#include "cppdefs.h" MODULE tl_conv_bry3d_mod #if defined TANGENT && defined FOUR_DVAR && defined SOLVE3D && \ defined ADJUST_BOUNDARY ! !svn $Id: tl_conv_bry3d.F 889 2018-02-10 03:32:52Z arango $ !================================================== Hernan G. Arango === ! Copyright (c) 2002-2019 The ROMS/TOMS Group Andrew M. Moore ! ! Licensed under a MIT/X style license ! ! See License_ROMS.txt ! !======================================================================= ! ! ! These routines applies the background error covariance to data ! ! assimilation fields via the space convolution of the diffusion ! ! equation (filter) for 3D state variables. The diffusion filter ! ! is solved using an implicit or explicit vertical algorithm. ! ! ! ! For Gaussian (bell-shaped) correlations, the space convolution ! ! of the diffusion operator is an efficient way to estimate the ! ! finite domain error covariances. ! ! ! ! On Input: ! ! ! ! ng Nested grid number ! ! tile Tile partition ! ! model Calling model identifier ! ! boundary Boundary edge to convolve ! ! edge Boundary edges index ! ! LBij Lower bound MIN(I,J)-dimension ! ! LBij Lower bound MAX(I,J)-dimension ! ! LBi I-dimension lower bound ! ! UBi I-dimension upper bound ! ! LBj J-dimension lower bound ! ! UBj J-dimension upper bound ! ! LBk K-dimension lower bound ! ! UBk K-dimension upper bound ! ! Nghost Number of ghost points ! ! NHsteps Number of horizontal diffusion integration steps ! ! NVsteps Number of vertical diffusion integration steps ! ! DTsizeH Horizontal diffusion pseudo time-step size ! ! DTsizeV Vertical diffusion pseudo time-step size ! ! Kh Horizontal diffusion coefficients ! ! Kv Vertical diffusion coefficients ! ! tl_A 3D boundary state variable to diffuse ! ! ! ! On Output: ! ! ! ! tl_A Convolved 3D boundary state variable ! ! ! ! Routines: ! ! ! ! tl_conv_r3d_bry_tile Tangent linear 3D boundary convolution at ! ! RHO-points ! ! tl_conv_u3d_bry_tile Tangent linear 3D boundary convolution at ! ! U-points ! ! tl_conv_v3d_bry_tile Tangent linear 3D boundary convolution at ! ! V-points ! ! ! !======================================================================= ! implicit none ! PUBLIC ! CONTAINS ! !*********************************************************************** SUBROUTINE tl_conv_r3d_bry_tile (ng, tile, model, boundary, & & edge, LBij, UBij, & & LBi, UBi, LBj, UBj, LBk, UBk, & & IminS, ImaxS, JminS, JmaxS, & & Nghost, NHsteps, NVsteps, & & DTsizeH, DTsizeV, & & Kh, Kv, & & pm, pn, pmon_u, pnom_v, & # ifdef MASKING & rmask, umask, vmask, & # endif & Hz, z_r, & & tl_A) !*********************************************************************** ! USE mod_param USE mod_scalars ! USE bc_bry3d_mod, ONLY: bc_r3d_bry_tile # ifdef DISTRIBUTE USE mp_exchange_mod, ONLY : mp_exchange3d_bry # endif ! ! Imported variable declarations. ! integer, intent(in) :: ng, tile, model, boundary integer, intent(in) :: edge(4) integer, intent(in) :: LBij, UBij integer, intent(in) :: LBi, UBi, LBj, UBj, LBk, UBk integer, intent(in) :: IminS, ImaxS, JminS, JmaxS integer, intent(in) :: Nghost, NHsteps, NVsteps real(r8), intent(in) :: DTsizeH, DTsizeV ! # ifdef ASSUMED_SHAPE real(r8), intent(in) :: pm(LBi:,LBj:) real(r8), intent(in) :: pn(LBi:,LBj:) real(r8), intent(in) :: pmon_u(LBi:,LBj:) real(r8), intent(in) :: pnom_v(LBi:,LBj:) # ifdef MASKING real(r8), intent(in) :: rmask(LBi:,LBj:) real(r8), intent(in) :: umask(LBi:,LBj:) real(r8), intent(in) :: vmask(LBi:,LBj:) # endif real(r8), intent(in) :: Hz(LBi:,LBj:,:) real(r8), intent(in) :: z_r(LBi:,LBj:,:) real(r8), intent(in) :: Kh(LBi:,LBj:) real(r8), intent(in) :: Kv(LBi:,LBj:,0:) real(r8), intent(inout) :: tl_A(LBij:,LBk:) # else real(r8), intent(in) :: pm(LBi:UBi,LBj:UBj) real(r8), intent(in) :: pn(LBi:UBi,LBj:UBj) real(r8), intent(in) :: pmon_u(LBi:UBi,LBj:UBj) real(r8), intent(in) :: pnom_v(LBi:UBi,LBj:UBj) # ifdef MASKING real(r8), intent(in) :: rmask(LBi:UBi,LBj:UBj) real(r8), intent(in) :: umask(LBi:UBi,LBj:UBj) real(r8), intent(in) :: vmask(LBi:UBi,LBj:UBj) # endif real(r8), intent(in) :: Hz(LBi:UBi,LBj:UBj,N(ng)) real(r8), intent(in) :: z_r(LBi:UBi,LBj:UBj,N(ng)) real(r8), intent(in) :: Kh(LBi:UBi,LBj:UBj) real(r8), intent(in) :: Kv(LBi:UBi,LBj:UBj,0:UBk) real(r8), intent(inout) :: tl_A(LBij:UBij,LBk:UBk) # endif ! ! Local variable declarations. ! logical, dimension(4) :: Lconvolve integer :: Nnew, Nold, Nsav, i, j, k, step real(r8) :: cff, cff1 real(r8), dimension(LBij:UBij,LBk:UBk,2) :: tl_Awrk real(r8), dimension(JminS:JmaxS,LBk:UBk) :: tl_FE real(r8), dimension(IminS:ImaxS,LBk:UBk) :: tl_FX real(r8), dimension(LBij:UBij) :: Hfac # ifdef VCONVOLUTION # ifndef SPLINES_VCONV real(r8), dimension(LBij:UBij,0:N(ng)) :: FC # endif # if !defined IMPLICIT_VCONV || defined SPLINES_VCONV real(r8), dimension(LBij:UBij,N(ng)) :: oHz # endif # if defined IMPLICIT_VCONV || defined SPLINES_VCONV real(r8), dimension(LBij:UBij,0:N(ng)) :: BC real(r8), dimension(LBij:UBij,0:N(ng)) :: CF # ifdef SPLINES_VCONV real(r8), dimension(LBij:UBij,0:N(ng)) :: FC # endif real(r8), dimension(LBij:UBij,0:N(ng)) :: tl_DC # else real(r8), dimension(LBij:UBij,0:N(ng)) :: tl_FS # endif # endif # include "set_bounds.h" ! !----------------------------------------------------------------------- ! Space convolution of the diffusion equation for a 2D state variable ! at RHO-points. !----------------------------------------------------------------------- ! Lconvolve(iwest )=DOMAIN(ng)%Western_Edge (tile) Lconvolve(ieast )=DOMAIN(ng)%Eastern_Edge (tile) Lconvolve(isouth)=DOMAIN(ng)%Southern_Edge(tile) Lconvolve(inorth)=DOMAIN(ng)%Northern_Edge(tile) ! ! Compute metrics factors. Notice that "z_r" and "Hz" are assumed to ! be time invariant in the vertical convolution. Scratch array are ! used for efficiency. ! IF (Lconvolve(boundary)) THEN IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN i=edge(boundary) DO j=Jstr-1,Jend+1 Hfac(j)=DTsizeH*pm(i,j)*pn(i,j) # ifdef VCONVOLUTION # ifndef SPLINES_VCONV FC(j,N(ng))=0.0_r8 DO k=1,N(ng)-1 # ifdef IMPLICIT_VCONV FC(j,k)=-DTsizeV*Kv(i,j,k)/ & & (z_r(i,j,k+1)-z_r(i,j,k)) # else FC(j,k)=DTsizeV*Kv(i,j,k)/ & & (z_r(i,j,k+1)-z_r(i,j,k)) # endif END DO FC(j,0)=0.0_r8 # endif # if !defined IMPLICIT_VCONV || defined SPLINES_VCONV DO k=1,N(ng) oHz(j,k)=1.0_r8/Hz(i,j,k) END DO # endif # endif END DO ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN j=edge(boundary) DO i=Istr-1,Iend+1 Hfac(i)=DTsizeH*pm(i,j)*pn(i,j) # ifdef VCONVOLUTION # ifndef SPLINES_VCONV FC(i,N(ng))=0.0_r8 DO k=1,N(ng)-1 # ifdef IMPLICIT_VCONV FC(i,k)=-DTsizeV*Kv(i,j,k)/ & & (z_r(i,j,k+1)-z_r(i,j,k)) # else FC(i,k)=DTsizeV*Kv(i,j,k)/ & & (z_r(i,j,k+1)-z_r(i,j,k)) # endif END DO FC(i,0)=0.0_r8 # endif # if !defined IMPLICIT_VCONV || defined SPLINES_VCONV DO k=1,N(ng) oHz(i,k)=1.0_r8/Hz(i,j,k) END DO # endif # endif END DO END IF END IF ! ! Set integration indices and initial conditions. ! Nold=1 Nnew=2 !> CALL bc_r3d_bry_tile (ng, tile, boundary, & !> & LBij, UBij, 1, N(ng), & !> & A) !