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