Refactor spherical_harmonics_forward

  Refactored the spherical_harmonics_forward routine in MOM_spherical_harmonics
to work in rescaled units by making use of the unscale arguments to
reproducing_sum().  A total of 4 rescaling variables were moved into unscale
arguments, and a block of code that restores the scaling of the output variables
was eliminated.  All answers and diagnostics are bitwise identical, and no
interfaces are changed.

src/parameterizations/lateral/MOM_spherical_harmonics.F90

@@ -61,10 +61,7 @@ subroutine spherical_harmonics_forward(G, CS, var, Snm_Re, Snm_Im, Nd, tmp_scale
     pmn,   & ! Current associated Legendre polynomials of degree n and order m [nondim]
     pmnm1, & ! Associated Legendre polynomials of degree n-1 and order m [nondim]
     pmnm2    ! Associated Legendre polynomials of degree n-2 and order m [nondim]
-  real :: scale ! A rescaling factor to temporarily convert var to MKS units during the
-                ! reproducing sums [a A-1 ~> 1]
-  real :: I_scale ! The inverse of scale [A a-1 ~> 1]
-  real :: sum_tot ! The total of all components output by the reproducing sum in arbitrary units [a]
+  real :: sum_tot ! The total of all components output by the reproducing sum in arbitrary units [A]
   integer :: i, j, k
   integer :: is, ie, js, je, isd, ied, jsd, jed
   integer :: m, n, l
@@ -88,22 +85,21 @@ subroutine spherical_harmonics_forward(G, CS, var, Snm_Re, Snm_Im, Nd, tmp_scale
   do l=1,Ltot ; Snm_Re(l) = 0.0; Snm_Im(l) = 0.0 ; enddo
 
   if (CS%reprod_sum) then
-    scale = 1.0 ; if (present(tmp_scale)) scale = tmp_scale
     do m=0,Nmax
       l = order2index(m, Nmax)
 
       do j=js,je ; do i=is,ie
-        CS%Snm_Re_raw(i,j,l) = (scale*var(i,j)) * CS%Pmm(i,j,m+1) * CS%cos_lonT_wtd(i,j,m+1)
-        CS%Snm_Im_raw(i,j,l) = (scale*var(i,j)) * CS%Pmm(i,j,m+1) * CS%sin_lonT_wtd(i,j,m+1)
+        CS%Snm_Re_raw(i,j,l) = var(i,j) * CS%Pmm(i,j,m+1) * CS%cos_lonT_wtd(i,j,m+1)
+        CS%Snm_Im_raw(i,j,l) = var(i,j) * CS%Pmm(i,j,m+1) * CS%sin_lonT_wtd(i,j,m+1)
         pmnm2(i,j) = 0.0
         pmnm1(i,j) = CS%Pmm(i,j,m+1)
       enddo ; enddo
 
       do n = m+1, Nmax ; do j=js,je ; do i=is,ie
         pmn(i,j) = &
           CS%a_recur(n+1,m+1) * CS%cos_clatT(i,j) * pmnm1(i,j) - CS%b_recur(n+1,m+1) * pmnm2(i,j)
-        CS%Snm_Re_raw(i,j,l+n-m) = (scale*var(i,j)) * pmn(i,j) * CS%cos_lonT_wtd(i,j,m+1)
-        CS%Snm_Im_raw(i,j,l+n-m) = (scale*var(i,j)) * pmn(i,j) * CS%sin_lonT_wtd(i,j,m+1)
+        CS%Snm_Re_raw(i,j,l+n-m) = var(i,j) * pmn(i,j) * CS%cos_lonT_wtd(i,j,m+1)
+        CS%Snm_Im_raw(i,j,l+n-m) = var(i,j) * pmn(i,j) * CS%sin_lonT_wtd(i,j,m+1)
         pmnm2(i,j) = pmnm1(i,j)
         pmnm1(i,j) = pmn(i,j)
       enddo ; enddo ; enddo
@@ -133,15 +129,8 @@ subroutine spherical_harmonics_forward(G, CS, var, Snm_Re, Snm_Im, Nd, tmp_scale
   if (id_clock_sht_global_sum>0) call cpu_clock_begin(id_clock_sht_global_sum)
 
   if (CS%reprod_sum) then
-    sum_tot = reproducing_sum(CS%Snm_Re_raw(:,:,1:Ltot), sums=Snm_Re(1:Ltot))
-    sum_tot = reproducing_sum(CS%Snm_Im_raw(:,:,1:Ltot), sums=Snm_Im(1:Ltot))
-    if (scale /= 1.0) then
-      I_scale = 1.0 / scale
-      do l=1,Ltot
-        Snm_Re(l) = I_scale * Snm_Re(l)
-        Snm_Im(l) = I_scale * Snm_Im(l)
-      enddo
-    endif
+    sum_tot = reproducing_sum(CS%Snm_Re_raw(:,:,1:Ltot), sums=Snm_Re(1:Ltot), unscale=tmp_scale)
+    sum_tot = reproducing_sum(CS%Snm_Im_raw(:,:,1:Ltot), sums=Snm_Im(1:Ltot), unscale=tmp_scale)
   else
     call sum_across_PEs(Snm_Re, Ltot)
     call sum_across_PEs(Snm_Im, Ltot)