| 1 | SUBROUTINE ice_sal_diff_CW(nlay_i,kideb,kiut) |
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| 2 | |
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| 3 | !!------------------------------------------------------------------ |
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| 4 | !! *** ROUTINE ice_sal_diff *** |
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| 5 | !! |
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| 6 | !! ** Purpose : |
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| 7 | !! This routine computes new salinities in the ice |
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| 8 | !! |
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| 9 | !! ** Method : Vertical salinity profile computation |
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| 10 | !! Resolves brine transport equation |
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| 11 | !! |
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| 12 | !! ** Steps |
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| 13 | !! |
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| 14 | !! ** Arguments |
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| 15 | !! |
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| 16 | !! ** Inputs / Outputs |
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| 17 | !! |
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| 18 | !! ** External |
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| 19 | !! |
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| 20 | !! ** References : Vancop. et al., 2008 |
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| 21 | !! |
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| 22 | !! ** History : |
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| 23 | !! (06-2003) Martin Vancop. LIM1D |
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| 24 | !! (06-2008) Martin Vancop. BIO-LIM |
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| 25 | !! (09-2008) Martin Vancop. Explicit gravity drainage |
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| 26 | !! |
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| 27 | !!------------------------------------------------------------------ |
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| 28 | |
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| 29 | USE lib_fortran |
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| 30 | |
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| 31 | INCLUDE 'type.com' |
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| 32 | INCLUDE 'para.com' |
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| 33 | INCLUDE 'const.com' |
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| 34 | INCLUDE 'ice.com' |
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| 35 | INCLUDE 'thermo.com' |
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| 36 | |
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| 37 | REAL(8), DIMENSION(nlay_i) :: |
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| 38 | & z_ms_i , !: mass of salt times thickness |
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| 39 | & z_sbr_i !: brine salinity |
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| 40 | |
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| 41 | REAL(8), DIMENSION(nlay_i) :: !: dummy factors for tracer equation |
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| 42 | & za , !: winter |
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| 43 | & zb , |
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| 44 | & ze , !: summer |
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| 45 | & zf , |
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| 46 | & zind , !: independent term in the tridiag system |
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| 47 | & zindw , !: independent term in the tridiag system |
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| 48 | & zinds , !: independent term in the tridiag system |
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| 49 | & zindtbis , !: |
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| 50 | & zdiagbis , !: |
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| 51 | & zflux !: flux of tracer under layer i |
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| 52 | |
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| 53 | REAL(8), DIMENSION(nlay_i,3) :: !: dummy factors for tracer equation |
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| 54 | & ztrid , !: tridiagonal matrix |
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| 55 | & ztridw , !: tridiagonal matrix, winter |
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| 56 | & ztrids !: tridiagonal matrix, summer |
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| 57 | |
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| 58 | REAL(8) :: |
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| 59 | & zdummy1 , !: dummy factors |
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| 60 | & zdummy2 , !: |
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| 61 | & zdummy3 , !: |
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| 62 | & zswitch_open , !: switch for brine network open or not |
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| 63 | & zswitchw , !: switch for winter drainage |
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| 64 | & zswitchs , !: switch for summer drainage |
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| 65 | & zeps = 1.0e-20 !: numerical limit |
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| 66 | |
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| 67 | ! Rayleigh number computation |
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| 68 | REAL(8) :: |
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| 69 | & ze_i_min , !: minimum brine volume |
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| 70 | & zc , !: temporary scalar for sea ice specific heat |
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| 71 | & zk , !: temporary scalar for sea ice thermal conductivity |
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| 72 | & zalphara !: multiplicator for diffusivity |
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| 73 | |
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| 74 | REAL(8), DIMENSION(nlay_i) :: |
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| 75 | & zsigma , !: brine salinity at layer interfaces |
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| 76 | & zperm , !: permeability |
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| 77 | & zpermin , !: minimum permeability |
