!--------------------------------------------------------------------------
   !---------------------------- gradient ----------------------------------
   !$OMP DO SCHEDULE(STATIC)
   DO edge = 1, edge_num
      ij_left = left(edge)
      ij_right = right(edge)
      DO l = 1, llm
         grad(l,edge) = 1.*(b(l,ij_right)-b(l,ij_left))
      END DO
   END DO
   !$OMP END DO
   !---------------------------- gradient ----------------------------------
   !--------------------------------------------------------------------------