> CALL bc_r3d_bry_tile (ng, tile, boundary, & & LBij, UBij, 1, N(ng), & & tl_A) # ifdef DISTRIBUTE !> CALL mp_exchange3d_bry (ng, tile, model, 1, boundary, & !> & LBij, UBij, 1, N(ng), & !> & Nghost, & !> & EWperiodic(ng), NSperiodic(ng), & !> & A) !> CALL mp_exchange3d_bry (ng, tile, model, 1, boundary, & & LBij, UBij, 1, N(ng), & & Nghost, & & EWperiodic(ng), NSperiodic(ng), & & tl_A) # endif IF (Lconvolve(boundary)) THEN IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN DO k=1,N(ng) DO j=Jstr-1,Jend+1 !> Awrk(j,k,Nold)=A(j,k) !> tl_Awrk(j,k,Nold)=tl_A(j,k) END DO END DO ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN DO k=1,N(ng) DO i=Istr-1,Iend+1 !> Awrk(i,k,Nold)=A(i,k) !> tl_Awrk(i,k,Nold)=tl_A(i,k) END DO END DO END IF END IF ! !----------------------------------------------------------------------- ! Integrate horizontal diffusion equation. !----------------------------------------------------------------------- ! DO step=1,NHsteps ! ! Compute XI- and ETA-components of diffusive flux. ! IF (Lconvolve(boundary)) THEN IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN i=edge(boundary) DO k=1,N(ng) DO j=Jstr,Jend+1 !> FE(j,k)=pnom_v(i,j)*0.5_r8*(Kh(i,j-1)+Kh(i,j))* & !> & (Awrk(j ,k,Nold)- & !> & Awrk(j-1,k,Nold)) !> tl_FE(j,k)=pnom_v(i,j)*0.5_r8*(Kh(i,j-1)+Kh(i,j))* & & (tl_Awrk(j ,k,Nold)- & & tl_Awrk(j-1,k,Nold)) # ifdef MASKING !> FE(j,k)=FE(j,k)*vmask(i,j) !> tl_FE(j,k)=tl_FE(j,k)*vmask(i,j) # endif END DO END DO ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN j=edge(boundary) DO k=1,N(ng) DO i=Istr,Iend+1 !> FX(i,k)=pmon_u(i,j)*0.5_r8*(Kh(i-1,j)+Kh(i,j))* & !> & (Awrk(i ,k,Nold)- & !> & Awrk(i-1,k,Nold)) !> tl_FX(i,k)=pmon_u(i,j)*0.5_r8*(Kh(i-1,j)+Kh(i,j))* & & (tl_Awrk(i ,k,Nold)- & & tl_Awrk(i-1,k,Nold)) # ifdef MASKING !> FX(i,k)=FX(i,k)*umask(i,j) !> tl_FX(i,k)=tl_FX(i,k)*umask(i,j) # endif END DO END DO END IF END IF ! ! Time-step horizontal diffusion equation. ! IF (Lconvolve(boundary)) THEN IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN DO k=1,N(ng) DO j=Jstr,Jend !> Awrk(j,k,Nnew)=Awrk(j,k,Nold)+ & !> & Hfac(j)* & !> & (FE(j+1,k)-FE(j,k)) !> tl_Awrk(j,k,Nnew)=tl_Awrk(j,k,Nold)+ & & Hfac(j)* & & (tl_FE(j+1,k)-tl_FE(j,k)) END DO END DO ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN DO k=1,N(ng) DO i=Istr,Iend !> Awrk(i,k,Nnew)=Awrk(i,k,Nold)+ & !> & Hfac(i)* & !> & (FX(i+1,k)-FX(i,k)) !> tl_Awrk(i,k,Nnew)=tl_Awrk(i,k,Nold)+ & & Hfac(i)* & & (tl_FX(i+1,k)-tl_FX(i,k)) END DO END DO END IF END IF ! ! Apply boundary conditions. ! !> CALL bc_r3d_bry_tile (ng, tile, boundary, & !> & LBij, UBij, 1, N(ng), & !> & Awrk(:,:,Nnew)) !> CALL bc_r3d_bry_tile (ng, tile, boundary, & & LBij, UBij, 1, N(ng), & & tl_Awrk(:,:,Nnew)) # ifdef DISTRIBUTE !> CALL mp_exchange3d_bry (ng, tile, model, 1, boundary, & !> & LBij, UBij, 1, N(ng), & !> & Nghost, & !> & EWperiodic(ng), NSperiodic(ng), & !> & Awrk(:,:,Nnew)) !> CALL mp_exchange3d_bry (ng, tile, model, 1, boundary, & & LBij, UBij, 1, N(ng), & & Nghost, & & EWperiodic(ng), NSperiodic(ng), & & tl_Awrk(:,:,Nnew)) # endif ! ! Update integration indices. ! Nsav=Nold Nold=Nnew Nnew=Nsav END DO # ifdef VCONVOLUTION # ifdef IMPLICIT_VCONV # ifdef SPLINES_VCONV ! !----------------------------------------------------------------------- ! Integrate vertical diffusion equation implicitly using parabolic ! splines. !----------------------------------------------------------------------- ! DO step=1,NVsteps ! ! Use conservative, parabolic spline reconstruction of vertical ! diffusion derivatives. Then, time step vertical diffusion term ! implicitly. ! IF (Lconvolve(boundary)) THEN IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN i=edge(boundary) cff1=1.0_r8/6.0_r8 DO j=Jstr,Jend DO k=1,N(ng)-1 FC(j,k)=cff1*Hz(i,j,k )- & & DTsizeV*Kv(i,j,k-1)*oHz(j,k ) CF(j,k)=cff1*Hz(i,j,k+1)- & & DTsizeV*Kv(i,j,k+1)*oHz(j,k+1) END DO CF(j,0)=0.0_r8 !> DC(j,0)=0.0_r8 !> tl_DC(j,0)=0.0_r8 END DO ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN j=edge(boundary) cff1=1.0_r8/6.0_r8 DO i=Istr,Iend DO k=1,N(ng)-1 FC(i,k)=cff1*Hz(i,j,k )- & & DTsizeV*Kv(i,j,k-1)*oHz(i,k ) CF(i,k)=cff1*Hz(i,j,k+1)- & & DTsizeV*Kv(i,j,k+1)*oHz(i,k+1) END DO CF(i,0)=0.0_r8 !> DC(i,0)=0.0_r8 !> tl_DC(i,0)=0.0_r8 END DO END IF ! ! LU decomposition and forward substitution. ! IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN i=edge(boundary) cff1=1.0_r8/3.0_r8 DO k=1,N(ng)-1 DO j=Jstr,Jend BC(j,k)=cff1*(Hz(i,j,k)+Hz(i,j,k+1))+ & & DTsizeV*Kv(i,j,k)* & & (oHz(j,k)+oHz(j,k+1)) cff=1.0_r8/(BC(j,k)-FC(j,k)*CF(j,k-1)) CF(j,k)=cff*CF(j,k) !> DC(j,k)=cff*(Awrk(j,k+1,Nold)- & !> & Awrk(j,k ,Nold)- & !> & FC(j,k)*DC(j,k-1)) !> tl_DC(j,k)=cff*(tl_Awrk(j,k+1,Nold)- & & tl_Awrk(j,k ,Nold)- & & FC(j,k)*tl_DC(j,k-1)) END DO END DO ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN j=edge(boundary) cff1=1.0_r8/3.0_r8 DO k=1,N(ng)-1 DO i=Istr,Iend BC(i,k)=cff1*(Hz(i,j,k)+Hz(i,j,k+1))+ & & DTsizeV*Kv(i,j,k)* & & (oHz(i,k)+oHz(i,k+1)) cff=1.0_r8/(BC(i,k)-FC(i,k)*CF(i,k-1)) CF(i,k)=cff*CF(i,k) !> DC(i,k)=cff*(Awrk(i,k+1,Nold)- & !> & Awrk(i,k ,Nold)- & !> & FC(i,k)*DC(i,k-1)) !> tl_DC(i,k)=cff*(tl_Awrk(i,k+1,Nold)- & & tl_Awrk(i,k ,Nold)- & & FC(i,k)*tl_DC(i,k-1)) END DO END DO END IF ! ! Backward substitution. ! IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN i=edge(boundary) DO j=Jstr,Jend !> DC(j,N(ng))=0.0_r8 !> tl_DC(j,N(ng))=0.0_r8 END DO DO k=N(ng)-1,1,-1 DO j=Jstr,Jend !> DC(j,k)=DC(j,k)-CF(j,k)*DC(j,k+1) !> tl_DC(j,k)=tl_DC(j,k)-CF(j,k)*tl_DC(j,k+1) END DO END DO DO k=1,N(ng) DO j=Jstr,Jend !> DC(j,k)=DC(j,k)*Kv(i,j,k) !> tl_DC(j,k)=tl_DC(j,k)*Kv(i,j,k) !> Awrk(j,k,Nnew)=Awrk(j,k,Nold)+ & !> & DTsizeV*oHz(j,k)* & !> & (DC(j,k)-DC(j,k-1)) !> tl_Awrk(j,k,Nnew)=tl_Awrk(j,k,Nold)+ & & DTsizeV*oHz(j,k)* & & (tl_DC(j,k)-tl_DC(j,k-1)) END DO END DO ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN j=edge(boundary) DO i=Istr,Iend !> DC(i,N(ng))=0.0_r8 !> tl_DC(i,N(ng))=0.0_r8 END DO DO k=N(ng)-1,1,-1 DO i=Istr,Iend !> DC(i,k)=DC(i,k)-CF(i,k)*DC(i,k+1) !> tl_DC(i,k)=tl_DC(i,k)-CF(i,k)*tl_DC(i,k+1) END DO END DO DO k=1,N(ng) DO i=Istr,Iend !> DC(i,k)=DC(i,k)*Kv(i,j,k) !> tl_DC(i,k)=tl_DC(i,k)*Kv(i,j,k) !> Awrk(i,k,Nnew)=Awrk(i,k,Nold)+ & !> & DTsizeV*oHz(i,k)* & !> & (DC(i,k)-DC(i,k-1)) !> tl_Awrk(i,k,Nnew)=tl_Awrk(i,k,Nold)+ & & DTsizeV*oHz(i,k)* & & (tl_DC(i,k)-tl_DC(i,k-1)) END DO END DO END IF END IF ! ! Update integration indices. ! Nsav=Nold Nold=Nnew Nnew=Nsav END DO # else ! !----------------------------------------------------------------------- ! Integrate vertical diffusion equation implicitly. !----------------------------------------------------------------------- ! DO step=1,NVsteps ! ! Compute diagonal matrix coefficients BC and load right-hand-side ! terms for the diffusion equation into DC. ! IF (Lconvolve(boundary)) THEN IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN i=edge(boundary) DO k=1,N(ng) DO j=Jstr,Jend BC(j,k)=Hz(i,j,k)-FC(j,k)-FC(j,k-1) !> DC(j,k)=Awrk(j,k,Nold)*Hz(i,j,k) !