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Nodal modulation
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This commit fixes a few (potential) inconsistencies between open
boundary tidal forcing and astronomical tidal forcing.

1. There was an inconsistency in the code that the nodal modulation
can be calculated in OBC tidal forcing but not in the astronomical
tidal forcing. This commit fixes this bug so that nodal modulation
is applied to both forcings.

2. In the previous version of MOM_open_boundary.F90, a different
set of tidal parameters can be set for open boundary tidal forcing,
leading to potential inconsistency with astronomical tidal forcing.
This commit obsoletes those for open boundary tidal forcing.

3. Another important bug fix is that the equilibrium phase is added
to the SAL term, which was missing in the original code.
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@c2xu
c2xu committed Jan 18, 2025
1 parent 40a59f7 commit cb68008
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Showing 3 changed files with 90 additions and 34 deletions.
20 changes: 12 additions & 8 deletions src/core/MOM_open_boundary.F90
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Expand Up @@ -1169,26 +1169,30 @@ subroutine initialize_obc_tides(OBC, US, param_file)
type(astro_longitudes) :: nodal_longitudes !< Solar and lunar longitudes for tidal forcing
type(time_type) :: nodal_time !< Model time to calculate nodal modulation for.
integer :: c !< Index to tidal constituent.
logical :: tides !< True if astronomical tides are also used.

call get_param(param_file, mdl, "OBC_TIDE_CONSTITUENTS", tide_constituent_str, &
"Names of tidal constituents being added to the open boundaries.", &
fail_if_missing=.true.)

call get_param(param_file, mdl, "OBC_TIDE_ADD_EQ_PHASE", OBC%add_eq_phase, &
call get_param(param_file, mdl, "TIDES", tides, &
"If true, apply tidal momentum forcing.", default=.false., do_not_log=.true.)

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call get_param(param_file, mdl, "TIDE_USE_EQ_PHASE", OBC%add_eq_phase, &
"If true, add the equilibrium phase argument to the specified tidal phases.", &
default=.false., fail_if_missing=.false.)
old_name="OBC_TIDE_ADD_EQ_PHASE", default=.false., do_not_log=tides)

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call get_param(param_file, mdl, "OBC_TIDE_ADD_NODAL", OBC%add_nodal_terms, &
call get_param(param_file, mdl, "TIDE_ADD_NODAL", OBC%add_nodal_terms, &
"If true, include 18.6 year nodal modulation in the boundary tidal forcing.", &
default=.false.)
old_name="OBC_TIDE_ADD_NODAL", default=.false., do_not_log=tides)

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call get_param(param_file, mdl, "OBC_TIDE_REF_DATE", tide_ref_date, &
call get_param(param_file, mdl, "TIDE_REF_DATE", tide_ref_date, &
"Reference date to use for tidal calculations and equilibrium phase.", &
fail_if_missing=.true.)
old_name="OBC_TIDE_REF_DATE", defaults=(/0, 0, 0/), do_not_log=tides)

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call get_param(param_file, mdl, "OBC_TIDE_NODAL_REF_DATE", nodal_ref_date, &
call get_param(param_file, mdl, "TIDE_NODAL_REF_DATE", nodal_ref_date, &
"Fixed reference date to use for nodal modulation of boundary tides.", &
fail_if_missing=.false., defaults=(/0, 0, 0/))
old_name="OBC_TIDE_NODAL_REF_DATE", defaults=(/0, 0, 0/), do_not_log=tides)

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if (.not. OBC%add_eq_phase) then
! If equilibrium phase argument is not added, the input phases
Expand Down
27 changes: 17 additions & 10 deletions src/diagnostics/MOM_harmonic_analysis.F90
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Expand Up @@ -46,7 +46,9 @@ module MOM_harmonic_analysis
time_ref !< Reference time (t = 0) used to calculate tidal forcing
real, dimension(MAX_CONSTITUENTS) :: &
freq, & !< The frequency of a tidal constituent [T-1 ~> s-1]
phase0 !< The phase of a tidal constituent at time 0 [rad]
phase0, & !< The phase of a tidal constituent at time 0 [rad]
tide_fn, & !< Amplitude modulation of tides by nodal cycle [nondim].
tide_un !< Phase modulation of tides by nodal cycle [rad].
real, allocatable :: FtF(:,:) !< Accumulator of (F' * F) for all fields [nondim]
integer :: nc !< The number of tidal constituents in use
integer :: length !< Number of fields of which harmonic analysis is to be performed
Expand All @@ -60,13 +62,16 @@ module MOM_harmonic_analysis

