) Madden-Julian Oscillation. Rev Geophys 43:1–36

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Water Problems Institute, Russian Academy of Sciences, Moscow, Russia

    Victor Privalsky

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  1. Victor Privalsky
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Corresponding author

Correspondence to Victor Privalsky .

Appendix

Appendix

  1. 1.

    https://www.cpc.ncep.noaa.gov/products/precip/CWlink/daily_ao_index/aao/monthly.aao.index.b79.current.ascii

  2. 2.

    https://climexp.knmi.nl/data/iamo_ersst_ts.dat

  3. 3.

    https://climexp.knmi.nl/data/iao_slp_ext.dat

  4. 4.

    https://www.esrl.noaa.gov/psd/gcos_wgsp/Timeseries/DMI

  5. 5.

    https://crudata.uea.ac.uk/cru/data/soi/soi.dat

  6. 6.

    https://climexp.knmi.nl/data/ihadisst1_nino3.4a.dat

  7. 7.

    https://climexp.knmi.nl/data/itelecon_nino34_gpcc.dat

  8. 8.

    https://climexp.knmi.nl/data/imei.dat

  9. 9.

    https://climexp.knmi.nl/data/inao_ijs_azo.dat

  10. 10.

    https://ds.data.jma.go.jp/tcc/tcc/products/elnino/decadal/npiwin.txt

  11. 11.

    https://www.ncdc.noaa.gov/teleconnections/pdo/

  12. 12.

    https://www.esrl.noaa.gov/psd/data/20thC_Rean/timeseries/monthly/PNA/pna.20crv2c.long.data

  13. 13.

    https://www.esrl.noaa.gov/psd/data/timeseries/IPOTPI/tpi.timeseries.hadisst11.data

  14. 14.

    https://data.giss.nasa.gov/gistemp/tabledata_v4/SH.Ts+dSST.txt

  15. 15.

    https://www.geo.fu-berlin.de/met/ag/strat/produkte/qbo/qbo.dat

  16. 16.

    http://www.bom.gov.au/climate/mjo/graphics/rmm.74toRealtime.txt

  17. 17.

    https://climexp.knmi.nl/data/icpc_aao.dat.

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Privalsky, V. (2021). Stochastic Models and Spectra of Climatic and Related Time Series. In: Time Series Analysis in Climatology and Related Sciences. Progress in Geophysics. Springer, Cham. https://doi.org/10.1007/978-3-030-58055-1_5

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