> tl_DC(j,k)=tl_Awrk(j,k,Nold)*Hz(i,j,k) END DO END DO ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN j=edge(boundary) DO k=1,N(ng) DO i=Istr,Iend BC(i,k)=Hz(i,j,k)-FC(i,k)-FC(i,k-1) !> DC(i,k)=Awrk(i,k,Nold)*Hz(i,j,k) !> tl_DC(i,k)=tl_Awrk(i,k,Nold)*Hz(i,j,k) END DO END DO END IF ! ! Solve the tridiagonal system. ! IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN DO j=Jstr,Jend cff=1.0_r8/BC(j,1) CF(j,1)=cff*FC(j,1) !> DC(j,1)=cff*DC(j,1) !> tl_DC(j,1)=cff*tl_DC(j,1) END DO DO k=2,N(ng)-1 DO j=Jstr,Jend cff=1.0_r8/(BC(j,k)-FC(j,k-1)*CF(j,k-1)) CF(j,k)=cff*FC(j,k) !> DC(j,k)=cff*(DC(j,k)-FC(j,k-1)*DC(j,k-1)) !> tl_DC(j,k)=cff*(tl_DC(j,k)-FC(j,k-1)*tl_DC(j,k-1)) END DO END DO ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN DO i=Istr,Iend cff=1.0_r8/BC(i,1) CF(i,1)=cff*FC(i,1) !> DC(i,1)=cff*DC(i,1) !> tl_DC(i,1)=cff*tl_DC(i,1) END DO DO k=2,N(ng)-1 DO i=Istr,Iend cff=1.0_r8/(BC(i,k)-FC(i,k-1)*CF(i,k-1)) CF(i,k)=cff*FC(i,k) !> DC(i,k)=cff*(DC(i,k)-FC(i,k-1)*DC(i,k-1)) !> tl_DC(i,k)=cff*(tl_DC(i,k)-FC(i,k-1)*tl_DC(i,k-1)) END DO END DO END IF ! ! Compute new solution by back substitution. ! IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN i=edge(boundary) DO j=Jstr,Jend !> DC(j,N(ng))=(DC(j,N(ng))- & !> & FC(j,N(ng)-1)*DC(j,N(ng)-1))/ & !> & (BC(j,N(ng))- & !> & FC(j,N(ng)-1)*CF(j,N(ng)-1)) !> tl_DC(j,N(ng))=(tl_DC(j,N(ng))- & & FC(j,N(ng)-1)*tl_DC(j,N(ng)-1))/ & & (BC(j,N(ng))- & & FC(j,N(ng)-1)*CF(j,N(ng)-1)) !> Awrk(j,N(ng),Nnew)=DC(j,N(ng)) !> tl_Awrk(j,N(ng),Nnew)=tl_DC(j,N(ng)) # ifdef MASKING !> Awrk(j,N(ng),Nnew)=Awrk(j,N(ng),Nnew)*rmask(i,j) !> tl_Awrk(j,N(ng),Nnew)=tl_Awrk(j,N(ng),Nnew)*rmask(i,j) # endif END DO DO k=N(ng)-1,1,-1 DO j=Jstr,Jend !> DC(j,k)=DC(j,k)-CF(j,k)*DC(j,k+1) !> tl_DC(j,k)=tl_DC(j,k)-CF(j,k)*tl_DC(j,k+1) !> Awrk(j,k,Nnew)=DC(j,k) !> tl_Awrk(j,k,Nnew)=tl_DC(j,k) # ifdef MASKING !> Awrk(j,k,Nnew)=Awrk(j,k,Nnew)*rmask(i,j) !> tl_Awrk(j,k,Nnew)=tl_Awrk(j,k,Nnew)*rmask(i,j) # endif END DO END DO ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN j=edge(boundary) DO i=Istr,Iend !> DC(i,N(ng))=(DC(i,N(ng))- & !> & FC(i,N(ng)-1)*DC(i,N(ng)-1))/ & !> & (BC(i,N(ng))- & !> & FC(i,N(ng)-1)*CF(i,N(ng)-1)) !> tl_DC(i,N(ng))=(tl_DC(i,N(ng))- & & FC(i,N(ng)-1)*tl_DC(i,N(ng)-1))/ & & (BC(i,N(ng))- & & FC(i,N(ng)-1)*CF(i,N(ng)-1)) !> Awrk(i,N(ng),Nnew)=DC(i,N(ng)) !> tl_Awrk(i,N(ng),Nnew)=tl_DC(i,N(ng)) # ifdef MASKING !> Awrk(i,N(ng),Nnew)=Awrk(i,N(ng),Nnew)*rmask(i,j) !> tl_Awrk(i,N(ng),Nnew)=tl_Awrk(i,N(ng),Nnew)*rmask(i,j) # endif END DO DO k=N(ng)-1,1,-1 DO i=Istr,Iend !> DC(i,k)=DC(i,k)-CF(i,k)*DC(i,k+1) !> tl_DC(i,k)=tl_DC(i,k)-CF(i,k)*tl_DC(i,k+1) !> Awrk(i,k,Nnew)=DC(i,k) !> tl_Awrk(i,k,Nnew)=tl_DC(i,k) # ifdef MASKING !> Awrk(i,k,Nnew)=Awrk(i,k,Nnew)*rmask(i,j) !> tl_Awrk(i,k,Nnew)=tl_Awrk(i,k,Nnew)*rmask(i,j) # endif END DO END DO END IF END IF ! ! Update integration indices. ! Nsav=Nold Nold=Nnew Nnew=Nsav END DO # endif # else ! !----------------------------------------------------------------------- ! Integrate vertical diffusion equation explicitly. !----------------------------------------------------------------------- ! DO step=1,NVsteps ! ! Compute vertical diffusive flux. Notice that "FC" is assumed to ! be time invariant. ! IF (Lconvolve(boundary)) THEN IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN i=edge(boundary) DO j=Jstr,Jend DO k=1,N(ng)-1 !> FS(j,k)=FC(j,k)*(Awrk(j,k+1,Nold)- & !> & Awrk(j,k ,Nold)) !> tl_FS(j,k)=FC(j,k)*(tl_Awrk(j,k+1,Nold)- & & tl_Awrk(j,k ,Nold)) # ifdef MASKING !> FS(j,k)=FS(j,k)*rmask(i,j) !> tl_FS(j,k)=tl_FS(j,k)*rmask(i,j) # endif END DO !> FS(j,0)=0.0_r8 !> tl_FS(j,0)=0.0_r8 !> FS(j,N(ng))=0.0_r8 !> tl_FS(j,N(ng))=0.0_r8 END DO ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN j=edge(boundary) DO i=Istr,Iend DO k=1,N(ng)-1 !> FS(i,k)=FC(i,k)*(Awrk(i,k+1,Nold)- & !> & Awrk(i,k ,Nold)) !> tl_FS(i,k)=FC(i,k)*(tl_Awrk(i,k+1,Nold)- & & tl_Awrk(i,k ,Nold)) # ifdef MASKING !> FS(i,k)=FS(i,k)*rmask(i,j) !> tl_FS(i,k)=tl_FS(i,k)*rmask(i,j) # endif END DO !> FS(i,0)=0.0_r8 !> tl_FS(i,0)=0.0_r8 !> FS(i,N(ng))=0.0_r8 !> tl_FS(i,N(ng))=0.0_r8 END DO END IF ! ! Time-step vertical diffusive term. Notice that "oHz" is assumed to ! be time invariant. ! IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN DO k=1,N(ng) DO j=Jstr,Jend !> Awrk(j,k,Nnew)=Awrk(j,k,Nold)+ & !> & oHz(j,k)*(FS(j,k )- & !> & FS(j,k-1)) !> tl_Awrk(j,k,Nnew)=tl_Awrk(j,k,Nold)+ & & oHz(j,k)*(tl_FS(j,k )- & & tl_FS(j,k-1)) END DO END DO ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN DO k=1,N(ng) DO i=Istr,Iend !> Awrk(i,k,Nnew)=Awrk(i,k,Nold)+ & !> & oHz(i,k)*(FS(i,k )- & !> & FS(i,k-1)) !> tl_Awrk(i,k,Nnew)=tl_Awrk(i,k,Nold)+ & & oHz(i,k)*(tl_FS(i,k )- & & tl_FS(i,k-1)) END DO END DO END IF END IF ! ! Update integration indices. ! Nsav=Nold Nold=Nnew Nnew=Nsav END DO # endif # endif ! !----------------------------------------------------------------------- ! Load convolved solution. !----------------------------------------------------------------------- ! IF (Lconvolve(boundary)) THEN IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN DO k=1,N(ng) DO j=Jstr,Jend !> A(j,k)=Awrk(j,k,Nold) !> tl_A(j,k)=tl_Awrk(j,k,Nold) END DO END DO ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN DO k=1,N(ng) DO i=Istr,Iend !> A(i,k)=Awrk(i,k,Nold) !> tl_A(i,k)=tl_Awrk(i,k,Nold) END DO END DO END IF END IF !> CALL bc_r3d_bry_tile (ng, tile, boundary, & !> & LBij, UBij, 1, N(ng), & !> & A) !> CALL bc_r3d_bry_tile (ng, tile, boundary, & & LBij, UBij, 1, N(ng), & & tl_A) # ifdef DISTRIBUTE !> CALL mp_exchange3d_bry (ng, tile, model, 1, boundary, & !> & LBij, UBij, 1, N(ng), & !> & Nghost, & !> & EWperiodic(ng), NSperiodic(ng), & !> & A) !> CALL mp_exchange3d_bry (ng, tile, model, 1, boundary, & & LBij, UBij, 1, N(ng), & & Nghost, & & EWperiodic(ng), NSperiodic(ng), & & tl_A) # endif RETURN END SUBROUTINE tl_conv_r3d_bry_tile ! !*********************************************************************** SUBROUTINE tl_conv_u3d_bry_tile (ng, tile, model, boundary, & & edge, LBij, UBij, & & LBi, UBi, LBj, UBj, LBk, UBk, & & IminS, ImaxS, JminS, JmaxS, & & Nghost, NHsteps, NVsteps, & & DTsizeH, DTsizeV, & & Kh, Kv, & & pm, pn, pmon_r, pnom_p, & # ifdef MASKING & umask, pmask, & # endif & Hz, z_r, & & tl_A) !