| [3] | 1 | MODULE trabbl |
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| 2 | !!============================================================================== |
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| 3 | !! *** MODULE trabbl *** |
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| 4 | !! Ocean physics : advective and/or diffusive bottom boundary layer scheme |
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| 5 | !!============================================================================== |
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| [2528] | 6 | !! History : OPA ! 1996-06 (L. Mortier) Original code |
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| 7 | !! 8.0 ! 1997-11 (G. Madec) Optimization |
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| 8 | !! NEMO 1.0 ! 2002-08 (G. Madec) free form + modules |
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| 9 | !! - ! 2004-01 (A. de Miranda, G. Madec, J.M. Molines ) add advective bbl |
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| [3764] | 10 | !! 3.3 ! 2009-11 (G. Madec) merge trabbl and trabbl_adv + style + optimization |
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| 11 | !! - ! 2010-04 (G. Madec) Campin & Goosse advective bbl |
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| [2528] | 12 | !! - ! 2010-06 (C. Ethe, G. Madec) merge TRA-TRC |
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| 13 | !! - ! 2010-11 (G. Madec) add mbk. arrays associated to the deepest ocean level |
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| [4990] | 14 | !! - ! 2013-04 (F. Roquet, G. Madec) use of eosbn2 instead of local hard coded alpha and beta |
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| [9019] | 15 | !! 4.0 ! 2017-04 (G. Madec) ln_trabbl namelist variable instead of a CPP key |
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| [503] | 16 | !!---------------------------------------------------------------------- |
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| [9019] | 17 | |
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| [3] | 18 | !!---------------------------------------------------------------------- |
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| [2715] | 19 | !! tra_bbl_alloc : allocate trabbl arrays |
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| [2528] | 20 | !! tra_bbl : update the tracer trends due to the bottom boundary layer (advective and/or diffusive) |
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| 21 | !! tra_bbl_dif : generic routine to compute bbl diffusive trend |
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| 22 | !! tra_bbl_adv : generic routine to compute bbl advective trend |
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| 23 | !! bbl : computation of bbl diffu. flux coef. & transport in bottom boundary layer |
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| 24 | !! tra_bbl_init : initialization, namelist read, parameters control |
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| [503] | 25 | !!---------------------------------------------------------------------- |
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| [2528] | 26 | USE oce ! ocean dynamics and active tracers |
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| 27 | USE dom_oce ! ocean space and time domain |
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| 28 | USE phycst ! physical constant |
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| 29 | USE eosbn2 ! equation of state |
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| [5836] | 30 | USE trd_oce ! trends: ocean variables |
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| [2528] | 31 | USE trdtra ! trends: active tracers |
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| [4990] | 32 | ! |
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| 33 | USE iom ! IOM library |
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| [2528] | 34 | USE in_out_manager ! I/O manager |
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| 35 | USE lbclnk ! ocean lateral boundary conditions |
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| 36 | USE prtctl ! Print control |
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| [3294] | 37 | USE timing ! Timing |
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| [4990] | 38 | USE lib_fortran ! Fortran utilities (allows no signed zero when 'key_nosignedzero' defined) |
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| [3] | 39 | |
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| 40 | IMPLICIT NONE |
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| 41 | PRIVATE |
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| 42 | |
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| [2528] | 43 | PUBLIC tra_bbl ! routine called by step.F90 |
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| [9124] | 44 | PUBLIC tra_bbl_init ! routine called by nemogcm.F90 |
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| [2528] | 45 | PUBLIC tra_bbl_dif ! routine called by trcbbl.F90 |
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| [9124] | 46 | PUBLIC tra_bbl_adv ! - - - |
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| [2528] | 47 | PUBLIC bbl ! routine called by trcbbl.F90 and dtadyn.F90 |
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| [3] | 48 | |
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| [4147] | 49 | ! !!* Namelist nambbl * |
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| [9019] | 50 | LOGICAL , PUBLIC :: ln_trabbl !: bottom boundary layer flag |
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| [4147] | 51 | INTEGER , PUBLIC :: nn_bbl_ldf !: =1 : diffusive bbl or not (=0) |
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| 52 | INTEGER , PUBLIC :: nn_bbl_adv !: =1/2 : advective bbl or not (=0) |
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| [2528] | 53 | ! ! =1 : advective bbl using the bottom ocean velocity |
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| 54 | ! ! =2 : - - using utr_bbl proportional to grad(rho) |
