| 1 | MODULE bdylib |
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| 2 | !!====================================================================== |
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| 3 | !! *** MODULE bdylib *** |
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| 4 | !! Unstructured Open Boundary Cond. : Library module of generic boundary algorithms. |
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| 5 | !!====================================================================== |
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| 6 | !! History : 3.6 ! 2013 (D. Storkey) original code |
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| 7 | !! 4.0 ! 2014 (T. Lovato) Generalize OBC structure |
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| 8 | !!---------------------------------------------------------------------- |
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| 9 | !!---------------------------------------------------------------------- |
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| 10 | !! bdy_orlanski_2d |
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| 11 | !! bdy_orlanski_3d |
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| 12 | !!---------------------------------------------------------------------- |
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| 13 | USE oce ! ocean dynamics and tracers |
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| 14 | USE dom_oce ! ocean space and time domain |
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| 15 | USE bdy_oce ! ocean open boundary conditions |
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| 16 | USE phycst ! physical constants |
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| 17 | ! |
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| 18 | USE in_out_manager ! |
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| 19 | USE lbclnk ! ocean lateral boundary conditions (or mpp link) |
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| 20 | USE lib_mpp, ONLY: ctl_stop |
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| 21 | |
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| 22 | IMPLICIT NONE |
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| 23 | PRIVATE |
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| 24 | |
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| 25 | PUBLIC bdy_frs, bdy_spe, bdy_nmn, bdy_orl |
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| 26 | PUBLIC bdy_orlanski_2d |
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| 27 | PUBLIC bdy_orlanski_3d |
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| 28 | |
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| 29 | !!---------------------------------------------------------------------- |
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| 30 | !! NEMO/OCE 4.0 , NEMO Consortium (2018) |
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| 31 | !! $Id$ |
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| 32 | !! Software governed by the CeCILL license (see ./LICENSE) |
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| 33 | !!---------------------------------------------------------------------- |
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| 34 | CONTAINS |
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| 35 | |
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| 36 | SUBROUTINE bdy_frs( idx, pta, dta ) |
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| 37 | !!---------------------------------------------------------------------- |
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| 38 | !! *** SUBROUTINE bdy_frs *** |
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| 39 | !! |
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| 40 | !! ** Purpose : Apply the Flow Relaxation Scheme for tracers at open boundaries. |
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| 41 | !! |
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| 42 | !! Reference : Engedahl H., 1995, Tellus, 365-382. |
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| 43 | !!---------------------------------------------------------------------- |
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| 44 | TYPE(OBC_INDEX), INTENT(in) :: idx ! OBC indices |
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| 45 | REAL(wp), DIMENSION(:,:), INTENT(in) :: dta ! OBC external data |
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| 46 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(inout) :: pta ! tracer trend |
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| 47 | !! |
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| 48 | REAL(wp) :: zwgt ! boundary weight |
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| 49 | INTEGER :: ib, ik, igrd ! dummy loop indices |
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| 50 | INTEGER :: ii, ij ! 2D addresses |
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| 51 | !!---------------------------------------------------------------------- |
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| 52 | ! |
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| 53 | igrd = 1 ! Everything is at T-points here |
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| 54 | DO ib = 1, idx%nblen(igrd) |
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| 55 | DO ik = 1, jpkm1 |
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| 56 | ii = idx%nbi(ib,igrd) |
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| 57 | ij = idx%nbj(ib,igrd) |
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| 58 | zwgt = idx%nbw(ib,igrd) |
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| 59 | pta(ii,ij,ik) = ( pta(ii,ij,ik) + zwgt * (dta(ib,ik) - pta(ii,ij,ik) ) ) * tmask(ii,ij,ik) |
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| 60 | END DO |
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| 61 | END DO |
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| 62 | ! |
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| 63 | END SUBROUTINE bdy_frs |
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| 64 | |
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| 65 | |
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| 66 | SUBROUTINE bdy_spe( idx, pta, dta ) |
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| 67 | !!---------------------------------------------------------------------- |