*********************************************************************** ! USE mod_param USE mod_scalars ! USE bc_bry3d_mod, ONLY: bc_u3d_bry_tile # ifdef DISTRIBUTE USE mp_exchange_mod, ONLY : mp_exchange3d_bry # endif ! ! Imported variable declarations. ! integer, intent(in) :: ng, tile, model, boundary integer, intent(in) :: edge(4) integer, intent(in) :: LBij, UBij integer, intent(in) :: LBi, UBi, LBj, UBj, LBk, UBk integer, intent(in) :: IminS, ImaxS, JminS, JmaxS integer, intent(in) :: Nghost, NHsteps, NVsteps real(r8), intent(in) :: DTsizeH, DTsizeV ! # ifdef ASSUMED_SHAPE real(r8), intent(in) :: pm(LBi:,LBj:) real(r8), intent(in) :: pn(LBi:,LBj:) real(r8), intent(in) :: pmon_r(LBi:,LBj:) real(r8), intent(in) :: pnom_p(LBi:,LBj:) # ifdef MASKING real(r8), intent(in) :: umask(LBi:,LBj:) real(r8), intent(in) :: pmask(LBi:,LBj:) # endif real(r8), intent(in) :: Hz(LBi:,LBj:,:) real(r8), intent(in) :: z_r(LBi:,LBj:,:) real(r8), intent(in) :: Kh(LBi:,LBj:) real(r8), intent(in) :: Kv(LBi:,LBj:,0:) real(r8), intent(inout) :: tl_A(LBij:,LBk:) # else real(r8), intent(in) :: pm(LBi:UBi,LBj:UBj) real(r8), intent(in) :: pn(LBi:UBi,LBj:UBj) real(r8), intent(in) :: pmon_r(LBi:UBi,LBj:UBj) real(r8), intent(in) :: pnom_p(LBi:UBi,LBj:UBj) # ifdef MASKING real(r8), intent(in) :: umask(LBi:UBi,LBj:UBj) real(r8), intent(in) :: pmask(LBi:UBi,LBj:UBj) # endif real(r8), intent(in) :: Hz(LBi:UBi,LBj:UBj,N(ng)) real(r8), intent(in) :: z_r(LBi:UBi,LBj:UBj,N(ng)) real(r8), intent(in) :: Kh(LBi:UBi,LBj:UBj) real(r8), intent(in) :: Kv(LBi:UBi,LBj:UBj,0:UBk) real(r8), intent(inout) :: tl_A(LBij:UBij,LBk:UBk) # endif ! ! Local variable declarations. ! logical, dimension(4) :: Lconvolve integer :: Nnew, Nold, Nsav, i, j, k, step real(r8) :: cff, cff1 real(r8), dimension(LBij:UBij,LBk:UBk,2) :: tl_Awrk real(r8), dimension(JminS:JmaxS,LBk:UBk) :: tl_FE real(r8), dimension(IminS:ImaxS,LBk:UBk) :: tl_FX real(r8), dimension(LBij:UBij) :: Hfac # ifdef VCONVOLUTION # ifndef SPLINES_VCONV real(r8), dimension(LBij:UBij,0:N(ng)) :: FC # endif # if !defined IMPLICIT_VCONV || defined SPLINES_VCONV real(r8), dimension(LBij:UBij,N(ng)) :: oHz # endif # if defined IMPLICIT_VCONV || defined SPLINES_VCONV real(r8), dimension(LBij:UBij,0:N(ng)) :: BC real(r8), dimension(LBij:UBij,0:N(ng)) :: CF # ifdef SPLINES_VCONV real(r8), dimension(LBij:UBij,0:N(ng)) :: FC # endif real(r8), dimension(LBij:UBij,0:N(ng)) :: tl_DC # else real(r8), dimension(LBij:UBij,0:N(ng)) :: tl_FS # endif # endif # include "set_bounds.h" ! !----------------------------------------------------------------------- ! Space convolution of the diffusion equation for a 2D state variable ! at RHO-points. !----------------------------------------------------------------------- ! Lconvolve(iwest )=DOMAIN(ng)%Western_Edge (tile) Lconvolve(ieast )=DOMAIN(ng)%Eastern_Edge (tile) Lconvolve(isouth)=DOMAIN(ng)%Southern_Edge(tile) Lconvolve(inorth)=DOMAIN(ng)%Northern_Edge(tile) ! ! Compute metrics factors. Notice that "z_r" and "Hz" are assumed to ! be time invariant in the vertical convolution. Scratch array are ! used for efficiency. ! IF (Lconvolve(boundary)) THEN cff=DTsizeH*0.25_r8 IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN i=edge(boundary) DO j=Jstr-1,Jend+1 Hfac(j)=cff*(pm(i-1,j)+pm(i,j))*(pn(i-1,j)+pn(i,j)) # ifdef VCONVOLUTION # ifndef SPLINES_VCONV FC(j,N(ng))=0.0_r8 DO k=1,N(ng)-1 # ifdef IMPLICIT_VCONV FC(j,k)=-DTsizeV*(Kv(i-1,j,k)+Kv(i,j,k))/ & & (z_r(i-1,j,k+1)+z_r(i,j,k+1)- & & z_r(i-1,j,k )-z_r(i,j,k )) # else FC(j,k)=DTsizeV*(Kv(i-1,j,k)+Kv(i,j,k))/ & & (z_r(i-1,j,k+1)+z_r(i,j,k+1)- & & z_r(i-1,j,k )-z_r(i,j,k )) # endif END DO FC(j,0)=0.0_r8 # endif # if !defined IMPLICIT_VCONV || defined SPLINES_VCONV DO k=1,N(ng) oHz(j,k)=2.0_r8/(Hz(i-1,j,k)+Hz(i,j,k)) END DO # endif # endif END DO ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN j=edge(boundary) DO i=IstrU-1,Iend+1 Hfac(i)=cff*(pm(i-1,j)+pm(i,j))*(pn(i-1,j)+pn(i,j)) # ifdef VCONVOLUTION # ifndef SPLINES_VCONV FC(i,N(ng))=0.0_r8 DO k=1,N(ng)-1 # ifdef IMPLICIT_VCONV FC(i,k)=-DTsizeV*(Kv(i-1,j,k)+Kv(i,j,k))/ & & (z_r(i-1,j,k+1)+z_r(i,j,k+1)- & & z_r(i-1,j,k )-z_r(i,j,k )) # else FC(i,k)=DTsizeV*(Kv(i-1,j,k)+Kv(i,j,k))/ & & (z_r(i-1,j,k+1)+z_r(i,j,k+1)- & & z_r(i-1,j,k )-z_r(i,j,k )) # endif END DO FC(i,0)=0.0_r8 # endif # if !defined IMPLICIT_VCONV || defined SPLINES_VCONV DO k=1,N(ng) oHz(i,k)=2.0_r8/(Hz(i-1,j,k)+Hz(i,j,k)) END DO # endif # endif END DO END IF END IF ! ! Set integration indices and initial conditions. ! Nold=1 Nnew=2 !> CALL bc_u3d_bry_tile (ng, tile, boundary, & !> & LBij, UBij, 1, N(ng), & !> & A) !> CALL bc_u3d_bry_tile (ng, tile, boundary, & & LBij, UBij, 1, N(ng), & & tl_A) # ifdef DISTRIBUTE !> CALL mp_exchange3d_bry (ng, tile, model, 1, boundary, & !> & LBij, UBij, 1, N(ng), & !> & Nghost, & !> & EWperiodic(ng), NSperiodic(ng), & !> & A) !> CALL mp_exchange3d_bry (ng, tile, model, 1, boundary, & & LBij, UBij, 1, N(ng), & & Nghost, & & EWperiodic(ng), NSperiodic(ng), & & tl_A) # endif IF (Lconvolve(boundary)) THEN IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN DO k=1,N(ng) DO j=Jstr-1,Jend+1 !> Awrk(j,k,Nold)=A(j,k) !> tl_Awrk(j,k,Nold)=tl_A(j,k) END DO END DO ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN DO k=1,N(ng) DO i=IstrU-1,Iend+1 !> Awrk(i,k,Nold)=A(i,k) !> tl_Awrk(i,k,Nold)=tl_A(i,k) END DO END DO END IF END IF ! !----------------------------------------------------------------------- ! Integrate horizontal diffusion equation. !----------------------------------------------------------------------- ! DO step=1,NHsteps ! ! Compute XI- and ETA-components of diffusive flux. ! IF (Lconvolve(boundary)) THEN IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN i=edge(boundary) DO k=1,N(ng) DO j=Jstr,Jend+1 !> FE(j,k)=pnom_p(i,j)* & !> & 0.25_r8*(Kh(i-1,j )+Kh(i,j )+ & !> & Kh(i-1,j-1)+Kh(i,j-1))* & !> & (Awrk(j ,k,Nold)- & !> & Awrk(j-1,k,Nold)) !> tl_FE(j,k)=pnom_p(i,j)* & & 0.25_r8*(Kh(i-1,j )+Kh(i,j )+ & & Kh(i-1,j-1)+Kh(i,j-1))* & & (tl_Awrk(j ,k,Nold)- & & tl_Awrk(j-1,k,Nold)) # ifdef MASKING !> FE(j,k)=FE(j,k)*pmask(i,j) !> tl_FE(j,k)=tl_FE(j,k)*pmask(i,j) # endif END DO END DO ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN j=edge(boundary) DO k=1,N(ng) DO i=IstrU-1,Iend !> FX(i,k)=pmon_r(i,j)*Kh(i,j)* & !> & (Awrk(i+1,k,Nold)- & !> & Awrk(i ,k,Nold)) !> tl_FX(i,k)=pmon_r(i,j)*Kh(i,j)* & & (tl_Awrk(i+1,k,Nold)- & & tl_Awrk(i ,k,Nold)) END DO END DO END IF ! ! Time-step horizontal diffusion equation. ! IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN DO k=1,N(ng) DO j=Jstr,Jend !> Awrk(j,k,Nnew)=Awrk(j,k,Nold)+ & !> & Hfac(j)* & !> & (FE(j+1,k)-FE(j,k)) !> tl_Awrk(j,k,Nnew)=tl_Awrk(j,k,Nold)+ & & Hfac(j)* & & (tl_FE(j+1,k)-tl_FE(j,k)) END DO END DO ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN DO k=1,N(ng) DO i=IstrU,Iend !> Awrk(i,k,Nnew)=Awrk(i,k,Nold)+ & !> & Hfac(i)* & !> & (FX(i,k)-FX(i-1,k)) !> tl_Awrk(i,k,Nnew)=tl_Awrk(i,k,Nold)+ & & Hfac(i)* & & (tl_FX(i,k)-tl_FX(i-1,k)) END DO END DO END IF END IF ! ! Apply boundary conditions. ! !> CALL bc_u3d_bry_tile (ng, tile, boundary, & !> & LBij, UBij, 1, N(ng), & !> & Awrk(:,:,Nnew)) !> CALL bc_u3d_bry_tile (ng, tile, boundary, & & LBij, UBij, 1, N(ng), & & tl_Awrk(:,:,Nnew)) # ifdef DISTRIBUTE !> CALL mp_exchange3d_bry (ng, tile, model, 1, boundary, & !> & LBij, UBij, 1, N(ng), & !> & Nghost, & !> & EWperiodic(ng), NSperiodic(ng), & !> & Awrk(:,:,Nnew)) !> CALL mp_exchange3d_bry (ng, tile, model, 1, boundary, & & LBij, UBij, 1, N(ng), & & Nghost, & & EWperiodic(ng), NSperiodic(ng), & & tl_Awrk(:,:,Nnew)) # endif ! ! Update integration indices. ! Nsav=Nold Nold=Nnew Nnew=Nsav END DO # ifdef VCONVOLUTION # ifdef IMPLICIT_VCONV # ifdef SPLINES_VCONV ! !