6 |
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7 |
SUBROUTINE leapfrog(ucov, vcov, teta, ps, masse, phis, q, time_0) |
SUBROUTINE leapfrog(ucov, vcov, teta, ps, masse, phis, q, time_0) |
8 |
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9 |
! From dyn3d/leapfrog.F, version 1.6 2005/04/13 08:58:34 |
! From dyn3d/leapfrog.F, version 1.6, 2005/04/13 08:58:34 |
10 |
! Auteurs: P. Le Van, L. Fairhead, F. Hourdin |
! Authors: P. Le Van, L. Fairhead, F. Hourdin |
11 |
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! Matsuno-leapfrog scheme. |
12 |
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13 |
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use addfi_m, only: addfi |
14 |
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use bilan_dyn_m, only: bilan_dyn |
15 |
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use caladvtrac_m, only: caladvtrac |
16 |
USE calfis_m, ONLY: calfis |
USE calfis_m, ONLY: calfis |
17 |
USE com_io_dyn, ONLY: histaveid |
USE com_io_dyn, ONLY: histaveid |
18 |
USE comconst, ONLY: daysec, dtphys, dtvr |
USE comconst, ONLY: daysec, dtphys, dtvr |
19 |
USE comgeom, ONLY: aire, apoln, apols |
USE comgeom, ONLY: aire_2d, apoln, apols |
20 |
USE comvert, ONLY: ap, bp |
USE comvert, ONLY: ap, bp |
21 |
USE conf_gcm_m, ONLY: day_step, iconser, iperiod, iphysiq, & |
USE conf_gcm_m, ONLY: day_step, iconser, iperiod, iphysiq, nday, offline, & |
22 |
nday, offline, periodav |
periodav |
23 |
USE dimens_m, ONLY: iim, llm, nqmx |
USE dimens_m, ONLY: iim, jjm, llm, nqmx |
24 |
USE dynetat0_m, ONLY: day_ini |
USE dynetat0_m, ONLY: day_ini |
25 |
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use dynredem1_m, only: dynredem1 |
26 |
USE exner_hyb_m, ONLY: exner_hyb |
USE exner_hyb_m, ONLY: exner_hyb |
27 |
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use filtreg_m, only: filtreg |
28 |
USE guide_m, ONLY: guide |
USE guide_m, ONLY: guide |
29 |
use inidissip_m, only: idissip |
use inidissip_m, only: idissip |
30 |
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use integrd_m, only: integrd |
31 |
USE logic, ONLY: iflag_phys, ok_guide |
USE logic, ONLY: iflag_phys, ok_guide |
32 |
USE paramet_m, ONLY: iip1, ip1jm, ip1jmp1, jjp1 |
USE paramet_m, ONLY: ip1jmp1 |
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USE pression_m, ONLY: pression |
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33 |
USE pressure_var, ONLY: p3d |
USE pressure_var, ONLY: p3d |
34 |
USE temps, ONLY: dt, itaufin |
USE temps, ONLY: itau_dyn |
35 |
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36 |
! Variables dynamiques: |
! Variables dynamiques: |
37 |
REAL vcov(ip1jm, llm), ucov(ip1jmp1, llm) ! vents covariants |
REAL, intent(inout):: ucov(ip1jmp1, llm) ! vent covariant |
38 |
REAL teta(ip1jmp1, llm) ! temperature potentielle |
REAL, intent(inout):: vcov((iim + 1) * jjm, llm) ! vent covariant |
39 |
REAL ps(ip1jmp1) ! pression au sol, en Pa |
REAL, intent(inout):: teta(iim + 1, jjm + 1, llm) ! potential temperature |
40 |
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REAL, intent(inout):: ps(iim + 1, jjm + 1) ! pression au sol, en Pa |
41 |
REAL masse(ip1jmp1, llm) ! masse d'air |
REAL masse(ip1jmp1, llm) ! masse d'air |
42 |
REAL phis(ip1jmp1) ! geopotentiel au sol |
REAL phis(ip1jmp1) ! geopotentiel au sol |
43 |
REAL q(ip1jmp1, llm, nqmx) ! mass fractions of advected fields |
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44 |
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REAL, intent(inout):: q(:, :, :, :) ! (iim + 1, jjm + 1, llm, nqmx) |
45 |
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! mass fractions of advected fields |
46 |
