| [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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| [10806] | 91 | SUBROUTINE tra_bbl( kt, ktlev1, ktlev2, kt2lev, pts_rhs ) |
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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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| [10806] | 103 | INTEGER, INTENT( in ) :: kt ! ocean time-step |
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| 104 | INTEGER, INTENT( in ) :: ktlev1, ktlev2 ! time level indices for 3-time-level source terms |
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| 105 | INTEGER, INTENT( in ) :: kt2lev ! time level index for 2-time-level source terms |
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| 106 | REAL(wp), INTENT( inout), DIMENSION(jpi,jpj,jpk,jpts) :: pts_rhs ! temperature and salinity trends |
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| [4990] | 107 | ! |
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| [9019] | 108 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: ztrdt, ztrds |
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| [2528] | 109 | !!---------------------------------------------------------------------- |
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| [3294] | 110 | ! |
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| [9019] | 111 | IF( ln_timing ) CALL timing_start( 'tra_bbl') |
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| [3294] | 112 | ! |
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| [9019] | 113 | IF( l_trdtra ) THEN !* Save the T-S input trends |
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| 114 | ALLOCATE( ztrdt(jpi,jpj,jpk) , ztrds(jpi,jpj,jpk) ) |
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| [10806] | 115 | ztrdt(:,:,:) = pts_rhs(:,:,:,jp_tem) |
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| 116 | ztrds(:,:,:) = pts_rhs(:,:,:,jp_sal) |
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| [2528] | 117 | ENDIF |
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| 118 | |
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| [10806] | 119 | IF( l_bbl ) CALL bbl( kt, nit000, ktlev1, ktlev2, kt2lev, 'TRA' ) !* bbl coef. and transport (only if not already done in trcbbl) |
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| [3764] | 120 | |
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| [4990] | 121 | IF( nn_bbl_ldf == 1 ) THEN !* Diffusive bbl |
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| [3294] | 122 | ! |
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| [10806] | 123 | CALL tra_bbl_dif( ts(:,:,:,:,ktlev1), e3t(:,:,:,ktlev2), pts_rhs, jpts ) |
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| [2528] | 124 | IF( ln_ctl ) & |
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| 125 | CALL prt_ctl( tab3d_1=tsa(:,:,:,jp_tem), clinfo1=' bbl_ldf - Ta: ', mask1=tmask, & |
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| [4990] | 126 | & tab3d_2=tsa(:,:,:,jp_sal), clinfo2= ' Sa: ', mask2=tmask, clinfo3='tra' ) |
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| [3764] | 127 | ! lateral boundary conditions ; just need for outputs |
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| [10425] | 128 | CALL lbc_lnk_multi( 'trabbl', ahu_bbl, 'U', 1. , ahv_bbl, 'V', 1. ) |
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| [3764] | 129 | CALL iom_put( "ahu_bbl", ahu_bbl ) ! bbl diffusive flux i-coef |
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| [2528] | 130 | CALL iom_put( "ahv_bbl", ahv_bbl ) ! bbl diffusive flux j-coef |
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| [3294] | 131 | ! |
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| [9168] | 132 | ENDIF |
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| [6140] | 133 | ! |
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| [4990] | 134 | IF( nn_bbl_adv /= 0 ) THEN !* Advective bbl |
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| [3294] | 135 | ! |
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| [10806] | 136 | CALL tra_bbl_adv( ts(:,:,:,:,ktlev1), e3t(:,:,:,ktlev2), pts_rhs, jpts ) |
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| [2528] | 137 | IF(ln_ctl) & |
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| 138 | CALL prt_ctl( tab3d_1=tsa(:,:,:,jp_tem), clinfo1=' bbl_adv - Ta: ', mask1=tmask, & |
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| [4990] | 139 | & tab3d_2=tsa(:,:,:,jp_sal), clinfo2= ' Sa: ', mask2=tmask, clinfo3='tra' ) |
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| [3764] | 140 | ! lateral boundary conditions ; just need for outputs |
