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Time-Varying Mean Sea Level

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Handbook of Geomathematics

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Abstract

After a general theoretical consideration of basic mathematical aspects, we give numerical and physical details for the last two decades, where global and reliable data are available. The concept of a “mean sea level” is in itself rather artificial, because sea level varies at various temporal and spatial scales. This is because the sea is in constant motion, affected by the high- and low-pressure zones above it, the tides, local gravitational differences, and so forth. What is possible to do is to calculate the mean sea level at that point and use it as a reference datum.Traditionally, coastal tide gauges measure sea-level variability. Since 1993 satellite altimetry provides near-global maps of sea-level change with high spatial and temporal resolution. Sea-level change has therefore in altimetry its primary global source of information.Coastal and global sea-level variability is here considered. The coastal variability is estimated from tide gauges, from altimeter data colocated to the tide gauges and from altimeter data along the world coasts. The global variability is derived from altimeter data. We show that the sea level has in the interval 1993–2012 an average positive trend of 3. 2 ± 0. 4 mm/year, which is higher than the average trend of 1. 8 ± 0. 5 mm/year derived from tide gauge data over the twentieth century. The trends are not spatially uniform but regionally dependent. The variability at interannual time scale appears to be related to the variability of climatic indices, like Northern Atlantic (NAO) and the El Nino-Southern Atlantic Oscillation (ENSO).At certain coastal locations, non-climatic components of relative sea-level change, mainly subsidence, are locally appreciable. The relative sea-level rise there is up to three to four times larger than the global mean sea-level rise.

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References

  • Allen M, Smith L (1994) Investigating the origins and significance of low frequency modes of climate variability. Geophys Res Lett 21:883–886

    Article  Google Scholar 

  • Becker M, Meyssignac B, Leletrel C, Llovel W, Cazenave A, Delcroix T (2012) Sea level variations at tropical Pacific islands since 1950. Global Planet Change 80–81:85–98. doi:10.1016/j.gloplacha2011.09.004

    Article  Google Scholar 

  • Beckley BD, Lemoine FG, Luthcke SB, Ray RD, Zelensky NP (2007) A reassessment of global and regional mean sea level trends from TOPEX and Jason-1 altimetry based on revised reference frame and orbits. Geophys Res Lett 34:L14608. doi:10.1029/2007GL030002

    Article  Google Scholar 

  • Berge-Nguyen M, Cazenave A, Lombard A, Llovel W, Viarre J, Cretaux JF (2008) Reconstruction of past decades sea level using thermosteric sea level, tide gauge, satellite altimetry and ocean reanalysis data. Global Planet Change 62: 1–13

    Article  Google Scholar 

  • Bindoff N, Willebrand J, Artale V, Cazenave A, Gregory J, Gulev S, Hanawa K, Le Quéré C, Levitus S, Nojiri Y, Shum CK, Talley L, Unnikrishnan A (2007) Observations: oceanic climate and sea level. In: Solomon S, Qin D, Manning M, Chen Z, Marquis M, Averyt KB, Tignor M, Miller HL (eds) Climate change 2007: the physical science basis. Contribution of workinggroup I to the fourth assessment report of the Intergovernmental Panel on Climate Change. Cambridge University Press, Cambridge, pp 385–428

    Google Scholar 

  • Bretherton C, Smith C, Wallace J (1992) An intercomparison of methods for finding coupled patterns in climate data change. J Clim 5:541–560

    Article  Google Scholar 

  • Bursa M, Groten E, Kenyon S, Kuba J, Radey K, Vatrt V, Vojtiskova M (2001) Earth dimension specified by geoid potential. Studia Geophys Geodetica 46:1–8

    Article  Google Scholar 

  • Bursa M, Kenyon S, Kouba J, Sima Z, Vatrt V, Vitek V, Vojtiskova M (2007) The geopotential value W∘ for specifying the relativistic atomic time scale and a global vertical reference system. J Geodesy 81:103–110

    Article  Google Scholar 

  • Calafat F, Gomis D (2009) Reconstruction of Mediterranean Sea level fields for the period 1945–2000. Global Planet Change 66:225–234. doi:10.1016/j.gloplacha.2008.12.015

    Article  Google Scholar 

  • Cardoso JF (1999) High-order contrasts for independent component analysis. Neural Comput 11:157–192. doi:10.1162/089976699300016863

    Article  Google Scholar 

  • Cardoso JF and Souloumiac A (1993) Blind beamforming for non Gaussian signals. IEE Proc 140:362–370