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| [4147] | 55 | REAL(wp), PUBLIC :: rn_ahtbbl !: along slope bbl diffusive coefficient [m2/s] |
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| 56 | REAL(wp), PUBLIC :: rn_gambbl !: lateral coeff. for bottom boundary layer scheme [s] |
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| [409] | 57 | |
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| [4990] | 58 | LOGICAL , PUBLIC :: l_bbl !: flag to compute bbl diffu. flux coef and transport |
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| [3764] | 59 | |
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| [2715] | 60 | REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:), PUBLIC :: utr_bbl , vtr_bbl ! u- (v-) transport in the bottom boundary layer |
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| 61 | REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:), PUBLIC :: ahu_bbl , ahv_bbl ! masked diffusive bbl coeff. at u & v-pts |
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| [3] | 62 | |
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| [3764] | 63 | INTEGER , ALLOCATABLE, SAVE, DIMENSION(:,:), PUBLIC :: mbku_d , mbkv_d ! vertical index of the "lower" bottom ocean U/V-level (PUBLIC for TAM) |
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| 64 | INTEGER , ALLOCATABLE, SAVE, DIMENSION(:,:), PUBLIC :: mgrhu , mgrhv ! = +/-1, sign of grad(H) in u-(v-)direction (PUBLIC for TAM) |
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| 65 | REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: ahu_bbl_0, ahv_bbl_0 ! diffusive bbl flux coefficients at u and v-points |
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| 66 | REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:), PUBLIC :: e3u_bbl_0, e3v_bbl_0 ! thichness of the bbl (e3) at u and v-points (PUBLIC for TAM) |
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| [3] | 67 | |
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| 68 | !! * Substitutions |
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| 69 | # include "vectopt_loop_substitute.h90" |
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| 70 | !!---------------------------------------------------------------------- |
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| [9598] | 71 | !! NEMO/OCE 4.0 , NEMO Consortium (2018) |
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| [2528] | 72 | !! $Id$ |
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| [10068] | 73 | !! Software governed by the CeCILL license (see ./LICENSE) |
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| [3] | 74 | !!---------------------------------------------------------------------- |
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| 75 | CONTAINS |
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| 76 | |
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| [2715] | 77 | INTEGER FUNCTION tra_bbl_alloc() |
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| 78 | !!---------------------------------------------------------------------- |
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| 79 | !! *** FUNCTION tra_bbl_alloc *** |
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| 80 | !!---------------------------------------------------------------------- |
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| [9019] | 81 | ALLOCATE( utr_bbl (jpi,jpj) , ahu_bbl (jpi,jpj) , mbku_d(jpi,jpj) , mgrhu(jpi,jpj) , & |
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| 82 | & vtr_bbl (jpi,jpj) , ahv_bbl (jpi,jpj) , mbkv_d(jpi,jpj) , mgrhv(jpi,jpj) , & |
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| 83 | & ahu_bbl_0(jpi,jpj) , ahv_bbl_0(jpi,jpj) , & |
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| 84 | & e3u_bbl_0(jpi,jpj) , e3v_bbl_0(jpi,jpj) , STAT=tra_bbl_alloc ) |
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| [2715] | 85 | ! |
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| [10425] | 86 | CALL mpp_sum ( 'trabbl', tra_bbl_alloc ) |
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| [2715] | 87 | IF( tra_bbl_alloc > 0 ) CALL ctl_warn('tra_bbl_alloc: allocation of arrays failed.') |
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| 88 | END FUNCTION tra_bbl_alloc |
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| 89 | |
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| 90 | |
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| [10954] | 91 | SUBROUTINE tra_bbl( kt, Kbb, Kmm, Krhs ) |
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| [3] | 92 | !!---------------------------------------------------------------------- |
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| [2528] | 93 | !! *** ROUTINE bbl *** |
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| [3764] | 94 | !! |
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| 95 | !! ** Purpose : Compute the before tracer (t & s) trend associated |
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| [2528] | 96 | !! with the bottom boundary layer and add it to the general |
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| 97 | !! trend of tracer equations. |
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| [3] | 98 | !! |
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| [2528] | 99 | !! ** Method : Depending on namtra_bbl namelist parameters the bbl |
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| 100 | !! diffusive and/or advective contribution to the tracer trend |
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| 101 | !! is added to the general tracer trend |
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| [3764] | 102 | !!---------------------------------------------------------------------- |
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| [10874] | 103 | INTEGER, INTENT( in ) :: kt ! ocean time-step |
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| [10954] | 104 | INTEGER, INTENT( in ) :: Kbb, Kmm, Krhs ! time level indices |
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| [4990] | 105 | ! |
