[6] | 1 | SUBROUTINE ice_th_diff(nlay_s,nlay_i,kideb,kiut) |
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| 2 | !!------------------------------------------------------------------ |
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| 3 | !! *** ROUTINE ice_th_diff *** |
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| 4 | !! ** Purpose : |
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| 5 | !! This routine determines the time evolution of snow and sea-ice |
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| 6 | !! temperature profiles. |
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| 7 | !! ** Method : |
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| 8 | !! This is done by solving the heat equation diffusion with |
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| 9 | !! a Neumann boundary condition at the surface and a Dirichlet one |
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| 10 | !! at the bottom. Solar radiation is partially absorbed into the ice. |
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| 11 | !! The specific heat and thermal conductivities depend on ice salinity |
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| 12 | !! and temperature to take into account brine pocket melting. The |
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| 13 | !! numerical |
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| 14 | !! scheme is an iterative Crank-Nicolson on a non-uniform multilayer grid |
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| 15 | !! in the ice and snow system. |
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| 16 | !! The successive steps of this routine are |
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| 17 | !! Vertical grid |
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| 18 | !! 1. Thermal conductivity at the interfaces of the ice layers |
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| 19 | !! 2. Internal absorbed radiation |
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| 20 | !! 3. Scale factors due to non-uniform grid |
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| 21 | !! 4. Kappa factors |
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| 22 | !! Then iterative procedure begins |
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| 23 | !! 5. specific heat in the ice |
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| 24 | !! 6. eta factors |
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| 25 | !! 7. surface flux computation |
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| 26 | !! 8. tridiagonal system terms |
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| 27 | !! 9. solving the tridiagonal system with Gauss elimination |
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| 28 | !! Iterative procedure ends according to a criterion on evolution |
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| 29 | !! of temperature |
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| 30 | !! |
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| 31 | !! ** Arguments : |
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| 32 | !! kideb , kiut : Starting and ending points on which the |
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| 33 | !! the computation is applied |
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| 34 | !! |
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| 35 | !! ** Inputs / Ouputs : (global commons) |
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| 36 | !! surface temperature : t_su_b |
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| 37 | !! ice/snow temperatures : t_i_b, t_s_b |
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| 38 | !! ice salinities : s_i_b |
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| 39 | !! number of layers in the ice/snow: nlay_i, nlay_s |
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| 40 | !! total ice/snow thickness : ht_i_b, ht_s_b |
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| 41 | !! |
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| 42 | !! ** External : |
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| 43 | !! |
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| 44 | !! ** References : |
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| 45 | !! |
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| 46 | !! ** History : |
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| 47 | !! (02-2003) Martin Vancoppenolle, Louvain-la-Neuve, Belgium |
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| 48 | !! |
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| 49 | |
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| 50 | USE lib_fortran |
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| 51 | |
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| 52 | INCLUDE 'type.com' |
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| 53 | INCLUDE 'para.com' |
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| 54 | INCLUDE 'const.com' |
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| 55 | INCLUDE 'ice.com' |
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| 56 | INCLUDE 'thermo.com' |
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| 57 | |
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| 58 | ! Local variables |
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| 59 | INTEGER numeqmin, numeqmax, numeq |
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| 60 | DIMENSION ztcond_i(0:nlay_i), |
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| 61 | & zkappa_s(0:nlay_s), |
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| 62 | & zkappa_i(0:nlay_i),ztstemp(0:nlay_s),ztitemp(0:nlay_i), |
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| 63 | & zspeche_i(0:nlay_i),ztsold(0:nlay_s),ztiold(0:nlay_i), |
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| 64 | & zeta_s(0:nlay_s),zeta_i(0:nlay_i),ztrid(2*maxnlay+1,3), |
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| 65 | & zindterm(2*maxnlay+1),zindtbis(2*maxnlay+1), |
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| 66 | & zdiagbis(2*maxnlay+1),ykn(nbpt),ykg(nbpt), |
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| 67 | & zrchu1(nbpt),zrchu2(nbpt),zqsat(nbpt) |
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| 68 | |
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| 69 | LOGICAL :: ln_write |
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| 70 | |
