Data source:

1) Ocean tidal model GOT56P. 

   It defines height of 16 primary tidal constituents:

   sigma1, Q1, O1, P1, S1, K1, J1, OO1, 2N2, mu2, N2, M2, S2,
   K2, M4, MS4, 

   4 minor 3rd degree constituents:

   3M1, 3N2, 3L2, M3

   and 17 inferred constituents:

   2Q1, chi1, tau1, rho1, M1, pi1, psi1, phi1, theta1, SO1, eps2,
   nu2, L2, lambda2, T2, R2, eta2, that a computed using admittance's.


   For any inferred constituents in the diurnal band, the resonance effect 
   from the Earth's fluid core has been accounted for (Ray, 2017).
   
   These constituents are defined on a uniform grid resolution 
   0.125 x 0.125 degrees. 

   The model description can be found in 
   Ray,~R., (2013). "Precise comparisons of bottom-pressure and altimetric 
   ocean tides", JGR, 118, 4570--4584.

   In addition, 10 sidelobes of the main tidal constituents
   Q1-, O1-, K1-, K1+, N2-, M2-, K2+ were added.
   Their frequencies differ from the frequencies of the main tides by
   -+ 1.06D-8 rad/sec. The complex amplitudes of water height of sidelobe
   (H') and the main tide (H) are related to the complex amplitudes of 
   their tide generating potentials A and A' via the admittance 
   relationship:

   H'c + i H's     A'c + A's
   ----------- = -----------
   Hc  + i Hs      Ac  + i As

   Here Hc denotes the cosine term in harmonic constituent and Hs 
   denotes the sine term of the harmonic constituent.

   The most important altimeter datasets used for the development of 
   GOT56 are the long series of 10-day measurements obtained from 
   missions Topex/Poseidon, Jason-1, Jason-2, Jason-3, and Sentinel-6A 
   In addition, CryoSat-2 measurements have been heavily used over
   polar regions. The series of altimeters launched by the European 
   Space Agency: ERS-1, ERS-2, Envisat, Sentinel-3A, Sentinel-3B, 
   as well as the SARAL mission, launched by ISRO and CNES -- are 
   less useful for tide work because of their sun-synchronous orbits, 
   but some of those data have been used here to help map lunar tides 
   in some regions.

2) Long-periodic (zonal) ocean tides.

   In addition, 6 long periodic tides from Ray & Erofeeva (2014) model
   are included:

   node, sa, ssa, mm, mf, mt

   These long-periodic data give results of simulations of tidal 
   constituents in the long-period band, from 9 days to annual, plus 
   a self-consistent equilibrium tide at 18.6 years.  The dynamic tides 
   are described in the following paper 

   R. D. Ray & S. Y. Erofeeva, "Long-period tidal variations in the 
   length of day", https://doi.org/10.1002/2013JB010830

   In total, 53 tidal constituents are considered.

   The original GOT56 model was extrapolated inland up to 6 cells.
   Extrapolation was performed by convolution with the exponential
   kernel. The inland extrapolation was done to avoid Gibbs phenomena
   when windowed land-sea mask is applied before spherical harmonics
   transform.

   Bibliography:

   Ray, R.~D., (2025) Precise comparisons of bottom-pressure and 
     Documentation for Goddard Ocean Tide Solution GOT5: Global Tides 
     from Multi-mission Satellite Altimetry, NASA Technical Memorandum,
     TM-20250002085.
     https://ntrs.nasa.gov/api/citations/20250002085/downloads/GOT5-TechMemo.pdf

   Ray, R. D. (2017). On tidal inference in the diurnal band. Journal 
     of Atmospheric and Oceanic Technology, 34, 437--446. 
     doi: 10.1175/JTECH-D-16-0142.1

   Ray, R.~D., (2013) Precise comparisons of bottom-pressure and 
     altimetric ocean tides, J. Geophys., Res., 118, 4570--4584.

   Ray, R., (1999), A global ocean tide model from Topex/Poseidon 
     altimetry: GOT99.2, NASA Tech Memo 209478, 58 pages, Sept. 1999.

   Schrama,E. and R Ray, (1994), Journal of Geophysical Research, 
     v.99, p 24799.

3) The Love numbers have been computed using REAR software,
   Melini  D.,  Gegout  P.,  Spada  G,  King  M.  (2014), "REAR -- 
   a regional  Elastic  Rebound  calculator. User manual for version 1.0", 
   available on-line at  http://hpc.rm.ingv.it/rear.
   Earth reference model STW105 (Kustowski et al., 2007), which is an update 
   of PREM (Dziewonski and Anderson, 1981) was used. The elastic rheology 
   of the Earth derives from the waves speed and the density, with the top 
   three kilometers of oceanic water replaced by underneath rock materials.  
   The model defines the Earth (hydrostatic) equilibrium, the pressure and  
   the gravity inside the Earth; numerical computations allow to take 
   compressibility into account. The Love numbers are computed in the 
   coordinate system with the centrum at the center of mass of the total 
   Earth: solid Earth, ocean, and the atmosphere. Therefore, loading 
   displacements computed with using such Love numbers are the displacements 
   with respect to the center of mass of the total Earth that includes 
   the ocean.

4) The land/sea mask was derived from the MOD44W model using the 
   following procedure: a) original MOD4WW mask was re-sampled to 
   resolution 86400x43000 over longitude and latitude with Closed 
   basins, such as lakes and the Caspian Sea are considered land;
   b) spherical harmonics transform of degree/order 21,599 was performed;
   c) the spherical harmonics transform of the mask was multiplied
   by Blackman window of degree/order 2,699; d) the inverse spherical
   harmonics transform of degree/order 2,699 was performed over the 
   results to for, the final bandlimited land-sea mask with resolution 
   10800x5401 over longitude and latitude (2'x2'or ~3.7 km). 
   The land-sea mask at a given cell is a number in a range -0.0004 to 
   1.0006 that is equal to the ratio of the area covered by land (i.e. 
   non-ocean in this context) to the total area of the cell.

5) Sampling correction was applied. The sampling correction was computed 
   using the band-limited windowed land-sea mask with resolution 15"x15"
   (464x464m). The sampling correction mitigates artifacts of using 
   band-limited windowed mask truncated at degree/order 2,699 instead of 
   using the true mask, which is not bandlimited to degree/order at 
   least 100,000.

