#include "cppdefs.h" MODULE conv_3d_mod #if defined NONLINEAR && defined FOUR_DVAR && defined SOLVE3D ! !git $Id$ !svn $Id: conv_3d.F 1151 2023-02-09 03:08:53Z arango $ !================================================== Hernan G. Arango === ! Copyright (c) 2002-2023 The ROMS/TOMS Group Andrew M. Moore ! ! Licensed under a MIT/X style license ! ! See License_ROMS.md ! !======================================================================= ! ! ! 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. ! ! ! ! Notice that "z_r" and "Hz" are assumed to be time invariant in ! ! the spatial convolution. That it, they are not adjointable. ! ! ! ! On Input: ! ! ! ! ng Nested grid number. ! ! model Calling model identifier. ! ! Istr Starting tile index in the I-direction. ! ! Iend Ending tile index in the I-direction. ! ! Jstr Starting tile index in the J-direction. ! ! Jend Ending tile index in the J-direction. ! ! 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. ! ! A 3D state variable to diffuse. ! ! ! ! On Output: ! ! ! ! A Convolved 3D state variable. ! ! ! ! Routines: ! ! ! ! conv_r3d_tile Nonlinear 3D convolution at RHO-points ! ! conv_u3d_tile Nonlinear 3D convolution at U-points ! ! conv_v3d_tile Nonlinear 3D convolution at V-points ! ! ! !======================================================================= ! implicit none ! PUBLIC ! CONTAINS ! !*********************************************************************** SUBROUTINE conv_r3d_tile (ng, tile, model, & & LBi, UBi, LBj, UBj, LBk, UBk, & & IminS, ImaxS, JminS, JmaxS, & & Nghost, NHsteps, NVsteps, & & DTsizeH, DTsizeV, & & Kh, Kv, & & pm, pn, & # ifdef GEOPOTENTIAL_HCONV & on_u, om_v, & # else & pmon_u, pnom_v, & # endif # ifdef MASKING & rmask, umask, vmask, & # endif & Hz, z_r, & & A) !*********************************************************************** ! USE mod_param USE mod_scalars ! USE bc_3d_mod, ONLY: dabc_r3d_tile # ifdef DISTRIBUTE USE mp_exchange_mod, ONLY : mp_exchange3d # endif ! ! Imported variable declarations. ! integer, intent(in) :: ng, tile, model 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:) # ifdef GEOPOTENTIAL_HCONV real(r8), intent(in) :: on_u(LBi:,LBj:) real(r8), intent(in) :: om_v(LBi:,LBj:) # else real(r8), intent(in) :: pmon_u(LBi:,LBj:) real(r8), intent(in) :: pnom_v(LBi:,LBj:) # endif # 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) :: A(LBi:,LBj:,LBk:) # else real(r8), intent(in) :: pm(LBi:UBi,LBj:UBj) real(r8), intent(in) :: pn(LBi:UBi,LBj:UBj) # ifdef GEOPOTENTIAL_HCONV real(r8), intent(in) :: on_u(LBi:UBi,LBj:UBj) real(r8), intent(in) :: om_v(LBi:UBi,LBj:UBj) # else real(r8), intent(in) :: pmon_u(LBi:UBi,LBj:UBj) real(r8), intent(in) :: pnom_v(LBi:UBi,LBj:UBj) # endif # 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) :: A(LBi:UBi,LBj:UBj,LBk:UBk) # endif ! ! Local variable declarations. ! integer :: Nnew, Nold, Nsav, i, j, k, k1, k2, step real(r8) :: cff, cff1, cff2, cff3, cff4 real(r8), dimension(LBi:UBi,LBj:UBj,LBk:UBk,2) :: Awrk real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: FE real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: FX real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: Hfac # ifdef VCONVOLUTION # ifndef SPLINES_VCONV real(r8), dimension(IminS:ImaxS,JminS:JmaxS,0:N(ng)) :: FC # endif # if !defined IMPLICIT_VCONV || defined SPLINES_VCONV real(r8), dimension(IminS:ImaxS,JminS:JmaxS,N(ng)) :: oHz # endif # if defined IMPLICIT_VCONV || defined SPLINES_VCONV real(r8), dimension(IminS:ImaxS,0:N(ng)) :: BC real(r8), dimension(IminS:ImaxS,0:N(ng)) :: CF real(r8), dimension(IminS:ImaxS,0:N(ng)) :: DC # ifdef SPLINES_VCONV real(r8), dimension(IminS:ImaxS,0:N(ng)) :: FC # endif # else real(r8), dimension(IminS:ImaxS,0:N(ng)) :: FS # endif # endif # ifdef GEOPOTENTIAL_HCONV real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: FZ real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: dAdz real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: dAdx real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: dAde real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: dZdx real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: dZde # endif # include "set_bounds.h" ! !----------------------------------------------------------------------- ! Space convolution of the diffusion equation for a 3D state variable ! at RHO-points. !----------------------------------------------------------------------- ! ! 