| 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 | !! Same module for both PISCES and PISCES-QUOTA |
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| 6 | !!========================================================================= |
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| 7 | !! History : 1.0 ! 2004 (O. Aumont) Original code |
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| 8 | !! 2.0 ! 2007-12 (C. Ethe, G. Madec) F90 |
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| 9 | !! 3.4 ! 2011-06 (O. Aumont, C. Ethe) Quota model for iron |
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| 10 | !! 3.6 ! 2016-03 (O. Aumont) Quota model and diverse |
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| 11 | !! 4.0 ! 2018 (O. Aumont) Variable lability parameterization |
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| 12 | !!---------------------------------------------------------------------- |
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| 13 | !! p4z_poc : Compute remineralization/dissolution of organic compounds |
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| 14 | !! p4z_poc_init : Initialisation of parameters for remineralisation |
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| 15 | !! alngam and gamain : computation of the incomplete gamma function |
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| 16 | !!---------------------------------------------------------------------- |
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| 17 | USE oce_trc ! shared variables between ocean and passive tracers |
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| 18 | USE trc ! passive tracers common variables |
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| 19 | USE sms_pisces ! PISCES Source Minus Sink variables |
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| 20 | USE prtctl ! print control for debugging |
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| 21 | USE iom ! I/O manager |
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| 22 | |
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| 23 | IMPLICIT NONE |
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| 24 | PRIVATE |
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| 25 | |
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| 26 | PUBLIC p4z_poc ! called in p4zbio.F90 |
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| 27 | PUBLIC p4z_poc_init ! called in trcini_pisces.F90 |
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| 28 | PUBLIC alngam ! |
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| 29 | PUBLIC gamain ! |
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| 30 | |
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| 31 | REAL(wp), PUBLIC :: xremip !: remineralisation rate of DOC |
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| 32 | REAL(wp), PUBLIC :: xremipc !: remineralisation rate of DOC |
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| 33 | REAL(wp), PUBLIC :: xremipn !: remineralisation rate of DON |
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| 34 | REAL(wp), PUBLIC :: xremipp !: remineralisation rate of DOP |
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| 35 | INTEGER , PUBLIC :: jcpoc !: number of lability classes |
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| 36 | REAL(wp), PUBLIC :: rshape !: shape factor of the gamma distribution |
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| 37 | |
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| 38 | REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:) :: alphan, reminp !: variable lability of POC and initial distribution |
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| 39 | REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:,:) :: alphap !: lability distribution of small particles |
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| 40 | |
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| 41 | |
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| 42 | !! * Substitutions |
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| 43 | # include "do_loop_substitute.h90" |
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| 44 | # include "domzgr_substitute.h90" |
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| 45 | !!---------------------------------------------------------------------- |
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| 46 | !! NEMO/TOP 4.0 , NEMO Consortium (2018) |
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| 47 | !! $Id$ |
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| 48 | !! Software governed by the CeCILL license (see ./LICENSE) |
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| 49 | !!---------------------------------------------------------------------- |
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| 50 | CONTAINS |
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| 51 | |
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| 52 | SUBROUTINE p4z_poc( kt, knt, Kbb, Kmm, Krhs ) |
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| 53 | !!--------------------------------------------------------------------- |
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| 54 | !! *** ROUTINE p4z_poc *** |
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| 55 | !! |
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| 56 | !! ** Purpose : Compute remineralization of organic particles |
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| 57 | !! A reactivity-continuum parameterization is chosen |
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| 58 | !! to describe the lability of the organic particles |
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| 59 | !! As a consequence, the remineralisation rates of the |
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| 60 | !! the different pools change with time as a function of |
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| 61 | !! the lability distribution |
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| 62 | !! |
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| 63 | !! ** Method : - Computation of the remineralisation rates is performed |
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| 64 | !! according to reactivity continuum formalism described |
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| 65 | !! in Aumont et al. (2017). |
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| 66 | !!--------------------------------------------------------------------- |
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| 67 | INTEGER, INTENT(in) :: kt, knt ! ocean time step and ??? |
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| 68 | INTEGER, INTENT(in) :: Kbb, Kmm, Krhs ! time level indices |
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| 69 | ! |
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| 70 | INTEGER :: ji, jj, jk, jn |
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| 71 | REAL(wp) :: zremip, zremig, zdep, zorem, zorem2, zofer |
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| 72 | REAL(wp) :: zopon, zopop, zopoc, zopoc2, zopon2, zopop2 |