----------------------------------------------------------------------- ! Integrate vertical diffusion equation implicitly using parabolic ! splines. !----------------------------------------------------------------------- ! DO step=1,NVsteps ! ! Use conservative, parabolic spline reconstruction of vertical ! diffusion derivatives. Then, time step vertical diffusion term ! implicitly. ! IF (Lconvolve(boundary)) THEN IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN i=edge(boundary) cff1=0.5_r8*(1.0_r8/6.0_r8) DO j=Jstr,Jend DO k=1,N(ng)-1 FC(j,k)=cff1*(Hz(i-1,j,k )+Hz(i,j,k ))- & & DTsizeV*Kv(i,j,k-1)*oHz(j,k ) CF(j,k)=cff1*(Hz(i-1,j,k+1)+Hz(i,j,k+1))- & & DTsizeV*Kv(i,j,k+1)*oHz(j,k+1) END DO CF(j,0)=0.0_r8 !> DC(j,0)=0.0_r8 !> tl_DC(j,0)=0.0_r8 END DO ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN j=edge(boundary) cff1=0.5_r8*(1.0_r8/6.0_r8) DO i=IstrU,Iend DO k=1,N(ng)-1 FC(i,k)=cff1*(Hz(i-1,j,k )+Hz(i,j,k ))- & & DTsizeV*Kv(i,j,k-1)*oHz(i,k ) CF(i,k)=cff1*(Hz(i-1,j,k+1)+Hz(i,j,k+1))- & & DTsizeV*Kv(i,j,k+1)*oHz(i,k+1) END DO CF(i,0)=0.0_r8 !> DC(i,0)=0.0_r8 !> tl_DC(i,0)=0.0_r8 END DO END IF ! ! LU decomposition and forward substitution. ! IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN i=edge(boundary) cff1=0.5_r8*(1.0_r8/3.0_r8) DO k=1,N(ng)-1 DO j=Jstr,Jend BC(j,k)=cff1*(Hz(i-1,j,k )+Hz(i,j,k )+ & & Hz(i-1,j,k+1)+Hz(i,j,k+1))+ & & DTsizeV*Kv(i,j,k)* & & (oHz(j,k)+oHz(j,k+1)) cff=1.0_r8/(BC(j,k)-FC(j,k)*CF(j,k-1)) CF(j,k)=cff*CF(j,k) !> DC(j,k)=cff*(Awrk(j,k+1,Nold)- & !> & Awrk(j,k ,Nold)- & !> & FC(j,k)*DC(j,k-1)) !> tl_DC(j,k)=cff*(tl_Awrk(j,k+1,Nold)- & & tl_Awrk(j,k ,Nold)- & & FC(j,k)*tl_DC(j,k-1)) END DO END DO ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN j=edge(boundary) cff1=0.5_r8*(1.0_r8/3.0_r8) DO k=1,N(ng)-1 DO i=IstrU,Iend BC(i,k)=cff1*(Hz(i-1,j,k )+Hz(i,j,k )+ & & Hz(i-1,j,k+1)+Hz(i,j,k+1))+ & & DTsizeV*Kv(i,j,k)* & & (oHz(i,k)+oHz(i,k+1)) cff=1.0_r8/(BC(i,k)-FC(i,k)*CF(i,k-1)) CF(i,k)=cff*CF(i,k) !> DC(i,k)=cff*(Awrk(i,k+1,Nold)- & !> & Awrk(i,k ,Nold)- & !> & FC(i,k)*DC(i,k-1)) !> tl_DC(i,k)=cff*(tl_Awrk(i,k+1,Nold)- & & tl_Awrk(i,k ,Nold)- & & FC(i,k)*tl_DC(i,k-1)) END DO END DO END IF ! ! Backward substitution. ! IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN i=edge(boundary) DO j=Jstr,Jend !> DC(j,N(ng))=0.0_r8 !> tl_DC(j,N(ng))=0.0_r8 END DO DO k=N(ng)-1,1,-1 DO j=Jstr,Jend !> DC(j,k)=DC(j,k)-CF(j,k)*DC(j,k+1) !> tl_DC(j,k)=tl_DC(j,k)-CF(j,k)*tl_DC(j,k+1) END DO END DO DO k=1,N(ng) DO j=Jstr,Jend !> DC(j,k)=DC(j,k)*Kv(i,j,k) !> tl_DC(j,k)=tl_DC(j,k)*Kv(i,j,k) !> Awrk(j,k,Nnew)=Awrk(j,k,Nold)+ & !> & DTsizeV*oHz(j,k)* & !> & (DC(j,k)-DC(j,k-1)) !> tl_Awrk(j,k,Nnew)=tl_Awrk(j,k,Nold)+ & & DTsizeV*oHz(j,k)* & & (tl_DC(j,k)-tl_DC(j,k-1)) END DO END DO ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN j=edge(boundary) DO i=IstrU,Iend !> DC(i,N(ng))=0.0_r8 !> tl_DC(i,N(ng))=0.0_r8 END DO DO k=N(ng)-1,1,-1 DO i=IstrU,Iend !> DC(i,k)=DC(i,k)-CF(i,k)*DC(i,k+1) !> tl_DC(i,k)=tl_DC(i,k)-CF(i,k)*tl_DC(i,k+1) END DO END DO DO k=1,N(ng) DO i=IstrU,Iend !> DC(i,k)=DC(i,k)*Kv(i,j,k) !> tl_DC(i,k)=tl_DC(i,k)*Kv(i,j,k) !> Awrk(i,k,Nnew)=Awrk(i,k,Nold)+ & !> & DTsizeV*oHz(i,k)* & !> & (DC(i,k)-DC(i,k-1)) !> tl_Awrk(i,k,Nnew)=tl_Awrk(i,k,Nold)+ & & DTsizeV*oHz(i,k)* & & (tl_DC(i,k)-tl_DC(i,k-1)) END DO END DO END IF END IF ! ! Update integration indices. ! Nsav=Nold Nold=Nnew Nnew=Nsav END DO # else ! !----------------------------------------------------------------------- ! Integrate vertical diffusion equation implicitly. !----------------------------------------------------------------------- ! DO step=1,NVsteps ! ! Compute diagonal matrix coefficients BC and load right-hand-side ! terms for the diffusion equation into DC. ! IF (Lconvolve(boundary)) THEN IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN i=edge(boundary) DO k=1,N(ng) DO j=Jstr,Jend cff=0.5_r8*(Hz(i-1,j,k)+Hz(i,j,k)) BC(j,k)=cff-FC(j,k)-FC(j,k-1) !> DC(j,k)=Awrk(j,k,Nold)*cff !> tl_DC(j,k)=tl_Awrk(j,k,Nold)*cff END DO END DO ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN j=edge(boundary) DO k=1,N(ng) DO i=IstrU,Iend cff=0.5_r8*(Hz(i-1,j,k)+Hz(i,j,k)) BC(i,k)=cff-FC(i,k)-FC(i,k-1) !> DC(i,k)=Awrk(i,k,Nold)*cff !> tl_DC(i,k)=tl_Awrk(i,k,Nold)*cff END DO END DO END IF ! ! Solve the tridiagonal system. ! IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN DO j=Jstr,Jend cff=1.0_r8/BC(j,1) CF(j,1)=cff*FC(j,1) !> DC(j,1)=cff*DC(j,1) !> tl_DC(j,1)=cff*tl_DC(j,1) END DO DO k=2,N(ng)-1 DO j=Jstr,Jend cff=1.0_r8/(BC(j,k)-FC(j,k-1)*CF(j,k-1)) CF(j,k)=cff*FC(j,k) !> DC(j,k)=cff*(DC(j,k)-FC(j,k-1)*DC(j,k-1)) !> tl_DC(j,k)=cff*(tl_DC(j,k)-FC(j,k-1)*tl_DC(j,k-1)) END DO END DO ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN DO i=IstrU,Iend cff=1.0_r8/BC(i,1) CF(i,1)=cff*FC(i,1) !> DC(i,1)=cff*DC(i,1) !> tl_DC(i,1)=cff*tl_DC(i,1) END DO DO k=2,N(ng)-1 DO i=IstrU,Iend cff=1.0_r8/(BC(i,k)-FC(i,k-1)*CF(i,k-1)) CF(i,k)=cff*FC(i,k) !> DC(i,k)=cff*(DC(i,k)-FC(i,k-1)*DC(i,k-1)) !> tl_DC(i,k)=cff*(tl_DC(i,k)-FC(i,k-1)*tl_DC(i,k-1)) END DO END DO END IF ! ! Compute new solution by back substitution. ! IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN i=edge(boundary) DO j=Jstr,Jend !> DC(j,N(ng))=(DC(j,N(ng))- & !> & FC(j,N(ng)-1)*DC(j,N(ng)-1))/ & !> & (BC(j,N(ng))- & !> & FC(j,N(ng)-1)*CF(j,N(ng)-1)) !> tl_DC(j,N(ng))=(tl_DC(j,N(ng))- & & FC(j,N(ng)-1)*tl_DC(j,N(ng)-1))/ & & (BC(j,N(ng))- & & FC(j,N(ng)-1)*CF(j,N(ng)-1)) !> Awrk(j,N(ng),Nnew)=DC(j,N(ng)) !> tl_Awrk(j,N(ng),Nnew)=tl_DC(j,N(ng)) # ifdef MASKING !> Awrk(j,N(ng),Nnew)=Awrk(j,N(ng),Nnew)*umask(i,j) !> tl_Awrk(j,N(ng),Nnew)=tl_Awrk(j,N(ng),Nnew)*umask(i,j) # endif END DO DO k=N(ng)-1,1,-1 DO j=Jstr,Jend !> DC(j,k)=DC(j,k)-CF(j,k)*DC(j,k+1) !> tl_DC(j,k)=tl_DC(j,k)-CF(j,k)*tl_DC(j,k+1) !> Awrk(j,k,Nnew)=DC(j,k) !> tl_Awrk(j,k,Nnew)=tl_DC(j,k) # ifdef MASKING !> Awrk(j,k,Nnew)=Awrk(j,k,Nnew)*umask(i,j) !> tl_Awrk(j,k,Nnew)=tl_Awrk(j,k,Nnew)*umask(i,j) # endif END DO END DO ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN j=edge(boundary) DO i=IstrU,Iend !> DC(i,N(ng))=(DC(i,N(ng))- & !> & FC(i,N(ng)-1)*DC(i,N(ng)-1))/ & !> & (BC(i,N(ng))- & !> & FC(i,N(ng)-1)*CF(i,N(ng)-1)) !> tl_DC(i,N(ng))=(tl_DC(i,N(ng))- & & FC(i,N(ng)-1)*tl_DC(i,N(ng)-1))/ & & (BC(i,N(ng))- & & FC(i,N(ng)-1)*CF(i,N(ng)-1)) !> Awrk(i,N(ng),Nnew)=DC(i,N(ng)) !> tl_Awrk(i,N(ng),Nnew)=tl_DC(i,N(ng)) # ifdef MASKING !> Awrk(i,N(ng),Nnew)=Awrk(i,N(ng),Nnew)*umask(i,j) !> tl_Awrk(i,N(ng),Nnew)=tl_Awrk(i,N(ng),Nnew)*umask(i,j) # endif END DO DO k=N(ng)-1,1,-1 DO i=IstrU,Iend !> DC(i,k)=DC(i,k)-CF(i,k)*DC(i,k+1) !> tl_DC(i,k)=tl_DC(i,k)-CF(i,k)*tl_DC(i,k+1) !> Awrk(i,k,Nnew)=DC(i,k) !> tl_Awrk(i,k,Nnew)=tl_DC(i,k) # ifdef MASKING !> Awrk(i,k,Nnew)=Awrk(i,k,Nnew)*umask(i,j) !> tl_Awrk(i,k,Nnew)=tl_Awrk(i,k,Nnew)*umask(i,j) # endif END DO END DO END IF END IF ! ! Update integration indices. ! Nsav=Nold Nold=Nnew Nnew=Nsav END DO # endif # else ! !