trunk/dyn3d/leapfrog.f

module leapfrog_m

  IMPLICIT NONE

contains

  SUBROUTINE leapfrog(ucov, vcov, teta, ps, masse, phis, q, time_0)

    ! From dyn3d/leapfrog.F, version 1.6, 2005/04/13 08:58:34
    ! Authors: P. Le Van, L. Fairhead, F. Hourdin
    ! Matsuno-leapfrog scheme.

    use addfi_m, only: addfi
    use bilan_dyn_m, only: bilan_dyn
    use caladvtrac_m, only: caladvtrac
    use caldyn_m, only: caldyn
    USE calfis_m, ONLY: calfis
    USE comconst, ONLY: daysec, dtphys, dtvr
    USE comgeom, ONLY: aire_2d, apoln, apols
    USE comvert, ONLY: ap, bp
    USE conf_gcm_m, ONLY: day_step, iconser, iperiod, iphysiq, nday, offline, &
         iflag_phys, ok_guide
    USE dimens_m, ONLY: iim, jjm, llm, nqmx
    use dissip_m, only: dissip
    USE dynetat0_m, ONLY: day_ini
    use dynredem1_m, only: dynredem1
    USE exner_hyb_m, ONLY: exner_hyb
    use filtreg_m, only: filtreg
    use geopot_m, only: geopot
    USE guide_m, ONLY: guide
    use inidissip_m, only: idissip
    use integrd_m, only: integrd
    use nr_util, only: assert
    USE pressure_var, ONLY: p3d
    USE temps, ONLY: itau_dyn
    use writedynav_m, only: writedynav

    ! Variables dynamiques:
    REAL, intent(inout):: ucov(:, :, :) ! (iim + 1, jjm + 1, llm) vent covariant
    REAL, intent(inout):: vcov(:, :, :) ! (iim + 1, jjm, llm) ! vent covariant

    REAL, intent(inout):: teta(:, :, :) ! (iim + 1, jjm + 1, llm)
    ! potential temperature

    REAL, intent(inout):: ps(:, :) ! (iim + 1, jjm + 1) pression au sol, en Pa
    REAL masse((iim + 1) * (jjm + 1), llm) ! masse d'air
    REAL phis((iim + 1) * (jjm + 1)) ! geopotentiel au sol

    REAL, intent(inout):: q(:, :, :, :) ! (iim + 1, jjm + 1, llm, nqmx)
    ! mass fractions of advected fields

    REAL, intent(in):: time_0

    ! Variables local to the procedure:

    ! Variables dynamiques:

    REAL pks((iim + 1) * (jjm + 1)) ! exner au sol
    REAL pk(iim + 1, jjm + 1, llm) ! exner au milieu des couches
    REAL pkf((iim + 1) * (jjm + 1), llm) ! exner filt.au milieu des couches
    REAL phi(iim + 1, jjm + 1, llm) ! geopotential
    REAL w((iim + 1) * (jjm + 1), llm) ! vitesse verticale

    ! Variables dynamiques intermediaire pour le transport
    ! Flux de masse :
    REAL pbaru((iim + 1) * (jjm + 1), llm), pbarv((iim + 1) * jjm, llm)

    ! Variables dynamiques au pas - 1
    REAL vcovm1(iim + 1, jjm, llm), ucovm1(iim + 1, jjm + 1, llm)
    REAL tetam1(iim + 1, jjm + 1, llm), psm1(iim + 1, jjm + 1)
    REAL massem1((iim + 1) * (jjm + 1), llm)

    ! Tendances dynamiques
    REAL dv((iim + 1) * jjm, llm), dudyn((iim + 1) * (jjm + 1), llm)
    REAL dteta(iim + 1, jjm + 1, llm), dq((iim + 1) * (jjm + 1), llm, nqmx)
    real dp((iim + 1) * (jjm + 1))

    ! Tendances de la dissipation :
    REAL dvdis(iim + 1, jjm, llm), dudis(iim + 1, jjm + 1, llm)
    REAL dtetadis(iim + 1, jjm + 1, llm)

    ! Tendances physiques
    REAL dvfi((iim + 1) * jjm, llm), dufi((iim + 1) * (jjm + 1), llm)
    REAL dtetafi(iim + 1, jjm + 1, llm), dqfi((iim + 1) * (jjm + 1), llm, nqmx)
    real dpfi((iim + 1) * (jjm + 1))