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47 |
REAL, intent(in):: time_0 |
REAL, intent(in):: time_0 |
48 |
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49 |
! Variables local to the procedure: |
! Variables local to the procedure: |
51 |
! Variables dynamiques: |
! Variables dynamiques: |
52 |
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53 |
REAL pks(ip1jmp1) ! exner au sol |
REAL pks(ip1jmp1) ! exner au sol |
54 |
REAL pk(ip1jmp1, llm) ! exner au milieu des couches |
REAL pk(iim + 1, jjm + 1, llm) ! exner au milieu des couches |
55 |
REAL pkf(ip1jmp1, llm) ! exner filt.au milieu des couches |
REAL pkf(ip1jmp1, llm) ! exner filt.au milieu des couches |
56 |
REAL phi(ip1jmp1, llm) ! geopotential |
REAL phi(ip1jmp1, llm) ! geopotential |
57 |
REAL w(ip1jmp1, llm) ! vitesse verticale |
REAL w(ip1jmp1, llm) ! vitesse verticale |
58 |
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59 |
! variables dynamiques intermediaire pour le transport |
! variables dynamiques intermediaire pour le transport |
60 |
REAL pbaru(ip1jmp1, llm), pbarv(ip1jm, llm) !flux de masse |
REAL pbaru(ip1jmp1, llm), pbarv((iim + 1) * jjm, llm) !flux de masse |
61 |
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62 |
! variables dynamiques au pas - 1 |
! variables dynamiques au pas - 1 |
63 |
REAL vcovm1(ip1jm, llm), ucovm1(ip1jmp1, llm) |
REAL vcovm1((iim + 1) * jjm, llm), ucovm1(ip1jmp1, llm) |
64 |
REAL tetam1(ip1jmp1, llm), psm1(ip1jmp1) |
REAL tetam1(iim + 1, jjm + 1, llm), psm1(iim + 1, jjm + 1) |
65 |
REAL massem1(ip1jmp1, llm) |
REAL massem1(ip1jmp1, llm) |
66 |
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67 |
! tendances dynamiques |
! tendances dynamiques |
68 |
REAL dv(ip1jm, llm), du(ip1jmp1, llm) |
REAL dv((iim + 1) * jjm, llm), du(ip1jmp1, llm) |
69 |
REAL dteta(ip1jmp1, llm), dq(ip1jmp1, llm, nqmx), dp(ip1jmp1) |
REAL dteta(ip1jmp1, llm), dq(ip1jmp1, llm, nqmx), dp(ip1jmp1) |
70 |
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71 |
! tendances de la dissipation |
! tendances de la dissipation |
72 |
REAL dvdis(ip1jm, llm), dudis(ip1jmp1, llm) |
REAL dvdis((iim + 1) * jjm, llm), dudis(ip1jmp1, llm) |
73 |
REAL dtetadis(ip1jmp1, llm) |
REAL dtetadis(iim + 1, jjm + 1, llm) |
74 |
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75 |
! tendances physiques |
! tendances physiques |
76 |
REAL dvfi(ip1jm, llm), dufi(ip1jmp1, llm) |
REAL dvfi((iim + 1) * jjm, llm), dufi(ip1jmp1, llm) |
77 |
REAL dtetafi(ip1jmp1, llm), dqfi(ip1jmp1, llm, nqmx), dpfi(ip1jmp1) |
REAL dtetafi(ip1jmp1, llm), dqfi(ip1jmp1, llm, nqmx), dpfi(ip1jmp1) |
78 |
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79 |
! variables pour le fichier histoire |
! variables pour le fichier histoire |
80 |
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REAL tppn(iim), tpps(iim), tpn, tps |
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81 |
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 |
82 |
INTEGER iday ! jour julien |
INTEGER itaufin |
83 |
REAL time ! time of day, as a fraction of day length |
REAL time ! time of day, as a fraction of day length |
84 |
real finvmaold(ip1jmp1, llm) |
real finvmaold(ip1jmp1, llm) |
85 |
LOGICAL:: lafin=.false. |
INTEGER l |
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INTEGER ij, l |
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86 |
REAL rdayvrai, rdaym_ini |
REAL rdayvrai, rdaym_ini |
87 |
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88 |
! Variables test conservation energie |
! Variables test conservation energie |
89 |
REAL ecin(ip1jmp1, llm), ecin0(ip1jmp1, llm) |
REAL ecin(iim + 1, jjm + 1, llm), ecin0(iim + 1, jjm + 1, llm) |
90 |
