diff --git a/src/parameterizations/lateral/MOM_mixed_layer_restrat.F90 b/src/parameterizations/lateral/MOM_mixed_layer_restrat.F90 index c10a55309b..0efe322a1d 100644 --- a/src/parameterizations/lateral/MOM_mixed_layer_restrat.F90 +++ b/src/parameterizations/lateral/MOM_mixed_layer_restrat.F90 @@ -120,6 +120,7 @@ module MOM_mixed_layer_restrat integer :: id_wpup = -1 integer :: id_ustar = -1 integer :: id_bflux = -1 + integer :: id_lfbod = -1 !>@} end type mixedlayer_restrat_CS @@ -807,6 +808,7 @@ subroutine mixedlayer_restrat_Bodner(CS, G, GV, US, h, uhtr, vhtr, tv, forces, d wpup ! Turbulent vertical momentum [L H T-2 ~> m2 s-2 or kg m-1 s-2] real :: uDml_diag(SZIB_(G),SZJ_(G)) ! A 2D copy of uDml for diagnostics [H L2 T-1 ~> m3 s-1 or kg s-1] real :: vDml_diag(SZI_(G),SZJB_(G)) ! A 2D copy of vDml for diagnostics [H L2 T-1 ~> m3 s-1 or kg s-1] + real :: lf_bodner_diag(SZI_(G),SZJ_(G)) ! Front width as in Bodner et al., 2023 (B22), eq 24 [L ~> m] real :: U_star_2d(SZI_(G),SZJ_(G)) ! The wind friction velocity, calculated using the Boussinesq ! reference density or the time-evolving surface density in non-Boussinesq ! mode [Z T-1 ~> m s-1] @@ -829,6 +831,9 @@ subroutine mixedlayer_restrat_Bodner(CS, G, GV, US, h, uhtr, vhtr, tv, forces, d real :: u_star3 ! Cube of surface friction velocity [Z3 T-3 ~> m3 s-3] real :: r_wpup ! reciprocal of vertical momentum flux [T2 L-1 H-1 ~> s2 m-2 or m s2 kg-1] real :: absf ! absolute value of f, interpolated to velocity points [T-1 ~> s-1] + real :: f_h ! Coriolis parameter at h-points [T-1 ~> s-1] + real :: f2_h ! Coriolis parameter at h-points squared [T-2 ~> s-2] + real :: absurdly_small_freq2 ! Frequency squared used to avoid division by 0 [T-2 ~> s-2] real :: grid_dsd ! combination of grid scales [L2 ~> m2] real :: h_sml ! "Little h", the active mixing depth with diurnal cycle removed [H ~> m or kg m-2] real :: h_big ! "Big H", the mixed layer depth based on a time filtered "little h" [H ~> m or kg m-2] @@ -862,6 +867,9 @@ subroutine mixedlayer_restrat_Bodner(CS, G, GV, US, h, uhtr, vhtr, tv, forces, d covTS(:) = 0.0 ! Might be in tv% in the future. Not implemented for the time being. varS(:) = 0.0 ! Ditto. + ! This value is roughly (pi / (the age of the universe) )^2. + absurdly_small_freq2 = 1e-34*US%T_to_s**2 + if (.not.associated(tv%eqn_of_state)) call MOM_error(FATAL, "mixedlayer_restrat_Bodner: "// & "An equation of state must be used with this module.") if (.not.CS%MLE_use_PBL_MLD) call MOM_error(FATAL, "mixedlayer_restrat_Bodner: "// & @@ -934,8 +942,8 @@ subroutine mixedlayer_restrat_Bodner(CS, G, GV, US, h, uhtr, vhtr, tv, forces, d ! This expression differs by a factor of 1. / (Rho_0 * SpV_avg) compared with the other ! expressions below, and it is invariant to the value of Rho_0 in non-Boussinesq mode. wpup(i,j) = max((cuberoot( CS%mstar * U_star_2d(i,j)**3 + & - CS%nstar * max(0., -bflux(i,j)) * BLD(i,j) ))**2, CS%min_wstar2) * & - ( US%Z_to_L * GV%RZ_to_H / tv%SpV_avg(i,j,1)) + CS%nstar * max(0., -bflux(i,j)) * BLD(i,j) ))**2, CS%min_wstar2) & + * (US%Z_to_L * GV%RZ_to_H / tv%SpV_avg(i,j,1)) ! The final line above converts from [Z2 T-2 ~> m2 s-2] to [L H T-2 ~> m2 s-2 or Pa]. ! Some rescaling factors and the division by specific volume compensating for other ! factors that are in find_ustar_mech, and others effectively converting the wind @@ -952,14 +960,13 @@ subroutine mixedlayer_restrat_Bodner(CS, G, GV, US, h, uhtr, vhtr, tv, forces, d w_star3 = max(0., -bflux(i,j)) * BLD(i,j) ! In [Z3 T-3 ~> m3 s-3] u_star3 = U_star_2d(i,j)**3 ! In [Z3 T-3 ~> m3 s-3] wpup(i,j) = max(m2_s2_to_Z2_T2 * (Z3_T3_to_m3_s3 * ( CS%mstar * u_star3 + CS%nstar * w_star3 ) )**two_thirds, & - CS%min_wstar2) * & - ( US%Z_to_L * US%Z_to_m * GV%m_to_H ) ! In [L H T-2 ~> m2 s-2 or kg m-1 s-2] + CS%min_wstar2) * US%Z_to_L * GV%Z_to_H ! In [L H T-2 ~> m2 s-2 or kg m-1 s-2] enddo ; enddo else do j=js-1,je+1 ; do i=is-1,ie+1 w_star3 = max(0., -bflux(i,j)) * BLD(i,j) ! In [Z3 T-3 ~> m3 s-3] - wpup(i,j) = max( (cuberoot(CS%mstar * U_star_2d(i,j)**3 + CS%nstar * w_star3))**2, CS%min_wstar2 ) * & - ( US%Z_to_L * US%Z_to_m * GV%m_to_H ) ! In [L H T-2 ~> m2 s-2 or kg m-1 s-2] + wpup(i,j) = max( (cuberoot(CS%mstar * U_star_2d(i,j)**3 + CS%nstar * w_star3))**2, CS%min_wstar2 ) & + * US%Z_to_L * GV%Z_to_H ! In [L H T-2 ~> m2 s-2 or kg m-1 s-2] enddo ; enddo endif @@ -970,6 +977,35 @@ subroutine mixedlayer_restrat_Bodner(CS, G, GV, US, h, uhtr, vhtr, tv, forces, d CS%wpup_filtered(i,j) = wpup(i,j) enddo ; enddo + if (CS%id_lfbod > 0) then + do j=js-1,je+1 ; do i=is-1,ie+1 + ! Calculate front length used in B22 formula (eq 24). + w_star3 = max(0., -bflux(i,j)) * BLD(i,j) + u_star3 = U_star_2d(i,j)**3 + + ! Include an absurdly_small_freq2 to prevent division by zero. + f_h = 0.25 * ((G%CoriolisBu(I,J) + G%CoriolisBu(I-1,J-1)) & + + (G%CoriolisBu(I-1,J) + G%CoriolisBu(I,J-1))) + f2_h = max(f_h**2, absurdly_small_freq2) + + lf_bodner_diag(i,j) = & + 0.25 * cuberoot(CS%mstar * u_star3 + CS%nstar * w_star3)**2 & + / (f2_h * max(little_h(i,j), GV%Angstrom_H)) + enddo ; enddo + + ! Rescale from [Z2 H-1 to L] + if (allocated(tv%SpV_avg) .and. .not.(GV%Boussinesq .or. GV%semi_Boussinesq)) then + do j=js-1,je+1 ; do i=is-1,ie+1 + lf_bodner_diag(i,j) = lf_bodner_diag(i,j) & + * (US%Z_to_L * GV%RZ_to_H / tv%SpV_avg(i,j,1)) + enddo ; enddo + else + do j=js-1,je+1 ; do i=is-1,ie+1 + lf_bodner_diag(i,j) = lf_bodner_diag(i,j) * US%Z_to_L * GV%Z_to_H + enddo ; enddo + endif + endif + if (CS%debug) then call hchksum(little_h,'mle_Bodner: little_h', G%HI, haloshift=1, scale=GV%H_to_mks) call hchksum(big_H,'mle_Bodner: big_H', G%HI, haloshift=1, scale=GV%H_to_mks) @@ -1155,6 +1191,7 @@ subroutine mixedlayer_restrat_Bodner(CS, G, GV, US, h, uhtr, vhtr, tv, forces, d if (CS%id_vhml > 0) call post_data(CS%id_vhml, vhml, CS%diag) if (CS%id_uDml > 0) call post_data(CS%id_uDml, uDml_diag, CS%diag) if (CS%id_vDml > 0) call post_data(CS%id_vDml, vDml_diag, CS%diag) + if (CS%id_lfbod > 0) call post_data(CS%id_lfbod, lf_bodner_diag, CS%diag) if (CS%id_uml > 0) then do J=js,je ; do i=is-1,ie @@ -1776,14 +1813,17 @@ logical function mixedlayer_restrat_init(Time, G, GV, US, param_file, diag, CS, 'm s-1', conversion=US%L_T_to_m_s) if (CS%use_Bodner) then CS%id_wpup = register_diag_field('ocean_model', 'MLE_wpup', diag%axesT1, Time, & - 'Vertical turbulent momentum flux in Bodner mixed layer restratificiation parameterization', & + 'Vertical turbulent momentum flux in Bodner mixed layer restratification parameterization', & 'm2 s-2', conversion=US%L_to_m*GV%H_to_m*US%s_to_T**2) CS%id_ustar = register_diag_field('ocean_model', 'MLE_ustar', diag%axesT1, Time, & - 'Surface turbulent friction velicity, u*, in Bodner mixed layer restratificiation parameterization', & + 'Surface turbulent friction velocity, u*, in Bodner mixed layer restratification parameterization', & 'm s-1', conversion=(US%Z_to_m*US%s_to_T)) CS%id_bflux = register_diag_field('ocean_model', 'MLE_bflux', diag%axesT1, Time, & - 'Surface buoyancy flux, B0, in Bodner mixed layer restratificiation parameterization', & + 'Surface buoyancy flux, B0, in Bodner mixed layer restratification parameterization', & 'm2 s-3', conversion=(US%Z_to_m**2*US%s_to_T**3)) + CS%id_lfbod = register_diag_field('ocean_model', 'lf_bodner', diag%axesT1, Time, & + 'Front length in Bodner mixed layer restratificiation parameterization', & + 'm', conversion=US%L_to_m) endif ! If MLD_filtered is being used, we need to update halo regions after a restart