MOM_PressureForce_Montgomery.F90

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!> Provides the Montgomery potential form of pressure gradient
module mom_pressureforce_mont
 
! This file is part of MOM6. See LICENSE.md for the license.
 
use mom_diag_mediator, only : post_data, register_diag_field
use mom_diag_mediator, only : safe_alloc_ptr, diag_ctrl, time_type
use mom_error_handler, only : mom_error, mom_mesg, fatal, warning, is_root_pe
use mom_file_parser, only : get_param, log_param, log_version, param_file_type
use mom_grid, only : ocean_grid_type
use mom_tidal_forcing, only : calc_tidal_forcing, tidal_forcing_cs
use mom_unit_scaling, only : unit_scale_type
use mom_variables, only : thermo_var_ptrs
use mom_verticalgrid, only : verticalgrid_type
use mom_eos, only : calculate_density, calculate_density_derivs
use mom_eos, only : int_specific_vol_dp, query_compressible
 
implicit none ; private
 
#include <MOM_memory.h>
 
public pressureforce_mont_bouss, pressureforce_mont_nonbouss, set_pbce_bouss
public set_pbce_nonbouss, pressureforce_mont_init, pressureforce_mont_end
 
! A note on unit descriptions in comments: MOM6 uses units that can be rescaled for dimensional
! consistency testing. These are noted in comments with units like Z, H, L, and T, along with
! their mks counterparts with notation like "a velocity [Z T-1 ~> m s-1]".  If the units
! vary with the Boussinesq approximation, the Boussinesq variant is given first.
 
!> Control structure for the Montgomery potential form of pressure gradient
type, public :: pressureforce_mont_cs ; private
  logical :: tides          !< If true, apply tidal momentum forcing.
  real    :: rho0           !< The density used in the Boussinesq
                            !! approximation [kg m-3].
  real    :: rho_atm        !< The assumed atmospheric density [kg m-3].
                            !! By default, Rho_atm is 0.
  real    :: gfs_scale      !< Ratio between gravity applied to top interface and the
                            !! gravitational acceleration of the planet [nondim].
                            !! Usually this ratio is 1.
  type(time_type), pointer :: time => null() !< A pointer to the ocean model's clock.
  type(diag_ctrl), pointer :: diag => null() !< A structure that is used to regulate
                            !! the timing of diagnostic output.
  real, pointer :: pfu_bc(:,:,:) => null() !< Zonal accelerations due to pressure gradients
                            !! deriving from density gradients within layers [L T-2 ~> m s-2].
  real, pointer :: pfv_bc(:,:,:) => null() !< Meridional accelerations due to pressure gradients
                            !! deriving from density gradients within layers [L T-2 ~> m s-2].
  !>@{ Diagnostic IDs
  integer :: id_pfu_bc = -1, id_pfv_bc = -1, id_e_tidal = -1
  !!@}
  type(tidal_forcing_cs), pointer :: tides_csp => null() !< The tidal forcing control structure
end type pressureforce_mont_cs
 
contains
 
!> \brief Non-Boussinesq Montgomery-potential form of pressure gradient
!!
!! Determines the acceleration due to pressure forces in a
!! non-Boussinesq fluid using the compressibility compensated (if appropriate)
!! Montgomery-potential form described in Hallberg (Ocean Mod., 2005).
!!
!! To work, the following fields must be set outside of the usual (is:ie,js:je)
!! range before this subroutine is called:
!!   h(isB:ie+1,jsB:je+1), T(isB:ie+1,jsB:je+1), and S(isB:ie+1,jsB:je+1).
subroutine pressureforce_mont_nonbouss(h, tv, PFu, PFv, G, GV, US, CS, p_atm, pbce, eta)
  type(ocean_grid_type),                     intent(in)  :: g   !< Ocean grid structure.
  type(verticalgrid_type),                   intent(in)  :: gv  !< Vertical grid structure.
  type(unit_scale_type),                     intent(in)  :: us  !< A dimensional unit scaling type
  real, dimension(SZI_(G),SZJ_(G),SZK_(G)),  intent(in)  :: h   !< Layer thickness, [H ~> kg m-2].
  type(thermo_var_ptrs),                     intent(in)  :: tv  !< Thermodynamic variables.
  real, dimension(SZIB_(G),SZJ_(G),SZK_(G)), intent(out) :: pfu !< Zonal acceleration due to pressure gradients
                                                                !! (equal to -dM/dx) [L T-2 ~> m s-2].
  real, dimension(SZI_(G),SZJB_(G),SZK_(G)), intent(out) :: pfv !< Meridional acceleration due to pressure gradients
                                                                !! (equal to -dM/dy) [L T-2 ~> m s-2].
  type(pressureforce_mont_cs),               pointer     :: cs  !< Control structure for Montgomery potential PGF
  real, dimension(:,:),            optional, pointer     :: p_atm !< The pressure at the ice-ocean or
                                                                !! atmosphere-ocean [Pa].
  real, dimension(SZI_(G),SZJ_(G),SZK_(G)), &
                                   optional, intent(out) :: pbce !< The baroclinic pressure anomaly in
                                                                !! each layer due to free surface height anomalies,
                                                                !! [L2 T-2 H-1 ~> m s-2 or m4 kg-1 s-2].
  real, dimension(SZI_(G),SZJ_(G)), optional, intent(out) :: eta !< Free surface height [H ~> kg m-1].
 
  ! Local variables
  real, dimension(SZI_(G),SZJ_(G),SZK_(G)) :: &
    m, &          ! The Montgomery potential, M = (p/rho + gz)  [L2 T-2 ~> m2 s-2].
    alpha_star, & ! Compression adjusted specific volume [R-1 ~> m3 kg-1].
    dz_geo        !   The change in geopotential across a layer [m2 s-2].
  real, dimension(SZI_(G),SZJ_(G),SZK_(G)+1) :: p ! Interface pressure [Pa].
                ! p may be adjusted (with a nonlinear equation of state) so that
                ! its derivative compensates for the adiabatic compressibility
                ! in seawater, but p will still be close to the pressure.
  real, dimension(SZI_(G),SZJ_(G),SZK_(G)), target :: &
    t_tmp, &    ! Temporary array of temperatures where layers that are lighter
                ! than the mixed layer have the mixed layer's properties [degC].
    s_tmp       ! Temporary array of salinities where layers that are lighter
                ! than the mixed layer have the mixed layer's properties [ppt].
 
  real, dimension(SZI_(G)) :: rho_cv_bl  ! The coordinate potential density in the
                  ! deepest variable density near-surface layer [R ~> kg m-3].
 
