Refactor Love_scaling calculation in SAL module

* Precalcualte a local field `coef_rhoE` to avoid in-loop division and
if-blocks. The unit of coef_rhoE depends on use_bpa.
* Fix a few unit description typos in SAL module and two other files.

Author: herrwang0

src/core/MOM_open_boundary.F90

@@ -5443,7 +5443,7 @@ subroutine update_segment_tracer_reservoirs(G, GV, uhr, vhr, h, OBC, dt, Reg)
           endif
           I_scale = 1.0 ; if (segment%tr_Reg%Tr(m)%scale /= 0.0) I_scale = 1.0 / segment%tr_Reg%Tr(m)%scale
           if (allocated(segment%tr_Reg%Tr(m)%tres)) then ; do k=1,nz
-            ! Calculate weights. Both a and u_L are nodim. Adding them together has no meaning.
+            ! Calculate weights. Both a and u_L are nondim. Adding them together has no meaning.
             ! However, since they cannot be both non-zero, adding them works like a switch.
             ! When InvLscale_out is 0 and outflow, only interior data is applied to reservoirs
             ! When InvLscale_in is 0 and inflow, only nudged data is applied to reservoirs

src/parameterizations/lateral/MOM_self_attr_load.F90

@@ -38,12 +38,12 @@ module MOM_self_attr_load
   type(sht_CS), allocatable :: sht
     !< Spherical harmonic transforms (SHT) control structure
   integer :: sal_sht_Nd
-    !< Maximum degree for spherical harmonic transforms [nodim]
+    !< Maximum degree for spherical harmonic transforms [nondim]
   real, allocatable :: ebot_ref(:,:)
     !< Reference bottom pressure scaled by Rho_0 and G_Earth[Z ~> m]
   real, allocatable :: Love_scaling(:)
     !< Dimensional coefficients for harmonic SAL, which are functions of Love numbers
-    !! [nondim or Z T2 L-2 R-1 ~> m Pa-1]
+    !! [nondim] or [Z T2 L-2 R-1 ~> m Pa-1], depending on the value of use_ppa.
   real, allocatable :: Snm_Re(:), &    !< Real SHT coefficient for SHT SAL [Z ~> m]
                        Snm_Im(:)       !< Imaginary SHT coefficient for SHT SAL [Z ~> m]
 end type SAL_CS
@@ -69,7 +69,7 @@ subroutine calc_SAL(eta, eta_sal, G, CS, tmp_scale)
               !! to MKS units in reproducing sumes [m Z-1 ~> 1]
 
   ! Local variables
-  real, dimension(SZI_(G),SZJ_(G)) :: bpa ! SSH or bottom pressure anomaly [Z ~> m or R L2 T-2 ~> Pa]
+  real, dimension(SZI_(G),SZJ_(G)) :: bpa ! SSH or bottom pressure anomaly [Z ~> m] or [R L2 T-2 ~> Pa]
   integer :: n, m, l
   integer :: Isq, Ieq, Jsq, Jeq
   integer :: i, j
@@ -136,6 +136,8 @@ subroutine calc_love_scaling(rhoW, rhoE, grav, CS)
   type(SAL_CS), intent(inout) :: CS !< The control structure returned by a previous call to SAL_init.
 
   ! Local variables
+  real :: coef_rhoE ! A scaling coefficient of solid Earth density. coef_rhoE = rhoW / rhoE with USE_BPA=False
+      ! and coef_rhoE = 1.0 / (rhoE * grav) with USE_BPA=True. [nondim] or [Z T2 L-2 R-1 ~> m Pa-1]
   real, dimension(:), allocatable :: HDat, LDat, KDat ! Love numbers converted in CF reference frames [nondim]
   real :: H1, L1, K1 ! Temporary variables to store degree 1 Love numbers [nondim]
   integer :: n_tot ! Size of the stored Love numbers [nondim]
@@ -160,13 +162,16 @@ subroutine calc_love_scaling(rhoW, rhoE, grav, CS)
     KDat(2) = (-1.0 / 3.0) * H1 - (2.0 / 3.0) * L1 - 1.0
   endif
 
+  if (CS%use_bpa) then
+    coef_rhoE = 1.0 / (rhoE * grav) ! [Z T2 L-2 R-1 ~> m Pa-1]
+  else
+    coef_rhoE = rhoW / rhoE ! [nondim]
+  endif
+
   do m=0,nlm ; do n=m,nlm
-    l = order2index(m,nlm)
-    if (CS%use_bpa) then
-      CS%Love_scaling(l+n-m) = (3.0 / real(2*n+1)) * (1.0 / (rhoE * grav)) * (1.0 + KDat(n+1) - HDat(n+1))
-    else
-      CS%Love_scaling(l+n-m) = (3.0 / real(2*n+1)) * (rhoW / rhoE) * (1.0 + KDat(n+1) - HDat(n+1))
-    endif
+    l = order2index(m, nlm)
+    ! Love_scaling has the same as coef_rhoE.
+    CS%Love_scaling(l+n-m) = (3.0 / real(2*n+1)) * coef_rhoE * (1.0 + KDat(n+1) - HDat(n+1))
   enddo ; enddo
 end subroutine calc_love_scaling
 
@@ -315,6 +320,8 @@ end subroutine SAL_end
 
 !> \namespace self_attr_load
 !!
+!! \section section_SAL Self attraction and loading
+!!
 !! This module contains methods to calculate self-attraction and loading (SAL) as a function of sea surface height or
 !! bottom pressure anomaly. SAL is primarily used for fast evolving processes like tides or storm surges, but the
 !! effect applies to all motions.

src/parameterizations/vertical/MOM_diapyc_energy_req.F90

@@ -73,7 +73,7 @@ subroutine diapyc_energy_req_test(h_3d, dt, tv, G, GV, US, CS, Kd_int)
     Kd, &        ! A column of diapycnal diffusivities at interfaces [H Z T-1 ~> m2 s-1 or kg m-1 s-1].
     h_top, h_bot ! Distances from the top or bottom [H ~> m or kg m-2].
   real :: dz_h_int  ! The ratio of the vertical distances across the layers surrounding an interface
-                 ! over the layer thicknesses [H Z-1 ~> nonodim or kg m-3]
+                 ! over the layer thicknesses [H Z-1 ~> nondim or kg m-3]
   real :: ustar  ! The local friction velocity [Z T-1 ~> m s-1]
   real :: absf   ! The absolute value of the Coriolis parameter [T-1 ~> s-1]
   real :: htot   ! The sum of the thicknesses [H ~> m or kg m-2].