Data source:

1) Ocean tidal model FES2012. It defines height of 32 tidal constituents 
   at the uniform grid with resolution 0.0625 x 0.0625 degrees. 

   See project web pages about more information about FES2012

   http://www.aviso.oceanobs.com/en/data/products/auxiliary-products/
   global-tide-fes2004-fes99/description-fes2012.html

   http://www.legos.obs-mip.fr/recherches/equipes/ecola/projets/fes2012

   Not all tides were used. Tides E2, M3, MKS2, MN4, MS4 were dropped
   since their phases and amplitudes were not unambiguously defined.

   In addition, 10 sidelobes of the main tidal constituents
   MF+, MTM+, Q1-, O1-, K1-, K1+, J1+, 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.

   In total, 36 tidal constituents are considered.

   The original FES2012 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.

   In addition to gravity tides from FES2012 model, two other tides
   are modeled: pole tide and long periodic zonal tide. The oceanic
   response to these tides is considered equilibrium.
   The pole tide is the response of the oceanic mass to changes of
   the centrifugal potential due to the polar motion. The polar motion
   is modeled as a sum of a constant shift, secular drift, and three
   harmonic terms: with annual frequency, CW1 and CW2 frequencies.
   The periods that corresponds to CW1 and CW2 frequencies are 
   445.41 and 431.2 days respectively. Only the response to these three 
   harmonic terms is modeled. Amplitudes and phases of these harmonics 
   were fitted to series of polar motion over [1984, 2014]. 
   NB: one should avoid a temptation to interpret these frequencies:
   these are just fitting parameters. The rms of post-fit residuals 
   is 0.029 mas. This harmonic model allows to predict pole tide for the 
   period of [1984, 2020].

   Two zonal equilibrium ties are added: annual tide and nodal 
   (period 18.6 years) tides.

2) 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.

3) 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.

4) 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.


