| 1 | MODULE p4zpoc |
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| 2 | !!====================================================================== |
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| 3 | !! *** MODULE p4zpoc *** |
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| 4 | !! TOP : PISCES Compute remineralization of organic particles |
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| 5 | !!========================================================================= |
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| 6 | !! History : 1.0 ! 2004 (O. Aumont) Original code |
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| 7 | !! 2.0 ! 2007-12 (C. Ethe, G. Madec) F90 |
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| 8 | !! 3.4 ! 2011-06 (O. Aumont, C. Ethe) Quota model for iron |
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| 9 | !! 3.6 ! 2016-03 (O. Aumont) Quota model and diverse |
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| 10 | !!---------------------------------------------------------------------- |
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| 11 | !! p4z_poc : Compute remineralization/dissolution of organic compounds |
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| 12 | !! p4z_poc_init : Initialisation of parameters for remineralisation |
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| 13 | !!---------------------------------------------------------------------- |
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| 14 | USE oce_trc ! shared variables between ocean and passive tracers |
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| 15 | USE trc ! passive tracers common variables |
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| 16 | USE sms_pisces ! PISCES Source Minus Sink variables |
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| 17 | USE prtctl_trc ! print control for debugging |
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| 18 | USE iom ! I/O manager |
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| 19 | |
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| 20 | |
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| 21 | IMPLICIT NONE |
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| 22 | PRIVATE |
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| 23 | |
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| 24 | PUBLIC p4z_poc ! called in p4zbio.F90 |
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| 25 | PUBLIC p4z_poc_init ! called in trcsms_pisces.F90 |
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| 26 | PUBLIC alngam |
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| 27 | PUBLIC gamain |
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| 28 | |
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| 29 | !! * Shared module variables |
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| 30 | REAL(wp), PUBLIC :: xremip !: remineralisation rate of DOC |
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| 31 | REAL(wp), PUBLIC :: xremipc !: remineralisation rate of DOC |
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| 32 | REAL(wp), PUBLIC :: xremipn !: remineralisation rate of DON |
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| 33 | REAL(wp), PUBLIC :: xremipp !: remineralisation rate of DOP |
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| 34 | INTEGER , PUBLIC :: jcpoc !: number of lability classes |
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| 35 | REAL(wp), PUBLIC :: rshape !: shape factor of the gamma distribution |
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| 36 | |
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| 37 | REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:) :: alphan, reminp |
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| 38 | REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:,:) :: alphap |
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| 39 | |
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| 40 | |
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| 41 | !!---------------------------------------------------------------------- |
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| 42 | !! NEMO/TOP 3.3 , NEMO Consortium (2010) |
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| 43 | !! $Id: p4zrem.F90 3160 2011-11-20 14:27:18Z cetlod $ |
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| 44 | !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) |
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| 45 | !!---------------------------------------------------------------------- |
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| 46 | CONTAINS |
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| 47 | |
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| 48 | SUBROUTINE p4z_poc( kt, knt ) |
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| 49 | !!--------------------------------------------------------------------- |
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| 50 | !! *** ROUTINE p4z_poc *** |
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| 51 | !! |
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| 52 | !! ** Purpose : Compute remineralization of organic particles |
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| 53 | !! |
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| 54 | !! ** Method : - ??? |
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| 55 | !!--------------------------------------------------------------------- |
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| 56 | ! |
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| 57 | INTEGER, INTENT(in) :: kt, knt ! ocean time step |
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| 58 | ! |
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| 59 | INTEGER :: ji, jj, jk, jn |
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| 60 | REAL(wp) :: zremip, zremig, zdep, zorem, zorem2, zofer |
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| 61 | REAL(wp) :: zopon, zopop, zopoc, zopoc2, zopon2, zopop2 |
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| 62 | REAL(wp) :: zsizek, zsizek1, alphat, remint, solgoc, zpoc |
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| 63 | REAL(wp) :: zofer2, zofer3 |
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| 64 | REAL(wp) :: zrfact2 |
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| 65 | CHARACTER (len=25) :: charout |
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| 66 | REAL(wp), POINTER, DIMENSION(:,: ) :: totprod, totthick, totcons |
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| 67 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zremipoc, zremigoc, zorem3, ztremint |
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| 68 | REAL(wp), POINTER, DIMENSION(:,:,:,:) :: alphag |
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| 69 | !!--------------------------------------------------------------------- |
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| 70 | ! |
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| 71 | IF( nn_timing == 1 ) CALL timing_start('p4z_poc') |
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| 72 | ! |
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| 73 | ! Allocate temporary workspace |
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| 74 | CALL wrk_alloc( jpi, jpj, totprod, totthick, totcons ) |
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| 75 | CALL wrk_alloc( jpi, jpj, jpk, zremipoc, zremigoc, zorem3, ztremint ) |
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| 76 | ALLOCATE( alphag(jpi,jpj,jpk,jcpoc) ) |
