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DSD-NL 2018 Improvement of the harmonic tides in Simona - Kramer

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Presentatie door Werner Kramer, VORtech, op de Simona gebruikersmiddag 2018, tijdens de Deltares Software Dagen - Editie 2018. Donderdag, 7 juni 2018, Delft.

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DSD-NL 2018 Improvement of the harmonic tides in Simona - Kramer

  1. 1. Improvement of the harmonic tides in Simona Werner Kramer 07-06-2018 1
  2. 2. Representation of the 18.6-year nodal cycle in DCSMv6 – Firmijn Zijl Last year it was found that the accuracy with which the tide is represented in the models DCSMv6 and DCSMv6- ZUNOv4 has deteriorated significantly over the years; at important locations with -40% (Zijl, 2015).
  3. 3. Restults for CSM8 cadzand 25-07-2016 3
  4. 4. Tides in Simona U.S. Coast and Geodetic Survey, Paul Schureman, (1928)
  5. 5. Moon gravity force on Earth 𝒂 = βˆ’ 𝐺 𝑀moon π‘Ÿ2 𝒓 Definition: The tidal force is an apparent force that stretches a body towards the center of mass of another body due to a gradient (difference in strength) in gravitational field from the other body
  6. 6. Moon gravity force on Earth apparent force in the non-inertial frame moving with earth force is not pulling the water (normal component) the tangential components pushes water along the surface
  7. 7. M1, M2 and mixed tides Earth is making a full rotation each 23:56 plane of the orbit of moon is make an angle with the equator
  8. 8. S2 and M2 tides gradient in gravitational field of the sun is weaker
  9. 9. earth & moon orbits https://www.youtube.com/watch?v=jWCBhV feAQU
  10. 10. angles equator, ecliptic and plane of moon’s orbit 5Β° 23.5Β°
  11. 11. orbit parameters
  12. 12. orbit parameters typical time scales 𝜏 1 lunar day= 1.035050 solar days (24h) 𝑠 27.321 solar days β„Ž 365.242 solar days 𝑝 8.85 Julian years 𝑁 18.61 Julian years 𝑝𝑙 20942 Julian years
  13. 13. Tidal constituents 𝑦 = 𝑓𝐻 cos(𝑉 + 𝑒 βˆ’ πœ…) 𝑦 = 𝑓𝐻 cos(𝑉𝑑=0 + πœ”π‘‘ + 𝑒 βˆ’ πœ…) nodal precession 109 M2 M2 28.98410420 BZZZZZZ 2 0 0 0 0 0 0 y 128 S2 S2 29.99999994 BBXZZZZ 2 2 -2 0 0 0 0 z 131 K2 K2 30.08213720 BBZZZZZ 2 2 0 0 0 0 0 y 𝜏 𝑠 β„Ž 𝑝 𝑁 𝑝𝑙 𝑓
  14. 14. CSM8 harmonic boundaries 25-07-2016 14 BOUNDAries HARMonic GEneral # Rvw set Csm8 , set konstanten ( 01-01-1900 , GMT ) # Gebaseerd op gecalibreerde rvw (oc76 + handm) 'M2 ','S2 ','N2 ','K2 ', 'O1 ','K1 ','Q1 ','P1 ', 'NU2 ','L2 β€˜ CONSTAnts S : P901, TID= .00000000E+00, AZEro= .0000000E+00 AMPL= 1.81594 .62490 .36832 .16089 .06360 .06010 .01966 .01819 .06382 .05695 PHASE= 1.96559 2.70036 1.73841 2.47748 5.72382 1.24285 4.81509 1.05558 1.45477 1.75424 S : P902, TID= .00000000E+00, AZEro= .0000000E+00 AMPL= 1.57991 .53022 .32657 .13741 .06480 .06194 .02034 .01849 .05709 .05045 PHASE= 1.98618 2.69086 1.71814 2.47395 5.74498 1.30748 4.82661 1.14444 1.48267 1.83034 # TIHARM = 360
  15. 15. Simona harmonic tides REFDATE: calculate 𝑉0,𝑓 and 𝑒 TSTART -> TSTOP: each step y = f𝑀 cos 𝑉0 + πœ”π‘‘ + 𝑒 TIHARM recalculate 𝑓 and 𝑒 REFDATE = 1996-01-01 REFDATE = 2015-01-01 0 9993600 10519200 525600
  16. 16. Radial speeds in WAQUA vs Schureman 25-07-2016 16 M2 8.43113E-03 28.9840899 28.9841042 -0.1250771 MSP2 8.44308E-03 29.0251710 NA MKS2 8.45503E-03 29.0662521 NA M2(KS)2 8.47892E-03 29.1483798 NA 2SN(MK)2 8.54440E-03 29.3734835 NA LABDA2 8.56829E-03 29.4556113 29.4556253 -0.1229112 2MN2 8.58949E-03 29.5284915 NA L2 8.58949E-03 29.5284915 29.5284789 0.11054092 L2A 8.58949E-03 29.5284915 NA L2B 8.59219E-03 29.5377734 NA 2SK2 8.70275E-03 29.9178507 NA T2 8.71470E-03 29.9589318 29.9589333 -0.0132949 S2 8.72665E-03 30.0000129 30.0000000 0.11270683
  17. 17. 25-07-2016 17 Restults with IHO Tidal committee frequencies
  18. 18. Restults with IHO Tidal committee frequencies 25-07-2016 18
  19. 19. Conclusion β€’ Specified radial frequencies were not precise β€’ Only problem for long runs or large TSTART β€’ Use REFDATE (and TIHARM!) β€’ Solution1a: use values provided by IHO tidal committee, single precision β€’ Solution1b: use values provided by IHO tidal committee, double precision β€’ Solution2: calculate phases (V) every time step from orbit equations 25-07-2016 19

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