----------------------------------------------------------------------- ! Integrate vertical diffusion equation explicitly. !----------------------------------------------------------------------- ! DO step=1,NVsteps ! ! Compute vertical diffusive flux. Notice that "FC" is assumed to ! be time invariant. ! IF (Lconvolve(boundary)) THEN IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN i=edge(boundary) DO j=Jstr,Jend DO k=1,N(ng)-1 !> FS(j,k)=FC(j,k)*(Awrk(j,k+1,Nold)- & !> & Awrk(j,k ,Nold)) !> tl_FS(j,k)=FC(j,k)*(tl_Awrk(j,k+1,Nold)- & & tl_Awrk(j,k ,Nold)) # ifdef MASKING !> FS(j,k)=FS(j,k)*umask(i,j) !> tl_FS(j,k)=tl_FS(j,k)*umask(i,j) # endif END DO !> FS(j,0)=0.0_r8 !> tl_FS(j,0)=0.0_r8 !> FS(j,N(ng))=0.0_r8 !> tl_FS(j,N(ng))=0.0_r8 END DO ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN j=edge(boundary) DO i=IstrU,Iend DO k=1,N(ng)-1 !> FS(i,k)=FC(i,k)*(Awrk(i,k+1,Nold)- & !> & Awrk(i,k ,Nold)) !> tl_FS(i,k)=FC(i,k)*(tl_Awrk(i,k+1,Nold)- & & tl_Awrk(i,k ,Nold)) # ifdef MASKING !> FS(i,k)=FS(i,k)*umask(i,j) !> tl_FS(i,k)=tl_FS(i,k)*umask(i,j) # endif END DO !> FS(i,0)=0.0_r8 !> tl_FS(i,0)=0.0_r8 !> FS(i,N(ng))=0.0_r8 !> tl_FS(i,N(ng))=0.0_r8 END DO END IF ! ! Time-step vertical diffusive term. Notice that "oHz" is assumed to ! be time invariant. ! IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN DO k=1,N(ng) DO j=Jstr,Jend !> Awrk(j,k,Nnew)=Awrk(j,k,Nold)+ & !> & oHz(j,k)*(FS(j,k )- & !> & FS(j,k-1)) !> tl_Awrk(j,k,Nnew)=tl_Awrk(j,k,Nold)+ & & oHz(j,k)*(tl_FS(j,k )- & & tl_FS(j,k-1)) END DO END DO ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN DO k=1,N(ng) DO i=IstrU,Iend !> Awrk(i,k,Nnew)=Awrk(i,k,Nold)+ & !> & oHz(i,k)*(FS(i,k )- & !> & FS(i,k-1)) !> tl_Awrk(i,k,Nnew)=tl_Awrk(i,k,Nold)+ & & oHz(i,k)*(tl_FS(i,k )- & & tl_FS(i,k-1)) END DO END DO END IF END IF ! ! Update integration indices. ! Nsav=Nold Nold=Nnew Nnew=Nsav END DO # endif # endif ! !----------------------------------------------------------------------- ! Load convolved solution. !----------------------------------------------------------------------- ! IF (Lconvolve(boundary)) THEN IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN DO k=1,N(ng) DO j=Jstr,Jend !> A(j,k)=Awrk(j,k,Nold) !> tl_A(j,k)=tl_Awrk(j,k,Nold) END DO END DO ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN DO k=1,N(ng) DO i=Istr,Iend !> A(i,k)=Awrk(i,k,Nold) !> tl_A(i,k)=tl_Awrk(i,k,Nold) END DO END DO END IF END IF !> CALL bc_u3d_bry_tile (ng, tile, boundary, & !> & LBij, UBij, 1, N(ng), & !> & A) !> CALL bc_u3d_bry_tile (ng, tile, boundary, & & LBij, UBij, 1, N(ng), & & tl_A) # ifdef DISTRIBUTE !> CALL mp_exchange3d_bry (ng, tile, model, 1, boundary, & !> & LBij, UBij, 1, N(ng), & !> & Nghost, & !> & EWperiodic(ng), NSperiodic(ng), & !> & A) !> CALL mp_exchange3d_bry (ng, tile, model, 1, boundary, & & LBij, UBij, 1, N(ng), & & Nghost, & & EWperiodic(ng), NSperiodic(ng), & & tl_A) # endif RETURN END SUBROUTINE tl_conv_u3d_bry_tile ! !*********************************************************************** SUBROUTINE tl_conv_v3d_bry_tile (ng, tile, model, boundary, & & edge, LBij, UBij, & & LBi, UBi, LBj, UBj, LBk, UBk, & & IminS, ImaxS, JminS, JmaxS, & & Nghost, NHsteps, NVsteps, & & DTsizeH, DTsizeV, & & Kh, Kv, & & pm, pn, pmon_p, pnom_r, & # ifdef MASKING & vmask, pmask, & # endif & Hz, z_r, & & tl_A) !*********************************************************************** ! USE mod_param USE mod_scalars ! USE bc_bry3d_mod, ONLY: bc_v3d_bry_tile # ifdef DISTRIBUTE USE mp_exchange_mod, ONLY : mp_exchange3d_bry # endif ! ! Imported variable declarations. ! integer, intent(in) :: ng, tile, model, boundary integer, intent(in) :: edge(4) integer, intent(in) :: LBij, UBij integer, intent(in) :: LBi, UBi, LBj, UBj, LBk, UBk integer, intent(in) :: IminS, ImaxS, JminS, JmaxS integer, intent(in) :: Nghost, NHsteps, NVsteps real(r8), intent(in) :: DTsizeH, DTsizeV ! # ifdef ASSUMED_SHAPE real(r8), intent(in) :: pm(LBi:,LBj:) real(r8), intent(in) :: pn(LBi:,LBj:) real(r8), intent(in) :: pmon_p(LBi:,LBj:) real(r8), intent(in) :: pnom_r(LBi:,LBj:) # ifdef MASKING real(r8), intent(in) :: vmask(LBi:,LBj:) real(r8), intent(in) :: pmask(LBi:,LBj:) # endif real(r8), intent(in) :: Hz(LBi:,LBj:,:) real(r8), intent(in) :: z_r(LBi:,LBj:,:) real(r8), intent(in) :: Kh(LBi:,LBj:) real(r8), intent(in) :: Kv(LBi:,LBj:,0:) real(r8), intent(inout) :: tl_A(LBij:,LBk:) # else real(r8), intent(in) :: pm(LBi:UBi,LBj:UBj) real(r8), intent(in) :: pn(LBi:UBi,LBj:UBj) real(r8), intent(in) :: pmon_p(LBi:UBi,LBj:UBj) real(r8), intent(in) :: pnom_r(LBi:UBi,LBj:UBj) # ifdef MASKING real(r8), intent(in) :: vmask(LBi:UBi,LBj:UBj) real(r8), intent(in) :: pmask(LBi:UBi,LBj:UBj) # endif real(r8), intent(in) :: Hz(LBi:UBi,LBj:UBj,N(ng)) real(r8), intent(in) :: z_r(LBi:UBi,LBj:UBj,N(ng)) real(r8), intent(in) :: Kh(LBi:UBi,LBj:UBj) real(r8), intent(in) :: Kv(LBi:UBi,LBj:UBj,0:UBk) real(r8), intent(inout) :: tl_A(LBij:UBij,LBk:UBk) # endif ! ! Local variable declarations. ! logical, dimension(4) :: Lconvolve integer :: Nnew, Nold, Nsav, i, ib, j, k, step real(r8) :: cff, cff1 real(r8), dimension(LBij:UBij,LBk:UBk,2) :: tl_Awrk real(r8), dimension(JminS:JmaxS,LBk:UBk) :: tl_FE real(r8), dimension(IminS:ImaxS,LBk:UBk) :: tl_FX real(r8), dimension(LBij:UBij) :: Hfac # ifdef VCONVOLUTION # ifndef SPLINES_VCONV real(r8), dimension(LBij:UBij,0:N(ng)) :: FC # endif # if !defined IMPLICIT_VCONV || defined SPLINES_VCONV real(r8), dimension(LBij:UBij,N(ng)) :: oHz # endif # if defined IMPLICIT_VCONV || defined SPLINES_VCONV real(r8), dimension(LBij:UBij,0:N(ng)) :: BC real(r8), dimension(LBij:UBij,0:N(ng)) :: CF # ifdef SPLINES_VCONV real(r8), dimension(LBij:UBij,0:N(ng)) :: FC # endif real(r8), dimension(LBij:UBij,0:N(ng)) :: tl_DC # else real(r8), dimension(LBij:UBij,0:N(ng)) :: tl_FS # endif # endif # include "set_bounds.h" ! !----------------------------------------------------------------------- ! Space convolution of the diffusion equation for a 2D state variable ! at RHO-points. !----------------------------------------------------------------------- ! Lconvolve(iwest )=DOMAIN(ng)%Western_Edge (tile) Lconvolve(ieast )=DOMAIN(ng)%Eastern_Edge (tile) Lconvolve(isouth)=DOMAIN(ng)%Southern_Edge(tile) Lconvolve(inorth)=DOMAIN(ng)%Northern_Edge(tile) ! ! Compute metrics factors. Notice that "z_r" and "Hz" are assumed to ! be time invariant in the vertical convolution. Scratch array are ! used for efficiency. ! IF (Lconvolve(boundary)) THEN cff=DTsizeH*0.25_r8 IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN i=edge(boundary) DO j=JstrV-1,Jend+1 Hfac(j)=cff*(pm(i,j-1)+pm(i,j))*(pn(i,j-1)+pn(i,j)) # ifdef VCONVOLUTION # ifndef SPLINES_VCONV FC(j,N(ng))=0.0_r8 DO k=1,N(ng)-1 # ifdef IMPLICIT_VCONV FC(j,k)=-DTsizeV*(Kv(i,j-1,k)+Kv(i,j,k))/ & & (z_r(i,j-1,k+1)+z_r(i,j,k+1)- & & z_r(i,j-1,k )-z_r(i,j,k )) # else FC(j,k)=DTsizeV*(Kv(i,j-1,k)+Kv(i,j,k))/ & & (z_r(i,j-1,k+1)+z_r(i,j,k+1)- & & z_r(i,j-1,k )-z_r(i,j,k )) # endif END DO FC(j,0)=0.0_r8 # endif # if !defined IMPLICIT_VCONV || defined SPLINES_VCONV DO k=1,N(ng) oHz(j,k)=2.0_r8/(Hz(i,j-1,k)+Hz(i,j,k)) END DO # endif # endif END DO ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN j=edge(boundary) DO i=Istr-1,Iend+1 Hfac(i)=cff*(pm(i,j-1)+pm(i,j))*(pn(i,j-1)+pn(i,j)) # ifdef VCONVOLUTION # ifndef SPLINES_VCONV FC(i,N(ng))=0.0_r8 DO k=1,N(ng)-1 # ifdef IMPLICIT_VCONV FC(i,k)=-DTsizeV*(Kv(i,j-1,k)+Kv(i,j,k))/ & & (z_r(i,j-1,k+1)+z_r(i,j,k+1)- & & z_r(i,j-1,k )-z_r(i,j,k )) # else FC(i,k)=DTsizeV*(Kv(i,j-1,k)+Kv(i,j,k))/ & & (z_r(i,j-1,k+1)+z_r(i,j,k+1)- & & z_r(i,j-1,k )-z_r(i,j,k )) # endif END DO FC(i,0)=0.0_r8 # endif # if !defined IMPLICIT_VCONV || defined SPLINES_VCONV DO k=1,N(ng) oHz(i,k)=2.0_r8/(Hz(i,j-1,k)+Hz(i,j,k)) END DO # endif # endif END DO END IF END IF ! ! Set integration indices and initial conditions. ! Nold=1 Nnew=2 !