(*)Fix rescaling when SPLIT_BOTTOM_STRESS = True

  Corrected the dimensional rescaling of the explicit bottom stresses that are
passed to btstep() when SPLIT_BOTTOM_STRESS = True.  Without this correction,
solutions would not pass the dimensional consistency tests in this case.
Thankfully, the parameter setting in question does not seem to be widely used,
and even if it is, answers will not change when Z_RESCALE_POWER = 0.  All
answers and output in the MOM6-examples test suite are bitwise identical.

src/core/MOM_barotropic.F90

@@ -338,9 +338,9 @@ module MOM_barotropic
                   !! the time-integrated barotropic velocity [L ~> m], beyond which the marginal
                   !! open face area is FA_u_EE. uBT_EE must be non-positive.
   real :: uh_crvW !< The curvature of face area with velocity for flow from the west [H T2 L-1 ~> s2 or kg s2 m-3]
-                  !! or [H L-1 ~> 1 or kg m-3] with INTEGRAL_BT_CONTINUITY.
+                  !! or [H L-1 ~> nondim or kg m-3] with INTEGRAL_BT_CONTINUITY.
   real :: uh_crvE !< The curvature of face area with velocity for flow from the east [H T2 L-1 ~> s2 or kg s2 m-3]
-                  !! or [H L-1 ~> 1 or kg m-3] with INTEGRAL_BT_CONTINUITY.
+                  !! or [H L-1 ~> nondim or kg m-3] with INTEGRAL_BT_CONTINUITY.
   real :: uh_WW   !< The zonal transport when ubt=ubt_WW [H L2 T-1 ~> m3 s-1 or kg s-1], or the equivalent
                   !! time-integrated transport with INTEGRAL_BT_CONTINUITY [H L2 ~> m3 or kg].
   real :: uh_EE   !< The zonal transport when ubt=ubt_EE [H L2 T-1 ~> m3 s-1 or kg s-1], or the equivalent
@@ -364,9 +364,9 @@ module MOM_barotropic
                   !! the time-integrated barotropic velocity [L ~> m], beyond which the marginal
                   !! open face area is FA_v_NN.  vBT_NN must be non-positive.
   real :: vh_crvS !< The curvature of face area with velocity for flow from the south [H T2 L-1 ~> s2 or kg s2 m-3]
-                  !! or [H L-1 ~> 1 or kg m-3] with INTEGRAL_BT_CONTINUITY.
+                  !! or [H L-1 ~> nondim or kg m-3] with INTEGRAL_BT_CONTINUITY.
   real :: vh_crvN !< The curvature of face area with velocity for flow from the north [H T2 L-1 ~> s2 or kg s2 m-3]
-                  !! or [H L-1 ~> 1 or kg m-3] with INTEGRAL_BT_CONTINUITY.
+                  !! or [H L-1 ~> nondim or kg m-3] with INTEGRAL_BT_CONTINUITY.
   real :: vh_SS   !< The meridional transport when vbt=vbt_SS [H L2 T-1 ~> m3 s-1 or kg s-1], or the equivalent
                   !! time-integrated transport with INTEGRAL_BT_CONTINUITY [H L2 ~> m3 or kg].
   real :: vh_NN   !< The meridional transport when vbt=vbt_NN [H L2 T-1 ~> m3 s-1 or kg s-1], or the equivalent
@@ -622,24 +622,23 @@ subroutine btstep(U_in, V_in, eta_in, dt, bc_accel_u, bc_accel_v, forces, pbce,
     vhbt_prev, vhbt_sum_prev, & ! Previous transports stored for OBCs [L2 H T-1 ~> m3 s-1]
     vbt_int_prev, & ! Previous value of time-integrated velocity stored for OBCs [L ~> m]
     vhbt_int_prev   ! Previous value of time-integrated transport stored for OBCs [L2 H ~> m3]
-  real :: mass_to_Z   ! The depth unit conversion divided by the mean density (Rho0) [Z m-1 R-1 ~> m3 kg-1] !### R-1
-  real :: mass_accel_to_Z ! The inverse of the mean density (Rho0) [R-1 ~> m3 kg-1].
-  real :: visc_rem    ! A work variable that may equal visc_rem_[uv].  Nondim.
+  real :: mass_to_Z   ! The inverse of the the mean density (Rho0) [R-1 ~> m3 kg-1]
+  real :: visc_rem    ! A work variable that may equal visc_rem_[uv] [nondim]
   real :: vel_prev    ! The previous velocity [L T-1 ~> m s-1].
   real :: dtbt        ! The barotropic time step [T ~> s].
   real :: bebt        ! A copy of CS%bebt [nondim].
   real :: be_proj     ! The fractional amount by which velocities are projected
-                      ! when project_velocity is true. For now be_proj is set
+                      ! when project_velocity is true [nondim]. For now be_proj is set
                       ! to equal bebt, as they have similar roles and meanings.
   real :: Idt         ! The inverse of dt [T-1 ~> s-1].
   real :: det_de      ! The partial derivative due to self-attraction and loading
-                      ! of the reference geopotential with the sea surface height.
+                      ! of the reference geopotential with the sea surface height [nondim].
                       ! This is typically ~0.09 or less.
   real :: dgeo_de     ! The constant of proportionality between geopotential and
-                      ! sea surface height.  It is a nondimensional number of
+                      ! sea surface height [nondim].  It is a nondimensional number of
                       ! order 1.  For stability, this may be made larger
                       ! than the physical problem would suggest.
-  real :: Instep      ! The inverse of the number of barotropic time steps to take.
+  real :: Instep      ! The inverse of the number of barotropic time steps to take [nondim].
   real :: wt_end      ! The weighting of the final value of eta_PF [nondim]
   integer :: nstep    ! The number of barotropic time steps to take.
   type(time_type) :: &
@@ -772,8 +771,7 @@ subroutine btstep(U_in, V_in, eta_in, dt, bc_accel_u, bc_accel_v, forces, pbce,
   Idtbt = 1.0 / dtbt
   bebt = CS%bebt
   be_proj = CS%bebt
-  mass_accel_to_Z = 1.0 / GV%Rho0
-  mass_to_Z = US%m_to_Z / GV%Rho0  !### THis should be the same as mass_accel_to_Z.
+  mass_to_Z = 1.0 / GV%Rho0
 