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| [9019] | 106 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: ztrdt, ztrds |
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| [2528] | 107 | !!---------------------------------------------------------------------- |
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| [3294] | 108 | ! |
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| [9019] | 109 | IF( ln_timing ) CALL timing_start( 'tra_bbl') |
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| [3294] | 110 | ! |
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| [9019] | 111 | IF( l_trdtra ) THEN !* Save the T-S input trends |
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| 112 | ALLOCATE( ztrdt(jpi,jpj,jpk) , ztrds(jpi,jpj,jpk) ) |
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| [10954] | 113 | ztrdt(:,:,:) = ts(:,:,:,jp_tem,Krhs) |
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| 114 | ztrds(:,:,:) = ts(:,:,:,jp_sal,Krhs) |
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| [2528] | 115 | ENDIF |
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| 116 | |
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| [10954] | 117 | IF( l_bbl ) CALL bbl( kt, nit000, 'TRA', Kbb, Kmm ) !* bbl coef. and transport (only if not already done in trcbbl) |
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| [3764] | 118 | |
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| [4990] | 119 | IF( nn_bbl_ldf == 1 ) THEN !* Diffusive bbl |
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| [3294] | 120 | ! |
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| [10954] | 121 | CALL tra_bbl_dif( ts(:,:,:,:,Kbb), ts(:,:,:,:,Krhs), jpts, Kmm ) |
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| [2528] | 122 | IF( ln_ctl ) & |
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| [10954] | 123 | CALL prt_ctl( tab3d_1=ts(:,:,:,jp_tem,Krhs), clinfo1=' bbl_ldf - Ta: ', mask1=tmask, & |
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| 124 | & tab3d_2=ts(:,:,:,jp_sal,Krhs), clinfo2= ' Sa: ', mask2=tmask, clinfo3='tra' ) |
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| [3764] | 125 | ! lateral boundary conditions ; just need for outputs |
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| [10425] | 126 | CALL lbc_lnk_multi( 'trabbl', ahu_bbl, 'U', 1. , ahv_bbl, 'V', 1. ) |
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| [3764] | 127 | CALL iom_put( "ahu_bbl", ahu_bbl ) ! bbl diffusive flux i-coef |
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| [2528] | 128 | CALL iom_put( "ahv_bbl", ahv_bbl ) ! bbl diffusive flux j-coef |
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| [3294] | 129 | ! |
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| [9168] | 130 | ENDIF |
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| [6140] | 131 | ! |
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| [4990] | 132 | IF( nn_bbl_adv /= 0 ) THEN !* Advective bbl |
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| [3294] | 133 | ! |
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| [10954] | 134 | CALL tra_bbl_adv( ts(:,:,:,:,Kbb), ts(:,:,:,:,Krhs), jpts, Kmm ) |
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| [2528] | 135 | IF(ln_ctl) & |
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| [10954] | 136 | CALL prt_ctl( tab3d_1=ts(:,:,:,jp_tem,Krhs), clinfo1=' bbl_adv - Ta: ', mask1=tmask, & |
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| 137 | & tab3d_2=ts(:,:,:,jp_sal,Krhs), clinfo2= ' Sa: ', mask2=tmask, clinfo3='tra' ) |
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| [3764] | 138 | ! lateral boundary conditions ; just need for outputs |
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| [10425] | 139 | CALL lbc_lnk_multi( 'trabbl', utr_bbl, 'U', 1. , vtr_bbl, 'V', 1. ) |
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| [3764] | 140 | CALL iom_put( "uoce_bbl", utr_bbl ) ! bbl i-transport |
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| [2528] | 141 | CALL iom_put( "voce_bbl", vtr_bbl ) ! bbl j-transport |
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| [3294] | 142 | ! |
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| [9168] | 143 | ENDIF |
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| [2528] | 144 | |
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| [6140] | 145 | IF( l_trdtra ) THEN ! send the trends for further diagnostics |
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| [10954] | 146 | ztrdt(:,:,:) = ts(:,:,:,jp_tem,Krhs) - ztrdt(:,:,:) |
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| 147 | ztrds(:,:,:) = ts(:,:,:,jp_sal,Krhs) - ztrds(:,:,:) |
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| [10946] | 148 | CALL trd_tra( kt, Kmm, Krhs, 'TRA', jp_tem, jptra_bbl, ztrdt ) |
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| 149 | CALL trd_tra( kt, Kmm, Krhs, 'TRA', jp_sal, jptra_bbl, ztrds ) |
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| [9019] | 150 | DEALLOCATE( ztrdt, ztrds ) |
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| [2528] | 151 | ENDIF |
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| 152 | ! |
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| [9019] | 153 | IF( ln_timing ) CALL timing_stop( 'tra_bbl') |
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| [3294] | 154 | ! |
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| [2528] | 155 | END SUBROUTINE tra_bbl |
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| 156 | |
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| 157 | |
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| [10954] | 158 | SUBROUTINE tra_bbl_dif( ptb, pta, kjpt, Kmm ) |
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| [2528] | 159 | !!---------------------------------------------------------------------- |
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| 160 | !! *** ROUTINE tra_bbl_dif *** |
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| [3764] | 161 | !! |