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| 68 | !! *** SUBROUTINE bdy_spe *** |
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| 69 | !! |
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| 70 | !! ** Purpose : Apply a specified value for tracers at open boundaries. |
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| 71 | !! |
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| 72 | !!---------------------------------------------------------------------- |
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| 73 | TYPE(OBC_INDEX), INTENT(in) :: idx ! OBC indices |
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| 74 | REAL(wp), DIMENSION(:,:), INTENT(in) :: dta ! OBC external data |
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| 75 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(inout) :: pta ! tracer trend |
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| 76 | !! |
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| 77 | REAL(wp) :: zwgt ! boundary weight |
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| 78 | INTEGER :: ib, ik, igrd ! dummy loop indices |
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| 79 | INTEGER :: ii, ij ! 2D addresses |
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| 80 | !!---------------------------------------------------------------------- |
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| 81 | ! |
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| 82 | igrd = 1 ! Everything is at T-points here |
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| 83 | DO ib = 1, idx%nblenrim(igrd) |
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| 84 | ii = idx%nbi(ib,igrd) |
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| 85 | ij = idx%nbj(ib,igrd) |
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| 86 | DO ik = 1, jpkm1 |
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| 87 | pta(ii,ij,ik) = dta(ib,ik) * tmask(ii,ij,ik) |
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| 88 | END DO |
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| 89 | END DO |
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| 90 | ! |
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| 91 | END SUBROUTINE bdy_spe |
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| 92 | |
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| 93 | |
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| 94 | SUBROUTINE bdy_orl( idx, ptb, pta, dta, ll_npo ) |
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| 95 | !!---------------------------------------------------------------------- |
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| 96 | !! *** SUBROUTINE bdy_orl *** |
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| 97 | !! |
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| 98 | !! ** Purpose : Apply Orlanski radiation for tracers at open boundaries. |
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| 99 | !! This is a wrapper routine for bdy_orlanski_3d below |
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| 100 | !! |
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| 101 | !!---------------------------------------------------------------------- |
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| 102 | TYPE(OBC_INDEX), INTENT(in) :: idx ! OBC indices |
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| 103 | REAL(wp), DIMENSION(:,:), INTENT(in) :: dta ! OBC external data |
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| 104 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(inout) :: ptb ! before tracer field |
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| 105 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(inout) :: pta ! tracer trend |
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| 106 | LOGICAL, INTENT(in) :: ll_npo ! switch for NPO version |
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| 107 | !! |
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| 108 | INTEGER :: igrd ! grid index |
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| 109 | !!---------------------------------------------------------------------- |
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| 110 | ! |
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| 111 | igrd = 1 ! Everything is at T-points here |
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| 112 | ! |
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| 113 | CALL bdy_orlanski_3d( idx, igrd, ptb(:,:,:), pta(:,:,:), dta, ll_npo ) |
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| 114 | ! |
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| 115 | END SUBROUTINE bdy_orl |
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| 116 | |
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| 117 | |
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| 118 | SUBROUTINE bdy_orlanski_2d( idx, igrd, phib, phia, phi_ext, ll_npo ) |
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| 119 | !!---------------------------------------------------------------------- |
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| 120 | !! *** SUBROUTINE bdy_orlanski_2d *** |
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| 121 | !! |
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| 122 | !! - Apply Orlanski radiation condition adaptively to 2D fields: |
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| 123 | !! - radiation plus weak nudging at outflow points |
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| 124 | !! - no radiation and strong nudging at inflow points |
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| 125 | !! |
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| 126 | !! |
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| 127 | !! References: Marchesiello, McWilliams and Shchepetkin, Ocean Modelling vol. 3 (2001) |
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| 128 | !!---------------------------------------------------------------------- |
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| 129 | TYPE(OBC_INDEX), INTENT(in ) :: idx ! BDY indices |
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| 130 | INTEGER , INTENT(in ) :: igrd ! grid index |
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| 131 | REAL(wp), DIMENSION(:,:), INTENT(in ) :: phib ! model before 2D field |