> CALL bc_v3d_bry_tile (ng, tile, boundary, & !> & LBij, UBij, 1, N(ng), & !> & A) !> CALL bc_v3d_bry_tile (ng, tile, boundary, & & LBij, UBij, 1, N(ng), & & tl_A) # ifdef DISTRIBUTE !> CALL mp_exchange3d_bry (ng, tile, model, 1, boundary, & !> & LBij, UBij, 1, N(ng), & !> & Nghost, !> & EWperiodic(ng), NSperiodic(ng), & !> & A) !> CALL mp_exchange3d_bry (ng, tile, model, 1, boundary, & & LBij, UBij, 1, N(ng), & & Nghost, & & EWperiodic(ng), NSperiodic(ng), & & tl_A) # endif IF (Lconvolve(boundary)) THEN IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN DO k=1,N(ng) DO j=JstrV-1,Jend+1 !> Awrk(j,k,Nold)=A(j,k) !> tl_Awrk(j,k,Nold)=tl_A(j,k) END DO END DO ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN DO k=1,N(ng) DO i=Istr-1,Iend+1 !> Awrk(i,k,Nold)=A(i,k) !> tl_Awrk(i,k,Nold)=tl_A(i,k) END DO END DO END IF END IF ! !----------------------------------------------------------------------- ! Integrate horizontal diffusion equation. !----------------------------------------------------------------------- ! DO step=1,NHsteps ! ! Compute XI- and ETA-components of diffusive flux. ! IF (Lconvolve(boundary)) THEN IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN i=edge(boundary) DO k=1,N(ng) DO j=JstrV-1,Jend !> FE(j,k)=pnom_r(i,j)*Kh(i,j)* & !> & (Awrk(j+1,k,Nold)- & !> & Awrk(j ,k,Nold)) !> tl_FE(j,k)=pnom_r(i,j)*Kh(i,j)* & & (tl_Awrk(j+1,k,Nold)- & & tl_Awrk(j ,k,Nold)) END DO END DO ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN j=edge(boundary) DO k=1,N(ng) DO i=Istr,Iend+1 !> FX(i,k)=pmon_p(i,j)* & !> & 0.25_r8*(Kh(i-1,j )+Kh(i,j )+ & !> & Kh(i-1,j-1)+Kh(i,j-1))* & !> & (Awrk(i ,k,Nold)- & !> & Awrk(i-1,k,Nold)) !> tl_FX(i,k)=pmon_p(i,j)* & & 0.25_r8*(Kh(i-1,j )+Kh(i,j )+ & & Kh(i-1,j-1)+Kh(i,j-1))* & & (tl_Awrk(i ,k,Nold)- & & tl_Awrk(i-1,k,Nold)) # ifdef MASKING !> FX(i,k)=FX(i,k)*pmask(i,j) !> tl_FX(i,k)=tl_FX(i,k)*pmask(i,j) # endif END DO END DO END IF END IF ! ! Time-step horizontal diffusion equation. ! IF (Lconvolve(boundary)) THEN IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN DO k=1,N(ng) DO j=JstrV,Jend !> Awrk(j,k,Nnew)=Awrk(j,k,Nold)+ & !> & Hfac(j)* & !> & (FE(j,k)-FE(j-1,k)) !> tl_Awrk(j,k,Nnew)=tl_Awrk(j,k,Nold)+ & & Hfac(j)* & & (tl_FE(j,k)-tl_FE(j-1,k)) END DO END DO ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN DO k=1,N(ng) DO i=Istr,Iend !> Awrk(i,k,Nnew)=Awrk(i,k,Nold)+ & !> & Hfac(i)* & !> & (FX(i+1,k)-FX(i,k)) !> tl_Awrk(i,k,Nnew)=tl_Awrk(i,k,Nold)+ & & Hfac(i)* & & (tl_FX(i+1,k)-tl_FX(i,k)) END DO END DO END IF END IF ! ! Apply boundary conditions. ! !> CALL bc_v3d_bry_tile (ng, tile, boundary, & !> & LBij, UBij, 1, N(ng), & !> & Awrk(:,:,Nnew)) !> CALL bc_v3d_bry_tile (ng, tile, boundary, & & LBij, UBij, 1, N(ng), & & tl_Awrk(:,:,Nnew)) # ifdef DISTRIBUTE !> CALL mp_exchange3d_bry (ng, tile, model, 1, boundary, & !> & LBij, UBij, 1, N(ng), & !> & Nghost, & !> & EWperiodic(ng), NSperiodic(ng), & !> & Awrk(:,:,Nnew)) !> CALL mp_exchange3d_bry (ng, tile, model, 1, boundary, & & LBij, UBij, 1, N(ng), & & Nghost, & & EWperiodic(ng), NSperiodic(ng), & & tl_Awrk(:,:,Nnew)) # endif ! ! Update integration indices. ! Nsav=Nold Nold=Nnew Nnew=Nsav END DO # ifdef VCONVOLUTION # ifdef IMPLICIT_VCONV # ifdef SPLINES_VCONV ! !----------------------------------------------------------------------- ! Integrate vertical diffusion equation implicitly using parabolic ! splines. !----------------------------------------------------------------------- ! DO step=1,NVsteps ! ! Use conservative, parabolic spline reconstruction of vertical ! diffusion derivatives. Then, time step vertical diffusion term ! implicitly. ! IF (Lconvolve(boundary)) THEN IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN i=edge(boundary) cff1=0.5_r8*(1.0_r8/6.0_r8) DO j=JstrV,Jend DO k=1,N(ng)-1 FC(j,k)=cff1*(Hz(i,j-1,k )+Hz(i,j,k ))- & & DTsizeV*Kv(i,j,k-1)*oHz(j,k ) CF(j,k)=cff1*(Hz(i,j-1,k+1)+Hz(i,j,k+1))- & & DTsizeV*Kv(i,j,k+1)*oHz(j,k+1) END DO CF(j,0)=0.0_r8 !> DC(j,0)=0.0_r8 !> tl_DC(j,0)=0.0_r8 END DO ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN j=edge(boundary) cff1=0.5_r8*(1.0_r8/6.0_r8) DO i=Istr,Iend DO k=1,N(ng)-1 FC(i,k)=cff1*(Hz(i,j-1,k )+Hz(i,j,k ))- & & DTsizeV*Kv(i,j,k-1)*oHz(i,k ) CF(i,k)=cff1*(Hz(i,j-1,k+1)+Hz(i,j,k+1))- & & DTsizeV*Kv(i,j,k+1)*oHz(i,k+1) END DO CF(i,0)=0.0_r8 !> DC(i,0)=0.0_r8 !> tl_DC(i,0)=0.0_r8 END DO END IF ! ! LU decomposition and forward substitution. ! IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN i=edge(boundary) cff1=0.5_r8*(1.0_r8/3.0_r8) DO k=1,N(ng)-1 DO j=JstrV,Jend BC(j,k)=cff1*(Hz(i,j-1,k )+Hz(i,j,k )+ & & Hz(i,j-1,k+1)+Hz(i,j,k+1))+ & & DTsizeV*Kv(i,j,k)* & & (oHz(j,k)+oHz(j,k+1)) cff=1.0_r8/(BC(j,k)-FC(j,k)*CF(j,k-1)) CF(j,k)=cff*CF(j,k) !> DC(j,k)=cff*(Awrk(j,k+1,Nold)- & !> & Awrk(j,k ,Nold)- & !> & FC(j,k)*DC(j,k-1)) !> tl_DC(j,k)=cff*(tl_Awrk(j,k+1,Nold)- & & tl_Awrk(j,k ,Nold)- & & FC(j,k)*tl_DC(j,k-1)) END DO END DO ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN j=edge(boundary) cff1=0.5_r8*(1.0_r8/3.0_r8) DO k=1,N(ng)-1 DO i=Istr,Iend BC(i,k)=cff1*(Hz(i,j-1,k )+Hz(i,j,k )+ & & Hz(i,j-1,k+1)+Hz(i,j,k+1))+ & & DTsizeV*Kv(i,j,k)* & & (oHz(i,k)+oHz(i,k+1)) cff=1.0_r8/(BC(i,k)-FC(i,k)*CF(i,k-1)) CF(i,k)=cff*CF(i,k) !> DC(i,k)=cff*(Awrk(i,k+1,Nold)- & !> & Awrk(i,k ,Nold)- & !> & FC(i,k)*DC(i,k-1)) !> tl_DC(i,k)=cff*(tl_Awrk(i,k+1,Nold)- & & tl_Awrk(i,k ,Nold)- & & FC(i,k)*tl_DC(i,k-1)) END DO END DO END IF ! ! Backward substitution. ! IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN i=edge(boundary) DO j=JstrV,Jend !> DC(j,N(ng))=0.0_r8 !> tl_DC(j,N(ng))=0.0_r8 END DO DO k=N(ng)-1,1,-1 DO j=JstrV,Jend !> DC(j,k)=DC(j,k)-CF(j,k)*DC(j,k+1) !> tl_DC(j,k)=tl_DC(j,k)-CF(j,k)*tl_DC(j,k+1) END DO END DO DO k=1,N(ng) DO j=JstrV,Jend !> DC(j,k)=DC(j,k)*Kv(i,j,k) !> tl_DC(j,k)=tl_DC(j,k)*Kv(i,j,k) !> Awrk(j,k,Nnew)=Awrk(j,k,Nold)+ & !> & DTsizeV*oHz(j,k)* & !> & (DC(j,k)-DC(j,k-1)) !> tl_Awrk(j,k,Nnew)=tl_Awrk(j,k,Nold)+ & & DTsizeV*oHz(j,k)* & & (tl_DC(j,k)-tl_DC(j,k-1)) END DO END DO ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN j=edge(boundary) DO i=Istr,Iend !> DC(i,N(ng))=0.0_r8 !> tl_DC(i,N(ng))=0.0_r8 END DO DO k=N(ng)-1,1,-1 DO i=Istr,Iend !