! Tendance de la temp. potentiel d (theta) / d t due a la |
! Tendance de la temp. potentiel d (theta) / d t due a la |
91 |
! tansformation d'energie cinetique en energie thermique |
! tansformation d'energie cinetique en energie thermique |
92 |
! cree par la dissipation |
! cree par la dissipation |
93 |
REAL dtetaecdt(ip1jmp1, llm) |
REAL dtetaecdt(iim + 1, jjm + 1, llm) |
94 |
REAL vcont(ip1jm, llm), ucont(ip1jmp1, llm) |
REAL vcont((iim + 1) * jjm, llm), ucont(ip1jmp1, llm) |
95 |
CHARACTER*15 ztit |
logical leapf |
96 |
INTEGER:: ip_ebil_dyn = 0 ! PRINT level for energy conserv. diag. |
real dt |
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logical:: dissip_conservative = .true. |
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logical forward, leapf, apphys, conser, apdiss |
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98 |
!--------------------------------------------------- |
!--------------------------------------------------- |
99 |
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100 |
print *, "Call sequence information: leapfrog" |
print *, "Call sequence information: leapfrog" |
101 |
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102 |
itaufin = nday * day_step |
itaufin = nday * day_step |
103 |
itau = 0 |
! "day_step" is a multiple of "iperiod", therefore "itaufin" is one too |
104 |
iday = day_ini |
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time = time_0 |
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105 |
dq = 0. |
dq = 0. |
106 |
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107 |
! On initialise la pression et la fonction d'Exner : |
! On initialise la pression et la fonction d'Exner : |
108 |
CALL pression(ip1jmp1, ap, bp, ps, p3d) |
forall (l = 1: llm + 1) p3d(:, :, l) = ap(l) + bp(l) * ps |
109 |
CALL exner_hyb(ps, p3d, pks, pk, pkf) |
CALL exner_hyb(ps, p3d, pks, pk, pkf) |
110 |
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111 |
! Debut de l'integration temporelle: |
time_integration: do itau = 0, itaufin - 1 |
112 |
outer_loop:do |
leapf = mod(itau, iperiod) /= 0 |
113 |
if (ok_guide .and. (itaufin - itau - 1) * dtvr > 21600.) & |
if (leapf) then |
114 |
call guide(itau, ucov, vcov, teta, q, masse, ps) |
dt = 2 * dtvr |
115 |
vcovm1 = vcov |
else |
116 |
ucovm1 = ucov |
! Matsuno |
117 |
tetam1 = teta |
dt = dtvr |
118 |
massem1 = masse |
if (ok_guide .and. (itaufin - itau - 1) * dtvr > 21600.) & |
119 |
psm1 = ps |
call guide(itau, ucov, vcov, teta, q, masse, ps) |
120 |
forward = .TRUE. |
vcovm1 = vcov |
121 |
leapf = .FALSE. |
ucovm1 = ucov |
122 |
dt = dtvr |
tetam1 = teta |
123 |
finvmaold = masse |
massem1 = masse |
124 |
CALL filtreg(finvmaold, jjp1, llm, - 2, 2, .TRUE., 1) |
psm1 = ps |
125 |
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finvmaold = masse |
126 |
do |
CALL filtreg(finvmaold, jjm + 1, llm, - 2, 2, .TRUE., 1) |
127 |
! gestion des appels de la physique et des dissipations: |
end if |
128 |
apphys = MOD(itau + 1, iphysiq) == 0 .AND. iflag_phys /= 0 |
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129 |
conser = MOD(itau, iconser) == 0 |
! Calcul des tendances dynamiques: |
130 |
apdiss = MOD(itau + 1, idissip) == 0 |
CALL geopot(ip1jmp1, teta, pk, pks, phis, phi) |
131 |
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CALL caldyn(itau, ucov, vcov, teta, ps, masse, pk, pkf, phis, phi, & |
132 |
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MOD(itau, iconser) == 0, du, dv, dteta, dp, w, pbaru, pbarv, & |
133 |
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time_0) |
134 |
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135 |
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! Calcul des tendances advection des traceurs (dont l'humidité) |
