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 revision 616
    ! 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 disvert_m, ONLY: ap, bp
    USE conf_gcm_m, ONLY: day_step, iconser, iperiod, iphysiq, nday, offline, &
         iflag_phys, ok_guide, iecri
    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 fluxstokenc_m, only: fluxstokenc
    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
    use writehist_m, only: writehist

    ! 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, intent(inout):: masse(:, :, :) ! (iim + 1, jjm + 1, llm) masse d'air
    REAL, intent(in):: phis(:, :) ! (iim + 1, jjm + 1) surface geopotential

    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 filtré 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)
    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 énergie
    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".

    ! 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(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)

       CALL caladvtrac(q, pbaru, pbarv, p3d, masse, teta, pk)

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

       ! Intégrations 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(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, ps, pk, phis, phi, &
               dudyn, dv, w, dufi, dvfi, dtetafi, dqfi, dpfi, &
               lafin = itau + 1 == itaufin)

          ! Ajout des tendances physiques:
          CALL addfi(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
       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

       IF (MOD(itau + 1, iecri * day_step) == 0) THEN
          CALL geopot(teta, pk, pks, phis, phi)
          CALL writehist(itau, vcov, ucov, teta, phi, q, masse, ps)
       END IF
    end do time_integration

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

    ! Calcul des tendances dynamiques:
    CALL geopot(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	67	! From dyn3d/leapfrog.F, version 1.6, 2005/04/13 08:58:34 revision 616
10	guez	27	! 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	66	USE disvert_m, ONLY: ap, bp
21	guez	57	USE conf_gcm_m, ONLY: day_step, iconser, iperiod, iphysiq, nday, offline, &
22	guez	68	iflag_phys, ok_guide, iecri
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	69	use fluxstokenc_m, only: fluxstokenc
30	guez	43	use geopot_m, only: geopot
31	guez	26	USE guide_m, ONLY: guide
32			use inidissip_m, only: idissip
33	guez	32	use integrd_m, only: integrd
34	guez	55	use nr_util, only: assert
35	guez	26	USE pressure_var, ONLY: p3d
36	guez	28	USE temps, ONLY: itau_dyn
37	guez	56	use writedynav_m, only: writedynav
38	guez	69	use writehist_m, only: writehist
39	guez	3
40	guez	10	! Variables dynamiques:
41	guez	55	REAL, intent(inout):: ucov(:, :, :) ! (iim + 1, jjm + 1, llm) vent covariant
42			REAL, intent(inout):: vcov(:, :, :) ! (iim + 1, jjm, llm) ! vent covariant
43	guez	43
44			REAL, intent(inout):: teta(:, :, :) ! (iim + 1, jjm + 1, llm)
45			! potential temperature
46
47	guez	45	REAL, intent(inout):: ps(:, :) ! (iim + 1, jjm + 1) pression au sol, en Pa
48	guez	70	REAL, intent(inout):: masse(:, :, :) ! (iim + 1, jjm + 1, llm) masse d'air
49	guez	69	REAL, intent(in):: phis(:, :) ! (iim + 1, jjm + 1) surface geopotential
50	guez	40
51			REAL, intent(inout):: q(:, :, :, :) ! (iim + 1, jjm + 1, llm, nqmx)
52			! mass fractions of advected fields
53
54	guez	24	REAL, intent(in):: time_0
55	guez	10
56			! Variables local to the procedure:
57
58			! Variables dynamiques:
59
60	guez	70	REAL pks(iim + 1, jjm + 1) ! exner au sol
61	guez	29	REAL pk(iim + 1, jjm + 1, llm) ! exner au milieu des couches
62	guez	65	REAL pkf(iim + 1, jjm + 1, llm) ! exner filtré au milieu des couches
63	guez	47	REAL phi(iim + 1, jjm + 1, llm) ! geopotential
64	guez	55	REAL w((iim + 1) * (jjm + 1), llm) ! vitesse verticale
65	guez	3
66	guez	55	! Variables dynamiques intermediaire pour le transport
67			! Flux de masse :
68			REAL pbaru((iim + 1) * (jjm + 1), llm), pbarv((iim + 1) * jjm, llm)
69	guez	3
70	guez	56	! Variables dynamiques au pas - 1
71	guez	55	REAL vcovm1(iim + 1, jjm, llm), ucovm1(iim + 1, jjm + 1, llm)
72	guez	29	REAL tetam1(iim + 1, jjm + 1, llm), psm1(iim + 1, jjm + 1)
73	guez	67	REAL massem1(iim + 1, jjm + 1, llm)
74	guez	3
75	guez	56	! Tendances dynamiques
76	guez	88	REAL dv((iim + 1) * jjm, llm), dudyn(iim + 1, jjm + 1, llm)
77	guez	71	REAL dteta(iim + 1, jjm + 1, llm)
78	guez	55	real dp((iim + 1) * (jjm + 1))
79	guez	3
80	guez	56	! Tendances de la dissipation :