  real, dimension(SZI_(G),SZJ_(G)) :: &
    dm, &         !   A barotropic correction to the Montgomery potentials to
                  ! enable the use of a reduced gravity form of the equations
                  ! [m2 s-2].
    dp_star, &    ! Layer thickness after compensation for compressibility [Pa].
    ssh, &        ! The sea surface height anomaly, in depth units [Z ~> m].
    e_tidal, &    !   Bottom geopotential anomaly due to tidal forces from
                  ! astronomical sources and self-attraction and loading [Z ~> m].
    geopot_bot    !   Bottom geopotential relative to time-mean sea level,
                  ! including any tidal contributions [L2 T-2 ~> m2 s-2].
  real :: p_ref(szi_(g))     !   The pressure used to calculate the coordinate
                             ! density [Pa] (usually 2e7 Pa = 2000 dbar).
  real :: rho_in_situ(szi_(g)) !In-situ density of a layer [R ~> kg m-3].
  real :: pfu_bc, pfv_bc     ! The pressure gradient force due to along-layer
                             ! compensated density gradients [L T-2 ~> m s-2]
  real :: dp_neglect         ! A thickness that is so small it is usually lost
                             ! in roundoff and can be neglected [Pa].
  logical :: use_p_atm       ! If true, use the atmospheric pressure.
  logical :: use_eos         ! If true, density is calculated from T & S using
                             ! an equation of state.
  logical :: is_split        ! A flag indicating whether the pressure
                             ! gradient terms are to be split into
                             ! barotropic and baroclinic pieces.
  type(thermo_var_ptrs) :: tv_tmp! A structure of temporary T & S.
 
  real :: i_gearth           ! The inverse of g_Earth [s2 Z m-2 ~> s2 m-1]
!  real :: dalpha
  real :: pa_to_p_dyn ! A conversion factor from Pa (= kg m-1 s-2) to the units of
                      ! dynamic pressure (R L2 T-2) [ R L2 T-2 m s2 kg-1 ~> nondim]
  real :: pa_to_h     ! A factor to convert from Pa to the thicknesss units (H).
  real :: alpha_lay(szk_(g)) ! The specific volume of each layer [R-1 ~> m3 kg-1].
  real :: dalpha_int(szk_(g)+1) ! The change in specific volume across each
                             ! interface [R-1 ~> m3 kg-1].
  integer :: is, ie, js, je, isq, ieq, jsq, jeq, nz, nkmb
  integer :: i, j, k
  is = g%isc ; ie = g%iec ; js = g%jsc ; je = g%jec ; nz = g%ke
  nkmb=gv%nk_rho_varies
  isq = g%IscB ; ieq = g%IecB ; jsq = g%JscB ; jeq = g%JecB
 
  use_p_atm = .false.
  if (present(p_atm)) then ; if (associated(p_atm)) use_p_atm = .true. ; endif
  is_split = .false. ; if (present(pbce)) is_split = .true.
  use_eos = associated(tv%eqn_of_state)
 
  if (.not.associated(cs)) call mom_error(fatal, &
      "MOM_PressureForce_Mont: Module must be initialized before it is used.")
  if (use_eos) then
    if (query_compressible(tv%eqn_of_state)) call mom_error(fatal, &
      "PressureForce_Mont_nonBouss: The Montgomery form of the pressure force "//&
      "can no longer be used with a compressible EOS. Use #define ANALYTIC_FV_PGF.")
  endif
 
  pa_to_p_dyn = us%kg_m3_to_R * us%m_s_to_L_T**2
  i_gearth = 1.0 / (us%L_T_to_m_s**2 * gv%g_Earth)
  dp_neglect = gv%H_to_Pa * gv%H_subroundoff
  do k=1,nz ; alpha_lay(k) = 1.0 / (gv%Rlay(k)) ; enddo
  do k=2,nz ; dalpha_int(k) = alpha_lay(k-1) - alpha_lay(k) ; enddo
 
  if (use_p_atm) then
    !$OMP parallel do default(shared)
    do j=jsq,jeq+1 ; do i=isq,ieq+1 ; p(i,j,1) = p_atm(i,j) ; enddo ; enddo
  else
    !$OMP parallel do default(shared)
    do j=jsq,jeq+1 ; do i=isq,ieq+1 ; p(i,j,1) = 0.0 ; enddo ; enddo
  endif
  !$OMP parallel do default(shared)
  do j=jsq,jeq+1 ; do k=1,nz ; do i=isq,ieq+1
    p(i,j,k+1) = p(i,j,k) + gv%H_to_Pa * h(i,j,k)
  enddo ; enddo ; enddo
 
  if (present(eta)) then
    pa_to_h = 1.0 / gv%H_to_Pa
    if (use_p_atm) then
      !$OMP parallel do default(shared)
      do j=jsq,jeq+1 ; do i=isq,ieq+1
        eta(i,j) = (p(i,j,nz+1) - p_atm(i,j))*pa_to_h ! eta has the same units as h.
      enddo ; enddo
    else
      !$OMP parallel do default(shared)
      do j=jsq,jeq+1 ; do i=isq,ieq+1
        eta(i,j) = p(i,j,nz+1)*pa_to_h ! eta has the same units as h.
      enddo ; enddo
    endif
  endif
 
  if (cs%tides) then
    !   Determine the sea surface height anomalies, to enable the calculation
    ! of self-attraction and loading.
    !$OMP parallel do default(shared)
    do j=jsq,jeq+1 ; do i=isq,ieq+1
      ssh(i,j) = -g%bathyT(i,j)
    enddo ; enddo
    if (use_eos) then
      !$OMP parallel do default(shared)
      do k=1,nz
        call int_specific_vol_dp(tv%T(:,:,k), tv%S(:,:,k), p(:,:,k), p(:,:,k+1), &
                                 0.0, g%HI, tv%eqn_of_state, dz_geo(:,:,k), halo_size=1)
      enddo
      !$OMP parallel do default(shared)
      do j=jsq,jeq+1 ; do k=1,nz; do i=isq,ieq+1
        ssh(i,j) = ssh(i,j) + i_gearth * dz_geo(i,j,k)
      enddo ; enddo ; enddo
    else
      !$OMP parallel do default(shared)
      do j=jsq,jeq+1 ; do k=1,nz ; do i=isq,ieq+1
        ssh(i,j) = ssh(i,j) + gv%H_to_RZ * h(i,j,k) * alpha_lay(k)
      enddo ; enddo ; enddo
    endif
 
    call calc_tidal_forcing(cs%Time, ssh, e_tidal, g, cs%tides_CSp, m_to_z=us%m_to_Z)
    !$OMP parallel do default(shared)
    do j=jsq,jeq+1 ; do i=isq,ieq+1
      geopot_bot(i,j) = -gv%g_Earth*(e_tidal(i,j) + g%bathyT(i,j))
    enddo ; enddo
  else
    !$OMP parallel do default(shared)
    do j=jsq,jeq+1 ; do i=isq,ieq+1
      geopot_bot(i,j) = -gv%g_Earth*g%bathyT(i,j)
    enddo ; enddo
  endif
 
  if (use_eos) then
    !   Calculate in-situ specific volumes (alpha_star).
 
