+Add ALE_remap_interface_vals and ALE_remap_vertex_vals

  Added ALE_remap_interface_vals and ALE_remap_vertex_vals to handle the
interpolation of variables that are at the interfaces atop tracer cells or above
the corners of the tracers cells from one grid to another.  Because these are
not yet used (but have been tested in calls that will be added with the next
commit, all answers are bitwise identical, but there are two new publicly
visible routines.

src/ALE/MOM_ALE.F90

@@ -129,6 +129,8 @@ module MOM_ALE
 public ALE_remap_scalar
 public ALE_remap_tracers
 public ALE_remap_velocities
+public ALE_remap_interface_vals
+public ALE_remap_vertex_vals
 public ALE_PLM_edge_values
 public TS_PLM_edge_values
 public TS_PPM_edge_values
@@ -974,6 +976,89 @@ subroutine ALE_remap_velocities(CS, G, GV, h_old, h_new, u, v, OBC, dzInterface,
 
 end subroutine ALE_remap_velocities
 
+!> Interpolate to find an updated array of values at interfaces after remapping.
+subroutine ALE_remap_interface_vals(CS, G, GV, h_old, h_new, int_val)
+  type(ALE_CS),                              intent(in)    :: CS       !< ALE control structure
+  type(ocean_grid_type),                     intent(in)    :: G        !< Ocean grid structure
+  type(verticalGrid_type),                   intent(in)    :: GV       !< Ocean vertical grid structure
+  real, dimension(SZI_(G),SZJ_(G),SZK_(GV)), intent(in)    :: h_old    !< Thickness of source grid
+                                                                       !! [H ~> m or kg m-2]
+  real, dimension(SZI_(G),SZJ_(G),SZK_(GV)), intent(in)    :: h_new    !< Thickness of destination grid
+                                                                       !! [H ~> m or kg m-2]
+  real, dimension(SZI_(G),SZJ_(G),SZK_(GV)+1), &
+                                             intent(inout) :: int_val  !< The interface values to interpolate [A]
+
+  real :: val_src(GV%ke)  ! A column of interface values on the source grid [A]
+  real :: val_tgt(GV%ke)  ! A column of interface values on the target grid [A]
+  real :: h_src(GV%ke)    ! A column of source grid layer thicknesses [H ~> m or kg m-2]
+  real :: h_tgt(GV%ke)    ! A column of target grid layer thicknesses [H ~> m or kg m-2]
+  real :: h_neglect, h_neglect_edge  ! Tiny thicknesses used in remapping [H ~> m or kg m-2]
+  logical :: show_call_tree
+  integer :: i, j, k, nz
+
+  do j=G%jsc,G%jec ; do i=G%isc,G%iec ; if (G%mask2dT(i,j)>0.) then
+    do k=1,nz
+      h_src(k) = h_old(i,j,k)
+      h_tgt(k) = h_new(i,j,k)
+    enddo
+
+    do K=1,nz+1
+      val_src(K) = int_val(i,j,K)
+    enddo
+
+    call interpolate_column(nz, h_src, val_src, nz, h_tgt, val_tgt, .false.)
+
+    do K=1,nz+1
+      int_val(i,j,K) = val_tgt(K)
+    enddo
+  endif ; enddo ; enddo
+
+end subroutine ALE_remap_interface_vals
+
+!> Interpolate to find an updated array of values at vertices of tracer cells after remapping.
+subroutine ALE_remap_vertex_vals(CS, G, GV, h_old, h_new, vert_val)
+  type(ALE_CS),                              intent(in)    :: CS       !< ALE control structure
+  type(ocean_grid_type),                     intent(in)    :: G        !< Ocean grid structure
+  type(verticalGrid_type),                   intent(in)    :: GV       !< Ocean vertical grid structure
+  real, dimension(SZI_(G),SZJ_(G),SZK_(GV)), intent(in)    :: h_old    !< Thickness of source grid
+                                                                       !! [H ~> m or kg m-2]
+  real, dimension(SZI_(G),SZJ_(G),SZK_(GV)), intent(in)    :: h_new    !< Thickness of destination grid
+                                                                       !! [H ~> m or kg m-2]
+  real, dimension(SZIB_(G),SZJB_(G),SZK_(GV)+1), &
+                                             intent(inout) :: vert_val  !< The interface values to interpolate [A]
+
+  real :: val_src(GV%ke)  ! A column of interface values on the source grid [A]
+  real :: val_tgt(GV%ke)  ! A column of interface values on the target grid [A]
+  real :: h_src(GV%ke)    ! A column of source grid layer thicknesses [H ~> m or kg m-2]
+  real :: h_tgt(GV%ke)    ! A column of target grid layer thicknesses [H ~> m or kg m-2]
+  real :: I_mask_sum      ! The inverse of the tracer point masks surrounding a corner [nondim]
+  real :: h_neglect, h_neglect_edge  ! Tiny thicknesses used in remapping [H ~> m or kg m-2]
+  logical :: show_call_tree
+  integer :: i, j, k, nz
+
+  do J=G%JscB,G%JecB ; do I=G%IscB,G%IecB
+    if ((G%mask2dT(i,j) + G%mask2dT(i+1,j+1)) + (G%mask2dT(i+1,j) + G%mask2dT(i,j+1)) > 0.0 ) then
+      I_mask_sum = 1.0 / ((G%mask2dT(i,j) + G%mask2dT(i+1,j+1)) + (G%mask2dT(i+1,j) + G%mask2dT(i,j+1)))
+
+    do k=1,nz
+      h_src(k) = ((G%mask2dT(i,j) * h_old(i,j,k) + G%mask2dT(i+1,j+1) * h_old(i+1,j+1,k)) + &
+                  (G%mask2dT(i+1,j) * h_old(i+1,j,k) + G%mask2dT(i,j+1) * h_old(i,j+1,k)) ) * I_mask_sum
+      h_tgt(k) = ((G%mask2dT(i,j) * h_new(i,j,k) + G%mask2dT(i+1,j+1) * h_new(i+1,j+1,k)) + &
+                  (G%mask2dT(i+1,j) * h_new(i+1,j,k) + G%mask2dT(i,j+1) * h_new(i,j+1,k)) ) * I_mask_sum
+    enddo
+
+    do K=1,nz+1
+      val_src(K) = vert_val(I,J,K)
+    enddo
+
+    call interpolate_column(nz, h_src, val_src, nz, h_tgt, val_tgt, .false.)
+
+    do K=1,nz+1
+      vert_val(I,J,K) = val_tgt(K)
+    enddo
+  endif ; enddo ; enddo
+
+end subroutine ALE_remap_vertex_vals
 
 !> Mask out thicknesses to 0 when their running sum exceeds a specified value.
 subroutine apply_partial_cell_mask(h1, h_mask)