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. ! DO j=Jstr-1,Jend+1 DO i=Istr-1,Iend+1 Hfac(i,j)=DTsizeH*pm(i,j)*pn(i,j) # ifdef VCONVOLUTION # ifndef SPLINES_VCONV FC(i,j,N(ng))=0.0_r8 DO k=1,N(ng)-1 # ifdef IMPLICIT_VCONV FC(i,j,k)=-DTsizeV*Kv(i,j,k)/(z_r(i,j,k+1)-z_r(i,j,k)) # else FC(i,j,k)=DTsizeV*Kv(i,j,k)/(z_r(i,j,k+1)-z_r(i,j,k)) # endif END DO FC(i,j,0)=0.0_r8 # endif # if !defined IMPLICIT_VCONV || defined SPLINES_VCONV DO k=1,N(ng) oHz(i,j,k)=1.0_r8/Hz(i,j,k) END DO # endif # endif END DO END DO ! ! Set integration indices and initial conditions. ! Nold=1 Nnew=2 CALL dabc_r3d_tile (ng, tile, & & LBi, UBi, LBj, UBj, LBk, UBk, & & A) # ifdef DISTRIBUTE CALL mp_exchange3d (ng, tile, model, 1, & & LBi, UBi, LBj, UBj, LBk, UBk, & & Nghost, & & EWperiodic(ng), NSperiodic(ng), & & A) # endif DO k=1,N(ng) DO j=Jstr-1,Jend+1 DO i=Istr-1,Iend+1 Awrk(i,j,k,Nold)=A(i,j,k) END DO END DO END DO ! !----------------------------------------------------------------------- ! Integrate horizontal diffusion equation. !----------------------------------------------------------------------- ! DO step=1,NHsteps # ifdef GEOPOTENTIAL_HCONV ! ! Diffusion along geopotential surfaces: Compute horizontal and ! vertical gradients. Notice the recursive blocking sequence. The ! vertical placement of the gradients is: ! ! dAdx,dAde(:,:,k1) k rho-points ! dAdx,dAde(:,:,k2) k+1 rho-points ! FZ,dAdz(:,:,k1) k-1/2 W-points ! FZ,dAdz(:,:,k2) k+1/2 W-points ! k2=1 K_LOOP : DO k=0,N(ng) k1=k2 k2=3-k1 IF (k.lt.N(ng)) THEN DO j=Jstr,Jend DO i=Istr,Iend+1 cff=0.5_r8*(pm(i-1,j)+pm(i,j)) # ifdef MASKING cff=cff*umask(i,j) # endif dZdx(i,j,k2)=cff*(z_r(i ,j,k+1)- & & z_r(i-1,j,k+1)) # ifdef MASKING dAdx(i,j,k2)=cff*(Awrk(i ,j,k+1,Nold)*rmask(i ,j)- & & Awrk(i-1,j,k+1,Nold)*rmask(i-1,j)) # else dAdx(i,j,k2)=cff*(Awrk(i ,j,k+1,Nold)- & & Awrk(i-1,j,k+1,Nold)) # endif END DO END DO DO j=Jstr,Jend+1 DO i=Istr,Iend cff=0.5_r8*(pn(i,j-1)+pn(i,j)) # ifdef MASKING cff=cff*vmask(i,j) # endif dZde(i,j,k2)=cff*(z_r(i,j ,k+1)- & & z_r(i,j-1,k+1)) # ifdef MASKING dAde(i,j,k2)=cff*(Awrk(i,j ,k+1,Nold)*rmask(i,j )- & & Awrk(i,j-1,k+1,Nold)*rmask(i,j-1)) # else dAde(i,j,k2)=cff*(Awrk(i,j ,k+1,Nold)- & & Awrk(i,j-1,k+1,Nold)) # endif END DO END DO END IF IF ((k.eq.0).or.(k.eq.N(ng))) THEN DO j=Jstr-1,Jend+1 DO i=Istr-1,Iend+1 dAdz(i,j,k2)=0.0_r8 FZ(i,j,k2)=0.0_r8 END DO END DO ELSE DO j=Jstr-1,Jend+1 DO i=Istr-1,Iend+1 cff=1.0_r8/(z_r(i,j,k+1)-z_r(i,j,k)) dAdz(i,j,k2)=cff*(Awrk(i,j,k+1,Nold)- & & Awrk(i,j,k ,Nold)) # ifdef MASKING dAdz(i,j,k2)=dAdz(i,j,k2)*rmask(i,j) # endif END DO END DO END IF ! ! Compute components of the rotated A flux (A m3/s) along geopotential ! surfaces. ! IF (k.gt.0) THEN DO j=Jstr,Jend DO i=Istr,Iend+1 cff=0.25_r8*(Kh(i-1,j)+Kh(i-1,j))*on_u(i,j) cff1=MIN(dZdx(i,j,k1),0.0_r8) cff2=MAX(dZdx(i,j,k1),0.0_r8) FX(i,j)=cff* & & (Hz(i,j,k)+Hz(i-1,j,k))* & & (dAdx(i,j,k1)- & & 0.5_r8*(cff1*(dAdz(i-1,j,k1)+ & & dAdz(i ,j,k2))+ & & cff2*(dAdz(i-1,j,k2)+ & & dAdz(i ,j,k1)))) END DO END DO DO j=Jstr,Jend+1 DO i=Istr,Iend cff=0.25_r8*(Kh(i,j-1)+Kh(i,j))*om_v(i,j) cff1=MIN(dZde(i,j,k1),0.0_r8) cff2=MAX(dZde(i,j,k1),0.0_r8) FE(i,j)=cff* & & (Hz(i,j,k)+Hz(i,j-1,k))* & & (dAde(i,j,k1)- & & 0.5_r8*(cff1*(dAdz(i,j-1,k1)+ & & dAdz(i,j ,k2))+ & & cff2*(dAdz(i,j-1,k2)+ & & dAdz(i,j ,k1)))) END DO END DO IF (k.lt.N(ng)) THEN DO j=Jstr,Jend DO i=Istr,Iend cff=0.5_r8*Kh(i,j) cff1=MIN(dZdx(i ,j,k1),0.0_r8) cff2=MIN(dZdx(i+1,j,k2),0.0_r8) cff3=MAX(dZdx(i ,j,k2),0.0_r8) cff4=MAX(dZdx(i+1,j,k1),0.0_r8) FZ(i,j,k2)=cff* & & (cff1*(cff1*dAdz(i,j,k2)-dAdx(i ,j,k1))+ & & cff2*(cff2*dAdz(i,j,k2)-dAdx(i+1,j,k2))+ & & cff3*(cff3*dAdz(i,j,k2)-dAdx(i ,j,k2))+ & & cff4*(cff4*dAdz(i,j,k2)-dAdx(i+1,j,k1))) cff1=MIN(dZde(i,j ,k1),0.0_r8) cff2=MIN(dZde(i,j+1,k2),0.0_r8) cff3=MAX(dZde(i,j ,k2),0.0_r8) cff4=MAX(dZde(i,j+1,k1),0.0_r8) FZ(i,j,k2)=FZ(i,j,k2)+ & & cff* & & (cff1*(cff1*dAdz(i,j,k2)-dAde(i,j ,k1))+ & & cff2*(cff2*dAdz(i,j,k2)-dAde(i,j+1,k2))+ & & cff3*(cff3*dAdz(i,j,k2)-dAde(i,j ,k2))+ & & cff4*(cff4*dAdz(i,j,k2)-dAde(i,j+1,k1))) END DO END DO END IF ! ! Time-step harmonic, geopotential diffusion term (m Tunits). ! DO j=Jstr,Jend DO i=Istr,Iend Awrk(i,j,k,Nnew)=Awrk(i,j,k,Nold)+ & & Hfac(i,j)* & & (FX(i+1,j )-FX(i,j)+ & & FE(i ,j+1)-FE(i,j))+ & & DTsizeH* & & (FZ(i,j,k2)-FZ(i,j,k1)) END DO END DO END IF END DO K_LOOP # else ! ! Diffusion along S-coordinates: compute XI- and ETA-components of ! diffusive flux. ! DO k=1,N(ng) DO j=Jstr,Jend DO i=Istr,Iend+1 FX(i,j)=pmon_u(i,j)*0.5_r8*(Kh(i-1,j)+Kh(i,j))* & & (Awrk(i,j,k,Nold)-Awrk(i-1,j,k,Nold)) # ifdef MASKING FX(i,j)=FX(i,j)*umask(i,j) # endif END DO END DO DO j=Jstr,Jend+1 DO i=Istr,Iend FE(i,j)=pnom_v(i,j)*0.5_r8*(Kh(i,j-1)+Kh(i,j))* & & (Awrk(i,j,k,Nold)-Awrk(i,j-1,k,Nold)) # ifdef MASKING FE(i,j)=FE(i,j)*vmask(i,j) # endif END DO END DO ! ! Time-step horizontal diffusion equation. ! DO j=Jstr,Jend DO i=Istr,Iend Awrk(i,j,k,Nnew)=Awrk(i,j,k,Nold)+ & & Hfac(i,j)* & & (FX(i+1,j)-FX(i,j)+ & & FE(i,j+1)-FE(i,j)) END DO END DO END DO # endif ! ! Apply boundary conditions. ! CALL dabc_r3d_tile (ng, tile, & & LBi, UBi, LBj, UBj, LBk, UBk, & & Awrk(:,:,:,Nnew)) # ifdef DISTRIBUTE CALL mp_exchange3d (ng, tile, model, 1, & & LBi, UBi, LBj, UBj, LBk, UBk, & & Nghost, & & EWperiodic(ng), NSperiodic(ng), & & 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. ! DO j=Jstr,Jend cff1=1.0_r8/6.0_r8 DO k=1,N(ng)-1 DO i=Istr,Iend FC(i,k)=cff1*Hz(i,j,k )- & & DTsizeV*Kv(i,j,k-1)*oHz(i,j,k ) CF(i,k)=cff1*Hz(i,j,k+1)- & & DTsizeV*Kv(i,j,k+1)*oHz(i,j,k+1) END DO END DO DO i=Istr,Iend CF(i,0)=0.0_r8 DC(i,0)=0.0_r8 END DO ! ! LU decomposition and forward substitution. ! 