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| 132 | REAL(wp), DIMENSION(:,:), INTENT(inout) :: phia ! model after 2D field (to be updated) |
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| 133 | REAL(wp), DIMENSION(:) , INTENT(in ) :: phi_ext ! external forcing data |
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| 134 | LOGICAL , INTENT(in ) :: ll_npo ! switch for NPO version |
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| 135 | ! |
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| 136 | INTEGER :: jb ! dummy loop indices |
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| 137 | INTEGER :: ii, ij, iibm1, iibm2, ijbm1, ijbm2 ! 2D addresses |
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| 138 | INTEGER :: iijm1, iijp1, ijjm1, ijjp1 ! 2D addresses |
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| 139 | INTEGER :: iibm1jp1, iibm1jm1, ijbm1jp1, ijbm1jm1 ! 2D addresses |
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| 140 | INTEGER :: ii_offset, ij_offset ! offsets for mask indices |
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| 141 | INTEGER :: flagu, flagv ! short cuts |
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| 142 | REAL(wp) :: zmask_x, zmask_y1, zmask_y2 |
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| 143 | REAL(wp) :: zex1, zex2, zey, zey1, zey2 |
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| 144 | REAL(wp) :: zdt, zdx, zdy, znor2, zrx, zry ! intermediate calculations |
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| 145 | REAL(wp) :: zout, zwgt, zdy_centred |
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| 146 | REAL(wp) :: zdy_1, zdy_2, zsign_ups |
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| 147 | REAL(wp), PARAMETER :: zepsilon = 1.e-30 ! local small value |
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| 148 | REAL(wp), POINTER, DIMENSION(:,:) :: pmask ! land/sea mask for field |
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| 149 | REAL(wp), POINTER, DIMENSION(:,:) :: pmask_xdif ! land/sea mask for x-derivatives |
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| 150 | REAL(wp), POINTER, DIMENSION(:,:) :: pmask_ydif ! land/sea mask for y-derivatives |
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| 151 | REAL(wp), POINTER, DIMENSION(:,:) :: pe_xdif ! scale factors for x-derivatives |
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| 152 | REAL(wp), POINTER, DIMENSION(:,:) :: pe_ydif ! scale factors for y-derivatives |
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| 153 | !!---------------------------------------------------------------------- |
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| 154 | ! |
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| 155 | ! ----------------------------------! |
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| 156 | ! Orlanski boundary conditions :! |
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| 157 | ! ----------------------------------! |
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| 158 | |
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| 159 | SELECT CASE(igrd) |
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| 160 | CASE(1) |
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| 161 | pmask => tmask(:,:,1) |
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| 162 | pmask_xdif => umask(:,:,1) |
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| 163 | pmask_ydif => vmask(:,:,1) |
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| 164 | pe_xdif => e1u(:,:) |
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| 165 | pe_ydif => e2v(:,:) |
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| 166 | ii_offset = 0 |
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| 167 | ij_offset = 0 |
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| 168 | CASE(2) |
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| 169 | pmask => umask(:,:,1) |
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| 170 | pmask_xdif => tmask(:,:,1) |
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| 171 | pmask_ydif => fmask(:,:,1) |
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| 172 | pe_xdif => e1t(:,:) |
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| 173 | pe_ydif => e2f(:,:) |
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| 174 | ii_offset = 1 |
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| 175 | ij_offset = 0 |
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| 176 | CASE(3) |
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| 177 | pmask => vmask(:,:,1) |
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| 178 | pmask_xdif => fmask(:,:,1) |
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| 179 | pmask_ydif => tmask(:,:,1) |
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| 180 | pe_xdif => e1f(:,:) |
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| 181 | pe_ydif => e2t(:,:) |
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| 182 | ii_offset = 0 |
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| 183 | ij_offset = 1 |
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| 184 | CASE DEFAULT ; CALL ctl_stop( 'unrecognised value for igrd in bdy_orlanksi_2d' ) |
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| 185 | END SELECT |
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| 186 | ! |
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| 187 | DO jb = 1, idx%nblenrim(igrd) |
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| 188 | ii = idx%nbi(jb,igrd) |
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| 189 | ij = idx%nbj(jb,igrd) |
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| 190 | flagu = int( idx%flagu(jb,igrd) ) |
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| 191 | flagv = int( idx%flagv(jb,igrd) ) |
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| 192 | ! |
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| 193 | ! Calculate positions of b-1 and b-2 points for this rim point |
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| 194 | ! also (b-1,j-1) and (b-1,j+1) points |
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| 195 | iibm1 = ii + flagu ; iibm2 = ii + 2*flagu |
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| 196 | ijbm1 = ij + flagv ; ijbm2 = ij + 2*flagv |
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| 197 | ! |