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| [2528] | 162 | !! ** Purpose : Computes the bottom boundary horizontal and vertical |
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| [3764] | 163 | !! advection terms. |
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| [2528] | 164 | !! |
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| [4990] | 165 | !! ** Method : * diffusive bbl only (nn_bbl_ldf=1) : |
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| [2528] | 166 | !! When the product grad( rho) * grad(h) < 0 (where grad is an |
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| 167 | !! along bottom slope gradient) an additional lateral 2nd order |
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| 168 | !! diffusion along the bottom slope is added to the general |
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| 169 | !! tracer trend, otherwise the additional trend is set to 0. |
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| 170 | !! A typical value of ahbt is 2000 m2/s (equivalent to |
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| [3] | 171 | !! a downslope velocity of 20 cm/s if the condition for slope |
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| 172 | !! convection is satified) |
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| 173 | !! |
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| [10874] | 174 | !! ** Action : pta increased by the bbl diffusive trend |
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| [3] | 175 | !! |
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| [503] | 176 | !! References : Beckmann, A., and R. Doscher, 1997, J. Phys.Oceanogr., 581-591. |
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| [2528] | 177 | !! Campin, J.-M., and H. Goosse, 1999, Tellus, 412-430. |
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| [3764] | 178 | !!---------------------------------------------------------------------- |
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| [2715] | 179 | INTEGER , INTENT(in ) :: kjpt ! number of tracers |
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| [10874] | 180 | REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(in ) :: ptb ! before and now tracer fields |
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| 181 | REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(inout) :: pta ! tracer trend |
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| [10954] | 182 | INTEGER , INTENT(in ) :: Kmm ! time level indices |
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| [2715] | 183 | ! |
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| [2528] | 184 | INTEGER :: ji, jj, jn ! dummy loop indices |
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| 185 | INTEGER :: ik ! local integers |
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| 186 | REAL(wp) :: zbtr ! local scalars |
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| [9019] | 187 | REAL(wp), DIMENSION(jpi,jpj) :: zptb ! workspace |
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| [3] | 188 | !!---------------------------------------------------------------------- |
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| [2528] | 189 | ! |
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| 190 | DO jn = 1, kjpt ! tracer loop |
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| 191 | ! ! =========== |
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| 192 | DO jj = 1, jpj |
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| [3764] | 193 | DO ji = 1, jpi |
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| [5836] | 194 | ik = mbkt(ji,jj) ! bottom T-level index |
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| [10874] | 195 | zptb(ji,jj) = ptb(ji,jj,ik,jn) ! bottom before T and S |
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| [2528] | 196 | END DO |
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| 197 | END DO |
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| [4990] | 198 | ! |
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| 199 | DO jj = 2, jpjm1 ! Compute the trend |
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| [2528] | 200 | DO ji = 2, jpim1 |
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| [5836] | 201 | ik = mbkt(ji,jj) ! bottom T-level index |
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| [10874] | 202 | pta(ji,jj,ik,jn) = pta(ji,jj,ik,jn) & |
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| [5836] | 203 | & + ( ahu_bbl(ji ,jj ) * ( zptb(ji+1,jj ) - zptb(ji ,jj ) ) & |
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| 204 | & - ahu_bbl(ji-1,jj ) * ( zptb(ji ,jj ) - zptb(ji-1,jj ) ) & |
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| 205 | & + ahv_bbl(ji ,jj ) * ( zptb(ji ,jj+1) - zptb(ji ,jj ) ) & |
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| 206 | & - ahv_bbl(ji ,jj-1) * ( zptb(ji ,jj ) - zptb(ji ,jj-1) ) ) & |
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| [10954] | 207 | & * r1_e1e2t(ji,jj) / e3t(ji,jj,ik,Kmm) |
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| [2528] | 208 | END DO |
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| [3] | 209 | END DO |
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| [2528] | 210 | ! ! =========== |
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| 211 | END DO ! end tracer |
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| 212 | ! ! =========== |
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| 213 | END SUBROUTINE tra_bbl_dif |
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| [3] | 214 | |
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| [3764] | 215 | |
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| [10954] | 216 | SUBROUTINE tra_bbl_adv( ptb, pta, kjpt, Kmm ) |
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| [2528] | 217 | !!---------------------------------------------------------------------- |
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| 218 | !! *** ROUTINE trc_bbl *** |
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| 219 | !! |