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| [10425] | 141 | CALL lbc_lnk_multi( 'trabbl', utr_bbl, 'U', 1. , vtr_bbl, 'V', 1. ) |
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| [3764] | 142 | CALL iom_put( "uoce_bbl", utr_bbl ) ! bbl i-transport |
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| [2528] | 143 | CALL iom_put( "voce_bbl", vtr_bbl ) ! bbl j-transport |
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| [3294] | 144 | ! |
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| [9168] | 145 | ENDIF |
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| [2528] | 146 | |
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| [6140] | 147 | IF( l_trdtra ) THEN ! send the trends for further diagnostics |
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| [10806] | 148 | ztrdt(:,:,:) = pts_rhs(:,:,:,jp_tem) - ztrdt(:,:,:) |
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| 149 | ztrds(:,:,:) = pts_rhs(:,:,:,jp_sal) - ztrds(:,:,:) |
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| [4990] | 150 | CALL trd_tra( kt, 'TRA', jp_tem, jptra_bbl, ztrdt ) |
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| 151 | CALL trd_tra( kt, 'TRA', jp_sal, jptra_bbl, ztrds ) |
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| [9019] | 152 | DEALLOCATE( ztrdt, ztrds ) |
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| [2528] | 153 | ENDIF |
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| 154 | ! |
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| [9019] | 155 | IF( ln_timing ) CALL timing_stop( 'tra_bbl') |
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| [3294] | 156 | ! |
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| [2528] | 157 | END SUBROUTINE tra_bbl |
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| 158 | |
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| 159 | |
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| [10806] | 160 | SUBROUTINE tra_bbl_dif( pt, pe3t, pt_rhs, kjpt ) |
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| [2528] | 161 | !!---------------------------------------------------------------------- |
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| 162 | !! *** ROUTINE tra_bbl_dif *** |
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| [3764] | 163 | !! |
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| [2528] | 164 | !! ** Purpose : Computes the bottom boundary horizontal and vertical |
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| [3764] | 165 | !! advection terms. |
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| [2528] | 166 | !! |
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| [4990] | 167 | !! ** Method : * diffusive bbl only (nn_bbl_ldf=1) : |
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| [2528] | 168 | !! When the product grad( rho) * grad(h) < 0 (where grad is an |
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| 169 | !! along bottom slope gradient) an additional lateral 2nd order |
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| 170 | !! diffusion along the bottom slope is added to the general |
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| 171 | !! tracer trend, otherwise the additional trend is set to 0. |
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| 172 | !! A typical value of ahbt is 2000 m2/s (equivalent to |
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| [3] | 173 | !! a downslope velocity of 20 cm/s if the condition for slope |
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| 174 | !! convection is satified) |
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| 175 | !! |
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| [10806] | 176 | !! ** Action : pt_rhs increased by the bbl diffusive trend |
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| [3] | 177 | !! |
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| [503] | 178 | !! References : Beckmann, A., and R. Doscher, 1997, J. Phys.Oceanogr., 581-591. |
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| [2528] | 179 | !! Campin, J.-M., and H. Goosse, 1999, Tellus, 412-430. |
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| [3764] | 180 | !!---------------------------------------------------------------------- |
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| [2715] | 181 | INTEGER , INTENT(in ) :: kjpt ! number of tracers |
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| [10806] | 182 | REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(in ) :: pt ! tracer fields |
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| 183 | REAL(wp), DIMENSION(jpi,jpj,jpk) , INTENT(in ) :: pe3t ! thickness fields |
