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Update MOM_mixed_layer_restrat.F90 #568

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Feb 25, 2024
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Update MOM_mixed_layer_restrat.F90 #568

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b4c39f1
Update MOM_mixed_layer_restrat.F90
amoebaliz Dec 12, 2023
9856fee
Bodner diag: Fix ustar and dims
marshallward Feb 9, 2024
7032df3
Bodner diagnostic: Restore scaling to L
marshallward Feb 20, 2024
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58 changes: 49 additions & 9 deletions src/parameterizations/lateral/MOM_mixed_layer_restrat.F90
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Original file line number Diff line number Diff line change
Expand Up @@ -120,6 +120,7 @@
integer :: id_wpup = -1
integer :: id_ustar = -1
integer :: id_bflux = -1
integer :: id_lfbod = -1
!>@}

end type mixedlayer_restrat_CS
Expand Down Expand Up @@ -807,6 +808,7 @@
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]
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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]
Expand All @@ -829,6 +831,9 @@
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]
Expand Down Expand Up @@ -862,6 +867,9 @@
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: "// &
Expand Down Expand Up @@ -934,8 +942,8 @@
! 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))

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! 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
Expand All @@ -952,14 +960,13 @@
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]

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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

Expand All @@ -970,6 +977,35 @@
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))
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In order to convert this to units of [L ~> m], the denominator should be multiplied by (US%L_to_Z * GV%H_to_RZ* tv%SpV_avg(i,j,1)) when in fully non-Boussinesq mode or in Boussinesq mode the denominator should be multiplied by (GV%H_to_Z*US%L_to_Z). (Compare this with the expressions that set wpup at lines 943 and 968.) Were we to make this change here, the conversion factor at line 1814 would need to be changed to US%L_to_m, while the units of lf_bodner_diag on line 811 would stay as they are.

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I have implemented this suggestion.

enddo ; enddo
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This line has a horizontal indexing error in non-Boussinesq mode because in that case the appropriate rescaling factor is a function of (i,j).


! 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

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lf_bodner_diag(i,j) = lf_bodner_diag(i,j) &
* (US%Z_to_L * GV%RZ_to_H / tv%SpV_avg(i,j,1))

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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)
Expand Down Expand Up @@ -1155,6 +1191,7 @@
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
Expand Down Expand Up @@ -1776,14 +1813,17 @@
'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
Expand Down
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