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| 73 | REAL(wp) :: zsizek, zsizek1, alphat, remint, solgoc, zpoc |
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| 74 | REAL(wp) :: zofer2, zofer3 |
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| 75 | REAL(wp) :: zrfact2 |
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| 76 | CHARACTER (len=25) :: charout |
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| 77 | REAL(wp), DIMENSION(jpi,jpj ) :: totprod, totthick, totcons |
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| 78 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zremipoc, zremigoc, zorem3, ztremint, zfolimi |
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| 79 | REAL(wp), DIMENSION(jpi,jpj,jpk,jcpoc) :: alphag |
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| 80 | !!--------------------------------------------------------------------- |
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| 81 | ! |
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| 82 | IF( ln_timing ) CALL timing_start('p4z_poc') |
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| 83 | ! |
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| 84 | ! Initialization of local variables |
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| 85 | ! --------------------------------- |
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| 86 | |
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| 87 | ! Here we compute the GOC -> POC rate due to the shrinking |
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| 88 | ! of the fecal pellets/aggregates as a result of bacterial |
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| 89 | ! solubilization |
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| 90 | ! This is based on a fractal dimension of 2.56 and a spectral |
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| 91 | ! slope of -3.6 (identical to what is used in p4zsink to compute |
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| 92 | ! aggregation |
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| 93 | solgoc = 0.04/ 2.56 * 1./ ( 1.-50**(-0.04) ) |
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| 94 | |
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| 95 | ! Initialisation of temporary arrays |
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| 96 | IF( ln_p4z ) THEN |
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| 97 | zremipoc(:,:,:) = xremip |
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| 98 | zremigoc(:,:,:) = xremip |
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| 99 | ELSE ! ln_p5z |
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| 100 | zremipoc(:,:,:) = xremipc |
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| 101 | zremigoc(:,:,:) = xremipc |
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| 102 | ENDIF |
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| 103 | zorem3(:,:,:) = 0. |
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| 104 | orem (:,:,:) = 0. |
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| 105 | ztremint(:,:,:) = 0. |
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| 106 | zfolimi (:,:,:) = 0. |
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| 107 | |
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| 108 | ! Initialisation of the lability distributions that are set to |
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| 109 | ! the distribution of newly produced organic particles |
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| 110 | DO jn = 1, jcpoc |
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| 111 | alphag(:,:,:,jn) = alphan(jn) |
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| 112 | alphap(:,:,:,jn) = alphan(jn) |
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| 113 | END DO |
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| 114 | |
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| 115 | ! Lability parameterization. This is the big particles part (GOC) |
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| 116 | ! This lability parameterization is always active. However, if only one |
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| 117 | ! lability class is specified in the namelist, this is equivalent to |
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| 118 | ! a standard parameterisation with a constant lability |
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| 119 | ! ----------------------------------------------------------------------- |
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| 120 | ztremint(:,:,:) = zremigoc(:,:,:) |
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| 121 | DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 1, jpkm1) |
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| 122 | IF (tmask(ji,jj,jk) == 1.) THEN |
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| 123 | zdep = hmld(ji,jj) |
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| 124 | ! |
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| 125 | ! In the case of GOC, lability is constant in the mixed layer |
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| 126 | ! It is computed only below the mixed layer depth |
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| 127 | ! ------------------------------------------------------------ |
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| 128 | ! |
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| 129 | IF( gdept(ji,jj,jk,Kmm) > zdep ) THEN |
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| 130 | alphat = 0. |
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| 131 | remint = 0. |
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| 132 | ! |
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| 133 | zsizek1 = e3t(ji,jj,jk-1,Kmm) / 2. / (wsbio4(ji,jj,jk-1) + rtrn) * tgfunc(ji,jj,jk-1) |
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| 134 | zsizek = e3t(ji,jj,jk,Kmm) / 2. / (wsbio4(ji,jj,jk) + rtrn) * tgfunc(ji,jj,jk) |
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| 135 | ! |
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| 136 | IF ( gdept(ji,jj,jk-1,Kmm) <= zdep ) THEN |
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| 137 | ! |
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| 138 | ! The first level just below the mixed layer needs a |
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| 139 | ! specific treatment because lability is supposed constant |
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| 140 | ! everywhere within the mixed layer. This means that |
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| 141 | ! change in lability in the bottom part of the previous cell |
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| 142 | ! should not be computed |
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| 143 | ! ---------------------------------------------------------- |
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| 144 | ! |
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| 145 | ! POC concentration is computed using the lagrangian |