    Google Scholar 

  • Cardoso J-F, Souloumiac A (1993) An efficient technique for blind separation of complex sources. In: Proceedings of the IEEE SP workshop on higher-order statistics, Lake Tahoe, pp 275–279

    Google Scholar 

  • Cazenave A, Llovel W (2010) Contemporary sea level rise. Annu Rev Mar Sci 2:145–173. doi:10.1146/annurev-marine-120308–081105

    Article  Google Scholar 

  • Cazenave A, Nerem RS (2004) Present-day sea level change observations and causes. Rev Geophys 42:RG3001. doi:101029/2003RG000139

    Google Scholar 

  • Cazenave A, Dominh K, Guinehut S, Berthier E, Llovel W, Ramillien G, Ablain M, Larnicol G (2009) Sea level budget over 20032008: a reevaluation from GRACE space gravimetry, satellite altimetry and Argo. Global Planet Change 65(1–2):83–88

    Article  Google Scholar 

  • Chelton DB, Ries JC, Haines BJ, Fu LL, Callahan P (2001) Satellite altimetry. In: Fu LL, Cazanave A (eds) Satellite altimetry and earth sciences. Academic, New York, pp 57–64

    Google Scholar 

  • Church JA, White NJ (2006) A 20th century acceleration in global sea-level rise. Geophys Res Lett 33:L01602. doi:10.1029/2005GL024826

    Article  Google Scholar 

  • Church D, White N (2011) Sea-level rise from the late 19th to the early 21st century. Surv Geophys. doi:10.1007/s10712-011-9119-1

    Google Scholar 

  • Church JA, White NJ, Coleman R, Lambeck K, Mitrovica JX (2004) Estimates of the regional distribution of sea level rise over the 1950–2000 period. J Climate 17(13):2609–2625

    Article  Google Scholar 

  • Church J, White NJ, Arrup T, Wilson WS, Woodworth PL, Dominigues CM, Hunter JR, Lambeck K (2008) Understanding global sea levels: past, present and future. Sustain Sci 3:9–22. doi:/10.1007/s11625-008-0042-4

    Google Scholar 

  • Domingues CM, Church J, White NJ, Gleckler PJ, Wijffels SE, Barker PM, Dunn JR (2008) Improved estimates of upper-ocean warming and multi-decadal sea level rise. Nat Lett 453. doi:10.1038/nature07080

    Google Scholar 

  • Douglas BC (2001) Sea level change in the era of the recording tide gauge. In: Sea level rise, history and consequences. International geophysics series, vol 75. Academic, London

    Google Scholar 

  • Fenoglio-Marc L (2001) Analysis and representation of regional sea level variability fromaltimetry and atmospheric data. Geophys J Int 145:1–18

    Article  Google Scholar 

  • Fenoglio-Marc L, Tel E (2010) Coastal and global sea level change. J Geodyn 49(3–4):151–160. doi:10.1016/j.jog.2009.12.003

    Article  Google Scholar 

  • Fenoglio-Marc L, Groten E, Dietz C (2004) Vertical land motion in the mediterranean Sea from altimetry and tide gauge stations. Marine Geodesy 27:683–701

    Article  Google Scholar 

  • Fenoglio-Marc L, Schoene T, Illigner J, Becker M, Manurung P, Khaid (2012). Sea level change and vertical motion from satellite altimetry, tide gauges and GPS in the Indonesian region. Marine Geodesy 35(sup1):137–150. doi:http://dx.doi.org/10.1080/~01490419.2012.718682

  • Fenoglio-Marc L, Mariotti A, Sannino G, Meyssignac B, Carillo A, Struglia M (2013) Decadal variability of the net water ux at the Mediterranean Gibraltar Strait. Global Planet Change 100: 1–10

    Article  Google Scholar 

  • Groten E (2003) Ist die Modellbildung in der Geodäsie hinreichend zukunftstauglich? Zeitschr f Vermessungsw 3:192–195

    Google Scholar 

  • Haines G (1985) Spherical cap harmonic analysis. J Geophys Res 90:2583–2591

    Article  Google Scholar 

  • Henry O, Prandi P, Llovel W, Cazenave A, Jevrejeva S, Stammer D, Meyssignac B, Koldunov N (2012) Tide gauge based sea level variations since 1950 along the Norwegian and Russian coasts of the Artic Ocean: conribution of the steric and mass components. J Geophys Res 117:C09,023. doi:10.1029/2011JC007706