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,j,k)+oHz(i,j,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,j,k+1,Nold)-Awrk(i,j,k,Nold)- & & FC(i,k)*DC(i,k-1)) END DO END DO ! ! Backward substitution. ! DO i=Istr,Iend 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) END DO END DO ! DO k=1,N(ng) DO i=Istr,Iend DC(i,k)=DC(i,k)*Kv(i,j,k) Awrk(i,j,k,Nnew)=Awrk(i,j,k,Nold)+ & & DTsizeV*oHz(i,j,k)* & & (DC(i,k)-DC(i,k-1)) END DO END DO END DO ! ! 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. ! DO j=Jstr,Jend DO k=1,N(ng) DO i=Istr,Iend BC(i,k)=Hz(i,j,k)-FC(i,j,k)-FC(i,j,k-1) DC(i,k)=Awrk(i,j,k,Nold)*Hz(i,j,k) END DO END DO ! ! Solve the tridiagonal system. ! DO i=Istr,Iend cff=1.0_r8/BC(i,1) CF(i,1)=cff*FC(i,j,1) DC(i,1)=cff*DC(i,1) END DO DO k=2,N(ng)-1 DO i=Istr,Iend cff=1.0_r8/(BC(i,k)-FC(i,j,k-1)*CF(i,k-1)) CF(i,k)=cff*FC(i,j,k) DC(i,k)=cff*(DC(i,k)-FC(i,j,k-1)*DC(i,k-1)) END DO END DO ! ! Compute new solution by back substitution. ! DO i=Istr,Iend DC(i,N(ng))=(DC(i,N(ng))- & & FC(i,j,N(ng)-1)*DC(i,N(ng)-1))/ & & (BC(i,N(ng))-FC(i,j,N(ng)-1)*CF(i,N(ng)-1)) Awrk(i,j,N(ng),Nnew)=DC(i,N(ng)) # ifdef MASKING Awrk(i,j,N(ng),Nnew)=Awrk(i,j,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) Awrk(i,j,k,Nnew)=DC(i,k) # ifdef MASKING Awrk(i,j,k,Nnew)=Awrk(i,j,k,Nnew)*rmask(i,j) # endif END DO END DO END DO ! ! 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. ! DO j=Jstr,Jend DO k=1,N(ng)-1 DO i=Istr,Iend FS(i,k)=FC(i,j,k)*(Awrk(i,j,k+1,Nold)- & & Awrk(i,j,k ,Nold)) # ifdef MASKING FS(i,k)=FS(i,k)*rmask(i,j) # endif END DO END DO DO i=Istr,Iend FS(i,0)=0.0_r8 FS(i,N(ng))=0.0_r8 END DO ! ! Time-step vertical diffusive term. Notice that "oHz" is assumed to ! be time invariant. ! DO k=1,N(ng) DO i=Istr,Iend Awrk(i,j,k,Nnew)=Awrk(i,j,k,Nold)+ & & oHz(i,j,k)*(FS(i,k )- & & FS(i,k-1)) END DO END DO END DO ! ! Update integration indices. ! Nsav=Nold Nold=Nnew Nnew=Nsav END DO # endif # endif ! !----------------------------------------------------------------------- ! Load convolved solution. !----------------------------------------------------------------------- ! DO k=1,N(ng) DO j=Jstr,Jend DO i=Istr,Iend A(i,j,k)=Awrk(i,j,k,Nold) END DO END DO END DO CALL dabc_r3d_tile (ng, tile, & & LBi, UBi, LBj, UBj, LBk, UBk, & & A) # ifdef DISTRIBUTE CALL mp_exchange3d (ng, tile, model, 1, & & LBi, UBi, LBj, UBj, LBk, UBk, & & Nghost, & & EWperiodic(ng), NSperiodic(ng), & & A) # endif RETURN END SUBROUTINE conv_r3d_tile ! !*********************************************************************** SUBROUTINE conv_u3d_tile (ng, tile, model, & & LBi, UBi, LBj, UBj, LBk, UBk, & & IminS, ImaxS, JminS, JmaxS, & & Nghost, NHsteps, NVsteps, & & DTsizeH, DTsizeV, & & Kh, Kv, & & pm, pn, & # ifdef GEOPOTENTIAL_HCONV & on_r, om_p, & # else & pmon_r, pnom_p, & # endif # ifdef MASKING # ifdef GEOPOTENTIAL_HCONV & pmask, rmask, umask, vmask, & # else & umask, pmask, & # endif # endif & Hz, z_r, & & A) !*********************************************************************** ! USE mod_param USE mod_scalars ! USE bc_3d_mod, ONLY: dabc_u3d_tile # ifdef DISTRIBUTE USE mp_exchange_mod, ONLY : mp_exchange3d # endif ! ! Imported variable declarations. ! integer, intent(in) :: ng, tile, model 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:) # ifdef GEOPOTENTIAL_HCONV real(r8), intent(in) :: on_r(LBi:,LBj:) real(r8), intent(in) :: om_p(LBi:,LBj:) # else real(r8), intent(in) :: pmon_r(LBi:,LBj:) real(r8), intent(in) :: pnom_p(LBi:,LBj:) # endif # ifdef MASKING # ifdef GEOPOTENTIAL_HCONV real(r8), intent(in) :: pmask(LBi:,LBj:) real(r8), intent(in) :: rmask(LBi:,LBj:) real(r8), intent(in) :: umask(LBi:,LBj:) real(r8), intent(in) :: vmask(LBi:,LBj:) # else real(r8), intent(in) :: umask(LBi:,LBj:) real(r8), intent(in) :: pmask(LBi:,LBj:) # endif # 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) :: A(LBi:,LBj:,LBk:) # else real(r8), intent(in) :: pm(LBi:UBi,LBj:UBj) real(r8), intent(in) :: pn(LBi:UBi,LBj:UBj) # ifdef GEOPOTENTIAL_HCONV real(r8), intent(in) :: on_r(LBi:UBi,LBj:UBj) real(r8), intent(in) :: om_p(LBi:UBi,LBj:UBj) # else real(r8), intent(in) :: pmon_r(LBi:UBi,LBj:UBj) real(r8), intent(in) :: pnom_p(LBi:UBi,LBj:UBj) # endif # ifdef MASKING # ifdef GEOPOTENTIAL_HCONV real(r8), intent(in) :: pmask(LBi:UBi,LBj:UBj) 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) # else real(r8), intent(in) :: umask(LBi:UBi,LBj:UBj) real(r8), intent(in) :: pmask(LBi:UBi,LBj:UBj) # endif # 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) :: A(LBi:UBi,LBj:UBj,LBk:UBk) # endif ! ! Local variable declarations. ! integer :: Nnew, Nold, Nsav, i, j, k, k1, k2, step real(r8) :: cff, cff1, cff2, cff3, cff4 real(r8), dimension(LBi:UBi,LBj:UBj,LBk:UBk,2) :: Awrk real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: FE real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: FX real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: Hfac # ifdef VCONVOLUTION # ifndef SPLINES_VCONV real(r8), dimension(IminS:ImaxS,JminS:JmaxS,0:N(ng)) :: FC # endif # if !defined IMPLICIT_VCONV || defined SPLINES_VCONV real(r8), dimension(IminS:ImaxS,JminS:JmaxS,N(ng)) :: oHz # endif # if defined IMPLICIT_VCONV || defined SPLINES_VCONV real(r8), dimension(IminS:ImaxS,0:N(ng)) :: BC real(r8), dimension(IminS:ImaxS,0:N(ng)) :: CF real(r8), dimension(IminS:ImaxS,0:N(ng)) :: DC # ifdef SPLINES_VCONV real(r8), dimension(IminS:ImaxS,0:N(ng)) :: FC real(r8), dimension(IminS:ImaxS,N(ng)) :: Hzk # endif # else real(r8), dimension(IminS:ImaxS,0:N(ng)) :: FS # endif # endif # ifdef GEOPOTENTIAL_HCONV real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: dZdx real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: dZde real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: FZ real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: dAdz real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: dAdx real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: dAde real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: dZdx_r real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: dZde_p # endif # include "set_bounds.h" ! !----------------------------------------------------------------------- ! Space convolution of the diffusion equation for a 3D state variable ! at U-points. !----------------------------------------------------------------------- ! ! 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. ! cff=DTsizeH*0.25_r8 DO j=Jstr-1,Jend+1 DO i=IstrU-1,Iend+1 Hfac(i,j)=cff*(pm(i-1,j)+pm(i,j))*(pn(i-1,j)+pn(i,j)) # ifdef VCONVOLUTION # ifndef SPLINES_VCONV FC(i,j,N(ng))=0.0_r8 DO k=1,N(ng)-1 # ifdef IMPLICIT_VCONV FC(i,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(i,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(i,j,0)=0.0_r8 # endif # if !defined IMPLICIT_VCONV || defined SPLINES_VCONV DO k=1,N(ng) oHz(i,j,k)=2.0_r8/(Hz(i-1,j,k)+Hz(i,j,k)) END DO # endif # endif END DO END DO ! ! Set integration indices and initial conditions. ! Nold=1 Nnew=2 CALL dabc_u3d_tile (ng, tile, & & LBi, UBi, LBj, UBj, LBk, UBk, & & A) # ifdef DISTRIBUTE CALL mp_exchange3d (ng, tile, model, 1, & & LBi, UBi, LBj, UBj, LBk, UBk, & & Nghost, & & EWperiodic(ng), NSperiodic(ng), & & A) # endif DO k=1,N(ng) DO j=Jstr-1,Jend+1 DO i=IstrU-1,Iend+1 Awrk(i,j,k,Nold)=A(i,j,k) END DO END DO END DO ! !----------------------------------------------------------------------- ! Integrate horizontal diffusion equation. !----------------------------------------------------------------------- ! DO step=1,NHsteps # ifdef GEOPOTENTIAL_HCONV ! ! Diffusion along geopotential surfaces: Compute horizontal and ! vertical gradients. Notice the recursive blocking sequence. The ! vertical placement of the gradients is: ! ! dAdx,dAde(:,:,k1) k rho-points ! dAdx,dAde(:,:,k2) k+1 rho-points ! FZ,dAdz(:,:,k1) k-1/2 W-points ! FZ,dAdz(:,:,k2) k+1/2 W-points ! k2=1 K_LOOP : DO k=0,N(ng) k1=k2 k2=3-k1 IF (k.lt.N(ng)) THEN DO j=Jstr,Jend DO i=IstrU-1,Iend+1 cff=0.5_r8*(pm(i-1,j)+pm(i,j)) # ifdef MASKING cff=cff*umask(i,j) # endif dZdx(i,j)=cff*(z_r(i ,j,k+1)- & & z_r(i-1,j,k+1)) END DO END DO ! DO j=Jstr,Jend+1 DO i=IstrU-1,Iend cff=0.5_r8*(pn(i,j-1)+pn(i,j)) # ifdef MASKING cff=cff*vmask(i,j) # endif dZde(i,j)=cff*(z_r(i,j ,k+1)- & & z_r(i,j-1,k+1)) END DO END DO ! DO j=Jstr,Jend DO i=IstrU-1,Iend # ifdef MASKING dAdx(i,j,k2)=pm(i,j)* & & (Awrk(i+1,j,k+1,Nold)*umask(i+1,j)- & & Awrk(i ,j,k+1,Nold)*umask(i ,j)) dAdx(i,j,k2)=dAdx(i,j,k2)*rmask(i,j) # else dAdx(i,j,k2)=pm(i,j)*(Awrk(i+1,j,k+1,Nold)- & & Awrk(i ,j,k+1,Nold)) # endif dZdx_r(i,j,k2)=0.5_r8*(dZdx(i ,j)+ & & dZdx(i+1,j)) END DO END DO ! DO j=Jstr,Jend+1 DO i=IstrU,Iend cff=0.25_r8*(pn(i-1,j )+pn(i,j )+ & & pn(i-1,j-1)+pn(i,j-1)) # ifdef MASKING dAde(i,j,k2)=cff* & & (Awrk(i,j ,k+1,Nold)*umask(i,j )- & & Awrk(i,j-1,k+1,Nold)*umask(i,j-1)) dAde(i,j,k2)=dAde(i,j,k2)*pmask(i,j) # else dAde(i,j,k2)=cff*(Awrk(i,j ,k+1,Nold)- & & Awrk(i,j-1,k+1,Nold)) # endif dZde_p(i,j,k2)=0.5_r8*(dZde(i-1,j)+ & & dZde(i ,j)) END DO END DO END IF ! IF ((k.eq.0).or.