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| 184 | REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(inout) :: pt_rhs ! tracer trend |
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| [2715] | 185 | ! |
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| [2528] | 186 | INTEGER :: ji, jj, jn ! dummy loop indices |
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| 187 | INTEGER :: ik ! local integers |
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| 188 | REAL(wp) :: zbtr ! local scalars |
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| [9019] | 189 | REAL(wp), DIMENSION(jpi,jpj) :: zptb ! workspace |
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| [3] | 190 | !!---------------------------------------------------------------------- |
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| [2528] | 191 | ! |
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| 192 | DO jn = 1, kjpt ! tracer loop |
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| 193 | ! ! =========== |
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| 194 | DO jj = 1, jpj |
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| [3764] | 195 | DO ji = 1, jpi |
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| [5836] | 196 | ik = mbkt(ji,jj) ! bottom T-level index |
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| [10806] | 197 | zptb(ji,jj) = pt(ji,jj,ik,jn) ! bottom before T and S |
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| [2528] | 198 | END DO |
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| 199 | END DO |
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| [4990] | 200 | ! |
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| 201 | DO jj = 2, jpjm1 ! Compute the trend |
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| [2528] | 202 | DO ji = 2, jpim1 |
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| [5836] | 203 | ik = mbkt(ji,jj) ! bottom T-level index |
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| [10806] | 204 | pt_rhs(ji,jj,ik,jn) = pt_rhs(ji,jj,ik,jn) & |
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| [5836] | 205 | & + ( ahu_bbl(ji ,jj ) * ( zptb(ji+1,jj ) - zptb(ji ,jj ) ) & |
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| 206 | & - ahu_bbl(ji-1,jj ) * ( zptb(ji ,jj ) - zptb(ji-1,jj ) ) & |
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| 207 | & + ahv_bbl(ji ,jj ) * ( zptb(ji ,jj+1) - zptb(ji ,jj ) ) & |
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| 208 | & - ahv_bbl(ji ,jj-1) * ( zptb(ji ,jj ) - zptb(ji ,jj-1) ) ) & |
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| [10806] | 209 | & * r1_e1e2t(ji,jj) / pe3t(ji,jj,ik) |
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| [2528] | 210 | END DO |
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| [3] | 211 | END DO |
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| [2528] | 212 | ! ! =========== |
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| 213 | END DO ! end tracer |
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| 214 | ! ! =========== |
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| 215 | END SUBROUTINE tra_bbl_dif |
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| [3] | 216 | |
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| [3764] | 217 | |
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| [10806] | 218 | SUBROUTINE tra_bbl_adv( pt, pe3t, pt_rhs, kjpt ) |
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| [2528] | 219 | !!---------------------------------------------------------------------- |
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| 220 | !! *** ROUTINE trc_bbl *** |
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| 221 | !! |
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| [3764] | 222 | !! ** Purpose : Compute the before passive tracer trend associated |
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| [2528] | 223 | !! with the bottom boundary layer and add it to the general trend |
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| 224 | !! of tracer equations. |
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| 225 | !! ** Method : advective bbl (nn_bbl_adv = 1 or 2) : |
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| 226 | !! nn_bbl_adv = 1 use of the ocean near bottom velocity as bbl velocity |
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| [3764] | 227 | !! nn_bbl_adv = 2 follow Campin and Goosse (1999) implentation i.e. |
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| 228 | !! transport proportional to the along-slope density gradient |
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| [2528] | 229 | !! |