    Google Scholar 

  • Holgate SJ (2007) On the decadal rates of sea level change during the twentieth century. Geophys Res Lett 34:L01602. doi:10.1029/2006GL028492

    Article  Google Scholar 

  • Holgate SJ, Woodworth PL (2004) Evidence for enhanced coastal sea level rise during the 1990s. Geophys Res Lett 31:L07305. doi:10.1029/ 2004GL019626

    Article  Google Scholar 

  • Horel JD (1984) Complex principal component analysis: theory and examples. J Climate Appl Meteor 23:1661–1673

    Article  Google Scholar 

  • Hyvarinen A, Karhunen J, Oja E (2001) Independent component analysis. Wiley, New York

    Book  Google Scholar 

  • Jevrejeva S, Grinsted A, Moore JC, Holgate S (2006) Non linear trends and multiyear cycles in sea level records. J Geophys Res 111:C09012. doi:10.1029/2005JC003299

    Google Scholar 

  • Kohl A, Stammer D (2008) Decadal sea level changes in the 50-year GECCO ocean synthesis. J Climate 21:1876–1890. http://dx.doi.org/10.1175/2007JCLI2081.1

  • Leuliette E, Nerem RS, Mitchum G (2004) Calibra-tion of Topex/Poseidon and Jason altimeter data to construct a continuous record of mean sea level change. Marine Geodesy 27:79–94. doi:10.1080/01490410490465193

    Article  Google Scholar 

  • Levitus S, Antonov JI, Boyler T, Stephens C (2000) Warming of the world ocean. Science 287:2225–2229

    Article  Google Scholar 

  • Lombard A, Cazenave A, Le Traon P-Y, Ishii M (2005) Contribution of thermal expansion to present-day sea-level change revisited. Global Planet Change 47(1):1–16

    Article  Google Scholar 

  • Masters D, Nerem S, Choe C, Beckley B, Leuliette E, White N, Ablain M (2012) Comparison of global mean sea level time series from TOPEX/Poseidon, Jason-1, and Jason-2. Marine Geodesy 35(1):20–41

    Article  Google Scholar 

  • Meier F, Dyurgerov MB, Rick UK, O’Neel S, Pfeffer W, Anderson RS, Anderson SP, Glazovsky AF (2007) Glaciers dominate Eustatic sea level rise in the 21th century. Science 317(5841):1064–1067. doi: 10.1126/science. 1143906

    Article  Google Scholar 

  • Meyssignac B, Calafat F, Somot S, Rupolo V, Stocchi P, Llovel W, Cazenave A (2011) Two-dimensional reconstruction of the Mediterranean sea level over 1970–2006 from tide gage data and regional ocean circulation model outputs. Global Planet Change 77:49–61. doi:http://dx.doi.org/10.1016/j.gloplacha.2011.03.002

  • Meyssignac B, Salas y Melia D, Becker M, Llovel W, Cazenave A (2012a) Tropical Pacific spatial trend patterns in observed sea level: internal variability and/or anthropogenic signature? Climate Past 8:787–802. doi:10.5194/cp-8-787-2012

    Google Scholar 

  • Meyssignac B, Becker M, Llovel W, Cazenave A (2012b) An assessment of two-dimensional past sea level reconstructions over 1950–2009 based on Tide-Gauge data and different input sea level grids. Surv Geophys 33(5):945–972

    Article  Google Scholar 

  • Mitchum G (2000) An improved calibration of satellite altimetric heights using tide gauge sea level with adjustment for land motion. Marine Geodesy 23:145–166

    Article  Google Scholar 

  • Moore J, Jevrejeva S, Grinsted A (2011) The historical global sea-level budget. Ann Glaciol 52(59):8–14

    Article  Google Scholar 

  • Nerem RS, Chambers D, Choe C, Mitchum GT (2010) Estimating mean sea level change from the TOPEX and Jason altimeter missions. Marine Geodesy 33(1 supp 1):435

    Google Scholar 

  • Overland JE, Preisendorfer RW (1982) A significance test for principal components applied to a cyclone climatology. Mon Weather Rev 110(1):1–4

    Article  Google Scholar 

  • Paulson A, Zhong S, Wahr J (2007) Inference of mantle viscosity from GRACE and relative sea level data. Geophys J Int 171:497–508. doi:10.111/j.1365-246X.2007.03556.x