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| 78 | & zrhodiff , !: density difference |
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| 79 | & zlevel , !: height of the water column |
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| 80 | & zthdiff , !: thermal diffusivity |
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| 81 | & zgrad_t !: temperature gradient in the ice |
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| 82 | |
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| 83 | INTEGER :: |
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| 84 | & layer2 , !: layer loop index |
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| 85 | & indtr !: index of tridiagonal system |
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| 86 | |
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| 87 | CHARACTER(len=4) :: |
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| 88 | & bc = 'conc' !: Boundary condition 'conc' or 'flux' |
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| 89 | |
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| 90 | REAL(8) :: |
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| 91 | & z_ms_i_ini , !: initial mass of salt |
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| 92 | & z_ms_i_fin , !: final mass of salt |
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| 93 | & z_fs_b , !: basal flux of salt |
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| 94 | & z_fs_su , !: surface flux of salt |
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| 95 | & z_dms_i !: mass variation |
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| 96 | |
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| 97 | LOGICAL :: |
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| 98 | & ln_write , |
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| 99 | & ln_con , |
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| 100 | & ln_sal , |
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| 101 | & ln_be , |
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| 102 | & ln_gd , |
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| 103 | & ln_fl |
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| 104 | |
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| 105 | ln_write = .TRUE. ! write outputs |
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| 106 | ln_con = .TRUE. ! conservation check |
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| 107 | ln_sal = .TRUE. ! compute salinity variations or not |
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| 108 | ln_be = .TRUE. ! compute brine expulsion or not |
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| 109 | ln_gd = .TRUE. ! compute gravity drainage or not |
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| 110 | ln_fl = .TRUE. ! compute flushing or not |
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| 111 | |
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| 112 | IF ( ln_write ) THEN |
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| 113 | WRITE(numout,*) |
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| 114 | WRITE(numout,*) ' ** ice_sal_diff_CW : ' |
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| 115 | WRITE(numout,*) ' ~~~~~~~~~~~~~~~~~~~~~ ' |
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| 116 | WRITE(numout,*) ' Cox and weeks based gravity drainage ' |
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| 117 | WRITE(numout,*) ' ln_sal = ', ln_sal |
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| 118 | ENDIF |
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| 119 | |
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| 120 | IF ( ln_sal ) THEN |
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| 121 | ! |
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| 122 | !------------------------------------------------------------------------------| |
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| 123 | ! 1) Initialization |
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| 124 | !------------------------------------------------------------------------------| |
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| 125 | ! |
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| 126 | IF ( ln_write ) THEN |
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| 127 | WRITE(numout,*) ' - Initialization ... ' |
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| 128 | ENDIF |
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| 129 | |
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| 130 | DO 10 ji = kideb, kiut |
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| 131 | |
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| 132 | ! gravity drainage parameter (Cox and Weeks 88) |
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| 133 | zeta = 20. |
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| 134 | |
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| 135 | ! brine diffusivity |
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| 136 | diff_br(:) = 0.0 |
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| 137 | |
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| 138 | !--------------------------- |
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| 139 | ! Brine volume and salinity |
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| 140 | !--------------------------- |
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| 141 | DO layer = 1, nlay_i |
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| 142 | e_i_b(layer) = - tmut * s_i_b(ji,layer) / ( t_i_b(ji,layer) |
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| 143 | & - tpw ) |
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| 144 | z_sbr_i(layer) = s_i_b(ji,layer) / e_i_b(layer) |
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| 145 | END DO |
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| 146 | |
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| 147 | !---------- |
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| 148 | ! Switches |
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| 149 | !---------- |
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| 150 | ! summer switch = 1 if Tsu ge tpw and min brine volume superior than e_thr_flu |
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| 151 | zswitchs = MAX( 0.0, SIGN ( 1.0d0, t_su_b(ji) - tpw ) ) ! 0 si hiver 1 si ete |
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| 152 | zbvmin = 1.0 |
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| 153 | DO layer = 1, nlay_i |