    !   With a bulk mixed layer, replace the T & S of any layers that are
    ! lighter than the the buffer layer with the properties of the buffer
    ! layer.  These layers will be massless anyway, and it avoids any
    ! formal calculations with hydrostatically unstable profiles.
    if (nkmb>0) then
      tv_tmp%T => t_tmp ; tv_tmp%S => s_tmp
      tv_tmp%eqn_of_state => tv%eqn_of_state
      do i=isq,ieq+1 ; p_ref(i) = tv%P_Ref ; enddo
      !$OMP parallel do default(shared) private(Rho_cv_BL)
      do j=jsq,jeq+1
        do k=1,nkmb ; do i=isq,ieq+1
          tv_tmp%T(i,j,k) = tv%T(i,j,k) ; tv_tmp%S(i,j,k) = tv%S(i,j,k)
        enddo ; enddo
        call calculate_density(tv%T(:,j,nkmb), tv%S(:,j,nkmb), p_ref, &
                        rho_cv_bl(:), isq, ieq-isq+2, tv%eqn_of_state, scale=us%kg_m3_to_R)
        do k=nkmb+1,nz ; do i=isq,ieq+1
          if (gv%Rlay(k) < rho_cv_bl(i)) then
            tv_tmp%T(i,j,k) = tv%T(i,j,nkmb) ; tv_tmp%S(i,j,k) = tv%S(i,j,nkmb)
          else
            tv_tmp%T(i,j,k) = tv%T(i,j,k) ; tv_tmp%S(i,j,k) = tv%S(i,j,k)
          endif
        enddo ; enddo
      enddo
    else
      tv_tmp%T => tv%T ; tv_tmp%S => tv%S
      tv_tmp%eqn_of_state => tv%eqn_of_state
      do i=isq,ieq+1 ; p_ref(i) = 0 ; enddo
    endif
    !$OMP parallel do default(shared) private(rho_in_situ)
    do k=1,nz ; do j=jsq,jeq+1
      call calculate_density(tv_tmp%T(:,j,k),tv_tmp%S(:,j,k),p_ref, &
                             rho_in_situ,isq,ieq-isq+2,tv%eqn_of_state, scale=us%kg_m3_to_R)
      do i=isq,ieq+1 ; alpha_star(i,j,k) = 1.0 / rho_in_situ(i) ; enddo
    enddo ; enddo
  endif                                               ! use_EOS
 
  if (use_eos) then
    !$OMP parallel do default(shared)
    do j=jsq,jeq+1
      do i=isq,ieq+1
        m(i,j,nz) = geopot_bot(i,j) + pa_to_p_dyn*p(i,j,nz+1) * alpha_star(i,j,nz)
      enddo
      do k=nz-1,1,-1 ; do i=isq,ieq+1
        m(i,j,k) = m(i,j,k+1) + pa_to_p_dyn*p(i,j,k+1) * (alpha_star(i,j,k) - alpha_star(i,j,k+1))
      enddo ; enddo
    enddo
  else ! not use_EOS
    !$OMP parallel do default(shared)
    do j=jsq,jeq+1
      do i=isq,ieq+1
        m(i,j,nz) = geopot_bot(i,j) + pa_to_p_dyn*p(i,j,nz+1) * alpha_lay(nz)
      enddo
      do k=nz-1,1,-1 ; do i=isq,ieq+1
        m(i,j,k) = m(i,j,k+1) + pa_to_p_dyn*p(i,j,k+1) * dalpha_int(k+1)
      enddo ; enddo
    enddo
  endif ! use_EOS
 
  if (cs%GFS_scale < 1.0) then
    ! Adjust the Montgomery potential to make this a reduced gravity model.
    !$OMP parallel do default(shared)
    do j=jsq,jeq+1 ; do i=isq,ieq+1
      dm(i,j) = (cs%GFS_scale - 1.0) * m(i,j,1)
    enddo ; enddo
    !$OMP parallel do default(shared)
    do k=1,nz ; do j=jsq,jeq+1 ; do i=isq,ieq+1
      m(i,j,k) = m(i,j,k) + dm(i,j)
    enddo ; enddo ; enddo
 
    !   Could instead do the following, to avoid taking small differences
    ! of large numbers...
!   do j=Jsq,Jeq+1 ; do i=Isq,Ieq+1
!     M(i,j,1) = CS%GFS_scale * M(i,j,1)
!   enddo ; enddo
!   if (use_EOS) then
!     do k=2,nz ; do j=Jsq,Jeq+1 ; do i=Isq,Ieq+1
!       M(i,j,k) = M(i,j,k-1) - Pa_to_p_dyn*p(i,j,K) * (alpha_star(i,j,k-1) - alpha_star(i,j,k))
!     enddo ; enddo ; enddo
!   else ! not use_EOS
!     do k=2,nz ; do j=Jsq,Jeq+1 ; do i=Isq,Ieq+1
!        M(i,j,k) = M(i,j,k-1) - Pa_to_p_dyn*p(i,j,K) * dalpha_int(K)
!     enddo ; enddo ; enddo
!   endif ! use_EOS
 
  endif
 
  ! Note that ddM/dPb = alpha_star(i,j,1)
  if (present(pbce)) then
    call set_pbce_nonbouss(p, tv_tmp, g, gv, us, cs%GFS_scale, pbce, alpha_star)
  endif
 
!    Calculate the pressure force. On a Cartesian grid,
!      PFu = - dM/dx   and  PFv = - dM/dy.
  if (use_eos) then
    !$OMP parallel do default(shared) private(dp_star,PFu_bc,PFv_bc)
    do k=1,nz
      do j=jsq,jeq+1 ; do i=isq,ieq+1
        dp_star(i,j) = (p(i,j,k+1) - p(i,j,k)) + dp_neglect
      enddo ; enddo
      do j=js,je ; do i=isq,ieq
        ! PFu_bc = p* grad alpha*
        pfu_bc = (alpha_star(i+1,j,k) - alpha_star(i,j,k)) * (g%IdxCu(i,j) * pa_to_p_dyn * &
          ((dp_star(i,j) * dp_star(i+1,j) + (p(i,j,k) * dp_star(i+1,j) + &
           p(i+1,j,k) * dp_star(i,j))) / (dp_star(i,j) + dp_star(i+1,j))))
        pfu(i,j,k) = -(m(i+1,j,k) - m(i,j,k)) * g%IdxCu(i,j) + pfu_bc
        if (associated(cs%PFu_bc)) cs%PFu_bc(i,j,k) = pfu_bc
      enddo ; enddo
      do j=jsq,jeq ; do i=is,ie
        pfv_bc = (alpha_star(i,j+1,k) - alpha_star(i,j,k)) * (g%IdyCv(i,j) * pa_to_p_dyn * &
          ((dp_star(i,j) * dp_star(i,j+1) + (p(i,j,k) * dp_star(i,j+1) + &
          p(i,j+1,k) * dp_star(i,j))) / (dp_star(i,j) + dp_star(i,j+1))))
        pfv(i,j,k) = -(m(i,j+1,k) - m(i,j,k)) * g%IdyCv(i,j) + pfv_bc
        if (associated(cs%PFv_bc)) cs%PFv_bc(i,j,k) = pfv_bc
      enddo ; enddo
    enddo ! k-loop
  else ! .not. use_EOS
    !$OMP parallel do default(shared)
    do k=1,nz
      do j=js,je ; do i=isq,ieq
        pfu(i,j,k) = -(m(i+1,j,k) - m(i,j,k)) * g%IdxCu(i,j)
      enddo ; enddo
      do j=jsq,jeq ; do i=is,ie
        pfv(i,j,k) = -(m(i,j+1,k) - m(i,j,k)) * g%IdyCv(i,j)
      enddo ; enddo
    enddo
  endif ! use_EOS
 