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| 198 | iijm1 = ii - abs(flagv) ; iijp1 = ii + abs(flagv) |
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| 199 | ijjm1 = ij - abs(flagu) ; ijjp1 = ij + abs(flagu) |
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| 200 | ! |
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| 201 | iibm1jm1 = ii + flagu - abs(flagv) ; iibm1jp1 = ii + flagu + abs(flagv) |
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| 202 | ijbm1jm1 = ij + flagv - abs(flagu) ; ijbm1jp1 = ij + flagv + abs(flagu) |
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| 203 | ! |
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| 204 | ! Calculate scale factors for calculation of spatial derivatives. |
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| 205 | zex1 = ( abs(iibm1-iibm2) * pe_xdif(iibm1+ii_offset,ijbm1 ) & |
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| 206 | & + abs(ijbm1-ijbm2) * pe_ydif(iibm1 ,ijbm1+ij_offset) ) |
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| 207 | zex2 = ( abs(iibm1-iibm2) * pe_xdif(iibm2+ii_offset,ijbm2 ) & |
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| 208 | & + abs(ijbm1-ijbm2) * pe_ydif(iibm2 ,ijbm2+ij_offset) ) |
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| 209 | zey1 = ( (iibm1-iibm1jm1) * pe_xdif(iibm1jm1+ii_offset,ijbm1jm1 ) & |
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| 210 | & + (ijbm1-ijbm1jm1) * pe_ydif(iibm1jm1 ,ijbm1jm1+ij_offset) ) |
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| 211 | zey2 = ( (iibm1jp1-iibm1) * pe_xdif(iibm1+ii_offset,ijbm1) & |
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| 212 | & + (ijbm1jp1-ijbm1) * pe_ydif(iibm1 ,ijbm1+ij_offset) ) |
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| 213 | ! make sure scale factors are nonzero |
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| 214 | if( zey1 .lt. rsmall ) zey1 = zey2 |
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| 215 | if( zey2 .lt. rsmall ) zey2 = zey1 |
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| 216 | zex1 = max(zex1,rsmall); zex2 = max(zex2,rsmall) |
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| 217 | zey1 = max(zey1,rsmall); zey2 = max(zey2,rsmall); |
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| 218 | ! |
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| 219 | ! Calculate masks for calculation of spatial derivatives. |
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| 220 | zmask_x = ( abs(iibm1-iibm2) * pmask_xdif(iibm2+ii_offset,ijbm2 ) & |
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| 221 | & + abs(ijbm1-ijbm2) * pmask_ydif(iibm2 ,ijbm2+ij_offset) ) |
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| 222 | zmask_y1 = ( (iibm1-iibm1jm1) * pmask_xdif(iibm1jm1+ii_offset,ijbm1jm1 ) & |
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| 223 | & + (ijbm1-ijbm1jm1) * pmask_ydif(iibm1jm1 ,ijbm1jm1+ij_offset) ) |
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| 224 | zmask_y2 = ( (iibm1jp1-iibm1) * pmask_xdif(iibm1+ii_offset,ijbm1) & |
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| 225 | & + (ijbm1jp1-ijbm1) * pmask_ydif(iibm1 ,ijbm1+ij_offset) ) |
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| 226 | |
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| 227 | ! Calculation of terms required for both versions of the scheme. |
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| 228 | ! Mask derivatives to ensure correct land boundary conditions for each variable. |
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| 229 | ! Centred derivative is calculated as average of "left" and "right" derivatives for |
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| 230 | ! this reason. |
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| 231 | ! Note no rdt factor in expression for zdt because it cancels in the expressions for |
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| 232 | ! zrx and zry. |
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| 233 | zdt = phia(iibm1,ijbm1) - phib(iibm1,ijbm1) |
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| 234 | zdx = ( ( phia(iibm1,ijbm1) - phia(iibm2,ijbm2) ) / zex2 ) * zmask_x |
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| 235 | zdy_1 = ( ( phib(iibm1 ,ijbm1 ) - phib(iibm1jm1,ijbm1jm1) ) / zey1 ) * zmask_y1 |
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| 236 | zdy_2 = ( ( phib(iibm1jp1,ijbm1jp1) - phib(iibm1 ,ijbm1) ) / zey2 ) * zmask_y2 |
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| 237 | zdy_centred = 0.5 * ( zdy_1 + zdy_2 ) |
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| 238 | !!$ zdy_centred = phib(iibm1jp1,ijbm1jp1) - phib(iibm1jm1,ijbm1jm1) |
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| 239 | ! upstream differencing for tangential derivatives |
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| 240 | zsign_ups = sign( 1., zdt * zdy_centred ) |
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| 241 | zsign_ups = 0.5*( zsign_ups + abs(zsign_ups) ) |
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| 242 | zdy = zsign_ups * zdy_1 + (1. - zsign_ups) * zdy_2 |
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| 243 | znor2 = zdx * zdx + zdy * zdy |
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| 244 | znor2 = max(znor2,zepsilon) |
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| 245 | ! |
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| 246 | zrx = zdt * zdx / ( zex1 * znor2 ) |
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| 247 | !!$ zrx = min(zrx,2.0_wp) |
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| 248 | zout = sign( 1., zrx ) |
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| 249 | zout = 0.5*( zout + abs(zout) ) |
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| 250 | zwgt = 2.*rdt*( (1.-zout) * idx%nbd(jb,igrd) + zout * idx%nbdout(jb,igrd) ) |
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| 251 | ! only apply radiation on outflow points |
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| 252 | if( ll_npo ) then !! NPO version !! |
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| 253 | phia(ii,ij) = (1.-zout) * ( phib(ii,ij) + zwgt * ( phi_ext(jb) - phib(ii,ij) ) ) & |
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| 254 | & + zout * ( phib(ii,ij) + zrx*phia(iibm1,ijbm1) & |