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| 77 | |
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| 78 | ! Initialization of local variables |
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| 79 | ! --------------------------------- |
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| 80 | |
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| 81 | ! Here we compute the GOC -> POC rate due to the shrinking |
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| 82 | ! of the fecal pellets/aggregates as a result of bacterial |
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| 83 | ! solubilization |
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| 84 | ! This is based on a fractal dimension of 2.56 and a spectral |
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| 85 | ! slope of -3.6 (identical to what is used in p4zsink to compute |
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| 86 | ! aggregation |
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| 87 | solgoc = 0.04/ 2.56 * 1./ ( 1.-50**(-0.04) ) |
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| 88 | |
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| 89 | ! Initialisation of temprary arrys |
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| 90 | IF( ln_p4z ) THEN |
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| 91 | !$OMP PARALLEL DO schedule(static) private(jk, jj, ji) |
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| 92 | DO jk = 1, jpk |
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| 93 | DO jj = 1, jpj |
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| 94 | DO ji = 1, jpi |
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| 95 | zremipoc(ji,jj,jk) = xremip |
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| 96 | zremigoc(ji,jj,jk) = xremip |
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| 97 | END DO |
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| 98 | END DO |
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| 99 | END DO |
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| 100 | ELSE ! ln_p5z |
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| 101 | !$OMP PARALLEL DO schedule(static) private(jk, jj, ji) |
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| 102 | DO jk = 1, jpk |
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| 103 | DO jj = 1, jpj |
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| 104 | DO ji = 1, jpi |
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| 105 | zremipoc(ji,jj,jk) = xremipc |
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| 106 | zremigoc(ji,jj,jk) = xremipc |
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| 107 | END DO |
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| 108 | END DO |
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| 109 | END DO |
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| 110 | ENDIF |
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| 111 | !$OMP PARALLEL |
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| 112 | !$OMP DO schedule(static) private(jk, jj, ji) |
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| 113 | DO jk = 1, jpk |
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| 114 | DO jj = 1, jpj |
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| 115 | DO ji = 1, jpi |
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| 116 | zorem3 (ji,jj,jk) = 0. |
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| 117 | orem (ji,jj,jk) = 0. |
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| 118 | ztremint(ji,jj,jk) = 0. |
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| 119 | END DO |
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| 120 | END DO |
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| 121 | END DO |
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| 122 | !OMP END DO NOWAIT |
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| 123 | DO jn = 1, jcpoc |
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| 124 | !$OMP DO schedule(static) private(jk, jj, ji) |
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| 125 | DO jk = 1, jpk |
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| 126 | DO jj = 1, jpj |
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| 127 | DO ji = 1, jpi |
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| 128 | alphag(ji,jj,jk,jn) = alphan(jn) |
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| 129 | alphap(ji,jj,jk,jn) = alphan(jn) |
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| 130 | END DO |
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| 131 | END DO |
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| 132 | END DO |
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| 133 | END DO |
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| 134 | !$OMP END PARALLEL |
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| 135 | |
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| 136 | ! ----------------------------------------------------------------------- |
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| 137 | ! Lability parameterization. This is the big particles part (GOC) |
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| 138 | ! This lability parameterization can be activated only with the standard |
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| 139 | ! particle scheme. Does not work with Kriest parameterization. |
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| 140 | ! ----------------------------------------------------------------------- |
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| 141 | DO jk = 2, jpkm1 |
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| 142 | !$OMP PARALLEL DO schedule(static) private(jj,ji,zdep,alphat,remint,zsizek1,zsizek,zpoc,jn) |
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| 143 | DO jj = 1, jpj |
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| 144 | DO ji = 1, jpi |
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| 145 | IF (tmask(ji,jj,jk) == 1.) THEN |
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| 146 | zdep = hmld(ji,jj) |
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| 147 | ! |
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| 148 | ! In the case of GOC, lability is constant in the mixed layer |
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| 149 | ! It is computed only below the mixed layer depth |
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| 150 | ! ------------------------------------------------------------ |
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| 151 | ! |
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| 152 | IF( gdept_n(ji,jj,jk) > zdep ) THEN |
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| 153 | zsizek1 = e3t_n(ji,jj,jk-1) / 2. / (wsbio4(ji,jj,jk-1) + rtrn) * tgfunc(ji,jj,jk-1) |
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| 154 | zsizek = e3t_n(ji,jj,jk) / 2. / (wsbio4(ji,jj,jk) + rtrn) * tgfunc(ji,jj,jk) |
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| 155 | ! |
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| 156 | IF ( gdept_n(ji,jj,jk-1) <= zdep ) THEN |
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| 157 | ! |
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| 158 | ! The first level just below the mixed layer needs a |
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| 159 | ! specific treatment because lability is supposed constant |
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| 160 | ! everywhere within the mixed layer. This means that |
