1、Ocean Tide mapping from satellite with a view towards the Northwest European Shelf. Dr Ole B. Andersen, Danish National Space Center, Copenhagen, Denmark,Ocean Tides W. Zahel Colloquium | Hamburg Germany - 31. March 2006 | OA | side 2Overview.Introduction (why the interest in tides). Satellite Altim

2、etry and tidal modelling. Development of Ocean Tide models over the last 15 years. State of the Art Ocean tide models. Ocean Loading Tidal Inversion/assimilation (OTIS) on the NW European ShelfShallow water tides globallySummary Ocean Tides W. Zahel Colloquium | Hamburg Germany - 31. March 2006 | OA

3、 | side 3Tides are FascinatingOcean Tides W. Zahel Colloquium | Hamburg Germany - 31. March 2006 | OA | side 4Tides are FunTidal surfingOcean Tides W. Zahel Colloquium | Hamburg Germany - 31. March 2006 | OA | side 5Tides can be ”dangerous” BUT TIDES ARE PREDICTABLEQuestion is HOW.Ocean Tides W. Zah

4、el Colloquium | Hamburg Germany - 31. March 2006 | OA | side 6Starting in Ocean tidesIn 1992Ocean Tides W. Zahel Colloquium | Hamburg Germany - 31. March 2006 | OA | side 7Tide GaugesTidal Observations - TraditionalOcean Tides W. Zahel Colloquium | Hamburg Germany - 31. March 2006 | OA | side 8Satel

5、lite altimetry revolutionized tidal mapping. Ocean Tides W. Zahel Colloquium | Hamburg Germany - 31. March 2006 | OA | side 9Ocean Tides W. Zahel Colloquium | Hamburg Germany - 31. March 2006 | OA | side 10T/P Track coverageOcean Tides W. Zahel Colloquium | Hamburg Germany - 31. March 2006 | OA | si

6、de 11T/P Tracks and Tide Gauges on the NW European Shelf. Ocean Tides W. Zahel Colloquium | Hamburg Germany - 31. March 2006 | OA | side 12Observations The difference. Satellites observes ”globally”, but in-frequent. Tide gauges frequent but mostly at the coast (inter/extrapolation is an issue)Satel

7、lite observes geocentric tide: This is ocean + Load tide hsat = h0 +hlTide Gauge observes the ocean tide. It moves up and down with the load. Hgauge = hoLoading is an issue.Ocean Tides W. Zahel Colloquium | Hamburg Germany - 31. March 2006 | OA | side 13Alias PeriodsOcean Tides W. Zahel Colloquium |

8、 Hamburg Germany - 31. March 2006 | OA | side 14North Sea Aberdeen Altimetry versus Tide GaugeIncluding tides correlation 95%Ocean Tides W. Zahel Colloquium | Hamburg Germany - 31. March 2006 | OA | side 15Tidal Modelling Tidal SchoolsThe pointwise estimated constituents (amplitude and phase) must b

9、e interpolated onto some grid.Including tidal currents six param for each const required.(Regular Arakawa C or Finite Element. 3 Schools: Empirically Interpolating altimetry only ”Best fit to observations” - No currents / only heightsFree Pure Hydrodynamic. ”Knowledge from hydrodynamic equations. Tu

10、ned using obs. This also gives tidal currents. ”Best fit to hydrodynamic”Assimilation. Global Inversion. Assimilate altimetry+tide gauge with hydrodynamic modelBy pertubating model using observations. ”Best fit to observations and hydrodynamic”O(jiān)cean Tides W. Zahel Colloquium | Hamburg Germany - 31.

11、March 2006 | OA | side 16Development over the past 15 yearsPre T/P and ERS era, Global standard was Schwiderski (1980), Zahel (1991); Hendershott (1990)1991- first empirical altimetric solution (GEOSAT) GEOSAT: Cartwright and Ray (1991)1994-1995 first set of T/P solutions:empirical: Schrama and Ray

12、(1994), Eanes / CSR3 (1995),Andersen (1995), Desai-Whar (1995)hydrod.+Assim. : Egbert et al (1994), Le Provost et al /FES 95(1995), Kantha(1995), .2001: preliminary JASON 1 tide solutions:empirical: Ray / GOT 99(2000), Eanes / CSR4 (2001), hydrod.+Assim. : Egbert (2000), Lefevre et al/ FES 99 (2002)