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| 255 | & + zwgt * ( phi_ext(jb) - phib(ii,ij) ) ) / ( 1. + zrx ) |
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| 256 | else !! full oblique radiation !! |
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| 257 | zsign_ups = sign( 1., zdt * zdy ) |
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| 258 | zsign_ups = 0.5*( zsign_ups + abs(zsign_ups) ) |
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| 259 | zey = zsign_ups * zey1 + (1.-zsign_ups) * zey2 |
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| 260 | zry = zdt * zdy / ( zey * znor2 ) |
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| 261 | phia(ii,ij) = (1.-zout) * ( phib(ii,ij) + zwgt * ( phi_ext(jb) - phib(ii,ij) ) ) & |
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| 262 | & + zout * ( phib(ii,ij) + zrx*phia(iibm1,ijbm1) & |
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| 263 | & - zsign_ups * zry * ( phib(ii ,ij ) - phib(iijm1,ijjm1 ) ) & |
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| 264 | & - (1.-zsign_ups) * zry * ( phib(iijp1,ijjp1) - phib(ii ,ij ) ) & |
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| 265 | & + zwgt * ( phi_ext(jb) - phib(ii,ij) ) ) / ( 1. + zrx ) |
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| 266 | end if |
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| 267 | phia(ii,ij) = phia(ii,ij) * pmask(ii,ij) |
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| 268 | END DO |
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| 269 | ! |
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| 270 | END SUBROUTINE bdy_orlanski_2d |
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| 271 | |
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| 272 | |
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| 273 | SUBROUTINE bdy_orlanski_3d( idx, igrd, phib, phia, phi_ext, ll_npo ) |
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| 274 | !!---------------------------------------------------------------------- |
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| 275 | !! *** SUBROUTINE bdy_orlanski_3d *** |
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| 276 | !! |
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| 277 | !! - Apply Orlanski radiation condition adaptively to 3D fields: |
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| 278 | !! - radiation plus weak nudging at outflow points |
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| 279 | !! - no radiation and strong nudging at inflow points |
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| 280 | !! |
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| 281 | !! |
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| 282 | !! References: Marchesiello, McWilliams and Shchepetkin, Ocean Modelling vol. 3 (2001) |
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| 283 | !!---------------------------------------------------------------------- |
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| 284 | TYPE(OBC_INDEX), INTENT(in ) :: idx ! BDY indices |
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| 285 | INTEGER , INTENT(in ) :: igrd ! grid index |
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| 286 | REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: phib ! model before 3D field |
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| 287 | REAL(wp), DIMENSION(:,:,:), INTENT(inout) :: phia ! model after 3D field (to be updated) |
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| 288 | REAL(wp), DIMENSION(:,:) , INTENT(in ) :: phi_ext ! external forcing data |
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| 289 | LOGICAL , INTENT(in ) :: ll_npo ! switch for NPO version |
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| 290 | ! |
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| 291 | INTEGER :: jb, jk ! dummy loop indices |
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| 292 | INTEGER :: ii, ij, iibm1, iibm2, ijbm1, ijbm2 ! 2D addresses |
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| 293 | INTEGER :: iijm1, iijp1, ijjm1, ijjp1 ! 2D addresses |
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| 294 | INTEGER :: iibm1jp1, iibm1jm1, ijbm1jp1, ijbm1jm1 ! 2D addresses |
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| 295 | INTEGER :: ii_offset, ij_offset ! offsets for mask indices |
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| 296 | INTEGER :: flagu, flagv ! short cuts |
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| 297 | REAL(wp) :: zmask_x, zmask_y1, zmask_y2 |
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| 298 | REAL(wp) :: zex1, zex2, zey, zey1, zey2 |
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| 299 | REAL(wp) :: zdt, zdx, zdy, znor2, zrx, zry ! intermediate calculations |
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| 300 | REAL(wp) :: zout, zwgt, zdy_centred |
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| 301 | REAL(wp) :: zdy_1, zdy_2, zsign_ups |
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| 302 | REAL(wp), PARAMETER :: zepsilon = 1.e-30 ! local small value |
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| 303 | REAL(wp), POINTER, DIMENSION(:,:,:) :: pmask ! land/sea mask for field |
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| 304 | REAL(wp), POINTER, DIMENSION(:,:,:) :: pmask_xdif ! land/sea mask for x-derivatives |
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| 305 | REAL(wp), POINTER, DIMENSION(:,:,:) :: pmask_ydif ! land/sea mask for y-derivatives |
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| 306 | REAL(wp), POINTER, DIMENSION(:,:) :: pe_xdif ! scale factors for x-derivatives |
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| 307 | REAL(wp), POINTER, DIMENSION(:,:) :: pe_ydif ! scale factors for y-derivatives |
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| 308 | !!---------------------------------------------------------------------- |
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| 309 | ! |
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| 310 | ! ----------------------------------! |
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| 311 | ! Orlanski boundary conditions :! |
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| 312 | ! ----------------------------------! |