(k.eq.N(ng))) THEN DO j=Jstr-1,Jend+1 DO i=IstrU-1,Iend+1 dAdz(i,j,k2)=0.0_r8 FZ(i,j,k2)=0.0_r8 END DO END DO ELSE DO j=Jstr-1,Jend+1 DO i=IstrU-1,Iend+1 cff=1.0_r8/(z_r(i,j,k+1)-z_r(i,j,k)) dAdz(i,j,k2)=cff*(Awrk(i,j,k+1,Nold)- & & Awrk(i,j,k ,Nold)) # ifdef MASKING dAdz(i,j,k2)=dAdz(i,j,k2)*umask(i,j) # endif END DO END DO END IF ! ! Compute components of the rotated A flux (A m3/s) along geopotential ! surfaces. ! IF (k.gt.0) THEN DO j=Jstr,Jend DO i=IstrU-1,Iend cff=Kh(i,j)*on_r(i,j) cff1=MIN(dZdx_r(i,j,k1),0.0_r8) cff2=MAX(dZdx_r(i,j,k1),0.0_r8) FX(i,j)=cff* & & Hz(i,j,k)* & & (dAdx(i,j,k1)- & & 0.5_r8*(cff1*(dAdz(i ,j,k1)+ & & dAdz(i+1,j,k2))+ & & cff2*(dAdz(i ,j,k2)+ & & dAdz(i+1,j,k1)))) END DO END DO DO j=Jstr,Jend+1 DO i=IstrU,Iend cff=0.0625_r8*(Kh(i-1,j-1)+Kh(i-1,j)+ & & Kh(i ,j-1)+Kh(i ,j))*om_p(i,j) cff1=MIN(dZde_p(i,j,k1),0.0_r8) cff2=MAX(dZde_p(i,j,k1),0.0_r8) FE(i,j)=cff* & & (Hz(i-1,j-1,k)+Hz(i-1,j,k)+ & & Hz(i ,j-1,k)+Hz(i ,j,k))* & & (dAde(i,j,k1)- & & 0.5_r8*(cff1*(dAdz(i,j-1,k1)+ & & dAdz(i,j ,k2))+ & & cff2*(dAdz(i,j-1,k2)+ & & dAdz(i,j ,k1)))) END DO END DO IF (k.lt.N(ng)) THEN DO j=Jstr,Jend DO i=IstrU,Iend cff=0.25_r8*(Kh(i-1,j)+Kh(i,j)) cff1=MIN(dZdx_r(i-1,j,k1),0.0_r8) cff2=MIN(dZdx_r(i ,j,k2),0.0_r8) cff3=MAX(dZdx_r(i-1,j,k2),0.0_r8) cff4=MAX(dZdx_r(i ,j,k1),0.0_r8) FZ(i,j,k2)=cff* & & (cff1*(cff1*dAdz(i,j,k2)-dAdx(i-1,j,k1))+ & & cff2*(cff2*dAdz(i,j,k2)-dAdx(i ,j,k2))+ & & cff3*(cff3*dAdz(i,j,k2)-dAdx(i-1,j,k2))+ & & cff4*(cff4*dAdz(i,j,k2)-dAdx(i ,j,k1))) cff1=MIN(dZde_p(i,j ,k1),0.0_r8) cff2=MIN(dZde_p(i,j+1,k2),0.0_r8) cff3=MAX(dZde_p(i,j ,k2),0.0_r8) cff4=MAX(dZde_p(i,j+1,k1),0.0_r8) FZ(i,j,k2)=FZ(i,j,k2)+ & & cff* & & (cff1*(cff1*dAdz(i,j,k2)-dAde(i,j ,k1))+ & & cff2*(cff2*dAdz(i,j,k2)-dAde(i,j+1,k2))+ & & cff3*(cff3*dAdz(i,j,k2)-dAde(i,j ,k2))+ & & cff4*(cff4*dAdz(i,j,k2)-dAde(i,j+1,k1))) END DO END DO END IF ! ! Time-step harmonic, geopotential diffusion term (m Tunits). ! DO j=Jstr,Jend DO i=IstrU,Iend Awrk(i,j,k,Nnew)=Awrk(i,j,k,Nold)+ & & Hfac(i,j)* & & (FX(i,j )-FX(i-1,j)+ & & FE(i,j+1)-FE(i ,j))+ & & DTsizeH* & & (FZ(i,j,k2)-FZ(i,j,k1)) END DO END DO END IF END DO K_LOOP # else ! ! Diffusion along S-coordinates: compute XI- and ETA-components of ! diffusive flux. ! DO k=1,N(ng) DO j=Jstr,Jend DO i=IstrU-1,Iend FX(i,j)=pmon_r(i,j)*Kh(i,j)* & & (Awrk(i+1,j,k,Nold)-Awrk(i,j,k,Nold)) END DO END DO DO j=Jstr,Jend+1 DO i=IstrU,Iend FE(i,j)=pnom_p(i,j)*0.25_r8*(Kh(i-1,j )+Kh(i,j )+ & & Kh(i-1,j-1)+Kh(i,j-1))* & & (Awrk(i,j,k,Nold)-Awrk(i,j-1,k,Nold)) # ifdef MASKING FE(i,j)=FE(i,j)*pmask(i,j) # endif END DO END DO ! ! Time-step horizontal diffusion equation. ! DO j=Jstr,Jend DO i=IstrU,Iend Awrk(i,j,k,Nnew)=Awrk(i,j,k,Nold)+ & & Hfac(i,j)* & & (FX(i,j)-FX(i-1,j)+ & & FE(i,j+1)-FE(i,j)) END DO END DO END DO # endif ! ! Apply boundary conditions. ! CALL dabc_u3d_tile (ng, tile, & & LBi, UBi, LBj, UBj, LBk, UBk, & & Awrk(:,:,:,Nnew)) # ifdef DISTRIBUTE CALL mp_exchange3d (ng, tile, model, 1, & & LBi, UBi, LBj, UBj, LBk, UBk, & & Nghost, & & EWperiodic(ng), NSperiodic(ng), & & 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. ! DO j=Jstr,Jend DO k=1,N(ng) DO i=IstrU,Iend Hzk(i,k)=0.5_r8*(Hz(i-1,j,k)+ & & Hz(i ,j,k)) END DO END DO cff1=1.0_r8/6.0_r8 DO k=1,N(ng)-1 DO i=IstrU,Iend FC(i,k)=cff1*Hzk(i,k )-DTsizeV*Kv(i,j,k-1)*oHz(i,j,k ) CF(i,k)=cff1*Hzk(i,k+1)-DTsizeV*Kv(i,j,k+1)*oHz(i,j,k+1) END DO END DO DO i=IstrU,Iend CF(i,0)=0.0_r8 DC(i,0)=0.0_r8 END DO ! ! LU decomposition and forward substitution. ! cff1=1.0_r8/3.0_r8 DO k=1,N(ng)-1 DO i=IstrU,Iend BC(i,k)=cff1*(Hzk(i,k)+Hzk(i,k+1))+ & & DTsizeV*Kv(i,j,k)*(oHz(i,j,k)+oHz(i,j,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,j,k+1,Nold)-Awrk(i,j,k,Nold)- & & FC(i,k)*DC(i,k-1)) END DO END DO ! ! Backward substitution. ! DO i=IstrU,Iend 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) END DO END DO ! DO k=1,N(ng) DO i=IstrU,Iend DC(i,k)=DC(i,k)*Kv(i,j,k) Awrk(i,j,k,Nnew)=Awrk(i,j,k,Nold)+ & & DTsizeV*oHz(i,j,k)* & & (DC(i,k)-DC(i,k-1)) END DO END DO END DO ! ! 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. ! DO j=Jstr,Jend 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,j,k)-FC(i,j,k-1) DC(i,k)=Awrk(i,j,k,Nold)*cff END DO END DO ! ! Solve the tridiagonal system. ! DO i=IstrU,Iend cff=1.0_r8/BC(i,1) CF(i,1)=cff*FC(i,j,1) DC(i,1)=cff*DC(i,1) END DO DO k=2,N(ng)-1 DO i=IstrU,Iend cff=1.0_r8/(BC(i,k)-FC(i,j,k-1)*CF(i,k-1)) CF(i,k)=cff*FC(i,j,k) DC(i,k)=cff*(DC(i,k)-FC(i,j,k-1)*DC(i,k-1)) END DO END DO ! ! Compute new solution by back substitution. ! DO i=IstrU,Iend DC(i,N(ng))=(DC(i,N(ng))- & & FC(i,j,N(ng)-1)*DC(i,N(ng)-1))/ & & (BC(i,N(ng))-FC(i,j,N(ng)-1)*CF(i,N(ng)-1)) Awrk(i,j,N(ng),Nnew)=DC(i,N(ng)) # ifdef MASKING Awrk(i,j,N(ng),Nnew)=Awrk(i,j,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) Awrk(i,j,k,Nnew)=DC(i,k) # ifdef MASKING Awrk(i,j,k,Nnew)=Awrk(i,j,k,Nnew)*umask(i,j) # endif END DO END DO END DO ! ! 