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| 154 | zbvmin = MIN( e_i_b(layer) , zbvmin ) ! minimum brine volume |
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| 155 | END DO |
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| 156 | IF ( zbvmin .LT. e_thr_flu ) zswitchs = 0.0 |
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| 157 | |
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| 158 | ! winter switch |
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| 159 | zswitchw = 1.0 - zswitchs |
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| 160 | |
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| 161 | !------------------ |
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| 162 | ! Percolating flux |
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| 163 | !------------------ |
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| 164 | ! Percolating flow ( rho dh * beta * switch / rhow ) |
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| 165 | qsummer = ( - rhog * MIN ( dh_i_surf(ji) , 0.0 ) |
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| 166 | & - rhon * MIN ( dh_s_tot(ji) , 0.0 ) ) |
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| 167 | qsummer = qsummer * flu_beta * zswitchs / 1000.0 |
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| 168 | |
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| 169 | !-------------------- |
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| 170 | ! Conservation check |
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| 171 | !-------------------- |
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| 172 | IF ( ln_con ) THEN |
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| 173 | CALL ice_sal_column( kideb , kiut , z_ms_i_ini , |
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| 174 | & s_i_b(1,1:nlay_i), |
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| 175 | & deltaz_i_phy, nlay_i, .FALSE. ) |
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| 176 | ENDIF ! ln_con |
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| 177 | |
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| 178 | IF ( ln_write ) THEN |
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| 179 | WRITE(numout,*) ' nlay_i : ', nlay_i |
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| 180 | WRITE(numout,*) ' kideb : ', kideb |
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| 181 | WRITE(numout,*) ' kiut : ', kiut |
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| 182 | WRITE(numout,*) ' ' |
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| 183 | WRITE(numout,*) ' deltaz_i_phy : ', ( deltaz_i_phy(layer), |
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| 184 | & layer = 1, nlay_i ) |
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| 185 | WRITE(numout,*) ' z_i_phy : ', ( z_i_phy(layer), |
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| 186 | & layer = 1, nlay_i ) |
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| 187 | WRITE(numout,*) ' s_i_b : ', ( s_i_b (ji,layer), |
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| 188 | & layer = 1, nlay_i ) |
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| 189 | WRITE(numout,*) ' t_i_b : ', ( t_i_b (ji,layer), |
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| 190 | & layer = 1, nlay_i ) |
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| 191 | WRITE(numout,*) ' e_i_b : ', ( e_i_b (layer), |
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| 192 | & layer = 1, nlay_i ) |
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| 193 | WRITE(numout,*) ' z_sbr_i : ', ( z_sbr_i (layer), |
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| 194 | & layer = 1, nlay_i ) |
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| 195 | WRITE(numout,*) |
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| 196 | WRITE(numout,*) ' zswitchs : ', zswitchs |
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| 197 | WRITE(numout,*) ' zswitchw : ', zswitchw |
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| 198 | WRITE(numout,*) |
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| 199 | ENDIF ! ln_write |
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| 200 | |
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| 201 | 10 CONTINUE |
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| 202 | |
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| 203 | ! |
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| 204 | !------------------------------------------------------------------------------| |
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| 205 | ! 2) Gravity drainage as from Cox and Weeks (1988) |
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| 206 | !------------------------------------------------------------------------------| |
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| 207 | ! |
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| 208 | IF ( zswitchw .EQ. 1.0 ) THEN |
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| 209 | |
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| 210 | DO 20 ji = kideb, kiut |
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| 211 | |
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| 212 | !---------------------- |
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| 213 | ! temperature gradient |
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| 214 | !---------------------- |
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| 215 | z_h_lay = ht_i_b(ji) / nlay_i |
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| 216 | zgrad_t(1) = 2. * ( t_i_b(ji,1) - ( ht_s_b(ji)*t_i_b(ji,1) + |
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| 217 | & z_h_lay*t_s_b(ji,1) ) / |
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| 218 | & ( z_h_lay + ht_s_b(ji) ) ) / z_h_lay |
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| 219 | |
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| 220 | DO layer = 2, nlay_i - 1 |
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| 221 | zgrad_t(layer) = ( t_i_b(ji,layer+1) - t_i_b(ji,layer-1) ) / |
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| 222 | & z_h_lay |
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| 223 | END DO |
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| 224 | zgrad_t(nlay_i) = - 2.*( t_i_b(ji,nlay_i) - t_bo_b(ji) ) / |
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| 225 | & z_h_lay |
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| 226 | |
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| 227 | IF ( ln_write ) WRITE(numout,*) ' zgrad_t : ', |