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| 161 | ! change in lability in the bottom part of the previous cell |
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| 162 | ! should not be computed |
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| 163 | ! ---------------------------------------------------------- |
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| 164 | ! |
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| 165 | ! POC concentration is computed using the lagrangian |
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| 166 | ! framework. It is only used for the lability param |
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| 167 | zpoc = trb(ji,jj,jk-1,jpgoc) + consgoc(ji,jj,jk) * rday / rfact2 & |
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| 168 | & * e3t_n(ji,jj,jk) / 2. / (wsbio4(ji,jj,jk) + rtrn) |
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| 169 | zpoc = MAX(0., zpoc) |
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| 170 | ! |
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| 171 | DO jn = 1, jcpoc |
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| 172 | ! |
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| 173 | ! Lagrangian based algorithm. The fraction of each |
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| 174 | ! lability class is computed starting from the previous |
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| 175 | ! level |
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| 176 | ! ----------------------------------------------------- |
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| 177 | ! |
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| 178 | ! the concentration of each lability class is calculated |
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| 179 | ! as the sum of the different sources and sinks |
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| 180 | ! Please note that production of new GOC experiences |
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| 181 | ! degradation |
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| 182 | alphag(ji,jj,jk,jn) = alphag(ji,jj,jk-1,jn) * exp( -reminp(jn) * zsizek ) * zpoc & |
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| 183 | & + prodgoc(ji,jj,jk) * alphan(jn) / tgfunc(ji,jj,jk) / reminp(jn) & |
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| 184 | & * ( 1. - exp( -reminp(jn) * zsizek ) ) * rday / rfact2 |
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| 185 | |
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| 186 | END DO |
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| 187 | ELSE |
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| 188 | ! |
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| 189 | ! standard algorithm in the rest of the water column |
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| 190 | ! See the comments in the previous block. |
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| 191 | ! --------------------------------------------------- |
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| 192 | ! |
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| 193 | zpoc = trb(ji,jj,jk-1,jpgoc) + consgoc(ji,jj,jk-1) * rday / rfact2 & |
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| 194 | & * e3t_n(ji,jj,jk-1) / 2. / (wsbio4(ji,jj,jk-1) + rtrn) + consgoc(ji,jj,jk) & |
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| 195 | & * rday / rfact2 * e3t_n(ji,jj,jk) / 2. / (wsbio4(ji,jj,jk) + rtrn) |
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| 196 | zpoc = max(0., zpoc) |
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| 197 | ! |
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| 198 | DO jn = 1, jcpoc |
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| 199 | alphag(ji,jj,jk,jn) = alphag(ji,jj,jk-1,jn) * exp( -reminp(jn) * ( zsizek & |
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| 200 | & + zsizek1 ) ) * zpoc + ( prodgoc(ji,jj,jk-1) / tgfunc(ji,jj,jk-1) * ( 1. & |
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| 201 | & - exp( -reminp(jn) * zsizek1 ) ) * exp( -reminp(jn) * zsizek ) + prodgoc(ji,jj,jk) & |
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| 202 | & / tgfunc(ji,jj,jk) * ( 1. - exp( -reminp(jn) * zsizek ) ) ) * rday / rfact2 / reminp(jn) |
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| 203 | END DO |
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| 204 | ENDIF |
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| 205 | ! |
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| 206 | alphat = SUM(alphag(ji,jj,jk,:)) |
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| 207 | remint = SUM(alphag(ji,jj,jk,:) * reminp(:)) |
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| 208 | ! |
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| 209 | DO jn = 1, jcpoc |
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| 210 | ! The contribution of each lability class at the current |
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| 211 | ! level is computed |
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| 212 | alphag(ji,jj,jk,jn) = alphag(ji,jj,jk,jn) / ( alphat + rtrn) |
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| 213 | END DO |
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| 214 | ! Computation of the mean remineralisation rate |
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| 215 | ztremint(ji,jj,jk) = MAX(0., remint / ( alphat + rtrn) ) |
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| 216 | ! |
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| 217 | ENDIF |
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| 218 | ENDIF |
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| 219 | END DO |
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| 220 | END DO |
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| 221 | END DO |
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| 222 | |
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| 223 | IF( ln_p4z ) THEN |
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| 224 | !$OMP PARALLEL DO schedule(static) private(jk, jj, ji) |
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| 225 | DO jk = 1, jpk |
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| 226 | DO jj = 1, jpj |
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| 227 | DO ji = 1, jpi |
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| 228 | zremigoc(ji,jj,jk) = MIN( xremip , ztremint(ji,jj,jk) ) |
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| 229 | END DO |
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| 230 | END DO |
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| 231 | END DO |
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| 232 | ELSE |
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| 233 | !$OMP PARALLEL DO schedule(static) private(jk, jj, ji) |
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| 234 | DO jk = 1, jpk |
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| 235 | DO jj = 1, jpj |
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| 236 | DO ji = 1, jpi |
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| 237 | zremigoc(ji,jj,jk) = MIN( xremipc, ztremint(ji,jj,jk) ) |
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| 238 | END DO |
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| 239 | END DO |
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| 240 | END DO |
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| 241 | ENDIF |
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| 242 | |
