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The Ocean Pole Tide: a Review

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The Ocean Pole Tide: a Review Executive Committee Program Committee Fig 1. Attendee Profile by Research Interest Yun-Tai CHEN David HIGGITT, Chair Institute of Geophysics, The University of Nottingham China Earthquake Administration SE 19% Ningbo China AS 23% The Ocean Pole Tide: A ReviewBenjamin Fong CHAO Tetsuo NAKAZAWA, AS Section Institute of Earth Sciences, BG 2% Korea Meteorological Administration Academia Sinica ST 16% HS 12% Wendy WANG, BG Section David HIGGITT College of Global Change and Earth The University of Notthingham, System Science, Beijing Normal University Ningbo China Richard Gross PS 10% IG 8% Kun-Yeun HAN, HS Section Adam SWITZER OS 10% Kyungpook National University Earth Observatory of Singapore Atmospheric Sciences (AS) Biogeosciences (BG) James GOFF, IG Section Hydrological Sciences (HS) Interdisciplinary Geosciences (IG) University of New South Wales Jet Propulsion Laboratory Ocean Sciences (OS) Planetary Sciences (PS) Robin ROBERTSON, OS Section Solar & Terrestrial Sciences (ST) Solid Earth Sciences (SE) University of New South Wales at the Australian Defense Force Academy California Institute of Technology Fig 2. Representation by Country/Region Noriyuki NAMIKI, PS Section National Astronomical Observatory of Pasadena, CA 91109–8099, USA Japan Nanan BALAN, ST Section National Institute for Space Research (Instituto Nacional de Pesquisas Espaciais- Asia Oceania Geosciences Society INPE) th 13 Annual Meeting Hai Thanh TRAN, SE Section Hanoi University of Mining and Geology Partners & Supporters of AOGS July 31 to August 5, 2016 Beijing, China Featured Exhibitors at GEOMEET – the AOGS Geosciences World Community Exhibition ADC BioScientific Ltd. • Advanced Geoscience Instruments Company (AGICO) • Advances in Atmospheric Sciences • American Geophysical Union • Bartington Instruments • Beta Analytic Inc • Cambridge University Press • CAMECA • Decagon Devices • Earth Observatory of Singapore/NTU • Earthquake Research Institute, University of Tokyo • Earth Science Research Promotion Center (National Central University) • European Geosciences Union • Gempa GmbH • GNS Science / Rafter Radiocarbon • Guralp Systems Limited • ICT international Pty Ltd • International Geological Congress • IODP • Isotopx Ltd • ITS Science & Medical Pte Ltd • International Union of Geodesy & Geophysics (IUGG) • Japan Geoscience Union • Kinemetrics, Inc • KIPP & ZONEN Asia Pacific Pte Ltd • Korea Institute of Geoscience and Mineral Resources • LI-COR Biosciences • NASA • National Institute of Polar Research• NIES GOSAT Project • Nanometrics Inc • Nu Instruments • Office of Naval Research Global • Picarro Inc. • Refraction Technology, Inc. • Sequoia Scientific, Inc. • Singapore Exhibition & Convention Bureau • Springer Verlag GmbH • Taiwan Earthquake Research Center • TAO Journal • Taylor & Francis © 2016 California Institute of Technology. U.S. Government sponsorship acknowledgedGroup • The Asahi Glass Foundation. • The Geological Society • Trimble Navigation • UGT GmbH • Wiley-Blackwell • WITec GmbH • World Scientific • Secretariat Office Meeting Matters International Pte Ltd Add: 1 Commonwealth Lane, #06-23 ONE COMMONWEALTH, Singapore 149544 Information & Updates: Tel: (65) 6472 3108 Fax: (65) 6472 3208 Email: [email protected] Log on to www.asiaoceania.org Outline of Presentation • Theory of pole tides • Solid Earth • Oceans • Observations of ocean pole tide • Tide gauge • Fourier analysis • Power spectrum analysis • Stacking • Satellite altimetry •Impact of ocean pole tide • Oceanography • Small, non-astronomically forced ocean tide • Geodesy • Period and Q of Chandler wobble Theory • Earth rotation • Not constant • Rate of rotation changes (length-of-day variations) • Earth wobbles as it rotates (polar motion) • Centrifugal force acting on Earth • Changes as Earth rotation changes • Deforms elastic solid Earth (solid Earth pole tide) • Changes in rotation rate cause size of Earth’s rotational bulge to change • Polar motion causes solid Earth pole tide • Deforms oceans (ocean pole tide) • Solid Earth pole tide • Y21 pattern, amplitude of a few centimeters • Ocean pole tide • Y21 pattern, amplitude of about 5 mm • Frequency same as forcing (polar motion) frequency Solid Earth Pole Tide at Wetzell & Kokee (Krásná, 2012) Primary signals: 12-month annual and 14-month Chandler 7 -Pattern6DESAI:OBSERVINGTHEPOLETIDEWITHSATELLITEALTIMETRY of Ocean Pole Tide Figure 2. Normalized classical and self-consistent equilibrium ocean pole tide admittance functions with mass conserved, Ec and Es, respectively. Solid contours are positive, dashed contours are negative, and the units are percent. (Desai, 2002) Ec and Es, rather than the corresponding admittance func- classical equilibrium admittance, and