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| 146 | ! framework. It is only used for the lability param |
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| 147 | zpoc = tr(ji,jj,jk-1,jpgoc,Kbb) + consgoc(ji,jj,jk) * rday / rfact2 & |
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| 148 | & * e3t(ji,jj,jk,Kmm) / 2. / (wsbio4(ji,jj,jk) + rtrn) |
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| 149 | zpoc = MAX(0., zpoc) |
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| 150 | ! |
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| 151 | DO jn = 1, jcpoc |
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| 152 | ! |
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| 153 | ! Lagrangian based algorithm. The fraction of each |
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| 154 | ! lability class is computed starting from the previous |
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| 155 | ! level |
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| 156 | ! ----------------------------------------------------- |
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| 157 | ! |
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| 158 | ! the concentration of each lability class is calculated |
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| 159 | ! as the sum of the different sources and sinks |
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| 160 | ! Please note that production of new GOC experiences |
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| 161 | ! degradation |
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| 162 | alphag(ji,jj,jk,jn) = alphag(ji,jj,jk-1,jn) * exp( -reminp(jn) * zsizek ) * zpoc & |
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| 163 | & + prodgoc(ji,jj,jk) * alphan(jn) / tgfunc(ji,jj,jk) / reminp(jn) & |
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| 164 | & * ( 1. - exp( -reminp(jn) * zsizek ) ) * rday / rfact2 |
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| 165 | alphat = alphat + alphag(ji,jj,jk,jn) |
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| 166 | remint = remint + alphag(ji,jj,jk,jn) * reminp(jn) |
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| 167 | END DO |
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| 168 | ELSE |
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| 169 | ! |
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| 170 | ! standard algorithm in the rest of the water column |
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| 171 | ! See the comments in the previous block. |
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| 172 | ! --------------------------------------------------- |
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| 173 | ! |
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| 174 | zpoc = tr(ji,jj,jk-1,jpgoc,Kbb) + consgoc(ji,jj,jk-1) * rday / rfact2 & |
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| 175 | & * e3t(ji,jj,jk-1,Kmm) / 2. / (wsbio4(ji,jj,jk-1) + rtrn) + consgoc(ji,jj,jk) & |
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| 176 | & * rday / rfact2 * e3t(ji,jj,jk,Kmm) / 2. / (wsbio4(ji,jj,jk) + rtrn) |
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| 177 | zpoc = max(0., zpoc) |
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| 178 | ! |
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| 179 | DO jn = 1, jcpoc |
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| 180 | alphag(ji,jj,jk,jn) = alphag(ji,jj,jk-1,jn) * exp( -reminp(jn) * ( zsizek & |
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| 181 | & + zsizek1 ) ) * zpoc + ( prodgoc(ji,jj,jk-1) / tgfunc(ji,jj,jk-1) * ( 1. & |
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| 182 | & - exp( -reminp(jn) * zsizek1 ) ) * exp( -reminp(jn) * zsizek ) + prodgoc(ji,jj,jk) & |
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| 183 | & / tgfunc(ji,jj,jk) * ( 1. - exp( -reminp(jn) * zsizek ) ) ) * rday / rfact2 / reminp(jn) * alphan(jn) |
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| 184 | alphat = alphat + alphag(ji,jj,jk,jn) |
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| 185 | remint = remint + alphag(ji,jj,jk,jn) * reminp(jn) |
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| 186 | END DO |
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| 187 | ENDIF |
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| 188 | ! |
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| 189 | DO jn = 1, jcpoc |
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| 190 | ! The contribution of each lability class at the current |
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| 191 | ! level is computed |
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| 192 | alphag(ji,jj,jk,jn) = alphag(ji,jj,jk,jn) / ( alphat + rtrn) |
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| 193 | END DO |
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| 194 | ! Computation of the mean remineralisation rate |
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| 195 | ztremint(ji,jj,jk) = MAX(0., remint / ( alphat + rtrn) ) |
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| 196 | ! |
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| 197 | ENDIF |
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| 198 | ENDIF |
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| 199 | END_3D |
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| 200 | |
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| 201 | IF( ln_p4z ) THEN ; zremigoc(:,:,:) = MIN( xremip , ztremint(:,:,:) ) |
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| 202 | ELSE ; zremigoc(:,:,:) = MIN( xremipc, ztremint(:,:,:) ) |
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| 203 | ENDIF |
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| 204 | |
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| 205 | IF( ln_p4z ) THEN |
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| 206 | ! The standard PISCES part |
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| 207 | DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 1, jpkm1) |
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| 208 | ! POC degradation by bacterial activity. It is a function |
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| 209 | ! of the mean lability and of temperature. This also includes |
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| 210 | ! shrinking of particles due to the bacterial activity |
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| 211 | ! ----------------------------------------------------------- |
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| 212 | zremig = zremigoc(ji,jj,jk) * xstep * tgfunc(ji,jj,jk) |
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| 213 | zorem2 = zremig * tr(ji,jj,jk,jpgoc,Kbb) |
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| 214 | orem(ji,jj,jk) = zorem2 |
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| 215 | zorem3(ji,jj,jk) = zremig * solgoc * tr(ji,jj,jk,jpgoc,Kbb) |
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| 216 | zofer2 = zremig * tr(ji,jj,jk,jpbfe,Kbb) |