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| 243 | IF( ln_p4z ) THEN |
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| 244 | !$OMP PARALLEL DO schedule(static) private(jk,jj,ji,zremig,zorem2,zofer2,zofer3) |
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| 245 | DO jk = 1, jpkm1 |
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| 246 | DO jj = 1, jpj |
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| 247 | DO ji = 1, jpi |
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| 248 | ! POC disaggregation by turbulence and bacterial activity. |
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| 249 | ! -------------------------------------------------------- |
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| 250 | zremig = zremigoc(ji,jj,jk) * xstep * tgfunc(ji,jj,jk) |
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| 251 | zorem2 = zremig * trb(ji,jj,jk,jpgoc) |
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| 252 | orem(ji,jj,jk) = zorem2 |
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| 253 | zorem3(ji,jj,jk) = zremig * solgoc * trb(ji,jj,jk,jpgoc) |
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| 254 | zofer2 = zremig * trb(ji,jj,jk,jpbfe) |
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| 255 | zofer3 = zremig * solgoc * trb(ji,jj,jk,jpbfe) |
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| 256 | |
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| 257 | ! ------------------------------------- |
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| 258 | tra(ji,jj,jk,jppoc) = tra(ji,jj,jk,jppoc) + zorem3(ji,jj,jk) |
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| 259 | tra(ji,jj,jk,jpgoc) = tra(ji,jj,jk,jpgoc) - zorem2 - zorem3(ji,jj,jk) |
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| 260 | tra(ji,jj,jk,jpsfe) = tra(ji,jj,jk,jpsfe) + zofer3 |
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| 261 | tra(ji,jj,jk,jpbfe) = tra(ji,jj,jk,jpbfe) - zofer2 - zofer3 |
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| 262 | tra(ji,jj,jk,jpdoc) = tra(ji,jj,jk,jpdoc) + zorem2 |
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| 263 | tra(ji,jj,jk,jpfer) = tra(ji,jj,jk,jpfer) + zofer2 |
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| 264 | END DO |
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| 265 | END DO |
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| 266 | END DO |
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| 267 | ELSE |
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| 268 | !$OMP PARALLEL DO schedule(static) private(jk,jj,ji,zremig,zopoc2,zofer2,zopon2,zopop2) |
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| 269 | DO jk = 1, jpkm1 |
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| 270 | DO jj = 1, jpj |
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| 271 | DO ji = 1, jpi |
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| 272 | ! POC disaggregation by turbulence and bacterial activity. |
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| 273 | ! -------------------------------------------------------- |
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| 274 | zremig = zremigoc(ji,jj,jk) * xstep * tgfunc(ji,jj,jk) |
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| 275 | zopoc2 = zremig * trb(ji,jj,jk,jpgoc) |
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| 276 | orem(ji,jj,jk) = zopoc2 |
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| 277 | zorem3(ji,jj,jk) = zremig * solgoc * trb(ji,jj,jk,jpgoc) |
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| 278 | zopon2 = xremipn / xremipc * zremig * trb(ji,jj,jk,jpgon) |
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| 279 | zopop2 = xremipp / xremipc * zremig * trb(ji,jj,jk,jpgop) |
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| 280 | zofer2 = xremipn / xremipc * zremig * trb(ji,jj,jk,jpbfe) |
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| 281 | |
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| 282 | ! ------------------------------------- |
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| 283 | tra(ji,jj,jk,jppoc) = tra(ji,jj,jk,jppoc) + zorem3(ji,jj,jk) |
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| 284 | tra(ji,jj,jk,jppon) = tra(ji,jj,jk,jppon) + solgoc * zopon2 |
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| 285 | tra(ji,jj,jk,jppop) = tra(ji,jj,jk,jppop) + solgoc * zopop2 |
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| 286 | tra(ji,jj,jk,jpsfe) = tra(ji,jj,jk,jpsfe) + solgoc * zofer2 |
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| 287 | tra(ji,jj,jk,jpdoc) = tra(ji,jj,jk,jpdoc) + zopoc2 |
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| 288 | tra(ji,jj,jk,jpdon) = tra(ji,jj,jk,jpdon) + zopon2 |
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| 289 | tra(ji,jj,jk,jpdop) = tra(ji,jj,jk,jpdop) + zopop2 |
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| 290 | tra(ji,jj,jk,jpfer) = tra(ji,jj,jk,jpfer) + zofer2 |
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| 291 | tra(ji,jj,jk,jpgoc) = tra(ji,jj,jk,jpgoc) - zopoc2 - zorem3(ji,jj,jk) |
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| 292 | tra(ji,jj,jk,jpgon) = tra(ji,jj,jk,jpgon) - zopon2 * (1. + solgoc) |
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| 293 | tra(ji,jj,jk,jpgop) = tra(ji,jj,jk,jpgop) - zopop2 * (1. + solgoc) |
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| 294 | tra(ji,jj,jk,jpbfe) = tra(ji,jj,jk,jpbfe) - zofer2 * (1. + solgoc) |
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| 295 | END DO |
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| 296 | END DO |
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| 297 | END DO |
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| 298 | ENDIF |
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| 299 | |
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| 300 | IF(ln_ctl) THEN ! print mean trends (used for debugging) |
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| 301 | WRITE(charout, FMT="('poc1')") |
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| 302 | CALL prt_ctl_trc_info(charout) |
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| 303 | CALL prt_ctl_trc(tab4d=tra, mask=tmask, clinfo=ctrcnm) |
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| 304 | ENDIF |
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| 305 | |
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| 306 | ! ------------------------------------------------------------------ |
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| 307 | ! Lability parameterization for the small OM particles. This param |
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| 308 | ! is based on the same theoretical background as the big particles. |
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| 309 | ! However, because of its low sinking speed, lability is not supposed |
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| 310 | ! to be equal to its initial value (the value of the freshly produced |
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| 311 | ! organic matter). It is however uniform in the mixed layer. |
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| 312 | ! ------------------------------------------------------------------- |
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| 313 | ! |
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| 314 | !$OMP PARALLEL |
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| 315 | !$OMP DO schedule(static) private(jj,ji) |
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| 316 | DO jj = 1, jpj |
