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bdylib.F90
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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