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| 71 | ! Local constants |
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| 72 | zeps = 1.0d-20 |
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| 73 | zg1s = 2.0 |
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| 74 | zg1 = 2.0 |
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| 75 | zbeta = 0.117 ! factor for thermal conductivity |
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| 76 | zerrmax = 1.0d-11 ! max error at the surface |
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| 77 | |
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| 78 | ! new lines |
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| 79 | zerrmax = 1.0e-4 |
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| 80 | nconv_max = 50 |
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| 81 | |
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| 82 | ln_write = .TRUE. |
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| 83 | |
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| 84 | DO 5 ji = kideb, kiut |
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| 85 | |
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| 86 | IF ( ln_write ) THEN |
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| 87 | WRITE(numout,*) ' ** ice_th_diff : ' |
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| 88 | WRITE(numout,*) ' ~~~~~~~~~~~~~~~~ ' |
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| 89 | WRITE(numout,*) ' nlay_i: ', nlay_i |
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| 90 | WRITE(numout,*) ' nlay_s: ', nlay_s |
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| 91 | WRITE(numout,*) ' t_su_b: ', t_su_b(ji) |
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| 92 | WRITE(numout,*) ' t_s_b : ', ( t_s_b(ji,layer), |
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| 93 | & layer = 1, nlay_s ) |
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| 94 | WRITE(numout,*) ' t_i_b : ', ( t_i_b(ji,layer), |
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| 95 | & layer = 1, nlay_i ) |
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| 96 | WRITE(numout,*) ' t_bo_b : ', t_bo_b(ji) |
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| 97 | WRITE(numout,*) ' ht_i_b : ', ht_i_b(ji) |
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| 98 | WRITE(numout,*) ' ht_s_b : ', ht_s_b(ji) |
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| 99 | ENDIF |
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| 100 | |
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| 101 | ! Switches |
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| 102 | ! isnow equals 1 if snow is present and 0 if absent |
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| 103 | isnow = int(1.0-max(0.0,sign(1.0d0,-ht_s_b(ji)))) |
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| 104 | ! imelt equals 1 if surface is melting and 0 if not |
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| 105 | imelt = int(max(0.0,sign(1.0d0,t_su_b(ji)-tpw))) |
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| 106 | |
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| 107 | tfs(ji) = real(isnow)*tfsn+ (1.0-real(isnow))*tfsg |
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| 108 | |
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| 109 | ! Oceanic heat flux and precipitations |
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| 110 | fbbqb(ji) = oce_flx |
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| 111 | |
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| 112 | IF ( ln_write ) THEN |
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| 113 | WRITE(numout,*) ' isnow : ', isnow |
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| 114 | WRITE(numout,*) ' imelt : ', imelt |
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| 115 | WRITE(numout,*) ' tfs : ', tfs(ji) |
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| 116 | ENDIF |
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| 117 | |
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| 118 | 5 CONTINUE |
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| 119 | ! |
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| 120 | !------------------------------------------------------------------------------ |
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| 121 | ! 1) Thermal conductivity at the ice interfaces |
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| 122 | !------------------------------------------------------------------------------ |
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| 123 | ! |
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| 124 | ! Pringle et al., JGR 2007 formula |
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| 125 | ! 2.11 + 0.09 S/T - 0.011.T |
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| 126 | |
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| 127 | DO 10 ji = kideb, kiut |
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| 128 | |
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| 129 | ! thermal conductivity in the snow |
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| 130 | ykn(ji) = xkn |
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| 131 | zkimin = 0.1 |
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| 132 | |
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| 133 | ztcond_i(0) = xkg + betak1*s_i_b(ji,1) |
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| 134 | & / MIN( -zeps , t_i_b(ji,1) - tpw ) |
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| 135 | & - betak2* ( t_i_b(ji,1) - tpw ) |
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| 136 | ztcond_i(0) = MAX( ztcond_i(0) , zkimin ) |
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| 137 | |
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| 138 | DO layer = 1, nlay_i-1 |
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| 139 | ztcond_i(layer) = xkg + betak1*( s_i_b(ji,layer) |
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| 140 | & + s_i_b(ji,layer+1) ) / MIN(-zeps, |
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| 141 | & t_i_b(ji,layer)+t_i_b(ji,layer+1)-2.0*tpw) |
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| 142 | & - betak2 * 0.5 * ( t_i_b(ji,layer) + ! bugfix fred dupont add 0.5 |
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| 143 | & t_i_b(ji,layer+1) - 2.0*tpw ) |
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| 144 | ztcond_i(layer) = MAX( ztcond_i(layer) , zkimin ) |