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| 317 | DO ji = 1, jpi |
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| 318 | totprod(ji,jj) = 0. |
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| 319 | totthick(ji,jj) = 0. |
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| 320 | totcons(ji,jj) = 0. |
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| 321 | END DO |
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| 322 | END DO |
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| 323 | ! intregrated production and consumption of POC in the mixed layer |
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| 324 | ! ---------------------------------------------------------------- |
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| 325 | ! |
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| 326 | DO jk = 1, jpkm1 |
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| 327 | !$OMP DO schedule(static) private(jj,ji,zdep) |
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| 328 | DO jj = 1, jpj |
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| 329 | DO ji = 1, jpi |
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| 330 | zdep = hmld(ji,jj) |
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| 331 | IF (tmask(ji,jj,jk) == 1. .AND. gdept_n(ji,jj,jk) <= zdep ) THEN |
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| 332 | totprod(ji,jj) = totprod(ji,jj) + prodpoc(ji,jj,jk) * e3t_n(ji,jj,jk) * rday/ rfact2 |
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| 333 | ! The temperature effect is included here |
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| 334 | totthick(ji,jj) = totthick(ji,jj) + e3t_n(ji,jj,jk)* tgfunc(ji,jj,jk) |
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| 335 | totcons(ji,jj) = totcons(ji,jj) - conspoc(ji,jj,jk) * e3t_n(ji,jj,jk) * rday/ rfact2 & |
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| 336 | & / ( trb(ji,jj,jk,jppoc) + rtrn ) |
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| 337 | ENDIF |
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| 338 | END DO |
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| 339 | END DO |
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| 340 | END DO |
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| 341 | !$OMP END PARALLEL |
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| 342 | |
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| 343 | ! Computation of the lability spectrum in the mixed layer. In the mixed |
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| 344 | ! layer, this spectrum is supposed to be uniform. |
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| 345 | ! --------------------------------------------------------------------- |
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| 346 | !$OMP DO schedule(static) private(jk,jj,ji,zdep,alphat,remint,jn) |
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| 347 | DO jk = 1, jpkm1 |
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| 348 | DO jj = 1, jpj |
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| 349 | DO ji = 1, jpi |
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| 350 | IF (tmask(ji,jj,jk) == 1.) THEN |
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| 351 | zdep = hmld(ji,jj) |
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| 352 | IF( gdept_n(ji,jj,jk) <= zdep ) THEN |
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| 353 | DO jn = 1, jcpoc |
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| 354 | ! For each lability class, the system is supposed to be |
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| 355 | ! at equilibrium: Prod - Sink - w alphap = 0. |
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| 356 | alphap(ji,jj,jk,jn) = totprod(ji,jj) * alphan(jn) / ( reminp(jn) & |
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| 357 | & * totthick(ji,jj) + totcons(ji,jj) + wsbio + rtrn ) |
|---|
| 358 | END DO |
|---|
| 359 | alphat = SUM(alphap(ji,jj,jk,:)) |
|---|
| 360 | DO jn = 1, jcpoc |
|---|
| 361 | alphap(ji,jj,jk,jn) = alphap(ji,jj,jk,jn) / ( alphat + rtrn) |
|---|
| 362 | END DO |
|---|
| 363 | remint = SUM(alphap(ji,jj,jk,:) * reminp(:)) |
|---|
| 364 | ! Mean remineralization rate in the mixed layer |
|---|
| 365 | ztremint(ji,jj,jk) = MAX( 0., remint ) |
|---|
| 366 | ENDIF |
|---|
| 367 | ENDIF |
|---|
| 368 | END DO |
|---|
| 369 | END DO |
|---|
| 370 | END DO |
|---|
| 371 | ! |
|---|
| 372 | IF( ln_p4z ) THEN |
|---|
| 373 | !$OMP PARALLEL DO schedule(static) private(jk, jj, ji) |
|---|
| 374 | DO jk = 1, jpk |
|---|
| 375 | DO jj = 1, jpj |
|---|
| 376 | DO ji = 1, jpi |
|---|
| 377 | zremipoc(ji,jj,jk) = MIN( xremip , ztremint(ji,jj,jk) ) |
|---|
| 378 | END DO |
|---|
| 379 | END DO |
|---|
| 380 | END DO |
|---|
| 381 | ELSE |
|---|
| 382 | !$OMP PARALLEL DO schedule(static) private(jk, jj, ji) |
|---|
| 383 | DO jk = 1, jpk |
|---|
| 384 | DO jj = 1, jpj |
|---|
| 385 | DO ji = 1, jpi |
|---|
| 386 | zremipoc(ji,jj,jk) = MIN( xremipc , ztremint(ji,jj,jk) ) |
|---|
| 387 | END DO |
|---|
| 388 | END DO |
|---|
| 389 | END DO |
|---|
| 390 | ENDIF |
|---|
| 391 | |
|---|
| 392 | ! ----------------------------------------------------------------------- |
|---|
| 393 | ! The lability parameterization is used here. The code is here |
|---|
| 394 | ! almost identical to what is done for big particles. The only difference |
|---|
| 395 | ! is that an additional source from GOC to POC is included. This means |
|---|
| 396 | ! that since we need the lability spectrum of GOC, GOC spectrum |
|---|
| 397 | ! should be determined before. |
|---|
| 398 | ! ----------------------------------------------------------------------- |
|---|
| 399 | ! |
|---|
| 400 | DO jk = 2, jpkm1 |
|---|
| 401 | !$OMP PARALLEL DO schedule(static) private(jj,ji,zdep,alphat,remint,zsizek1,zsizek,zpoc,jn) |
|---|
| 402 | DO jj = 1, jpj |
|---|
| 403 | DO ji = 1, jpi |
|---|
| 404 | IF (tmask(ji,jj,jk) == 1.) THEN |
|---|
| 405 | zdep = hmld(ji,jj) |
|---|
| 406 | IF( gdept_n(ji,jj,jk) > zdep ) THEN |
|---|
| 407 | ! |
|---|
| 408 | ! the scale factors are corrected with temperature |
|---|
| 409 | zsizek1 = e3t_n(ji,jj,jk-1) / 2. / (wsbio3(ji,jj,jk-1) + rtrn) * tgfunc(ji,jj,jk-1) |
|---|
| 410 | zsizek = e3t_n(ji,jj,jk) / 2. / (wsbio3(ji,jj,jk) + rtrn) * tgfunc(ji,jj,jk) |
|---|
| 411 | ! |
|---|
| 412 | ! Special treatment of the level just below the MXL |
|---|
| 413 | ! See the comments in the GOC section |
|---|
| 414 | ! --------------------------------------------------- |
|---|
| 415 | ! |
|---|
| 416 | IF ( gdept_n(ji,jj,jk-1) <= zdep ) THEN |
|---|
| 417 | ! |
|---|
| 418 | ! Computation of the POC concentration using the |
|---|
| 419 | ! lagrangian algorithm |
|---|
| 420 | zpoc = trb(ji,jj,jk-1,jppoc) + conspoc(ji,jj,jk) * rday / rfact2 & |
|---|
| 421 | & * e3t_n(ji,jj,jk) / 2. / (wsbio3(ji,jj,jk) + rtrn) |
|---|
| 422 | zpoc = max(0., zpoc) |
|---|
| 423 | ! |
|---|
| 424 | DO jn = 1, jcpoc |
|---|
| 425 | ! computation of the lability spectrum applying the |
|---|
| 426 | ! different sources and sinks |
|---|
| 427 | alphap(ji,jj,jk,jn) = alphap(ji,jj,jk-1,jn) * exp( -reminp(jn) * zsizek ) * zpoc & |
|---|
| 428 | & + ( prodpoc(ji,jj,jk) * alphan(jn) + zorem3(ji,jj,jk) * alphag(ji,jj,jk,jn) ) & |
|---|
| 429 | & / tgfunc(ji,jj,jk) / reminp(jn) * rday / rfact2 * ( 1. - exp( -reminp(jn) & |
|---|
| 430 | & * zsizek ) ) |
|---|
| 431 | alphap(ji,jj,jk,jn) = MAX( 0., alphap(ji,jj,jk,jn) ) |
|---|
| 432 | END DO |
|---|
| 433 | ELSE |
|---|
| 434 | ! |
|---|
| 435 | ! Lability parameterization for the interior of the ocean |