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. ! DO j=Jstr,Jend DO k=1,N(ng)-1 DO i=IstrU,Iend FS(i,k)=FC(i,j,k)*(Awrk(i,j,k+1,Nold)- & & Awrk(i,j,k ,Nold)) # ifdef MASKING FS(i,k)=FS(i,k)*umask(i,j) # endif END DO END DO DO i=IstrU,Iend FS(i,0)=0.0_r8 FS(i,N(ng))=0.0_r8 END DO ! ! Time-step vertical diffusive term. Notice that "oHz" is assumed to ! be time invariant. ! DO k=1,N(ng) DO i=IstrU,Iend Awrk(i,j,k,Nnew)=Awrk(i,j,k,Nold)+ & & oHz(i,j,k)*(FS(i,k )- & & FS(i,k-1)) END DO END DO END DO ! ! Update integration indices. ! Nsav=Nold Nold=Nnew Nnew=Nsav END DO # endif # endif ! !----------------------------------------------------------------------- ! Load convolved solution. !----------------------------------------------------------------------- ! DO k=1,N(ng) DO j=Jstr,Jend DO i=IstrU,Iend A(i,j,k)=Awrk(i,j,k,Nold) END DO END DO END DO CALL dabc_u3d_tile (ng, tile, & & LBi, UBi, LBj, UBj, LBk, UBk, & & A) # ifdef DISTRIBUTE CALL mp_exchange3d (ng, tile, model, 1, & & LBi, UBi, LBj, UBj, LBk, UBk, & & Nghost, & & EWperiodic(ng), NSperiodic(ng), & & A) # endif RETURN END SUBROUTINE conv_u3d_tile ! !*********************************************************************** SUBROUTINE conv_v3d_tile (ng, tile, model, & & LBi, UBi, LBj, UBj, LBk, UBk, & & IminS, ImaxS, JminS, JmaxS, & & Nghost, NHsteps, NVsteps, & & DTsizeH, DTsizeV, & & Kh, Kv, & & pm, pn, & # ifdef GEOPOTENTIAL_HCONV & on_p, om_r, & # else & pmon_p, pnom_r, & # endif # ifdef MASKING # ifdef GEOPOTENTIAL_HCONV & pmask, rmask, umask, vmask, & # else & vmask, pmask, & # endif # endif & Hz, z_r, & & A) !*********************************************************************** ! USE mod_param USE mod_scalars ! USE bc_3d_mod, ONLY: dabc_v3d_tile # ifdef DISTRIBUTE USE mp_exchange_mod, ONLY : mp_exchange3d # endif ! ! Imported variable declarations. ! integer, intent(in) :: ng, tile, model 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:) # ifdef GEOPOTENTIAL_HCONV real(r8), intent(in) :: on_p(LBi:,LBj:) real(r8), intent(in) :: om_r(LBi:,LBj:) # else real(r8), intent(in) :: pmon_p(LBi:,LBj:) real(r8), intent(in) :: pnom_r(LBi:,LBj:) # endif # ifdef MASKING # ifdef GEOPOTENTIAL_HCONV real(r8), intent(in) :: pmask(LBi:,LBj:) real(r8), intent(in) :: rmask(LBi:,LBj:) real(r8), intent(in) :: umask(LBi:,LBj:) real(r8), intent(in) :: vmask(LBi:,LBj:) # else real(r8), intent(in) :: vmask(LBi:,LBj:) real(r8), intent(in) :: pmask(LBi:,LBj:) # endif # 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) :: A(LBi:,LBj:,LBk:) # else real(r8), intent(in) :: pm(LBi:UBi,LBj:UBj) real(r8), intent(in) :: pn(LBi:UBi,LBj:UBj) # ifdef GEOPOTENTIAL_HCONV real(r8), intent(in) :: on_p(LBi:UBi,LBj:UBj) real(r8), intent(in) :: om_r(LBi:UBi,LBj:UBj) # else real(r8), intent(in) :: pmon_p(LBi:UBi,LBj:UBj) real(r8), intent(in) :: pnom_r(LBi:UBi,LBj:UBj) # endif # ifdef MASKING # ifdef GEOPOTENTIAL_HCONV real(r8), intent(in) :: pmask(LBi:UBi,LBj:UBj) 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) # else real(r8), intent(in) :: vmask(LBi:UBi,LBj:UBj) real(r8), intent(in) :: pmask(LBi:UBi,LBj:UBj) # endif # 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) :: A(LBi:UBi,LBj:UBj,LBk:UBk) # endif ! ! Local variable declarations. ! integer :: Nnew, Nold, Nsav, i, j, k, k1, k2, step real(r8) :: cff, cff1, cff2, cff3, cff4 real(r8), dimension(LBi:UBi,LBj:UBj,LBk:UBk,2) :: Awrk real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: FE real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: FX real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: Hfac # ifdef VCONVOLUTION # ifndef SPLINES_VCONV real(r8), dimension(IminS:ImaxS,JminS:JmaxS,0:N(ng)) :: FC # endif # if !defined IMPLICIT_VCONV || defined SPLINES_VCONV real(r8), dimension(IminS:ImaxS,JminS:JmaxS,N(ng)) :: oHz # endif # if defined IMPLICIT_VCONV || defined SPLINES_VCONV real(r8), dimension(IminS:ImaxS,0:N(ng)) :: BC real(r8), dimension(IminS:ImaxS,0:N(ng)) :: CF real(r8), dimension(IminS:ImaxS,0:N(ng)) :: DC # ifdef SPLINES_VCONV real(r8), dimension(IminS:ImaxS,0:N(ng)) :: FC real(r8), dimension(IminS:ImaxS,N(ng)) :: Hzk # endif # else real(r8), dimension(IminS:ImaxS,0:N(ng)) :: FS # endif # endif # ifdef GEOPOTENTIAL_HCONV real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: dZdx real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: dZde real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: FZ real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: dAdz real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: dAdx real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: dAde real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: dZdx_p real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: dZde_r # endif # include "set_bounds.h" ! !