# FES2014bv1 Ocean Tide Model
# 
# UPDATED 10 Oct 2021
#
# This ocean tide model incorporates the FES2014 ocean tide model that
# uses spherical harmonics to model tidal heights. Those heights are modeled
# as producing an induced and load response (representing deformation of the Earth).
# The deformation model uses Love numbers from elasticity to model the effect on 
# the gravitational field from the height. There is a short explanation of this 
# in IERS Conventions 2010 (Tech Note 36) Rev1.3, where section 6
# on the Geopotential is dated 01 Feb 2018. 
#
# The ocean tide model from the IERS 2010 document is from FES2004. Since that time, 
# a FES2012 and FES2014 model have been produced, but the IERS conventions only
# mentions the FES2004 model. 
#
# The FES2004 model involves:
# - a set of Cnm and Snm gravity coefficients (50x50 for long period, 
#   100x100 for diurnal and semi-dirurnal) for the main waves;
# - a set of wave heights (and an interpolation scheme in eq.(6.16)) for computing
#   Cnm and Snm gravity coefficients for secondary waves;
#   - Table 6.7 in the IERS document identifies for each secondary wave two pivot 
#     waves that are to be used in the interpolation (where a pivot wave is a main wave).
#   - Note: the table incorrectly shows T2 as being a main wave.
# - an equilibrium wave model for the Om1 and Om2 waves;
# - and a set of 100x00 spherical harmonic coefficients for tidal heights for the S1 wave,
#   which was not modeled as part of FES2004.
#   - The intent is to use eq.(6.21) to compute the Cnm and Snm gravity coeficients.
#   - However, only 5 of the 98 Love numbers that are required to use the formula are
#     provided by the document.
#   - And the formulae to apply ellipsoidal corrections to the the result of eq.(6.21)
#     are not provided in the document, though the text mentions that these corrections
#     have been applied for the data provided for the main waves.
#
# CNES (http://grace.obs-mip.fr) manages information derived using the GRACE satellite,
# including the FES2014bv1 ocean tide model expressed in gravity coefficients
# (see http://grace.obs-mip.fr/dealiasing_and_tides/ocean-tides/). The FES2014bv1
# model follows the same ideas as for the FES2004 model described above, with several
# corrections and improvements as noted on the website and explained therein.
#
# The FES2014bv1 model (as described at CNES and created by the GRACE Team) made the following updates:
# - For Om1 and Om2:
#   - The original amplitude and phase angle chi are used, not the updated values.
#      - The GRACE team believes the original values are actually correct, not the updated ones
#        which remain marked in the document as disputed.
#   - The GRACE team has provided a 100x100 set of Cnm and Snm gravity coefficients for Om1
#     wave so that the equilibrium formula in section 6.3.2 need not be used.
#   - The GRACE team believes that the use of just C20 to model Om2 is sufficiently accurate,
#     and its value has been provided so that the equilibrium formula in section 6.3.2 need not be used.
# - For S1:
#   - The GRACE Team has provided a 100x100 set of Cnm and Snm gravity coefficients for S1,
#     alleviating the need to use eq.(6.21), obtain additional Love numbers and find formulae for the
#     ellipsoidal corrections.
#     - The CNES website additionally provides a link to a page containing the first 250 Love numbers.
#   - The GRACE Team believes the correct phase angle chi is 180 deg, and not the 0 value reported
#     by the FES team (nor the value of pi/2 that would be computed using Table 6.6).
#   - The GRACE team uses an updated value for the Doodson number (164.555 vs the IERS Table 6.7 
#     value of 164.556).
# - For Sa:
#    - The GRACE team uses an updated value for the Doodson number (056.555 vs the IERS Table 6.7 
#      value of 056.554).
# - For Msq (Msq is labeled as Msqm in Table 6.7.):
#   - The original software created by the GRACE team used an incorrect phase angle phi for this wave.
#   - It's not clear whether the values provided by IERS in its fes2004_Cnm-Snm.dat file has this value
#      reported correctly or not.
# - For long period waves (waves whose first Doodson number is a 0):
#   - The GRACE team has provided a 100x100 set of Cnm and Snm gravity coefficients,
#     an improvement over the 50x50 set given for FES2004.
# - A 100x100 set of Cnm and Snm gravity coefficients have been created by the GRACE team for certain 
#   secondary waves listed in Table 6.7: MSf, J1, E2 (eps2), Mu2, Nu2, LA2 (lam2), L2, and R2.
#   - These no longer require using interpolation based upon pivot waves for their computation.
# - A 100x100 set of Cnm and Snm gravity coefficients have been created  by the GRACE team for 
#   additional waves not modeled by FES2004: MKS, M3, N4, MN4, MS4, S4, M6, and M8.
#
# NOTE: AGI's model of the ocean pole tide discussed in section 6.5 is modeled using only 
#       the C21-S21 coefs, using the equations in section 6.5 of the IERS document.
#
# Wave Constituent listing
#
# From Table 6.7 IERS Conventions 2010 Rev1.3, with updates for FES2014bv1.
#
#   The table lists constituents and values for FES2004. Much of the table applies
#   to FES2014bv1 as well. Updates for FES2014bv1 described above have been made.
#
#   NOTE: Entries 117.655, 245.555 and 245.645 identify a first pivot wave (135.455, 237.755,
#         and 237.755 respectively) that are not found in the table. In below, we have
#         assumed that these are typos and that the first pivot waves should be 135.655,
#         235.755, and 235.755 respectively.
#
# NOTE: first Doodson integer (n1) below is {0, 1, 2, 3, 4, 6, 8}
#       0 - long period, 1 - diurnal, 2 = semi-dirurnal, 4 - quarter-diurnal, etc.
#