|---|
| 436 | ! This is very similar to what is done in the previous |
|---|
| 437 | ! block |
|---|
| 438 | ! -------------------------------------------------------- |
|---|
| 439 | ! |
|---|
| 440 | zpoc = trb(ji,jj,jk-1,jppoc) + conspoc(ji,jj,jk-1) * rday / rfact2 & |
|---|
| 441 | & * e3t_n(ji,jj,jk-1) / 2. / (wsbio3(ji,jj,jk-1) + rtrn) + conspoc(ji,jj,jk) & |
|---|
| 442 | & * rday / rfact2 * e3t_n(ji,jj,jk) / 2. / (wsbio3(ji,jj,jk) + rtrn) |
|---|
| 443 | zpoc = max(0., zpoc) |
|---|
| 444 | ! |
|---|
| 445 | DO jn = 1, jcpoc |
|---|
| 446 | alphap(ji,jj,jk,jn) = alphap(ji,jj,jk-1,jn) * exp( -reminp(jn) & |
|---|
| 447 | & * ( zsizek + zsizek1 ) ) * zpoc + ( prodpoc(ji,jj,jk-1) * alphan(jn) & |
|---|
| 448 | & + zorem3(ji,jj,jk-1) * alphag(ji,jj,jk-1,jn) ) * rday / rfact2 / reminp(jn) & |
|---|
| 449 | & / tgfunc(ji,jj,jk-1) * ( 1. - exp( -reminp(jn) * zsizek1 ) ) * exp( -reminp(jn) & |
|---|
| 450 | & * zsizek ) + ( prodpoc(ji,jj,jk) * alphan(jn) + zorem3(ji,jj,jk) & |
|---|
| 451 | & * alphag(ji,jj,jk,jn) ) * rday / rfact2 / reminp(jn) / tgfunc(ji,jj,jk) * ( 1. & |
|---|
| 452 | & - exp( -reminp(jn) * zsizek ) ) |
|---|
| 453 | alphap(ji,jj,jk,jn) = max(0., alphap(ji,jj,jk,jn) ) |
|---|
| 454 | END DO |
|---|
| 455 | ENDIF |
|---|
| 456 | alphat = SUM(alphap(ji,jj,jk,:)) |
|---|
| 457 | ! Normalization of the lability spectrum so that the |
|---|
| 458 | ! integral is equal to 1 |
|---|
| 459 | DO jn = 1, jcpoc |
|---|
| 460 | alphap(ji,jj,jk,jn) = alphap(ji,jj,jk,jn) / ( alphat + rtrn) |
|---|
| 461 | END DO |
|---|
| 462 | remint = SUM(alphap(ji,jj,jk,:) * reminp(:)) |
|---|
| 463 | ! Mean remineralization rate in the water column |
|---|
| 464 | ztremint(ji,jj,jk) = MAX( 0., remint ) |
|---|
| 465 | ENDIF |
|---|
| 466 | ENDIF |
|---|
| 467 | END DO |
|---|
| 468 | END DO |
|---|
| 469 | END DO |
|---|
| 470 | |
|---|
| 471 | IF( ln_p4z ) THEN |
|---|
| 472 | !$OMP PARALLEL DO schedule(static) private(jk, jj, ji) |
|---|
| 473 | DO jk = 1, jpk |
|---|
| 474 | DO jj = 1, jpj |
|---|
| 475 | DO ji = 1, jpi |
|---|
| 476 | zremipoc(ji,jj,jk) = MIN( xremip , ztremint(ji,jj,jk) ) |
|---|
| 477 | END DO |
|---|
| 478 | END DO |
|---|
| 479 | END DO |
|---|
| 480 | ELSE |
|---|
| 481 | !$OMP PARALLEL DO schedule(static) private(jk, jj, ji) |
|---|
| 482 | DO jk = 1, jpk |
|---|
| 483 | DO jj = 1, jpj |
|---|
| 484 | DO ji = 1, jpi |
|---|
| 485 | zremipoc(ji,jj,jk) = MIN( xremipc , ztremint(ji,jj,jk) ) |
|---|
| 486 | END DO |
|---|
| 487 | END DO |
|---|
| 488 | END DO |
|---|
| 489 | ENDIF |
|---|
| 490 | |
|---|
| 491 | IF( ln_p4z ) THEN |
|---|
| 492 | !$OMP PARALLEL DO schedule(static) private(jk,jj,ji,zremip,zorem,zofer) |
|---|
| 493 | DO jk = 1, jpkm1 |
|---|
| 494 | DO jj = 1, jpj |
|---|
| 495 | DO ji = 1, jpi |
|---|
| 496 | IF (tmask(ji,jj,jk) == 1.) THEN |
|---|
| 497 | ! POC disaggregation by turbulence and bacterial activity. |
|---|
| 498 | ! -------------------------------------------------------- |
|---|
| 499 | zremip = zremipoc(ji,jj,jk) * xstep * tgfunc(ji,jj,jk) |
|---|
| 500 | zorem = zremip * trb(ji,jj,jk,jppoc) |
|---|
| 501 | zofer = zremip * trb(ji,jj,jk,jpsfe) |
|---|
| 502 | |
|---|
| 503 | tra(ji,jj,jk,jpdoc) = tra(ji,jj,jk,jpdoc) + zorem |
|---|
| 504 | orem(ji,jj,jk) = orem(ji,jj,jk) + zorem |
|---|
| 505 | tra(ji,jj,jk,jpfer) = tra(ji,jj,jk,jpfer) + zofer |
|---|
| 506 | tra(ji,jj,jk,jppoc) = tra(ji,jj,jk,jppoc) - zorem |
|---|
| 507 | tra(ji,jj,jk,jpsfe) = tra(ji,jj,jk,jpsfe) - zofer |
|---|
| 508 | ENDIF |
|---|
| 509 | END DO |
|---|
| 510 | END DO |
|---|
| 511 | END DO |
|---|
| 512 | ELSE |
|---|
| 513 | !$OMP PARALLEL DO schedule(static) private(jk,jj,ji,zremip,zopoc,zopon,zopop,zofer) |
|---|
| 514 | DO jk = 1, jpkm1 |
|---|
| 515 | DO jj = 1, jpj |
|---|
| 516 | DO ji = 1, jpi |
|---|
| 517 | ! POC disaggregation by turbulence and bacterial activity. |
|---|
| 518 | ! -------------------------------------------------------- |
|---|
| 519 | zremip = zremipoc(ji,jj,jk) * xstep * tgfunc(ji,jj,jk) |
|---|
| 520 | zopoc = zremip * trb(ji,jj,jk,jppoc) |
|---|
| 521 | orem(ji,jj,jk) = orem(ji,jj,jk) + zopoc |
|---|
| 522 | zopon = xremipn / xremipc * zremip * trb(ji,jj,jk,jppon) |
|---|
| 523 | zopop = xremipp / xremipc * zremip * trb(ji,jj,jk,jppop) |
|---|
| 524 | zofer = xremipn / xremipc * zremip * trb(ji,jj,jk,jpsfe) |
|---|
| 525 | |
|---|
| 526 | tra(ji,jj,jk,jppoc) = tra(ji,jj,jk,jppoc) - zopoc |
|---|
| 527 | tra(ji,jj,jk,jppon) = tra(ji,jj,jk,jppon) - zopon |
|---|
| 528 | tra(ji,jj,jk,jppop) = tra(ji,jj,jk,jppop) - zopop |
|---|
| 529 | tra(ji,jj,jk,jpsfe) = tra(ji,jj,jk,jpsfe) - zofer |
|---|
| 530 | tra(ji,jj,jk,jpdoc) = tra(ji,jj,jk,jpdoc) + zopoc |
|---|
| 531 | tra(ji,jj,jk,jpdon) = tra(ji,jj,jk,jpdon) + zopon |
|---|
| 532 | tra(ji,jj,jk,jpdop) = tra(ji,jj,jk,jpdop) + zopop |
|---|
| 533 | tra(ji,jj,jk,jpfer) = tra(ji,jj,jk,jpfer) + zofer |
|---|
| 534 | END DO |
|---|
| 535 | END DO |
|---|
| 536 | END DO |
|---|
| 537 | ENDIF |
|---|
| 538 | |
|---|
| 539 | IF( lk_iomput ) THEN |
|---|
| 540 | IF( knt == nrdttrc ) THEN |
|---|
| 541 | zrfact2 = 1.e3 * rfact2r |
|---|
| 542 | CALL iom_put( "REMINP" , zremipoc(:,:,:) * tmask(:,:,:) ) ! Remineralisation rate |
|---|
| 543 | CALL iom_put( "REMING" , zremigoc(:,:,:) * tmask(:,:,:) ) ! Remineralisation rate |
|---|
| 544 | ENDIF |
|---|
| 545 | ENDIF |
|---|
| 546 | |
|---|
| 547 | IF(ln_ctl) THEN ! print mean trends (used for debugging) |
|---|
| 548 | WRITE(charout, FMT="('poc2')") |
|---|
| 549 | CALL prt_ctl_trc_info(charout) |
|---|
| 550 | CALL prt_ctl_trc(tab4d=tra, mask=tmask, clinfo=ctrcnm) |
|---|
| 551 | ENDIF |
|---|
| 552 | ! |
|---|
| 553 | CALL wrk_dealloc( jpi, jpj, totprod, totthick, totcons ) |
|---|
| 554 | CALL wrk_dealloc( jpi, jpj, jpk, zremipoc, zremigoc, zorem3, ztremint ) |
|---|
| 555 | DEALLOCATE( alphag ) |
|---|
| 556 | ! |
|---|
| 557 | IF( nn_timing == 1 ) CALL timing_stop('p4z_poc') |
|---|
| 558 | ! |
|---|
| 559 | END SUBROUTINE p4z_poc |
|---|
| 560 | |
|---|
| 561 | |
|---|
| 562 | SUBROUTINE p4z_poc_init |
|---|
| 563 | !!---------------------------------------------------------------------- |
|---|
| 564 | !! *** ROUTINE p4z_poc_init *** |
|---|
| 565 | !! |
|---|
| 566 | !! ** Purpose : Initialization of remineralization parameters |
|---|
| 567 | !! |
|---|
| 568 | !! ** Method : Read the nampispoc namelist and check the parameters |
|---|
| 569 | !! called at the first timestep |
|---|
| 570 | !! |
|---|
| 571 | !! ** input : Namelist nampispoc |
|---|
| 572 | !! |
|---|
| 573 | !!---------------------------------------------------------------------- |
|---|
| 574 | INTEGER :: jn, jk, jj, ji |
|---|
| 575 | REAL(wp) :: remindelta, reminup, remindown |
|---|
| 576 | INTEGER :: ifault |
|---|
| 577 | |
|---|
| 578 | NAMELIST/nampispoc/ xremip, jcpoc, rshape, & |
|---|
| 579 | & xremipc, xremipn, xremipp |
|---|
| 580 | |
|---|
| 581 | |
|---|
| 582 | INTEGER :: ios ! Local integer output status for namelist read |
|---|
| 583 | |
|---|
| 584 | REWIND( numnatp_ref ) ! Namelist nampisrem in reference namelist : Pisces remineralization |
|---|
| 585 | READ ( numnatp_ref, nampispoc, IOSTAT = ios, ERR = 901) |
|---|
| 586 | 901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'nampispoc in reference namelist', lwp ) |
|---|
| 587 | |
|---|
| 588 | REWIND( numnatp_cfg ) ! Namelist nampisrem in configuration namelist : Pisces remineralization |
|---|
| 589 | READ ( numnatp_cfg, nampispoc, IOSTAT = ios, ERR = 902 ) |
|---|
| 590 | 902 IF( ios /= 0 ) CALL ctl_nam ( ios , 'nampispoc in configuration namelist', lwp ) |
|---|
| 591 | IF(lwm) WRITE ( numonp, nampispoc ) |
|---|
| 592 | |
|---|