  if (cs%id_PFu_bc>0) call post_data(cs%id_PFu_bc, cs%PFu_bc, cs%diag)
  if (cs%id_PFv_bc>0) call post_data(cs%id_PFv_bc, cs%PFv_bc, cs%diag)
  if (cs%id_e_tidal>0) call post_data(cs%id_e_tidal, e_tidal, cs%diag)
 
end subroutine pressureforce_mont_nonbouss
 
!> \brief Boussinesq Montgomery-potential form of pressure gradient
!!
!! Determines the acceleration due to pressure forces.
!!
!! To work, the following fields must be set outside of the usual (is:ie,js:je)
!! range before this subroutine is called:
!!   h(isB:ie+1,jsB:je+1), T(isB:ie+1,jsB:je+1), and S(isB:ie+1,jsB:je+1).
subroutine pressureforce_mont_bouss(h, tv, PFu, PFv, G, GV, US, CS, p_atm, pbce, eta)
  type(ocean_grid_type),                     intent(in)  :: g   !< Ocean grid structure.
  type(verticalgrid_type),                   intent(in)  :: gv  !< Vertical grid structure.
  type(unit_scale_type),                     intent(in)  :: us  !< A dimensional unit scaling type
  real, dimension(SZI_(G),SZJ_(G),SZK_(G)),  intent(in)  :: h   !< Layer thickness [H ~> m].
  type(thermo_var_ptrs),                     intent(in)  :: tv  !< Thermodynamic variables.
  real, dimension(SZIB_(G),SZJ_(G),SZK_(G)), intent(out) :: pfu !< Zonal acceleration due to pressure gradients
                                                                !! (equal to -dM/dx) [L T-2 ~> m s-2].
  real, dimension(SZI_(G),SZJB_(G),SZK_(G)), intent(out) :: pfv !< Meridional acceleration due to pressure gradients
                                                                !! (equal to -dM/dy) [L T-2 ~> m s2].
  type(pressureforce_mont_cs),               pointer     :: cs  !< Control structure for Montgomery potential PGF
  real, dimension(:,:),                     optional, pointer     :: p_atm !< The pressure at the ice-ocean or
                                                                !! atmosphere-ocean [Pa].
  real, dimension(SZI_(G),SZJ_(G),SZK_(G)), optional, intent(out) :: pbce !< The baroclinic pressure anomaly in
                                                                !! each layer due to free surface height anomalies
                                                                !! [L2 T-2 H-1 ~> m s-2].
  real, dimension(SZI_(G),SZJ_(G)),         optional, intent(out) :: eta !< Free surface height [H ~> m].
  ! Local variables
  real, dimension(SZI_(G),SZJ_(G),SZK_(G)) :: &
    m, &        ! The Montgomery potential, M = (p/rho + gz) [L2 T-2 ~> m2 s-2].
    rho_star    ! In-situ density divided by the derivative with depth of the
                ! corrected e times (G_Earth/Rho0) [m2 Z-1 s-2 ~> m s-2].
  real, dimension(SZI_(G),SZJ_(G),SZK_(G)+1) :: e ! Interface height in m.
                ! e may be adjusted (with a nonlinear equation of state) so that
                ! its derivative compensates for the adiabatic compressibility
                ! in seawater, but e will still be close to the interface depth.
  real, dimension(SZI_(G),SZJ_(G),SZK_(G)), target :: &
    t_tmp, &    ! Temporary array of temperatures where layers that are lighter
                ! than the mixed layer have the mixed layer's properties [degC].
    s_tmp       ! Temporary array of salinities where layers that are lighter
                ! than the mixed layer have the mixed layer's properties [ppt].
 
  real :: rho_cv_bl(szi_(g)) !   The coordinate potential density in
                ! the deepest variable density near-surface layer [R ~> kg m-3].
  real :: h_star(szi_(g),szj_(g)) ! Layer thickness after compensation
                             ! for compressibility [Z ~> m].
  real :: e_tidal(szi_(g),szj_(g)) ! Bottom geopotential anomaly due to tidal
                             ! forces from astronomical sources and self-
                             ! attraction and loading, in depth units [Z ~> m].
  real :: p_ref(szi_(g))     !   The pressure used to calculate the coordinate
                             ! density [Pa] (usually 2e7 Pa = 2000 dbar).
  real :: i_rho0             ! 1/Rho0 [m3 kg-1].
  real :: g_rho0             ! G_Earth / Rho0 [L2 Z-1 T-2 R-1 ~> m4 s-2 kg-1].
  real :: pfu_bc, pfv_bc     ! The pressure gradient force due to along-layer
                             ! compensated density gradients [L T-2 ~> m s-2]
  real :: h_neglect          ! A thickness that is so small it is usually lost
                             ! in roundoff and can be neglected [Z ~> m].
  logical :: use_p_atm       ! If true, use the atmospheric pressure.
  logical :: use_eos         ! If true, density is calculated from T & S using
                             ! an equation of state.
  logical :: is_split        ! A flag indicating whether the pressure
                             ! gradient terms are to be split into
                             ! barotropic and baroclinic pieces.
  type(thermo_var_ptrs) :: tv_tmp! A structure of temporary T & S.
  integer :: is, ie, js, je, isq, ieq, jsq, jeq, nz, nkmb
  integer :: i, j, k
 
  is = g%isc ; ie = g%iec ; js = g%jsc ; je = g%jec ; nz = g%ke
  nkmb=gv%nk_rho_varies
  isq = g%IscB ; ieq = g%IecB ; jsq = g%JscB ; jeq = g%JecB
 
  use_p_atm = .false.
  if (present(p_atm)) then ; if (associated(p_atm)) use_p_atm = .true. ; endif
  is_split = .false. ; if (present(pbce)) is_split = .true.
  use_eos = associated(tv%eqn_of_state)
 
  if (.not.associated(cs)) call mom_error(fatal, &
       "MOM_PressureForce_Mont: Module must be initialized before it is used.")
  if (use_eos) then
    if (query_compressible(tv%eqn_of_state)) call mom_error(fatal, &
      "PressureForce_Mont_Bouss: The Montgomery form of the pressure force "//&
      "can no longer be used with a compressible EOS. Use #define ANALYTIC_FV_PGF.")
  endif
 
  h_neglect = gv%H_subroundoff * gv%H_to_Z
  i_rho0 = 1.0/cs%Rho0
  g_rho0 = gv%g_Earth / gv%Rho0
 
  if (cs%tides) then
    !   Determine the surface height anomaly for calculating self attraction
    ! and loading.  This should really be based on bottom pressure anomalies,
    ! but that is not yet implemented, and the current form is correct for
    ! barotropic tides.
    !$OMP parallel do default(shared)
    do j=jsq,jeq+1
      do i=isq,ieq+1 ; e(i,j,1) = -g%bathyT(i,j) ; enddo
      do k=1,nz ; do i=isq,ieq+1
        e(i,j,1) = e(i,j,1) + h(i,j,k)*gv%H_to_Z
      enddo ; enddo
    enddo
    call calc_tidal_forcing(cs%Time, e(:,:,1), e_tidal, g, cs%tides_CSp, m_to_z=us%m_to_Z)
  endif
 