    ! Variables pour le fichier histoire

    INTEGER itau ! index of the time step of the dynamics, starts at 0
    INTEGER itaufin
    REAL time ! time of day, as a fraction of day length
    real finvmaold((iim + 1) * (jjm + 1), llm)
    INTEGER l
    REAL rdayvrai, rdaym_ini

    ! Variables test conservation energie
    REAL ecin(iim + 1, jjm + 1, llm), ecin0(iim + 1, jjm + 1, llm)

    REAL vcont((iim + 1) * jjm, llm), ucont((iim + 1) * (jjm + 1), llm)
    logical leapf
    real dt

    !---------------------------------------------------

    print *, "Call sequence information: leapfrog"
    call assert(shape(ucov) == (/iim + 1, jjm + 1, llm/), "leapfrog")

    itaufin = nday * day_step
    ! "day_step" is a multiple of "iperiod", therefore so is "itaufin".

    dq = 0.

    ! On initialise la pression et la fonction d'Exner :
    forall (l = 1: llm + 1) p3d(:, :, l) = ap(l) + bp(l) * ps
    CALL exner_hyb(ps, p3d, pks, pk, pkf)

    time_integration: do itau = 0, itaufin - 1
       leapf = mod(itau, iperiod) /= 0
       if (leapf) then
          dt = 2 * dtvr
       else
          ! Matsuno
          dt = dtvr
          if (ok_guide .and. (itaufin - itau - 1) * dtvr > 21600.) &
               call guide(itau, ucov, vcov, teta, q, masse, ps)
          vcovm1 = vcov
          ucovm1 = ucov
          tetam1 = teta
          massem1 = masse
          psm1 = ps
          finvmaold = masse
          CALL filtreg(finvmaold, jjm + 1, llm, - 2, 2, .TRUE.)
       end if

       ! Calcul des tendances dynamiques:
       CALL geopot((iim + 1) * (jjm + 1), teta, pk, pks, phis, phi)
       CALL caldyn(itau, ucov, vcov, teta, ps, masse, pk, pkf, phis, phi, &
            dudyn, dv, dteta, dp, w, pbaru, pbarv, time_0, &
            conser=MOD(itau, iconser)==0)

       ! Calcul des tendances advection des traceurs (dont l'humidité)
       CALL caladvtrac(q, pbaru, pbarv, p3d, masse, dq, teta, pk)

       ! Stokage du flux de masse pour traceurs offline:
       IF (offline) CALL fluxstokenc(pbaru, pbarv, masse, teta, phi, phis, &
            dtvr, itau)

       ! Integrations dynamique et traceurs:
       CALL integrd(vcovm1, ucovm1, tetam1, psm1, massem1, dv, dudyn, dteta, &
            dp, vcov, ucov, teta, q(:, :, :, :2), ps, masse, finvmaold, dt, &
            leapf)

       if (.not. leapf) then
          ! Matsuno backward
          forall (l = 1: llm + 1) p3d(:, :, l) = ap(l) + bp(l) * ps
          CALL exner_hyb(ps, p3d, pks, pk, pkf)

          ! Calcul des tendances dynamiques:
          CALL geopot((iim + 1) * (jjm + 1), teta, pk, pks, phis, phi)
          CALL caldyn(itau + 1, ucov, vcov, teta, ps, masse, pk, pkf, phis, &
               phi, dudyn, dv, dteta, dp, w, pbaru, pbarv, time_0, &
               conser=.false.)

          ! integrations dynamique et traceurs:
          CALL integrd(vcovm1, ucovm1, tetam1, psm1, massem1, dv, dudyn, &
               dteta, dp, vcov, ucov, teta, q(:, :, :, :2), ps, masse, &
               finvmaold, dtvr, leapf=.false.)
       end if

       IF (MOD(itau + 1, iphysiq) == 0 .AND. iflag_phys /= 0) THEN
          ! calcul des tendances physiques:

          forall (l = 1: llm + 1) p3d(:, :, l) = ap(l) + bp(l) * ps
          CALL exner_hyb(ps, p3d, pks, pk, pkf)

          rdaym_ini = itau * dtvr / daysec
          rdayvrai = rdaym_ini + day_ini
          time = REAL(mod(itau, day_step)) / day_step + time_0
          IF (time > 1.) time = time - 1.

