Abstract
The main purpose of this paper is to apply the singular spectrum analysis (SSA), based on the phase space, and the wavelet multiresolution analysis (WMA), based on the frequency space, to the weekly time series of global sea level anomaly (GSLA) derived from satellite altimetry data over 1993–2013, in order to assess its nonlinear trends and its seasonal signals. The SSA results show that the GSLA time series is mainly dominated by a nonlinear trend explaining 89.89 % of the total GSLA variability, followed by annual and semi-annual signals with an explained variance of 9.15 and 0.32 %, respectively. For the annual signal, both methods give similar results. Its amplitude is less than 14 mm with an average of about 11 mm, and its minimum and maximum occur in April and October, respectively. The calculation of sea level trend, by both methods, is direct without removing the seasonal signals from the original GSLA time series as the most commonly used in the literature. The global sea level trend obtained from the WMA is about 2.52 ± 0.01 mm/year which is in good agreement with 2.94 ± 0.05 mm/year estimated from the SSA. Furthermore, the SSA method is most suitable for seasonal adjustment, and the WMA method is more useful for providing the different rates of sea level rise. Indeed, the WMA reveals that the global sea level has risen with the rate of 3.43 ± 0.01 mm/year from January/1993 to January/1998, 0.66 ± 0.01 mm/year from February/1998 to May/2000, 5.71 ± 0.03 mm/year from June/2000 to October/2003, and 1.57 ± 0.01 mm/year since January/2004.
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References
Baratta D, Cicioni G, Masulli F, Studer L (2003) Application of an ensemble technique based on singular spectrum analysis to daily rainfall forecasting. Neural Netw 16:375–387
Barbosa SM, Fernandes MJ, Silva ME (2005) Space-time analysis of sea level in the North-East Atlantic from T/P satellite altimetry. IAG Symp 129:248–253
Barbosa SM, Silva ME, Fernandes MJ (2006) Wavelet analysis of the Lisbon and Gibraltar North Atlantic oscillation winter indices. Int J Climatol 26(5):581–593
Bastos A, Trigo RM, Barbosa SM (2013) Discrete wavelet analysis of the influence of the North Atlantic oscillation on Baltic Sea level. Tellus A 65:20077
Benzi R, Deidda R, Marrocu M (1997) Characterization of temperature and precipitation fields over Sardinia with principal component analysis and singular spectrum analysis. Int J Climatol 7(11):1231–1262
Boening C, Willis JK, Landerer FW, Nerem RS, Fasullo J (2012) The 2011 La Niña: so strong, the oceans fell. Geophys Res Lett 39(19):L19602
Cazenave A, Llovel W (2010) Contemporary sea level rise. Ann Rev Mar Sci 2:145–173
Cazenave A, Remy F (2011) Sea level and climate: measurements and causes of changes. Wiley Interdiscip Rev Clim Chang 2(5):647–662
Cazenave A, Henry O, Munier S, Delcroix T, Gordon AL, Meyssignac B, Llovel W, Palanisamy H, Becker M (2012) Estimating ENSO influence on the global mean sea level, 1993-2010. Mar Geod 35:82–97
Cazenave A, Dieng HB, Meyssignac B, von Schuckmann K, Decharme B, Berthier E (2014) The rate of sea-level rise. Nat Clim Chang 4:358–361
Chaux C (2006) Analyse en ondelettes M-bandes en arbre dual; application à la restauration d’images. PhD Thesis at the University of Marne-la-Vallée, France
Chen X, Feng Y, Huang NE (2014) Global sea level trend during 1993-2012. Glob Planet Chang 112:26–32
Church JA, White NJ (2011) Sea-level rise from the late 19th to the early 21st century. Surv Geophys 32:585–602
Church JA, White NJ, Konikow LF, Domingues CM, Cogley JG, Rignot E, Gregory JM, van den Broeke MR, Monaghan AJ, Velicogna I (2011) Revisiting the Earth’s sea-level and energy budgets from 1961 to 2008. Geophys Res Lett 38:L18601
Corte-Real J, Qian B, Xu H (1998) Regional climate change in Portugal: precipitation variability associated with large-scale atmospheric circulation. Int J Climatol 18:619–635
Daubechies I (1992) Ten lectures on wavelets. Society for Industrial and Applied Mathematics (SIAM) USA, 357 p
Feng W, Zhong M (2015) Global sea level variations from altimetry, GRACE and Argo data over 2005-2014. Geod Geodyn 6(4):274–279
Flinchem EP, Jay DA (2000) An introduction to wavelet transform tidal analysis methods. Estuar Coast Shelf Sci 51:177–200