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| 145 | END DO |
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| 146 | |
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| 147 | ztcond_i(nlay_i) = xkg + betak1*s_i_b(ji,nlay_i) / |
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| 148 | & MIN( -zeps , t_bo_b(ji) - tpw ) |
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| 149 | & - betak2 * ( t_bo_b(ji) - tpw ) |
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| 150 | ztcond_i(nlay_i) = MAX( ztcond_i(nlay_i) , zkimin ) |
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| 151 | |
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| 152 | IF ( ln_write ) THEN |
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| 153 | WRITE(numout,*) ' ztcond_i : ', ztcond_i(0:nlay_i) |
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| 154 | ENDIF |
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| 155 | |
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| 156 | 10 CONTINUE |
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| 157 | ! |
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| 158 | !------------------------------------------------------------------------------ |
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| 159 | ! 3) kappa factors |
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| 160 | !------------------------------------------------------------------------------ |
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| 161 | ! |
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| 162 | DO 30 ji = kideb, kiut |
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| 163 | ! snow |
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| 164 | zkappa_s(0) = ykn(ji)/max(zeps,deltaz_s_phy(1)) |
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| 165 | do layer = 1, nlay_s-1 |
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| 166 | zkappa_s(layer) = 2.0*ykn(ji)/ |
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| 167 | & max(zeps,deltaz_s_phy(layer)+deltaz_s_phy(layer+1)) |
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| 168 | end do |
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| 169 | zkappa_s(nlay_s) = ykn(ji)/max(zeps,deltaz_s_phy(nlay_s)) |
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| 170 | |
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| 171 | ! ice |
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| 172 | zkappa_i(0) = ztcond_i(0)/max(zeps,deltaz_i_phy(1)) |
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| 173 | do layer = 1, nlay_i-1 |
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| 174 | zkappa_i(layer) = 2.0*ztcond_i(layer)/ |
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| 175 | & max(zeps,deltaz_i_phy(layer)+deltaz_i_phy(layer+1)) |
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| 176 | end do |
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| 177 | zkappa_i(nlay_i) = ztcond_i(nlay_i) / |
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| 178 | & MAX(zeps,deltaz_i_phy(nlay_i)) |
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| 179 | |
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| 180 | ! interface |
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| 181 | zkappa_s(nlay_s) = 2.0*ykn(ji)*ztcond_i(0)/max(zeps, |
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| 182 | & (ztcond_i(0)*deltaz_s_phy(nlay_s) + |
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| 183 | & ykn(ji)*deltaz_i_phy(1))) |
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| 184 | zkappa_i(0) = zkappa_s(nlay_s)*real(isnow) |
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| 185 | & + zkappa_i(0)*(1.0-real(isnow)) |
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| 186 | |
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| 187 | IF ( ln_write ) THEN |
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| 188 | WRITE(numout,*) ' nlay_s : ', nlay_s |
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| 189 | WRITE(numout,*) ' zkappa_s : ', zkappa_s(0:nlay_s) |
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| 190 | WRITE(numout,*) ' zkappa_i : ', zkappa_i(0:nlay_i) |
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| 191 | ENDIF |
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| 192 | |
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| 193 | 30 CONTINUE |
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| 194 | ! |
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| 195 | !------------------------------------------------------------------------------| |
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| 196 | ! 4) iterative procedure begins | |
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| 197 | !------------------------------------------------------------------------------| |
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| 198 | ! |
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| 199 | DO 40 ji = kideb, kiut |
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| 200 | |
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| 201 | !------------------------------ |
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| 202 | ! keeping old values in memory |
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| 203 | !------------------------------ |
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| 204 | |
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| 205 | ztsuold = t_su_b(ji) |
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| 206 | t_su_b(ji) = min(t_su_b(ji),tfs(ji)-0.00001) |
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| 207 | DO layer = 1, nlay_s |
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| 208 | ztsold(layer) = t_s_b(ji,layer) |
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| 209 | END DO |
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| 210 | DO layer = 1, nlay_i |
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| 211 | ztiold(layer) = t_i_b(ji,layer) |
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| 212 | ti_old(layer) = ztiold(layer) |
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| 213 | END DO |
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| 214 | |
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| 215 | nconv = 0 |
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| 216 | |
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| 217 | 40 CONTINUE |