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| 217 | zofer3 = zremig * solgoc * tr(ji,jj,jk,jpbfe,Kbb) |
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| 218 | |
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| 219 | ! update of the TRA arrays |
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| 220 | tr(ji,jj,jk,jppoc,Krhs) = tr(ji,jj,jk,jppoc,Krhs) + zorem3(ji,jj,jk) |
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| 221 | tr(ji,jj,jk,jpgoc,Krhs) = tr(ji,jj,jk,jpgoc,Krhs) - zorem2 - zorem3(ji,jj,jk) |
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| 222 | tr(ji,jj,jk,jpsfe,Krhs) = tr(ji,jj,jk,jpsfe,Krhs) + zofer3 |
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| 223 | tr(ji,jj,jk,jpbfe,Krhs) = tr(ji,jj,jk,jpbfe,Krhs) - zofer2 - zofer3 |
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| 224 | tr(ji,jj,jk,jpdoc,Krhs) = tr(ji,jj,jk,jpdoc,Krhs) + zorem2 |
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| 225 | tr(ji,jj,jk,jpfer,Krhs) = tr(ji,jj,jk,jpfer,Krhs) + zofer2 |
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| 226 | zfolimi(ji,jj,jk) = zofer2 |
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| 227 | END_3D |
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| 228 | ELSE |
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| 229 | DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 1, jpkm1) |
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| 230 | ! POC degradation by bacterial activity. It is a function |
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| 231 | ! of the mean lability and of temperature. This also includes |
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| 232 | ! shrinking of particles due to the bacterial activity |
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| 233 | ! -------------------------------------------------------- |
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| 234 | zremig = zremigoc(ji,jj,jk) * xstep * tgfunc(ji,jj,jk) |
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| 235 | zopoc2 = zremig * tr(ji,jj,jk,jpgoc,Kbb) |
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| 236 | orem(ji,jj,jk) = zopoc2 |
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| 237 | zorem3(ji,jj,jk) = zremig * solgoc * tr(ji,jj,jk,jpgoc,Kbb) |
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| 238 | zopon2 = xremipn / xremipc * zremig * tr(ji,jj,jk,jpgon,Kbb) |
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| 239 | zopop2 = xremipp / xremipc * zremig * tr(ji,jj,jk,jpgop,Kbb) |
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| 240 | zofer2 = xremipn / xremipc * zremig * tr(ji,jj,jk,jpbfe,Kbb) |
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| 241 | |
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| 242 | ! update of the TRA arrays |
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| 243 | tr(ji,jj,jk,jppoc,Krhs) = tr(ji,jj,jk,jppoc,Krhs) + zorem3(ji,jj,jk) |
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| 244 | tr(ji,jj,jk,jppon,Krhs) = tr(ji,jj,jk,jppon,Krhs) + solgoc * zopon2 |
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| 245 | tr(ji,jj,jk,jppop,Krhs) = tr(ji,jj,jk,jppop,Krhs) + solgoc * zopop2 |
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| 246 | tr(ji,jj,jk,jpsfe,Krhs) = tr(ji,jj,jk,jpsfe,Krhs) + solgoc * zofer2 |
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| 247 | tr(ji,jj,jk,jpdoc,Krhs) = tr(ji,jj,jk,jpdoc,Krhs) + zopoc2 |
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| 248 | tr(ji,jj,jk,jpdon,Krhs) = tr(ji,jj,jk,jpdon,Krhs) + zopon2 |
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| 249 | tr(ji,jj,jk,jpdop,Krhs) = tr(ji,jj,jk,jpdop,Krhs) + zopop2 |
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| 250 | tr(ji,jj,jk,jpfer,Krhs) = tr(ji,jj,jk,jpfer,Krhs) + zofer2 |
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| 251 | tr(ji,jj,jk,jpgoc,Krhs) = tr(ji,jj,jk,jpgoc,Krhs) - zopoc2 - zorem3(ji,jj,jk) |
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| 252 | tr(ji,jj,jk,jpgon,Krhs) = tr(ji,jj,jk,jpgon,Krhs) - zopon2 * (1. + solgoc) |
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| 253 | tr(ji,jj,jk,jpgop,Krhs) = tr(ji,jj,jk,jpgop,Krhs) - zopop2 * (1. + solgoc) |
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| 254 | tr(ji,jj,jk,jpbfe,Krhs) = tr(ji,jj,jk,jpbfe,Krhs) - zofer2 * (1. + solgoc) |
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| 255 | zfolimi(ji,jj,jk) = zofer2 |
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| 256 | END_3D |
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| 257 | ENDIF |
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| 258 | |
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| 259 | IF(sn_cfctl%l_prttrc) THEN ! print mean trends (used for debugging) |
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| 260 | WRITE(charout, FMT="('poc1')") |
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| 261 | CALL prt_ctl_info( charout, cdcomp = 'top' ) |
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| 262 | CALL prt_ctl(tab4d_1=tr(:,:,:,:,Krhs), mask1=tmask, clinfo=ctrcnm) |
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| 263 | ENDIF |
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| 264 | |
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| 265 | ! Lability parameterization for the small OM particles. This param |
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| 266 | ! is based on the same theoretical background as the big particles. |
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| 267 | ! However, because of its low sinking speed, lability is not supposed |
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| 268 | ! to be equal to its initial value (the value of the freshly produced |
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| 269 | ! organic matter) in the MLD. It is however uniform in the mixed layer. |
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| 270 | ! --------------------------------------------------------------------- |
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| 271 | totprod (:,:) = 0. |
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| 272 | totthick(:,:) = 0. |
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| 273 | totcons (:,:) = 0. |
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| 274 | |
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| 275 | ! intregrated production and consumption of POC in the mixed layer |
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| 276 | ! ---------------------------------------------------------------- |
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| 277 | DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 1, jpkm1) |
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| 278 | zdep = hmld(ji,jj) |
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| 279 | IF (tmask(ji,jj,jk) == 1. .AND. gdept(ji,jj,jk,Kmm) <= zdep ) THEN |
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| 280 | totprod(ji,jj) = totprod(ji,jj) + prodpoc(ji,jj,jk) * e3t(ji,jj,jk,Kmm) * rday/ rfact2 |
