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module leapfrog_m |
module leapfrog_m |
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! This module is clean: no C preprocessor directive, no include line. |
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IMPLICIT NONE |
IMPLICIT NONE |
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contains |
contains |
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SUBROUTINE leapfrog(ucov, vcov, teta, ps, masse, phis, q, time_0) |
SUBROUTINE leapfrog(ucov, vcov, teta, ps, masse, phis, q) |
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! From dyn3d/leapfrog.F, version 1.6 2005/04/13 08:58:34 |
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! Version du 10/01/98, avec coordonnees verticales hybrides, avec |
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! nouveaux operat. dissipation * (gradiv2, divgrad2, nxgraro2) |
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! Auteur: P. Le Van /L. Fairhead/F.Hourdin |
! From dyn3d/leapfrog.F, version 1.6, 2005/04/13 08:58:34 revision 616 |
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! Objet: |
! Authors: P. Le Van, L. Fairhead, F. Hourdin |
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! GCM LMD nouvelle grille |
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! ... Dans inigeom, nouveaux calculs pour les elongations cu, cv |
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! et possibilite d'appeler une fonction f(y) a derivee tangente |
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! hyperbolique a la place de la fonction a derivee sinusoidale. |
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! ... Possibilité de choisir le schéma pour l'advection de |
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! q, en modifiant iadv dans "traceur.def" (10/02) . |
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! Pour Van-Leer + Vapeur d'eau saturee, iadv(1)=4. (F.Codron, 10/99) |
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! Pour Van-Leer iadv=10 |
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use dimens_m, only: iim, llm, nqmx |
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use paramet_m, only: ip1jmp1, ip1jm, ijmllm, ijp1llm, jjp1, iip1 |
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use comconst, only: dtvr, daysec, dtphys |
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use comvert, only: ap, bp |
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use conf_gcm_m, only: day_step, iconser, idissip, iphysiq, iperiod, nday, & |
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offline, periodav |
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use logic, only: ok_guide, iflag_phys |
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use comgeom |
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use serre |
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use temps, only: itaufin, day_ini, dt |
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use iniprint, only: prt_level |
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use com_io_dyn |
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use ener |
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use calfis_m, only: calfis |
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use exner_hyb_m, only: exner_hyb |
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use guide_m, only: guide |
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use pression_m, only: pression |
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use pressure_var, only: p3d |
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! Variables dynamiques: |
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REAL vcov(ip1jm, llm), ucov(ip1jmp1, llm) ! vents covariants |
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REAL teta(ip1jmp1, llm) ! temperature potentielle |
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REAL q(ip1jmp1, llm, nqmx) ! mass fractions of advected fields |
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REAL ps(ip1jmp1) ! pression au sol, en Pa |
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REAL masse(ip1jmp1, llm) ! masse d'air |
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REAL phis(ip1jmp1) ! geopotentiel au sol |
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REAL time_0 |
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! Variables local to the procedure: |
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! Variables dynamiques: |
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REAL pks(ip1jmp1) ! exner au sol |
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REAL pk(ip1jmp1, llm) ! exner au milieu des couches |
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REAL pkf(ip1jmp1, llm) ! exner filt.au milieu des couches |
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REAL phi(ip1jmp1, llm) ! geopotential |
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REAL w(ip1jmp1, llm) ! vitesse verticale |