136 |
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CALL caladvtrac(q, pbaru, pbarv, p3d, masse, dq, teta, pk) |
137 |
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138 |
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! Stokage du flux de masse pour traceurs offline: |
139 |
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IF (offline) CALL fluxstokenc(pbaru, pbarv, masse, teta, phi, phis, & |
140 |
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dtvr, itau) |
141 |
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142 |
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! integrations dynamique et traceurs: |
143 |
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CALL integrd(vcovm1, ucovm1, tetam1, psm1, massem1, dv, du, dteta, dp, & |
144 |
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vcov, ucov, teta, q(:, :, :, :2), ps, masse, finvmaold, dt, leapf) |
145 |
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146 |
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if (.not. leapf) then |
147 |
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! Matsuno backward |
148 |
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forall (l = 1: llm + 1) p3d(:, :, l) = ap(l) + bp(l) * ps |
149 |
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CALL exner_hyb(ps, p3d, pks, pk, pkf) |
150 |
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151 |
! calcul des tendances dynamiques: |
! Calcul des tendances dynamiques: |
152 |
CALL geopot(ip1jmp1, teta, pk, pks, phis, phi) |
CALL geopot(ip1jmp1, teta, pk, pks, phis, phi) |
153 |
CALL caldyn(itau, ucov, vcov, teta, ps, masse, pk, pkf, phis, phi, & |
CALL caldyn(itau + 1, ucov, vcov, teta, ps, masse, pk, pkf, phis, & |
154 |
conser, du, dv, dteta, dp, w, pbaru, pbarv, & |
phi, .false., du, dv, dteta, dp, w, pbaru, pbarv, time_0) |
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time + iday - day_ini) |
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IF (forward .OR. leapf) THEN |
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! calcul des tendances advection des traceurs (dont l'humidite) |
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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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! 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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155 |
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156 |
! integrations dynamique et traceurs: |
! integrations dynamique et traceurs: |
157 |
CALL integrd(2, vcovm1, ucovm1, tetam1, psm1, massem1, dv, du, & |
CALL integrd(vcovm1, ucovm1, tetam1, psm1, massem1, dv, du, dteta, & |
158 |
dteta, dq, dp, vcov, ucov, teta, q, ps, masse, phis, & |
dp, vcov, ucov, teta, q(:, :, :, :2), ps, masse, finvmaold, & |
159 |
finvmaold, leapf) |
dtvr, leapf=.false.) |
160 |
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end if |
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IF (apphys) THEN |
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! calcul des tendances physiques: |
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IF (itau + 1 == itaufin) lafin = .TRUE. |
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CALL pression(ip1jmp1, ap, bp, ps, p3d) |
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CALL exner_hyb(ps, p3d, pks, pk, pkf) |
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rdaym_ini = itau * dtvr / daysec |
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rdayvrai = rdaym_ini + day_ini |
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! Diagnostique de conservation de l'énergie : initialisation |