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| 281 | ! The temperature effect is included here |
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| 282 | totthick(ji,jj) = totthick(ji,jj) + e3t(ji,jj,jk,Kmm)* tgfunc(ji,jj,jk) |
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| 283 | totcons(ji,jj) = totcons(ji,jj) - conspoc(ji,jj,jk) * e3t(ji,jj,jk,Kmm) * rday/ rfact2 & |
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| 284 | & / ( tr(ji,jj,jk,jppoc,Kbb) + rtrn ) |
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| 285 | ENDIF |
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| 286 | END_3D |
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| 287 | |
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| 288 | ! Computation of the lability spectrum in the mixed layer. In the mixed |
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| 289 | ! layer, this spectrum is supposed to be uniform as a result of intense |
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| 290 | ! mixing. |
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| 291 | ! --------------------------------------------------------------------- |
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| 292 | ztremint(:,:,:) = zremipoc(:,:,:) |
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| 293 | DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 1, jpkm1) |
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| 294 | IF (tmask(ji,jj,jk) == 1.) THEN |
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| 295 | zdep = hmld(ji,jj) |
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| 296 | alphat = 0.0 |
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| 297 | remint = 0.0 |
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| 298 | IF( gdept(ji,jj,jk,Kmm) <= zdep ) THEN |
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| 299 | DO jn = 1, jcpoc |
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| 300 | ! For each lability class, the system is supposed to be |
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| 301 | ! at equilibrium: Prod - Sink - w alphap = 0. |
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| 302 | alphap(ji,jj,jk,jn) = totprod(ji,jj) * alphan(jn) / ( reminp(jn) & |
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| 303 | & * totthick(ji,jj) + totcons(ji,jj) + wsbio + rtrn ) |
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| 304 | alphat = alphat + alphap(ji,jj,jk,jn) |
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| 305 | END DO |
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| 306 | DO jn = 1, jcpoc |
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| 307 | alphap(ji,jj,jk,jn) = alphap(ji,jj,jk,jn) / ( alphat + rtrn) |
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| 308 | remint = remint + alphap(ji,jj,jk,jn) * reminp(jn) |
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| 309 | END DO |
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| 310 | ! Mean remineralization rate in the mixed layer |
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| 311 | ztremint(ji,jj,jk) = MAX( 0., remint ) |
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| 312 | ENDIF |
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| 313 | ENDIF |
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| 314 | END_3D |
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| 315 | ! |
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| 316 | IF( ln_p4z ) THEN ; zremipoc(:,:,:) = MIN( xremip , ztremint(:,:,:) ) |
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| 317 | ELSE ; zremipoc(:,:,:) = MIN( xremipc, ztremint(:,:,:) ) |
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| 318 | ENDIF |
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| 319 | |
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| 320 | ! The lability parameterization is used here. The code is here |
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| 321 | ! almost identical to what is done for big particles. The only difference |
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| 322 | ! is that an additional source from GOC to POC is included. This means |
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| 323 | ! that since we need the lability spectrum of GOC, GOC spectrum |
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| 324 | ! should be determined before. |
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| 325 | ! ----------------------------------------------------------------------- |
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| 326 | DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 2, jpkm1) |
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| 327 | IF (tmask(ji,jj,jk) == 1.) THEN |
|---|
| 328 | zdep = hmld(ji,jj) |
|---|
| 329 | IF( gdept(ji,jj,jk,Kmm) > zdep ) THEN |
|---|
| 330 | alphat = 0. |
|---|
| 331 | remint = 0. |
|---|
| 332 | ! |
|---|
| 333 | ! the scale factors are corrected with temperature |
|---|
| 334 | zsizek1 = e3t(ji,jj,jk-1,Kmm) / 2. / (wsbio3(ji,jj,jk-1) + rtrn) * tgfunc(ji,jj,jk-1) |
|---|
| 335 | zsizek = e3t(ji,jj,jk,Kmm) / 2. / (wsbio3(ji,jj,jk) + rtrn) * tgfunc(ji,jj,jk) |
|---|
| 336 | ! |
|---|
| 337 | ! Special treatment of the level just below the MXL |
|---|
| 338 | ! See the comments in the GOC section |
|---|
| 339 | ! --------------------------------------------------- |
|---|
| 340 | ! |
|---|
| 341 | IF ( gdept(ji,jj,jk-1,Kmm) <= zdep ) THEN |
|---|
| 342 | ! |
|---|
| 343 | ! Computation of the POC concentration using the |
|---|
| 344 | ! lagrangian algorithm |
|---|
| 345 | zpoc = tr(ji,jj,jk-1,jppoc,Kbb) + conspoc(ji,jj,jk) * rday / rfact2 & |
|---|
| 346 | & * e3t(ji,jj,jk,Kmm) / 2. / (wsbio3(ji,jj,jk) + rtrn) |
|---|
| 347 | zpoc = max(0., zpoc) |
|---|
| 348 | ! |
|---|
| 349 | DO jn = 1, jcpoc |
|---|
| 350 | ! computation of the lability spectrum applying the |
|---|
| 351 | ! different sources and sinks |
|---|
| 352 | alphap(ji,jj,jk,jn) = alphap(ji,jj,jk-1,jn) * exp( -reminp(jn) * zsizek ) * zpoc & |
|---|
| 353 | & + ( prodpoc(ji,jj,jk) * alphan(jn) + zorem3(ji,jj,jk) * alphag(ji,jj,jk,jn) ) & |
|---|
| 354 | & / tgfunc(ji,jj,jk) / reminp(jn) * rday / rfact2 * ( 1. - exp( -reminp(jn) & |
|---|
| 355 | & * zsizek ) ) |
|---|
| 356 | alphap(ji,jj,jk,jn) = MAX( 0., alphap(ji,jj,jk,jn) ) |
|---|
| 357 | alphat = alphat + alphap(ji,jj,jk,jn) |
|---|
| 358 | END DO |
|---|
| 359 | ELSE |
|---|
| 360 | ! |
|---|
| 361 | ! Lability parameterization for the interior of the ocean |
|---|
| 362 | ! This is very similar to what is done in the previous |
|---|
| 363 | ! block |
|---|
| 364 | ! -------------------------------------------------------- |
|---|
| 365 | ! |
|---|
| 366 | zpoc = tr(ji,jj,jk-1,jppoc,Kbb) + conspoc(ji,jj,jk-1) * rday / rfact2 & |
|---|
| 367 | & * e3t(ji,jj,jk-1,Kmm) / 2. / (wsbio3(ji,jj,jk-1) + rtrn) + conspoc(ji,jj,jk) & |
|---|
| 368 | & * rday / rfact2 * e3t(ji,jj,jk,Kmm) / 2. / (wsbio3(ji,jj,jk) + rtrn) |
|---|
| 369 | zpoc = max(0., zpoc) |
|---|
| 370 | ! |
|---|
| 371 | DO jn = 1, jcpoc |
|---|
| 372 | alphap(ji,jj,jk,jn) = alphap(ji,jj,jk-1,jn) * exp( -reminp(jn) & |
|---|
| 373 | & * ( zsizek + zsizek1 ) ) * zpoc + ( prodpoc(ji,jj,jk-1) * alphan(jn) & |
