Adds option to scale KHTH with depth

This commit adds the option to scale KHTH with
depth by setting DEPTH_SCALED_KHTH = True. The scalling is applied
as follows:
KHTH = MIN(1,H/H_0)**N * KHTH,
where H_0 is defined by DEPTH_SCALED_KHTH_H0,
and N by DEPTH_SCALED_KHTH_EXP.

src/core/MOM.F90

@@ -77,7 +77,7 @@ module MOM
 use MOM_hor_index,             only : hor_index_type, hor_index_init
 use MOM_interface_heights,     only : find_eta
 use MOM_lateral_mixing_coeffs, only : calc_slope_functions, VarMix_init
-use MOM_lateral_mixing_coeffs, only : calc_resoln_function, VarMix_CS
+use MOM_lateral_mixing_coeffs, only : calc_resoln_function, calc_depth_function, VarMix_CS
 use MOM_MEKE,                  only : MEKE_init, MEKE_alloc_register_restart, step_forward_MEKE, MEKE_CS
 use MOM_MEKE_types,            only : MEKE_type
 use MOM_mixed_layer_restrat,   only : mixedlayer_restrat, mixedlayer_restrat_init, mixedlayer_restrat_CS
@@ -565,6 +565,7 @@ subroutine step_MOM(forces, fluxes, sfc_state, Time_start, time_interval, CS, &
       call enable_averaging(cycle_time, Time_start + real_to_time(cycle_time), &
                             CS%diag)
       call calc_resoln_function(h, CS%tv, G, GV, US, CS%VarMix)
+      call calc_depth_function(h, CS%tv, G, GV, US, CS%VarMix)
       call disable_averaging(CS%diag)
     endif
   endif
@@ -1403,6 +1404,7 @@ subroutine step_offline(forces, fluxes, sfc_state, Time_start, time_interval, CS
           if (associated(CS%VarMix)) then
             call pass_var(CS%h, G%Domain)
             call calc_resoln_function(CS%h, CS%tv, G, GV, US, CS%VarMix)
+            call calc_depth_function(CS%h, CS%tv, G, GV, US, CS%VarMix)
             call calc_slope_functions(CS%h, CS%tv, REAL(dt_offline), G, GV, US, CS%VarMix)
           endif
           call tracer_hordiff(CS%h, REAL(dt_offline), CS%MEKE, CS%VarMix, G, GV, US, &
@@ -1428,6 +1430,7 @@ subroutine step_offline(forces, fluxes, sfc_state, Time_start, time_interval, CS
           if (associated(CS%VarMix)) then
             call pass_var(CS%h, G%Domain)
             call calc_resoln_function(CS%h, CS%tv, G, GV, US, CS%VarMix)
+            call calc_depth_function(CS%h, CS%tv, G, GV, US, CS%VarMix)
             call calc_slope_functions(CS%h, CS%tv, REAL(dt_offline), G, GV, US, CS%VarMix)
           endif
           call tracer_hordiff(CS%h, REAL(dt_offline), CS%MEKE, CS%VarMix, G, GV, US, &
@@ -1674,8 +1677,8 @@ subroutine initialize_MOM(Time, Time_init, param_file, dirs, CS, restart_CSp, &
                  "faster by eliminating subroutine calls.", default=.false.)
   call get_param(param_file, "MOM", "DO_DYNAMICS", CS%do_dynamics, &
                  "If False, skips the dynamics calls that update u & v, as well as "//&
-                 "the gravity wave adjustment to h. This is a fragile feature and "//&
-                 "thus undocumented.", default=.true., do_not_log=.true. )
+                 "the gravity wave adjustment to h. This may be a fragile feature, "//&
+                 "but can be useful during development", default=.true.)
   call get_param(param_file, "MOM", "ADVECT_TS", advect_TS, &
                  "If True, advect temperature and salinity horizontally "//&
                  "If False, T/S are registered for advection. "//&

