Journal of Geodesy

, Volume 91, Issue 1, pp 69–90 | Cite as

Differences between mean tide level and mean sea level

  • P. L. WoodworthEmail author
Original Article


This paper discusses the differences between mean tide level (MTL) and mean sea level (MSL) as demonstrated using information from a global tide gauge data set. The roles of the two main contributors to differences between MTL and MSL (the M4 harmonic of the M2 semidiurnal tide, and the combination of the diurnal tides K1 and O1) are described, with a particular focus on the spatial scales of variation in MTL–MSL due to each contributor. Findings from the tide gauge data set are contrasted with those from a state-of-the-art global tide model. The study is of interest within tidal science, but also has practical importance regarding the type of mean level used to define land survey datums. In addition, an appreciation of MTL–MSL difference is important in the use of the historical sea level data used in climate change research, with implications for some of the data stored in international databanks. Particular studies are made of how MTL and MSL might differ through the year, and if MTL is measured in daylight hours only, as has been the practice of some national geodetic agencies on occasions in the past.


Tide gauge measurements Ocean tides Hydrographic datums 



This work was undertaken when the author was an Honorary Research Fellow at the National Oceanography Centre in Liverpool. I would like to thank Mark Tamisiea and David Pugh (NOC) and Peter Hogarth (Kongsberg Maritime) for discussions on the need to understand possible MTL/MSL biases when both quantities are included in sea level time series. Richard Ray (Goddard Space Flight Center) and Thomas Wahl (University of Southampton) provided valuable comments and information. The International Hydrographic Organization tidal constants were made available via David Blackman (NOC). Many thanks are due to the providers of data to the GESLA-2 set. Some of the figures in this paper were generated using the Generic Mapping Tools (Wessel and Smith 1998).

Supplementary material

190_2016_938_MOESM1_ESM.pdf (722 kb)
Supplementary material 1 (pdf 721 KB)