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! variables dynamiques intermediaire pour le transport |
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REAL pbaru(ip1jmp1, llm), pbarv(ip1jm, llm) !flux de masse |
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! variables dynamiques au pas - 1 |
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REAL vcovm1(ip1jm, llm), ucovm1(ip1jmp1, llm) |
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REAL tetam1(ip1jmp1, llm), psm1(ip1jmp1) |
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REAL massem1(ip1jmp1, llm) |
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! tendances dynamiques |
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REAL dv(ip1jm, llm), du(ip1jmp1, llm) |
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REAL dteta(ip1jmp1, llm), dq(ip1jmp1, llm, nqmx), dp(ip1jmp1) |
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! tendances de la dissipation |
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REAL dvdis(ip1jm, llm), dudis(ip1jmp1, llm) |
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REAL dtetadis(ip1jmp1, llm) |
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! tendances physiques |
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REAL dvfi(ip1jm, llm), dufi(ip1jmp1, llm) |
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REAL dtetafi(ip1jmp1, llm), dqfi(ip1jmp1, llm, nqmx), dpfi(ip1jmp1) |
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! variables pour le fichier histoire |
! Int\'egration temporelle du mod\`ele : Matsuno-leapfrog scheme. |
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REAL tppn(iim), tpps(iim), tpn, tps |
use addfi_m, only: addfi |
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use bilan_dyn_m, only: bilan_dyn |
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use caladvtrac_m, only: caladvtrac |
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use caldyn_m, only: caldyn |
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USE calfis_m, ONLY: calfis |
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USE comconst, ONLY: dtvr |
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USE comgeom, ONLY: aire_2d, apoln, apols |
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use covcont_m, only: covcont |
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USE disvert_m, ONLY: ap, bp |
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USE conf_gcm_m, ONLY: day_step, iconser, iperiod, iphysiq, nday, iflag_phys |
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USE conf_guide_m, ONLY: ok_guide |
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USE dimensions, ONLY: iim, jjm, llm, nqmx |
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use dissip_m, only: dissip |
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USE dynetat0_m, ONLY: day_ini, itau_dyn |
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use dynredem1_m, only: dynredem1 |
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use enercin_m, only: enercin |
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USE exner_hyb_m, ONLY: exner_hyb |
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use filtreg_scal_m, only: filtreg_scal |
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use geopot_m, only: geopot |
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USE guide_m, ONLY: guide |
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use inidissip_m, only: idissip |
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use integrd_m, only: integrd |
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use nr_util, only: assert |
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use writehist_m, only: writehist |
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REAL, intent(inout):: ucov(:, :, :) ! (iim + 1, jjm + 1, llm) vent covariant |
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REAL, intent(inout):: vcov(:, :, :) ! (iim + 1, jjm, llm) ! vent covariant |
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REAL, intent(inout):: teta(:, :, :) ! (iim + 1, jjm + 1, llm) |
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! potential temperature |
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REAL, intent(inout):: ps(:, :) ! (iim + 1, jjm + 1) pression au sol, en Pa |
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REAL, intent(inout):: masse(:, :, :) ! (iim + 1, jjm + 1, llm) masse d'air |
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REAL, intent(in):: phis(:, :) ! (iim + 1, jjm + 1) surface geopotential |
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REAL, intent(inout):: q(:, :, :, :) ! (iim + 1, jjm + 1, llm, nqmx) |
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! mass fractions of advected fields |
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! Local: |
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REAL pks(iim + 1, jjm + 1) ! exner au sol |
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REAL pk(iim + 1, jjm + 1, llm) ! exner au milieu des couches |