!    Here layer interface heights, e, are calculated.
  if (cs%tides) then
    !$OMP parallel do default(shared)
    do j=jsq,jeq+1 ; do i=isq,ieq+1
      e(i,j,nz+1) = -(g%bathyT(i,j) + e_tidal(i,j))
    enddo ; enddo
  else
    !$OMP parallel do default(shared)
    do j=jsq,jeq+1 ; do i=isq,ieq+1
      e(i,j,nz+1) = -g%bathyT(i,j)
    enddo ; enddo
  endif
  !$OMP parallel do default(shared)
  do j=jsq,jeq+1 ; do k=nz,1,-1 ; do i=isq,ieq+1
    e(i,j,k) = e(i,j,k+1) + h(i,j,k)*gv%H_to_Z
  enddo ; enddo ; enddo
 
  if (use_eos) then
!   Calculate in-situ densities (rho_star).
 
! With a bulk mixed layer, replace the T & S of any layers that are
! lighter than the the buffer layer with the properties of the buffer
! layer.  These layers will be massless anyway, and it avoids any
! formal calculations with hydrostatically unstable profiles.
 
    if (nkmb>0) then
      tv_tmp%T => t_tmp ; tv_tmp%S => s_tmp
      tv_tmp%eqn_of_state => tv%eqn_of_state
 
      do i=isq,ieq+1 ; p_ref(i) = tv%P_Ref ; enddo
      !$OMP parallel do default(shared) private(Rho_cv_BL)
      do j=jsq,jeq+1
        do k=1,nkmb ; do i=isq,ieq+1
          tv_tmp%T(i,j,k) = tv%T(i,j,k) ; tv_tmp%S(i,j,k) = tv%S(i,j,k)
        enddo ; enddo
        call calculate_density(tv%T(:,j,nkmb), tv%S(:,j,nkmb), p_ref, &
                        rho_cv_bl(:), isq, ieq-isq+2, tv%eqn_of_state, scale=us%kg_m3_to_R)
 
        do k=nkmb+1,nz ; do i=isq,ieq+1
          if (gv%Rlay(k) < rho_cv_bl(i)) then
            tv_tmp%T(i,j,k) = tv%T(i,j,nkmb) ; tv_tmp%S(i,j,k) = tv%S(i,j,nkmb)
          else
            tv_tmp%T(i,j,k) = tv%T(i,j,k) ; tv_tmp%S(i,j,k) = tv%S(i,j,k)
          endif
        enddo ; enddo
      enddo
    else
      tv_tmp%T => tv%T ; tv_tmp%S => tv%S
      tv_tmp%eqn_of_state => tv%eqn_of_state
      do i=isq,ieq+1 ; p_ref(i) = 0.0 ; enddo
    endif
 
    ! This no longer includes any pressure dependency, since this routine
    ! will come down with a fatal error if there is any compressibility.
    !$OMP parallel do default(shared)
    do k=1,nz+1 ; do j=jsq,jeq+1
      call calculate_density(tv_tmp%T(:,j,k), tv_tmp%S(:,j,k), p_ref, rho_star(:,j,k), &
                             isq, ieq-isq+2, tv%eqn_of_state, scale=us%kg_m3_to_R*g_rho0)
    enddo ; enddo
  endif                                               ! use_EOS
 
!    Here the layer Montgomery potentials, M, are calculated.
  if (use_eos) then
    !$OMP parallel do default(shared)
    do j=jsq,jeq+1
      do i=isq,ieq+1
        m(i,j,1) = cs%GFS_scale * (rho_star(i,j,1) * e(i,j,1))
        if (use_p_atm) m(i,j,1) = m(i,j,1) + us%m_s_to_L_T**2*p_atm(i,j) * i_rho0
      enddo
      do k=2,nz ; do i=isq,ieq+1
        m(i,j,k) = m(i,j,k-1) + (rho_star(i,j,k) - rho_star(i,j,k-1)) * e(i,j,k)
      enddo ; enddo
    enddo
  else ! not use_EOS
    !$OMP parallel do default(shared)
    do j=jsq,jeq+1
      do i=isq,ieq+1
        m(i,j,1) = gv%g_prime(1) * e(i,j,1)
        if (use_p_atm) m(i,j,1) = m(i,j,1) + us%m_s_to_L_T**2*p_atm(i,j) * i_rho0
      enddo
      do k=2,nz ; do i=isq,ieq+1
        m(i,j,k) = m(i,j,k-1) + gv%g_prime(k) * e(i,j,k)
      enddo ; enddo
    enddo
  endif ! use_EOS
 
  if (present(pbce)) then
    call set_pbce_bouss(e, tv_tmp, g, gv, us, cs%Rho0, cs%GFS_scale, pbce, rho_star)
  endif
 
!    Calculate the pressure force. On a Cartesian grid,
!      PFu = - dM/dx   and  PFv = - dM/dy.
  if (use_eos) then
    !$OMP parallel do default(shared) private(h_star,PFu_bc,PFv_bc)
    do k=1,nz
      do j=jsq,jeq+1 ; do i=isq,ieq+1
        h_star(i,j) = (e(i,j,k) - e(i,j,k+1)) + h_neglect
      enddo ; enddo
      do j=js,je ; do i=isq,ieq
        pfu_bc = -1.0*(rho_star(i+1,j,k) - rho_star(i,j,k)) * (g%IdxCu(i,j) * &
          ((h_star(i,j) * h_star(i+1,j) - (e(i,j,k) * h_star(i+1,j) + &
          e(i+1,j,k) * h_star(i,j))) / (h_star(i,j) + h_star(i+1,j))))
        pfu(i,j,k) = -(m(i+1,j,k) - m(i,j,k)) * g%IdxCu(i,j) + pfu_bc
        if (associated(cs%PFu_bc)) cs%PFu_bc(i,j,k) = pfu_bc
      enddo ; enddo
      do j=jsq,jeq ; do i=is,ie
        pfv_bc = -1.0*(rho_star(i,j+1,k) - rho_star(i,j,k)) * (g%IdyCv(i,j) * &
          ((h_star(i,j) * h_star(i,j+1) - (e(i,j,k) * h_star(i,j+1) + &
          e(i,j+1,k) * h_star(i,j))) / (h_star(i,j) + h_star(i,j+1))))
        pfv(i,j,k) = -(m(i,j+1,k) - m(i,j,k)) * g%IdyCv(i,j) + pfv_bc
        if (associated(cs%PFv_bc)) cs%PFv_bc(i,j,k) = pfv_bc
      enddo ; enddo
    enddo ! k-loop
  else ! .not. use_EOS
    !$OMP parallel do default(shared)
    do k=1,nz
      do j=js,je ; do i=isq,ieq
        pfu(i,j,k) = -(m(i+1,j,k) - m(i,j,k)) * g%IdxCu(i,j)
      enddo ; enddo
      do j=jsq,jeq ; do i=is,ie
        pfv(i,j,k) = -(m(i,j+1,k) - m(i,j,k)) * g%IdyCv(i,j)
      enddo ; enddo
    enddo
  endif ! use_EOS
 