!> This subroutine sets static variables used by this module and initializes CS%list.
!! THIS MUST BE CALLED AT THE END OF tidal_forcing_init.
subroutine HA_init(Time, US, param_file, time_ref, nc, freq, phase0, const_name, CS)
subroutine HA_init(Time, US, param_file, time_ref, nc, freq, phase0, const_name, tide_fn, tide_un, CS)

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type(time_type), intent(in) :: Time !< The current model time
type(time_type), intent(in) :: time_ref !< Reference time (t = 0) used to calculate tidal forcing
type(unit_scale_type), intent(in) :: US !< A dimensional unit scaling type
type(param_file_type), intent(in) :: param_file !< A structure to parse for run-time parameters
real, dimension(MAX_CONSTITUENTS), intent(in) :: freq !< The frequency of a tidal constituent [T-1 ~> s-1]
real, dimension(MAX_CONSTITUENTS), intent(in) :: phase0 !< The phase of a tidal constituent at time 0 [rad]
real, dimension(MAX_CONSTITUENTS), intent(in) :: &
freq, & !< The frequency of a tidal constituent [T-1 ~> s-1]
phase0, & !< The phase of a tidal constituent at time 0 [rad]
tide_fn, & !< Amplitude modulation of tides by nodal cycle [nondim].
tide_un !< Phase modulation of tides by nodal cycle [rad].
integer, intent(in) :: nc !< The number of tidal constituents in use
character(len=16), intent(in) :: const_name(MAX_CONSTITUENTS) !< The name of each constituent
type(harmonic_analysis_CS), intent(out) :: CS !< Control structure of the MOM_harmonic_analysis module
Expand Down Expand Up @@ -135,6 +140,8 @@ subroutine HA_init(Time, US, param_file, time_ref, nc, freq, phase0, const_name,
CS%time_ref = time_ref
CS%freq = freq
CS%phase0 = phase0
CS%tide_fn = tide_fn
CS%tide_un = tide_un

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CS%nc = nc
CS%const_name = const_name
CS%length = 0
Expand Down Expand Up @@ -198,8 +205,8 @@ subroutine HA_accum_FtF(Time, CS)
do c=1,nc
icos = 2*c
isin = 2*c+1
cosomegat = cos(CS%freq(c) * now + CS%phase0(c))
sinomegat = sin(CS%freq(c) * now + CS%phase0(c))
cosomegat = CS%tide_fn(c) * cos(CS%freq(c) * now + CS%phase0(c) + CS%tide_un(c))
sinomegat = CS%tide_fn(c) * sin(CS%freq(c) * now + CS%phase0(c) + CS%tide_un(c))

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! First column, corresponding to the zero frequency constituent (mean)
CS%FtF(icos,1) = CS%FtF(icos,1) + cosomegat
Expand All @@ -208,8 +215,8 @@ subroutine HA_accum_FtF(Time, CS)
do cc=1,c
iccos = 2*cc
issin = 2*cc+1
ccosomegat = cos(CS%freq(cc) * now + CS%phase0(cc))
ssinomegat = sin(CS%freq(cc) * now + CS%phase0(cc))
ccosomegat = CS%tide_fn(cc) * cos(CS%freq(cc) * now + CS%phase0(cc) + CS%tide_un(cc))
ssinomegat = CS%tide_fn(cc) * sin(CS%freq(cc) * now + CS%phase0(cc) + CS%tide_un(cc))

