MODULE bdylib !!====================================================================== !! *** MODULE bdylib *** !! Unstructured Open Boundary Cond. : Library module of generic boundary algorithms. !!====================================================================== !! History : 3.6 ! 2013 (D. Storkey) new module !!---------------------------------------------------------------------- #if defined key_bdy !!---------------------------------------------------------------------- !! 'key_bdy' : Unstructured Open Boundary Condition !!---------------------------------------------------------------------- !! bdy_orlanski_2d !! bdy_orlanski_3d !!---------------------------------------------------------------------- USE timing ! Timing USE oce ! ocean dynamics and tracers USE dom_oce ! ocean space and time domain USE bdy_oce ! ocean open boundary conditions USE phycst ! physical constants USE lbclnk ! ocean lateral boundary conditions (or mpp link) USE in_out_manager ! IMPLICIT NONE PRIVATE PUBLIC bdy_orlanski_2d ! routine called where? PUBLIC bdy_orlanski_3d ! routine called where? !!---------------------------------------------------------------------- !! NEMO/OPA 3.3 , NEMO Consortium (2010) !! $Id$ !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) !!---------------------------------------------------------------------- CONTAINS SUBROUTINE bdy_orlanski_2d( idx, igrd, phib, phia, phi_ext, ll_npo ) !!---------------------------------------------------------------------- !! *** SUBROUTINE bdy_orlanski_2d *** !! !! - Apply Orlanski radiation condition adaptively to 2D fields: !! - radiation plus weak nudging at outflow points !! - no radiation and strong nudging at inflow points !! !! !! References: Marchesiello, McWilliams and Shchepetkin, Ocean Modelling vol. 3 (2001) !!---------------------------------------------------------------------- TYPE(OBC_INDEX), INTENT(in) :: idx ! BDY indices INTEGER, INTENT(in) :: igrd ! grid index REAL(wp), DIMENSION(:,:), INTENT(in) :: phib ! model before 2D field REAL(wp), DIMENSION(:,:), INTENT(inout) :: phia ! model after 2D field (to be updated) REAL(wp), DIMENSION(:), INTENT(in) :: phi_ext ! external forcing data LOGICAL, INTENT(in) :: ll_npo ! switch for NPO version INTEGER :: jb ! dummy loop indices INTEGER :: ii, ij, iibm1, iibm2, ijbm1, ijbm2 ! 2D addresses INTEGER :: iijm1, iijp1, ijjm1, ijjp1 ! 2D addresses INTEGER :: iibm1jp1, iibm1jm1, ijbm1jp1, ijbm1jm1 ! 2D addresses INTEGER :: ii_offset, ij_offset ! offsets for mask indices INTEGER :: flagu, flagv ! short cuts REAL(wp) :: zmask_x, zmask_y1, zmask_y2 REAL(wp) :: zex1, zex2, zey, zey1, zey2 REAL(wp) :: zdt, zdx, zdy, znor2, zrx, zry ! intermediate calculations REAL(wp) :: zout, zwgt, zdy_centred REAL(wp) :: zdy_1, zdy_2, zsign_ups REAL(wp), PARAMETER :: zepsilon = 1.e-30 ! local small value REAL(wp), POINTER, DIMENSION(:,:) :: pmask ! land/sea mask for field REAL(wp), POINTER, DIMENSION(:,:) :: pmask_xdif ! land/sea mask for x-derivatives REAL(wp), POINTER, DIMENSION(:,:) :: pmask_ydif ! land/sea mask for y-derivatives REAL(wp), POINTER, DIMENSION(:,:) :: pe_xdif ! scale factors for x-derivatives REAL(wp), POINTER, DIMENSION(:,:) :: pe_ydif ! scale factors for y-derivatives !!