!--------------------------------------------------------------------------
   !---------------------------- caldyn_vert_NH ----------------------------------
   !$OMP DO SCHEDULE(STATIC)
   DO ij = 1, primal_num
      l=1
      w_ij = ( W(l,ij)+.5*W(l+1,ij) )/mass(l,ij)
      wflux_ij = .5*(wflux(l,ij)+wflux(l+1,ij))
      W_etadot(l,ij) = wflux_ij*w_ij
      eta_dot(l,ij) = wflux_ij / mass(l,ij)
      wcov(l,ij) = w_ij*(geopot(l+1,ij)-geopot(l,ij))
      DO l = 2, llm-1
         w_ij = .5*( W(l,ij)+W(l+1,ij) )/mass(l,ij)
         wflux_ij = .5*(wflux(l,ij)+wflux(l+1,ij))
         W_etadot(l,ij) = wflux_ij*w_ij
         eta_dot(l,ij) = wflux_ij / mass(l,ij)
         wcov(l,ij) = w_ij*(geopot(l+1,ij)-geopot(l,ij))
      END DO
      l=llm
      w_ij = ( .5*W(l,ij)+W(l+1,ij) )/mass(l,ij)
      wflux_ij = .5*(wflux(l,ij)+wflux(l+1,ij))
      W_etadot(l,ij) = wflux_ij*w_ij
      eta_dot(l,ij) = wflux_ij / mass(l,ij)
      wcov(l,ij) = w_ij*(geopot(l+1,ij)-geopot(l,ij))
   END DO
   !$OMP END DO
   ! add NH term to du
   !$OMP DO SCHEDULE(STATIC)
   DO edge = 1, edge_num
      ij_left = left(edge)
      ij_right = right(edge)
      DO l = 1, llm
         du(l,edge) = du(l,edge) - .5*(wcov(l,ij_left)+wcov(l,ij_right))*1.*(eta_dot(l,ij_right)-eta_dot(l,ij_left))
      END DO
   END DO
   !$OMP END DO
   ! add NH terms to dW, dPhi
   ! FIXME : TODO top and bottom
   !$OMP DO SCHEDULE(STATIC)
   DO ij = 1, primal_num
      DO l = 2, llm
         dPhi(l,ij)=dPhi(l,ij)-wflux(l,ij)*(geopot(l+1,ij)-geopot(l-1,ij))/(mass(l-1,ij)+mass(l,ij))
      END DO
   END DO
   !$OMP END DO
   ! We need a barrier here because we compute W_etadot above and do a vertical difference below
   !$OMP BARRIER
   !$OMP DO SCHEDULE(STATIC)
   DO ij = 1, primal_num
      l=1
      dW(l,ij) = dW(l,ij) - W_etadot(l,ij)
      DO l = 2, llm
         dW(l,ij) = dW(l,ij) + W_etadot(l-1,ij) - W_etadot(l,ij)
      END DO
      l=llm+1
      dW(l,ij) = dW(l,ij) + W_etadot(l-1,ij)
   END DO
   !$OMP END DO
   !---------------------------- caldyn_vert_NH ----------------------------------
   !--------------------------------------------------------------------------