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! Interior of the matrix, corresponding to the products of cosine and sine terms
CS%FtF(icos,iccos) = CS%FtF(icos,iccos) + cosomegat * ccosomegat
Expand Down Expand Up @@ -290,8 +297,8 @@ subroutine HA_accum_FtSSH(key, data, Time, G, CS)
do c=1,nc
icos = 2*c
isin = 2*c+1
cosomegat = cos(CS%freq(c) * now + CS%phase0(c))
sinomegat = sin(CS%freq(c) * now + CS%phase0(c))
cosomegat = CS%tide_fn(c) * cos(CS%freq(c) * now + CS%phase0(c) + CS%tide_un(c))
sinomegat = CS%tide_fn(c) * sin(CS%freq(c) * now + CS%phase0(c) + CS%tide_un(c))

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do j=js,je ; do i=is,ie
ha1%FtSSH(i,j,icos) = ha1%FtSSH(i,j,icos) + (data(i,j) - ha1%ref(i,j)) * cosomegat
ha1%FtSSH(i,j,isin) = ha1%FtSSH(i,j,isin) + (data(i,j) - ha1%ref(i,j)) * sinomegat
Expand Down
77 changes: 61 additions & 16 deletions src/parameterizations/lateral/MOM_tidal_forcing.F90
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Expand Up @@ -70,7 +70,9 @@ module MOM_tidal_forcing
ampsal(:,:,:), & !< The amplitude of the SAL [Z ~> m].
cosphase_prev(:,:,:), & !< The cosine of the phase of the amphidromes in the previous tidal solutions [nondim].
sinphase_prev(:,:,:), & !< The sine of the phase of the amphidromes in the previous tidal solutions [nondim].
amp_prev(:,:,:) !< The amplitude of the previous tidal solution [Z ~> m].
amp_prev(:,:,:), & !< The amplitude of the previous tidal solution [Z ~> m].
tide_fn(:), & !< Amplitude modulation of tides by nodal cycle [nondim].
tide_un(:) !< Phase modulation of tides by nodal cycle [rad].
end type tidal_forcing_CS

integer :: id_clock_tides !< CPU clock for tides
Expand Down Expand Up @@ -251,9 +253,14 @@ subroutine tidal_forcing_init(Time, G, US, param_file, CS, HA_CS)
real, dimension(MAX_CONSTITUENTS) :: amp_def ! Default amplitude for each tidal constituent [m]
real, dimension(MAX_CONSTITUENTS) :: love_def ! Default love number for each constituent [nondim]
integer, dimension(3) :: tide_ref_date !< Reference date (t = 0) for tidal forcing.
integer, dimension(3) :: nodal_ref_date !< Reference date for calculating nodal modulation for tidal forcing.
logical :: use_M2, use_S2, use_N2, use_K2, use_K1, use_O1, use_P1, use_Q1
logical :: use_MF, use_MM
logical :: tides ! True if a tidal forcing is to be used.
logical :: add_nodal_terms = .false. !< If true, insert terms for the 18.6 year modulation when
!! calculating tidal forcing.
type(time_type) :: nodal_time !< Model time to calculate nodal modulation for.
type(astro_longitudes) :: nodal_longitudes !< Solar and lunar longitudes for tidal forcing
logical :: HA_ssh, HA_ubt, HA_vbt
! This include declares and sets the variable "version".
# include "version_variable.h"
Expand Down Expand Up @@ -385,11 +392,11 @@ subroutine tidal_forcing_init(Time, G, US, param_file, CS, HA_CS)
call get_param(param_file, mdl, "TIDE_REF_DATE", tide_ref_date, &
"Year,month,day to use as reference date for tidal forcing. "//&
"If not specified, defaults to 0.", &
defaults=(/0, 0, 0/))
old_name="OBC_TIDE_REF_DATE", defaults=(/0, 0, 0/))

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call get_param(param_file, mdl, "TIDE_USE_EQ_PHASE", CS%use_eq_phase, &
"Correct phases by calculating equilibrium phase arguments for TIDE_REF_DATE. ", &
default=.false., fail_if_missing=.false.)
old_name="OBC_TIDE_ADD_EQ_PHASE", default=.false., fail_if_missing=.false.)

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if (sum(tide_ref_date) == 0) then ! tide_ref_date defaults to 0.
CS%time_ref = set_date(1, 1, 1, 0, 0, 0)
Expand Down Expand Up @@ -528,8 +535,46 @@ subroutine tidal_forcing_init(Time, G, US, param_file, CS, HA_CS)
enddo
endif

call get_param(param_file, mdl, "TIDE_ADD_NODAL", add_nodal_terms, &
"If true, include 18.6 year nodal modulation in the astronomical tidal forcing.", &
old_name="OBC_TIDE_ADD_NODAL", default=.false.)

