MODULE wvelocity_mod ! !git $Id$ !svn $Id: wvelocity.F 1180 2023-07-13 02:42:10Z arango $ !======================================================================= ! Copyright (c) 2002-2023 The ROMS/TOMS Group ! ! Licensed under a MIT/X style license ! ! See License_ROMS.md Hernan G. Arango ! !========================================== Alexander F. Shchepetkin === ! ! ! This subroutines computes vertical velocity (m/s) at W-points ! ! from the vertical mass flux (omega*hz/m*n). This computation ! ! is done solely for output purposes. ! ! ! !======================================================================= ! implicit none PRIVATE PUBLIC :: wvelocity CONTAINS ! !*********************************************************************** SUBROUTINE wvelocity (ng, tile, Ninp) !*********************************************************************** ! USE mod_param USE mod_coupling USE mod_grid USE mod_ocean USE mod_stepping ! ! Imported variable declarations. ! integer, intent(in) :: ng, tile, Ninp ! ! Local variable declarations. ! integer :: IminS, ImaxS, JminS, JmaxS integer :: LBi, UBi, LBj, UBj, LBij, UBij ! ! Set horizontal starting and ending indices for automatic private ! storage arrays. ! IminS=BOUNDS(ng)%Istr(tile)-3 ImaxS=BOUNDS(ng)%Iend(tile)+3 JminS=BOUNDS(ng)%Jstr(tile)-3 JmaxS=BOUNDS(ng)%Jend(tile)+3 ! ! Determine array lower and upper bounds in the I- and J-directions. ! LBi=BOUNDS(ng)%LBi(tile) UBi=BOUNDS(ng)%UBi(tile) LBj=BOUNDS(ng)%LBj(tile) UBj=BOUNDS(ng)%UBj(tile) ! ! Set array lower and upper bounds for MIN(I,J) directions and ! MAX(I,J) directions. ! LBij=BOUNDS(ng)%LBij UBij=BOUNDS(ng)%UBij ! CALL wvelocity_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & Ninp, & & GRID(ng) % pm, & & GRID(ng) % pn, & & GRID(ng) % z_r, & & GRID(ng) % z_w, & & COUPLING(ng) % DU_avg1, & & COUPLING(ng) % DV_avg1, & & OCEAN(ng) % u, & & OCEAN(ng) % v, & & OCEAN(ng) % W, & & OCEAN(ng) % wvel) RETURN END SUBROUTINE wvelocity ! !*********************************************************************** SUBROUTINE wvelocity_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & Ninp, & & pm, pn, z_r, z_w, & & DU_avg1, DV_avg1, & & u, v, W, & & wvel) !*********************************************************************** ! USE mod_param USE mod_ncparam USE mod_scalars ! USE bc_3d_mod, ONLY : bc_w3d_tile USE exchange_2d_mod USE mp_exchange_mod, ONLY : mp_exchange2d, mp_exchange3d ! ! Imported variable declarations. ! integer, intent(in) :: ng, tile integer, intent(in) :: LBi, UBi, LBj, UBj integer, intent(in) :: IminS, ImaxS, JminS, JmaxS integer, intent(in) :: Ninp ! real(r8), intent(in) :: pm(LBi:,LBj:) real(r8), intent(in) :: pn(LBi:,LBj:) real(r8), intent(in) :: z_r(LBi:,LBj:,:) real(r8), intent(in) :: z_w(LBi:,LBj:,0:) real(r8), intent(inout) :: DU_avg1(LBi:,LBj:) real(r8), intent(inout) :: DV_avg1(LBi:,LBj:) real(r8), intent(in) :: u(LBi:,LBj:,:,:) real(r8), intent(in) :: v(LBi:,LBj:,:,:) real(r8), intent(in) :: W(LBi:,LBj:,0:) real(r8), intent(out) :: wvel(LBi:,LBj:,0:) ! ! Local variable declarations. ! integer :: i, j, k real(r8) :: cff1, cff2, cff3, cff4, cff5, slope real(r8), dimension(IminS:ImaxS,JminS:JmaxS,N(ng)) :: vert real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: wrk ! !