13、, NAO(2002)2004: more recent gobal solutionsempirical: Ray (2002) / GOT2001hydrod.+Assim. : FES 2004 TPXO 7Ocean Tides W. Zahel Colloquium | Hamburg Germany - 31. March 2006 | OA | side 17From Le Provost, TP SWT, 2003 Ocean Tides W. Zahel Colloquium | Hamburg Germany - 31. March 2006 | OA | side 18A

14、ccuracy Improvement2.12.2Ocean Tides W. Zahel Colloquium | Hamburg Germany - 31. March 2006 | OA | side 19Ocean Tides - M2 loopOcean Tides W. Zahel Colloquium | Hamburg Germany - 31. March 2006 | OA | side 20M2 Ocean Tide LoadingDISPLACEMENTS (cm) AND GRAVITY (gal)Courtesy of - and with bes

15、t regards: Trevor Baker. Ocean Tides W. Zahel Colloquium | Hamburg Germany - 31. March 2006 | OA | side 21Ocean Tides and Ocean LoadingThe improvement in Ocean tide determinationAlso affects ocean loadingComputation. Difference in M2 loading amplitudeBetween C&R-91 and FES95.1Ranges 1 cm Ocean Tides

16、 W. Zahel Colloquium | Hamburg Germany - 31. March 2006 | OA | side 22Ocean LoadingOcean Tides W. Zahel Colloquium | Hamburg Germany - 31. March 2006 | OA | side 23Present Status of Ocean Tide ModelsRecent Global altimetric ocean tide models NAO (Japan), CSR (Texas), FES (Grenoble), GOT (Ray), TPXO(

17、Egbert) NAO99CSR4.0 FES2004 GOT2002 TPXO6All models are very similar and accurate in deep oceanAccuracy in the order of 2-3 cm Major differences are seen on the shelves.Accuracy decreases with proximity to coast to 20-50 cm. We need to improve global ocean tide models on shelves.Increase resolution

18、Improve bathymetry. Include shallow water tidal constituents.Use new altimetry data (investigate the impact of T/P 2). Seasonal modulation of tidal amplitudes (Andersen & Hues, 2001).Ocean Tides W. Zahel Colloquium | Hamburg Germany - 31. March 2006 | OA | side 24Shallow Water Tides. Jointly work wi

19、th.Gary Egbert and Lana Erofeeva (OSU)Richard Ray (NASA/GSFC)Ocean Tides W. Zahel Colloquium | Hamburg Germany - 31. March 2006 | OA | side 25Shallow water constituents Ocean Tides W. Zahel Colloquium | Hamburg Germany - 31. March 2006 | OA | side 26Pros and Cons of Satellite AltimetryTrack ”resolut

20、ion” is problematic in shallow water. T/P+T/P2+JASON 280 km (Equator) M4 can be accurately determined (400) T/P2 decrease this to 140 km - Few obs will give in-accurate M4 estimate ( importance of accurate bathymetryOcean Tides W. Zahel Colloquium | Hamburg Germany - 31. March 2006 | OA | side 32Dat

21、a and Region for OTIS model4 Assimilation models created(G. Egbert and L. Erofeeva)Forward non-linear model usedTo create prior model (1/12 ). Joint model with 11 constituents.(M2,S2,K2,N2,K1,O1,M4,MN4,MS4)Boundary for all const: TPXO7But linearlized shallow-water eqFor the data assimilation. Standa

22、rd OTIS covariance used. Prior: Non-linear time stepping modelInv-1:Uses all T/P-Jason data on original T/P tracks.Inv-2:As Inv-1, but deleting some data in EnCEC area.Inv-3:As Inv-2, plus Topex2 interleaved data.Inv-4:As Inv-3, plus a subset of gauge data.Ocean Tides W. Zahel Colloquium | Hamburg G

23、ermany - 31. March 2006 | OA | side 33Errors in continuity Equationcontinuity equationError in in continuity equation for M4 due to M2 forcing:Forcing is highly concentrated in very shallow areasMore realistic (localized) forcing errors better inverse solution?Errors in the continuity equation contr

24、ibute only about 10% to the elevation error, and are thus probably negligible. Standard OTIS covariance was usedOcean Tides W. Zahel Colloquium | Hamburg Germany - 31. March 2006 | OA | side 34Tide Gauge MisfitRMS misfit to TopexM4 comparisonBestWorstOcean Tides W. Zahel Colloquium | Hamburg Germany - 31. March 2006 | OA | side 35INV-4 Model (Most accurate M4 model)Oce