   !--- setup the weight when computing vbt_trans and ubt_trans
   if (project_velocity) then
@@ -1243,7 +1241,7 @@ subroutine btstep(U_in, V_in, eta_in, dt, bc_accel_u, bc_accel_v, forces, pbce,
       endif
     endif
 
-    BT_force_u(I,j) = forces%taux(I,j) * mass_accel_to_Z * CS%IDatu(I,j)*visc_rem_u(I,j,1)
+    BT_force_u(I,j) = forces%taux(I,j) * mass_to_Z * CS%IDatu(I,j)*visc_rem_u(I,j,1)
   else
     BT_force_u(I,j) = 0.0
   endif ; enddo ; enddo
@@ -1269,11 +1267,11 @@ subroutine btstep(U_in, V_in, eta_in, dt, bc_accel_u, bc_accel_v, forces, pbce,
       endif
     endif
 
-    BT_force_v(i,J) = forces%tauy(i,J) * mass_accel_to_Z * CS%IDatv(i,J)*visc_rem_v(i,J,1)
+    BT_force_v(i,J) = forces%tauy(i,J) * mass_to_Z * CS%IDatv(i,J)*visc_rem_v(i,J,1)
   else
     BT_force_v(i,J) = 0.0
   endif ; enddo ; enddo
-    if (associated(taux_bot) .and. associated(tauy_bot)) then
+  if (associated(taux_bot) .and. associated(tauy_bot)) then
     !$OMP parallel do default(shared)
     do j=js,je ; do I=is-1,ie ; if (G%mask2dCu(I,j) > 0.0) then
       BT_force_u(I,j) = BT_force_u(I,j) - taux_bot(I,j) * mass_to_Z  * CS%IDatu(I,j)