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| 228 | & ( zgrad_t(layer), layer = 1, nlay_i ) |
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| 229 | |
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| 230 | igrd = 1 ! switch for gravity drainage ( 1 if yes ) |
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| 231 | zdummysb = - FLOAT(igrd) * rhog / 1000. * ht_i_b(ji) ! salt flux [ kg NaCl.m-2.s-1 ] |
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| 232 | zdsdt = 0.0 |
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| 233 | DO layer = nlay_i, 1, -1 |
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| 234 | IF ( e_i_b(layer) .LE. e_thr_flu ) igrd = 0 |
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| 235 | IF ( zgrad_t(layer) .LE. 0 ) igrd = 0 ! temperature gradient must |
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| 236 | ! be directed downwards |
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| 237 | zds_grd = MIN ( 0.0, delta_cw * ( 1.0 - zeta * e_i_b(layer) |
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| 238 | & * zgrad_t(layer) * ddtb * igrd ) ) |
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| 239 | sn_i_b(layer) = s_i_b(ji,layer) + zds_grd |
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| 240 | zdsdt = zdsdt + FLOAT(igrd) * zds_grd / ddtb / FLOAT(nlay_i) |
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| 241 | END DO |
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| 242 | fsb = zdummysb * zdsdt |
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| 243 | |
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| 244 | 20 CONTINUE |
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| 245 | |
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| 246 | ENDIF ! zswitchw |
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| 247 | |
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| 248 | ! |
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| 249 | !------------------------------------------------------------------------------| |
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| 250 | ! 3) Compute dummy factors for tracer diffusion equation |
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| 251 | !------------------------------------------------------------------------------| |
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| 252 | |
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| 253 | IF ( ln_write ) THEN |
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| 254 | WRITE(numout,*) ' - Compute dummy factors for tracer diffusion' |
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| 255 | WRITE(numout,*) ' ' |
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| 256 | ENDIF |
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| 257 | |
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| 258 | DO 30 ji = kideb, kiut |
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| 259 | |
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| 260 | !---------------- |
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| 261 | ! Winter factors |
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| 262 | !---------------- |
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| 263 | IF ( zswitchw .EQ. 1. ) THEN |
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| 264 | za(:) = 0.0 |
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| 265 | zb(:) = 0.0 |
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| 266 | ENDIF |
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| 267 | |
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| 268 | !---------------------- |
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| 269 | ! Summer factors |
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| 270 | !---------------------- |
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| 271 | ! ze factors |
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| 272 | DO layer = 1, nlay_i |
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| 273 | ze(layer) = qsummer * zswitchs / |
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| 274 | & ( e_i_b(layer) * deltaz_i_phy(layer) ) |
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| 275 | END DO ! layer |
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| 276 | |
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| 277 | ! zf factors |
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| 278 | ! could remove those, they are totally useless!!! ;-) |
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| 279 | DO layer = 1, nlay_i - 1 |
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| 280 | zf(layer) = 1./2. * deltaz_i_phy(layer) / |
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| 281 | & ( z_i_phy(layer+1) - z_i_phy(layer) ) |
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| 282 | END DO ! layer |
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| 283 | |
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| 284 | IF ( ln_write ) THEN |
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| 285 | WRITE(numout,*) |
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| 286 | WRITE(numout,*) ' -Summer factors ' |
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| 287 | WRITE(numout,*) ' ze : ', ( ze(layer), layer = 1, nlay_i ) |
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| 288 | WRITE(numout,*) ' zf : ', ( zf(layer), layer = 1, nlay_i ) |
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| 289 | ENDIF |
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| 290 | |
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| 291 | 30 CONTINUE |
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| 292 | ! |
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| 293 | !----------------------------------------------------------------------- |
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| 294 | ! 4) Tridiagonal system terms for tracer diffusion equation, winter |
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| 295 | !----------------------------------------------------------------------- |
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| 296 | ! |
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| 297 | DO 40 ji = kideb, kiut |
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| 298 | |
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| 299 | ztridw(:,:) = 0. |
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| 300 | |
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| 301 | 40 CONTINUE |
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| 302 | ! |
