MODULE omega_mod

  USE icosa
  PRIVATE

  PUBLIC :: w_omega, compute_omega

CONTAINS

  SUBROUTINE w_omega(f_ps, f_u, f_omega) ! Compute omega = Dp/Dt
    TYPE(t_field),POINTER :: f_ps(:), f_u(:), f_omega(:)
    INTEGER :: ind
    REAL(rstd),POINTER :: ps(:), u(:,:), om(:,:)
    DO ind=1,ndomain
       IF (.NOT. assigned_domain(ind)) CYCLE
       CALL swap_dimensions(ind)
       CALL swap_geometry(ind)
       ps=f_ps(ind)
       u=f_u(ind)
       om=f_omega(ind)
       CALL compute_omega(ps,u,om)
    END DO
  END SUBROUTINE W_omega



  SUBROUTINE compute_omega(ps,u, w)
    USE disvert_mod, ONLY : ap,bp
    USE omp_para
    IMPLICIT NONE
    REAL(rstd),INTENT(IN) :: u(iim*3*jjm,llm), ps(iim*jjm)
    REAL(rstd),INTENT(OUT):: w(iim*jjm,llm)
    REAL(rstd):: convm(iim*jjm,llm+1)
    REAL(rstd):: p(iim*jjm,llm+1), rhodz(iim*jjm,llm), Fe(iim*3*jjm,llm)
    REAL(rstd):: ugradps
    
    INTEGER :: i,j,l,ij

!$OMP BARRIER    
    IF (is_omp_level_master) THEN
      DO    l    = 1, llm+1
         DO j=jj_begin-1,jj_end+1
           DO i=ii_begin-1,ii_end+1
               ij=(j-1)*iim+i
               p(ij,l) = ap(l) + bp(l) * ps(ij)
            ENDDO
         ENDDO
      ENDDO
    
!!! Compute mass
      DO l = 1, llm
         DO j=jj_begin-1,jj_end+1
            DO i=ii_begin-1,ii_end+1
               ij=(j-1)*iim+i
               rhodz(ij,l) = ( p(ij,l) - p(ij,l+1) ) / g
            ENDDO
         ENDDO
      ENDDO
    
!!!  Compute mass flux
      DO l = 1, llm
         DO j=jj_begin-1,jj_end+1
            DO i=ii_begin-1,ii_end+1
               ij=(j-1)*iim+i
               Fe(ij+u_right,l)=0.5*(rhodz(ij,l)+rhodz(ij+t_right,l))*u(ij+u_right,l)*le(ij+u_right)
               Fe(ij+u_lup,l)=0.5*(rhodz(ij,l)+rhodz(ij+t_lup,l))*u(ij+u_lup,l)*le(ij+u_lup)
               Fe(ij+u_ldown,l)=0.5*(rhodz(ij,l)+rhodz(ij+t_ldown,l))*u(ij+u_ldown,l)*le(ij+u_ldown)
            ENDDO
         ENDDO
      ENDDO
    
!!! mass flux convergence computation  
    
    ! horizontal convergence
      DO l = 1, llm
         DO j=jj_begin,jj_end
            DO i=ii_begin,ii_end
               ij=(j-1)*iim+i
               ! convm = +div(mass flux), sign convention as in Ringler et al. 2012, eq. 21
               convm(ij,l)= 1./Ai(ij)*(ne(ij,right)*Fe(ij+u_right,l)   +  &
                    ne(ij,rup)*Fe(ij+u_rup,l)       +  &  
                    ne(ij,lup)*Fe(ij+u_lup,l)       +  &  
                    ne(ij,left)*Fe(ij+u_left,l)     +  &  
                    ne(ij,ldown)*Fe(ij+u_ldown,l)   +  &  
                    ne(ij,rdown)*Fe(ij+u_rdown,l))
            ENDDO
         ENDDO
      ENDDO
    
      ! vertical integration from up to down
      DO  l = llm-1, 1, -1
         DO j=jj_begin,jj_end
            DO i=ii_begin,ii_end
               ij=(j-1)*iim+i
               convm(ij,l) = convm(ij,l) + convm(ij,l+1)
            ENDDO
         ENDDO
      ENDDO
      convm(:,llm+1)=0.

!!! Compute dps
    !  DO j=jj_begin,jj_end
    !    DO i=ii_begin,ii_end
    !      ij=(j-1)*iim+i
    !      ! dps/dt = -int(div flux)dz
    !      dps(ij)=-convm(ij,1) * g 
    !      convm(ij,llm+1)=0.
    !    ENDDO
    !  ENDDO
    
    ! Compute Omega = Dp/Dt
    ! with p = A(eta)+B(eta)ps
    !      Dp/Dt = dp/deta.Deta/Dt + B(eta)Dps/Dt
    !            = -mg.Deta/Dt + B.Dps/Dt
    ! By definition the mass flux through model levels is W=m.Deta/Dt with m=-1/g dp/deta
    ! therefore 
    !  Dp/Dt = -g.W + B.dps/dt + Bu.grad ps
    !        = B.u.grad ps - g*convm
    
!!! Compute vertical flux through model layers
    !  DO l = 1,llm-1
    !    DO j=jj_begin,jj_end
    !      DO i=ii_begin,ii_end
    !        ij=(j-1)*iim+i
    !        ! w = int(z,ztop,div(flux)dz) + B(eta)dps/dt
    !        ! => w>0 for upward transport
    !        w( ij, l+1 ) = convm( ij, l+1 ) - bp(l+1) * convm( ij, 1 ) ! g.W = g.convm + B dps/dt
    !      ENDDO
    !    ENDDO
    !  ENDDO
    
    
!!! Compute omega
    ! -grad ps : ( ne(ij,ldown)*ps(ij,l) + ne(ij+t_ldown,rup)*ps(ij+t_ldown,l) ) ) / de(ij+u_ldown)

       DO l = 1,llm
         DO j=jj_begin,jj_end 
           DO i=ii_begin,ii_end
             ij=(j-1)*iim+i
             ugradps = &
                  le(ij+u_right)*u(ij+u_right,l)*( ne(ij,right)*ps(ij) + ne(ij+t_right,left)*ps(ij+t_right) )  &
                  + le(ij+u_rup)*u(ij+u_rup,l)*( ne(ij,rup)*ps(ij) + ne(ij+t_rup,ldown)*ps(ij+t_rup) )  &
                  + le(ij+u_lup)*u(ij+u_lup,l)*( ne(ij,lup)*ps(ij) + ne(ij+t_lup,rdown)*ps(ij+t_lup) )         &
                  + le(ij+u_left)*u(ij+u_left,l)*( ne(ij,left)*ps(ij) + ne(ij+t_left,right)*ps(ij+t_left) )    &
                  + le(ij+u_ldown)*u(ij+u_ldown,l)*( ne(ij,ldown)*ps(ij) + ne(ij+t_ldown,rup)*ps(ij+t_ldown) ) &
                  + le(ij+u_rdown)*u(ij+u_rdown,l)*( ne(ij,rdown)*ps(ij) + ne(ij+t_rdown,lup)*ps(ij+t_rdown) )
             ugradps = .5*(bp(l)+bp(l+1)) *ugradps/(-4*Ai(ij))  ! sign convention as in Ringler et al. 2010, Eq. 22 p.3072
             w( ij, l) =  ugradps - g*.5*(convm( ij,l+1)+convm(ij,l)) 
          ENDDO
        ENDDO
      ENDDO
    ENDIF
!$OMP BARRIER
    
  END SUBROUTINE compute_omega
  
END MODULE omega_mod