Better fix to eta outside of OBCs issue

 - It hasn't yet caused a blowup that I know of, but better to
   prevent any trouble while we're thinking about it.

src/core/MOM_barotropic.F90

@@ -742,6 +742,7 @@ subroutine btstep(U_in, V_in, eta_in, dt, bc_accel_u, bc_accel_v, forces, pbce,
   integer :: isd, ied, jsd, jed, IsdB, IedB, JsdB, JedB
   integer :: ioff, joff
   integer :: l_seg
+  real :: factor(SZI_(G),SZJ_(G))     ! If non-zero, work on given points.
 
   if (.not.CS%module_is_initialized) call MOM_error(FATAL, &
       "btstep: Module MOM_barotropic must be initialized before it is used.")
@@ -2457,17 +2458,52 @@ subroutine btstep(U_in, V_in, eta_in, dt, bc_accel_u, bc_accel_v, forces, pbce,
                       haloshift=iev-ie, unscale=US%L_to_m**2*GV%H_to_m)
     endif
 
+    do j=jsv,jev
+      do i=isv,iev
+        factor(i,j) = CS%IareaT(i,j)
+      enddo
+    enddo
+
+    ! Update factor so that nothing changes outside of the OBC (problem for interior OBCs only)
+    if (associated(OBC)) then ; if (OBC%OBC_pe) then
+      do j=jsv,jev
+        if (OBC%specified_u_BCs_exist_globally .or. OBC%open_u_BCs_exist_globally) then
+          do i=isv,iev-1 ; if (OBC%segnum_u(I,j) /= OBC_NONE) then
+            if (OBC%segment(OBC%segnum_u(I,j))%direction == OBC_DIRECTION_E) then
+              factor(i+1,j) = 0.0
+            elseif (OBC%segment(OBC%segnum_u(I,j))%direction == OBC_DIRECTION_W) then
+              factor(i,j) = 0.0
+            endif
+          endif ; enddo
+        endif
+        if (OBC%specified_v_BCs_exist_globally .or. OBC%open_v_BCs_exist_globally) then
+          do i=isv,iev
+            if (OBC%segnum_v(i,J-1) /= OBC_NONE) then
+              if (OBC%segment(OBC%segnum_v(i,J-1))%direction == OBC_DIRECTION_N) then
+                factor(i,j) = 0.0
+              endif
+            endif
+            if (OBC%segnum_v(i,J) /= OBC_NONE) then
+              if (OBC%segment(OBC%segnum_v(i,J))%direction == OBC_DIRECTION_S) then
+                factor(i,j) = 0.0
+              endif
+            endif
+          enddo
+        endif
+      enddo
+    endif ; endif
+
     if (integral_BT_cont) then
       !$OMP do
       do j=jsv,jev ; do i=isv,iev
-        eta(i,j) = (eta_IC(i,j) + n*eta_src(i,j)) + CS%IareaT(i,j) * &
+        eta(i,j) = (eta_IC(i,j) + n*eta_src(i,j)) + factor(i,j) * &
                    ((uhbt_int(I-1,j) - uhbt_int(I,j)) + (vhbt_int(i,J-1) - vhbt_int(i,J)))
         eta_wtd(i,j) = eta_wtd(i,j) + eta(i,j) * wt_eta(n)
       enddo ; enddo
     else
       !$OMP do
       do j=jsv,jev ; do i=isv,iev
-        eta(i,j) = (eta(i,j) + eta_src(i,j)) + (dtbt * CS%IareaT(i,j)) * &
+        eta(i,j) = (eta(i,j) + eta_src(i,j)) + (dtbt * factor(i,j)) * &
                    ((uhbt(I-1,j) - uhbt(I,j)) + (vhbt(i,J-1) - vhbt(i,J)))
         eta_wtd(i,j) = eta_wtd(i,j) + eta(i,j) * wt_eta(n)
       enddo ; enddo