Merge pull request mom-ocean#1470 from Hallberg-NOAA/OBC_cg_depth_fix

(*)Use summed thicknesses in OBC wave speed

src/core/MOM_open_boundary.F90

@@ -3811,8 +3811,7 @@ subroutine update_OBC_segment_data(G, GV, US, OBC, tv, h, Time)
           segment%h(I,j,k) = h(i+ishift,j,k)
           segment%Htot(I,j) = segment%Htot(I,j) + segment%h(I,j,k)
         enddo
-        segment%Cg(I,j) = sqrt(GV%g_prime(1)*G%bathyT(i+ishift,j))
-        !### This should be: segment%Cg(I,j) = sqrt(GV%g_prime(1)*segment%Htot(I,j)*GV%H_to_Z)
+        segment%Cg(I,j) = sqrt(GV%g_prime(1)*segment%Htot(I,j)*GV%H_to_Z)
       enddo
     else! (segment%direction == OBC_DIRECTION_N .or. segment%direction == OBC_DIRECTION_S)
       allocate(normal_trans_bt(segment%HI%isd:segment%HI%ied,segment%HI%JsdB:segment%HI%JedB))
@@ -3825,8 +3824,7 @@ subroutine update_OBC_segment_data(G, GV, US, OBC, tv, h, Time)
           segment%h(i,J,k) = h(i,j+jshift,k)
           segment%Htot(i,J) = segment%Htot(i,J) + segment%h(i,J,k)
         enddo
-        segment%Cg(i,J) = sqrt(GV%g_prime(1)*G%bathyT(i,j+jshift))
-        !### This should be: segment%Cg(i,J) = sqrt(GV%g_prime(1)*segment%Htot(i,J)*GV%H_to_Z)
+        segment%Cg(i,J) = sqrt(GV%g_prime(1)*segment%Htot(i,J)*GV%H_to_Z)
       enddo
     endif
 

src/user/Kelvin_initialization.F90

@@ -211,15 +211,11 @@ subroutine Kelvin_set_OBC_data(OBC, CS, G, GV, US, h, Time)
   km_to_L_scale = 1000.0*US%m_to_L
 
   do j=jsd,jed ; do i=isd,ied
-    depth_tot(i,j) = G%bathyT(i,j)
+    depth_tot(i,j) = 0.0
   enddo ; enddo
-  !### Instead this should be:
-  ! do j=jsd,jed ; do i=isd,ied
-  !   depth_tot(i,j) = 0.0
-  ! enddo ; enddo
-  ! do j=jsd,jed ; do i=isd,ied
-  !   depth_tot(i,j) = depth_tot(i,j) + GV%H_to_Z * h(i,j,k)
-  ! enddo ; enddo
+  do k=1,nz ; do j=jsd,jed ; do i=isd,ied
+    depth_tot(i,j) = depth_tot(i,j) + GV%H_to_Z * h(i,j,k)
+  enddo ; enddo ; enddo
 
   if (CS%mode == 0) then
     mag_SSH = 1.0*US%m_to_Z