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| 303 | !----------------------------------------------------------------------- |
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| 304 | ! 5) Tridiagonal system terms for tracer diffusion equation, summer |
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| 305 | !----------------------------------------------------------------------- |
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| 306 | ! |
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| 307 | DO 50 ji = kideb, kiut |
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| 308 | |
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| 309 | DO layer = 1, nlay_i |
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| 310 | ztrids(layer,1) = - ze(layer) |
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| 311 | ztrids(layer,2) = 1.0 + ze(layer) |
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| 312 | ztrids(layer,3) = 0.0 |
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| 313 | zinds(layer) = z_sbr_i(layer) |
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| 314 | END DO |
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| 315 | ztrids(1,1) = 0.0 |
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| 316 | |
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| 317 | IF ( ln_write ) THEN |
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| 318 | WRITE(numout,*) |
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| 319 | WRITE(numout,*) ' -Tridiag terms, summer ... ' |
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| 320 | WRITE(numout,*) |
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| 321 | DO layer = 1, nlay_i |
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| 322 | WRITE(numout,*) ' layer : ', layer |
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| 323 | WRITE(numout,*) ' ztrids : ', ztrids(layer,1), |
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| 324 | & ztrids(layer,2), ztrids(layer,3) |
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| 325 | WRITE(numout,*) ' zinds : ',zinds(layer) |
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| 326 | END DO |
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| 327 | ENDIF |
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| 328 | |
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| 329 | 50 CONTINUE |
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| 330 | |
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| 331 | ! |
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| 332 | !----------------------------------------------------------------------- |
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| 333 | ! 6) Partitionning tridiag system between summer and winter |
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| 334 | !----------------------------------------------------------------------- |
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| 335 | ! |
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| 336 | DO 60 ji = kideb, kiut |
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| 337 | |
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| 338 | DO indtr = 1, 3 |
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| 339 | DO layer = 1, nlay_i |
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| 340 | ztrid(layer,indtr) = zswitchs * ztrids(layer,indtr) |
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| 341 | END DO ! layer |
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| 342 | END DO ! indtr |
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| 343 | |
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| 344 | DO layer = 1, nlay_i |
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| 345 | zind(layer) = zswitchs * zinds(layer) |
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| 346 | END DO ! layer |
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| 347 | |
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| 348 | IF ( ln_write ) THEN |
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| 349 | WRITE(numout,*) |
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| 350 | WRITE(numout,*) ' -Tridiag terms...' |
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| 351 | WRITE(numout,*) |
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| 352 | WRITE(numout,*) ' zswitchw : ', zswitchw |
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| 353 | WRITE(numout,*) ' zswitchs : ', zswitchs |
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| 354 | DO layer = 1, nlay_i |
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| 355 | WRITE(numout,*) ' layer : ', layer |
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| 356 | WRITE(numout,*) ' ztrid : ', ztrid(layer,1), |
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| 357 | & ztrid(layer,2), ztrid(layer,3) |
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| 358 | WRITE(numout,*) ' zind : ', zind(layer) |
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| 359 | END DO ! layer |
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| 360 | ENDIF |
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| 361 | |
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| 362 | 60 CONTINUE |
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| 363 | ! |
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| 364 | !----------------------------------------------------------------------- |
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| 365 | ! 7) Solving the tridiagonal system |
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| 366 | !----------------------------------------------------------------------- |
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| 367 | ! |
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| 368 | DO 70 ji = kideb, kiut |
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| 369 | |
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| 370 | ! The tridiagonal system is solved with Gauss elimination |
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| 371 | ! Thomas algorithm, from Computational fluid Dynamics, J.D. ANDERSON, |
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| 372 | ! McGraw-Hill 1984. |
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| 373 | |
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| 374 | zindtbis(1) = zind(1) |
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| 375 | zdiagbis(1) = ztrid(1,2) |
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| 376 | |
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| 377 | DO layer = 2, nlay_i |
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| 378 | zdiagbis(layer) = ztrid(layer,2) - ztrid(layer,1) * |