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| 230 | !! References : Beckmann, A., and R. Doscher, 1997, J. Phys.Oceanogr., 581-591. |
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| 231 | !! Campin, J.-M., and H. Goosse, 1999, Tellus, 412-430. |
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| [3764] | 232 | !!---------------------------------------------------------------------- |
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| [2715] | 233 | INTEGER , INTENT(in ) :: kjpt ! number of tracers |
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| [10806] | 234 | REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(in ) :: pt ! before and now tracer fields |
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| 235 | REAL(wp), DIMENSION(jpi,jpj,jpk) , INTENT(in ) :: pe3t ! thickness fields |
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| 236 | REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(inout) :: pt_rhs ! tracer trend |
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| [2715] | 237 | ! |
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| [2528] | 238 | INTEGER :: ji, jj, jk, jn ! dummy loop indices |
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| 239 | INTEGER :: iis , iid , ijs , ijd ! local integers |
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| 240 | INTEGER :: ikus, ikud, ikvs, ikvd ! - - |
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| 241 | REAL(wp) :: zbtr, ztra ! local scalars |
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| 242 | REAL(wp) :: zu_bbl, zv_bbl ! - - |
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| 243 | !!---------------------------------------------------------------------- |
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| 244 | ! |
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| 245 | ! ! =========== |
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| 246 | DO jn = 1, kjpt ! tracer loop |
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| [3764] | 247 | ! ! =========== |
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| [457] | 248 | DO jj = 1, jpjm1 |
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| [2528] | 249 | DO ji = 1, jpim1 ! CAUTION start from i=1 to update i=2 when cyclic east-west |
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| 250 | IF( utr_bbl(ji,jj) /= 0.e0 ) THEN ! non-zero i-direction bbl advection |
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| 251 | ! down-slope i/k-indices (deep) & up-slope i/k indices (shelf) |
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| 252 | iid = ji + MAX( 0, mgrhu(ji,jj) ) ; iis = ji + 1 - MAX( 0, mgrhu(ji,jj) ) |
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| 253 | ikud = mbku_d(ji,jj) ; ikus = mbku(ji,jj) |
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| 254 | zu_bbl = ABS( utr_bbl(ji,jj) ) |
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| 255 | ! |
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| 256 | ! ! up -slope T-point (shelf bottom point) |
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| [10806] | 257 | zbtr = r1_e1e2t(iis,jj) / pe3t(iis,jj,ikus) |
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| 258 | ztra = zu_bbl * ( pt(iid,jj,ikus,jn) - pt(iis,jj,ikus,jn) ) * zbtr |
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| 259 | pt_rhs(iis,jj,ikus,jn) = pt_rhs(iis,jj,ikus,jn) + ztra |
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| [3764] | 260 | ! |
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| [2528] | 261 | DO jk = ikus, ikud-1 ! down-slope upper to down T-point (deep column) |
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| [10806] | 262 | zbtr = r1_e1e2t(iid,jj) / pe3t(iid,jj,jk) |
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| 263 | ztra = zu_bbl * ( pt(iid,jj,jk+1,jn) - pt(iid,jj,jk,jn) ) * zbtr |
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| 264 | pt_rhs(iid,jj,jk,jn) = pt_rhs(iid,jj,jk,jn) + ztra |
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| [2528] | 265 | END DO |
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| [3764] | 266 | ! |
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| [10806] | 267 | zbtr = r1_e1e2t(iid,jj) / pe3t(iid,jj,ikud) |
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| 268 | ztra = zu_bbl * ( pt(iis,jj,ikus,jn) - pt(iid,jj,ikud,jn) ) * zbtr |
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| 269 | pt_rhs(iid,jj,ikud,jn) = pt_rhs(iid,jj,ikud,jn) + ztra |
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| [2528] | 270 | ENDIF |
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| 271 | ! |
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| 272 | IF( vtr_bbl(ji,jj) /= 0.e0 ) THEN ! non-zero j-direction bbl advection |