---------------------------------------------------------------------- IF( nn_timing == 1 ) CALL timing_start('bdy_orlanski_2d') ! ----------------------------------! ! Orlanski boundary conditions :! ! ----------------------------------! SELECT CASE(igrd) CASE(1) pmask => tmask(:,:,1) pmask_xdif => umask(:,:,1) pmask_ydif => vmask(:,:,1) pe_xdif => e1u(:,:) pe_ydif => e2v(:,:) ii_offset = 0 ij_offset = 0 CASE(2) pmask => umask(:,:,1) pmask_xdif => tmask(:,:,1) pmask_ydif => fmask(:,:,1) pe_xdif => e1t(:,:) pe_ydif => e2f(:,:) ii_offset = 1 ij_offset = 0 CASE(3) pmask => vmask(:,:,1) pmask_xdif => fmask(:,:,1) pmask_ydif => tmask(:,:,1) pe_xdif => e1f(:,:) pe_ydif => e2t(:,:) ii_offset = 0 ij_offset = 1 CASE DEFAULT ; CALL ctl_stop( 'unrecognised value for igrd in bdy_orlanksi_2d' ) END SELECT ! DO jb = 1, idx%nblenrim(igrd) ii = idx%nbi(jb,igrd) ij = idx%nbj(jb,igrd) flagu = int( idx%flagu(jb,igrd) ) flagv = int( idx%flagv(jb,igrd) ) ! ! Calculate positions of b-1 and b-2 points for this rim point ! also (b-1,j-1) and (b-1,j+1) points iibm1 = ii + flagu ; iibm2 = ii + 2*flagu ijbm1 = ij + flagv ; ijbm2 = ij + 2*flagv ! iijm1 = ii - abs(flagv) ; iijp1 = ii + abs(flagv) ijjm1 = ij - abs(flagu) ; ijjp1 = ij + abs(flagu) ! iibm1jm1 = ii + flagu - abs(flagv) ; iibm1jp1 = ii + flagu + abs(flagv) ijbm1jm1 = ij + flagv - abs(flagu) ; ijbm1jp1 = ij + flagv + abs(flagu) ! ! Calculate scale factors for calculation of spatial derivatives. zex1 = ( abs(iibm1-iibm2) * pe_xdif(iibm1+ii_offset,ijbm1 ) & & + abs(ijbm1-ijbm2) * pe_ydif(iibm1 ,ijbm1+ij_offset) ) zex2 = ( abs(iibm1-iibm2) * pe_xdif(iibm2+ii_offset,ijbm2 ) & & + abs(ijbm1-ijbm2) * pe_ydif(iibm2 ,ijbm2+ij_offset) ) zey1 = ( (iibm1-iibm1jm1) * pe_xdif(iibm1jm1+ii_offset,ijbm1jm1 ) & & + (ijbm1-ijbm1jm1) * pe_ydif(iibm1jm1 ,ijbm1jm1+ij_offset) ) zey2 = ( (iibm1jp1-iibm1) * pe_xdif(iibm1+ii_offset,ijbm1) & & + (ijbm1jp1-ijbm1) * pe_ydif(iibm1 ,ijbm1+ij_offset) ) ! make sure scale factors are nonzero if( zey1 .lt. rsmall ) zey1 = zey2 if( zey2 .lt. rsmall ) zey2 = zey1 zex1 = max(zex1,rsmall); zex2 = max(zex2,rsmall) zey1 = max(zey1,rsmall); zey2 = max(zey2,rsmall); ! ! Calculate masks for calculation of spatial derivatives. zmask_x = ( abs(iibm1-iibm2) * pmask_xdif(iibm2+ii_offset,ijbm2 ) & & + abs(ijbm1-ijbm2) * pmask_ydif(iibm2 ,ijbm2+ij_offset) ) zmask_y1 = ( (iibm1-iibm1jm1) * pmask_xdif(iibm1jm1+ii_offset,ijbm1jm1 ) & & + (ijbm1-ijbm1jm1) * pmask_ydif(iibm1jm1 ,ijbm1jm1+ij_offset) ) zmask_y2 = ( (iibm1jp1-iibm1) * pmask_xdif(iibm1+ii_offset,ijbm1) & & + (ijbm1jp1-ijbm1) * pmask_ydif(iibm1 ,ijbm1+ij_offset) ) ! Calculation of terms required for both versions of the scheme. ! Mask derivatives to ensure correct land boundary conditions for each variable. ! Centred derivative is calculated as average of "left" and "right" derivatives for ! this reason. ! Note no rdt factor in expression for zdt because it cancels in the expressions for ! zrx and zry. zdt = phia(iibm1,ijbm1) - phib(iibm1,ijbm1) zdx = ( ( phia(iibm1,ijbm1) - phia(iibm2,ijbm2) ) / zex2 ) * zmask_x zdy_1 = ( ( phib(iibm1 ,ijbm1 ) - phib(iibm1jm1,ijbm1jm1) ) / zey1 ) * zmask_y1 zdy_2 = ( ( phib(iibm1jp1,ijbm1jp1) - phib(iibm1 ,ijbm1) ) / zey2 ) * zmask_y2 zdy_centred = 0.5 * ( zdy_1 + zdy_2 ) !!