src/parameterizations/lateral/MOM_lateral_mixing_coeffs.F90

@@ -29,6 +29,8 @@ module MOM_lateral_mixing_coeffs
                                   !! when the deformation radius is well resolved.
   logical :: Resoln_scaled_KhTh   !< If true, scale away the thickness diffusivity
                                   !! when the deformation radius is well resolved.
+  logical :: Depth_scaled_KhTh    !< If true, the interface depth diffusivity is scaled away
+                                  !! when the depth is shallower than a reference depth.
   logical :: Resoln_scaled_KhTr   !< If true, scale away the tracer diffusivity
                                   !! when the deformation radius is well resolved.
   logical :: interpolate_Res_fn   !< If true, interpolate the resolution function
@@ -48,6 +50,8 @@ module MOM_lateral_mixing_coeffs
                                   !! This parameter is set depending on other parameters.
   logical :: calculate_res_fns    !< If true, calculate all the resolution factors.
                                   !! This parameter is set depending on other parameters.
+  logical :: calculate_depth_fns !< If true, calculate all the depth factors.
+                                  !! This parameter is set depending on other parameters.
   logical :: calculate_Eady_growth_rate !< If true, calculate all the Eady growth rate.
                                   !! This parameter is set depending on other parameters.
   real, dimension(:,:), pointer :: &
@@ -64,6 +68,10 @@ module MOM_lateral_mixing_coeffs
                           !! deformation radius to the grid spacing at u points [nondim].
     Res_fn_v => NULL(), & !< Non-dimensional function of the ratio the first baroclinic
                           !! deformation radius to the grid spacing at v points [nondim].
+    Depth_fn_u => NULL(), & !< Non-dimensional function of the ratio of the depth to
+                            !! a reference depth (maximum 1) at u points [nondim]
+    Depth_fn_v => NULL(), & !< Non-dimensional function of the ratio of the depth to
+                            !! a reference depth (maximum 1) at v points [nondim]
     beta_dx2_h => NULL(), & !< The magnitude of the gradient of the Coriolis parameter
                             !! times the grid spacing squared at h points [L T-1 ~> m s-1].
     beta_dx2_q => NULL(), & !< The magnitude of the gradient of the Coriolis parameter
@@ -111,6 +119,8 @@ module MOM_lateral_mixing_coeffs
   real :: Res_coef_visc   !< A non-dimensional number that determines the function
                           !! of resolution, used for lateral viscosity, as:
                           !!  F = 1 / (1 + (Res_coef_visc*Ld/dx)^Res_fn_power)
+  real :: depth_scaled_khth_h0 !< The depth above which KHTH is linearly scaled away [Z ~> m]
+  real :: depth_scaled_khth_exp !< The exponent used in the depth dependent scaling function for KHTH [nondim]
   real :: kappa_smooth    !< A diffusivity for smoothing T/S in vanished layers [Z2 T-1 ~> m2 s-1]
   integer :: Res_fn_power_khth !< The power of dx/Ld in the KhTh resolution function.  Any
                                !! positive integer power may be used, but even powers
@@ -140,10 +150,48 @@ module MOM_lateral_mixing_coeffs
 end type VarMix_CS
 
 public VarMix_init, calc_slope_functions, calc_resoln_function
-public calc_QG_Leith_viscosity
+public calc_QG_Leith_viscosity, calc_depth_function
 