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| 273 | ! down-slope j/k-indices (deep) & up-slope j/k indices (shelf) |
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| 274 | ijd = jj + MAX( 0, mgrhv(ji,jj) ) ; ijs = jj + 1 - MAX( 0, mgrhv(ji,jj) ) |
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| 275 | ikvd = mbkv_d(ji,jj) ; ikvs = mbkv(ji,jj) |
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| 276 | zv_bbl = ABS( vtr_bbl(ji,jj) ) |
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| [3764] | 277 | ! |
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| [2528] | 278 | ! up -slope T-point (shelf bottom point) |
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| [10806] | 279 | zbtr = r1_e1e2t(ji,ijs) / pe3t(ji,ijs,ikvs) |
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| 280 | ztra = zv_bbl * ( pt(ji,ijd,ikvs,jn) - pt(ji,ijs,ikvs,jn) ) * zbtr |
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| 281 | pt_rhs(ji,ijs,ikvs,jn) = pt_rhs(ji,ijs,ikvs,jn) + ztra |
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| [3764] | 282 | ! |
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| [2528] | 283 | DO jk = ikvs, ikvd-1 ! down-slope upper to down T-point (deep column) |
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| [10806] | 284 | zbtr = r1_e1e2t(ji,ijd) / pe3t(ji,ijd,jk) |
|---|
| 285 | ztra = zv_bbl * ( pt(ji,ijd,jk+1,jn) - pt(ji,ijd,jk,jn) ) * zbtr |
|---|
| 286 | pt_rhs(ji,ijd,jk,jn) = pt_rhs(ji,ijd,jk,jn) + ztra |
|---|
| [2528] | 287 | END DO |
|---|
| 288 | ! ! down-slope T-point (deep bottom point) |
|---|
| [10806] | 289 | zbtr = r1_e1e2t(ji,ijd) / pe3t(ji,ijd,ikvd) |
|---|
| 290 | ztra = zv_bbl * ( pt(ji,ijs,ikvs,jn) - pt(ji,ijd,ikvd,jn) ) * zbtr |
|---|
| 291 | pt_rhs(ji,ijd,ikvd,jn) = pt_rhs(ji,ijd,ikvd,jn) + ztra |
|---|
| [2528] | 292 | ENDIF |
|---|
| [457] | 293 | END DO |
|---|
| [2528] | 294 | ! |
|---|
| [457] | 295 | END DO |
|---|
| [9019] | 296 | ! ! =========== |
|---|
| 297 | END DO ! end tracer |
|---|
| 298 | ! ! =========== |
|---|
| [2528] | 299 | END SUBROUTINE tra_bbl_adv |
|---|
| [3] | 300 | |
|---|
| 301 | |
|---|
| [10806] | 302 | SUBROUTINE bbl( kt, kit000, ktlev1, ktlev2, kt2lev, cdtype ) |
|---|
| [2528] | 303 | !!---------------------------------------------------------------------- |
|---|
| 304 | !! *** ROUTINE bbl *** |
|---|
| [3764] | 305 | !! |
|---|
| [2528] | 306 | !! ** Purpose : Computes the bottom boundary horizontal and vertical |
|---|
| [3764] | 307 | !! advection terms. |
|---|
| [2528] | 308 | !! |
|---|
| [4990] | 309 | !! ** Method : * diffusive bbl (nn_bbl_ldf=1) : |
|---|
| [2528] | 310 | !! When the product grad( rho) * grad(h) < 0 (where grad is an |
|---|
| 311 | !! along bottom slope gradient) an additional lateral 2nd order |
|---|
| 312 | !! diffusion along the bottom slope is added to the general |
|---|
| 313 | !! tracer trend, otherwise the additional trend is set to 0. |
|---|
| 314 | !! A typical value of ahbt is 2000 m2/s (equivalent to |
|---|
| 315 | !! a downslope velocity of 20 cm/s if the condition for slope |
|---|
| 316 | !! convection is satified) |
|---|
| [4990] | 317 | !! * advective bbl (nn_bbl_adv=1 or 2) : |
|---|
| [2528] | 318 | !! nn_bbl_adv = 1 use of the ocean velocity as bbl velocity |
|---|
| 319 | !! nn_bbl_adv = 2 follow Campin and Goosse (1999) implentation |
|---|
| 320 | !! i.e. transport proportional to the along-slope density gradient |
|---|
| 321 | !! |
|---|
| 322 | !! NB: the along slope density gradient is evaluated using the |
|---|
| 323 | !! local density (i.e. referenced at a common local depth). |
|---|
| 324 | !! |
|---|
| 325 | !! References : Beckmann, A., and R. Doscher, 1997, J. Phys.Oceanogr., 581-591. |
|---|
| 326 | !! Campin, J.-M., and H. Goosse, 1999, Tellus, 412-430. |
|---|
| [3764] | 327 | !!---------------------------------------------------------------------- |
|---|
| [2528] | 328 | INTEGER , INTENT(in ) :: kt ! ocean time-step index |
|---|
| [4990] | 329 | INTEGER , INTENT(in ) :: kit000 ! first time step index |
|---|
| [10806] | 330 | INTEGER , INTENT(in ) :: ktlev1, ktlev2 ! time level indices for 3-time-levelsource terms |
|---|
| 331 | INTEGER , INTENT(in ) :: kt2lev ! time level index for 2-time-level source terms |
|---|
| [2528] | 332 | CHARACTER(len=3), INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator) |
|---|
| [6140] | 333 | ! |
|---|
| [2528] | 334 | INTEGER :: ji, jj ! dummy loop indices |
|---|
| 335 | INTEGER :: ik ! local integers |
|---|
| [4990] | 336 | INTEGER :: iis, iid, ikus, ikud ! - - |
|---|
| 337 | INTEGER :: ijs, ijd, ikvs, ikvd ! - - |
|---|
| 338 | REAL(wp) :: za, zb, zgdrho ! local scalars |