    Google Scholar 

  • Peltier WR (2004) Global glacial isostasy and the surface of the ice-age earth: the ICE-5G (VM2) model and GRACE. Ann Rev Earth Planet Sci 32:111–149

    Article  Google Scholar 

  • Peltier R (2009) Closure of the budget of global sea level rise over the GRACE era: the importance and magnitudes of the required corrections for global glacial isostatic adjustment. Quat Sci Rev 28(17–18):1658–1674. doi:10.1016/j.quascirev.2009.04.004

    Article  Google Scholar 

  • Prandi P, Cazenave A, Becker M (2009) Is coastal mean sea level rising faster than the global mean? A comparison between tide gauges and satellite altimetry over 1993–2007. Geophys Res Lett 36:L05602. doi:10.1029/2008GL036564

    Article  Google Scholar 

  • Preisendorfer RW (1988) Principal component analysis in meteorology and oceanography. In: Developments in atmospheric science, Vol 17. Elsevier, Amsterdam

    Google Scholar 

  • Rietbroek R, Fritsche M, Brunnabend S-E, Daras I, Kusche J, Schröter J, Flechtner F, Dietrich R (2012) Global surface mass from a new combination of GRACE, modelled OBP and reprocessed GPS data. J Geodyn 59–60:64–71

    Article  Google Scholar 

  • Rignot E, Box JE, Burgess E, Hanna E (2008) Mass balance of the Greenland ice sheet from 1958 to 2007. Geophys Res Lett 35:L20502. doi:10.1029/2008GL035417

    Article  Google Scholar 

  • Spada G, Stocchi P (2007) Selen: a Fortran 90 program for solving the sea-level equation. Comput Geosci 33:538–562

    Article  Google Scholar 

  • Timmerman A, McGregor S, Jin F-F (2010) Wind effects on past and future regional sea level trends in the southern Indo-Pacific. J Climate 23:4429–443. doi:http://dx.doi.org/10.1175/2010JCLI3519.1

  • Trenberth KE (1984) Signal versus noise in the southern oscillation. Mon Weather Rev 112: 326–332

    Article  Google Scholar 

  • Trenberth KE, Hurrel JW (1994) Decadal atmosphere-ocean variations in the Pacific. Climate Dyn 9:303–319

    Article  Google Scholar 

  • Trisirisatayawong I, Naeije M, Simons W, Fenoglio-Marc L (2011) Sea level change in the Gulf of Thailand from GPS-corrected tide gauge data and multi-satellite altimetry. Global Planet Change 76:137–151. doi:10.1016/j.gloplacha.2010.12.010

    Article  Google Scholar 

  • White NJ, Church JA, Gregory JM (2005) Coastal and global averaged sea level rise for 1950 to 2000. Geophys Res Lett 32:L01601. doi:101029/ 2004GL021391

    Google Scholar 

  • Wilks D (1995) Statistical methods in the atmos-pheric sciences. Academic, San Diego

    Google Scholar 

  • Willis JK, Chambers DP, Nerem S (2008) Assessing the global averaged sea level budget on seasonal and interannual timescales. J Geophys Res 113:C06015. doi:10.1029/2007JC004517

    Google Scholar 

  • Woolf DK, Shaw A, Tsimplis MN (2005) The influence of the North Atlantic oscillation on sea-level variability in the North Atlantic region. Global Atmosp Ocean Syst 9:145–167. doi:10.1080/10236730310001633803

    Article  Google Scholar 

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Authors and Affiliations

  1. Institute of Geodesy, Technical University Darmstadt, Darmstadt, Germany

    Luciana Fenoglio-Marc

  2. Institute of Physical Geodesy, Technical University Darmstadt, Darmstadt, Germany

    Erwin Groten

Authors
  1. Luciana Fenoglio-Marc
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  2. Erwin Groten
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Correspondence to Luciana Fenoglio-Marc .

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Editors and Affiliations

  1. Geomathematics Group, University of Kaiserslautern, Kaiserslautern, Germany

    Willi Freeden

  2. Department of Mathematics, University of Central Florida, Orlando, Florida, USA

    M. Zuhair Nashed

  3. Computational Mathematics, Technische Universität Braunschweig, Braunschweig, Germany

    Thomas Sonar

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Fenoglio-Marc, L., Groten, E. (2015). Time-Varying Mean Sea Level. In: Freeden, W., Nashed, M., Sonar, T. (eds) Handbook of Geomathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54551-1_12

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