|---|
| 374 | & + zorem3(ji,jj,jk-1) * alphag(ji,jj,jk-1,jn) ) * rday / rfact2 / reminp(jn) & |
|---|
| 375 | & / tgfunc(ji,jj,jk-1) * ( 1. - exp( -reminp(jn) * zsizek1 ) ) * exp( -reminp(jn) & |
|---|
| 376 | & * zsizek ) + ( prodpoc(ji,jj,jk) * alphan(jn) + zorem3(ji,jj,jk) & |
|---|
| 377 | & * alphag(ji,jj,jk,jn) ) * rday / rfact2 / reminp(jn) / tgfunc(ji,jj,jk) * ( 1. & |
|---|
| 378 | & - exp( -reminp(jn) * zsizek ) ) |
|---|
| 379 | alphap(ji,jj,jk,jn) = max(0., alphap(ji,jj,jk,jn) ) |
|---|
| 380 | alphat = alphat + alphap(ji,jj,jk,jn) |
|---|
| 381 | END DO |
|---|
| 382 | ENDIF |
|---|
| 383 | ! Normalization of the lability spectrum so that the |
|---|
| 384 | ! integral is equal to 1 |
|---|
| 385 | DO jn = 1, jcpoc |
|---|
| 386 | alphap(ji,jj,jk,jn) = alphap(ji,jj,jk,jn) / ( alphat + rtrn) |
|---|
| 387 | remint = remint + alphap(ji,jj,jk,jn) * reminp(jn) |
|---|
| 388 | END DO |
|---|
| 389 | ! Mean remineralization rate in the water column |
|---|
| 390 | ztremint(ji,jj,jk) = MAX( 0., remint ) |
|---|
| 391 | ENDIF |
|---|
| 392 | ENDIF |
|---|
| 393 | END_3D |
|---|
| 394 | |
|---|
| 395 | IF( ln_p4z ) THEN ; zremipoc(:,:,:) = MIN( xremip , ztremint(:,:,:) ) |
|---|
| 396 | ELSE ; zremipoc(:,:,:) = MIN( xremipc, ztremint(:,:,:) ) |
|---|
| 397 | ENDIF |
|---|
| 398 | |
|---|
| 399 | IF( ln_p4z ) THEN |
|---|
| 400 | DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 1, jpkm1) |
|---|
| 401 | IF (tmask(ji,jj,jk) == 1.) THEN |
|---|
| 402 | ! POC disaggregation by turbulence and bacterial activity.It is a function |
|---|
| 403 | ! of the mean lability and of temperature |
|---|
| 404 | ! -------------------------------------------------------- |
|---|
| 405 | zremip = zremipoc(ji,jj,jk) * xstep * tgfunc(ji,jj,jk) |
|---|
| 406 | zorem = zremip * tr(ji,jj,jk,jppoc,Kbb) |
|---|
| 407 | zofer = zremip * tr(ji,jj,jk,jpsfe,Kbb) |
|---|
| 408 | |
|---|
| 409 | ! Update of the TRA arrays |
|---|
| 410 | tr(ji,jj,jk,jpdoc,Krhs) = tr(ji,jj,jk,jpdoc,Krhs) + zorem |
|---|
| 411 | orem(ji,jj,jk) = orem(ji,jj,jk) + zorem |
|---|
| 412 | tr(ji,jj,jk,jpfer,Krhs) = tr(ji,jj,jk,jpfer,Krhs) + zofer |
|---|
| 413 | tr(ji,jj,jk,jppoc,Krhs) = tr(ji,jj,jk,jppoc,Krhs) - zorem |
|---|
| 414 | tr(ji,jj,jk,jpsfe,Krhs) = tr(ji,jj,jk,jpsfe,Krhs) - zofer |
|---|
| 415 | zfolimi(ji,jj,jk) = zfolimi(ji,jj,jk) + zofer |
|---|
| 416 | ENDIF |
|---|
| 417 | END_3D |
|---|
| 418 | ELSE |
|---|
| 419 | DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 1, jpkm1) |
|---|
| 420 | ! POC disaggregation by turbulence and bacterial activity.It is a function |
|---|
| 421 | ! of the mean lability and of temperature |
|---|
| 422 | !-------------------------------------------------------- |
|---|
| 423 | zremip = zremipoc(ji,jj,jk) * xstep * tgfunc(ji,jj,jk) |
|---|
| 424 | zopoc = zremip * tr(ji,jj,jk,jppoc,Kbb) |
|---|
| 425 | orem(ji,jj,jk) = orem(ji,jj,jk) + zopoc |
|---|
| 426 | zopon = xremipn / xremipc * zremip * tr(ji,jj,jk,jppon,Kbb) |
|---|
| 427 | zopop = xremipp / xremipc * zremip * tr(ji,jj,jk,jppop,Kbb) |
|---|
| 428 | zofer = xremipn / xremipc * zremip * tr(ji,jj,jk,jpsfe,Kbb) |
|---|
| 429 | |
|---|
| 430 | ! Update of the TRA arrays |
|---|
| 431 | tr(ji,jj,jk,jppoc,Krhs) = tr(ji,jj,jk,jppoc,Krhs) - zopoc |
|---|
| 432 | tr(ji,jj,jk,jppon,Krhs) = tr(ji,jj,jk,jppon,Krhs) - zopon |
|---|
| 433 | tr(ji,jj,jk,jppop,Krhs) = tr(ji,jj,jk,jppop,Krhs) - zopop |
|---|
| 434 | tr(ji,jj,jk,jpsfe,Krhs) = tr(ji,jj,jk,jpsfe,Krhs) - zofer |
|---|
| 435 | tr(ji,jj,jk,jpdoc,Krhs) = tr(ji,jj,jk,jpdoc,Krhs) + zopoc |
|---|
| 436 | tr(ji,jj,jk,jpdon,Krhs) = tr(ji,jj,jk,jpdon,Krhs) + zopon |
|---|
| 437 | tr(ji,jj,jk,jpdop,Krhs) = tr(ji,jj,jk,jpdop,Krhs) + zopop |
|---|
| 438 | tr(ji,jj,jk,jpfer,Krhs) = tr(ji,jj,jk,jpfer,Krhs) + zofer |
|---|
| 439 | zfolimi(ji,jj,jk) = zfolimi(ji,jj,jk) + zofer |
|---|
| 440 | END_3D |
|---|
| 441 | ENDIF |
|---|
| 442 | |
|---|
| 443 | IF( lk_iomput ) THEN |
|---|
| 444 | IF( knt == nrdttrc ) THEN |
|---|
| 445 | zrfact2 = 1.e3 * rfact2r |
|---|
| 446 | CALL iom_put( "REMINP" , zremipoc(:,:,:) * tmask(:,:,:) ) ! Remineralisation rate of small particles |
|---|
| 447 | CALL iom_put( "REMING" , zremigoc(:,:,:) * tmask(:,:,:) ) ! Remineralisation rate of large particles |
|---|
| 448 | CALL iom_put( "REMINF" , zfolimi(:,:,:) * tmask(:,:,:) * 1.e+9 * zrfact2 ) ! Remineralisation of biogenic particulate iron |
|---|
| 449 | ENDIF |
|---|
| 450 | ENDIF |
|---|
| 451 | |
|---|
| 452 | IF(sn_cfctl%l_prttrc) THEN ! print mean trends (used for debugging) |
|---|
| 453 | WRITE(charout, FMT="('poc2')") |
|---|
| 454 | CALL prt_ctl_info( charout, cdcomp = 'top' ) |
|---|
| 455 | CALL prt_ctl(tab4d_1=tr(:,:,:,:,Krhs), mask1=tmask, clinfo=ctrcnm) |
|---|
| 456 | ENDIF |
|---|
| 457 | ! |
|---|
| 458 | ! |
|---|
| 459 | IF( ln_timing ) CALL timing_stop('p4z_poc') |
|---|
| 460 | ! |
|---|
| 461 | END SUBROUTINE p4z_poc |
|---|
| 462 | |
|---|
| 463 | |
|---|
| 464 | SUBROUTINE p4z_poc_init |
|---|
| 465 | !!---------------------------------------------------------------------- |
|---|
| 466 | !! *** ROUTINE p4z_poc_init *** |
|---|
| 467 | !! |
|---|
| 468 | !! ** Purpose : Initialization of remineralization parameters |
|---|
| 469 | !! |
|---|
| 470 | !! ** Method : Read the nampispoc namelist and check the parameters |
|---|
| 471 | !! called at the first timestep |
|---|
| 472 | !! |
|---|
| 473 | !! ** input : Namelist nampispoc |
|---|
| 474 | !!---------------------------------------------------------------------- |
|---|
| 475 | INTEGER :: jn ! dummy loop index |
|---|
| 476 | INTEGER :: ios, ifault ! Local integer |
|---|
| 477 | REAL(wp):: remindelta, reminup, remindown |
|---|
| 478 | !! |
|---|
| 479 | NAMELIST/nampispoc/ xremip , jcpoc , rshape, & |
|---|
| 480 | & xremipc, xremipn, xremipp |
|---|
| 481 | !!---------------------------------------------------------------------- |
|---|
| 482 | ! |
|---|
| 483 | IF(lwp) THEN |
|---|
| 484 | WRITE(numout,*) |
|---|
| 485 | WRITE(numout,*) 'p4z_poc_init : Initialization of remineralization parameters' |
|---|
| 486 | WRITE(numout,*) '~~~~~~~~~~~~' |
|---|
| 487 | ENDIF |
|---|
| 488 | ! |
|---|
| 489 | READ ( numnatp_ref, nampispoc, IOSTAT = ios, ERR = 901) |
|---|
| 490 | 901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'nampispoc in reference namelist' ) |
|---|
| 491 | READ ( numnatp_cfg, nampispoc, IOSTAT = ios, ERR = 902 ) |
|---|
| 492 | 902 IF( ios > 0 ) CALL ctl_nam ( ios , 'nampispoc in configuration namelist' ) |
|---|
| 493 | IF(lwm) WRITE( numonp, nampispoc ) |
|---|
| 494 | |
|---|
| 495 | IF(lwp) THEN ! control print |
|---|
| 496 | WRITE(numout,*) ' Namelist : nampispoc' |
|---|
| 497 | IF( ln_p4z ) THEN |
|---|
| 498 | WRITE(numout,*) ' remineralisation rate of POC xremip =', xremip |
|---|
| 499 | ELSE |
|---|
| 500 | WRITE(numout,*) ' remineralisation rate of POC xremipc =', xremipc |
|---|
| 501 | WRITE(numout,*) ' remineralisation rate of PON xremipn =', xremipn |
|---|
| 502 | WRITE(numout,*) ' remineralisation rate of POP xremipp =', xremipp |
|---|
| 503 | ENDIF |
|---|
| 504 | WRITE(numout,*) ' Number of lability classes for POC jcpoc =', jcpoc |