  if (present(eta)) then
    if (cs%tides) then
    ! eta is the sea surface height relative to a time-invariant geoid, for
    ! comparison with what is used for eta in btstep.  See how e was calculated
    ! about 200 lines above.
      !$OMP parallel do default(shared)
      do j=jsq,jeq+1 ; do i=isq,ieq+1
        eta(i,j) = e(i,j,1)*gv%Z_to_H + e_tidal(i,j)*gv%Z_to_H
      enddo ; enddo
    else
      !$OMP parallel do default(shared)
      do j=jsq,jeq+1 ; do i=isq,ieq+1
        eta(i,j) = e(i,j,1)*gv%Z_to_H
      enddo ; enddo
    endif
  endif
 
  if (cs%id_PFu_bc>0) call post_data(cs%id_PFu_bc, cs%PFu_bc, cs%diag)
  if (cs%id_PFv_bc>0) call post_data(cs%id_PFv_bc, cs%PFv_bc, cs%diag)
  if (cs%id_e_tidal>0) call post_data(cs%id_e_tidal, e_tidal, cs%diag)
 
end subroutine pressureforce_mont_bouss
 
!> Determines the partial derivative of the acceleration due
!! to pressure forces with the free surface height.
subroutine set_pbce_bouss(e, tv, G, GV, US, Rho0, GFS_scale, pbce, rho_star)
  type(ocean_grid_type),                intent(in)  :: g    !< Ocean grid structure
  type(verticalgrid_type),              intent(in)  :: gv   !< Vertical grid structure
  real, dimension(SZI_(G),SZJ_(G),SZK_(G)+1), intent(in) :: e !< Interface height [Z ~> m].
  type(thermo_var_ptrs),                intent(in)  :: tv   !< Thermodynamic variables
  type(unit_scale_type),                intent(in)  :: us   !< A dimensional unit scaling type
  real,                                 intent(in)  :: rho0 !< The "Boussinesq" ocean density [kg m-3].
  real,                                 intent(in)  :: gfs_scale !< Ratio between gravity applied to top
                                                            !! interface and the gravitational acceleration of
                                                            !! the planet [nondim]. Usually this ratio is 1.
  real, dimension(SZI_(G),SZJ_(G),SZK_(G)), &
                                        intent(out) :: pbce !< The baroclinic pressure anomaly in each layer due
                                                            !! to free surface height anomalies
                                                            !! [L2 T-2 H-1 ~> m s-2].
  real, dimension(SZI_(G),SZJ_(G),SZK_(G)), &
                              optional, intent(in)  :: rho_star !< The layer densities (maybe compressibility
                                                            !! compensated), times g/rho_0 [L2 Z-1 T-2 ~> m s-2].
 
  ! Local variables
  real :: ihtot(szi_(g))     ! The inverse of the sum of the layer thicknesses [H-1 ~> m-1 or m2 kg-1].
  real :: press(szi_(g))     ! Interface pressure [Pa].
  real :: t_int(szi_(g))     ! Interface temperature [degC].
  real :: s_int(szi_(g))     ! Interface salinity [ppt].
  real :: dr_dt(szi_(g))     ! Partial derivative of density with temperature [R degC-1 ~> kg m-3 degC-1].
  real :: dr_ds(szi_(g))     ! Partial derivative of density with salinity [R ppt-1 ~> kg m-3 ppt-1].
  real :: rho_in_situ(szi_(g)) ! In-situ density at the top of a layer [R ~> kg m-3].
  real :: g_rho0             ! A scaled version of g_Earth / Rho0 [L2 m3 Z-1 T-2 kg-1 ~> m4 s-2 kg-1]
  real :: rho0xg             ! g_Earth * Rho0 [kg s-2 m-1 Z-1 ~> kg s-2 m-2]
  logical :: use_eos         ! If true, density is calculated from T & S using
                             ! an equation of state.
  real :: z_neglect          ! A thickness that is so small it is usually lost
                             ! in roundoff and can be neglected [Z ~> m].
  integer :: isq, ieq, jsq, jeq, nz, i, j, k
 
  isq = g%IscB ; ieq = g%IecB ; jsq = g%JscB ; jeq = g%JecB ; nz = g%ke
 
  rho0xg = rho0*us%L_T_to_m_s**2 * gv%g_Earth
  g_rho0 = gv%g_Earth / gv%Rho0
  use_eos = associated(tv%eqn_of_state)
  z_neglect = gv%H_subroundoff*gv%H_to_Z
 