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| [3764] | 220 | !! ** Purpose : Compute the before passive tracer trend associated |
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| [2528] | 221 | !! with the bottom boundary layer and add it to the general trend |
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| 222 | !! of tracer equations. |
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| 223 | !! ** Method : advective bbl (nn_bbl_adv = 1 or 2) : |
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| 224 | !! nn_bbl_adv = 1 use of the ocean near bottom velocity as bbl velocity |
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| [3764] | 225 | !! nn_bbl_adv = 2 follow Campin and Goosse (1999) implentation i.e. |
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| 226 | !! transport proportional to the along-slope density gradient |
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| [2528] | 227 | !! |
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| 228 | !! References : Beckmann, A., and R. Doscher, 1997, J. Phys.Oceanogr., 581-591. |
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| 229 | !! Campin, J.-M., and H. Goosse, 1999, Tellus, 412-430. |
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| [3764] | 230 | !!---------------------------------------------------------------------- |
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| [2715] | 231 | INTEGER , INTENT(in ) :: kjpt ! number of tracers |
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| [10874] | 232 | REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(in ) :: ptb ! before and now tracer fields |
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| 233 | REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(inout) :: pta ! tracer trend |
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| [10954] | 234 | INTEGER , INTENT(in ) :: Kmm ! time level indices |
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| [2715] | 235 | ! |
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| [2528] | 236 | INTEGER :: ji, jj, jk, jn ! dummy loop indices |
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| 237 | INTEGER :: iis , iid , ijs , ijd ! local integers |
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| 238 | INTEGER :: ikus, ikud, ikvs, ikvd ! - - |
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| 239 | REAL(wp) :: zbtr, ztra ! local scalars |
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| 240 | REAL(wp) :: zu_bbl, zv_bbl ! - - |
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| 241 | !!---------------------------------------------------------------------- |
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| 242 | ! |
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| 243 | ! ! =========== |
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| 244 | DO jn = 1, kjpt ! tracer loop |
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| [3764] | 245 | ! ! =========== |
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| [457] | 246 | DO jj = 1, jpjm1 |
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| [2528] | 247 | DO ji = 1, jpim1 ! CAUTION start from i=1 to update i=2 when cyclic east-west |
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| 248 | IF( utr_bbl(ji,jj) /= 0.e0 ) THEN ! non-zero i-direction bbl advection |
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| 249 | ! down-slope i/k-indices (deep) & up-slope i/k indices (shelf) |
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| 250 | iid = ji + MAX( 0, mgrhu(ji,jj) ) ; iis = ji + 1 - MAX( 0, mgrhu(ji,jj) ) |
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| 251 | ikud = mbku_d(ji,jj) ; ikus = mbku(ji,jj) |
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| 252 | zu_bbl = ABS( utr_bbl(ji,jj) ) |
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| 253 | ! |
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| 254 | ! ! up -slope T-point (shelf bottom point) |
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| [10954] | 255 | zbtr = r1_e1e2t(iis,jj) / e3t(iis,jj,ikus,Kmm) |
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| [10874] | 256 | ztra = zu_bbl * ( ptb(iid,jj,ikus,jn) - ptb(iis,jj,ikus,jn) ) * zbtr |
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| 257 | pta(iis,jj,ikus,jn) = pta(iis,jj,ikus,jn) + ztra |
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| [3764] | 258 | ! |
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| [2528] | 259 | DO jk = ikus, ikud-1 ! down-slope upper to down T-point (deep column) |
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| [10954] | 260 | zbtr = r1_e1e2t(iid,jj) / e3t(iid,jj,jk,Kmm) |
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| [10874] | 261 | ztra = zu_bbl * ( ptb(iid,jj,jk+1,jn) - ptb(iid,jj,jk,jn) ) * zbtr |
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| 262 | pta(iid,jj,jk,jn) = pta(iid,jj,jk,jn) + ztra |
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| [2528] | 263 | END DO |
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| [3764] | 264 | ! |
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| [10954] | 265 | zbtr = r1_e1e2t(iid,jj) / e3t(iid,jj,ikud,Kmm) |
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| [10874] | 266 | ztra = zu_bbl * ( ptb(iis,jj,ikus,jn) - ptb(iid,jj,ikud,jn) ) * zbtr |
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| 267 | pta(iid,jj,ikud,jn) = pta(iid,jj,ikud,jn) + ztra |
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| [2528] | 268 | ENDIF |
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| 269 | ! |
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| 270 | IF( vtr_bbl(ji,jj) /= 0.e0 ) THEN ! non-zero j-direction bbl advection |
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| 271 | ! down-slope j/k-indices (deep) & up-slope j/k indices (shelf) |
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| 272 | ijd = jj + MAX( 0, mgrhv(ji,jj) ) ; ijs = jj + 1 - MAX( 0, mgrhv(ji,jj) ) |
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| 273 | ikvd = mbkv_d(ji,jj) ; ikvs = mbkv(ji,jj) |