|---|
| 339 | REAL(wp) :: zsign, zsigna, zgbbl ! - - |
|---|
| 340 | REAL(wp), DIMENSION(jpi,jpj,jpts) :: zts, zab ! 3D workspace |
|---|
| 341 | REAL(wp), DIMENSION(jpi,jpj) :: zub, zvb, zdep ! 2D workspace |
|---|
| [2528] | 342 | !!---------------------------------------------------------------------- |
|---|
| [3294] | 343 | ! |
|---|
| 344 | IF( kt == kit000 ) THEN |
|---|
| [2528] | 345 | IF(lwp) WRITE(numout,*) |
|---|
| 346 | IF(lwp) WRITE(numout,*) 'trabbl:bbl : Compute bbl velocities and diffusive coefficients in ', cdtype |
|---|
| 347 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~' |
|---|
| 348 | ENDIF |
|---|
| [4990] | 349 | ! !* bottom variables (T, S, alpha, beta, depth, velocity) |
|---|
| [2528] | 350 | DO jj = 1, jpj |
|---|
| 351 | DO ji = 1, jpi |
|---|
| [4990] | 352 | ik = mbkt(ji,jj) ! bottom T-level index |
|---|
| [10806] | 353 | zts (ji,jj,jp_tem) = ts(ji,jj,ik,jp_tem,ktlev1) ! bottom before T and S |
|---|
| 354 | zts (ji,jj,jp_sal) = ts(ji,jj,ik,jp_sal,ktlev1) |
|---|
| [2528] | 355 | ! |
|---|
| [10806] | 356 | zdep(ji,jj) = gdept(ji,jj,ik,kt2lev) ! bottom T-level reference depth |
|---|
| 357 | zub (ji,jj) = uu(ji,jj,mbku(ji,jj),ktlev2) ! bottom velocity |
|---|
| 358 | zvb (ji,jj) = vv(ji,jj,mbkv(ji,jj),ktlev2) |
|---|
| [2528] | 359 | END DO |
|---|
| 360 | END DO |
|---|
| [4990] | 361 | ! |
|---|
| 362 | CALL eos_rab( zts, zdep, zab ) |
|---|
| 363 | ! |
|---|
| [2528] | 364 | ! !-------------------! |
|---|
| 365 | IF( nn_bbl_ldf == 1 ) THEN ! diffusive bbl ! |
|---|
| 366 | ! !-------------------! |
|---|
| 367 | DO jj = 1, jpjm1 ! (criteria for non zero flux: grad(rho).grad(h) < 0 ) |
|---|
| [4990] | 368 | DO ji = 1, fs_jpim1 ! vector opt. |
|---|
| 369 | ! ! i-direction |
|---|
| 370 | za = zab(ji+1,jj,jp_tem) + zab(ji,jj,jp_tem) ! 2*(alpha,beta) at u-point |
|---|
| 371 | zb = zab(ji+1,jj,jp_sal) + zab(ji,jj,jp_sal) |
|---|
| 372 | ! ! 2*masked bottom density gradient |
|---|
| 373 | zgdrho = ( za * ( zts(ji+1,jj,jp_tem) - zts(ji,jj,jp_tem) ) & |
|---|
| 374 | & - zb * ( zts(ji+1,jj,jp_sal) - zts(ji,jj,jp_sal) ) ) * umask(ji,jj,1) |
|---|
| [3764] | 375 | ! |
|---|
| [4990] | 376 | zsign = SIGN( 0.5, -zgdrho * REAL( mgrhu(ji,jj) ) ) ! sign of ( i-gradient * i-slope ) |
|---|
| 377 | ahu_bbl(ji,jj) = ( 0.5 - zsign ) * ahu_bbl_0(ji,jj) ! masked diffusive flux coeff. |
|---|
| [1601] | 378 | ! |
|---|
| [4990] | 379 | ! ! j-direction |
|---|
| 380 | za = zab(ji,jj+1,jp_tem) + zab(ji,jj,jp_tem) ! 2*(alpha,beta) at v-point |
|---|
| 381 | zb = zab(ji,jj+1,jp_sal) + zab(ji,jj,jp_sal) |
|---|
| 382 | ! ! 2*masked bottom density gradient |
|---|
| 383 | zgdrho = ( za * ( zts(ji,jj+1,jp_tem) - zts(ji,jj,jp_tem) ) & |
|---|
| 384 | & - zb * ( zts(ji,jj+1,jp_sal) - zts(ji,jj,jp_sal) ) ) * vmask(ji,jj,1) |
|---|
| [3764] | 385 | ! |
|---|
| [4990] | 386 | zsign = SIGN( 0.5, -zgdrho * REAL( mgrhv(ji,jj) ) ) ! sign of ( j-gradient * j-slope ) |
|---|
| [2528] | 387 | ahv_bbl(ji,jj) = ( 0.5 - zsign ) * ahv_bbl_0(ji,jj) |
|---|
| [1601] | 388 | END DO |
|---|
| [3] | 389 | END DO |
|---|
| [1601] | 390 | ! |
|---|
| [2528] | 391 | ENDIF |
|---|
| [6140] | 392 | ! |
|---|
| [2528] | 393 | ! !-------------------! |
|---|
| 394 | IF( nn_bbl_adv /= 0 ) THEN ! advective bbl ! |
|---|
| 395 | ! !-------------------! |
|---|
| 396 | SELECT CASE ( nn_bbl_adv ) !* bbl transport type |
|---|
| [503] | 397 | ! |
|---|
| [2528] | 398 | CASE( 1 ) != use of upper velocity |
|---|
| 399 | DO jj = 1, jpjm1 ! criteria: grad(rho).grad(h)<0 and grad(rho).grad(h)<0 |
|---|
| 400 | DO ji = 1, fs_jpim1 ! vector opt. |
|---|
| [4990] | 401 | ! ! i-direction |
|---|
| 402 | za = zab(ji+1,jj,jp_tem) + zab(ji,jj,jp_tem) ! 2*(alpha,beta) at u-point |
|---|
| 403 | zb = zab(ji+1,jj,jp_sal) + zab(ji,jj,jp_sal) |
|---|
| 404 | ! ! 2*masked bottom density gradient |
|---|
| 405 | zgdrho = ( za * ( zts(ji+1,jj,jp_tem) - zts(ji,jj,jp_tem) ) & |
|---|
| 406 | - zb * ( zts(ji+1,jj,jp_sal) - zts(ji,jj,jp_sal) ) ) * umask(ji,jj,1) |
|---|
| [3764] | 407 | ! |
|---|
| [4990] | 408 | zsign = SIGN( 0.5, - zgdrho * REAL( mgrhu(ji,jj) ) ) ! sign of i-gradient * i-slope |
|---|
| 409 | zsigna= SIGN( 0.5, zub(ji,jj) * REAL( mgrhu(ji,jj) ) ) ! sign of u * i-slope |
|---|
| [2528] | 410 | ! |
|---|
| [4990] | 411 | ! ! bbl velocity |
|---|
| [2528] | 412 | utr_bbl(ji,jj) = ( 0.5 + zsigna ) * ( 0.5 - zsign ) * e2u(ji,jj) * e3u_bbl_0(ji,jj) * zub(ji,jj) |
|---|
| 413 | ! |
|---|
| [4990] | 414 | ! ! j-direction |
|---|
| 415 | za = zab(ji,jj+1,jp_tem) + zab(ji,jj,jp_tem) ! 2*(alpha,beta) at v-point |
|---|
| 416 | zb = zab(ji,jj+1,jp_sal) + zab(ji,jj,jp_sal) |
|---|
| 417 | ! ! 2*masked bottom density gradient |
|---|