  if (use_eos) then
    if (present(rho_star)) then
     !$OMP parallel do default(shared) private(Ihtot)
      do j=jsq,jeq+1
        do i=isq,ieq+1
          ihtot(i) = gv%H_to_Z / ((e(i,j,1)-e(i,j,nz+1)) + z_neglect)
          pbce(i,j,1) = gfs_scale * rho_star(i,j,1) * gv%H_to_Z
        enddo
        do k=2,nz ; do i=isq,ieq+1
          pbce(i,j,k) = pbce(i,j,k-1) + (rho_star(i,j,k)-rho_star(i,j,k-1)) * &
                        ((e(i,j,k) - e(i,j,nz+1)) * ihtot(i))
        enddo ; enddo
      enddo ! end of j loop
    else
      !$OMP parallel do default(shared) private(Ihtot,press,rho_in_situ,T_int,S_int,dR_dT,dR_dS)
      do j=jsq,jeq+1
        do i=isq,ieq+1
          ihtot(i) = gv%H_to_Z / ((e(i,j,1)-e(i,j,nz+1)) + z_neglect)
          press(i) = -rho0xg*e(i,j,1)
        enddo
        call calculate_density(tv%T(:,j,1), tv%S(:,j,1), press, rho_in_situ, &
                               isq, ieq-isq+2, tv%eqn_of_state, scale=us%kg_m3_to_R)
        do i=isq,ieq+1
          pbce(i,j,1) = g_rho0*(gfs_scale * rho_in_situ(i)) * gv%H_to_Z
        enddo
        do k=2,nz
          do i=isq,ieq+1
            press(i) = -rho0xg*e(i,j,k)
            t_int(i) = 0.5*(tv%T(i,j,k-1)+tv%T(i,j,k))
            s_int(i) = 0.5*(tv%S(i,j,k-1)+tv%S(i,j,k))
          enddo
          call calculate_density_derivs(t_int, s_int, press, dr_dt, dr_ds, &
                                        isq, ieq-isq+2, tv%eqn_of_state, scale=us%kg_m3_to_R)
          do i=isq,ieq+1
            pbce(i,j,k) = pbce(i,j,k-1) + g_rho0 * &
               ((e(i,j,k) - e(i,j,nz+1)) * ihtot(i)) * &
               (dr_dt(i)*(tv%T(i,j,k)-tv%T(i,j,k-1)) + &
                dr_ds(i)*(tv%S(i,j,k)-tv%S(i,j,k-1)))
          enddo
        enddo
      enddo ! end of j loop
    endif
  else ! not use_EOS
    !$OMP parallel do default(shared) private(Ihtot)
    do j=jsq,jeq+1
      do i=isq,ieq+1
        ihtot(i) = 1.0 / ((e(i,j,1)-e(i,j,nz+1)) + z_neglect)
        pbce(i,j,1) = gv%g_prime(1) * gv%H_to_Z
      enddo
      do k=2,nz ; do i=isq,ieq+1
        pbce(i,j,k) = pbce(i,j,k-1) + &
                      (gv%g_prime(k)*gv%H_to_Z) * ((e(i,j,k) - e(i,j,nz+1)) * ihtot(i))
     enddo ; enddo
    enddo ! end of j loop
  endif ! use_EOS
 
end subroutine set_pbce_bouss
 
!> Determines the partial derivative of the acceleration due
!! to pressure forces with the column mass.
subroutine set_pbce_nonbouss(p, tv, G, GV, US, GFS_scale, pbce, alpha_star)
  type(ocean_grid_type),                intent(in)  :: g  !< Ocean grid structure
  type(verticalgrid_type),              intent(in)  :: gv !< Vertical grid structure
  real, dimension(SZI_(G),SZJ_(G),SZK_(G)+1), intent(in) :: p !< Interface pressures [Pa].
  type(thermo_var_ptrs),                intent(in)  :: tv !< Thermodynamic variables
  type(unit_scale_type),                intent(in)  :: us   !< A dimensional unit scaling type
  real,                                 intent(in)  :: gfs_scale !< Ratio between gravity applied to top
                                                          !! interface and the gravitational acceleration of
                                                          !! the planet [nondim]. Usually this ratio is 1.
  real, dimension(SZI_(G),SZJ_(G),SZK_(G)), intent(out) :: pbce !< The baroclinic pressure anomaly in each layer due
                                                                !! to free surface height anomalies
                                                                !! [L2 H-1 T-2 ~> m4 kg-1 s-2].
  real, dimension(SZI_(G),SZJ_(G),SZK_(G)), optional, intent(in) :: alpha_star !< The layer specific volumes
                                                          !! (maybe compressibility compensated) [R-1 ~> m3 kg-1].
  ! Local variables
  real, dimension(SZI_(G),SZJ_(G)) :: &
    dpbce, &      !   A barotropic correction to the pbce to enable the use of
                  ! a reduced gravity form of the equations [L2 H-1 T-2 ~> m4 kg-1 s-2].
    c_htot        ! dP_dH divided by the total ocean pressure [R L2 T-2 H-1 Pa-1 ~> m2 kg-1].
  real :: t_int(szi_(g))     ! Interface temperature [degC].
  real :: s_int(szi_(g))     ! Interface salinity [ppt].
  real :: dr_dt(szi_(g))     ! Partial derivative of density with temperature [R degC-1 ~> kg m-3 degC-1].
  real :: dr_ds(szi_(g))     ! Partial derivative of density with salinity [R ppt-1 ~> kg m-3 ppt-1].
  real :: rho_in_situ(szi_(g)) ! In-situ density at an interface [R ~> kg m-3].
  real :: alpha_lay(szk_(g)) ! The specific volume of each layer [R-1 ~> m3 kg-1].
  real :: dalpha_int(szk_(g)+1) ! The change in specific volume across each interface [R-1 ~> m3 kg-1].
  real :: dp_dh              ! A factor that converts from thickness to pressure times other dimensional
                             ! conversion factors [R L2 T-2 H-1 ~> Pa m2 kg-1].
  real :: dp_neglect         ! A thickness that is so small it is usually lost
                             ! in roundoff and can be neglected [Pa].
  logical :: use_eos         ! If true, density is calculated from T & S using
                             ! an equation of state.
  integer :: isq, ieq, jsq, jeq, nz, i, j, k
 
  isq = g%IscB ; ieq = g%IecB ; jsq = g%JscB ; jeq = g%JecB ; nz = g%ke
 
  use_eos = associated(tv%eqn_of_state)
 
  dp_dh = gv%g_Earth * gv%H_to_RZ
  dp_neglect = gv%H_to_Pa * gv%H_subroundoff
 
  if (use_eos) then
    if (present(alpha_star)) then
      !$OMP parallel do default(shared)
      do j=jsq,jeq+1
        do i=isq,ieq+1
          c_htot(i,j) = dp_dh / ((p(i,j,nz+1)-p(i,j,1)) + dp_neglect)
          pbce(i,j,nz) = dp_dh * alpha_star(i,j,nz)
        enddo
        do k=nz-1,1,-1 ; do i=isq,ieq+1
          pbce(i,j,k) = pbce(i,j,k+1) + ((p(i,j,k+1)-p(i,j,1)) * c_htot(i,j)) * &
              (alpha_star(i,j,k) - alpha_star(i,j,k+1))
        enddo ; enddo
      enddo
    else
      !$OMP parallel do default(shared) private(T_int,S_int,dR_dT,dR_dS,rho_in_situ)
      do j=jsq,jeq+1
        call calculate_density(tv%T(:,j,nz), tv%S(:,j,nz), p(:,j,nz+1), &
                               rho_in_situ, isq, ieq-isq+2, tv%eqn_of_state, scale=us%kg_m3_to_R)
        do i=isq,ieq+1
          c_htot(i,j) = dp_dh / ((p(i,j,nz+1)-p(i,j,1)) + dp_neglect)
          pbce(i,j,nz) = dp_dh / (rho_in_situ(i))
        enddo
        do k=nz-1,1,-1
          do i=isq,ieq+1
            t_int(i) = 0.5*(tv%T(i,j,k)+tv%T(i,j,k+1))
            s_int(i) = 0.5*(tv%S(i,j,k)+tv%S(i,j,k+1))
          enddo
          call calculate_density(t_int, s_int, p(:,j,k+1), rho_in_situ, &
                                      isq, ieq-isq+2, tv%eqn_of_state, scale=us%kg_m3_to_R)
          call calculate_density_derivs(t_int, s_int, p(:,j,k+1), dr_dt, dr_ds, &
                                      isq, ieq-isq+2, tv%eqn_of_state, scale=us%kg_m3_to_R)
          do i=isq,ieq+1
            pbce(i,j,k) = pbce(i,j,k+1) + ((p(i,j,k+1)-p(i,j,1))*c_htot(i,j)) *  &
                ((dr_dt(i)*(tv%T(i,j,k+1)-tv%T(i,j,k)) + &
                  dr_ds(i)*(tv%S(i,j,k+1)-tv%S(i,j,k))) / (rho_in_situ(i)**2))
          enddo
        enddo
      enddo
    endif
  else ! not use_EOS
 
    do k=1,nz ; alpha_lay(k) = 1.0 / (gv%Rlay(k)) ; enddo
    do k=2,nz ; dalpha_int(k) = alpha_lay(k-1) - alpha_lay(k) ; enddo
 