----------------------------------------------------------------------- ! Set lower and upper tile bounds and staggered variables bounds for ! this horizontal domain partition. Notice that if tile=-1, it will ! set the values for the global grid. !----------------------------------------------------------------------- ! integer :: Istr, IstrB, IstrP, IstrR, IstrT, IstrM, IstrU integer :: Iend, IendB, IendP, IendR, IendT integer :: Jstr, JstrB, JstrP, JstrR, JstrT, JstrM, JstrV integer :: Jend, JendB, JendP, JendR, JendT integer :: Istrm3, Istrm2, Istrm1, IstrUm2, IstrUm1 integer :: Iendp1, Iendp2, Iendp2i, Iendp3 integer :: Jstrm3, Jstrm2, Jstrm1, JstrVm2, JstrVm1 integer :: Jendp1, Jendp2, Jendp2i, Jendp3 ! Istr =BOUNDS(ng) % Istr (tile) IstrB =BOUNDS(ng) % IstrB (tile) IstrM =BOUNDS(ng) % IstrM (tile) IstrP =BOUNDS(ng) % IstrP (tile) IstrR =BOUNDS(ng) % IstrR (tile) IstrT =BOUNDS(ng) % IstrT (tile) IstrU =BOUNDS(ng) % IstrU (tile) Iend =BOUNDS(ng) % Iend (tile) IendB =BOUNDS(ng) % IendB (tile) IendP =BOUNDS(ng) % IendP (tile) IendR =BOUNDS(ng) % IendR (tile) IendT =BOUNDS(ng) % IendT (tile) Jstr =BOUNDS(ng) % Jstr (tile) JstrB =BOUNDS(ng) % JstrB (tile) JstrM =BOUNDS(ng) % JstrM (tile) JstrP =BOUNDS(ng) % JstrP (tile) JstrR =BOUNDS(ng) % JstrR (tile) JstrT =BOUNDS(ng) % JstrT (tile) JstrV =BOUNDS(ng) % JstrV (tile) Jend =BOUNDS(ng) % Jend (tile) JendB =BOUNDS(ng) % JendB (tile) JendP =BOUNDS(ng) % JendP (tile) JendR =BOUNDS(ng) % JendR (tile) JendT =BOUNDS(ng) % JendT (tile) ! Istrm3 =BOUNDS(ng) % Istrm3 (tile) ! Istr-3 Istrm2 =BOUNDS(ng) % Istrm2 (tile) ! Istr-2 Istrm1 =BOUNDS(ng) % Istrm1 (tile) ! Istr-1 IstrUm2=BOUNDS(ng) % IstrUm2(tile) ! IstrU-2 IstrUm1=BOUNDS(ng) % IstrUm1(tile) ! IstrU-1 Iendp1 =BOUNDS(ng) % Iendp1 (tile) ! Iend+1 Iendp2 =BOUNDS(ng) % Iendp2 (tile) ! Iend+2 Iendp2i=BOUNDS(ng) % Iendp2i(tile) ! Iend+2 interior Iendp3 =BOUNDS(ng) % Iendp3 (tile) ! Iend+3 Jstrm3 =BOUNDS(ng) % Jstrm3 (tile) ! Jstr-3 Jstrm2 =BOUNDS(ng) % Jstrm2 (tile) ! Jstr-2 Jstrm1 =BOUNDS(ng) % Jstrm1 (tile) ! Jstr-1 JstrVm2=BOUNDS(ng) % JstrVm2(tile) ! JstrV-2 JstrVm1=BOUNDS(ng) % JstrVm1(tile) ! JstrV-1 Jendp1 =BOUNDS(ng) % Jendp1 (tile) ! Jend+1 Jendp2 =BOUNDS(ng) % Jendp2 (tile) ! Jend+2 Jendp2i=BOUNDS(ng) % Jendp2i(tile) ! Jend+2 interior Jendp3 =BOUNDS(ng) % Jendp3 (tile) ! Jend+3 ! !----------------------------------------------------------------------- ! Compute "true" vertical velocity (m/s). !----------------------------------------------------------------------- ! ! In ROMS, the terrain-following vertical velocity, omega, is given by: ! ! Hz * omega = w - d(z)/d(t) - div(z) ! ! where w is the "true" vertical velocity and ! ! div(z) = pm * u * d(z)/d(xi) + pn * v * d(z)/d(eta) ! ! The vertical coordinate is a function of several parameter but only ! the free-surface is time dependent. However, in sediment applications ! with stratigraphy, the bathymetry (h) also evolves in time. ! ! Exchange time-averaged fields. ! IF (EWperiodic(ng).or.NSperiodic(ng)) THEN CALL exchange_u2d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & DU_avg1) CALL exchange_v2d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & DV_avg1) END IF CALL mp_exchange2d (ng, tile, iNLM, 2, & & LBi, UBi, LBj, UBj, & & NghostPoints, & & EWperiodic(ng), NSperiodic(ng), & & DU_avg1, DV_avg1) ! ! Compute contribution due to quasi-horizontal motions along ! S-coordinate surfaces: (Ui + Vj)*GRADs(z). ! DO k=1,N(ng) DO j=Jstr,Jend DO i=Istr,Iend+1 wrk(i,j)=u(i,j,k,Ninp)*(z_r(i,j,k)-z_r(i-1,j,k))* & & (pm(i-1,j)+pm(i,j)) END DO DO i=Istr,Iend vert(i,j,k)=0.25_r8*(wrk(i,j)+wrk(i+1,j)) END DO END DO DO j=Jstr,Jend+1 DO i=Istr,Iend wrk(i,j)=v(i,j,k,Ninp)*(z_r(i,j,k)-z_r(i,j-1,k))* & & (pn(i,j-1)+pn(i,j)) END DO END DO DO j=Jstr,Jend DO i=Istr,Iend vert(i,j,k)=vert(i,j,k)+0.25_r8*(wrk(i,j)+wrk(i,j+1)) END DO END DO END DO ! ! Compute contribution due to time tendency of the free-surface, ! d(zeta)/d(t), which is the vertical velocity at the free-surface ! and it is expressed in terms of barotropic mass flux divergence. ! Notice that it is divided by the total depth of the water column. ! This is needed because this contribution is linearly distributed ! throughout the water column by multiplying it by the distance from ! the bottom to the depth at which the vertical velocity is computed. ! cff1=3.0_r8/8.0_r8 cff2=3.0_r8/4.0_r8 cff3=1.0_r8/8.0_r8 cff4=9.0_r8/16.0_r8 cff5=1.0_r8/16.0_r8 J_LOOP : DO j=Jstr,Jend DO i=Istr,Iend wrk(i,j)=(DU_avg1(i,j)-DU_avg1(i+1,j)+ & & DV_avg1(i,j)-DV_avg1(i,j+1))/ & & (z_w(i,j,N(ng))-z_w(i,j,0)) END DO ! ! Notice that a cubic interpolation is used to shift the "vert" ! contribution from vertical RHO- to W-points. ! DO i=Istr,Iend slope=(z_r(i,j,1)-z_w(i,j,0))/ & & (z_r(i,j,2)-z_r(i,j,1)) ! extrapolation slope wvel(i,j,0)=cff1*(vert(i,j,1)- & & slope*(vert(i,j,2)- & & vert(i,j,1)))+ & & cff2*vert(i,j,1)- & & cff3*vert(i,j,2) wvel(i,j,1)=pm(i,j)*pn(i,j)* & & (W(i,j,1)+ & & wrk(i,j)*(z_w(i,j,1)-z_w(i,j,0)))+ & & cff1*vert(i,j,1)+ & & cff2*vert(i,j,2)- & & cff3*vert(i,j,3) END DO DO k=2,N(ng)-2 DO i=Istr,Iend wvel(i,j,k)=pm(i,j)*pn(i,j)* & & (W(i,j,k)+ & & wrk(i,j)*(z_w(i,j,k)-z_w(i,j,0)))+ & & cff4*(vert(i,j,k )+vert(i,j,k+1))- & & cff5*(vert(i,j,k-1)+vert(i,j,k+2)) END DO END DO DO i=Istr,Iend slope=(z_w(i,j,N(ng))-z_r(i,j,N(ng) ))/ & & (z_r(i,j,N(ng))-z_r(i,j,N(ng)-1)) ! extrapolation slope wvel(i,j,N(ng))=pm(i,j)*pn(i,j)* & & wrk(i,j)*(z_w(i,j,N(ng))-z_w(i,j,0))+ & & cff1*(vert(i,j,N(ng))+ & & slope*(vert(i,j,N(ng) )- & & vert(i,j,N(ng)-1)))+ & & cff2*vert(i,j,N(ng) )- & & cff3*vert(i,j,N(ng)-1) wvel(i,j,N(ng)-1)=pm(i,j)*pn(i,j)* & & (W(i,j,N(ng)-1)+ & & wrk(i,j)*(z_w(i,j,N(ng)-1)-z_w(i,j,0)))+ & & cff1*vert(i,j,N(ng) )+ & & cff2*vert(i,j,N(ng)-1)- & & cff3*vert(i,j,N(ng)-2) END DO END DO J_LOOP ! ! Set lateral boundary conditions. ! CALL bc_w3d_tile (ng, tile, & & LBi, UBi, LBj, UBj, 0, N(ng), & & wvel) CALL mp_exchange3d (ng, tile, iNLM, 1, & & LBi, UBi, LBj, UBj, 0, N(ng), & & NghostPoints, & & EWperiodic(ng), NSperiodic(ng), & & wvel) RETURN END SUBROUTINE wvelocity_tile END MODULE wvelocity_mod