----------------------------------------------------------------------- ! Space convolution of the diffusion equation for a 3D state variable ! at V-points. !----------------------------------------------------------------------- ! ! 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. ! cff=DTsizeH*0.25_r8 DO j=JstrV-1,Jend+1 DO i=Istr-1,Iend+1 Hfac(i,j)=cff*(pm(i,j-1)+pm(i,j))*(pn(i,j-1)+pn(i,j)) # ifdef VCONVOLUTION # ifndef SPLINES_VCONV FC(i,j,N(ng))=0.0_r8 DO k=1,N(ng)-1 # ifdef IMPLICIT_VCONV FC(i,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(i,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(i,j,0)=0.0_r8 # endif # if !defined IMPLICIT_VCONV || defined SPLINES_VCONV DO k=1,N(ng) oHz(i,j,k)=2.0_r8/(Hz(i,j-1,k)+Hz(i,j,k)) END DO # endif # endif END DO END DO ! ! Set integration indices and initial conditions. ! Nold=1 Nnew=2 CALL dabc_v3d_tile (ng, tile, & & LBi, UBi, LBj, UBj, LBk, UBk, & & A) # ifdef DISTRIBUTE CALL mp_exchange3d (ng, tile, model, 1, & & LBi, UBi, LBj, UBj, LBk, UBk, & & Nghost, & & EWperiodic(ng), NSperiodic(ng), & & A) # endif DO k=1,N(ng) DO j=JstrV-1,Jend+1 DO i=Istr-1,Iend+1 Awrk(i,j,k,Nold)=A(i,j,k) END DO END DO END DO ! !----------------------------------------------------------------------- ! Integrate horizontal diffusion equation. !----------------------------------------------------------------------- ! DO step=1,NHsteps # ifdef GEOPOTENTIAL_HCONV ! ! Diffusion along geopotential surfaces: Compute horizontal and ! vertical gradients. Notice the recursive blocking sequence. The ! vertical placement of the gradients is: ! ! dAdx,dAde(:,:,k1) k rho-points ! dAdx,dAde(:,:,k2) k+1 rho-points ! FZ,dAdz(:,:,k1) k-1/2 W-points ! FZ,dAdz(:,:,k2) k+1/2 W-points ! k2=1 K_LOOP : DO k=0,N(ng) k1=k2 k2=3-k1 IF (k.lt.N(ng)) THEN DO j=JstrV-1,Jend DO i=Istr,Iend+1 cff=0.5_r8*(pm(i-1,j)+pm(i,j)) # ifdef MASKING cff=cff*umask(i,j) # endif dZdx(i,j)=cff*(z_r(i ,j,k+1)- & & z_r(i-1,j,k+1)) END DO END DO ! DO j=JstrV-1,Jend+1 DO i=Istr,Iend cff=0.5_r8*(pn(i,j-1)+pn(i,j)) # ifdef MASKING cff=cff*vmask(i,j) # endif dZde(i,j)=cff*(z_r(i,j ,k+1)- & & z_r(i,j-1,k+1)) END DO END DO ! DO j=JstrV,Jend DO i=Istr,Iend+1 cff=0.25_r8*(pm(i-1,j-1)+pm(i-1,j)+ & & pm(i ,j-1)+pm(i ,j)) # ifdef MASKING dAdx(i,j,k2)=cff* & & (Awrk(i ,j,k+1,Nold)*vmask(i ,j)- & & Awrk(i-1,j,k+1,Nold)*vmask(i-1,j)) dAdx(i,j,k2)=dAdx(i,j,k2)*pmask(i,j) # else dAdx(i,j,k2)=cff*(Awrk(i ,j,k+1,Nold)- & & Awrk(i-1,j,k+1,Nold)) # endif dZdx_p(i,j,k2)=0.5_r8*(dZdx(i,j-1)+ & & dZdx(i,j )) END DO END DO ! DO j=JstrV-1,Jend DO i=Istr,Iend # ifdef MASKING dAde(i,j,k2)=pn(i,j)* & & (Awrk(i,j+1,k+1,Nold)*vmask(i,j+1)- & & Awrk(i,j ,k+1,Nold)*vmask(i,j )) dAde(i,j,k2)=dAde(i,j,k2)*rmask(i,j) # else dAde(i,j,k2)=pn(i,j)*(Awrk(i,j+1,k+1,Nold)- & & Awrk(i,j ,k+1,Nold)) # endif dZde_r(i,j,k2)=0.5_r8*(dZde(i,j )+ & & dZde(i,j+1)) END DO END DO END IF ! IF ((k.eq.0).or.(k.eq.N(ng))) THEN DO j=JstrV-1,Jend+1 DO i=Istr-1,Iend+1 dAdz(i,j,k2)=0.0_r8 FZ(i,j,k2)=0.0_r8 END DO END DO ELSE DO j=JstrV-1,Jend+1 DO i=Istr-1,Iend+1 cff=1.0_r8/(z_r(i,j,k+1)-z_r(i,j,k)) dAdz(i,j,k2)=cff*(Awrk(i,j,k+1,Nold)- & & Awrk(i,j,k ,Nold)) # ifdef MASKING dAdz(i,j,k2)=dAdz(i,j,k2)*vmask(i,j) # endif END DO END DO END IF ! ! Compute components of the rotated A flux (A m3/s) along geopotential ! surfaces. ! IF (k.gt.0) THEN DO j=JstrV,Jend DO i=Istr,Iend+1 cff=0.0625_r8*(Kh(i-1,j-1)+Kh(i-1,j)+ & & Kh(i ,j-1)+Kh(i ,j))*on_p(i,j) cff1=MIN(dZdx_p(i,j,k1),0.0_r8) cff2=MAX(dZdx_p(i,j,k1),0.0_r8) FX(i,j)=cff* & & (Hz(i-1,j-1,k)+Hz(i-1,j,k)+ & & Hz(i ,j-1,k)+Hz(i ,j,k))* & & (dAdx(i,j,k1)- & & 0.5_r8*(cff1*(dAdz(i-1,j,k1)+ & & dAdz(i ,j,k2))+ & & cff2*(dAdz(i-1,j,k2)+ & & dAdz(i ,j,k1)))) END DO END DO DO j=JstrV-1,Jend DO i=Istr,Iend cff=Kh(i,j)*om_r(i,j) cff1=MIN(dZde_r(i,j,k1),0.0_r8) cff2=MAX(dZde_r(i,j,k1),0.0_r8) FE(i,j)=cff* & & Hz(i,j,k)* & & (dAde(i,j,k1)- & & 0.5_r8*(cff1*(dAdz(i,j ,k1)+ & & dAdz(i,j+1,k2))+ & & cff2*(dAdz(i,j ,k2)+ & & dAdz(i,j+1,k1)))) END DO END DO IF (k.lt.N(ng)) THEN DO j=JstrV,Jend DO i=Istr,Iend cff=0.5_r8*(Kh(i,j-1)+Kh(i,j)) cff1=MIN(dZdx_p(i ,j,k1),0.0_r8) cff2=MIN(dZdx_p(i+1,j,k2),0.0_r8) cff3=MAX(dZdx_p(i ,j,k2),0.0_r8) cff4=MAX(dZdx_p(i+1,j,k1),0.0_r8) FZ(i,j,k2)=cff* & & (cff1*(cff1*dAdz(i,j,k2)-dAdx(i ,j,k1))+ & & cff2*(cff2*dAdz(i,j,k2)-dAdx(i+1,j,k2))+ & & cff3*(cff3*dAdz(i,j,k2)-dAdx(i ,j,k2))+ & & cff4*(cff4*dAdz(i,j,k2)-dAdx(i+1,j,k1))) cff1=MIN(dZde_r(i,j-1,k1),0.0_r8) cff2=MIN(dZde_r(i,j ,k2),0.0_r8) cff3=MAX(dZde_r(i,j-1,k2),0.0_r8) cff4=MAX(dZde_r(i,j ,k1),0.0_r8) FZ(i,j,k2)=FZ(i,j,k2)+ & & cff* & & (cff1*(cff1*dAdz(i,j,k2)-dAde(i,j-1,k1))+ & & cff2*(cff2*dAdz(i,j,k2)-dAde(i,j ,k2))+ & & cff3*(cff3*dAdz(i,j,k2)-dAde(i,j-1,k2))+ & & cff4*(cff4*dAdz(i,j,k2)-dAde(i,j ,k1))) END DO END DO END IF ! ! Time-step harmonic, geopotential diffusion term (m Tunits). ! DO j=JstrV,Jend DO i=Istr,Iend Awrk(i,j,k,Nnew)=Awrk(i,j,k,Nold)+ & & Hfac(i,j)* & & (FX(i+1,j)-FX(i,j )+ & & FE(i ,j)-FE(i,j-1))+ & & DTsizeH* & & (FZ(i,j,k2)-FZ(i,j,k1)) END DO END DO END IF END DO K_LOOP # else ! ! Compute XI- and ETA-components of diffusive flux. ! DO k=1,N(ng) DO j=JstrV,Jend DO i=Istr,Iend+1 FX(i,j)=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,j,k,Nold)-Awrk(i-1,j,k,Nold)) # ifdef MASKING FX(i,j)=FX(i,j)*pmask(i,j) # endif END DO END DO DO j=JstrV-1,Jend DO i=Istr,Iend FE(i,j)=pnom_r(i,j)*Kh(i,j)* & & (Awrk(i,j+1,k,Nold)-Awrk(i,j,k,Nold)) END DO END DO ! ! Time-step horizontal diffusion equation. ! DO j=JstrV,Jend DO i=Istr,Iend Awrk(i,j,k,Nnew)=Awrk(i,j,k,Nold)+ & & Hfac(i,j)* & & (FX(i+1,j)-FX(i,j)+ & & FE(i,j)-FE(i,j-1)) END DO END DO END DO # endif ! ! Apply boundary conditions. ! CALL dabc_v3d_tile (ng, tile, & & LBi, UBi, LBj, UBj, LBk, UBk, & & Awrk(:,:,:,Nnew)) # ifdef DISTRIBUTE CALL mp_exchange3d (ng, tile, model, 1, & & LBi, UBi, LBj, UBj, LBk, UBk, & & Nghost, & & EWperiodic(ng), NSperiodic(ng), & & 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. ! DO j=JstrV,Jend DO k=1,N(ng) DO i=Istr,Iend Hzk(i,k)=0.5_r8*(Hz(i,j-1,k)+ & & Hz(i,j ,k)) END DO END DO cff1=1.0_r8/6.0_r8 DO k=1,N(ng)-1 DO i=Istr,Iend FC(i,k)=cff1*Hzk(i,k )-DTsizeV*Kv(i,j,k-1)*oHz(i,j,k ) CF(i,k)=cff1*Hzk(i,k+1)-DTsizeV*Kv(i,j,k+1)*oHz(i,j,k+1) END DO END DO DO i=Istr,Iend CF(i,0)=0.0_r8 DC(i,0)=0.0_r8 END DO ! ! LU decomposition and forward substitution. ! cff1=1.0_r8/3.0_r8 DO k=1,N(ng)-1 DO i=Istr,Iend BC(i,k)=cff1*(Hzk(i,k)+Hzk(i,k+1))+ & & DTsizeV*Kv(i,j,k)*(oHz(i,j,k)+oHz(i,j,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,j,k+1,Nold)-Awrk(i,j,k,Nold)- & & FC(i,k)*DC(i,k-1)) END DO END DO ! ! Backward substitution. ! DO i=Istr,Iend 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) END DO END DO ! DO k=1,N(ng) DO i=Istr,Iend DC(i,k)=DC(i,k)*Kv(i,j,k) Awrk(i,j,k,Nnew)=Awrk(i,j,k,Nold)+ & & DTsizeV*oHz(i,j,k)* & & (DC(i,k)-DC(i,k-1)) END DO END DO END DO ! ! Update integration indices. ! Nsav=Nold Nold=Nnew Nnew=Nsav END DO # else ! !----------------------------------------------------------------------- ! Integerate 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. ! DO j=JstrV,Jend 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,j,k)-FC(i,j,k-1) DC(i,k)=Awrk(i,j,k,Nold)*cff END DO END DO ! ! Solve the tridiagonal system. ! DO i=Istr,Iend cff=1.0_r8/BC(i,1) CF(i,1)=cff*FC(i,j,1) DC(i,1)=cff*DC(i,1) END DO DO k=2,N(ng)-1 DO i=Istr,Iend cff=1.0_r8/(BC(i,k)-FC(i,j,k-1)*CF(i,k-1)) CF(i,k)=cff*FC(i,j,k) DC(i,k)=cff*(DC(i,k)-FC(i,j,k-1)*DC(i,k-1)) END DO END DO ! ! Compute new solution by back substitution. ! DO i=Istr,Iend DC(i,N(ng))=(DC(i,N(ng))- & & FC(i,j,N(ng)-1)*DC(i,N(ng)-1))/ & & (BC(i,N(ng))-FC(i,j,N(ng)-1)*CF(i,N(ng)-1)) Awrk(i,j,N(ng),Nnew)=DC(i,N(ng)) # ifdef MASKING Awrk(i,j,N(ng),Nnew)=Awrk(i,j,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) Awrk(i,j,k,Nnew)=DC(i,k) # ifdef MASKING Awrk(i,j,k,Nnew)=Awrk(i,j,k,Nnew)*vmask(i,j) # endif END DO END DO END DO ! ! Update integration indices. ! Nsav=Nold Nold=Nnew Nnew=Nsav END DO # endif # else ! !----------------------------------------------------------------------- ! Integerate vertical diffusion equation explicitly. !----------------------------------------------------------------------- ! DO step=1,NVsteps ! ! Compute vertical diffusive flux. Notice that "FC" is assumed to ! be time invariant. ! DO j=JstrV,Jend DO k=1,N(ng)-1 DO i=Istr,Iend FS(i,k)=FC(i,j,k)*(Awrk(i,j,k+1,Nold)- & & Awrk(i,j,k ,Nold)) # ifdef MASKING FS(i,k)=FS(i,k)*vmask(i,j) # endif END DO END DO DO i=Istr,Iend FS(i,0)=0.0_r8 FS(i,N(ng))=0.0_r8 END DO ! ! Time-step vertical diffusive term. Notice that "oHz" is assumed to ! be time invariant. ! DO k=1,N(ng) DO i=Istr,Iend Awrk(i,j,k,Nnew)=Awrk(i,j,k,Nold)+ & & oHz(i,j,k)*(FS(i,k )- & & FS(i,k-1)) END DO END DO END DO ! ! Update integration indices. ! Nsav=Nold Nold=Nnew Nnew=Nsav END DO # endif # endif ! !----------------------------------------------------------------------- ! Load convolved solution. !----------------------------------------------------------------------- ! DO k=1,N(ng) DO j=JstrV,Jend DO i=Istr,Iend A(i,j,k)=Awrk(i,j,k,Nold) END DO END DO END DO CALL dabc_v3d_tile (ng, tile, & & LBi, UBi, LBj, UBj, LBk, UBk, & & A) # ifdef DISTRIBUTE CALL mp_exchange3d (ng, tile, model, 1, & & LBi, UBi, LBj, UBj, LBk, UBk, & & Nghost, & & EWperiodic(ng), NSperiodic(ng), & & A) # endif RETURN END SUBROUTINE conv_v3d_tile #endif END MODULE conv_3d_mod