| 593 | IF(lwp) THEN ! control print |
|---|
| 594 | WRITE(numout,*) ' ' |
|---|
| 595 | WRITE(numout,*) ' Namelist parameters for remineralization, nampispoc' |
|---|
| 596 | WRITE(numout,*) ' ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~' |
|---|
| 597 | IF( ln_p4z ) THEN |
|---|
| 598 | WRITE(numout,*) ' remineralisation rate of POC xremip =', xremip |
|---|
| 599 | ELSE |
|---|
| 600 | WRITE(numout,*) ' remineralisation rate of POC xremipc =', xremipc |
|---|
| 601 | WRITE(numout,*) ' remineralisation rate of PON xremipn =', xremipn |
|---|
| 602 | WRITE(numout,*) ' remineralisation rate of POP xremipp =', xremipp |
|---|
| 603 | ENDIF |
|---|
| 604 | WRITE(numout,*) ' Number of lability classes for POC jcpoc =', jcpoc |
|---|
| 605 | WRITE(numout,*) ' Shape factor of the gamma distribution rshape =', rshape |
|---|
| 606 | ENDIF |
|---|
| 607 | ! |
|---|
| 608 | ! Discretization along the lability space |
|---|
| 609 | ! --------------------------------------- |
|---|
| 610 | ! |
|---|
| 611 | ALLOCATE( alphan(jcpoc), reminp(jcpoc) ) |
|---|
| 612 | ALLOCATE( alphap(jpi,jpj,jpk,jcpoc) ) |
|---|
| 613 | ! |
|---|
| 614 | IF (jcpoc > 1) THEN |
|---|
| 615 | ! |
|---|
| 616 | remindelta = LOG(4. * 1000. ) / REAL(jcpoc-1, wp) |
|---|
| 617 | reminup = 1./ 400. * EXP(remindelta) |
|---|
| 618 | ! |
|---|
| 619 | ! Discretization based on incomplete gamma functions |
|---|
| 620 | ! As incomplete gamma functions are not available in standard |
|---|
| 621 | ! fortran 95, they have been coded as functions in this module (gamain) |
|---|
| 622 | ! --------------------------------------------------------------------- |
|---|
| 623 | ! |
|---|
| 624 | alphan(1) = gamain(reminup, rshape, ifault) |
|---|
| 625 | reminp(1) = gamain(reminup, rshape+1.0, ifault) * xremip / alphan(1) |
|---|
| 626 | DO jn = 2, jcpoc-1 |
|---|
| 627 | reminup = 1./ 400. * EXP( REAL(jn, wp) * remindelta) |
|---|
| 628 | remindown = 1. / 400. * EXP( REAL(jn-1, wp) * remindelta) |
|---|
| 629 | alphan(jn) = gamain(reminup, rshape, ifault) - gamain(remindown, rshape, ifault) |
|---|
| 630 | reminp(jn) = gamain(reminup, rshape+1.0, ifault) - gamain(remindown, rshape+1.0, ifault) |
|---|
| 631 | reminp(jn) = reminp(jn) * xremip / alphan(jn) |
|---|
| 632 | END DO |
|---|
| 633 | remindown = 1. / 400. * EXP( REAL(jcpoc-1, wp) * remindelta) |
|---|
| 634 | alphan(jcpoc) = 1.0 - gamain(remindown, rshape, ifault) |
|---|
| 635 | reminp(jcpoc) = 1.0 - gamain(remindown, rshape+1.0, ifault) |
|---|
| 636 | reminp(jcpoc) = reminp(jcpoc) * xremip / alphan(jcpoc) |
|---|
| 637 | |
|---|
| 638 | ELSE |
|---|
| 639 | alphan(jcpoc) = 1. |
|---|
| 640 | reminp(jcpoc) = xremip |
|---|
| 641 | ENDIF |
|---|
| 642 | |
|---|
| 643 | DO jn = 1, jcpoc |
|---|
| 644 | !$OMP PARALLEL DO schedule(static) private(jk, jj, ji) |
|---|
| 645 | DO jk = 1, jpk |
|---|
| 646 | DO jj = 1, jpj |
|---|
| 647 | DO ji = 1, jpi |
|---|
| 648 | alphap(ji,jj,jk,jn) = alphan(jn) |
|---|
| 649 | END DO |
|---|
| 650 | END DO |
|---|
| 651 | END DO |
|---|
| 652 | END DO |
|---|
| 653 | |
|---|
| 654 | END SUBROUTINE p4z_poc_init |
|---|
| 655 | |
|---|
| 656 | REAL FUNCTION alngam( xvalue, ifault ) |
|---|
| 657 | |
|---|
| 658 | !*****************************************************************************80 |
|---|
| 659 | ! |
|---|
| 660 | !! ALNGAM computes the logarithm of the gamma function. |
|---|
| 661 | ! |
|---|
| 662 | ! Modified: |
|---|
| 663 | ! |
|---|
| 664 | ! 13 January 2008 |
|---|
| 665 | ! |
|---|
| 666 | ! Author: |
|---|
| 667 | ! |
|---|
| 668 | ! Allan Macleod |
|---|
| 669 | ! FORTRAN90 version by John Burkardt |
|---|
| 670 | ! |
|---|
| 671 | ! Reference: |
|---|
| 672 | ! |
|---|
| 673 | ! Allan Macleod, |
|---|
| 674 | ! Algorithm AS 245, |
|---|
| 675 | ! A Robust and Reliable Algorithm for the Logarithm of the Gamma Function, |
|---|
| 676 | ! Applied Statistics, |
|---|
| 677 | ! Volume 38, Number 2, 1989, pages 397-402. |
|---|
| 678 | ! |
|---|
| 679 | ! Parameters: |
|---|
| 680 | ! |
|---|
| 681 | ! Input, real ( kind = 8 ) XVALUE, the argument of the Gamma function. |
|---|
| 682 | ! |
|---|
| 683 | ! Output, integer ( kind = 4 ) IFAULT, error flag. |
|---|
| 684 | ! 0, no error occurred. |
|---|
| 685 | ! 1, XVALUE is less than or equal to 0. |
|---|
| 686 | ! 2, XVALUE is too big. |
|---|
| 687 | ! |
|---|
| 688 | ! Output, real ( kind = 8 ) ALNGAM, the logarithm of the gamma function of X. |
|---|
| 689 | ! |
|---|
| 690 | implicit none |
|---|
| 691 | |
|---|
| 692 | real(wp), parameter :: alr2pi = 0.918938533204673E+00 |
|---|
| 693 | integer:: ifault |
|---|
| 694 | real(wp), dimension ( 9 ) :: r1 = (/ & |
|---|
| 695 | -2.66685511495E+00, & |
|---|
| 696 | -24.4387534237E+00, & |
|---|
| 697 | -21.9698958928E+00, & |
|---|
| 698 | 11.1667541262E+00, & |
|---|
| 699 | 3.13060547623E+00, & |
|---|
| 700 | 0.607771387771E+00, & |
|---|
| 701 | 11.9400905721E+00, & |
|---|
| 702 | 31.4690115749E+00, & |
|---|
| 703 | 15.2346874070E+00 /) |
|---|
| 704 | real(wp), dimension ( 9 ) :: r2 = (/ & |
|---|
| 705 | -78.3359299449E+00, & |
|---|
| 706 | -142.046296688E+00, & |
|---|
| 707 | 137.519416416E+00, & |
|---|
| 708 | 78.6994924154E+00, & |
|---|
| 709 | 4.16438922228E+00, & |
|---|
| 710 | 47.0668766060E+00, & |
|---|
| 711 | 313.399215894E+00, & |
|---|
| 712 | 263.505074721E+00, & |
|---|
| 713 | 43.3400022514E+00 /) |
|---|
| 714 | real(wp), dimension ( 9 ) :: r3 = (/ & |
|---|
| 715 | -2.12159572323E+05, & |
|---|
| 716 | 2.30661510616E+05, & |
|---|
| 717 | 2.74647644705E+04, & |
|---|
| 718 | -4.02621119975E+04, & |
|---|
| 719 | -2.29660729780E+03, & |
|---|
| 720 | -1.16328495004E+05, & |
|---|
| 721 | -1.46025937511E+05, & |
|---|
| 722 | -2.42357409629E+04, & |
|---|
| 723 | -5.70691009324E+02 /) |
|---|
| 724 | real(wp), dimension ( 5 ) :: r4 = (/ & |
|---|
| 725 | 0.279195317918525E+00, & |
|---|
| 726 | 0.4917317610505968E+00, & |
|---|
| 727 | 0.0692910599291889E+00, & |
|---|
| 728 | 3.350343815022304E+00, & |
|---|
| 729 | 6.012459259764103E+00 /) |
|---|
| 730 | real (wp) :: x |
|---|
| 731 | real (wp) :: x1 |
|---|
| 732 | real (wp) :: x2 |
|---|
| 733 | real (wp), parameter :: xlge = 5.10E+05 |
|---|
| 734 | real (wp), parameter :: xlgst = 1.0E+30 |
|---|
| 735 | real (wp) :: xvalue |
|---|
| 736 | real (wp) :: y |
|---|
| 737 | |
|---|
| 738 | x = xvalue |
|---|
| 739 | alngam = 0.0E+00 |
|---|
| 740 | ! |
|---|
| 741 | ! Check the input. |
|---|
| 742 | ! |
|---|
| 743 | if ( xlgst <= x ) then |
|---|
| 744 | ifault = 2 |
|---|
| 745 | return |
|---|
| 746 | end if |
|---|
| 747 | if ( x <= 0.0E+00 ) then |
|---|
| 748 | ifault = 1 |
|---|
| 749 | return |
|---|
| 750 | end if |
|---|
| 751 | |
|---|
| 752 | ifault = 0 |
|---|
| 753 | ! |
|---|
| 754 | ! Calculation for 0 < X < 0.5 and 0.5 <= X < 1.5 combined. |
|---|
| 755 | ! |
|---|
| 756 | if ( x < 1.5E+00 ) then |
|---|
| 757 | |
|---|
| 758 | if ( x < 0.5E+00 ) then |
|---|
| 759 | alngam = - log ( x ) |
|---|
| 760 | y = x + 1.0E+00 |
|---|
| 761 | ! |
|---|
| 762 | ! Test whether X < machine epsilon. |
|---|
| 763 | ! |
|---|
| 764 | if ( y == 1.0E+00 ) then |
|---|
| 765 | return |
|---|
| 766 | end if |
|---|
| 767 | |
|---|
| 768 | else |
|---|
| 769 | |
|---|
| 770 | alngam = 0.0E+00 |
|---|
| 771 | y = x |
|---|
| 772 | x = ( x - 0.5E+00 ) - 0.5E+00 |
|---|
| 773 | |
|---|
| 774 | end if |
|---|
| 775 | |
|---|
| 776 | alngam = alngam + x * (((( & |
|---|
| 777 | r1(5) * y & |
|---|
| 778 | + r1(4) ) * y & |
|---|
| 779 | + r1(3) ) * y & |
|---|
| 780 | + r1(2) ) * y & |
|---|
| 781 | + r1(1) ) / (((( & |
|---|
| 782 | y & |
|---|
| 783 | + r1(9) ) * y & |
|---|
| 784 | + r1(8) ) * y & |
|---|