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| 379 | & ztrid(layer-1,3) / zdiagbis(layer-1) |
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| 380 | zindtbis(layer) = zind(layer) - ztrid(layer,1) * |
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| 381 | & zindtbis(layer-1) / zdiagbis(layer-1) |
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| 382 | END DO |
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| 383 | |
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| 384 | ! Recover brine salinity |
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| 385 | z_sbr_i(nlay_i) = zindtbis(nlay_i) / zdiagbis(nlay_i) |
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| 386 | DO layer = nlay_i - 1 , 1 , -1 |
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| 387 | z_sbr_i(layer) = ( zindtbis(layer) - ztrid(layer,3)* |
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| 388 | & z_sbr_i(layer+1)) / zdiagbis(layer) |
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| 389 | END DO |
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| 390 | ! Recover ice salinity |
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| 391 | IF ( zswitchs .EQ. 1.0 ) THEN |
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| 392 | DO layer = 1, nlay_i |
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| 393 | sn_i_b(layer) = z_sbr_i(layer) * e_i_b(layer) |
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| 394 | ! s_i_b(ji,layer) = z_sbr_i(layer) * e_i_b(layer) |
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| 395 | END DO |
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| 396 | ENDIF |
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| 397 | |
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| 398 | IF ( ln_write ) THEN |
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| 399 | WRITE(numout,*) |
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| 400 | WRITE(numout,*) ' -Solving the tridiagonal system ... ' |
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| 401 | WRITE(numout,*) |
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| 402 | WRITE(numout,*) ' zdiagbis: ', ( zdiagbis(layer) , |
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| 403 | & layer = 1, nlay_i ) |
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| 404 | WRITE(numout,*) ' zindtbis: ', ( zdiagbis(layer) , |
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| 405 | & layer = 1, nlay_i ) |
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| 406 | WRITE(numout,*) ' z_sbr_i : ', ( z_sbr_i(layer) , |
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| 407 | & layer = 1, nlay_i ) |
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| 408 | WRITE(numout,*) ' sn_i_b : ', ( sn_i_b(layer) , |
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| 409 | & layer = 1, nlay_i ) |
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| 410 | ENDIF |
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| 411 | |
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| 412 | 70 CONTINUE |
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| 413 | ! |
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| 414 | !----------------------------------------------------------------------- |
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| 415 | ! 8) Mass of salt conserved ? |
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| 416 | !----------------------------------------------------------------------- |
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| 417 | ! |
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| 418 | DO 80 ji = kideb, kiut |
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| 419 | |
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| 420 | ! Final mass of salt |
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| 421 | CALL ice_sal_column( kideb , kiut , z_ms_i_fin , |
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| 422 | & sn_i_b(1:nlay_i), |
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| 423 | & deltaz_i_phy, nlay_i, .FALSE. ) |
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| 424 | |
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| 425 | ! Bottom flux ( positive upwards ) |
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| 426 | zswitch_open = 0.0 |
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| 427 | IF ( e_i_b(nlay_i) .GE. e_thr_flu ) zswitch_open = 1.0 |
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| 428 | zfb = zswitchw * ( - e_i_b( nlay_i ) ! had a minus before |
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| 429 | & * diff_br(nlay_i) * 2.0 |
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| 430 | & / deltaz_i_phy(nlay_i) * ( z_sbr_i(nlay_i) |
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| 431 | & - oce_sal ) ) * zswitch_open |
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| 432 | & + zswitchs * ( - qsummer * z_sbr_i(nlay_i) ) |
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| 433 | & / ddtb |
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| 434 | |
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| 435 | zflux(nlay_i) = zfb |
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| 436 | |
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| 437 | ! Surface flux of salt |
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| 438 | zfsu = zswitchw * 0.0 |
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| 439 | |
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| 440 | ! conservation check |
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| 441 | CALL ice_sal_conserv(kideb,kiut,'ice_sal_diff : ',zerror, |
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| 442 | & z_ms_i_ini,z_ms_i_fin, |
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| 443 | & zfb , zfsu , ddtb) |
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| 444 | |
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| 445 | 80 CONTINUE |
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| 446 | |
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| 447 | ENDIF ! ln_sal |
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| 448 | ! |
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| 449 | !------------------------------------------------------------------------------| |
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| 450 | ! End of la sous-routine |
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| 451 | WRITE(numout,*) |
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| 452 | END SUBROUTINE |
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