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| 218 | |
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| 219 | !------------------------------ |
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| 220 | ! Beginning of the loop |
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| 221 | !------------------------------ |
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| 222 | |
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| 223 | zerrit = 10000.0 |
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| 224 | |
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| 225 | ! DO WHILE ( zerrit .GT. zerrmax ) |
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| 226 | DO WHILE ( ( zerrit .GT. zerrmax ) .AND. ( nconv < nconv_max ) ) |
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| 227 | |
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| 228 | do 42 ji = kideb, kiut |
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| 229 | |
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| 230 | !45 CONTINUE |
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| 231 | |
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| 232 | nconv = nconv+1 |
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| 233 | |
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| 234 | ztsutemp = t_su_b(ji) |
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| 235 | DO layer = 1, nlay_s |
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| 236 | ztstemp(layer) = t_s_b(ji,layer) |
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| 237 | END DO |
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| 238 | DO layer = 1, nlay_i |
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| 239 | ztitemp(layer) = t_i_b(ji,layer) |
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| 240 | END DO |
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| 241 | |
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| 242 | IF ( ln_write ) THEN |
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| 243 | WRITE(numout,*) ' zerrit : ', zerrit |
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| 244 | WRITE(numout,*) ' nconv : ', nconv |
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| 245 | WRITE(numout,*) ' t_s_b : ', t_s_b(ji,1) |
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| 246 | WRITE(numout,*) ' t_i_b : ', ( t_i_b(ji,layer), layer = 1, |
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| 247 | & nlay_i ) |
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| 248 | ENDIF |
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| 249 | |
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| 250 | ! |
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| 251 | !------------------------------------------------------------------------------| |
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| 252 | ! 5) specific heat in the ice | |
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| 253 | !------------------------------------------------------------------------------| |
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| 254 | ! |
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| 255 | DO layer = 1, nlay_i |
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| 256 | zspeche_i(layer) = cpg + lfus*tmut*s_i_b(ji,layer)/ |
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| 257 | & MAX((t_i_b(ji,layer)-tpw)*(ztiold(layer)-tpw),zeps) |
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| 258 | END DO |
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| 259 | ! |
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| 260 | !------------------------------------------------------------------------------| |
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| 261 | ! 6) eta factors | |
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| 262 | !------------------------------------------------------------------------------| |
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| 263 | ! |
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| 264 | DO layer = 1, nlay_s |
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| 265 | zeta_s(layer) = ddtb / max(rhon*cpg*deltaz_s_phy(layer),zeps) |
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| 266 | END DO |
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| 267 | |
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| 268 | DO layer = 1, nlay_i |
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| 269 | zeta_i(layer) = ddtb / max(rhog*deltaz_i_phy(layer) * |
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| 270 | & zspeche_i(layer) |
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| 271 | & ,zeps) |
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| 272 | END DO |
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| 273 | |
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| 274 | ! |
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| 275 | !------------------------------------------------------------------------------| |
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| 276 | ! 7) surface flux computation | |
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| 277 | !------------------------------------------------------------------------------| |
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| 278 | ! |
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| 279 | t_su_b(ji) = min(t_su_b(ji),tfs(ji)) |
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| 280 | imelt = int(max(0.0,sign(1.0d0,t_su_b(ji)-tpw))) |
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| 281 | ! pressure of water vapor saturation (Pa) |
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| 282 | es = 611.0*10.0**(9.5*(t_su_b(ji)-273.16)/ |
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| 283 | & (t_su_b(ji)-7.66)) |
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| 284 | ! net longwave radiative flux |
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| 285 | ! MV BUG |
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| 286 | ! fratsb(ji) = emig*(ratbqb(ji)- |
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| 287 | ! & stefan*t_su_b(ji)*t_su_b(ji)*t_su_b(ji)*t_su_b(ji)) |
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| 288 | fratsb(ji) = ratbqb(ji) - emig * |
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| 289 | & stefan*t_su_b(ji)*t_su_b(ji)*t_su_b(ji)*t_su_b(ji) |
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| 290 | ! sensible and latent heat flux |