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IF (ip_ebil_dyn >= 1) THEN |
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ztit='bil dyn' |
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CALL diagedyn(ztit, 2, 1, 1, dtphys, ucov, vcov, ps, p3d, pk, & |
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teta, q(:, :, 1), q(:, :, 2)) |
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ENDIF |
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CALL calfis(nqmx, lafin, rdayvrai, time, ucov, vcov, teta, q, & |
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masse, ps, pk, phis, phi, du, dv, dteta, dq, w, & |
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dufi, dvfi, dtetafi, dqfi, dpfi) |
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! ajout des tendances physiques: |
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CALL addfi(nqmx, dtphys, & |
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ucov, vcov, teta, q, ps, & |
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dufi, dvfi, dtetafi, dqfi, dpfi) |
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! Diagnostique de conservation de l'énergie : difference |
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IF (ip_ebil_dyn >= 1) THEN |
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ztit = 'bil phys' |
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CALL diagedyn(ztit, 2, 1, 1, dtphys, ucov, vcov, ps, p3d, pk, & |
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teta, q(:, :, 1), q(:, :, 2)) |
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ENDIF |
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ENDIF |
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161 |
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162 |
CALL pression(ip1jmp1, ap, bp, ps, p3d) |
IF (MOD(itau + 1, iphysiq) == 0 .AND. iflag_phys /= 0) THEN |
163 |
CALL exner_hyb(ps, p3d, pks, pk, pkf) |
! calcul des tendances physiques: |
164 |
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165 |
IF (apdiss) THEN |
forall (l = 1: llm + 1) p3d(:, :, l) = ap(l) + bp(l) * ps |
166 |
! dissipation horizontale et verticale des petites echelles: |
CALL exner_hyb(ps, p3d, pks, pk, pkf) |
167 |
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168 |
! calcul de l'energie cinetique avant dissipation |
rdaym_ini = itau * dtvr / daysec |
169 |
call covcont(llm, ucov, vcov, ucont, vcont) |
rdayvrai = rdaym_ini + day_ini |
170 |
call enercin(vcov, ucov, vcont, ucont, ecin0) |
time = REAL(mod(itau, day_step)) / day_step + time_0 |
171 |
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IF (time > 1.) time = time - 1. |
172 |
! dissipation |
|
173 |
CALL dissip(vcov, ucov, teta, p3d, dvdis, dudis, dtetadis) |
CALL calfis(rdayvrai, time, ucov, vcov, teta, q, masse, ps, pk, & |
174 |
ucov=ucov + dudis |
phis, phi, du, dv, dteta, dq, w, dufi, dvfi, dtetafi, dqfi, & |
175 |
vcov=vcov + dvdis |
dpfi, lafin=itau+1==itaufin) |
176 |
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177 |
if (dissip_conservative) then |
! ajout des tendances physiques: |
178 |
! On rajoute la tendance due a la transform. Ec -> E |
CALL addfi(nqmx, dtphys, ucov, vcov, teta, q, ps, dufi, dvfi, & |
179 |
! therm. cree lors de la dissipation |
dtetafi, dqfi, dpfi) |
180 |
call covcont(llm, ucov, vcov, ucont, vcont) |
ENDIF |
181 |
call enercin(vcov, ucov, vcont, ucont, ecin) |
|
182 |
dtetaecdt= (ecin0 - ecin) / pk |
forall (l = 1: llm + 1) p3d(:, :, l) = ap(l) + bp(l) * ps |
183 |
dtetadis=dtetadis + dtetaecdt |
CALL exner_hyb(ps, p3d, pks, pk, pkf) |
184 |
endif |
|
185 |
teta=teta + dtetadis |
IF (MOD(itau + 1, idissip) == 0) THEN |