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REAL pkf(iim + 1, jjm + 1, llm) ! exner filtr\'e au milieu des couches |
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REAL phi(iim + 1, jjm + 1, llm) ! geopotential |
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REAL w(iim + 1, jjm + 1, llm) ! vitesse verticale |
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! Variables dynamiques interm\'ediaires pour le transport |
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! Flux de masse : |
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REAL pbaru(iim + 1, jjm + 1, llm), pbarv(iim + 1, jjm, llm) |
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! Variables dynamiques au pas - 1 |
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REAL vcovm1(iim + 1, jjm, llm), ucovm1(iim + 1, jjm + 1, llm) |
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REAL tetam1(iim + 1, jjm + 1, llm), psm1(iim + 1, jjm + 1) |
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REAL massem1(iim + 1, jjm + 1, llm) |
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! Tendances dynamiques |
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REAL dv((iim + 1) * jjm, llm), du(iim + 1, jjm + 1, llm) |
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REAL dteta(iim + 1, jjm + 1, llm) |
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real dp(iim + 1, jjm + 1) |
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! Tendances de la dissipation : |
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REAL dvdis(iim + 1, jjm, llm), dudis(iim + 1, jjm + 1, llm) |
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REAL dtetadis(iim + 1, jjm + 1, llm) |
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! Tendances physiques |
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REAL dvfi(iim + 1, jjm, llm), dufi(iim + 1, jjm + 1, llm) |
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REAL dtetafi(iim + 1, jjm + 1, llm), dqfi(iim + 1, jjm + 1, llm, nqmx) |
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! Variables pour le fichier histoire |
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INTEGER itau ! index of the time step of the dynamics, starts at 0 |
INTEGER itau ! index of the time step of the dynamics, starts at 0 |
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integer itaufinp1 |
INTEGER itaufin |
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INTEGER iday ! jour julien |
INTEGER l |
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REAL time ! time of day, as a fraction of day length |
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REAL SSUM |
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real finvmaold(ip1jmp1, llm) |
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LOGICAL :: lafin=.false. |
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INTEGER ij, l |
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REAL rdayvrai, rdaym_ini |
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!+jld variables test conservation energie |
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REAL ecin(ip1jmp1, llm), ecin0(ip1jmp1, llm) |
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! Tendance de la temp. potentiel d (theta) / d t due a la |
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! tansformation d'energie cinetique en energie thermique |
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! cree par la dissipation |
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REAL dtetaecdt(ip1jmp1, llm) |
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REAL vcont(ip1jm, llm), ucont(ip1jmp1, llm) |
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CHARACTER*15 ztit |
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INTEGER:: ip_ebil_dyn = 0 ! PRINT level for energy conserv. diag. |
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logical:: dissip_conservative = .true. |
! Variables test conservation \'energie |
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logical forward, leapf, apphys, conser, apdiss |
REAL ecin(iim + 1, jjm + 1, llm), ecin0(iim + 1, jjm + 1, llm) |
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REAL vcont((iim + 1) * jjm, llm), ucont((iim + 1) * (jjm + 1), llm) |
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logical leapf |
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real dt ! time step, in s |
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REAL p3d(iim + 1, jjm + 1, llm + 1) ! pressure at layer interfaces, in Pa |
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! ("p3d(i, j, l)" is at longitude "rlonv(i)", latitude "rlatu(j)", |
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! for interface "l") |
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!--------------------------------------------------- |
!--------------------------------------------------- |
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print *, "Call sequence information: leapfrog" |