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| 313 | ! |
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| 314 | SELECT CASE(igrd) |
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| 315 | CASE(1) |
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| 316 | pmask => tmask(:,:,:) |
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| 317 | pmask_xdif => umask(:,:,:) |
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| 318 | pmask_ydif => vmask(:,:,:) |
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| 319 | pe_xdif => e1u(:,:) |
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| 320 | pe_ydif => e2v(:,:) |
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| 321 | ii_offset = 0 |
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| 322 | ij_offset = 0 |
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| 323 | CASE(2) |
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| 324 | pmask => umask(:,:,:) |
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| 325 | pmask_xdif => tmask(:,:,:) |
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| 326 | pmask_ydif => fmask(:,:,:) |
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| 327 | pe_xdif => e1t(:,:) |
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| 328 | pe_ydif => e2f(:,:) |
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| 329 | ii_offset = 1 |
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| 330 | ij_offset = 0 |
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| 331 | CASE(3) |
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| 332 | pmask => vmask(:,:,:) |
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| 333 | pmask_xdif => fmask(:,:,:) |
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| 334 | pmask_ydif => tmask(:,:,:) |
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| 335 | pe_xdif => e1f(:,:) |
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| 336 | pe_ydif => e2t(:,:) |
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| 337 | ii_offset = 0 |
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| 338 | ij_offset = 1 |
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| 339 | CASE DEFAULT ; CALL ctl_stop( 'unrecognised value for igrd in bdy_orlanksi_2d' ) |
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| 340 | END SELECT |
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| 341 | |
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| 342 | DO jk = 1, jpk |
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| 343 | ! |
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| 344 | DO jb = 1, idx%nblenrim(igrd) |
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| 345 | ii = idx%nbi(jb,igrd) |
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| 346 | ij = idx%nbj(jb,igrd) |
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| 347 | flagu = int( idx%flagu(jb,igrd) ) |
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| 348 | flagv = int( idx%flagv(jb,igrd) ) |
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| 349 | ! |
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| 350 | ! calculate positions of b-1 and b-2 points for this rim point |
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| 351 | ! also (b-1,j-1) and (b-1,j+1) points |
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| 352 | iibm1 = ii + flagu ; iibm2 = ii + 2*flagu |
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| 353 | ijbm1 = ij + flagv ; ijbm2 = ij + 2*flagv |
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| 354 | ! |
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| 355 | iijm1 = ii - abs(flagv) ; iijp1 = ii + abs(flagv) |
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| 356 | ijjm1 = ij - abs(flagu) ; ijjp1 = ij + abs(flagu) |
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| 357 | ! |
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| 358 | iibm1jm1 = ii + flagu - abs(flagv) ; iibm1jp1 = ii + flagu + abs(flagv) |
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| 359 | ijbm1jm1 = ij + flagv - abs(flagu) ; ijbm1jp1 = ij + flagv + abs(flagu) |
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| 360 | ! |
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| 361 | ! Calculate scale factors for calculation of spatial derivatives. |
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| 362 | zex1 = ( abs(iibm1-iibm2) * pe_xdif(iibm1+ii_offset,ijbm1 ) & |
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| 363 | & + abs(ijbm1-ijbm2) * pe_ydif(iibm1 ,ijbm1+ij_offset) ) |
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| 364 | zex2 = ( abs(iibm1-iibm2) * pe_xdif(iibm2+ii_offset,ijbm2 ) & |
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| 365 | & + abs(ijbm1-ijbm2) * pe_ydif(iibm2 ,ijbm2+ij_offset) ) |
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| 366 | zey1 = ( (iibm1-iibm1jm1) * pe_xdif(iibm1jm1+ii_offset,ijbm1jm1 ) & |
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| 367 | & + (ijbm1-ijbm1jm1) * pe_ydif(iibm1jm1 ,ijbm1jm1+ij_offset) ) |
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| 368 | zey2 = ( (iibm1jp1-iibm1) * pe_xdif(iibm1+ii_offset,ijbm1) & |
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| 369 | & + (ijbm1jp1-ijbm1) * pe_ydif(iibm1 ,ijbm1+ij_offset) ) |
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| 370 | ! make sure scale factors are nonzero |
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| 371 | if( zey1 .lt. rsmall ) zey1 = zey2 |
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| 372 | if( zey2 .lt. rsmall ) zey2 = zey1 |
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| 373 | zex1 = max(zex1,rsmall); zex2 = max(zex2,rsmall); |
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| 374 | zey1 = max(zey1,rsmall); zey2 = max(zey2,rsmall); |
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| 375 | ! |
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| 376 | ! Calculate masks for calculation of spatial derivatives. |
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| 377 | zmask_x = ( abs(iibm1-iibm2) * pmask_xdif(iibm2+ii_offset,ijbm2 ,jk) & |
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| 378 | & + abs(ijbm1-ijbm2) * pmask_ydif(iibm2 ,ijbm2+ij_offset,jk) ) |
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| 379 | zmask_y1 = ( (iibm1-iibm1jm1) * pmask_xdif(iibm1jm1+ii_offset,ijbm1jm1 ,jk) & |