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| 291 | CALL flx(ht_i_b(ji),t_su_b(ji),tabqb(ji),qabqb(ji),fcsb(ji), |
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| 292 | & fleb(ji),qsfcb(ji),zrchu1(ji),zrchu2(ji),vabqb(ji),zref) |
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| 293 | fcsb(ji) = -fcsb(ji) |
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| 294 | fleb(ji) = MIN( -fleb(ji) , 0.0 ) ! always negative, as precip |
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| 295 | ! energy already added |
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| 296 | |
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| 297 | ! qsfcb(ji) = zqsat(ji) |
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| 298 | |
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| 299 | ! intermediate variable |
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| 300 | zssdqw = qsfcb(ji)*qsfcb(ji)*psbqb(ji)/ |
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| 301 | & (0.622*es)*alog(10.0)*9.5* |
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| 302 | & ((273.16-7.66)/(t_su_b(ji)-7.66)**2.0) |
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| 303 | ! derivative of the surface atmospheric net flux |
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| 304 | dzf = -4.0*emig*stefan*t_su_b(ji) |
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| 305 | & *t_su_b(ji)*t_su_b(ji) |
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| 306 | & -(zrchu1(ji)+zrchu2(ji)*zssdqw) |
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| 307 | ! surface atmospheric net flux |
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| 308 | zf = ab(ji)*fsolgb(ji)+fratsb(ji) |
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| 309 | & +fcsb(ji)+fleb(ji) |
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| 310 | |
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| 311 | ! |
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| 312 | !------------------------------------------------------------------------------| |
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| 313 | ! 8) tridiagonal system terms | |
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| 314 | !------------------------------------------------------------------------------| |
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| 315 | ! |
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| 316 | ! layer denotes the number of the layer in the snow or in the ice |
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| 317 | ! numeq denotes the reference number of the equation in the tridiagonal |
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| 318 | ! system, terms of tridiagonal system are indexed as following : |
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| 319 | ! 1 is subdiagonal term, 2 is diagonal and 3 is superdiagonal one |
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| 320 | |
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| 321 | ! ice interior terms (top equation has the same form as the others) |
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| 322 | DO numeq = 1, maxnlay |
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| 323 | ztrid(numeq,1) = 0.0 |
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| 324 | ztrid(numeq,2) = 0.0 |
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| 325 | ztrid(numeq,3) = 0.0 |
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| 326 | zindterm(numeq) = 0.0 |
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| 327 | zindtbis(numeq) = 0.0 |
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| 328 | zdiagbis(numeq) = 0.0 |
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| 329 | END DO |
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| 330 | DO numeq = nlay_s + 2, nlay_s + nlay_i |
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| 331 | layer = numeq - nlay_s - 1 |
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| 332 | ztrid(numeq,1) = - zeta_i(layer)*zkappa_i(layer-1) |
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| 333 | ztrid(numeq,2) = 1.0 + zeta_i(layer)*(zkappa_i(layer-1) + |
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| 334 | & zkappa_i(layer)) |
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| 335 | ztrid(numeq,3) = - zeta_i(layer)*zkappa_i(layer) |
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| 336 | zindterm(numeq) = ztiold(layer) + zeta_i(layer)* |
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| 337 | ! & ( radab_phy_i(layer) + radab_alg_i(layer) ) |
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| 338 | & radab_i(layer) |
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| 339 | END DO |
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| 340 | ! ice bottom terms |
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| 341 | numeq = nlay_s + nlay_i + 1 |
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| 342 | ztrid(numeq,1) = - zeta_i(nlay_i)*zkappa_i(nlay_i-1) |
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| 343 | ztrid(numeq,2) = 1.0 + zeta_i(nlay_i)*( zkappa_i(nlay_i)*zg1 |
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| 344 | & + zkappa_i(nlay_i-1) ) |
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| 345 | ztrid(numeq,3) = 0.0 |
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| 346 | zindterm(numeq) = ztiold(nlay_i) + zeta_i(nlay_i)* |
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| 347 | ! & ( radab_phy_i(nlay_i) + radab_alg_i(nlay_i) |
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| 348 | & ( radab_i(nlay_i) |
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| 349 | & + zkappa_i(nlay_i)*zg1 |
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| 350 | & *t_bo_b(ji) ) |
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| 351 | |
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| 352 | IF (ht_s_b(ji).GT.0.0) THEN |
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| 353 | ! |
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| 354 | !------------------------------------------------------------------------------| |
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| 355 | ! snow-covered cells | |
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| 356 | !------------------------------------------------------------------------------| |
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| 357 | ! |
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| 358 | ! snow interior terms (bottom equation has the same form as the others) |