also show that the tions Zc and Zs is preferred here because the normalized normalized self-consistent equilibrium admittance has this functions are determined without any prior knowledge of same characteristic. the body Love number, g2. [24]TheloadLovenumbersg0n are also in the strictest [23]Figure2providesmapsofthetwonormalized sense complex parameters whose phase would reflect the lag admittance functions. The spatial distribution of the two in the response of the solid Earth to the load of the oceans, normalized equilibrium admittance functions are similar but but such an effect can be thought of as a third-order effect. the self-consistent equilibrium admittances are noticeably For example, the normalized self-consistent equilibrium amplified. If the continents, self-gravitation, and loading of admittance function might be approximated by (q, l) O the oceans were to be ignored then the normalized equili- (1 + g20 a2a21) P21 exp(il). Assuming that the magnitude of brium admittances would be exclusively defined by a g20 = 1.6935 from the real load Love numbers of Farrell degree 2 order 1 spherical harmonic coefficient a21 =1. [1972], then an unusually large phase of 1–2° in g20 would The presence of oceans serves to reduce this principal result in the factor (1 + g20 a2a21)decreasinginamplitudeby coefficient by 30% to a value of 0.7022, while the self- <0.01%, and having a phase of 0.14–0.28°.Therefore,real gravitation and load of the oceans then amplifies this load Love numbers are always assumed here. coefficient by 20% to a value of 0.8439. It is worth noting that the normalized classical equilibrium admittance is 3.4. Geocentric Pole Tide Deformations of the Sea mathematically required to have a real valued degree 2 Surface order 1 spherical harmonic coefficient such that the imag- [25]Satellitealtimetersobserveradialgeocentricdis- inary part b21 =0(seeAppendixA).Numericalcomputa- placements of the ocean surface and therefore observe the tions verify this convenient characteristic of the normalized sum total of the radial body, ocean, and load tide deforma- History of Ocean Pole Tide • Predicted by Lord Kelvin in 1876 “The sea would be set into vibration, one ocean up and another down …” (Presidential Address, BAAS, 1876) source: likesuccess.com History of Ocean Pole Tide, cont. • Early questionable observations • Detect 14-month signal in 7-yr segments of tide gauge data • A. S. Christie (“The latitude variation tide”, 1900) • H. G. Bakhuyzen (“Über die Änderung der Meereshöhe und ihre Beziehung zur Polhöhenschwankung”, 1913) • E. Przbyllok (Veröff. des Preuss, Geodäsischen Inst., 1919) • J. Baussan (”La composante de Chandler dans la variation des niveaux marins”, 1951) • I. Maximov (“The polar tide in the Earth’s ocean”,1956) • Haubrich and Munk (1959) • Applied power spectrum analysis to tide gauge data • Questioned earlier claims of detection (data too noisy) Haubrich2376 andHAUBRICH ANDMunk MUNK (1959) SWINEMI•NDE1900-1943 104 lO3 104 II II NETHERLAND STATIONS 1041 • NETHERLAND 1865- 1951 STATIONS 103 cyclesper year FI(•. 1--Power spectra for Swinemiinde and the Netherlands stations; solid circles,*low-resolution spectra; open circles,high-resolution spectra. The spectra are obtainedby computingthe month from 1900 to 1954 accordingto (7), cosine transforms of the autocorrelations. The using the unsmoothedlatitude data [Walker result is a smoothedspectrum. As always,there and Young,1957, Table Ia] and settingI -]- k are conflictingdesires between high resolution -- h -- 0.68 [Jeffreys,1952, p. 206]. The values (small A[) and statisticalreliability (large v). so obtained were analyzedwith the recorded For the low-resolutionspectra (A[ -- 0.125cpy) sea level to obtain the normalized co- and there is appreciablesmoothing; for the high- quadrature-spectra,P and Q (Fig. 4). If the resolutionspectra (A• -- 0.0125 cpy) there is recordedtide is in phasewith and proportional little smoothing,and the uncertainty limits are to the equilibriumtide, then P -- i and Q - 0 very large. In the latter casewe might as well over the frequenciesof the pole tide; if the have computed the power for each harmonic recorded tide lags by 90ø, then P -- 0 and of the record, without resorting to autocorrela- Q-1. tion. The method was used only becauseit was T•EoR•e available in convenient machine-programed form. For a rigid earth the period of free nutation Co- and quadrature-spectra--Theequilibrium would be 10 months. But deformations are tide for each station was computed for each caused both in the solid earth and in the oceans History of Ocean Pole Tide, cont. • Early questionable observations • Detect 14-month signal in 7-yr segments of tide gauge data • A. S. Christie (“The latitude variation tide”, 1900) • H. G. Bakhuyzen (“Über die Änderung der Meereshöhe und ihre Beziehung
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