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| 380 | & + (ijbm1-ijbm1jm1) * pmask_ydif(iibm1jm1 ,ijbm1jm1+ij_offset,jk) ) |
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| 381 | zmask_y2 = ( (iibm1jp1-iibm1) * pmask_xdif(iibm1+ii_offset,ijbm1 ,jk) & |
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| 382 | & + (ijbm1jp1-ijbm1) * pmask_ydif(iibm1 ,ijbm1+ij_offset,jk) ) |
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| 383 | ! |
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| 384 | ! Calculate normal (zrx) and tangential (zry) components of radiation velocities. |
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| 385 | ! Mask derivatives to ensure correct land boundary conditions for each variable. |
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| 386 | ! Centred derivative is calculated as average of "left" and "right" derivatives for |
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| 387 | ! this reason. |
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| 388 | zdt = phia(iibm1,ijbm1,jk) - phib(iibm1,ijbm1,jk) |
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| 389 | zdx = ( ( phia(iibm1,ijbm1,jk) - phia(iibm2,ijbm2,jk) ) / zex2 ) * zmask_x |
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| 390 | zdy_1 = ( ( phib(iibm1 ,ijbm1 ,jk) - phib(iibm1jm1,ijbm1jm1,jk) ) / zey1 ) * zmask_y1 |
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| 391 | zdy_2 = ( ( phib(iibm1jp1,ijbm1jp1,jk) - phib(iibm1 ,ijbm1 ,jk) ) / zey2 ) * zmask_y2 |
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| 392 | zdy_centred = 0.5 * ( zdy_1 + zdy_2 ) |
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| 393 | !!$ zdy_centred = phib(iibm1jp1,ijbm1jp1,jk) - phib(iibm1jm1,ijbm1jm1,jk) |
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| 394 | ! upstream differencing for tangential derivatives |
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| 395 | zsign_ups = sign( 1., zdt * zdy_centred ) |
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| 396 | zsign_ups = 0.5*( zsign_ups + abs(zsign_ups) ) |
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| 397 | zdy = zsign_ups * zdy_1 + (1. - zsign_ups) * zdy_2 |
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| 398 | znor2 = zdx * zdx + zdy * zdy |
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| 399 | znor2 = max(znor2,zepsilon) |
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| 400 | ! |
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| 401 | ! update boundary value: |
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| 402 | zrx = zdt * zdx / ( zex1 * znor2 ) |
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| 403 | !!$ zrx = min(zrx,2.0_wp) |
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| 404 | zout = sign( 1., zrx ) |
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| 405 | zout = 0.5*( zout + abs(zout) ) |
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| 406 | zwgt = 2.*rdt*( (1.-zout) * idx%nbd(jb,igrd) + zout * idx%nbdout(jb,igrd) ) |
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| 407 | ! only apply radiation on outflow points |
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| 408 | if( ll_npo ) then !! NPO version !! |
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| 409 | phia(ii,ij,jk) = (1.-zout) * ( phib(ii,ij,jk) + zwgt * ( phi_ext(jb,jk) - phib(ii,ij,jk) ) ) & |
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| 410 | & + zout * ( phib(ii,ij,jk) + zrx*phia(iibm1,ijbm1,jk) & |
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| 411 | & + zwgt * ( phi_ext(jb,jk) - phib(ii,ij,jk) ) ) / ( 1. + zrx ) |
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| 412 | else !! full oblique radiation !! |
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| 413 | zsign_ups = sign( 1., zdt * zdy ) |
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| 414 | zsign_ups = 0.5*( zsign_ups + abs(zsign_ups) ) |
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| 415 | zey = zsign_ups * zey1 + (1.-zsign_ups) * zey2 |
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| 416 | zry = zdt * zdy / ( zey * znor2 ) |
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| 417 | phia(ii,ij,jk) = (1.-zout) * ( phib(ii,ij,jk) + zwgt * ( phi_ext(jb,jk) - phib(ii,ij,jk) ) ) & |
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| 418 | & + zout * ( phib(ii,ij,jk) + zrx*phia(iibm1,ijbm1,jk) & |
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| 419 | & - zsign_ups * zry * ( phib(ii ,ij ,jk) - phib(iijm1,ijjm1,jk) ) & |
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| 420 | & - (1.-zsign_ups) * zry * ( phib(iijp1,ijjp1,jk) - phib(ii ,ij ,jk) ) & |
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| 421 | & + zwgt * ( phi_ext(jb,jk) - phib(ii,ij,jk) ) ) / ( 1. + zrx ) |
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| 422 | end if |
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| 423 | phia(ii,ij,jk) = phia(ii,ij,jk) * pmask(ii,ij,jk) |
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| 424 | END DO |
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| 425 | ! |
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| 426 | END DO |
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| 427 | ! |
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| 428 | END SUBROUTINE bdy_orlanski_3d |
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| 429 | |
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| 430 | SUBROUTINE bdy_nmn( idx, igrd, phia ) |
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| 431 | !!---------------------------------------------------------------------- |
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| 432 | !! *** SUBROUTINE bdy_nmn *** |
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| 433 | !! |
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| 434 | !! ** Purpose : Duplicate the value at open boundaries, zero gradient. |
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| 435 | !! |
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| 436 | !!---------------------------------------------------------------------- |
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| 437 | INTEGER, INTENT(in) :: igrd ! grid index |
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| 438 | REAL(wp), DIMENSION(:,:,:), INTENT(inout) :: phia ! model after 3D field (to be updated) |
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| 439 | TYPE(OBC_INDEX), INTENT(in) :: idx ! OBC indices |