print *, "Call sequence information: leapfrog" |
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call assert(shape(ucov) == (/iim + 1, jjm + 1, llm/), "leapfrog") |
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itaufin = nday * day_step |
itaufin = nday * day_step |
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itaufinp1 = itaufin + 1 |
! "day_step" is a multiple of "iperiod", therefore so is "itaufin". |
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itau = 0 |
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iday = day_ini |
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time = time_0 |
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IF (time > 1.) THEN |
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time = time - 1. |
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iday = iday + 1 |
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ENDIF |
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! On initialise la pression et la fonction d'Exner : |
! On initialise la pression et la fonction d'Exner : |
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dq=0. |
forall (l = 1: llm + 1) p3d(:, :, l) = ap(l) + bp(l) * ps |
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CALL pression(ip1jmp1, ap, bp, ps, p3d) |
CALL exner_hyb(ps, p3d, pks, pk) |
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CALL exner_hyb(ps, p3d, pks, pk, pkf) |
pkf = pk |
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CALL filtreg_scal(pkf, direct = .true., intensive = .true.) |
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! Debut de l'integration temporelle: |
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outer_loop:do |
time_integration: do itau = 0, itaufin - 1 |
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if (ok_guide.and.(itaufin - itau - 1) * dtvr > 21600) then |
leapf = mod(itau, iperiod) /= 0 |
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call guide(itau, ucov, vcov, teta, q, masse, ps) |
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if (leapf) then |
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dt = 2 * dtvr |
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else |
else |
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IF (prt_level > 9) print *, & |
! Matsuno |
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'Attention : on ne guide pas les 6 dernieres heures.' |
dt = dtvr |
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endif |
if (ok_guide) call guide(itau, ucov, vcov, teta, q(:, :, :, 1), ps) |
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vcovm1 = vcov |
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CALL SCOPY(ijmllm, vcov, 1, vcovm1, 1) |
ucovm1 = ucov |
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CALL SCOPY(ijp1llm, ucov, 1, ucovm1, 1) |
tetam1 = teta |
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CALL SCOPY(ijp1llm, teta, 1, tetam1, 1) |
massem1 = masse |
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CALL SCOPY(ijp1llm, masse, 1, massem1, 1) |
psm1 = ps |
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CALL SCOPY(ip1jmp1, ps, 1, psm1, 1) |
end if |
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forward = .TRUE. |
! Calcul des tendances dynamiques: |
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leapf = .FALSE. |
CALL geopot(teta, pk, pks, phis, phi) |
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dt = dtvr |
CALL caldyn(itau, ucov, vcov, teta, ps, masse, pk, pkf, phis, phi, du, & |
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dv, dteta, dp, w, pbaru, pbarv, conser = MOD(itau, iconser) == 0) |
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CALL SCOPY(ijp1llm, masse, 1, finvmaold, 1) |
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CALL filtreg(finvmaold, jjp1, llm, - 2, 2, .TRUE., 1) |
CALL caladvtrac(q, pbaru, pbarv, p3d, masse, teta, pk) |
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do |
! Int\'egrations dynamique et traceurs: |
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! gestion des appels de la physique et des dissipations: |
CALL integrd(vcovm1, ucovm1, tetam1, psm1, massem1, dv, du, dteta, dp, & |
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vcov, ucov, teta, q(:, :, :, :2), ps, masse, dt, leapf) |
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apphys = .FALSE. |
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conser = .FALSE. |
forall (l = 1: llm + 1) p3d(:, :, l) = ap(l) + bp(l) * ps |
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apdiss = .FALSE. |
CALL exner_hyb(ps, p3d, pks, pk) |
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pkf = pk |
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IF (MOD(itau, iconser) == 0) conser = .TRUE. |
CALL filtreg_scal(pkf, direct = .true., intensive = .true.) |
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IF (MOD(itau + 1, idissip) == 0) apdiss = .TRUE. |