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call get_param(param_file, mdl, "TIDE_NODAL_REF_DATE", nodal_ref_date, &
"Fixed reference date to use for nodal modulation of astronomical tidal forcing.", &
old_name="OBC_TIDE_REF_DATE", fail_if_missing=.false., defaults=(/0, 0, 0/))

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! If the nodal correction is based on a different time, initialize that.
! Otherwise, it can use N from the time reference.
if (add_nodal_terms) then
if (sum(nodal_ref_date) /= 0) then
! A reference date was provided for the nodal correction
nodal_time = set_date(nodal_ref_date(1), nodal_ref_date(2), nodal_ref_date(3))
call astro_longitudes_init(nodal_time, nodal_longitudes)
elseif (CS%use_eq_phase) then

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! Astronomical longitudes were already calculated for use in equilibrium phases,
! so use nodal longitude from that.
nodal_longitudes = CS%tidal_longitudes

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else
! Tidal reference time is a required parameter, so calculate the longitudes from that.
call astro_longitudes_init(CS%time_ref, nodal_longitudes)

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endif
endif

allocate(CS%tide_fn(nc))
allocate(CS%tide_un(nc))

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do c=1,nc

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! Find nodal corrections if needed
if (add_nodal_terms) then
call nodal_fu(trim(CS%const_name(c)), nodal_longitudes%N, CS%tide_fn(c), CS%tide_un(c))

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else
CS%tide_fn(c) = 1.0
CS%tide_un(c) = 0.0

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endif
enddo

if (present(HA_CS)) then
call HA_init(Time, US, param_file, CS%time_ref, CS%nc, CS%freq, CS%phase0, CS%const_name, HA_CS)
call HA_init(Time, US, param_file, CS%time_ref, CS%nc, CS%freq, CS%phase0, CS%const_name, &
CS%tide_fn, CS%tide_un, HA_CS)

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call get_param(param_file, mdl, "HA_SSH", HA_ssh, &
"If true, perform harmonic analysis of sea serface height.", default=.false.)
if (HA_ssh) call HA_register('ssh', 'h', HA_CS)
Expand Down Expand Up @@ -614,26 +659,26 @@ subroutine calc_tidal_forcing(Time, e_tide_eq, e_tide_sal, G, US, CS)

do c=1,CS%nc
m = CS%struct(c)
amp_cosomegat = CS%amp(c)*CS%love_no(c) * cos(CS%freq(c)*now + CS%phase0(c))
amp_sinomegat = CS%amp(c)*CS%love_no(c) * sin(CS%freq(c)*now + CS%phase0(c))
amp_cosomegat = CS%amp(c)*CS%love_no(c)*CS%tide_fn(c) * cos(CS%freq(c)*now + (CS%phase0(c) + CS%tide_un(c)))
amp_sinomegat = CS%amp(c)*CS%love_no(c)*CS%tide_fn(c) * sin(CS%freq(c)*now + (CS%phase0(c) + CS%tide_un(c)))

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do j=Jsq,Jeq+1 ; do i=Isq,Ieq+1
e_tide_eq(i,j) = e_tide_eq(i,j) + (amp_cosomegat*CS%cos_struct(i,j,m) + &
amp_sinomegat*CS%sin_struct(i,j,m))
enddo ; enddo
enddo

if (CS%use_tidal_sal_file) then ; do c=1,CS%nc
cosomegat = cos(CS%freq(c)*now)
sinomegat = sin(CS%freq(c)*now)
cosomegat = CS%tide_fn(c) * cos(CS%freq(c)*now + (CS%phase0(c) + CS%tide_un(c)))
sinomegat = CS%tide_fn(c) * sin(CS%freq(c)*now + (CS%phase0(c) + CS%tide_un(c)))