          CALL calfis(rdayvrai, time, ucov, vcov, teta, q, masse, ps, pk, &
               phis, phi, dudyn, dv, dq, w, dufi, dvfi, dtetafi, dqfi, dpfi, &
               lafin=itau+1==itaufin)

          ! ajout des tendances physiques:
          CALL addfi(nqmx, dtphys, ucov, vcov, teta, q, ps, dufi, dvfi, &
               dtetafi, dqfi, dpfi)
       ENDIF

       forall (l = 1: llm + 1) p3d(:, :, l) = ap(l) + bp(l) * ps
       CALL exner_hyb(ps, p3d, pks, pk, pkf)

       IF (MOD(itau + 1, idissip) == 0) THEN
          ! Dissipation horizontale et verticale des petites échelles

          ! calcul de l'énergie cinétique avant dissipation
          call covcont(llm, ucov, vcov, ucont, vcont)
          call enercin(vcov, ucov, vcont, ucont, ecin0)

          ! dissipation
          CALL dissip(vcov, ucov, teta, p3d, dvdis, dudis, dtetadis)
          ucov = ucov + dudis
          vcov = vcov + dvdis

          ! On ajoute la tendance due à la transformation énergie
          ! cinétique en énergie thermique par la dissipation
          call covcont(llm, ucov, vcov, ucont, vcont)
          call enercin(vcov, ucov, vcont, ucont, ecin)
          dtetadis = dtetadis + (ecin0 - ecin) / pk
          teta = teta + dtetadis

          ! Calcul de la valeur moyenne aux pôles :
          forall (l = 1: llm)
             teta(:, 1, l) = SUM(aire_2d(:iim, 1) * teta(:iim, 1, l)) &
                  / apoln
             teta(:, jjm + 1, l) = SUM(aire_2d(:iim, jjm+1) &
                  * teta(:iim, jjm + 1, l)) / apols
          END forall

          ps(:, 1) = SUM(aire_2d(:iim, 1) * ps(:iim, 1)) / apoln
          ps(:, jjm + 1) = SUM(aire_2d(:iim, jjm+1) * ps(:iim, jjm + 1)) &
               / apols
       END IF

       IF (MOD(itau + 1, iperiod) == 0) THEN
          ! Écriture du fichier histoire moyenne:
          CALL writedynav(vcov, ucov, teta, pk, phi, q, masse, ps, phis, &
               time = itau + 1)
          call bilan_dyn(ps, masse, pk, pbaru, pbarv, teta, phi, ucov, vcov, &
               q(:, :, :, 1))
       ENDIF
    end do time_integration

    CALL dynredem1("restart.nc", vcov, ucov, teta, q, masse, ps, &
         itau=itau_dyn+itaufin)

    ! Calcul des tendances dynamiques:
    CALL geopot((iim + 1) * (jjm + 1), teta, pk, pks, phis, phi)
    CALL caldyn(itaufin, ucov, vcov, teta, ps, masse, pk, pkf, phis, phi, &
         dudyn, dv, dteta, dp, w, pbaru, pbarv, time_0, &
         conser=MOD(itaufin, iconser)==0)