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| 359 | do numeq = 3, nlay_s + 1 |
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| 360 | layer = numeq - 1 |
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| 361 | ztrid(numeq,1) = - zeta_s(layer)*zkappa_s(layer-1) |
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| 362 | ztrid(numeq,2) = 1.0 + zeta_s(layer)*( zkappa_s(layer-1) + |
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| 363 | & zkappa_s(layer) ) |
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| 364 | ztrid(numeq,3) = - zeta_s(layer)*zkappa_s(layer) |
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| 365 | zindterm(numeq) = ztsold(layer) + zeta_s(layer)* |
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| 366 | & radab_s(layer) |
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| 367 | end do |
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| 368 | |
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| 369 | ! case of only one layer in the ice (ice equation is altered) |
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| 370 | if (nlay_i.eq.1) then |
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| 371 | ztrid(nlay_s+2,3) = 0.0 |
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| 372 | zindterm(nlay_s+2) = zindterm(nlay_s+2) + zkappa_i(1)* |
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| 373 | & t_bo_b(ji) |
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| 374 | endif |
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| 375 | |
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| 376 | IF (t_su_b(ji).LT.tpw) THEN |
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| 377 | ! |
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| 378 | !------------------------------------------------------------------------------| |
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| 379 | ! case 1 : no surface melting - snow present | |
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| 380 | !------------------------------------------------------------------------------| |
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| 381 | ! |
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| 382 | zdifcase = 1.0 |
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| 383 | numeqmin = 1 |
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| 384 | numeqmax = nlay_i + nlay_s + 1 |
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| 385 | |
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| 386 | ! surface equation |
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| 387 | ztrid(1,1) = 0.0 |
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| 388 | ztrid(1,2) = dzf - zg1s*zkappa_s(0) |
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| 389 | ztrid(1,3) = zg1s*zkappa_s(0) |
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| 390 | zindterm(1) = dzf*t_su_b(ji) - zf |
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| 391 | |
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| 392 | ! first layer of snow equation |
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| 393 | ztrid(2,1) = - zkappa_s(0)*zg1s*zeta_s(1) |
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| 394 | ztrid(2,2) = 1.0 + zeta_s(1)*(zkappa_s(1) + zkappa_s(0)*zg1s) |
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| 395 | ztrid(2,3) = - zeta_s(1)* zkappa_s(1) |
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| 396 | zindterm(2) = ztsold(1) + zeta_s(1)*radab_s(1) |
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| 397 | |
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| 398 | else |
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| 399 | ! |
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| 400 | !------------------------------------------------------------------------------| |
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| 401 | ! case 2 : surface is melting - snow present | |
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| 402 | !------------------------------------------------------------------------------| |
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| 403 | ! |
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| 404 | zdifcase = 2.0 |
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| 405 | numeqmin = 2 |
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| 406 | numeqmax = nlay_i + nlay_s + 1 |
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| 407 | |
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| 408 | ! first layer of snow equation |
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| 409 | ztrid(2,1) = 0.0 |
---|
| 410 | ztrid(2,2) = 1.0 + zeta_s(1)*(zkappa_s(1) + zkappa_s(0)*zg1s) |
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| 411 | ztrid(2,3) = - zeta_s(1)*zkappa_s(1) |
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| 412 | zindterm(2) = ztsold(1) + zeta_s(1)*(radab_s(1) + zkappa_s(0)* |
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| 413 | & zg1s*t_su_b(ji)) |
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| 414 | |
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| 415 | ENDIF |
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| 416 | ELSE |
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| 417 | ! |
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| 418 | !------------------------------------------------------------------------------| |
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| 419 | ! cells without snow | |
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| 420 | !------------------------------------------------------------------------------| |
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| 421 | ! |
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| 422 | IF (t_su_b(ji).lt.tpw) THEN |
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| 423 | ! |
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| 424 | !------------------------------------------------------------------------------| |
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| 425 | ! case 3 : no surface melting - no snow | |
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| 426 | !------------------------------------------------------------------------------| |
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| 427 | ! |
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| 428 | zdifcase = 3.0 |
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| 429 | numeqmin = nlay_s + 1 |