    !$OMP parallel do default(shared)
    do j=jsq,jeq+1
      do i=isq,ieq+1
        c_htot(i,j) = dp_dh / ((p(i,j,nz+1)-p(i,j,1)) + dp_neglect)
        pbce(i,j,nz) = dp_dh * alpha_lay(nz)
      enddo
      do k=nz-1,1,-1 ; do i=isq,ieq+1
        pbce(i,j,k) = pbce(i,j,k+1) + ((p(i,j,k+1)-p(i,j,1))*c_htot(i,j)) * &
                      dalpha_int(k+1)
      enddo ; enddo
    enddo
  endif ! use_EOS
 
  if (gfs_scale < 1.0) then
    ! Adjust the Montgomery potential to make this a reduced gravity model.
    !$OMP parallel do default(shared)
    do j=jsq,jeq+1 ; do i=isq,ieq+1
      dpbce(i,j) = (gfs_scale - 1.0) * pbce(i,j,1)
    enddo ; enddo
    !$OMP parallel do default(shared)
    do k=1,nz ; do j=jsq,jeq+1 ; do i=isq,ieq+1
      pbce(i,j,k) = pbce(i,j,k) + dpbce(i,j)
    enddo ; enddo ; enddo
  endif
 
end subroutine set_pbce_nonbouss
 
!> Initialize the Montgomery-potential form of PGF control structure
subroutine pressureforce_mont_init(Time, G, GV, US, param_file, diag, CS, tides_CSp)
  type(time_type), target, intent(in)    :: time !< Current model time
  type(ocean_grid_type),   intent(in)    :: g  !< ocean grid structure
  type(verticalgrid_type), intent(in)    :: gv !< Vertical grid structure
  type(unit_scale_type),   intent(in)    :: us !< A dimensional unit scaling type
  type(param_file_type),   intent(in)    :: param_file !< Parameter file handles
  type(diag_ctrl), target, intent(inout) :: diag !< Diagnostics control structure
  type(pressureforce_mont_cs),  pointer  :: cs !< Montgomery PGF control structure
  type(tidal_forcing_cs), optional, pointer :: tides_csp !< Tides control structure
 
  ! Local variables
  logical :: use_temperature, use_eos
  ! This include declares and sets the variable "version".
# include "version_variable.h"
  character(len=40)  :: mdl   ! This module's name.
 
  if (associated(cs)) then
    call mom_error(warning, "PressureForce_init called with an associated "// &
                            "control structure.")
    return
  else ; allocate(cs) ; endif
 
  cs%diag => diag ; cs%Time => time
  if (present(tides_csp)) then
    if (associated(tides_csp)) cs%tides_CSp => tides_csp
  endif
 
  mdl = "MOM_PressureForce_Mont"
  call log_version(param_file, mdl, version, "")
  call get_param(param_file, mdl, "RHO_0", cs%Rho0, &
                 "The mean ocean density used with BOUSSINESQ true to "//&
                 "calculate accelerations and the mass for conservation "//&
                 "properties, or with BOUSSINSEQ false to convert some "//&
                 "parameters from vertical units of m to kg m-2.", &
                 units="kg m-3", default=1035.0)
  call get_param(param_file, mdl, "TIDES", cs%tides, &
                 "If true, apply tidal momentum forcing.", default=.false.)
  call get_param(param_file, mdl, "USE_EOS", use_eos, default=.true., &
                 do_not_log=.true.) ! Input for diagnostic use only.
 
  if (use_eos) then
    cs%id_PFu_bc = register_diag_field('ocean_model', 'PFu_bc', diag%axesCuL, time, &
         'Density Gradient Zonal Pressure Force Accel.', "meter second-2", conversion=us%L_T2_to_m_s2)
    cs%id_PFv_bc = register_diag_field('ocean_model', 'PFv_bc', diag%axesCvL, time, &
         'Density Gradient Meridional Pressure Force Accel.', "meter second-2", conversion=us%L_T2_to_m_s2)
    if (cs%id_PFu_bc > 0) then
      call safe_alloc_ptr(cs%PFu_bc,g%IsdB,g%IedB,g%jsd,g%jed,g%ke)
      cs%PFu_bc(:,:,:) = 0.0
    endif
    if (cs%id_PFv_bc > 0) then
      call safe_alloc_ptr(cs%PFv_bc,g%isd,g%ied,g%JsdB,g%JedB,g%ke)
      cs%PFv_bc(:,:,:) = 0.0
    endif
  endif
 
  if (cs%tides) then
    cs%id_e_tidal = register_diag_field('ocean_model', 'e_tidal', diag%axesT1, &
        time, 'Tidal Forcing Astronomical and SAL Height Anomaly', 'meter', conversion=us%Z_to_m)
  endif
 
  cs%GFS_scale = 1.0
  if (gv%g_prime(1) /= gv%g_Earth) cs%GFS_scale = gv%g_prime(1) / gv%g_Earth
 
  call log_param(param_file, mdl, "GFS / G_EARTH", cs%GFS_scale)
 
end subroutine pressureforce_mont_init
 
!> Deallocates the Montgomery-potential form of PGF control structure
subroutine pressureforce_mont_end(CS)
  type(pressureforce_mont_cs), pointer :: cs  !< Control structure for Montgomery potential PGF
  if (associated(cs)) deallocate(cs)
end subroutine pressureforce_mont_end
 
!>\namespace mom_pressureforce_mont
!!
!! Provides the Boussunesq and non-Boussinesq forms of the horizontal
!! accelerations due to pressure gradients using the Montgomery potential. A
!! second-order accurate, centered scheme is used. If a split time stepping
!! scheme is used, the vertical decomposition into barotropic and baroclinic
!! contributions described by Hallberg (J Comp Phys 1997) is used.  With a
!! nonlinear equation of state, compressibility is added along the lines proposed
!! by Sun et al. (JPO 1999), but with compressibility coefficients based on a fit
!! to a user-provided reference profile.
 
end module mom_pressureforce_mont