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IF (MOD(itau + 1, iphysiq) == 0 .AND. iflag_phys /= 0) apphys=.TRUE. |
if (.not. leapf) then |
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! Matsuno backward |
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! calcul des tendances dynamiques: |
! Calcul des tendances dynamiques: |
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CALL geopot(teta, pk, pks, phis, phi) |
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CALL geopot(ip1jmp1, teta, pk, pks, phis, phi) |
CALL caldyn(itau + 1, ucov, vcov, teta, ps, masse, pk, pkf, phis, & |
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phi, du, dv, dteta, dp, w, pbaru, pbarv, conser = .false.) |
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CALL caldyn(itau, ucov, vcov, teta, ps, masse, pk, pkf, phis, phi, & |
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conser, du, dv, dteta, dp, w, pbaru, pbarv, & |
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time + iday - day_ini) |
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! calcul des tendances advection des traceurs (dont l'humidite) |
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IF (forward .OR. leapf) THEN |
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CALL caladvtrac(q, pbaru, pbarv, p3d, masse, dq, teta, pk) |
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IF (offline) THEN |
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!maf stokage du flux de masse pour traceurs OFF-LINE |
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CALL fluxstokenc(pbaru, pbarv, masse, teta, phi, phis, dtvr, & |
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itau) |
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ENDIF |
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ENDIF |
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! integrations dynamique et traceurs: |
! integrations dynamique et traceurs: |
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CALL integrd(2, vcovm1, ucovm1, tetam1, psm1, massem1, dv, du, & |
CALL integrd(vcovm1, ucovm1, tetam1, psm1, massem1, dv, du, dteta, & |
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dteta, dq, dp, vcov, ucov, teta, q, ps, masse, phis, & |
dp, vcov, ucov, teta, q(:, :, :, :2), ps, masse, dtvr, & |
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finvmaold, leapf) |
leapf=.false.) |
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! calcul des tendances physiques: |
forall (l = 1: llm + 1) p3d(:, :, l) = ap(l) + bp(l) * ps |
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CALL exner_hyb(ps, p3d, pks, pk) |
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IF (apphys) THEN |
pkf = pk |
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IF (itau + 1 == itaufin) lafin = .TRUE. |
CALL filtreg_scal(pkf, direct = .true., intensive = .true.) |
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end if |
| 161 |
CALL pression(ip1jmp1, ap, bp, ps, p3d) |
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CALL exner_hyb(ps, p3d, pks, pk, pkf) |
IF (MOD(itau + 1, iphysiq) == 0 .AND. iflag_phys) THEN |
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CALL calfis(ucov, vcov, teta, q, p3d, pk, phis, phi, w, dufi, dvfi, & |
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rdaym_ini = itau * dtvr / daysec |
dtetafi, dqfi, dayvrai = itau / day_step + day_ini, & |
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rdayvrai = rdaym_ini + day_ini |
time = REAL(mod(itau, day_step)) / day_step, & |
| 166 |
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lafin = itau + 1 == itaufin) |
| 167 |
! Interface avec les routines de phylmd (phymars ...) |
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CALL addfi(ucov, vcov, teta, q, dufi, dvfi, dtetafi, dqfi) |
| 169 |
! Diagnostique de conservation de l'énergie : initialisation |
ENDIF |
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IF (ip_ebil_dyn >= 1) THEN |
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ztit='bil dyn' |
IF (MOD(itau + 1, idissip) == 0) THEN |
| 172 |
CALL diagedyn(ztit, 2, 1, 1, dtphys, ucov, vcov, ps, p3d, pk, & |
! Dissipation horizontale et verticale des petites \'echelles |
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teta, q(:, :, 1), q(:, :, 2)) |
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ENDIF |
! calcul de l'\'energie cin\'etique avant dissipation |
| 175 |
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call covcont(llm, ucov, vcov, ucont, vcont) |
| 176 |
CALL calfis(nqmx, lafin, rdayvrai, time, ucov, vcov, teta, q, & |
call enercin(vcov, ucov, vcont, ucont, ecin0) |
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masse, ps, pk, phis, phi, du, dv, dteta, dq, w, & |
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dufi, dvfi, dtetafi, dqfi, dpfi) |
! dissipation |
| 179 |
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CALL dissip(vcov, ucov, teta, p3d, dvdis, dudis, dtetadis) |
| 180 |
! ajout des tendances physiques: |
ucov = ucov + dudis |
| 181 |
CALL addfi(nqmx, dtphys, & |