---|
| 430 | numeqmax = nlay_i + nlay_s + 1 |
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| 431 | |
---|
| 432 | ! surface equation |
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| 433 | ztrid(numeqmin,1) = 0.0 |
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| 434 | ztrid(numeqmin,2) = dzf - zkappa_i(0)*zg1 |
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| 435 | ztrid(numeqmin,3) = zkappa_i(0)*zg1 |
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| 436 | zindterm(numeqmin) = dzf*t_su_b(ji) - zf |
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| 437 | |
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| 438 | ! first layer of ice equation |
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| 439 | ztrid(numeqmin+1,1) = - zkappa_i(0)*zg1*zeta_i(1) |
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| 440 | ztrid(numeqmin+1,2) = 1.0 + zeta_i(1)*(zkappa_i(1) + zkappa_i(0)* |
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| 441 | & zg1) |
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| 442 | ztrid(numeqmin+1,3) = - zeta_i(1)*zkappa_i(1) |
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| 443 | zindterm(numeqmin+1)= ztiold(1) + zeta_i(1)*radab_i(1) ! ( radab_phy_i(1) + |
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| 444 | ! & radab_alg_i(1) ) |
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| 445 | |
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| 446 | ! case of only one layer in the ice (surface & ice equations are altered) |
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| 447 | if (nlay_i.eq.1) then |
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| 448 | ztrid(numeqmin,1) = 0.0 |
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| 449 | ztrid(numeqmin,2) = dzf - zkappa_i(0)*2.0 |
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| 450 | ztrid(numeqmin,3) = zkappa_i(0)*2.0 |
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| 451 | |
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| 452 | ztrid(numeqmin+1,1) = -zkappa_i(0)*2.0*zeta_i(1) |
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| 453 | ztrid(numeqmin+1,2) = 1.0 + zeta_i(1)*(zkappa_i(0)*2.0 + |
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| 454 | & zkappa_i(1)) |
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| 455 | ztrid(numeqmin+1,3) = 0.0 |
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| 456 | |
---|
| 457 | zindterm(numeqmin+1) = ztiold(1) + zeta_i(1)* |
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| 458 | ! & ( radab_phy_i(1) + radab_alg_i(1) + |
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| 459 | & ( radab_i(1) + |
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| 460 | & zkappa_i(1)*t_bo_b(ji) ) |
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| 461 | endif |
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| 462 | |
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| 463 | else |
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| 464 | ! |
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| 465 | !------------------------------------------------------------------------------| |
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| 466 | ! case 4 : surface is melting - no snow | |
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| 467 | !------------------------------------------------------------------------------| |
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| 468 | ! |
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| 469 | zdifcase = 4.0 |
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| 470 | numeqmin = nlay_s + 2 |
---|
| 471 | numeqmax = nlay_i + nlay_s + 1 |
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| 472 | |
---|
| 473 | ! first layer of ice equation |
---|
| 474 | ztrid(numeqmin,1) = 0.0 |
---|
| 475 | ztrid(numeqmin,2) = 1.0 + zeta_i(1)*(zkappa_i(1) + zkappa_i(0)* |
---|
| 476 | & zg1) |
---|
| 477 | ztrid(numeqmin,3) = - zeta_i(1)* zkappa_i(1) |
---|
| 478 | zindterm(numeqmin) = ztiold(1) + zeta_i(1)* ( radab_i(1) + !(radab_phy_i(1) + |
---|
| 479 | ! & radab_alg_i(1) + |
---|
| 480 | & zkappa_i(0)*zg1*t_su_b(ji) ) |
---|
| 481 | |
---|
| 482 | ! case of only one layer in the ice (surface & ice equations are altered) |
---|
| 483 | if (nlay_i.eq.1) then |
---|
| 484 | ztrid(numeqmin,1) = 0.0 |
---|
| 485 | ztrid(numeqmin,2) = 1.0 + zeta_i(1)*(zkappa_i(0)*2.0 + |
---|
| 486 | & zkappa_i(1)) |
---|
| 487 | ztrid(numeqmin,3) = 0.0 |
---|
| 488 | zindterm(numeqmin) = ztiold(1) + zeta_i(1)* |
---|
| 489 | ! & (radab_phy_i(1) + radab_alg_i(1) |
---|
| 490 | & ( radab_i(1) + |
---|
| 491 | & + zkappa_i(1)*t_bo_b(ji) ) |
---|
| 492 | & + t_su_b(ji)*zeta_i(1)*zkappa_i(0)*2.0 |
---|
| 493 | endif |
---|
| 494 | |
---|
| 495 | endif |
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| 496 | endif |
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| 497 | ! |
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| 498 | !------------------------------------------------------------------------------| |
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| 499 | ! 9) tridiagonal system solving | |
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| 500 | !------------------------------------------------------------------------------| |
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| 501 | ! |
---|
| 502 | ! solving the tridiagonal system with Gauss elimination |
---|
| 503 | ! Thomas algorithm, from Computational fluid Dynamics, J.D. ANDERSON, |
---|
| 504 | ! McGraw-Hill 1984. |
---|
| 505 | ! computing temporary results |
---|
| 506 | zindtbis(numeqmin) = zindterm(numeqmin) |
---|
| 507 | zdiagbis(numeqmin) = ztrid(numeqmin,2) |
---|
| 508 | |
---|
| 509 | do numeq = numeqmin+1, numeqmax |
---|
| 510 | zdiagbis(numeq) = ztrid(numeq,2) - ztrid(numeq,1)* |
---|
| 511 | & ztrid(numeq-1,3)/zdiagbis(numeq-1) |
---|
| 512 | zindtbis(numeq) = zindterm(numeq) - ztrid(numeq,1)* |
---|
| 513 | & zindtbis(numeq-1)/zdiagbis(numeq-1) |
---|
| 514 | end do |
---|
| 515 | |
---|
| 516 | ! ice temperatures |
---|
| 517 | t_i_b(ji,nlay_i) = zindtbis(numeqmax)/zdiagbis(numeqmax) |
---|
| 518 | ! do numeq = nlay_i + nlay_s + 1, nlay_s + 2, -1 |
---|
| 519 | do numeq = nlay_i + nlay_s, nlay_s + 2, -1 |
---|
| 520 | layer = numeq - nlay_s - 1 |
---|
| 521 | t_i_b(ji,layer) = (zindtbis(numeq) - ztrid(numeq,3)* |
---|
| 522 | & t_i_b(ji,layer+1))/zdiagbis(numeq) |
---|
| 523 | end do |
---|
| 524 | |
---|
| 525 | ! snow temperatures |