| 418 | zgdrho = ( za * ( zts(ji,jj+1,jp_tem) - zts(ji,jj,jp_tem) ) & |
|---|
| 419 | & - zb * ( zts(ji,jj+1,jp_sal) - zts(ji,jj,jp_sal) ) ) * vmask(ji,jj,1) |
|---|
| 420 | zsign = SIGN( 0.5, - zgdrho * REAL( mgrhv(ji,jj) ) ) ! sign of j-gradient * j-slope |
|---|
| 421 | zsigna= SIGN( 0.5, zvb(ji,jj) * REAL( mgrhv(ji,jj) ) ) ! sign of u * i-slope |
|---|
| [2528] | 422 | ! |
|---|
| [4990] | 423 | ! ! bbl transport |
|---|
| [2528] | 424 | vtr_bbl(ji,jj) = ( 0.5 + zsigna ) * ( 0.5 - zsign ) * e1v(ji,jj) * e3v_bbl_0(ji,jj) * zvb(ji,jj) |
|---|
| 425 | END DO |
|---|
| 426 | END DO |
|---|
| [503] | 427 | ! |
|---|
| [2528] | 428 | CASE( 2 ) != bbl velocity = F( delta rho ) |
|---|
| 429 | zgbbl = grav * rn_gambbl |
|---|
| 430 | DO jj = 1, jpjm1 ! criteria: rho_up > rho_down |
|---|
| 431 | DO ji = 1, fs_jpim1 ! vector opt. |
|---|
| [4990] | 432 | ! ! i-direction |
|---|
| [2528] | 433 | ! down-slope T-point i/k-index (deep) & up-slope T-point i/k-index (shelf) |
|---|
| [4990] | 434 | iid = ji + MAX( 0, mgrhu(ji,jj) ) |
|---|
| 435 | iis = ji + 1 - MAX( 0, mgrhu(ji,jj) ) |
|---|
| [2528] | 436 | ! |
|---|
| [4990] | 437 | ikud = mbku_d(ji,jj) |
|---|
| 438 | ikus = mbku(ji,jj) |
|---|
| [2528] | 439 | ! |
|---|
| [4990] | 440 | za = zab(ji+1,jj,jp_tem) + zab(ji,jj,jp_tem) ! 2*(alpha,beta) at u-point |
|---|
| 441 | zb = zab(ji+1,jj,jp_sal) + zab(ji,jj,jp_sal) |
|---|
| 442 | ! ! masked bottom density gradient |
|---|
| 443 | zgdrho = 0.5 * ( za * ( zts(iid,jj,jp_tem) - zts(iis,jj,jp_tem) ) & |
|---|
| 444 | & - zb * ( zts(iid,jj,jp_sal) - zts(iis,jj,jp_sal) ) ) * umask(ji,jj,1) |
|---|
| 445 | zgdrho = MAX( 0.e0, zgdrho ) ! only if shelf is denser than deep |
|---|
| 446 | ! |
|---|
| 447 | ! ! bbl transport (down-slope direction) |
|---|
| [2528] | 448 | utr_bbl(ji,jj) = e2u(ji,jj) * e3u_bbl_0(ji,jj) * zgbbl * zgdrho * REAL( mgrhu(ji,jj) ) |
|---|
| 449 | ! |
|---|
| [4990] | 450 | ! ! j-direction |
|---|
| [2528] | 451 | ! down-slope T-point j/k-index (deep) & of the up -slope T-point j/k-index (shelf) |
|---|
| [4990] | 452 | ijd = jj + MAX( 0, mgrhv(ji,jj) ) |
|---|
| 453 | ijs = jj + 1 - MAX( 0, mgrhv(ji,jj) ) |
|---|
| [2528] | 454 | ! |
|---|
| [4990] | 455 | ikvd = mbkv_d(ji,jj) |
|---|
| 456 | ikvs = mbkv(ji,jj) |
|---|
| [2528] | 457 | ! |
|---|
| [4990] | 458 | za = zab(ji,jj+1,jp_tem) + zab(ji,jj,jp_tem) ! 2*(alpha,beta) at v-point |
|---|
| 459 | zb = zab(ji,jj+1,jp_sal) + zab(ji,jj,jp_sal) |
|---|
| 460 | ! ! masked bottom density gradient |
|---|
| 461 | zgdrho = 0.5 * ( za * ( zts(ji,ijd,jp_tem) - zts(ji,ijs,jp_tem) ) & |
|---|
| 462 | & - zb * ( zts(ji,ijd,jp_sal) - zts(ji,ijs,jp_sal) ) ) * vmask(ji,jj,1) |
|---|
| 463 | zgdrho = MAX( 0.e0, zgdrho ) ! only if shelf is denser than deep |
|---|
| 464 | ! |
|---|
| 465 | ! ! bbl transport (down-slope direction) |
|---|
| [2528] | 466 | vtr_bbl(ji,jj) = e1v(ji,jj) * e3v_bbl_0(ji,jj) * zgbbl * zgdrho * REAL( mgrhv(ji,jj) ) |
|---|
| 467 | END DO |
|---|
| 468 | END DO |
|---|
| [3] | 469 | END SELECT |
|---|
| [2528] | 470 | ! |
|---|
| [3] | 471 | ENDIF |
|---|
| [503] | 472 | ! |
|---|
| [2528] | 473 | END SUBROUTINE bbl |
|---|
| [3] | 474 | |
|---|
| 475 | |
|---|
| 476 | SUBROUTINE tra_bbl_init |
|---|
| 477 | !!---------------------------------------------------------------------- |
|---|
| 478 | !! *** ROUTINE tra_bbl_init *** |
|---|
| 479 | !! |
|---|
| 480 | !! ** Purpose : Initialization for the bottom boundary layer scheme. |
|---|
| 481 | !! |
|---|
| 482 | !! ** Method : Read the nambbl namelist and check the parameters |
|---|
| [3294] | 483 | !! called by nemo_init at the first timestep (kit000) |
|---|
| [3] | 484 | !!---------------------------------------------------------------------- |
|---|
| [9019] | 485 | INTEGER :: ji, jj ! dummy loop indices |
|---|
| 486 | INTEGER :: ii0, ii1, ij0, ij1, ios ! local integer |
|---|
| [9094] | 487 | REAL(wp), DIMENSION(jpi,jpj) :: zmbku, zmbkv ! workspace |
|---|
| [9019] | 488 | !! |
|---|
| 489 | NAMELIST/nambbl/ ln_trabbl, nn_bbl_ldf, nn_bbl_adv, rn_ahtbbl, rn_gambbl |
|---|
| [3] | 490 | !!---------------------------------------------------------------------- |
|---|
| [3294] | 491 | ! |
|---|
| [4147] | 492 | REWIND( numnam_ref ) ! Namelist nambbl in reference namelist : Bottom boundary layer scheme |
|---|
| 493 | READ ( numnam_ref, nambbl, IOSTAT = ios, ERR = 901) |
|---|
| [6140] | 494 | 901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'nambbl in reference namelist', lwp ) |
|---|
| 495 | ! |
|---|
| [4147] | 496 | REWIND( numnam_cfg ) ! Namelist nambbl in configuration namelist : Bottom boundary layer scheme |
|---|
| 497 | READ ( numnam_cfg, nambbl, IOSTAT = ios, ERR = 902 ) |
|---|