 contains
 
+!> Calculates and stires the non-dimensional depth functions.
+subroutine calc_depth_function(h, tv, G, GV, US, CS)
+  type(ocean_grid_type),                    intent(inout) :: G  !< Ocean grid structure
+  real, dimension(SZI_(G),SZJ_(G),SZK_(G)), intent(in)    :: h  !< Layer thickness [H ~> m or kg m-2]
+  type(thermo_var_ptrs),                    intent(in)    :: tv !< Thermodynamic variables
+  type(verticalGrid_type),                  intent(in)    :: GV !< Vertical grid structure
+  type(unit_scale_type),                    intent(in)    :: US !< A dimensional unit scaling type
+  type(VarMix_CS),                          pointer       :: CS !< Variable mixing coefficients
+
+  ! Local variables
+  integer :: is, ie, js, je, Isq, Ieq, Jsq, Jeq, nz
+  integer :: i, j, k
+  real    :: H0 ! local variable for reference depth
+  real    :: expo ! exponent used in the depth dependent scaling
+  is = G%isc ; ie = G%iec ; js = G%jsc ; je = G%jec ; nz = G%ke
+  Isq = G%IscB ; Ieq = G%IecB ; Jsq = G%JscB ; Jeq = G%JecB
+
+  if (.not. associated(CS)) call MOM_error(FATAL, "calc_depth_function:"// &
+         "Module must be initialized before it is used.")
+  if (.not. CS%calculate_depth_fns) return
+  if (.not. associated(CS%Depth_fn_u)) call MOM_error(FATAL, &
+    "calc_depth_function: %Depth_fn_u is not associated with Depth_scaled_KhTh.")
+  if (.not. associated(CS%Depth_fn_v)) call MOM_error(FATAL, &
+    "calc_depth_function: %Depth_fn_v is not associated with Depth_scaled_KhTh.")
+
+  H0 = CS%depth_scaled_khth_h0
+  expo = CS%depth_scaled_khth_exp
+!$OMP do
+  do j=js,je ; do I=is-1,Ieq
+    CS%Depth_fn_u(I,j) = (MIN(1.0, 0.5*(G%bathyT(i,j) + G%bathyT(i+1,j))/H0))**expo
+  enddo ; enddo
+!$OMP do
+  do J=js-1,Jeq ; do i=is,ie
+    CS%Depth_fn_v(i,J) = (MIN(1.0, 0.5*(G%bathyT(i,j) + G%bathyT(i,j+1))/H0))**expo
+  enddo ; enddo
+
+end subroutine calc_depth_function
+
 !> Calculates and stores the non-dimensional resolution functions
 subroutine calc_resoln_function(h, tv, G, GV, US, CS)
   type(ocean_grid_type),                    intent(inout) :: G  !< Ocean grid structure
@@ -913,7 +961,7 @@ subroutine VarMix_init(Time, G, GV, US, param_file, diag, CS)
   CS%calculate_Rd_dx = .false.
   CS%calculate_res_fns = .false.
   CS%calculate_Eady_growth_rate = .false.
-
+  CS%calculate_depth_fns = .false.
   ! Read all relevant parameters and write them to the model log.
   call log_version(param_file, mdl, version, "")
   call get_param(param_file, mdl, "USE_VARIABLE_MIXING", CS%use_variable_mixing,&
@@ -929,6 +977,13 @@ subroutine VarMix_init(Time, G, GV, US, param_file, diag, CS)
                  "If true, the Laplacian lateral viscosity is scaled away "//&
                  "when the first baroclinic deformation radius is well "//&
                  "resolved.", default=.false.)
+  call get_param(param_file, mdl, "DEPTH_SCALED_KHTH", CS%Depth_scaled_KhTh, &
+                 "If true, the interface depth diffusivity is scaled away "//&
+                 "when the depth is shallower than a reference depth: "//&
+                 "KHTH = MIN(1,H/H0)**N * KHTH, where H0 is a reference"//&
+                 "depth, controlled via DEPTH_SCALED_KHTH_H0, and the"//&
+                 "exponent (N) is controlled via DEPTH_SCALED_KHTH_EXP.",&
+                 default=.false.)
   call get_param(param_file, mdl, "RESOLN_SCALED_KHTH", CS%Resoln_scaled_KhTh, &
                  "If true, the interface depth diffusivity is scaled away "//&
                  "when the first baroclinic deformation radius is well "//&
@@ -978,6 +1033,7 @@ subroutine VarMix_init(Time, G, GV, US, param_file, diag, CS)
 
   call get_param(param_file, mdl, "DEBUG", CS%debug, default=.false., do_not_log=.true.)
 