|---|
| 505 | WRITE(numout,*) ' Shape factor of the gamma distribution rshape =', rshape |
|---|
| 506 | ENDIF |
|---|
| 507 | ! |
|---|
| 508 | ! Discretization along the lability space |
|---|
| 509 | ! --------------------------------------- |
|---|
| 510 | ! |
|---|
| 511 | ALLOCATE( alphan(jcpoc) , reminp(jcpoc) , alphap(jpi,jpj,jpk,jcpoc) ) |
|---|
| 512 | ! |
|---|
| 513 | IF (jcpoc > 1) THEN ! Case when more than one lability class is used |
|---|
| 514 | ! |
|---|
| 515 | remindelta = LOG(4. * 1000. ) / REAL(jcpoc-1, wp) |
|---|
| 516 | reminup = 1./ 400. * EXP(remindelta) |
|---|
| 517 | ! |
|---|
| 518 | ! Discretization based on incomplete gamma functions |
|---|
| 519 | ! As incomplete gamma functions are not available in standard |
|---|
| 520 | ! fortran 95, they have been coded as functions in this module (gamain) |
|---|
| 521 | ! --------------------------------------------------------------------- |
|---|
| 522 | ! |
|---|
| 523 | alphan(1) = gamain(reminup, rshape, ifault) |
|---|
| 524 | reminp(1) = gamain(reminup, rshape+1.0, ifault) * xremip / alphan(1) |
|---|
| 525 | DO jn = 2, jcpoc-1 |
|---|
| 526 | reminup = 1./ 400. * EXP( REAL(jn, wp) * remindelta) |
|---|
| 527 | remindown = 1. / 400. * EXP( REAL(jn-1, wp) * remindelta) |
|---|
| 528 | alphan(jn) = gamain(reminup, rshape, ifault) - gamain(remindown, rshape, ifault) |
|---|
| 529 | reminp(jn) = gamain(reminup, rshape+1.0, ifault) - gamain(remindown, rshape+1.0, ifault) |
|---|
| 530 | reminp(jn) = reminp(jn) * xremip / alphan(jn) |
|---|
| 531 | END DO |
|---|
| 532 | remindown = 1. / 400. * EXP( REAL(jcpoc-1, wp) * remindelta) |
|---|
| 533 | alphan(jcpoc) = 1.0 - gamain(remindown, rshape, ifault) |
|---|
| 534 | reminp(jcpoc) = 1.0 - gamain(remindown, rshape+1.0, ifault) |
|---|
| 535 | reminp(jcpoc) = reminp(jcpoc) * xremip / alphan(jcpoc) |
|---|
| 536 | |
|---|
| 537 | ELSE ! Only one lability class is used |
|---|
| 538 | alphan(jcpoc) = 1. |
|---|
| 539 | reminp(jcpoc) = xremip |
|---|
| 540 | ENDIF |
|---|
| 541 | |
|---|
| 542 | DO jn = 1, jcpoc |
|---|
| 543 | alphap(:,:,:,jn) = alphan(jn) |
|---|
| 544 | END DO |
|---|
| 545 | |
|---|
| 546 | END SUBROUTINE p4z_poc_init |
|---|
| 547 | |
|---|
| 548 | |
|---|
| 549 | REAL FUNCTION alngam( xvalue, ifault ) |
|---|
| 550 | !*****************************************************************************80 |
|---|
| 551 | ! |
|---|
| 552 | !! ALNGAM computes the logarithm of the gamma function. |
|---|
| 553 | ! |
|---|
| 554 | ! Modified: 13 January 2008 |
|---|
| 555 | ! |
|---|
| 556 | ! Author : Allan Macleod |
|---|
| 557 | ! FORTRAN90 version by John Burkardt |
|---|
| 558 | ! |
|---|
| 559 | ! Reference: |
|---|
| 560 | ! Allan Macleod, Algorithm AS 245, |
|---|
| 561 | ! A Robust and Reliable Algorithm for the Logarithm of the Gamma Function, |
|---|
| 562 | ! Applied Statistics, |
|---|
| 563 | ! Volume 38, Number 2, 1989, pages 397-402. |
|---|
| 564 | ! |
|---|
| 565 | ! Parameters: |
|---|
| 566 | ! |
|---|
| 567 | ! Input, real ( kind = 8 ) XVALUE, the argument of the Gamma function. |
|---|
| 568 | ! |
|---|
| 569 | ! Output, integer ( kind = 4 ) IFAULT, error flag. |
|---|
| 570 | ! 0, no error occurred. |
|---|
| 571 | ! 1, XVALUE is less than or equal to 0. |
|---|
| 572 | ! 2, XVALUE is too big. |
|---|
| 573 | ! |
|---|
| 574 | ! Output, real ( kind = 8 ) ALNGAM, the logarithm of the gamma function of X. |
|---|
| 575 | !*****************************************************************************80 |
|---|
| 576 | implicit none |
|---|
| 577 | |
|---|
| 578 | real(wp), parameter :: alr2pi = 0.918938533204673E+00 |
|---|
| 579 | integer:: ifault |
|---|
| 580 | real(wp), dimension ( 9 ) :: r1 = (/ & |
|---|
| 581 | -2.66685511495E+00, & |
|---|
| 582 | -24.4387534237E+00, & |
|---|
| 583 | -21.9698958928E+00, & |
|---|
| 584 | 11.1667541262E+00, & |
|---|
| 585 | 3.13060547623E+00, & |
|---|
| 586 | 0.607771387771E+00, & |
|---|
| 587 | 11.9400905721E+00, & |
|---|
| 588 | 31.4690115749E+00, & |
|---|
| 589 | 15.2346874070E+00 /) |
|---|
| 590 | real(wp), dimension ( 9 ) :: r2 = (/ & |
|---|
| 591 | -78.3359299449E+00, & |
|---|
| 592 | -142.046296688E+00, & |
|---|
| 593 | 137.519416416E+00, & |
|---|
| 594 | 78.6994924154E+00, & |
|---|
| 595 | 4.16438922228E+00, & |
|---|
| 596 | 47.0668766060E+00, & |
|---|
| 597 | 313.399215894E+00, & |
|---|
| 598 | 263.505074721E+00, & |
|---|
| 599 | 43.3400022514E+00 /) |
|---|
| 600 | real(wp), dimension ( 9 ) :: r3 = (/ & |
|---|
| 601 | -2.12159572323E+05, & |
|---|
| 602 | 2.30661510616E+05, & |
|---|
| 603 | 2.74647644705E+04, & |
|---|
| 604 | -4.02621119975E+04, & |
|---|
| 605 | -2.29660729780E+03, & |
|---|
| 606 | -1.16328495004E+05, & |
|---|
| 607 | -1.46025937511E+05, & |
|---|
| 608 | -2.42357409629E+04, & |
|---|
| 609 | -5.70691009324E+02 /) |
|---|
| 610 | real(wp), dimension ( 5 ) :: r4 = (/ & |
|---|
| 611 | 0.279195317918525E+00, & |
|---|
| 612 | 0.4917317610505968E+00, & |
|---|
| 613 | 0.0692910599291889E+00, & |
|---|
| 614 | 3.350343815022304E+00, & |
|---|
| 615 | 6.012459259764103E+00 /) |
|---|
| 616 | real (wp) :: x |
|---|
| 617 | real (wp) :: x1 |
|---|
| 618 | real (wp) :: x2 |
|---|
| 619 | real (wp), parameter :: xlge = 5.10E+05 |
|---|
| 620 | real (wp), parameter :: xlgst = 1.0E+30 |
|---|
| 621 | real (wp) :: xvalue |
|---|
| 622 | real (wp) :: y |
|---|
| 623 | |
|---|
| 624 | x = xvalue |
|---|
| 625 | alngam = 0.0E+00 |
|---|
| 626 | ! |
|---|
| 627 | ! Check the input. |
|---|
| 628 | ! |
|---|
| 629 | if ( xlgst <= x ) then |
|---|
| 630 | ifault = 2 |
|---|
| 631 | return |
|---|
| 632 | end if |
|---|
| 633 | if ( x <= 0.0E+00 ) then |
|---|
| 634 | ifault = 1 |
|---|
| 635 | return |
|---|
| 636 | end if |
|---|
| 637 | |
|---|
| 638 | ifault = 0 |
|---|
| 639 | ! |
|---|
| 640 | ! Calculation for 0 < X < 0.5 and 0.5 <= X < 1.5 combined. |
|---|
| 641 | ! |
|---|
| 642 | if ( x < 1.5E+00 ) then |
|---|
| 643 | |
|---|
| 644 | if ( x < 0.5E+00 ) then |
|---|
| 645 | alngam = - log ( x ) |
|---|
| 646 | y = x + 1.0E+00 |
|---|
| 647 | ! |
|---|
| 648 | ! Test whether X < machine epsilon. |
|---|
| 649 | ! |
|---|
| 650 | if ( y == 1.0E+00 ) then |
|---|
| 651 | return |
|---|
| 652 | end if |
|---|
| 653 | |
|---|
| 654 | else |
|---|
| 655 | |
|---|
| 656 | alngam = 0.0E+00 |
|---|
| 657 | y = x |
|---|
| 658 | x = ( x - 0.5E+00 ) - 0.5E+00 |
|---|
| 659 | |
|---|
| 660 | end if |
|---|
| 661 | |
|---|
| 662 | alngam = alngam + x * (((( & |
|---|
| 663 | r1(5) * y & |
|---|
| 664 | + r1(4) ) * y & |
|---|
| 665 | + r1(3) ) * y & |
|---|
| 666 | + r1(2) ) * y & |
|---|
| 667 | + r1(1) ) / (((( & |
|---|
| 668 | y & |
|---|
| 669 | + r1(9) ) * y & |
|---|
| 670 | + r1(8) ) * y & |
|---|
| 671 | + r1(7) ) * y & |
|---|
| 672 | + r1(6) ) |
|---|
| 673 | |
|---|
| 674 | return |
|---|
| 675 | |
|---|
| 676 | end if |
|---|
| 677 | ! |
|---|
| 678 | ! Calculation for 1.5 <= X < 4.0. |
|---|
| 679 | ! |
|---|
| 680 | if ( x < 4.0E+00 ) then |
|---|
| 681 | |
|---|
| 682 | y = ( x - 1.0E+00 ) - 1.0E+00 |
|---|
| 683 | |
|---|
| 684 | alngam = y * (((( & |
|---|
| 685 | r2(5) * x & |
|---|
| 686 | + r2(4) ) * x & |
|---|
| 687 | + r2(3) ) * x & |