  END SUBROUTINE leapfrog

end module leapfrog_m
1	guez	3	module leapfrog_m
2
3			IMPLICIT NONE
4
5			contains
6
7	guez	23	SUBROUTINE leapfrog(ucov, vcov, teta, ps, masse, phis, q, time_0)
8	guez	3
9	guez	27	! From dyn3d/leapfrog.F, version 1.6, 2005/04/13 08:58:34
10			! Authors: P. Le Van, L. Fairhead, F. Hourdin
11	guez	36	! Matsuno-leapfrog scheme.
12	guez	3
13	guez	37	use addfi_m, only: addfi
14	guez	40	use bilan_dyn_m, only: bilan_dyn
15			use caladvtrac_m, only: caladvtrac
16	guez	43	use caldyn_m, only: caldyn
17	guez	26	USE calfis_m, ONLY: calfis
18			USE comconst, ONLY: daysec, dtphys, dtvr
19	guez	29	USE comgeom, ONLY: aire_2d, apoln, apols
20	guez	26	USE comvert, ONLY: ap, bp
21	guez	57	USE conf_gcm_m, ONLY: day_step, iconser, iperiod, iphysiq, nday, offline, &
22			iflag_phys, ok_guide
23	guez	29	USE dimens_m, ONLY: iim, jjm, llm, nqmx
24	guez	47	use dissip_m, only: dissip
25	guez	26	USE dynetat0_m, ONLY: day_ini
26	guez	27	use dynredem1_m, only: dynredem1
27	guez	26	USE exner_hyb_m, ONLY: exner_hyb
28	guez	27	use filtreg_m, only: filtreg
29	guez	43	use geopot_m, only: geopot
30	guez	26	USE guide_m, ONLY: guide
31			use inidissip_m, only: idissip
32	guez	32	use integrd_m, only: integrd
33	guez	55	use nr_util, only: assert
34	guez	26	USE pressure_var, ONLY: p3d
35	guez	28	USE temps, ONLY: itau_dyn
36	guez	56	use writedynav_m, only: writedynav
37	guez	3
38	guez	10	! Variables dynamiques:
39	guez	55	REAL, intent(inout):: ucov(:, :, :) ! (iim + 1, jjm + 1, llm) vent covariant
40			REAL, intent(inout):: vcov(:, :, :) ! (iim + 1, jjm, llm) ! vent covariant
41	guez	43
42			REAL, intent(inout):: teta(:, :, :) ! (iim + 1, jjm + 1, llm)
43			! potential temperature
44
45	guez	45	REAL, intent(inout):: ps(:, :) ! (iim + 1, jjm + 1) pression au sol, en Pa
46	guez	55	REAL masse((iim + 1) * (jjm + 1), llm) ! masse d'air
47			REAL phis((iim + 1) * (jjm + 1)) ! geopotentiel au sol
48	guez	40
49			REAL, intent(inout):: q(:, :, :, :) ! (iim + 1, jjm + 1, llm, nqmx)
50			! mass fractions of advected fields
51
52	guez	24	REAL, intent(in):: time_0
53	guez	10
54			! Variables local to the procedure:
55
56			! Variables dynamiques:
57
58	guez	55	REAL pks((iim + 1) * (jjm + 1)) ! exner au sol
59	guez	29	REAL pk(iim + 1, jjm + 1, llm) ! exner au milieu des couches
60	guez	55	REAL pkf((iim + 1) * (jjm + 1), llm) ! exner filt.au milieu des couches
61	guez	47	REAL phi(iim + 1, jjm + 1, llm) ! geopotential
62	guez	55	REAL w((iim + 1) * (jjm + 1), llm) ! vitesse verticale
63	guez	3
64	guez	55	! Variables dynamiques intermediaire pour le transport
65			! Flux de masse :
66			REAL pbaru((iim + 1) * (jjm + 1), llm), pbarv((iim + 1) * jjm, llm)
67	guez	3
68	guez	56	! Variables dynamiques au pas - 1
69	guez	55	REAL vcovm1(iim + 1, jjm, llm), ucovm1(iim + 1, jjm + 1, llm)
70	guez	29	REAL tetam1(iim + 1, jjm + 1, llm), psm1(iim + 1, jjm + 1)
71	guez	55	REAL massem1((iim + 1) * (jjm + 1), llm)
72	guez	3
73	guez	56	! Tendances dynamiques
74	guez	55	REAL dv((iim + 1) * jjm, llm), dudyn((iim + 1) * (jjm + 1), llm)
75			REAL dteta(iim + 1, jjm + 1, llm), dq((iim + 1) * (jjm + 1), llm, nqmx)
76			real dp((iim + 1) * (jjm + 1))
77	guez	3
78	guez	56	! Tendances de la dissipation :
79	guez	55	REAL dvdis(iim + 1, jjm, llm), dudis(iim + 1, jjm + 1, llm)
80	guez	29	REAL dtetadis(iim + 1, jjm + 1, llm)