+
   if (CS%Resoln_use_ebt .or. CS%khth_use_ebt_struct) then
     in_use = .true.
     call get_param(param_file, mdl, "RESOLN_N2_FILTER_DEPTH", N2_filter_depth, &
@@ -1160,6 +1216,18 @@ subroutine VarMix_init(Time, G, GV, US, param_file, diag, CS)
 
   endif
 
+  if (CS%Depth_scaled_KhTh) then
+    CS%calculate_depth_fns = .true.
+    allocate(CS%Depth_fn_u(IsdB:IedB,jsd:jed))     ; CS%Depth_fn_u(:,:) = 0.0
+    allocate(CS%Depth_fn_v(isd:ied,JsdB:JedB))     ; CS%Depth_fn_v(:,:) = 0.0
+    call get_param(param_file, mdl, "DEPTH_SCALED_KHTH_H0", CS%depth_scaled_khth_h0, &
+    "The depth above which KHTH is scaled away.",&
+    units="m", default=1000.)
+    call get_param(param_file, mdl, "DEPTH_SCALED_KHTH_EXP", CS%depth_scaled_khth_exp, &
+    "The exponent used in the depth dependent scaling function for KHTH.",&
+    units="nondim", default=3.0)
+  endif
+
   ! Resolution %Rd_dx_h
   CS%id_Rd_dx = register_diag_field('ocean_model', 'Rd_dx', diag%axesT1, Time, &
        'Ratio between deformation radius and grid spacing', 'm m-1')

src/parameterizations/lateral/MOM_thickness_diffuse.F90

@@ -137,12 +137,13 @@ subroutine thickness_diffuse(h, uhtr, vhtr, tv, dt, G, GV, US, MEKE, VarMix, CDp
   real, dimension(SZI_(G), SZJB_(G)) :: &
     KH_v_CFL      ! The maximum stable interface height diffusivity at v grid points [L2 T-1 ~> m2 s-1]
   real :: Khth_Loc_u(SZIB_(G), SZJ_(G))
+  real :: Khth_Loc_v(SZI_(G), SZJB_(G))
   real :: Khth_Loc(SZIB_(G), SZJB_(G))  ! locally calculated thickness diffusivity [L2 T-1 ~> m2 s-1]
   real :: h_neglect ! A thickness that is so small it is usually lost
                     ! in roundoff and can be neglected [H ~> m or kg m-2].
   real, dimension(:,:), pointer :: cg1 => null() !< Wave speed [L T-1 ~> m s-1]
   real :: dt_in_T   ! Time increment [T ~> s]
-  logical :: use_VarMix, Resoln_scaled, use_stored_slopes, khth_use_ebt_struct, use_Visbeck
+  logical :: use_VarMix, Resoln_scaled, Depth_scaled, use_stored_slopes, khth_use_ebt_struct, use_Visbeck
   logical :: use_QG_Leith
   integer :: i, j, k, is, ie, js, je, nz
   real :: hu(SZI_(G), SZJ_(G))       ! u-thickness [H ~> m or kg m-2]
@@ -168,10 +169,12 @@ subroutine thickness_diffuse(h, uhtr, vhtr, tv, dt, G, GV, US, MEKE, VarMix, CDp
 
   use_VarMix = .false. ; Resoln_scaled = .false. ; use_stored_slopes = .false.
   khth_use_ebt_struct = .false. ; use_Visbeck = .false. ; use_QG_Leith = .false.
+  Depth_scaled = .false.
 
   if (associated(VarMix)) then
     use_VarMix = VarMix%use_variable_mixing .and. (CS%KHTH_Slope_Cff > 0.)
     Resoln_scaled = VarMix%Resoln_scaled_KhTh
+    Depth_scaled = VarMix%Depth_scaled_KhTh
     use_stored_slopes = VarMix%use_stored_slopes
     khth_use_ebt_struct = VarMix%khth_use_ebt_struct
     use_Visbeck = VarMix%use_Visbeck
@@ -238,6 +241,13 @@ subroutine thickness_diffuse(h, uhtr, vhtr, tv, dt, G, GV, US, MEKE, VarMix, CDp
     enddo ; enddo
   endif
 
+  if (Depth_scaled) then
+!$OMP do
+    do j=js,je; do I=is-1,ie
+      Khth_loc_u(I,j) = Khth_loc_u(I,j) * VarMix%Depth_fn_u(I,j)
+    enddo ; enddo
+  endif
+
   if (CS%Khth_Max > 0) then
 !$OMP do
     do j=js,je; do I=is-1,ie
@@ -284,55 +294,62 @@ subroutine thickness_diffuse(h, uhtr, vhtr, tv, dt, G, GV, US, MEKE, VarMix, CDp
 