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| 440 | !! |
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| 441 | REAL(wp) :: zcoef, zcoef1, zcoef2 |
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| 442 | REAL(wp), POINTER, DIMENSION(:,:,:) :: pmask ! land/sea mask for field |
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| 443 | REAL(wp), POINTER, DIMENSION(:,:) :: bdypmask ! land/sea mask for field |
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| 444 | INTEGER :: ib, ik ! dummy loop indices |
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| 445 | INTEGER :: ii, ij, ip, jp ! 2D addresses |
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| 446 | !!---------------------------------------------------------------------- |
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| 447 | ! |
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| 448 | SELECT CASE(igrd) |
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| 449 | CASE(1) |
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| 450 | pmask => tmask(:,:,:) |
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| 451 | bdypmask => bdytmask(:,:) |
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| 452 | CASE(2) |
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| 453 | pmask => umask(:,:,:) |
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| 454 | bdypmask => bdyumask(:,:) |
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| 455 | CASE(3) |
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| 456 | pmask => vmask(:,:,:) |
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| 457 | bdypmask => bdyvmask(:,:) |
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| 458 | CASE DEFAULT ; CALL ctl_stop( 'unrecognised value for igrd in bdy_nmn' ) |
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| 459 | END SELECT |
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| 460 | DO ib = 1, idx%nblenrim(igrd) |
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| 461 | ii = idx%nbi(ib,igrd) |
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| 462 | ij = idx%nbj(ib,igrd) |
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| 463 | DO ik = 1, jpkm1 |
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| 464 | ! search the sense of the gradient |
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| 465 | zcoef1 = bdypmask(ii-1,ij )*pmask(ii-1,ij,ik) + bdypmask(ii+1,ij )*pmask(ii+1,ij,ik) |
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| 466 | zcoef2 = bdypmask(ii ,ij-1)*pmask(ii,ij-1,ik) + bdypmask(ii ,ij+1)*pmask(ii,ij+1,ik) |
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| 467 | IF ( nint(zcoef1+zcoef2) == 0) THEN |
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| 468 | ! corner **** we probably only want to set the tangentail component for the dynamics here |
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| 469 | zcoef = pmask(ii-1,ij,ik) + pmask(ii+1,ij,ik) + pmask(ii,ij-1,ik) + pmask(ii,ij+1,ik) |
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| 470 | IF (zcoef > .5_wp) THEN ! Only set none isolated points. |
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| 471 | phia(ii,ij,ik) = phia(ii-1,ij ,ik) * pmask(ii-1,ij ,ik) + & |
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| 472 | & phia(ii+1,ij ,ik) * pmask(ii+1,ij ,ik) + & |
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| 473 | & phia(ii ,ij-1,ik) * pmask(ii ,ij-1,ik) + & |
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| 474 | & phia(ii ,ij+1,ik) * pmask(ii ,ij+1,ik) |
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| 475 | phia(ii,ij,ik) = ( phia(ii,ij,ik) / zcoef ) * pmask(ii,ij,ik) |
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| 476 | ELSE |
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| 477 | phia(ii,ij,ik) = phia(ii,ij ,ik) * pmask(ii,ij ,ik) |
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| 478 | ENDIF |
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| 479 | ELSEIF ( nint(zcoef1+zcoef2) == 2) THEN |
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| 480 | ! oblique corner **** we probably only want to set the normal component for the dynamics here |
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| 481 | zcoef = pmask(ii-1,ij,ik)*bdypmask(ii-1,ij ) + pmask(ii+1,ij,ik)*bdypmask(ii+1,ij ) + & |
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| 482 | & pmask(ii,ij-1,ik)*bdypmask(ii,ij -1 ) + pmask(ii,ij+1,ik)*bdypmask(ii,ij+1 ) |
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| 483 | phia(ii,ij,ik) = phia(ii-1,ij ,ik) * pmask(ii-1,ij ,ik)*bdypmask(ii-1,ij ) + & |
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| 484 | & phia(ii+1,ij ,ik) * pmask(ii+1,ij ,ik)*bdypmask(ii+1,ij ) + & |
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| 485 | & phia(ii ,ij-1,ik) * pmask(ii ,ij-1,ik)*bdypmask(ii,ij -1 ) + & |
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| 486 | & phia(ii ,ij+1,ik) * pmask(ii ,ij+1,ik)*bdypmask(ii,ij+1 ) |
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| 487 | |
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| 488 | phia(ii,ij,ik) = ( phia(ii,ij,ik) / MAX(1._wp, zcoef) ) * pmask(ii,ij,ik) |
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| 489 | ELSE |
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| 490 | ip = nint(bdypmask(ii+1,ij )*pmask(ii+1,ij,ik) - bdypmask(ii-1,ij )*pmask(ii-1,ij,ik)) |
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| 491 | jp = nint(bdypmask(ii ,ij+1)*pmask(ii,ij+1,ik) - bdypmask(ii ,ij-1)*pmask(ii,ij-1,ik)) |
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| 492 | phia(ii,ij,ik) = phia(ii+ip,ij+jp,ik) * pmask(ii+ip,ij+jp,ik) |
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| 493 | ENDIF |
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| 494 | END DO |
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| 495 | END DO |
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| 496 | ! |
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| 497 | END SUBROUTINE bdy_nmn |
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| 498 | |
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| 499 | !!====================================================================== |
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| 500 | END MODULE bdylib |
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