81	guez	3
82	guez	56	! Tendances physiques
83	guez	55	REAL dvfi((iim + 1) * jjm, llm), dufi((iim + 1) * (jjm + 1), llm)
84			REAL dtetafi(iim + 1, jjm + 1, llm), dqfi((iim + 1) * (jjm + 1), llm, nqmx)
85			real dpfi((iim + 1) * (jjm + 1))
86	guez	3
87	guez	56	! Variables pour le fichier histoire
88	guez	3
89	guez	22	INTEGER itau ! index of the time step of the dynamics, starts at 0
90	guez	27	INTEGER itaufin
91	guez	20	REAL time ! time of day, as a fraction of day length
92	guez	55	real finvmaold((iim + 1) * (jjm + 1), llm)
93	guez	33	INTEGER l
94	guez	3	REAL rdayvrai, rdaym_ini
95
96	guez	24	! Variables test conservation energie
97	guez	29	REAL ecin(iim + 1, jjm + 1, llm), ecin0(iim + 1, jjm + 1, llm)
98	guez	43
99	guez	55	REAL vcont((iim + 1) * jjm, llm), ucont((iim + 1) * (jjm + 1), llm)
100	guez	33	logical leapf
101			real dt
102	guez	3
103			!---------------------------------------------------
104
105			print *, "Call sequence information: leapfrog"
106	guez	55	call assert(shape(ucov) == (/iim + 1, jjm + 1, llm/), "leapfrog")
107	guez	3
108			itaufin = nday * day_step
109	guez	62	! "day_step" is a multiple of "iperiod", therefore so is "itaufin".
110	guez	30
111	guez	24	dq = 0.
112	guez	33
113	guez	3	! On initialise la pression et la fonction d'Exner :
114	guez	37	forall (l = 1: llm + 1) p3d(:, :, l) = ap(l) + bp(l) * ps
115	guez	10	CALL exner_hyb(ps, p3d, pks, pk, pkf)
116	guez	3
117	guez	40	time_integration: do itau = 0, itaufin - 1
118	guez	33	leapf = mod(itau, iperiod) /= 0
119			if (leapf) then
120			dt = 2 * dtvr
121			else
122			! Matsuno
123			dt = dtvr
124			if (ok_guide .and. (itaufin - itau - 1) * dtvr > 21600.) &
125			call guide(itau, ucov, vcov, teta, q, masse, ps)
126			vcovm1 = vcov
127			ucovm1 = ucov
128			tetam1 = teta
129			massem1 = masse
130			psm1 = ps
131			finvmaold = masse
132	guez	64	CALL filtreg(finvmaold, jjm + 1, llm, - 2, 2, .TRUE.)
133	guez	33	end if
134	guez	30
135			! Calcul des tendances dynamiques:
136	guez	55	CALL geopot((iim + 1) * (jjm + 1), teta, pk, pks, phis, phi)
137	guez	30	CALL caldyn(itau, ucov, vcov, teta, ps, masse, pk, pkf, phis, phi, &
138	guez	47	dudyn, dv, dteta, dp, w, pbaru, pbarv, time_0, &
139			conser=MOD(itau, iconser)==0)
140	guez	30
141			! Calcul des tendances advection des traceurs (dont l'humidité)
142			CALL caladvtrac(q, pbaru, pbarv, p3d, masse, dq, teta, pk)
143	guez	33
144	guez	30	! Stokage du flux de masse pour traceurs offline:
145			IF (offline) CALL fluxstokenc(pbaru, pbarv, masse, teta, phi, phis, &
146			dtvr, itau)
147
148	guez	46	! Integrations dynamique et traceurs:
149	guez	47	CALL integrd(vcovm1, ucovm1, tetam1, psm1, massem1, dv, dudyn, dteta, &
150			dp, vcov, ucov, teta, q(:, :, :, :2), ps, masse, finvmaold, dt, &
151			leapf)
152	guez	30
153	guez	33	if (.not. leapf) then
154			! Matsuno backward
155	guez	37	forall (l = 1: llm + 1) p3d(:, :, l) = ap(l) + bp(l) * ps
156	guez	33	CALL exner_hyb(ps, p3d, pks, pk, pkf)
157	guez	30
158	guez	27	! Calcul des tendances dynamiques:
159	guez	55	CALL geopot((iim + 1) * (jjm + 1), teta, pk, pks, phis, phi)
160	guez	33	CALL caldyn(itau + 1, ucov, vcov, teta, ps, masse, pk, pkf, phis, &
161	guez	47	phi, dudyn, dv, dteta, dp, w, pbaru, pbarv, time_0, &
162			conser=.false.)
163	guez	3