> DC(i,k)=DC(i,k)-CF(i,k)*DC(i,k+1) !> tl_DC(i,k)=tl_DC(i,k)-CF(i,k)*tl_DC(i,k+1) END DO END DO DO k=1,N(ng) DO i=Istr,Iend !> DC(i,k)=DC(i,k)*Kv(i,j,k) !> tl_DC(i,k)=tl_DC(i,k)*Kv(i,j,k) !> Awrk(i,k,Nnew)=Awrk(i,k,Nold)+ & !> & DTsizeV*oHz(i,k)* & !> & (DC(i,k)-DC(i,k-1)) !> tl_Awrk(i,k,Nnew)=tl_Awrk(i,k,Nold)+ & & DTsizeV*oHz(i,k)* & & (tl_DC(i,k)-tl_DC(i,k-1)) END DO END DO END IF END IF ! ! Update integration indices. ! Nsav=Nold Nold=Nnew Nnew=Nsav END DO # else ! !----------------------------------------------------------------------- ! Integrate vertical diffusion equation implicitly. !----------------------------------------------------------------------- ! DO step=1,NVsteps ! ! Compute diagonal matrix coefficients BC and load right-hand-side ! terms for the diffusion equation into DC. ! IF (Lconvolve(boundary)) THEN IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN i=edge(boundary) DO k=1,N(ng) DO j=JstrV,Jend cff=0.5_r8*(Hz(i,j-1,k)+Hz(i,j,k)) BC(j,k)=cff-FC(j,k)-FC(j,k-1) !> DC(j,k)=Awrk(j,k,Nold)*cff !> tl_DC(j,k)=tl_Awrk(j,k,Nold)*cff END DO END DO ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN j=edge(boundary) DO k=1,N(ng) DO i=Istr,Iend cff=0.5_r8*(Hz(i,j-1,k)+Hz(i,j,k)) BC(i,k)=cff-FC(i,k)-FC(i,k-1) !> DC(i,k)=Awrk(i,k,Nold)*cff !> tl_DC(i,k)=tl_Awrk(i,k,Nold)*cff END DO END DO END IF ! ! Solve the tridiagonal system. ! IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN DO j=JstrV,Jend cff=1.0_r8/BC(j,1) CF(j,1)=cff*FC(j,1) !> DC(j,1)=cff*DC(j,1) !> tl_DC(j,1)=cff*tl_DC(j,1) END DO DO k=2,N(ng)-1 DO j=JstrV,Jend cff=1.0_r8/(BC(j,k)-FC(j,k-1)*CF(j,k-1)) CF(j,k)=cff*FC(j,k) !> DC(j,k)=cff*(DC(j,k)-FC(j,k-1)*DC(j,k-1)) !> tl_DC(j,k)=cff*(tl_DC(j,k)-FC(j,k-1)*tl_DC(j,k-1)) END DO END DO ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN DO i=Istr,Iend cff=1.0_r8/BC(i,1) CF(i,1)=cff*FC(i,1) !> DC(i,1)=cff*DC(i,1) !> tl_DC(i,1)=cff*tl_DC(i,1) END DO DO k=2,N(ng)-1 DO i=Istr,Iend cff=1.0_r8/(BC(i,k)-FC(i,k-1)*CF(i,k-1)) CF(i,k)=cff*FC(i,k) !> DC(i,k)=cff*(DC(i,k)-FC(i,k-1)*DC(i,k-1)) !> tl_DC(i,k)=cff*(tl_DC(i,k)-FC(i,k-1)*tl_DC(i,k-1)) END DO END DO END IF ! ! Compute new solution by back substitution. ! IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN i=edge(boundary) DO j=JstrV,Jend !> DC(j,N(ng))=(DC(j,N(ng))- & !> & FC(j,N(ng)-1)*DC(j,N(ng)-1))/ & !> & (BC(j,N(ng))- & !> & FC(j,N(ng)-1)*CF(j,N(ng)-1)) !> tl_DC(j,N(ng))=(tl_DC(j,N(ng))- & & FC(j,N(ng)-1)*tl_DC(j,N(ng)-1))/ & & (BC(j,N(ng))- & & FC(j,N(ng)-1)*CF(j,N(ng)-1)) !> Awrk(j,N(ng),Nnew)=DC(j,N(ng)) !> tl_Awrk(j,N(ng),Nnew)=tl_DC(j,N(ng)) # ifdef MASKING !> Awrk(j,N(ng),Nnew)=Awrk(j,N(ng),Nnew)*vmask(i,j) !> tl_Awrk(j,N(ng),Nnew)=tl_Awrk(j,N(ng),Nnew)*vmask(i,j) # endif END DO DO k=N(ng)-1,1,-1 DO j=JstrV,Jend !> DC(j,k)=DC(j,k)-CF(j,k)*DC(j,k+1) !> tl_DC(j,k)=tl_DC(j,k)-CF(j,k)*tl_DC(j,k+1) !> Awrk(j,k,Nnew)=DC(j,k) !> tl_Awrk(j,k,Nnew)=tl_DC(j,k) # ifdef MASKING !> Awrk(j,k,Nnew)=Awrk(j,k,Nnew)*vmask(i,j) !> tl_Awrk(j,k,Nnew)=tl_Awrk(j,k,Nnew)*vmask(i,j) # endif END DO END DO ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN j=edge(boundary) DO i=Istr,Iend !> DC(i,N(ng))=(DC(i,N(ng))- & !> & FC(i,N(ng)-1)*DC(i,N(ng)-1))/ & !> & (BC(i,N(ng))- & !> & FC(i,N(ng)-1)*CF(i,N(ng)-1)) !> tl_DC(i,N(ng))=(tl_DC(i,N(ng))- & & FC(i,N(ng)-1)*tl_DC(i,N(ng)-1))/ & & (BC(i,N(ng))- & & FC(i,N(ng)-1)*CF(i,N(ng)-1)) !> Awrk(i,N(ng),Nnew)=DC(i,N(ng)) !> tl_Awrk(i,N(ng),Nnew)=tl_DC(i,N(ng)) # ifdef MASKING !> Awrk(i,N(ng),Nnew)=Awrk(i,N(ng),Nnew)*vmask(i,j) !> tl_Awrk(i,N(ng),Nnew)=tl_Awrk(i,N(ng),Nnew)*vmask(i,j) # endif END DO DO k=N(ng)-1,1,-1 DO i=Istr,Iend !> DC(i,k)=DC(i,k)-CF(i,k)*DC(i,k+1) !> tl_DC(i,k)=tl_DC(i,k)-CF(i,k)*tl_DC(i,k+1) !> Awrk(i,k,Nnew)=DC(i,k) !> tl_Awrk(i,k,Nnew)=tl_DC(i,k) # ifdef MASKING !> Awrk(i,k,Nnew)=Awrk(i,k,Nnew)*vmask(i,j) !> tl_Awrk(i,k,Nnew)=tl_Awrk(i,k,Nnew)*vmask(i,j) # endif END DO END DO END IF END IF ! ! Update integration indices. ! Nsav=Nold Nold=Nnew Nnew=Nsav END DO # endif # else ! !----------------------------------------------------------------------- ! Integrate vertical diffusion equation explicitly. !----------------------------------------------------------------------- ! DO step=1,NVsteps ! ! Compute vertical diffusive flux. Notice that "FC" is assumed to ! be time invariant. ! IF (Lconvolve(boundary)) THEN IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN i=edge(boundary) DO j=JstrV,Jend DO k=1,N(ng)-1 !> FS(j,k)=FC(j,k)*(Awrk(j,k+1,Nold)- & !> & Awrk(j,k ,Nold)) !> tl_FS(j,k)=FC(j,k)*(tl_Awrk(j,k+1,Nold)- & & tl_Awrk(j,k ,Nold)) # ifdef MASKING !> FS(j,k)=FS(j,k)*vmask(i,j) !> tl_FS(j,k)=tl_FS(j,k)*vmask(i,j) # endif END DO !> FS(j,0)=0.0_r8 !> tl_FS(j,0)=0.0_r8 !> FS(j,N(ng))=0.0_r8 !> tl_FS(j,N(ng))=0.0_r8 END DO ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN j=edge(boundary) DO i=Istr,Iend DO k=1,N(ng)-1 !> FS(i,k)=FC(i,k)*(Awrk(i,k+1,Nold)- & !> & Awrk(i,k ,Nold)) !> tl_FS(i,k)=FC(i,k)*(tl_Awrk(i,k+1,Nold)- & & tl_Awrk(i,k ,Nold)) # ifdef MASKING !> FS(i,k)=FS(i,k)*vmask(i,j) !> tl_FS(i,k)=tl_FS(i,k)*vmask(i,j) # endif END DO !> FS(i,0)=0.0_r8 !> tl_FS(i,0)=0.0_r8 !> FS(i,N(ng))=0.0_r8 !> tl_FS(i,N(ng))=0.0_r8 END DO END IF ! ! Time-step vertical diffusive term. Notice that "oHz" is assumed to ! be time invariant. ! IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN DO k=1,N(ng) DO j=JstrV,Jend !> Awrk(j,k,Nnew)=Awrk(j,k,Nold)+ & !> & oHz(j,k)*(FS(j,k )- & !> & FS(j,k-1)) !> tl_Awrk(j,k,Nnew)=tl_Awrk(j,k,Nold)+ & & oHz(j,k)*(tl_FS(j,k )- & & tl_FS(j,k-1)) END DO END DO ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN DO k=1,N(ng) DO i=Istr,Iend !> Awrk(i,k,Nnew)=Awrk(i,k,Nold)+ & !> & oHz(i,k)*(FS(i,k )- & !> & FS(i,k-1)) !> tl_Awrk(i,k,Nnew)=tl_Awrk(i,k,Nold)+ & & oHz(i,k)*(tl_FS(i,k )- & & tl_FS(i,k-1)) END DO END DO END IF END IF ! ! Update integration indices. ! Nsav=Nold Nold=Nnew Nnew=Nsav END DO # endif # endif ! !----------------------------------------------------------------------- ! Load convolved solution. !----------------------------------------------------------------------- ! IF (Lconvolve(boundary)) THEN IF ((boundary.eq.iwest).or.(boundary.eq.ieast)) THEN DO k=1,N(ng) DO j=JstrV,Jend !> A(j,k)=Awrk(j,k,Nold) !> tl_A(j,k)=tl_Awrk(j,k,Nold) END DO END DO ELSE IF ((boundary.eq.isouth).or.(boundary.eq.inorth)) THEN DO k=1,N(ng) DO i=Istr,Iend !> A(i,k)=Awrk(i,k,Nold) !> tl_A(i,k)=tl_Awrk(i,k,Nold) END DO END DO END IF END IF !> CALL bc_v3d_bry_tile (ng, tile, boundary, & !> & LBij, UBij, 1, N(ng), & !> & A) !> CALL bc_v3d_bry_tile (ng, tile, boundary, & & LBij, UBij, 1, N(ng), & & tl_A) # ifdef DISTRIBUTE !> CALL mp_exchange3d_bry (ng, tile, model, 1, boundary, & !> & LBij, UBij, 1, N(ng), & !> & Nghost, & !> & EWperiodic(ng), NSperiodic(ng), & !> & A) !> CALL mp_exchange3d_bry (ng, tile, model, 1, boundary, & & LBij, UBij, 1, N(ng), & & Nghost, & & EWperiodic(ng), NSperiodic(ng), & & tl_A) # endif RETURN END SUBROUTINE tl_conv_v3d_bry_tile #endif END MODULE tl_conv_bry3d_mod