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| 274 | zv_bbl = ABS( vtr_bbl(ji,jj) ) |
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| [3764] | 275 | ! |
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| [2528] | 276 | ! up -slope T-point (shelf bottom point) |
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| [10954] | 277 | zbtr = r1_e1e2t(ji,ijs) / e3t(ji,ijs,ikvs,Kmm) |
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| [10874] | 278 | ztra = zv_bbl * ( ptb(ji,ijd,ikvs,jn) - ptb(ji,ijs,ikvs,jn) ) * zbtr |
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| 279 | pta(ji,ijs,ikvs,jn) = pta(ji,ijs,ikvs,jn) + ztra |
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| [3764] | 280 | ! |
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| [2528] | 281 | DO jk = ikvs, ikvd-1 ! down-slope upper to down T-point (deep column) |
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| [10954] | 282 | zbtr = r1_e1e2t(ji,ijd) / e3t(ji,ijd,jk,Kmm) |
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| [10874] | 283 | ztra = zv_bbl * ( ptb(ji,ijd,jk+1,jn) - ptb(ji,ijd,jk,jn) ) * zbtr |
|---|
| 284 | pta(ji,ijd,jk,jn) = pta(ji,ijd,jk,jn) + ztra |
|---|
| [2528] | 285 | END DO |
|---|
| 286 | ! ! down-slope T-point (deep bottom point) |
|---|
| [10954] | 287 | zbtr = r1_e1e2t(ji,ijd) / e3t(ji,ijd,ikvd,Kmm) |
|---|
| [10874] | 288 | ztra = zv_bbl * ( ptb(ji,ijs,ikvs,jn) - ptb(ji,ijd,ikvd,jn) ) * zbtr |
|---|
| 289 | pta(ji,ijd,ikvd,jn) = pta(ji,ijd,ikvd,jn) + ztra |
|---|
| [2528] | 290 | ENDIF |
|---|
| [457] | 291 | END DO |
|---|
| [2528] | 292 | ! |
|---|
| [457] | 293 | END DO |
|---|
| [9019] | 294 | ! ! =========== |
|---|
| 295 | END DO ! end tracer |
|---|
| 296 | ! ! =========== |
|---|
| [2528] | 297 | END SUBROUTINE tra_bbl_adv |
|---|
| [3] | 298 | |
|---|
| 299 | |
|---|
| [10954] | 300 | SUBROUTINE bbl( kt, kit000, cdtype, Kbb, Kmm ) |
|---|
| [2528] | 301 | !!---------------------------------------------------------------------- |
|---|
| 302 | !! *** ROUTINE bbl *** |
|---|
| [3764] | 303 | !! |
|---|
| [2528] | 304 | !! ** Purpose : Computes the bottom boundary horizontal and vertical |
|---|
| [3764] | 305 | !! advection terms. |
|---|
| [2528] | 306 | !! |
|---|
| [4990] | 307 | !! ** Method : * diffusive bbl (nn_bbl_ldf=1) : |
|---|
| [2528] | 308 | !! When the product grad( rho) * grad(h) < 0 (where grad is an |
|---|
| 309 | !! along bottom slope gradient) an additional lateral 2nd order |
|---|
| 310 | !! diffusion along the bottom slope is added to the general |
|---|
| 311 | !! tracer trend, otherwise the additional trend is set to 0. |
|---|
| 312 | !! A typical value of ahbt is 2000 m2/s (equivalent to |
|---|
| 313 | !! a downslope velocity of 20 cm/s if the condition for slope |
|---|
| 314 | !! convection is satified) |
|---|
| [4990] | 315 | !! * advective bbl (nn_bbl_adv=1 or 2) : |
|---|
| [2528] | 316 | !! nn_bbl_adv = 1 use of the ocean velocity as bbl velocity |
|---|
| 317 | !! nn_bbl_adv = 2 follow Campin and Goosse (1999) implentation |
|---|
| 318 | !! i.e. transport proportional to the along-slope density gradient |
|---|
| 319 | !! |
|---|
| 320 | !! NB: the along slope density gradient is evaluated using the |
|---|
| 321 | !! local density (i.e. referenced at a common local depth). |
|---|
| 322 | !! |
|---|
| 323 | !! References : Beckmann, A., and R. Doscher, 1997, J. Phys.Oceanogr., 581-591. |
|---|
| 324 | !! Campin, J.-M., and H. Goosse, 1999, Tellus, 412-430. |
|---|
| [3764] | 325 | !!---------------------------------------------------------------------- |
|---|
| [2528] | 326 | INTEGER , INTENT(in ) :: kt ! ocean time-step index |
|---|
| [4990] | 327 | INTEGER , INTENT(in ) :: kit000 ! first time step index |
|---|
| [2528] | 328 | CHARACTER(len=3), INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator) |
|---|
| [10954] | 329 | INTEGER , INTENT(in ) :: Kbb, Kmm ! ocean time level index |
|---|
| [6140] | 330 | ! |
|---|
| [2528] | 331 | INTEGER :: ji, jj ! dummy loop indices |
|---|
| 332 | INTEGER :: ik ! local integers |
|---|
| [4990] | 333 | INTEGER :: iis, iid, ikus, ikud ! - - |
|---|
| 334 | INTEGER :: ijs, ijd, ikvs, ikvd ! - - |
|---|
| 335 | REAL(wp) :: za, zb, zgdrho ! local scalars |
|---|
| 336 | REAL(wp) :: zsign, zsigna, zgbbl ! - - |
|---|
| 337 | REAL(wp), DIMENSION(jpi,jpj,jpts) :: zts, zab ! 3D workspace |
|---|
| 338 | REAL(wp), DIMENSION(jpi,jpj) :: zub, zvb, zdep ! 2D workspace |
|---|
| [2528] | 339 | !!---------------------------------------------------------------------- |
|---|
| [3294] | 340 | ! |
|---|
| 341 | IF( kt == kit000 ) THEN |
|---|
| [2528] | 342 | IF(lwp) WRITE(numout,*) |
|---|
| 343 | IF(lwp) WRITE(numout,*) 'trabbl:bbl : Compute bbl velocities and diffusive coefficients in ', cdtype |
|---|
| 344 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~' |
|---|
| 345 | ENDIF |
|---|
| [4990] | 346 | ! !* bottom variables (T, S, alpha, beta, depth, velocity) |
|---|
| [2528] | 347 | DO jj = 1, jpj |
|---|
| 348 | DO ji = 1, jpi |
|---|
| [4990] | 349 | ik = mbkt(ji,jj) ! bottom T-level index |
|---|
| [10954] | 350 | zts (ji,jj,jp_tem) = ts(ji,jj,ik,jp_tem,Kbb) ! bottom before T and S |
|---|
| 351 | zts (ji,jj,jp_sal) = ts(ji,jj,ik,jp_sal,Kbb) |
|---|
| [2528] | 352 | ! |
|---|
| [10954] | 353 | zdep(ji,jj) = gdept(ji,jj,ik,Kmm) ! bottom T-level reference depth |
|---|
| 354 | zub (ji,jj) = uu(ji,jj,mbku(ji,jj),Kmm) ! bottom velocity |
|---|
| 355 | zvb (ji,jj) = vv(ji,jj,mbkv(ji,jj),Kmm) |
|---|
| [2528] | 356 | END DO |
|---|
| 357 | END DO |
|---|
| [4990] | 358 | ! |
|---|
| [10954] | 359 | CALL eos_rab( zts, zdep, zab, Kmm ) |
|---|
| [4990] | 360 | ! |
|---|
| [2528] | 361 | ! !-------------------! |
|---|
| 362 | IF( nn_bbl_ldf == 1 ) THEN ! diffusive bbl ! |
|---|
| 363 | ! !-------------------! |
|---|
| 364 | DO jj = 1, jpjm1 ! (criteria for non zero flux: grad(rho).grad(h) < 0 ) |
|---|
| [4990] | 365 | DO ji = 1, fs_jpim1 ! vector opt. |
|---|
| 366 | ! ! i-direction |
|---|
| 367 | za = zab(ji+1,jj,jp_tem) + zab(ji,jj,jp_tem) ! 2*(alpha,beta) at u-point |
|---|