  1. Amin M (1982) On analysis and prediction of tides on the west coast of Great Britain. Geophys J R Astr Soc 68:57–78. doi: 10.1111/j.1365-246X.1982.tb06962.x CrossRefGoogle Scholar
  2. Cheng Y, Andersen OB (2010) Improvement in global ocean tide model in shallow water regions. Poster, SV.1-68 45, Ocean Surface Topography Science Team Meeting, Lisbon, Oct. 18–22.
  3. Church JA, Clark PU Cazenave A, Gregory JM, Jevrejeva S, Levermann A, Merrifield MA, Milne GA, Nerem RS, Nunn PD, Payne AJ, Pfeffer WT, Stammer D, Unnikrishnan AS (2013) Sea level change. In: Stocker TF, Qin D, Plattner GK, Tignor M, Allen SK, Boschung J, Nauels A, Xia Y, Bex V, Midgley PM (eds) Climate change 2013: the physical science basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge University Press, Cambridge, New YorkGoogle Scholar
  4. De Bruyn HE (1900) On the relation of the mean sea level and the height of half-tide. In: Huygens Institute-Royal Netherlands Academy of Arts and Sciences (KNAW), Proceedings, vol 2, 1899–1900. KNAW, Amsterdam, pp 189–196Google Scholar
  5. Doodson AT, Warburg HD (1941) Admiralty manual of tides. His Majesty’s Stationery Office, p 270Google Scholar
  6. Godin G (1999) The propagation of tides up rivers with special considerations on the Upper Saint Lawrence River. Estuar Coastal Shelf Sci 48:307–324. doi: 10.1006/ecss.1998.0422 CrossRefGoogle Scholar
  7. Hicks SD (1980) The national tidal datum convention of 1980. U.S. Dept. of Commerce, National Oceanic and Atmospheric Administration, National Ocean Survey, Rockville 44 ppGoogle Scholar
  8. Hogarth P (2014) Preliminary analysis of acceleration of sea level rise through the twentieth century using extended tide gauge data sets (August 2014). J Geophys Res Oceans 119:7645–7659. doi: 10.1002/2014JC009976 CrossRefGoogle Scholar
  9. Holgate SJ, Matthews A, Woodworth PL, Rickards LJ, Tamisiea ME, Bradshaw E, Foden PR, Gordon KM, Jevrejeva S, Pugh J (2013) New data systems and products at the permanent service for mean sea level. J Coastal Res 29:493–504. doi: 10.2112/JCOASTRES-D-12-00175.1 CrossRefGoogle Scholar
  10. IAPO (1939) Monthly and annual mean heights of sea level up to and including the year 1936. In: Publication Scientifique No.5. Report of the International Association of Physical Oceanography, Liverpool, p 256.
  11. IAPO (1959) Permanent service for mean sea level. In: Monthly and annual mean heights of sea-level for the period of the International Geophysical Year (1957 to 1958) and unpublished data for earlier years. Publication Scientifique No.20. Report of the International Association of Physical Oceanography, p 65.
  12. IAPO (1963) Permanent service for mean sea level. In: Monthly and annual mean heights of sea-level 1959 to 1961. Publication Scientifique No.24. Report of the International Association of Physical Oceanography, p 59.
  13. James H (1861) Abstracts of the principal lines of spirit levelling in England and Wales. Eyre and Spottiswoode, LondonGoogle Scholar
  14. Lane A (2004) Bathymetric evolution of the Mersey Estuary, UK, 1906–1997: causes and effects. Estuar Coastal Shelf Sci 59:249–263. doi: 10.1016/j.ecss.2003.09.003 CrossRefGoogle Scholar
  15. Maul GA, Martin DM (1993) Sea level rise at Key West, Florida, 1846–1992: America’s longest instrument record? Geophys Res Lett 20:1955–1958. doi: 10.1029/93GL02371 CrossRefGoogle Scholar
  16. Menéndez M, Woodworth PL (2010) Changes in extreme high water levels based on a quasi-global tide-gauge dataset. J Geophys Res 115:C10011. doi: 10.1029/2009JC005997 CrossRefGoogle Scholar
  17. Nayak RK, Shetye SR (2003) Tides in the Gulf of Khambhat, west coast of India. Estuar Coastal Shelf Sci 57:249–254. doi: 10.1016/S0272-7714(02)00349-9 CrossRefGoogle Scholar
  18. NOAA (2009) Processing and tabulation of 6-minute water level data for hourly heights, tides and monthly means. NOAA CO-OPS Internal Document. Version 1. 30 November 2009. U.S. Dept. of Commerce, National Oceanic and Atmospheric Administration, National Ocean Survey, Rockville, Maryland, p 28Google Scholar
  19. Parker B (ed) (2007) Tidal analysis and prediction. National Oceanic and Atmospheric Administration Special Publication NOS CO-OPS 3. U.S. Department of Commerce, Washington, D.C., p 378Google Scholar