164			! integrations dynamique et traceurs:
165	guez	47	CALL integrd(vcovm1, ucovm1, tetam1, psm1, massem1, dv, dudyn, &
166			dteta, dp, vcov, ucov, teta, q(:, :, :, :2), ps, masse, &
167			finvmaold, dtvr, leapf=.false.)
168	guez	33	end if
169	guez	3
170	guez	33	IF (MOD(itau + 1, iphysiq) == 0 .AND. iflag_phys /= 0) THEN
171			! calcul des tendances physiques:
172	guez	3
173	guez	37	forall (l = 1: llm + 1) p3d(:, :, l) = ap(l) + bp(l) * ps
174	guez	33	CALL exner_hyb(ps, p3d, pks, pk, pkf)
175	guez	3
176	guez	33	rdaym_ini = itau * dtvr / daysec
177			rdayvrai = rdaym_ini + day_ini
178			time = REAL(mod(itau, day_step)) / day_step + time_0
179			IF (time > 1.) time = time - 1.
180	guez	3
181	guez	37	CALL calfis(rdayvrai, time, ucov, vcov, teta, q, masse, ps, pk, &
182	guez	47	phis, phi, dudyn, dv, dq, w, dufi, dvfi, dtetafi, dqfi, dpfi, &
183	guez	44	lafin=itau+1==itaufin)
184	guez	3
185	guez	33	! ajout des tendances physiques:
186			CALL addfi(nqmx, dtphys, ucov, vcov, teta, q, ps, dufi, dvfi, &
187			dtetafi, dqfi, dpfi)
188			ENDIF
189	guez	3
190	guez	37	forall (l = 1: llm + 1) p3d(:, :, l) = ap(l) + bp(l) * ps
191	guez	33	CALL exner_hyb(ps, p3d, pks, pk, pkf)
192	guez	3
193	guez	33	IF (MOD(itau + 1, idissip) == 0) THEN
194	guez	55	! Dissipation horizontale et verticale des petites échelles
195	guez	3
196	guez	55	! calcul de l'énergie cinétique avant dissipation
197	guez	33	call covcont(llm, ucov, vcov, ucont, vcont)
198			call enercin(vcov, ucov, vcont, ucont, ecin0)
199	guez	3
200	guez	33	! dissipation
201			CALL dissip(vcov, ucov, teta, p3d, dvdis, dudis, dtetadis)
202	guez	55	ucov = ucov + dudis
203			vcov = vcov + dvdis
204	guez	3
205	guez	55	! On ajoute la tendance due à la transformation énergie
206			! cinétique en énergie thermique par la dissipation
207	guez	33	call covcont(llm, ucov, vcov, ucont, vcont)
208			call enercin(vcov, ucov, vcont, ucont, ecin)
209	guez	56	dtetadis = dtetadis + (ecin0 - ecin) / pk
210	guez	55	teta = teta + dtetadis
211	guez	3
212	guez	33	! Calcul de la valeur moyenne aux pôles :
213			forall (l = 1: llm)
214			teta(:, 1, l) = SUM(aire_2d(:iim, 1) * teta(:iim, 1, l)) &
215			/ apoln
216			teta(:, jjm + 1, l) = SUM(aire_2d(:iim, jjm+1) &
217			* teta(:iim, jjm + 1, l)) / apols
218			END forall
219	guez	3
220	guez	33	ps(:, 1) = SUM(aire_2d(:iim, 1) * ps(:iim, 1)) / apoln
221			ps(:, jjm + 1) = SUM(aire_2d(:iim, jjm+1) * ps(:iim, jjm + 1)) &
222			/ apols
223			END IF
224	guez	3
225	guez	33	IF (MOD(itau + 1, iperiod) == 0) THEN
226	guez	40	! Écriture du fichier histoire moyenne:
227	guez	61	CALL writedynav(vcov, ucov, teta, pk, phi, q, masse, ps, phis, &
228			time = itau + 1)
229	guez	40	call bilan_dyn(ps, masse, pk, pbaru, pbarv, teta, phi, ucov, vcov, &
230	guez	57	q(:, :, :, 1))
231	guez	33	ENDIF
232	guez	40	end do time_integration
233	guez	3
234	guez	30	CALL dynredem1("restart.nc", vcov, ucov, teta, q, masse, ps, &
235			itau=itau_dyn+itaufin)
236
237			! Calcul des tendances dynamiques:
238	guez	55	CALL geopot((iim + 1) * (jjm + 1), teta, pk, pks, phis, phi)
239	guez	30	CALL caldyn(itaufin, ucov, vcov, teta, ps, masse, pk, pkf, phis, phi, &
240	guez	47	dudyn, dv, dteta, dp, w, pbaru, pbarv, time_0, &
241			conser=MOD(itaufin, iconser)==0)
242	guez	56
243	guez	3	END SUBROUTINE leapfrog
244
245			end module leapfrog_m