vcov = vcov + dvdis |
| 182 |
ucov, vcov, teta, q, ps, & |
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| 183 |
dufi, dvfi, dtetafi, dqfi, dpfi) |
! On ajoute la tendance due \`a la transformation \'energie |
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! cin\'etique en \'energie thermique par la dissipation |
| 185 |
! Diagnostique de conservation de l'énergie : difference |
call covcont(llm, ucov, vcov, ucont, vcont) |
| 186 |
IF (ip_ebil_dyn >= 1) THEN |
call enercin(vcov, ucov, vcont, ucont, ecin) |
| 187 |
ztit = 'bil phys' |
dtetadis = dtetadis + (ecin0 - ecin) / pk |
| 188 |
CALL diagedyn(ztit, 2, 1, 1, dtphys, ucov, vcov, ps, p3d, pk, & |
teta = teta + dtetadis |
| 189 |
teta, q(:, :, 1), q(:, :, 2)) |
|
| 190 |
ENDIF |
! Calcul de la valeur moyenne aux p\^oles : |
| 191 |
ENDIF |
forall (l = 1: llm) |
| 192 |
|
teta(:, 1, l) = SUM(aire_2d(:iim, 1) * teta(:iim, 1, l)) / apoln |
| 193 |
CALL pression(ip1jmp1, ap, bp, ps, p3d) |
teta(:, jjm + 1, l) = SUM(aire_2d(:iim, jjm + 1) & |
| 194 |
CALL exner_hyb(ps, p3d, pks, pk, pkf) |
* teta(:iim, jjm + 1, l)) / apols |
| 195 |
|
END forall |
| 196 |
! dissipation horizontale et verticale des petites echelles: |
END IF |
| 197 |
|
|
| 198 |
IF (apdiss) THEN |
IF (MOD(itau + 1, iperiod) == 0) THEN |
| 199 |
! calcul de l'energie cinetique avant dissipation |
call bilan_dyn(ps, masse, pk, pbaru, pbarv, teta, phi, ucov, vcov, & |
| 200 |
call covcont(llm, ucov, vcov, ucont, vcont) |
q(:, :, :, 1)) |
| 201 |
call enercin(vcov, ucov, vcont, ucont, ecin0) |
ENDIF |
| 202 |
|
|
| 203 |
! dissipation |
CALL geopot(teta, pk, pks, phis, phi) |
| 204 |
CALL dissip(vcov, ucov, teta, p3d, dvdis, dudis, dtetadis) |
CALL writehist(vcov, ucov, teta, pk, phi, q, masse, ps, & |
| 205 |
ucov=ucov + dudis |
itau_w = itau_dyn + itau + 1) |
| 206 |
vcov=vcov + dvdis |
end do time_integration |
| 207 |
|
|
| 208 |
if (dissip_conservative) then |
CALL dynredem1(vcov, ucov, teta, q, masse, ps, itau = itau_dyn + itaufin) |
| 209 |
! On rajoute la tendance due a la transform. Ec -> E |
|
| 210 |
! therm. cree lors de la dissipation |
! Calcul des tendances dynamiques: |
| 211 |
call covcont(llm, ucov, vcov, ucont, vcont) |
CALL geopot(teta, pk, pks, phis, phi) |
| 212 |
call enercin(vcov, ucov, vcont, ucont, ecin) |
CALL caldyn(itaufin, ucov, vcov, teta, ps, masse, pk, pkf, phis, phi, du, & |
| 213 |
dtetaecdt= (ecin0 - ecin) / pk |
dv, dteta, dp, w, pbaru, pbarv, conser = MOD(itaufin, iconser) == 0) |
|
dtetadis=dtetadis + dtetaecdt |
|
|
endif |
|
|
teta=teta + dtetadis |
|
|
|
|
|
! Calcul de la valeur moyenne, unique de h aux poles ..... |
|
|
|
|
|
DO l = 1, llm |
|
|
DO ij = 1, iim |
|
|
tppn(ij) = aire(ij) * teta(ij, l) |
|
|
tpps(ij) = aire(ij + ip1jm) * teta(ij + ip1jm, l) |
|
|
ENDDO |
|
|
tpn = SSUM(iim, tppn, 1) / apoln |
|
|
tps = SSUM(iim, tpps, 1) / apols |
|
|
|
|
|
DO ij = 1, iip1 |
|
|
teta(ij, l) = tpn |
|
|
teta(ij + ip1jm, l) = tps |
|
|
ENDDO |
|
|
ENDDO |
|
|
|
|
|
DO ij = 1, iim |
|
|
tppn(ij) = aire(ij) * ps(ij) |
|
|
tpps(ij) = aire(ij + ip1jm) * ps(ij + ip1jm) |
|
|
ENDDO |
|
|
tpn = SSUM(iim, tppn, 1) / apoln |
|
|
tps = SSUM(iim, tpps, 1) / apols |
|
|
|
|
|
DO ij = 1, iip1 |
|
|
ps(ij) = tpn |
|
|
ps(ij + ip1jm) = tps |
|
|
ENDDO |
|
|
|
|
|
END IF |
|
|
|
|
|
! fin de l'intégration dynamique et physique pour le pas "itau" |
|
|
! préparation du pas d'intégration suivant |
|
|
|
|
|
! schema matsuno + leapfrog |
|
|
IF (forward .OR. leapf) THEN |
|
|
itau = itau + 1 |
|
|
iday = day_ini + itau / day_step |
|
|
time = REAL(itau - (iday - day_ini) * day_step) / day_step & |
|
|
+ time_0 |
|
|
IF (time > 1.) THEN |
|
|
time = time - 1. |
|
|
iday = iday + 1 |
|
|
ENDIF |
|
|
ENDIF |
|
|
|
|
|
IF (itau == itaufinp1) exit outer_loop |
|
|
|
|
|
! ecriture du fichier histoire moyenne: |
|
|
|
|
|
! Comment out the following calls when you do not want the output |
|
|
! files "dyn_hist_ave.nc" and "dynzon.nc" |
|
|
IF (MOD(itau, iperiod) == 0 .OR. itau == itaufin) THEN |
|
|
CALL writedynav(histaveid, nqmx, itau, vcov, & |
|
|
ucov, teta, pk, phi, q, masse, ps, phis) |
|
|
call bilan_dyn(2, dtvr * iperiod, dtvr * day_step * periodav, & |
|
|
ps, masse, pk, pbaru, pbarv, teta, phi, ucov, vcov, q) |
|
|
ENDIF |
|
|
|
|
|
IF (itau == itaufin) THEN |
|
|
CALL dynredem1("restart.nc", vcov, ucov, teta, q, masse, ps) |
|
|
CLOSE(99) |
|
|
ENDIF |
|
|
|
|
|
! gestion de l'integration temporelle: |
|
|
|
|
|
IF (MOD(itau, iperiod) == 0) exit |
|
|
IF (MOD(itau - 1, iperiod) == 0) THEN |
|
|
IF (forward) THEN |
|
|
! fin du pas forward et debut du pas backward |
|
|
forward = .FALSE. |
|
|
leapf = .FALSE. |
|
|
ELSE |
|
|
! fin du pas backward et debut du premier pas leapfrog |
|
|
leapf = .TRUE. |
|
|
dt = 2. * dtvr |
|
|
END IF |
|
|
ELSE |
|
|
! pas leapfrog |
|
|
leapf = .TRUE. |
|
|
dt = 2. * dtvr |
|
|
END IF |
|
|
end do |
|
|
end do outer_loop |
|
| 214 |
|
|
| 215 |
END SUBROUTINE leapfrog |
END SUBROUTINE leapfrog |
| 216 |
|
|
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