186 |
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! dissipation horizontale et verticale des petites echelles: |
187 |
! Calcul de la valeur moyenne, unique de h aux poles ..... |
|
188 |
DO l = 1, llm |
! calcul de l'energie cinetique avant dissipation |
189 |
DO ij = 1, iim |
call covcont(llm, ucov, vcov, ucont, vcont) |
190 |
tppn(ij) = aire(ij) * teta(ij, l) |
call enercin(vcov, ucov, vcont, ucont, ecin0) |
191 |
tpps(ij) = aire(ij + ip1jm) * teta(ij + ip1jm, l) |
|
192 |
ENDDO |
! dissipation |
193 |
tpn = SUM(tppn) / apoln |
CALL dissip(vcov, ucov, teta, p3d, dvdis, dudis, dtetadis) |
194 |
tps = SUM(tpps) / apols |
ucov=ucov + dudis |
195 |
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vcov=vcov + dvdis |
196 |
DO ij = 1, iip1 |
|
197 |
teta(ij, l) = tpn |
! On rajoute la tendance due à la transformation Ec -> E |
198 |
teta(ij + ip1jm, l) = tps |
! thermique créée lors de la dissipation |
199 |
ENDDO |
call covcont(llm, ucov, vcov, ucont, vcont) |
200 |
ENDDO |
call enercin(vcov, ucov, vcont, ucont, ecin) |
201 |
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dtetaecdt= (ecin0 - ecin) / pk |
202 |
DO ij = 1, iim |
dtetadis=dtetadis + dtetaecdt |
203 |
tppn(ij) = aire(ij) * ps(ij) |
teta=teta + dtetadis |
204 |
tpps(ij) = aire(ij + ip1jm) * ps(ij + ip1jm) |
|
205 |
ENDDO |
! Calcul de la valeur moyenne aux pôles : |
206 |
tpn = SUM(tppn) / apoln |
forall (l = 1: llm) |
207 |
tps = SUM(tpps) / apols |
teta(:, 1, l) = SUM(aire_2d(:iim, 1) * teta(:iim, 1, l)) & |
208 |
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/ apoln |
209 |
DO ij = 1, iip1 |
teta(:, jjm + 1, l) = SUM(aire_2d(:iim, jjm+1) & |
210 |
ps(ij) = tpn |
* teta(:iim, jjm + 1, l)) / apols |
211 |
ps(ij + ip1jm) = tps |
END forall |
212 |
ENDDO |
|
213 |
END IF |
ps(:, 1) = SUM(aire_2d(:iim, 1) * ps(:iim, 1)) / apoln |
214 |
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ps(:, jjm + 1) = SUM(aire_2d(:iim, jjm+1) * ps(:iim, jjm + 1)) & |
215 |
! fin de l'intégration dynamique et physique pour le pas "itau" |
/ apols |
216 |
! préparation du pas d'intégration suivant |
END IF |
217 |
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|
218 |
! schema matsuno + leapfrog |
IF (MOD(itau + 1, iperiod) == 0) THEN |
219 |
IF (forward .OR. leapf) THEN |
! Écriture du fichier histoire moyenne: |
220 |
itau = itau + 1 |
CALL writedynav(histaveid, nqmx, itau + 1, vcov, ucov, teta, pk, & |
221 |
iday = day_ini + itau / day_step |
phi, q, masse, ps, phis) |
222 |
time = REAL(itau - (iday - day_ini) * day_step) / day_step & |
call bilan_dyn(ps, masse, pk, pbaru, pbarv, teta, phi, ucov, vcov, & |
223 |
+ time_0 |
q(:, :, :, 1), dt_app = dtvr * iperiod, & |
224 |
IF (time > 1.) THEN |
dt_cum = dtvr * day_step * periodav) |
225 |
time = time - 1. |
ENDIF |
226 |
iday = iday + 1 |
end do time_integration |
227 |
ENDIF |
|
228 |
ENDIF |
CALL dynredem1("restart.nc", vcov, ucov, teta, q, masse, ps, & |
229 |
|
itau=itau_dyn+itaufin) |
230 |
IF (itau == itaufin + 1) exit outer_loop |
|
231 |
|
! Calcul des tendances dynamiques: |
232 |
IF (MOD(itau, iperiod) == 0 .OR. itau == itaufin) THEN |
CALL geopot(ip1jmp1, teta, pk, pks, phis, phi) |
233 |
! ecriture du fichier histoire moyenne: |
CALL caldyn(itaufin, ucov, vcov, teta, ps, masse, pk, pkf, phis, phi, & |
234 |
CALL writedynav(histaveid, nqmx, itau, vcov, & |
MOD(itaufin, iconser) == 0, du, dv, dteta, dp, w, pbaru, pbarv, & |
235 |
ucov, teta, pk, phi, q, masse, ps, phis) |
time_0) |
|
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) |
|
|
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 |
|
236 |
|
|
237 |
END SUBROUTINE leapfrog |
END SUBROUTINE leapfrog |
238 |
|
|