|---|
| 688 | + r2(2) ) * x & |
|---|
| 689 | + r2(1) ) / (((( & |
|---|
| 690 | x & |
|---|
| 691 | + r2(9) ) * x & |
|---|
| 692 | + r2(8) ) * x & |
|---|
| 693 | + r2(7) ) * x & |
|---|
| 694 | + r2(6) ) |
|---|
| 695 | ! |
|---|
| 696 | ! Calculation for 4.0 <= X < 12.0. |
|---|
| 697 | ! |
|---|
| 698 | else if ( x < 12.0E+00 ) then |
|---|
| 699 | |
|---|
| 700 | alngam = (((( & |
|---|
| 701 | r3(5) * x & |
|---|
| 702 | + r3(4) ) * x & |
|---|
| 703 | + r3(3) ) * x & |
|---|
| 704 | + r3(2) ) * x & |
|---|
| 705 | + r3(1) ) / (((( & |
|---|
| 706 | x & |
|---|
| 707 | + r3(9) ) * x & |
|---|
| 708 | + r3(8) ) * x & |
|---|
| 709 | + r3(7) ) * x & |
|---|
| 710 | + r3(6) ) |
|---|
| 711 | ! |
|---|
| 712 | ! Calculation for 12.0 <= X. |
|---|
| 713 | ! |
|---|
| 714 | else |
|---|
| 715 | |
|---|
| 716 | y = log ( x ) |
|---|
| 717 | alngam = x * ( y - 1.0E+00 ) - 0.5E+00 * y + alr2pi |
|---|
| 718 | |
|---|
| 719 | if ( x <= xlge ) then |
|---|
| 720 | |
|---|
| 721 | x1 = 1.0E+00 / x |
|---|
| 722 | x2 = x1 * x1 |
|---|
| 723 | |
|---|
| 724 | alngam = alngam + x1 * ( ( & |
|---|
| 725 | r4(3) * & |
|---|
| 726 | x2 + r4(2) ) * & |
|---|
| 727 | x2 + r4(1) ) / ( ( & |
|---|
| 728 | x2 + r4(5) ) * & |
|---|
| 729 | x2 + r4(4) ) |
|---|
| 730 | |
|---|
| 731 | end if |
|---|
| 732 | |
|---|
| 733 | end if |
|---|
| 734 | |
|---|
| 735 | END FUNCTION alngam |
|---|
| 736 | |
|---|
| 737 | |
|---|
| 738 | REAL FUNCTION gamain( x, p, ifault ) |
|---|
| 739 | !*****************************************************************************80 |
|---|
| 740 | ! |
|---|
| 741 | !! GAMAIN computes the incomplete gamma ratio. |
|---|
| 742 | ! |
|---|
| 743 | ! Discussion: |
|---|
| 744 | ! |
|---|
| 745 | ! A series expansion is used if P > X or X <= 1. Otherwise, a |
|---|
| 746 | ! continued fraction approximation is used. |
|---|
| 747 | ! |
|---|
| 748 | ! Modified: |
|---|
| 749 | ! |
|---|
| 750 | ! 17 January 2008 |
|---|
| 751 | ! |
|---|
| 752 | ! Author: |
|---|
| 753 | ! |
|---|
| 754 | ! G Bhattacharjee |
|---|
| 755 | ! FORTRAN90 version by John Burkardt |
|---|
| 756 | ! |
|---|
| 757 | ! Reference: |
|---|
| 758 | ! |
|---|
| 759 | ! G Bhattacharjee, |
|---|
| 760 | ! Algorithm AS 32: |
|---|
| 761 | ! The Incomplete Gamma Integral, |
|---|
| 762 | ! Applied Statistics, |
|---|
| 763 | ! Volume 19, Number 3, 1970, pages 285-287. |
|---|
| 764 | ! |
|---|
| 765 | ! Parameters: |
|---|
| 766 | ! |
|---|
| 767 | ! Input, real ( kind = 8 ) X, P, the parameters of the incomplete |
|---|
| 768 | ! gamma ratio. 0 <= X, and 0 < P. |
|---|
| 769 | ! |
|---|
| 770 | ! Output, integer ( kind = 4 ) IFAULT, error flag. |
|---|
| 771 | ! 0, no errors. |
|---|
| 772 | ! 1, P <= 0. |
|---|
| 773 | ! 2, X < 0. |
|---|
| 774 | ! 3, underflow. |
|---|
| 775 | ! 4, error return from the Log Gamma routine. |
|---|
| 776 | ! |
|---|
| 777 | ! Output, real ( kind = 8 ) GAMAIN, the value of the incomplete |
|---|
| 778 | ! gamma ratio. |
|---|
| 779 | ! |
|---|
| 780 | implicit none |
|---|
| 781 | |
|---|
| 782 | real (wp) a |
|---|
| 783 | real (wp), parameter :: acu = 1.0E-08 |
|---|
| 784 | real (wp) an |
|---|
| 785 | real (wp) arg |
|---|
| 786 | real (wp) b |
|---|
| 787 | real (wp) dif |
|---|
| 788 | real (wp) factor |
|---|
| 789 | real (wp) g |
|---|
| 790 | real (wp) gin |
|---|
| 791 | integer i |
|---|
| 792 | integer ifault |
|---|
| 793 | real (wp), parameter :: oflo = 1.0E+37 |
|---|
| 794 | real (wp) p |
|---|
| 795 | real (wp) pn(6) |
|---|
| 796 | real (wp) rn |
|---|
| 797 | real (wp) term |
|---|
| 798 | real (wp), parameter :: uflo = 1.0E-37 |
|---|
| 799 | real (wp) x |
|---|
| 800 | ! |
|---|
| 801 | ! Check the input. |
|---|
| 802 | ! |
|---|
| 803 | if ( p <= 0.0E+00 ) then |
|---|
| 804 | ifault = 1 |
|---|
| 805 | gamain = 0.0E+00 |
|---|
| 806 | return |
|---|
| 807 | end if |
|---|
| 808 | |
|---|
| 809 | if ( x < 0.0E+00 ) then |
|---|
| 810 | ifault = 2 |
|---|
| 811 | gamain = 0.0E+00 |
|---|
| 812 | return |
|---|
| 813 | end if |
|---|
| 814 | |
|---|
| 815 | if ( x == 0.0E+00 ) then |
|---|
| 816 | ifault = 0 |
|---|
| 817 | gamain = 0.0E+00 |
|---|
| 818 | return |
|---|
| 819 | end if |
|---|
| 820 | |
|---|
| 821 | g = alngam ( p, ifault ) |
|---|
| 822 | |
|---|
| 823 | if ( ifault /= 0 ) then |
|---|
| 824 | ifault = 4 |
|---|
| 825 | gamain = 0.0E+00 |
|---|
| 826 | return |
|---|
| 827 | end if |
|---|
| 828 | |
|---|
| 829 | arg = p * log ( x ) - x - g |
|---|
| 830 | |
|---|
| 831 | if ( arg < log ( uflo ) ) then |
|---|
| 832 | ifault = 3 |
|---|
| 833 | gamain = 0.0E+00 |
|---|
| 834 | return |
|---|
| 835 | end if |
|---|
| 836 | |
|---|
| 837 | ifault = 0 |
|---|
| 838 | factor = exp ( arg ) |
|---|
| 839 | ! |
|---|
| 840 | ! Calculation by series expansion. |
|---|
| 841 | ! |
|---|
| 842 | if ( x <= 1.0E+00 .or. x < p ) then |
|---|
| 843 | |
|---|
| 844 | gin = 1.0E+00 |
|---|
| 845 | term = 1.0E+00 |
|---|
| 846 | rn = p |
|---|
| 847 | |
|---|
| 848 | do |
|---|
| 849 | |
|---|
| 850 | rn = rn + 1.0E+00 |
|---|
| 851 | term = term * x / rn |
|---|
| 852 | gin = gin + term |
|---|
| 853 | |
|---|
| 854 | if ( term <= acu ) then |
|---|
| 855 | exit |
|---|
| 856 | end if |
|---|
| 857 | |
|---|
| 858 | end do |
|---|
| 859 | |
|---|
| 860 | gamain = gin * factor / p |
|---|
| 861 | return |
|---|
| 862 | |
|---|
| 863 | end if |
|---|
| 864 | ! |
|---|
| 865 | ! Calculation by continued fraction. |
|---|
| 866 | ! |
|---|
| 867 | a = 1.0E+00 - p |
|---|
| 868 | b = a + x + 1.0E+00 |
|---|
| 869 | term = 0.0E+00 |
|---|
| 870 | |
|---|
| 871 | pn(1) = 1.0E+00 |
|---|
| 872 | pn(2) = x |
|---|
| 873 | pn(3) = x + 1.0E+00 |
|---|
| 874 | pn(4) = x * b |
|---|
| 875 | |
|---|
| 876 | gin = pn(3) / pn(4) |
|---|
| 877 | |
|---|
| 878 | do |
|---|
| 879 | |
|---|
| 880 | a = a + 1.0E+00 |
|---|
| 881 | b = b + 2.0E+00 |
|---|
| 882 | term = term + 1.0E+00 |
|---|
| 883 | an = a * term |
|---|
| 884 | do i = 1, 2 |
|---|
| 885 | pn(i+4) = b * pn(i+2) - an * pn(i) |
|---|
| 886 | end do |
|---|
| 887 | |
|---|
| 888 | if ( pn(6) /= 0.0E+00 ) then |
|---|
| 889 | |
|---|
| 890 | rn = pn(5) / pn(6) |
|---|
| 891 | dif = abs ( gin - rn ) |
|---|
| 892 | ! |
|---|
| 893 | ! Absolute error tolerance satisfied? |
|---|
| 894 | ! |
|---|
| 895 | if ( dif <= acu ) then |
|---|
| 896 | ! |
|---|
| 897 | ! Relative error tolerance satisfied? |
|---|
| 898 | ! |
|---|
| 899 | if ( dif <= acu * rn ) then |
|---|
| 900 | gamain = 1.0E+00 - factor * gin |
|---|
| 901 | exit |
|---|
| 902 | end if |
|---|
| 903 | |
|---|
| 904 | end if |
|---|
| 905 | |
|---|
| 906 | gin = rn |
|---|
| 907 | |
|---|
| 908 | end if |
|---|
| 909 | |
|---|
| 910 | do i = 1, 4 |
|---|
| 911 | pn(i) = pn(i+2) |
|---|
| 912 | end do |
|---|
| 913 | if ( oflo <= abs ( pn(5) ) ) then |
|---|
| 914 | |
|---|
| 915 | do i = 1, 4 |
|---|
| 916 | pn(i) = pn(i) / oflo |
|---|
| 917 | end do |
|---|
| 918 | |
|---|
| 919 | end if |
|---|
| 920 | |
|---|
| 921 | end do |
|---|
| 922 | |
|---|
| 923 | END FUNCTION gamain |
|---|
| 924 | |
|---|
| 925 | !!====================================================================== |
|---|
| 926 | END MODULE p4zpoc |
|---|