$ zdy_centred = phib(iibm1jp1,ijbm1jp1) - phib(iibm1jm1,ijbm1jm1) ! upstream differencing for tangential derivatives zsign_ups = sign( 1., zdt * zdy_centred ) zsign_ups = 0.5*( zsign_ups + abs(zsign_ups) ) zdy = zsign_ups * zdy_1 + (1. - zsign_ups) * zdy_2 znor2 = zdx * zdx + zdy * zdy znor2 = max(znor2,zepsilon) ! zrx = zdt * zdx / ( zex1 * znor2 ) !!$ zrx = min(zrx,2.0_wp) zout = sign( 1., zrx ) zout = 0.5*( zout + abs(zout) ) zwgt = 2.*rdt*( (1.-zout) * idx%nbd(jb,igrd) + zout * idx%nbdout(jb,igrd) ) ! only apply radiation on outflow points if( ll_npo ) then !! NPO version !! phia(ii,ij) = (1.-zout) * ( phib(ii,ij) + zwgt * ( phi_ext(jb) - phib(ii,ij) ) ) & & + zout * ( phib(ii,ij) + zrx*phia(iibm1,ijbm1) & & + zwgt * ( phi_ext(jb) - phib(ii,ij) ) ) / ( 1. + zrx ) else !! full oblique radiation !! zsign_ups = sign( 1., zdt * zdy ) zsign_ups = 0.5*( zsign_ups + abs(zsign_ups) ) zey = zsign_ups * zey1 + (1.-zsign_ups) * zey2 zry = zdt * zdy / ( zey * znor2 ) phia(ii,ij) = (1.-zout) * ( phib(ii,ij) + zwgt * ( phi_ext(jb) - phib(ii,ij) ) ) & & + zout * ( phib(ii,ij) + zrx*phia(iibm1,ijbm1) & & - zsign_ups * zry * ( phib(ii ,ij ) - phib(iijm1,ijjm1 ) ) & & - (1.-zsign_ups) * zry * ( phib(iijp1,ijjp1) - phib(ii ,ij ) ) & & + zwgt * ( phi_ext(jb) - phib(ii,ij) ) ) / ( 1. + zrx ) end if phia(ii,ij) = phia(ii,ij) * pmask(ii,ij) END DO ! IF( nn_timing == 1 ) CALL timing_stop('bdy_orlanski_2d') END SUBROUTINE bdy_orlanski_2d SUBROUTINE bdy_orlanski_3d( idx, igrd, phib, phia, phi_ext, ll_npo ) !!---------------------------------------------------------------------- !! *** SUBROUTINE bdy_orlanski_3d *** !! !! - Apply Orlanski radiation condition adaptively to 3D fields: !! - radiation plus weak nudging at outflow points !! - no radiation and strong nudging at inflow points !! !! !! References: Marchesiello, McWilliams and Shchepetkin, Ocean Modelling vol. 3 (2001) !!---------------------------------------------------------------------- TYPE(OBC_INDEX), INTENT(in) :: idx ! BDY indices INTEGER, INTENT(in) :: igrd ! grid index REAL(wp), DIMENSION(:,:,:), INTENT(in) :: phib ! model before 3D field REAL(wp), DIMENSION(:,:,:), INTENT(inout) :: phia ! model after 3D field (to be updated) REAL(wp), DIMENSION(:,:), INTENT(in) :: phi_ext ! external forcing data LOGICAL, INTENT(in) :: ll_npo ! switch for NPO version INTEGER :: jb, jk ! dummy loop indices INTEGER :: ii, ij, iibm1, iibm2, ijbm1, ijbm2 ! 2D addresses INTEGER :: iijm1, iijp1, ijjm1, ijjp1 ! 2D addresses INTEGER :: iibm1jp1, iibm1jm1, ijbm1jp1, ijbm1jm1 ! 