| 785 | + r1(7) ) * y & |
|---|
| 786 | + r1(6) ) |
|---|
| 787 | |
|---|
| 788 | return |
|---|
| 789 | |
|---|
| 790 | end if |
|---|
| 791 | ! |
|---|
| 792 | ! Calculation for 1.5 <= X < 4.0. |
|---|
| 793 | ! |
|---|
| 794 | if ( x < 4.0E+00 ) then |
|---|
| 795 | |
|---|
| 796 | y = ( x - 1.0E+00 ) - 1.0E+00 |
|---|
| 797 | |
|---|
| 798 | alngam = y * (((( & |
|---|
| 799 | r2(5) * x & |
|---|
| 800 | + r2(4) ) * x & |
|---|
| 801 | + r2(3) ) * x & |
|---|
| 802 | + r2(2) ) * x & |
|---|
| 803 | + r2(1) ) / (((( & |
|---|
| 804 | x & |
|---|
| 805 | + r2(9) ) * x & |
|---|
| 806 | + r2(8) ) * x & |
|---|
| 807 | + r2(7) ) * x & |
|---|
| 808 | + r2(6) ) |
|---|
| 809 | ! |
|---|
| 810 | ! Calculation for 4.0 <= X < 12.0. |
|---|
| 811 | ! |
|---|
| 812 | else if ( x < 12.0E+00 ) then |
|---|
| 813 | |
|---|
| 814 | alngam = (((( & |
|---|
| 815 | r3(5) * x & |
|---|
| 816 | + r3(4) ) * x & |
|---|
| 817 | + r3(3) ) * x & |
|---|
| 818 | + r3(2) ) * x & |
|---|
| 819 | + r3(1) ) / (((( & |
|---|
| 820 | x & |
|---|
| 821 | + r3(9) ) * x & |
|---|
| 822 | + r3(8) ) * x & |
|---|
| 823 | + r3(7) ) * x & |
|---|
| 824 | + r3(6) ) |
|---|
| 825 | ! |
|---|
| 826 | ! Calculation for 12.0 <= X. |
|---|
| 827 | ! |
|---|
| 828 | else |
|---|
| 829 | |
|---|
| 830 | y = log ( x ) |
|---|
| 831 | alngam = x * ( y - 1.0E+00 ) - 0.5E+00 * y + alr2pi |
|---|
| 832 | |
|---|
| 833 | if ( x <= xlge ) then |
|---|
| 834 | |
|---|
| 835 | x1 = 1.0E+00 / x |
|---|
| 836 | x2 = x1 * x1 |
|---|
| 837 | |
|---|
| 838 | alngam = alngam + x1 * ( ( & |
|---|
| 839 | r4(3) * & |
|---|
| 840 | x2 + r4(2) ) * & |
|---|
| 841 | x2 + r4(1) ) / ( ( & |
|---|
| 842 | x2 + r4(5) ) * & |
|---|
| 843 | x2 + r4(4) ) |
|---|
| 844 | |
|---|
| 845 | end if |
|---|
| 846 | |
|---|
| 847 | end if |
|---|
| 848 | |
|---|
| 849 | END FUNCTION alngam |
|---|
| 850 | |
|---|
| 851 | REAL FUNCTION gamain( x, p, ifault ) |
|---|
| 852 | |
|---|
| 853 | !*****************************************************************************80 |
|---|
| 854 | ! |
|---|
| 855 | !! GAMAIN computes the incomplete gamma ratio. |
|---|
| 856 | ! |
|---|
| 857 | ! Discussion: |
|---|
| 858 | ! |
|---|
| 859 | ! A series expansion is used if P > X or X <= 1. Otherwise, a |
|---|
| 860 | ! continued fraction approximation is used. |
|---|
| 861 | ! |
|---|
| 862 | ! Modified: |
|---|
| 863 | ! |
|---|
| 864 | ! 17 January 2008 |
|---|
| 865 | ! |
|---|
| 866 | ! Author: |
|---|
| 867 | ! |
|---|
| 868 | ! G Bhattacharjee |
|---|
| 869 | ! FORTRAN90 version by John Burkardt |
|---|
| 870 | ! |
|---|
| 871 | ! Reference: |
|---|
| 872 | ! |
|---|
| 873 | ! G Bhattacharjee, |
|---|
| 874 | ! Algorithm AS 32: |
|---|
| 875 | ! The Incomplete Gamma Integral, |
|---|
| 876 | ! Applied Statistics, |
|---|
| 877 | ! Volume 19, Number 3, 1970, pages 285-287. |
|---|
| 878 | ! |
|---|
| 879 | ! Parameters: |
|---|
| 880 | ! |
|---|
| 881 | ! Input, real ( kind = 8 ) X, P, the parameters of the incomplete |
|---|
| 882 | ! gamma ratio. 0 <= X, and 0 < P. |
|---|
| 883 | ! |
|---|
| 884 | ! Output, integer ( kind = 4 ) IFAULT, error flag. |
|---|
| 885 | ! 0, no errors. |
|---|
| 886 | ! 1, P <= 0. |
|---|
| 887 | ! 2, X < 0. |
|---|
| 888 | ! 3, underflow. |
|---|
| 889 | ! 4, error return from the Log Gamma routine. |
|---|
| 890 | ! |
|---|
| 891 | ! Output, real ( kind = 8 ) GAMAIN, the value of the incomplete |
|---|
| 892 | ! gamma ratio. |
|---|
| 893 | ! |
|---|
| 894 | implicit none |
|---|
| 895 | |
|---|
| 896 | real (wp) a |
|---|
| 897 | real (wp), parameter :: acu = 1.0E-08 |
|---|
| 898 | real (wp) an |
|---|
| 899 | real (wp) arg |
|---|
| 900 | real (wp) b |
|---|
| 901 | real (wp) dif |
|---|
| 902 | real (wp) factor |
|---|
| 903 | real (wp) g |
|---|
| 904 | real (wp) gin |
|---|
| 905 | integer i |
|---|
| 906 | integer ifault |
|---|
| 907 | real (wp), parameter :: oflo = 1.0E+37 |
|---|
| 908 | real (wp) p |
|---|
| 909 | real (wp) pn(6) |
|---|
| 910 | real (wp) rn |
|---|
| 911 | real (wp) term |
|---|
| 912 | real (wp), parameter :: uflo = 1.0E-37 |
|---|
| 913 | real (wp) x |
|---|
| 914 | ! |
|---|
| 915 | ! Check the input. |
|---|
| 916 | ! |
|---|
| 917 | if ( p <= 0.0E+00 ) then |
|---|
| 918 | ifault = 1 |
|---|
| 919 | gamain = 0.0E+00 |
|---|
| 920 | return |
|---|
| 921 | end if |
|---|
| 922 | |
|---|
| 923 | if ( x < 0.0E+00 ) then |
|---|
| 924 | ifault = 2 |
|---|
| 925 | gamain = 0.0E+00 |
|---|
| 926 | return |
|---|
| 927 | end if |
|---|
| 928 | |
|---|
| 929 | if ( x == 0.0E+00 ) then |
|---|
| 930 | ifault = 0 |
|---|
| 931 | gamain = 0.0E+00 |
|---|
| 932 | return |
|---|
| 933 | end if |
|---|
| 934 | |
|---|
| 935 | g = alngam ( p, ifault ) |
|---|
| 936 | |
|---|
| 937 | if ( ifault /= 0 ) then |
|---|
| 938 | ifault = 4 |
|---|
| 939 | gamain = 0.0E+00 |
|---|
| 940 | return |
|---|
| 941 | end if |
|---|
| 942 | |
|---|
| 943 | arg = p * log ( x ) - x - g |
|---|
| 944 | |
|---|
| 945 | if ( arg < log ( uflo ) ) then |
|---|
| 946 | ifault = 3 |
|---|
| 947 | gamain = 0.0E+00 |
|---|
| 948 | return |
|---|
| 949 | end if |
|---|
| 950 | |
|---|
| 951 | ifault = 0 |
|---|
| 952 | factor = exp ( arg ) |
|---|
| 953 | ! |
|---|
| 954 | ! Calculation by series expansion. |
|---|
| 955 | ! |
|---|
| 956 | if ( x <= 1.0E+00 .or. x < p ) then |
|---|
| 957 | |
|---|
| 958 | gin = 1.0E+00 |
|---|
| 959 | term = 1.0E+00 |
|---|
| 960 | rn = p |
|---|
| 961 | |
|---|
| 962 | do |
|---|
| 963 | |
|---|
| 964 | rn = rn + 1.0E+00 |
|---|
| 965 | term = term * x / rn |
|---|
| 966 | gin = gin + term |
|---|
| 967 | |
|---|
| 968 | if ( term <= acu ) then |
|---|
| 969 | exit |
|---|
| 970 | end if |
|---|
| 971 | |
|---|
| 972 | end do |
|---|
| 973 | |
|---|
| 974 | gamain = gin * factor / p |
|---|
| 975 | return |
|---|
| 976 | |
|---|
| 977 | end if |
|---|
| 978 | ! |
|---|
| 979 | ! Calculation by continued fraction. |
|---|
| 980 | ! |
|---|
| 981 | a = 1.0E+00 - p |
|---|
| 982 | b = a + x + 1.0E+00 |
|---|
| 983 | term = 0.0E+00 |
|---|
| 984 | |
|---|
| 985 | pn(1) = 1.0E+00 |
|---|
| 986 | pn(2) = x |
|---|
| 987 | pn(3) = x + 1.0E+00 |
|---|
| 988 | pn(4) = x * b |
|---|
| 989 | |
|---|
| 990 | gin = pn(3) / pn(4) |
|---|
| 991 | |
|---|
| 992 | do |
|---|
| 993 | |
|---|
| 994 | a = a + 1.0E+00 |
|---|
| 995 | b = b + 2.0E+00 |
|---|
| 996 | term = term + 1.0E+00 |
|---|
| 997 | an = a * term |
|---|
| 998 | do i = 1, 2 |
|---|
| 999 | pn(i+4) = b * pn(i+2) - an * pn(i) |
|---|
| 1000 | end do |
|---|
| 1001 | |
|---|
| 1002 | if ( pn(6) /= 0.0E+00 ) then |
|---|
| 1003 | |
|---|
| 1004 | rn = pn(5) / pn(6) |
|---|
| 1005 | dif = abs ( gin - rn ) |
|---|
| 1006 | ! |
|---|
| 1007 | ! Absolute error tolerance satisfied? |
|---|
| 1008 | ! |
|---|
| 1009 | if ( dif <= acu ) then |
|---|
| 1010 | ! |
|---|
| 1011 | ! Relative error tolerance satisfied? |
|---|
| 1012 | ! |
|---|
| 1013 | if ( dif <= acu * rn ) then |
|---|
| 1014 | gamain = 1.0E+00 - factor * gin |
|---|
| 1015 | exit |
|---|
| 1016 | end if |
|---|
| 1017 | |
|---|
| 1018 | end if |
|---|
| 1019 | |
|---|
| 1020 | gin = rn |
|---|
| 1021 | |
|---|
| 1022 | end if |
|---|
| 1023 | |
|---|
| 1024 | do i = 1, 4 |
|---|
| 1025 | pn(i) = pn(i+2) |
|---|
| 1026 | end do |
|---|
| 1027 | if ( oflo <= abs ( pn(5) ) ) then |
|---|
| 1028 | |
|---|
| 1029 | do i = 1, 4 |
|---|
| 1030 | pn(i) = pn(i) / oflo |
|---|
| 1031 | end do |
|---|
| 1032 | |
|---|
| 1033 | end if |
|---|
| 1034 | |
|---|
| 1035 | end do |
|---|
| 1036 | |
|---|
| 1037 | END FUNCTION gamain |
|---|
| 1038 | |
|---|
| 1039 | !!====================================================================== |
|---|
| 1040 | END MODULE p4zpoc |
|---|