| [9168] | 498 | 902 IF( ios > 0 ) CALL ctl_nam ( ios , 'nambbl in configuration namelist', lwp ) |
|---|
| [4624] | 499 | IF(lwm) WRITE ( numond, nambbl ) |
|---|
| [2528] | 500 | ! |
|---|
| 501 | l_bbl = .TRUE. !* flag to compute bbl coef and transport |
|---|
| 502 | ! |
|---|
| 503 | IF(lwp) THEN !* Parameter control and print |
|---|
| [3] | 504 | WRITE(numout,*) |
|---|
| [2528] | 505 | WRITE(numout,*) 'tra_bbl_init : bottom boundary layer initialisation' |
|---|
| [3] | 506 | WRITE(numout,*) '~~~~~~~~~~~~' |
|---|
| [9019] | 507 | WRITE(numout,*) ' Namelist nambbl : set bbl parameters' |
|---|
| 508 | WRITE(numout,*) ' bottom boundary layer flag ln_trabbl = ', ln_trabbl |
|---|
| [3] | 509 | ENDIF |
|---|
| [9019] | 510 | IF( .NOT.ln_trabbl ) RETURN |
|---|
| 511 | ! |
|---|
| 512 | IF(lwp) THEN |
|---|
| 513 | WRITE(numout,*) ' diffusive bbl (=1) or not (=0) nn_bbl_ldf = ', nn_bbl_ldf |
|---|
| 514 | WRITE(numout,*) ' advective bbl (=1/2) or not (=0) nn_bbl_adv = ', nn_bbl_adv |
|---|
| 515 | WRITE(numout,*) ' diffusive bbl coefficient rn_ahtbbl = ', rn_ahtbbl, ' m2/s' |
|---|
| 516 | WRITE(numout,*) ' advective bbl coefficient rn_gambbl = ', rn_gambbl, ' s' |
|---|
| 517 | ENDIF |
|---|
| 518 | ! |
|---|
| [2715] | 519 | ! ! allocate trabbl arrays |
|---|
| 520 | IF( tra_bbl_alloc() /= 0 ) CALL ctl_stop( 'STOP', 'tra_bbl_init : unable to allocate arrays' ) |
|---|
| [9019] | 521 | ! |
|---|
| [2528] | 522 | IF( nn_bbl_adv == 1 ) WRITE(numout,*) ' * Advective BBL using upper velocity' |
|---|
| 523 | IF( nn_bbl_adv == 2 ) WRITE(numout,*) ' * Advective BBL using velocity = F( delta rho)' |
|---|
| [9019] | 524 | ! |
|---|
| [2528] | 525 | ! !* vertical index of "deep" bottom u- and v-points |
|---|
| 526 | DO jj = 1, jpjm1 ! (the "shelf" bottom k-indices are mbku and mbkv) |
|---|
| 527 | DO ji = 1, jpim1 |
|---|
| 528 | mbku_d(ji,jj) = MAX( mbkt(ji+1,jj ) , mbkt(ji,jj) ) ! >= 1 as mbkt=1 over land |
|---|
| 529 | mbkv_d(ji,jj) = MAX( mbkt(ji ,jj+1) , mbkt(ji,jj) ) |
|---|
| [3] | 530 | END DO |
|---|
| 531 | END DO |
|---|
| [4990] | 532 | ! converte into REAL to use lbc_lnk ; impose a min value of 1 as a zero can be set in lbclnk |
|---|
| [9094] | 533 | zmbku(:,:) = REAL( mbku_d(:,:), wp ) ; zmbkv(:,:) = REAL( mbkv_d(:,:), wp ) |
|---|
| [10425] | 534 | CALL lbc_lnk_multi( 'trabbl', zmbku,'U',1., zmbkv,'V',1.) |
|---|
| [9919] | 535 | mbku_d(:,:) = MAX( INT( zmbku(:,:) ), 1 ) ; mbkv_d(:,:) = MAX( NINT( zmbkv(:,:) ), 1 ) |
|---|
| [9019] | 536 | ! |
|---|
| [9168] | 537 | ! !* sign of grad(H) at u- and v-points; zero if grad(H) = 0 |
|---|
| [8509] | 538 | mgrhu(:,:) = 0 ; mgrhv(:,:) = 0 |
|---|
| [3764] | 539 | DO jj = 1, jpjm1 |
|---|
| [3] | 540 | DO ji = 1, jpim1 |
|---|
| [8509] | 541 | IF( gdept_0(ji+1,jj,mbkt(ji+1,jj)) - gdept_0(ji,jj,mbkt(ji,jj)) /= 0._wp ) THEN |
|---|
| 542 | mgrhu(ji,jj) = INT( SIGN( 1.e0, gdept_0(ji+1,jj,mbkt(ji+1,jj)) - gdept_0(ji,jj,mbkt(ji,jj)) ) ) |
|---|
| 543 | ENDIF |
|---|
| 544 | ! |
|---|
| 545 | IF( gdept_0(ji,jj+1,mbkt(ji,jj+1)) - gdept_0(ji,jj,mbkt(ji,jj)) /= 0._wp ) THEN |
|---|
| 546 | mgrhv(ji,jj) = INT( SIGN( 1.e0, gdept_0(ji,jj+1,mbkt(ji,jj+1)) - gdept_0(ji,jj,mbkt(ji,jj)) ) ) |
|---|
| 547 | ENDIF |
|---|
| [3] | 548 | END DO |
|---|
| 549 | END DO |
|---|
| [7646] | 550 | ! |
|---|
| [3764] | 551 | DO jj = 1, jpjm1 !* bbl thickness at u- (v-) point |
|---|
| [4990] | 552 | DO ji = 1, jpim1 ! minimum of top & bottom e3u_0 (e3v_0) |
|---|
| [4292] | 553 | e3u_bbl_0(ji,jj) = MIN( e3u_0(ji,jj,mbkt(ji+1,jj )), e3u_0(ji,jj,mbkt(ji,jj)) ) |
|---|
| 554 | e3v_bbl_0(ji,jj) = MIN( e3v_0(ji,jj,mbkt(ji ,jj+1)), e3v_0(ji,jj,mbkt(ji,jj)) ) |
|---|
| [3764] | 555 | END DO |
|---|
| [2528] | 556 | END DO |
|---|
| [10425] | 557 | CALL lbc_lnk_multi( 'trabbl', e3u_bbl_0, 'U', 1. , e3v_bbl_0, 'V', 1. ) ! lateral boundary conditions |
|---|
| [7646] | 558 | ! |
|---|
| [3764] | 559 | ! !* masked diffusive flux coefficients |
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| [7753] | 560 | ahu_bbl_0(:,:) = rn_ahtbbl * e2_e1u(:,:) * e3u_bbl_0(:,:) * umask(:,:,1) |
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| 561 | ahv_bbl_0(:,:) = rn_ahtbbl * e1_e2v(:,:) * e3v_bbl_0(:,:) * vmask(:,:,1) |
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| [503] | 562 | ! |
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| [3] | 563 | END SUBROUTINE tra_bbl_init |
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| 564 | |
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| 565 | !!====================================================================== |
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| 566 | END MODULE trabbl |
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