---|
| 526 | if (ht_s_b(ji).gt.0.0) then |
---|
| 527 | t_s_b(ji,nlay_s) = (zindtbis(nlay_s+1) - ztrid(nlay_s+1,3)* |
---|
| 528 | & t_i_b(ji,1))/zdiagbis(nlay_s+1) |
---|
| 529 | if (nlay_s.gt.1) then |
---|
| 530 | do numeq = nlay_s, 2, -1 |
---|
| 531 | layer = numeq - 1 |
---|
| 532 | t_s_b(ji,layer) = (zindtbis(numeq) - ztrid(numeq,3)* |
---|
| 533 | & t_s_b(ji,layer+1))/zdiagbis(numeq) |
---|
| 534 | end do |
---|
| 535 | endif |
---|
| 536 | endif |
---|
| 537 | |
---|
| 538 | ! surface temperature |
---|
| 539 | if (t_su_b(ji).lt.tfs(ji)) then |
---|
| 540 | t_su_b(ji) = ( zindtbis(numeqmin) - ztrid(numeqmin,3)* |
---|
| 541 | & ( real(isnow)*t_s_b(ji,1) + |
---|
| 542 | & (1.0-real(isnow))*t_i_b(ji,1) ) ) / |
---|
| 543 | & zdiagbis(numeqmin) |
---|
| 544 | endif |
---|
| 545 | ! |
---|
| 546 | !-------------------------------------------------------------------------- |
---|
| 547 | ! 10) Has the scheme converged ?, end of the iterative procedure | |
---|
| 548 | !-------------------------------------------------------------------------- |
---|
| 549 | ! |
---|
| 550 | ! we verify that nothing has started to melt |
---|
| 551 | t_su_b(ji) = MIN( t_su_b(ji) , tfs(ji) ) |
---|
| 552 | DO layer = 1, nlay_i |
---|
| 553 | ztmelt_i = MIN( -tmut*s_i_b(ji,layer) + tpw , |
---|
| 554 | & 273.149999999d0) |
---|
| 555 | t_i_b(ji,layer) = MIN( t_i_b(ji,layer) ,ztmelt_i ) |
---|
| 556 | END DO |
---|
| 557 | |
---|
| 558 | ! zerrit is a residual which has to be under zerrmax |
---|
| 559 | zerrit = ABS(t_su_b(ji)-ztsutemp) |
---|
| 560 | DO layer = 1, nlay_s |
---|
| 561 | zerrit = MAX(zerrit,ABS(t_s_b(ji,layer) |
---|
| 562 | & - ztstemp(layer))) |
---|
| 563 | END DO |
---|
| 564 | DO layer = 1, nlay_i |
---|
| 565 | zerrit = max(zerrit,abs(t_i_b(ji,layer) - ztitemp(layer))) |
---|
| 566 | END DO |
---|
| 567 | |
---|
| 568 | 42 CONTINUE |
---|
| 569 | |
---|
| 570 | END DO |
---|
| 571 | |
---|
| 572 | DO 45 ji = kideb, kiut |
---|
| 573 | ! compute available energy for internal melt |
---|
| 574 | f_s_im(ji) = 0. |
---|
| 575 | DO layer = 1, nlay_s |
---|
| 576 | IF ( t_s_b(ji,layer) .GE. tfs(ji) ) THEN |
---|
| 577 | f_s_im(ji) = - rhon * ( cpg*( tfs(ji) - t_s_b(ji,layer))) |
---|
| 578 | & * ht_s_b(ji) / ddtb |
---|
| 579 | t_s_b(ji,layer) = MIN( t_s_b(ji,layer) ,tfs(ji) ) |
---|
| 580 | ENDIF |
---|
| 581 | END DO |
---|
| 582 | |
---|
| 583 | 45 CONTINUE |
---|
| 584 | ! |
---|
| 585 | !-------------------------------------------------------------------------- |
---|
| 586 | ! 11) Heat conduction fluxes | |
---|
| 587 | !-------------------------------------------------------------------------- |
---|
| 588 | ! |
---|
| 589 | |
---|
| 590 | DO 50 ji = kideb, kiut |
---|
| 591 | ! surface conduction flux |
---|
| 592 | fc_su(ji) = - real(isnow)*zkappa_s(0)*zg1s*(t_s_b(ji,1) - |
---|
| 593 | & t_su_b(ji)) |
---|
| 594 | & - (1.0-real(isnow))*zkappa_i(0)*zg1* |
---|
| 595 | & (t_i_b(ji,1) - t_su_b(ji)) |
---|
| 596 | |
---|
| 597 | ! bottom conduction flux |
---|
| 598 | fc_bo_i(ji) = - zkappa_i(nlay_i)* |
---|
| 599 | & ( zg1*(t_bo_b(ji) - t_i_b(ji,nlay_i)) ) |
---|
| 600 | |
---|
| 601 | ! internal conduction fluxes : snow |
---|
| 602 | !--upper snow value |
---|
| 603 | fc_s(ji,0) = - isnow* |
---|
| 604 | & zkappa_s(0) * zg1s * ( t_s_b(ji,1) - |
---|
| 605 | & t_su_b(ji) ) |
---|
| 606 | !--basal snow value |
---|
| 607 | fc_s(ji,1) = - isnow* |
---|
| 608 | & zkappa_s(1) * ( t_i_b(ji,1) - |
---|
| 609 | & t_s_b(ji,1) ) |
---|
| 610 | |
---|
| 611 | ! internal conduction fluxes : ice |
---|
| 612 | !--upper layer |
---|
| 613 | fc_i(ji,0) = - isnow * ! interface flux if there is snow |
---|
| 614 | & ( zkappa_i(0) * ( t_i_b(ji,1) - t_s_b(ji,nlay_s ) ) ) |
---|
| 615 | & - ( 1.0 - isnow ) * ( zkappa_i(0) * |
---|
| 616 | & zg1 * ( t_i_b(ji,1) - t_su_b(ji) ) ) ! upper flux if no |
---|
| 617 | !--internal ice layers |
---|
| 618 | DO layer = 1, nlay_i - 1 |
---|
| 619 | fc_i(ji,layer) = - zkappa_i(layer) * ( t_i_b(ji,layer+1) - |
---|
| 620 | & t_i_b(ji,layer) ) |
---|
| 621 | END DO |
---|
| 622 | !--under the basal ice layer |
---|
| 623 | fc_i(ji,nlay_i) = fc_bo_i(ji) |
---|
| 624 | |
---|
| 625 | ! case of only one layer in the ice |
---|
| 626 | IF (nlay_i.EQ.1) THEN |
---|
| 627 | fc_su(ji) = -real(isnow)*(zkappa_s(0)*(zg1s*(t_s_b(ji,1)- |
---|
| 628 | & t_su_b(ji)))) |
---|
| 629 | & -(1.0-real(isnow))*zkappa_i(0)*zg1*(t_i_b(ji,1)- |
---|
| 630 | & t_su_b(ji)) |
---|
| 631 | fc_bo_i(ji) = -zkappa_i(nlay_i)*zg1* |
---|
| 632 | & (t_bo_b(ji)-t_i_b(ji,nlay_i)) |
---|
| 633 | ENDIF |
---|
| 634 | ! |
---|
| 635 | !-------------------------------------------------------------------------- |
---|
| 636 | ! 12) Update atmospheric heat fluxes and energy of melting | |
---|
| 637 | !-------------------------------------------------------------------------- |
---|
| 638 | ! |
---|
| 639 | ! pressure of water vapor saturation (Pa) |
---|
| 640 | es = 611.0*10.0**(9.5*(t_su_b(ji)-273.16)/ |
---|
| 641 | & (t_su_b(ji)-7.66)) |
---|
| 642 | ! net longwave radiative flux |
---|
| 643 | ! MV BUG |
---|
| 644 | ! fratsb(ji) = emig*(ratbqb(ji)- |
---|
| 645 | ! & stefan*t_su_b(ji)*t_su_b(ji)*t_su_b(ji)*t_su_b(ji)) |
---|
| 646 | fratsb(ji) = ratbqb(ji) - emig * |
---|
| 647 | & stefan*t_su_b(ji)*t_su_b(ji)*t_su_b(ji)*t_su_b(ji) |
---|
| 648 | ! sensible and latent heat flux |
---|
| 649 | CALL flx(ht_i_b(ji),t_su_b(ji),tabqb(ji),qabqb(ji),fcsb(ji), |
---|
| 650 | & fleb(ji),qsfcb(ji),zrchu1(ji),zrchu2(ji),vabqb(ji),zref) |
---|
| 651 | |
---|
| 652 | fcsb(ji) = -fcsb(ji) |
---|
| 653 | fleb(ji) = MIN( -fleb(ji) , 0.0 ) ! always negative, as precip |
---|
| 654 | ! energy already added |
---|
| 655 | |
---|
| 656 | ! ice energy of melting |
---|
| 657 | CALL ice_th_enmelt(kideb, kiut, nlay_s, nlay_i) |
---|
| 658 | |
---|
| 659 | IF ( ln_write ) THEN |
---|
| 660 | WRITE(numout,*) ' nconv : ', nconv |
---|
| 661 | WRITE(numout,*) ' zerrit : ', zerrit |
---|
| 662 | WRITE(numout,*) ' t_su_b: ', t_su_b(ji) |
---|
| 663 | WRITE(numout,*) ' t_s_b : ', ( t_s_b(ji,layer), |
---|
| 664 | & layer = 1, nlay_s ) |
---|
| 665 | WRITE(numout,*) ' t_i_b : ', ( t_i_b(ji,layer), |
---|
| 666 | & layer = 1, nlay_i ) |
---|
| 667 | WRITE(numout,*) ' t_bo_b : ', t_bo_b(ji) |
---|
| 668 | WRITE(numout,*) |
---|
| 669 | ENDIF |
---|
| 670 | |
---|
| 671 | 50 CONTINUE |
---|
| 672 | ! |
---|
| 673 | !------------------------------------------------------------------------------ |
---|
| 674 | ! End of ice_th_diff |
---|
| 675 | END SUBROUTINE |
---|