| 368 | zb = zab(ji+1,jj,jp_sal) + zab(ji,jj,jp_sal) |
|---|
| 369 | ! ! 2*masked bottom density gradient |
|---|
| 370 | zgdrho = ( za * ( zts(ji+1,jj,jp_tem) - zts(ji,jj,jp_tem) ) & |
|---|
| 371 | & - zb * ( zts(ji+1,jj,jp_sal) - zts(ji,jj,jp_sal) ) ) * umask(ji,jj,1) |
|---|
| [3764] | 372 | ! |
|---|
| [4990] | 373 | zsign = SIGN( 0.5, -zgdrho * REAL( mgrhu(ji,jj) ) ) ! sign of ( i-gradient * i-slope ) |
|---|
| 374 | ahu_bbl(ji,jj) = ( 0.5 - zsign ) * ahu_bbl_0(ji,jj) ! masked diffusive flux coeff. |
|---|
| [1601] | 375 | ! |
|---|
| [4990] | 376 | ! ! j-direction |
|---|
| 377 | za = zab(ji,jj+1,jp_tem) + zab(ji,jj,jp_tem) ! 2*(alpha,beta) at v-point |
|---|
| 378 | zb = zab(ji,jj+1,jp_sal) + zab(ji,jj,jp_sal) |
|---|
| 379 | ! ! 2*masked bottom density gradient |
|---|
| 380 | zgdrho = ( za * ( zts(ji,jj+1,jp_tem) - zts(ji,jj,jp_tem) ) & |
|---|
| 381 | & - zb * ( zts(ji,jj+1,jp_sal) - zts(ji,jj,jp_sal) ) ) * vmask(ji,jj,1) |
|---|
| [3764] | 382 | ! |
|---|
| [4990] | 383 | zsign = SIGN( 0.5, -zgdrho * REAL( mgrhv(ji,jj) ) ) ! sign of ( j-gradient * j-slope ) |
|---|
| [2528] | 384 | ahv_bbl(ji,jj) = ( 0.5 - zsign ) * ahv_bbl_0(ji,jj) |
|---|
| [1601] | 385 | END DO |
|---|
| [3] | 386 | END DO |
|---|
| [1601] | 387 | ! |
|---|
| [2528] | 388 | ENDIF |
|---|
| [6140] | 389 | ! |
|---|
| [2528] | 390 | ! !-------------------! |
|---|
| 391 | IF( nn_bbl_adv /= 0 ) THEN ! advective bbl ! |
|---|
| 392 | ! !-------------------! |
|---|
| 393 | SELECT CASE ( nn_bbl_adv ) !* bbl transport type |
|---|
| [503] | 394 | ! |
|---|
| [2528] | 395 | CASE( 1 ) != use of upper velocity |
|---|
| 396 | DO jj = 1, jpjm1 ! criteria: grad(rho).grad(h)<0 and grad(rho).grad(h)<0 |
|---|
| 397 | DO ji = 1, fs_jpim1 ! vector opt. |
|---|
| [4990] | 398 | ! ! i-direction |
|---|
| 399 | za = zab(ji+1,jj,jp_tem) + zab(ji,jj,jp_tem) ! 2*(alpha,beta) at u-point |
|---|
| 400 | zb = zab(ji+1,jj,jp_sal) + zab(ji,jj,jp_sal) |
|---|
| 401 | ! ! 2*masked bottom density gradient |
|---|
| 402 | zgdrho = ( za * ( zts(ji+1,jj,jp_tem) - zts(ji,jj,jp_tem) ) & |
|---|
| 403 | - zb * ( zts(ji+1,jj,jp_sal) - zts(ji,jj,jp_sal) ) ) * umask(ji,jj,1) |
|---|
| [3764] | 404 | ! |
|---|
| [4990] | 405 | zsign = SIGN( 0.5, - zgdrho * REAL( mgrhu(ji,jj) ) ) ! sign of i-gradient * i-slope |
|---|
| 406 | zsigna= SIGN( 0.5, zub(ji,jj) * REAL( mgrhu(ji,jj) ) ) ! sign of u * i-slope |
|---|
| [2528] | 407 | ! |
|---|
| [4990] | 408 | ! ! bbl velocity |
|---|
| [2528] | 409 | utr_bbl(ji,jj) = ( 0.5 + zsigna ) * ( 0.5 - zsign ) * e2u(ji,jj) * e3u_bbl_0(ji,jj) * zub(ji,jj) |
|---|
| 410 | ! |
|---|
| [4990] | 411 | ! ! j-direction |
|---|
| 412 | za = zab(ji,jj+1,jp_tem) + zab(ji,jj,jp_tem) ! 2*(alpha,beta) at v-point |
|---|
| 413 | zb = zab(ji,jj+1,jp_sal) + zab(ji,jj,jp_sal) |
|---|
| 414 | ! ! 2*masked bottom density gradient |
|---|
| 415 | zgdrho = ( za * ( zts(ji,jj+1,jp_tem) - zts(ji,jj,jp_tem) ) & |
|---|
| 416 | & - zb * ( zts(ji,jj+1,jp_sal) - zts(ji,jj,jp_sal) ) ) * vmask(ji,jj,1) |
|---|
| 417 | zsign = SIGN( 0.5, - zgdrho * REAL( mgrhv(ji,jj) ) ) ! sign of j-gradient * j-slope |
|---|
| 418 | zsigna= SIGN( 0.5, zvb(ji,jj) * REAL( mgrhv(ji,jj) ) ) ! sign of u * i-slope |
|---|
| [2528] | 419 | ! |
|---|
| [4990] | 420 | ! ! bbl transport |
|---|
| [2528] | 421 | vtr_bbl(ji,jj) = ( 0.5 + zsigna ) * ( 0.5 - zsign ) * e1v(ji,jj) * e3v_bbl_0(ji,jj) * zvb(ji,jj) |
|---|
| 422 | END DO |
|---|
| 423 | END DO |
|---|
| [503] | 424 | ! |
|---|
| [2528] | 425 | CASE( 2 ) != bbl velocity = F( delta rho ) |
|---|
| 426 | zgbbl = grav * rn_gambbl |
|---|
| 427 | DO jj = 1, jpjm1 ! criteria: rho_up > rho_down |
|---|
| 428 | DO ji = 1, fs_jpim1 ! vector opt. |
|---|
| [4990] | 429 | ! ! i-direction |
|---|
| [2528] | 430 | ! down-slope T-point i/k-index (deep) & up-slope T-point i/k-index (shelf) |
|---|
| [4990] | 431 | iid = ji + MAX( 0, mgrhu(ji,jj) ) |
|---|
| 432 | iis = ji + 1 - MAX( 0, mgrhu(ji,jj) ) |
|---|
| [2528] | 433 | ! |
|---|
| [4990] | 434 | ikud = mbku_d(ji,jj) |
|---|
| 435 | ikus = mbku(ji,jj) |
|---|
| [2528] | 436 | ! |
|---|
| [4990] | 437 | za = zab(ji+1,jj,jp_tem) + zab(ji,jj,jp_tem) ! 2*(alpha,beta) at u-point |
|---|
| 438 | zb = zab(ji+1,jj,jp_sal) + zab(ji,jj,jp_sal) |
|---|
| 439 | ! ! masked bottom density gradient |
|---|
| 440 | zgdrho = 0.5 * ( za * ( zts(iid,jj,jp_tem) - zts(iis,jj,jp_tem) ) & |
|---|
| 441 | & - zb * ( zts(iid,jj,jp_sal) - zts(iis,jj,jp_sal) ) ) * umask(ji,jj,1) |
|---|
| 442 | zgdrho = MAX( 0.e0, zgdrho ) ! only if shelf is denser than deep |
|---|
| 443 | ! |
|---|
| 444 | ! ! bbl transport (down-slope direction) |
|---|
| [2528] | 445 | utr_bbl(ji,jj) = e2u(ji,jj) * e3u_bbl_0(ji,jj) * zgbbl * zgdrho * REAL( mgrhu(ji,jj) ) |
|---|
| 446 | ! |
|---|
| [4990] | 447 | ! ! j-direction |
|---|
| [2528] | 448 | ! down-slope T-point j/k-index (deep) & of the up -slope T-point j/k-index (shelf) |
|---|
| [4990] | 449 | ijd = jj + MAX( 0, mgrhv(ji,jj) ) |
|---|
| 450 | ijs = jj + 1 - MAX( 0, mgrhv(ji,jj) ) |
|---|
| [2528] | 451 | ! |
|---|
| [4990] | 452 | ikvd = mbkv_d(ji,jj) |
|---|
| 453 | ikvs = mbkv(ji,jj) |
|---|
| [2528] | 454 | ! |
|---|
| [4990] | 455 | za = zab(ji,jj+1,jp_tem) + zab(ji,jj,jp_tem) ! 2*(alpha,beta) at v-point |
|---|
| 456 | zb = zab(ji,jj+1,jp_sal) + zab(ji,jj,jp_sal) |
|---|
| 457 | ! ! masked bottom density gradient |
|---|
| 458 | zgdrho = 0.5 * ( za * ( zts(ji,ijd,jp_tem) - zts(ji,ijs,jp_tem) ) & |
|---|
| 459 | & - zb * ( zts(ji,ijd,jp_sal) - zts(ji,ijs,jp_sal) ) ) * vmask(ji,jj,1) |
|---|
| 460 | zgdrho = MAX( 0.e0, zgdrho ) ! only if shelf is denser than deep |
|---|
| 461 | ! |
|---|
| 462 | ! ! bbl transport (down-slope direction) |
|---|
| [2528] | 463 | vtr_bbl(ji,jj) = e1v(ji,jj) * e3v_bbl_0(ji,jj) * zgbbl * zgdrho * REAL( mgrhv(ji,jj) ) |
|---|
| 464 | END DO |
|---|
| 465 | END DO |
|---|
| [3] | 466 | END SELECT |
|---|
| [2528] | 467 | ! |
|---|
| [3] | 468 | ENDIF |
|---|
| [503] | 469 | ! |
|---|
| [2528] | 470 | END SUBROUTINE bbl |
|---|
| [3] | 471 | |
|---|
| 472 | |
|---|
| 473 | SUBROUTINE tra_bbl_init |
|---|