  20. Pouvreau N (2008) Trois cents ans de mesures marégraphiques en France: outils, méthodes et tendances des composantes du niveau de la mer au port de Brest. PhD thesis, University of La Rochelle, 2008Google Scholar
  21. Proctor R, Flather RA (1989) Storm surge prediction in the Bristol Channel—the floods of 13 December 1981. Cont Shelf Res 9:889–918. doi: 10.1016/0278-4343(89)90064-2 CrossRefGoogle Scholar
  22. Pugh DT, Woodworth PL (2014) Sea-level science: understanding tides, surges, tsunamis and mean sea-level changes. Cambridge University Press, Cambridge, p 408. ISBN 9781107028197Google Scholar
  23. Ray RD (1999) A global ocean tide model from Topex/Poseidon altimetry: GOT99. NASA Technical Memorandum 209478, Goddard Space Flight Center, Maryland, p 58Google Scholar
  24. Ray RD, Egbert GD (2004) The global S1 tide. J Phys Oceanogr 34:1922–1935. doi: 10.1175/1520-0485(2004)034<1922:TGST>2.0.CO;2
  25. Ray RD (2007) Propagation of the overtide M4 through the deep Atlantic Ocean. Geophys Res Lett 34:L21602. doi: 10.1029/2007GL031618 CrossRefGoogle Scholar
  26. Ray RD, Egbert GD, Erofeeva SY (2011) Tide predictions in shelf and coastal waters: status and prospects. In: Vignudelli S et al. (eds) Coastal altimetry, Chapter 8. Springer, Berlin, pp 191–216. doi: 10.1007/978-3-642-12796-0_8
  27. Rossiter JR (1958) Note on methods of determining monthly and annual values of mean water level. Int Hydrogr Rev 35:105–115Google Scholar
  28. Shetye SR (1999) Tides in the Gulf of Kutch, India. Cont Shelf Res 19:1771–1782. doi: 10.1016/S0278-4343(99)00038-2 CrossRefGoogle Scholar
  29. Simon B (2015) Coastal tides (Translated by D. Manley) Published by the Service Hydrographique et Océanographique de la Marine (SHOM), Brest, p 409. ISBN 2903581827.
  30. Stammer D et al (2014) Accuracy assessment of global barotropic ocean tide models. Rev Geophys 52:243–282. doi: 10.1002/2014RG000450 CrossRefGoogle Scholar
  31. Tsimplis MN, Woodworth PL (1994) The global distribution of the seasonal sea level cycle calculated from coastal tide gauge data. J Geophys Res 99:C8. doi: 10.1029/94JC01115 Google Scholar
  32. Tsimplis MN, Woolf DK, Osborn TJ, Wakelin S, Wolf J, Flather R, Shaw AGP, Woodworth P, Challenor P, Blackman D, Pert F, Yan Z, Jevrejeva S (2005) Towards a vulnerability assessment of the UK and northern European coasts: the role of regional climate variability. Philos Trans R Soc 363:1329–1358. doi: 10.1098/rsta.2005.1571 CrossRefGoogle Scholar
  33. Unnikrishnan AS, Shankar D (2007) Are sea-level-rise trends along the coasts of the north Indian Ocean consistent with global estimates? Global Planet Change 57:301–307. doi: 10.1016/j.gloplacha.2006.11.029
  34. USC&GS (1952) Manual of harmonic constant reductions. U.S. Coast and Geodetic Survey. Special Publication No.260. Washington, D.C.: U.S. Department of Commerce, p 74. Reprinted 1976.
  35. Wahl T, Jensen J, Frank T (2010) On analysing sea level rise in the German Bight since 1844. Nat Hazards Earth Syst Sci 10:171–179.
  36. Wessel P, Smith WHF (1998) New, improved version of generic mapping tools released. EOS Trans Am Geophys Union 79:579CrossRefGoogle Scholar
  37. Woodworth PL, Blackman DL, Pugh DT, Vassie JM (2005) On the role of diurnal tides in contributing to asymmetries in tidal probability distribution functions in areas of predominantly semi-diurnal tide. Estuar Coastal Shelf Sci 64:235–240. doi: 10.1016/j.ecss.2005.02.014 CrossRefGoogle Scholar
  38. Woodworth PL (2010) A survey of recent changes in the main components of the ocean tide. Cont Shelf Res 30:1680–1691. doi: 10.1016/j.csr.2010.07.002 CrossRefGoogle Scholar
  39. Woodworth PL, Menéndez M, Gehrels WR (2011) Evidence for century-timescale acceleration in mean sea levels and for recent changes in extreme sea levels. Surv Geophys 32:603–618. doi: 10.1007/s10712-011-9112-8 (erratum page 619)CrossRefGoogle Scholar
  40. Woodworth PL (2012) A note on the nodal tide in sea level records. J Coastal Res 28:316–323. doi: 10.2112/JCOASTRES-D-11A-00023.1 CrossRefGoogle Scholar
  41. Yallop BD (1996) A simple algorithm to calculate times of sunrise and sunset. Her Majesty’s Nautical Almanac Office, UK Hydrographic Office. NAO Technical Note No. 70, p 3Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.National Oceanography CentreJoseph Proudman BuildingLiverpoolUK

Personalised recommendations