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do j=Jsq,Jeq+1 ; do i=Isq,Ieq+1
e_tide_sal(i,j) = e_tide_sal(i,j) + CS%ampsal(i,j,c) * &
(cosomegat*CS%cosphasesal(i,j,c) + sinomegat*CS%sinphasesal(i,j,c))
enddo ; enddo
enddo ; endif

if (CS%use_tidal_sal_prev) then ; do c=1,CS%nc
cosomegat = cos(CS%freq(c)*now)
sinomegat = sin(CS%freq(c)*now)
cosomegat = CS%tide_fn(c) * cos(CS%freq(c)*now + (CS%phase0(c) + CS%tide_un(c)))
sinomegat = CS%tide_fn(c) * sin(CS%freq(c)*now + (CS%phase0(c) + CS%tide_un(c)))

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do j=Jsq,Jeq+1 ; do i=Isq,Ieq+1
e_tide_sal(i,j) = e_tide_sal(i,j) - CS%sal_scalar * CS%amp_prev(i,j,c) * &
(cosomegat*CS%cosphase_prev(i,j,c) + sinomegat*CS%sinphase_prev(i,j,c))
Expand Down Expand Up @@ -692,8 +737,8 @@ subroutine calc_tidal_forcing_legacy(Time, e_sal, e_sal_tide, e_tide_eq, e_tide_

do c=1,CS%nc
m = CS%struct(c)
amp_cosomegat = CS%amp(c)*CS%love_no(c) * cos(CS%freq(c)*now + CS%phase0(c))
amp_sinomegat = CS%amp(c)*CS%love_no(c) * sin(CS%freq(c)*now + CS%phase0(c))
amp_cosomegat = CS%amp(c)*CS%love_no(c)*CS%tide_fn(c) * cos(CS%freq(c)*now + (CS%phase0(c) + CS%tide_un(c)))
amp_sinomegat = CS%amp(c)*CS%love_no(c)*CS%tide_fn(c) * sin(CS%freq(c)*now + (CS%phase0(c) + CS%tide_un(c)))

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do j=Jsq,Jeq+1 ; do i=Isq,Ieq+1
amp_cossin = (amp_cosomegat*CS%cos_struct(i,j,m) + amp_sinomegat*CS%sin_struct(i,j,m))
e_sal_tide(i,j) = e_sal_tide(i,j) + amp_cossin
Expand All @@ -702,8 +747,8 @@ subroutine calc_tidal_forcing_legacy(Time, e_sal, e_sal_tide, e_tide_eq, e_tide_
enddo

if (CS%use_tidal_sal_file) then ; do c=1,CS%nc
cosomegat = cos(CS%freq(c)*now)
sinomegat = sin(CS%freq(c)*now)
cosomegat = CS%tide_fn(c) * cos(CS%freq(c)*now + (CS%phase0(c) + CS%tide_un(c)))
sinomegat = CS%tide_fn(c) * sin(CS%freq(c)*now + (CS%phase0(c) + CS%tide_un(c)))

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do j=Jsq,Jeq+1 ; do i=Isq,Ieq+1
amp_cossin = CS%ampsal(i,j,c) &
* (cosomegat*CS%cosphasesal(i,j,c) + sinomegat*CS%sinphasesal(i,j,c))
Expand All @@ -713,8 +758,8 @@ subroutine calc_tidal_forcing_legacy(Time, e_sal, e_sal_tide, e_tide_eq, e_tide_
enddo ; endif

if (CS%use_tidal_sal_prev) then ; do c=1,CS%nc
cosomegat = cos(CS%freq(c)*now)
sinomegat = sin(CS%freq(c)*now)
cosomegat = CS%tide_fn(c) * cos(CS%freq(c)*now + (CS%phase0(c) + CS%tide_un(c)))
sinomegat = CS%tide_fn(c) * sin(CS%freq(c)*now + (CS%phase0(c) + CS%tide_un(c)))

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src/parameterizations/lateral/MOM_tidal_forcing.F90#L761-L762 

Added lines #L761 - L762 were not covered by tests
do j=Jsq,Jeq+1 ; do i=Isq,Ieq+1
amp_cossin = -CS%sal_scalar * CS%amp_prev(i,j,c) &
* (cosomegat*CS%cosphase_prev(i,j,c) + sinomegat*CS%sinphase_prev(i,j,c))
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