 !$OMP do
   do J=js-1,je ; do i=is,ie
-    Khth_loc(i,j) = CS%Khth
+    Khth_loc_v(i,J) = CS%Khth
   enddo ; enddo
 
   if (use_VarMix) then
 !$OMP do
     if (use_Visbeck) then
       do J=js-1,je ; do i=is,ie
-        Khth_loc(i,j) = Khth_loc(i,j) + CS%KHTH_Slope_Cff*VarMix%L2v(i,J)*VarMix%SN_v(i,J)
+        Khth_loc_v(i,J) = Khth_loc_v(i,J) + CS%KHTH_Slope_Cff*VarMix%L2v(i,J)*VarMix%SN_v(i,J)
       enddo ; enddo
     endif
   endif
   if (associated(MEKE)) then ; if (associated(MEKE%Kh)) then
 !$OMP do
     if (CS%MEKE_GEOMETRIC) then
-      do j=js-1,je ; do I=is,ie
-        Khth_loc(I,j) = Khth_loc(I,j) + G%mask2dCv(i,J) * CS%MEKE_GEOMETRIC_alpha * &
+      do J=js-1,je ; do i=is,ie
+        Khth_loc_v(i,J) = Khth_loc_v(i,J) + G%mask2dCv(i,J) * CS%MEKE_GEOMETRIC_alpha * &
                         0.5*(MEKE%MEKE(i,j)+MEKE%MEKE(i,j+1)) / &
                         (VarMix%SN_v(i,J) + CS%MEKE_GEOMETRIC_epsilon)
       enddo ; enddo
     else
       do J=js-1,je ; do i=is,ie
-        Khth_loc(i,j) = Khth_loc(i,j) + MEKE%KhTh_fac*sqrt(MEKE%Kh(i,j)*MEKE%Kh(i,j+1))
+        Khth_loc_v(i,J) = Khth_loc_v(i,J) + MEKE%KhTh_fac*sqrt(MEKE%Kh(i,j)*MEKE%Kh(i,j+1))
       enddo ; enddo
     endif
   endif ; endif
 
   if (Resoln_scaled) then
+!$OMP do
+    do J=js-1,je; do i=is,ie
+      Khth_loc_v(i,J) = Khth_loc_v(i,J) * VarMix%Res_fn_v(i,J)
+    enddo ; enddo
+  endif
+
+  if (Depth_scaled) then
 !$OMP do
     do J=js-1,je ; do i=is,ie
-      Khth_loc(i,j) = Khth_loc(i,j) * VarMix%Res_fn_v(i,J)
+      Khth_loc_v(i,J) = Khth_loc_v(i,J) * VarMix%Depth_fn_v(i,J)
     enddo ; enddo
   endif
 
   if (CS%Khth_Max > 0) then
 !$OMP do
     do J=js-1,je ; do i=is,ie
-      Khth_loc(i,j) = max(CS%Khth_Min, min(Khth_loc(i,j), CS%Khth_Max))
+      Khth_loc_v(i,J) = max(CS%Khth_Min, min(Khth_loc_v(i,J), CS%Khth_Max))
     enddo ; enddo
   else
 !$OMP do
     do J=js-1,je ; do i=is,ie
-      Khth_loc(i,j) = max(CS%Khth_Min, Khth_loc(i,j))
+      Khth_loc_v(i,J) = max(CS%Khth_Min, Khth_loc_v(i,J))
     enddo ; enddo
   endif
 
   if (CS%max_Khth_CFL > 0.0) then
 !$OMP do
     do J=js-1,je ; do i=is,ie
-      KH_v(i,J,1) = min(KH_v_CFL(i,J), Khth_loc(i,j))
+      KH_v(i,J,1) = min(KH_v_CFL(i,J), Khth_loc_v(i,J))
     enddo ; enddo
   endif