2D addresses INTEGER :: ii_offset, ij_offset ! offsets for mask indices INTEGER :: flagu, flagv ! short cuts REAL(wp) :: zmask_x, zmask_y1, zmask_y2 REAL(wp) :: zex1, zex2, zey, zey1, zey2 REAL(wp) :: zdt, zdx, zdy, znor2, zrx, zry ! intermediate calculations REAL(wp) :: zout, zwgt, zdy_centred REAL(wp) :: zdy_1, zdy_2, zsign_ups REAL(wp), PARAMETER :: zepsilon = 1.e-30 ! local small value REAL(wp), POINTER, DIMENSION(:,:,:) :: pmask ! land/sea mask for field REAL(wp), POINTER, DIMENSION(:,:,:) :: pmask_xdif ! land/sea mask for x-derivatives REAL(wp), POINTER, DIMENSION(:,:,:) :: pmask_ydif ! land/sea mask for y-derivatives REAL(wp), POINTER, DIMENSION(:,:) :: pe_xdif ! scale factors for x-derivatives REAL(wp), POINTER, DIMENSION(:,:) :: pe_ydif ! scale factors for y-derivatives !!---------------------------------------------------------------------- IF( nn_timing == 1 ) CALL timing_start('bdy_orlanski_3d') ! ----------------------------------! ! Orlanski boundary conditions :! ! ----------------------------------! SELECT CASE(igrd) CASE(1) pmask => tmask(:,:,:) pmask_xdif => umask(:,:,:) pmask_ydif => vmask(:,:,:) pe_xdif => e1u(:,:) pe_ydif => e2v(:,:) ii_offset = 0 ij_offset = 0 CASE(2) pmask => umask(:,:,:) pmask_xdif => tmask(:,:,:) pmask_ydif => fmask(:,:,:) pe_xdif => e1t(:,:) pe_ydif => e2f(:,:) ii_offset = 1 ij_offset = 0 CASE(3) pmask => vmask(:,:,:) pmask_xdif => fmask(:,:,:) pmask_ydif => tmask(:,:,:) pe_xdif => e1f(:,:) pe_ydif => e2t(:,:) ii_offset = 0 ij_offset = 1 CASE DEFAULT ; CALL ctl_stop( 'unrecognised value for igrd in bdy_orlanksi_2d' ) END SELECT DO jk = 1, jpk ! DO jb = 1, idx%nblenrim(igrd) ii = idx%nbi(jb,igrd) ij = idx%nbj(jb,igrd) flagu = int( idx%flagu(jb,igrd) ) flagv = int( idx%flagv(jb,igrd) ) ! ! calculate positions of b-1 and b-2 points for this rim point ! also (b-1,j-1) and (b-1,j+1) points iibm1 = ii + flagu ; iibm2 = ii + 2*flagu ijbm1 = ij + flagv ; ijbm2 = ij + 2*flagv ! iijm1 = ii - abs(flagv) ; iijp1 = ii + abs(flagv) ijjm1 = ij - abs(flagu) ; ijjp1 = ij + abs(flagu) ! iibm1jm1 = ii + flagu - abs(flagv) ; iibm1jp1 = ii + flagu + abs(flagv) ijbm1jm1 = ij + flagv - abs(flagu) ; ijbm1jp1 = ij + flagv + abs(flagu) ! ! Calculate scale factors for calculation of spatial derivatives. zex1 = ( abs(iibm1-iibm2) * pe_xdif(iibm1+ii_offset,ijbm1 ) & & + abs(ijbm1-ijbm2) * pe_ydif(iibm1 ,ijbm1+ij_offset) ) zex2 = ( abs(iibm1-iibm2) * pe_xdif(iibm2+ii_offset,ijbm2 ) & & + abs(ijbm1-ijbm2) * pe_ydif(iibm2 ,ijbm2+ij_offset) ) zey1 = ( (iibm1-iibm1jm1) * pe_xdif(iibm1jm1+ii_offset,ijbm1jm1 ) & & + (ijbm1-ijbm1jm1) * pe_ydif(iibm1jm1 ,ijbm1jm1+ij_offset) ) zey2 = ( (iibm1jp1-iibm1) * pe_xdif(iibm1+ii_offset,ijbm1) & & + (ijbm1jp1-ijbm1) * pe_ydif(iibm1 ,ijbm1+ij_offset) ) ! make sure scale factors are nonzero if( zey1 .lt. rsmall ) zey1 = zey2 if( zey2 .lt. rsmall ) zey2 = zey1 zex1 = max(zex1,rsmall); zex2 = max(zex2,rsmall); zey1 = max(zey1,rsmall); zey2 = max(zey2,rsmall); ! ! Calculate masks for calculation of spatial derivatives. zmask_x = ( abs(iibm1-iibm2) * pmask_xdif(iibm2+ii_offset,ijbm2 ,jk) & & + abs(ijbm1-ijbm2) * pmask_ydif(iibm2 ,ijbm2+ij_offset,jk) ) zmask_y1 = ( (iibm1-iibm1jm1) * pmask_xdif(iibm1jm1+ii_offset,ijbm1jm1 ,jk) & & + (ijbm1-ijbm1jm1) * pmask_ydif(iibm1jm1 ,ijbm1jm1+ij_offset,jk) ) zmask_y2 = ( (iibm1jp1-iibm1) * pmask_xdif(iibm1+ii_offset,ijbm1 ,jk) & & + (ijbm1jp1-ijbm1) * pmask_ydif(iibm1 ,ijbm1+ij_offset,jk) ) ! ! Calculate normal (zrx) and tangential (zry) components of radiation velocities. ! Mask derivatives to ensure correct land boundary conditions for each variable. ! Centred derivative is calculated as average of "left" and "right" derivatives for ! this reason. zdt = phia(iibm1,ijbm1,jk) - phib(iibm1,ijbm1,jk) zdx = ( ( phia(iibm1,ijbm1,jk) - phia(iibm2,ijbm2,jk) ) / zex2 ) * zmask_x zdy_1 = ( ( phib(iibm1 ,ijbm1 ,jk) - phib(iibm1jm1,ijbm1jm1,jk) ) / zey1 ) * zmask_y1 zdy_2 = ( ( phib(iibm1jp1,ijbm1jp1,jk) - phib(iibm1 ,ijbm1 ,jk) ) / zey2 ) * zmask_y2 zdy_centred = 0.5 * ( zdy_1 + zdy_2 ) !!$ zdy_centred = phib(iibm1jp1,ijbm1jp1,jk) - phib(iibm1jm1,ijbm1jm1,jk) ! upstream differencing for tangential derivatives zsign_ups = sign( 1., zdt * zdy_centred ) zsign_ups = 0.5*( zsign_ups + abs(zsign_ups) ) zdy = zsign_ups * zdy_1 + (1. - zsign_ups) * zdy_2 znor2 = zdx * zdx + zdy * zdy znor2 = max(znor2,zepsilon) ! ! update boundary value: zrx = zdt * zdx / ( zex1 * znor2 ) !!$ zrx = min(zrx,2.0_wp) zout = sign( 1., zrx ) zout = 0.5*( zout + abs(zout) ) zwgt = 2.*rdt*( (1.-zout) * idx%nbd(jb,igrd) + zout * idx%nbdout(jb,igrd) ) ! only apply radiation on outflow points if( ll_npo ) then !! NPO version !! phia(ii,ij,jk) = (1.-zout) * ( phib(ii,ij,jk) + zwgt * ( phi_ext(jb,jk) - phib(ii,ij,jk) ) ) & & + zout * ( phib(ii,ij,jk) + zrx*phia(iibm1,ijbm1,jk) & & + zwgt * ( phi_ext(jb,jk) - phib(ii,ij,jk) ) ) / ( 1. + zrx ) else !! full oblique radiation !! zsign_ups = sign( 1., zdt * zdy ) zsign_ups = 0.5*( zsign_ups + abs(zsign_ups) ) zey = zsign_ups * zey1 + (1.-zsign_ups) * zey2 zry = zdt * zdy / ( zey * znor2 ) phia(ii,ij,jk) = (1.-zout) * ( phib(ii,ij,jk) + zwgt * ( phi_ext(jb,jk) - phib(ii,ij,jk) ) ) & & + zout * ( phib(ii,ij,jk) + zrx*phia(iibm1,ijbm1,jk) & & - zsign_ups * zry * ( phib(ii ,ij ,jk) - phib(iijm1,ijjm1,jk) ) & & - (1.-zsign_ups) * zry * ( phib(iijp1,ijjp1,jk) - phib(ii ,ij ,jk) ) & & + zwgt * ( phi_ext(jb,jk) - phib(ii,ij,jk) ) ) / ( 1. + zrx ) end if phia(ii,ij,jk) = phia(ii,ij,jk) * pmask(ii,ij,jk) END DO ! END DO IF( nn_timing == 1 ) CALL timing_stop('bdy_orlanski_3d') END SUBROUTINE bdy_orlanski_3d #else !!---------------------------------------------------------------------- !! Dummy module NO Unstruct Open Boundary Conditions !!---------------------------------------------------------------------- CONTAINS SUBROUTINE bdy_orlanski_2d( idx, igrd, phib, phia, phi_ext ) ! Empty routine WRITE(*,*) 'bdy_orlanski_2d: You should not have seen this print! error?', kt END SUBROUTINE bdy_orlanski_2d SUBROUTINE bdy_orlanski_3d( idx, igrd, phib, phia, phi_ext ) ! Empty routine WRITE(*,*) 'bdy_orlanski_3d: You should not have seen this print! error?', kt END SUBROUTINE bdy_orlanski_3d #endif !!====================================================================== END MODULE bdylib