Ghil M, Allen MR, Dettinger MD, Ide K, Kondrashov D, Mann ME, Robertson AW, Saunders A, Tian Y, Varadi F, Yiou P (2002) Advanced spectral methods for climatic time series. Rev Geophys 40(1):1–11
Hassani H (2007) Singular spectrum analysis: methodology and comparison. J Data Sci 5:239–257
Holschneider M (1998) Wavelets: an analysis tool. Oxford University Press, USA 423 p
Jevrejeva S, Moore JC, Grinsted A (2003) Influence of the Arctic Oscillation and El Nino-Southern Oscillation (ENSO) on ice conditions in the Baltic Sea: the wavelet approach. J Geophys Res 108(D21):4677–4687
Jevrejeva S, Moore JC, Woodwoth PL, Grinsted A (2005) Influence of large-scale atmospheric circulation on European sea level: results based on the wavelet transform method. Tellus A 57(2):183–193
Jevrejeva S, Grinsted A, Moore JC, Holgate S (2006) Nonlinear trends and multiyear cycles in sea level records. J Geophys Res 111:C09012
Krepper CM, Garcia NO, Jones PD (2003) Interannual variability in Uruguay river basin. Int J Climatol 23(1):103–115
Leuliette EW, Miller L (2009) Closing the sea level rise budget with altimetry, Argo, and GRACE. Geophys Res Lett 36(4):L04608
Leuliette EW, Scharroo R (2010) Integrating Jason-2 into a multiple-altimeter climate data record. Mar Geod 33(S1):504e17
Lionello P (2012) The climate of the Mediterranean region: from the past to the future. Elsevier edition, p 502
Llovel W, Becker M, Cazenave A, Jevrejeva S, Alkama R, Decharme B (2011) Terrestrial waters and sea level variations on interannual time scale. Glob Planet Chang 75(1–2):76–82
Mallat S (1989) A theory for multiresolution signal decomposition: the wavelet representation. IEEE Trans Pattern Anal 11(7):674–693
Mallat S (1999) A wavelet tour of signal processing,, second edn. Academic Press, USA, p. 637
Meyer Y (1992) Les Ondelettes : Algorithmes et Applications. Armand Colin, Paris, p. 172
Nerem RS, Chambers DP, Choe C, Mitchum GT (2010) Estimating mean sea level change from the TOPEX and Jason altimeter missions. Mar Geod 33:435–446
Ngo-Duc T, Laval K, Polcher J, Cazenave A (2005) Contribution of continental water to sea level variations during the 1997–1998 El Niño-Southern Oscillation event: comparison between Atmospheric Model Intercomparison Project simulations and TOPEX/Poseidon satellite data. J Geophys Res 110:D09103
Nicholls RJ, Cazenave A (2010) Sea-level rise and its impact on coastal zones. Science 328(5985):1517–1520
Paegle JN, Byerle LA, Mo KC (2000) Intraseasonal modulation of South American summer precipitation. Mon Weather Rev 128(3):837–850
Pfeffer WT (2011) Land ice and sea level rise: a thirty-year perspective. Oceanography 24(2):94–111
Rangelova EV, Grebenitcharsky RS, Sideris MG (2006) Identifying sea-level rates by a wavelet-based multiresolution analysis of altimetry and tide gauge data. Bureau Gravimétrique International & International Geoid Service Joint Bulletin, Newton’s Bulletin 3:104–115
Robertson AW, Mechoso CR (2003) Circulation regimes and low-frequency oscillations in the South Pacific sector. Mon Weather Rev 131:1566–1576
Rodo X, Pascual M, Fuchs G, Faruque ASG (2002) ENSO and cholera: a nonstationary link related to climate change ? Proc Natl Acad Sci U S A 99(20):12901–12906
Vautard R, Ghil M (1989) Singular spectrum analysis in nonlinear dynamics, with applications to paleoclimatic time series. Phys D 35:395–424
Vautard R, Yiou P, Ghil M (1992) Singular-spectrum analysis: a toolkit for short, noisy, chaotic signals. Phys D 58:95–126
Vautard R, Plaut G, Wang R, Brunet G (1999) Seasonal prediction of North American surface air temperatures using space-time principal components. J Clim 12(2):380–394
Wainer I, Venegas SA (2002) South Atlantic multidecadal variability in the climatic system model. J Clim 15(12):1408–1420
Yu JY, Mechoso CR (2001) A coupled atmosphere-ocean GCM study of the ENSO cycle. J Clim 14(10):2329–2350
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Khelifa, S., Gourine, B., Rami, A. et al. Assessment of nonlinear trends and seasonal variations in global sea level using singular spectrum analysis and wavelet multiresolution analysis. Arab J Geosci 9, 560 (2016). https://doi.org/10.1007/s12517-016-2584-6
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DOI: https://doi.org/10.1007/s12517-016-2584-6