| 474 | !!---------------------------------------------------------------------- |
|---|
| 475 | !! *** ROUTINE tra_bbl_init *** |
|---|
| 476 | !! |
|---|
| 477 | !! ** Purpose : Initialization for the bottom boundary layer scheme. |
|---|
| 478 | !! |
|---|
| 479 | !! ** Method : Read the nambbl namelist and check the parameters |
|---|
| [3294] | 480 | !! called by nemo_init at the first timestep (kit000) |
|---|
| [3] | 481 | !!---------------------------------------------------------------------- |
|---|
| [9019] | 482 | INTEGER :: ji, jj ! dummy loop indices |
|---|
| 483 | INTEGER :: ii0, ii1, ij0, ij1, ios ! local integer |
|---|
| [9094] | 484 | REAL(wp), DIMENSION(jpi,jpj) :: zmbku, zmbkv ! workspace |
|---|
| [9019] | 485 | !! |
|---|
| 486 | NAMELIST/nambbl/ ln_trabbl, nn_bbl_ldf, nn_bbl_adv, rn_ahtbbl, rn_gambbl |
|---|
| [3] | 487 | !!---------------------------------------------------------------------- |
|---|
| [3294] | 488 | ! |
|---|
| [4147] | 489 | REWIND( numnam_ref ) ! Namelist nambbl in reference namelist : Bottom boundary layer scheme |
|---|
| 490 | READ ( numnam_ref, nambbl, IOSTAT = ios, ERR = 901) |
|---|
| [6140] | 491 | 901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'nambbl in reference namelist', lwp ) |
|---|
| 492 | ! |
|---|
| [4147] | 493 | REWIND( numnam_cfg ) ! Namelist nambbl in configuration namelist : Bottom boundary layer scheme |
|---|
| 494 | READ ( numnam_cfg, nambbl, IOSTAT = ios, ERR = 902 ) |
|---|
| [9168] | 495 | 902 IF( ios > 0 ) CALL ctl_nam ( ios , 'nambbl in configuration namelist', lwp ) |
|---|
| [4624] | 496 | IF(lwm) WRITE ( numond, nambbl ) |
|---|
| [2528] | 497 | ! |
|---|
| 498 | l_bbl = .TRUE. !* flag to compute bbl coef and transport |
|---|
| 499 | ! |
|---|
| 500 | IF(lwp) THEN !* Parameter control and print |
|---|
| [3] | 501 | WRITE(numout,*) |
|---|
| [2528] | 502 | WRITE(numout,*) 'tra_bbl_init : bottom boundary layer initialisation' |
|---|
| [3] | 503 | WRITE(numout,*) '~~~~~~~~~~~~' |
|---|
| [9019] | 504 | WRITE(numout,*) ' Namelist nambbl : set bbl parameters' |
|---|
| 505 | WRITE(numout,*) ' bottom boundary layer flag ln_trabbl = ', ln_trabbl |
|---|
| [3] | 506 | ENDIF |
|---|
| [9019] | 507 | IF( .NOT.ln_trabbl ) RETURN |
|---|
| 508 | ! |
|---|
| 509 | IF(lwp) THEN |
|---|
| 510 | WRITE(numout,*) ' diffusive bbl (=1) or not (=0) nn_bbl_ldf = ', nn_bbl_ldf |
|---|
| 511 | WRITE(numout,*) ' advective bbl (=1/2) or not (=0) nn_bbl_adv = ', nn_bbl_adv |
|---|
| 512 | WRITE(numout,*) ' diffusive bbl coefficient rn_ahtbbl = ', rn_ahtbbl, ' m2/s' |
|---|
| 513 | WRITE(numout,*) ' advective bbl coefficient rn_gambbl = ', rn_gambbl, ' s' |
|---|
| 514 | ENDIF |
|---|
| 515 | ! |
|---|
| [2715] | 516 | ! ! allocate trabbl arrays |
|---|
| 517 | IF( tra_bbl_alloc() /= 0 ) CALL ctl_stop( 'STOP', 'tra_bbl_init : unable to allocate arrays' ) |
|---|
| [9019] | 518 | ! |
|---|
| [2528] | 519 | IF( nn_bbl_adv == 1 ) WRITE(numout,*) ' * Advective BBL using upper velocity' |
|---|
| 520 | IF( nn_bbl_adv == 2 ) WRITE(numout,*) ' * Advective BBL using velocity = F( delta rho)' |
|---|
| [9019] | 521 | ! |
|---|
| [2528] | 522 | ! !* vertical index of "deep" bottom u- and v-points |
|---|
| 523 | DO jj = 1, jpjm1 ! (the "shelf" bottom k-indices are mbku and mbkv) |
|---|
| 524 | DO ji = 1, jpim1 |
|---|
| 525 | mbku_d(ji,jj) = MAX( mbkt(ji+1,jj ) , mbkt(ji,jj) ) ! >= 1 as mbkt=1 over land |
|---|
| 526 | mbkv_d(ji,jj) = MAX( mbkt(ji ,jj+1) , mbkt(ji,jj) ) |
|---|
| [3] | 527 | END DO |
|---|
| 528 | END DO |
|---|
| [4990] | 529 | ! converte into REAL to use lbc_lnk ; impose a min value of 1 as a zero can be set in lbclnk |
|---|
| [9094] | 530 | zmbku(:,:) = REAL( mbku_d(:,:), wp ) ; zmbkv(:,:) = REAL( mbkv_d(:,:), wp ) |
|---|
| [10425] | 531 | CALL lbc_lnk_multi( 'trabbl', zmbku,'U',1., zmbkv,'V',1.) |
|---|
| [9919] | 532 | mbku_d(:,:) = MAX( INT( zmbku(:,:) ), 1 ) ; mbkv_d(:,:) = MAX( NINT( zmbkv(:,:) ), 1 ) |
|---|
| [9019] | 533 | ! |
|---|
| [9168] | 534 | ! !* sign of grad(H) at u- and v-points; zero if grad(H) = 0 |
|---|
| [8509] | 535 | mgrhu(:,:) = 0 ; mgrhv(:,:) = 0 |
|---|
| [3764] | 536 | DO jj = 1, jpjm1 |
|---|
| [3] | 537 | DO ji = 1, jpim1 |
|---|
| [8509] | 538 | IF( gdept_0(ji+1,jj,mbkt(ji+1,jj)) - gdept_0(ji,jj,mbkt(ji,jj)) /= 0._wp ) THEN |
|---|
| 539 | mgrhu(ji,jj) = INT( SIGN( 1.e0, gdept_0(ji+1,jj,mbkt(ji+1,jj)) - gdept_0(ji,jj,mbkt(ji,jj)) ) ) |
|---|
| 540 | ENDIF |
|---|
| 541 | ! |
|---|
| 542 | IF( gdept_0(ji,jj+1,mbkt(ji,jj+1)) - gdept_0(ji,jj,mbkt(ji,jj)) /= 0._wp ) THEN |
|---|
| 543 | mgrhv(ji,jj) = INT( SIGN( 1.e0, gdept_0(ji,jj+1,mbkt(ji,jj+1)) - gdept_0(ji,jj,mbkt(ji,jj)) ) ) |
|---|
| 544 | ENDIF |
|---|
| [3] | 545 | END DO |
|---|
| 546 | END DO |
|---|
| [7646] | 547 | ! |
|---|
| [3764] | 548 | DO jj = 1, jpjm1 !* bbl thickness at u- (v-) point |
|---|
| [4990] | 549 | DO ji = 1, jpim1 ! minimum of top & bottom e3u_0 (e3v_0) |
|---|
| [4292] | 550 | e3u_bbl_0(ji,jj) = MIN( e3u_0(ji,jj,mbkt(ji+1,jj )), e3u_0(ji,jj,mbkt(ji,jj)) ) |
|---|
| 551 | e3v_bbl_0(ji,jj) = MIN( e3v_0(ji,jj,mbkt(ji ,jj+1)), e3v_0(ji,jj,mbkt(ji,jj)) ) |
|---|
| [3764] | 552 | END DO |
|---|
| [2528] | 553 | END DO |
|---|
| [10425] | 554 | CALL lbc_lnk_multi( 'trabbl', e3u_bbl_0, 'U', 1. , e3v_bbl_0, 'V', 1. ) ! lateral boundary conditions |
|---|
| [7646] | 555 | ! |
|---|
| [3764] | 556 | ! !* masked diffusive flux coefficients |
|---|
| [7753] | 557 | ahu_bbl_0(:,:) = rn_ahtbbl * e2_e1u(:,:) * e3u_bbl_0(:,:) * umask(:,:,1) |
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| 558 | ahv_bbl_0(:,:) = rn_ahtbbl * e1_e2v(:,:) * e3v_bbl_0(:,:) * vmask(:,:,1) |
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| [503] | 559 | ! |
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| [3] | 560 | END SUBROUTINE tra_bbl_init |
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| 561 | |
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| 562 | !!====================================================================== |
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| 563 | END MODULE trabbl |
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