81	guez	55	REAL dvdis(iim + 1, jjm, llm), dudis(iim + 1, jjm + 1, llm)
82	guez	29	REAL dtetadis(iim + 1, jjm + 1, llm)
83	guez	3
84	guez	56	! Tendances physiques
85	guez	55	REAL dvfi((iim + 1) * jjm, llm), dufi((iim + 1) * (jjm + 1), llm)
86			REAL dtetafi(iim + 1, jjm + 1, llm), dqfi((iim + 1) * (jjm + 1), llm, nqmx)
87			real dpfi((iim + 1) * (jjm + 1))
88	guez	3
89	guez	56	! Variables pour le fichier histoire
90	guez	3
91	guez	22	INTEGER itau ! index of the time step of the dynamics, starts at 0
92	guez	27	INTEGER itaufin
93	guez	20	REAL time ! time of day, as a fraction of day length
94	guez	67	real finvmaold(iim + 1, jjm + 1, llm)
95	guez	33	INTEGER l
96	guez	3	REAL rdayvrai, rdaym_ini
97
98	guez	71	! Variables test conservation énergie
99	guez	29	REAL ecin(iim + 1, jjm + 1, llm), ecin0(iim + 1, jjm + 1, llm)
100	guez	43
101	guez	55	REAL vcont((iim + 1) * jjm, llm), ucont((iim + 1) * (jjm + 1), llm)
102	guez	33	logical leapf
103			real dt
104	guez	3
105			!---------------------------------------------------
106
107			print *, "Call sequence information: leapfrog"
108	guez	55	call assert(shape(ucov) == (/iim + 1, jjm + 1, llm/), "leapfrog")
109	guez	3
110			itaufin = nday * day_step
111	guez	62	! "day_step" is a multiple of "iperiod", therefore so is "itaufin".
112	guez	30
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	70	CALL geopot(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	guez	78	conser = MOD(itau, iconser) == 0)
140	guez	30
141	guez	71	CALL caladvtrac(q, pbaru, pbarv, p3d, masse, teta, pk)
142	guez	33
143	guez	30	! Stokage du flux de masse pour traceurs offline:
144			IF (offline) CALL fluxstokenc(pbaru, pbarv, masse, teta, phi, phis, &
145			dtvr, itau)
146
147	guez	70	! Intégrations dynamique et traceurs:
148	guez	47	CALL integrd(vcovm1, ucovm1, tetam1, psm1, massem1, dv, dudyn, dteta, &
149			dp, vcov, ucov, teta, q(:, :, :, :2), ps, masse, finvmaold, dt, &
150			leapf)
151	guez	30
152	guez	33	if (.not. leapf) then
153			! Matsuno backward
154	guez	37	forall (l = 1: llm + 1) p3d(:, :, l) = ap(l) + bp(l) * ps
155	guez	33	CALL exner_hyb(ps, p3d, pks, pk, pkf)
156	guez	30
157	guez	27	! Calcul des tendances dynamiques:
158	guez	70	CALL geopot(teta, pk, pks, phis, phi)
159	guez	33	CALL caldyn(itau + 1, ucov, vcov, teta, ps, masse, pk, pkf, phis, &
160	guez	47	phi, dudyn, dv, dteta, dp, w, pbaru, pbarv, time_0, &
161	guez	78	conser = .false.)
162	guez	3
163			! integrations dynamique et traceurs:
164	guez	47	CALL integrd(vcovm1, ucovm1, tetam1, psm1, massem1, dv, dudyn, &
165			dteta, dp, vcov, ucov, teta, q(:, :, :, :2), ps, masse, &
166			finvmaold, dtvr, leapf=.false.)
167	guez	33	end if
168	guez	3
169	guez	33	IF (MOD(itau + 1, iphysiq) == 0 .AND. iflag_phys /= 0) THEN
170	guez	69	! Calcul des tendances physiques:
171	guez	3
172	guez	37	forall (l = 1: llm + 1) p3d(:, :, l) = ap(l) + bp(l) * ps
173	guez	33	CALL exner_hyb(ps, p3d, pks, pk, pkf)
174	guez	3
175	guez	33	rdaym_ini = itau * dtvr / daysec
176			rdayvrai = rdaym_ini + day_ini
177			time = REAL(mod(itau, day_step)) / day_step + time_0
178			IF (time > 1.) time = time - 1.
179	guez	3
180	guez	71	CALL calfis(rdayvrai, time, ucov, vcov, teta, q, ps, pk, phis, phi, &
181			dudyn, dv, w, dufi, dvfi, dtetafi, dqfi, dpfi, &
182	guez	67	lafin = itau + 1 == itaufin)
183	guez	3
184	guez	69	! Ajout des tendances physiques:
185	guez	71	CALL addfi(ucov, vcov, teta, q, ps, dufi, dvfi, dtetafi, dqfi, dpfi)
186	guez	33	ENDIF
187	guez	3
188	guez	37	forall (l = 1: llm + 1) p3d(:, :, l) = ap(l) + bp(l) * ps
189	guez	33	CALL exner_hyb(ps, p3d, pks, pk, pkf)
190	guez	3
191	guez	33	IF (MOD(itau + 1, idissip) == 0) THEN
192	guez	55	! Dissipation horizontale et verticale des petites échelles
193	guez	3
194	guez	55	! calcul de l'énergie cinétique avant dissipation
195	guez	33	call covcont(llm, ucov, vcov, ucont, vcont)
196			call enercin(vcov, ucov, vcont, ucont, ecin0)
197	guez	3
198	guez	33	! dissipation
199			CALL dissip(vcov, ucov, teta, p3d, dvdis, dudis, dtetadis)
200	guez	55	ucov = ucov + dudis
201			vcov = vcov + dvdis
202	guez	3
203	guez	55	! On ajoute la tendance due à la transformation énergie
204			! cinétique en énergie thermique par la dissipation
205	guez	33	call covcont(llm, ucov, vcov, ucont, vcont)
206			call enercin(vcov, ucov, vcont, ucont, ecin)
207	guez	56	dtetadis = dtetadis + (ecin0 - ecin) / pk
208	guez	55	teta = teta + dtetadis
209	guez	3
210	guez	33	! Calcul de la valeur moyenne aux pôles :
211			forall (l = 1: llm)
212			teta(:, 1, l) = SUM(aire_2d(:iim, 1) * teta(:iim, 1, l)) &
213			/ apoln
214			teta(:, jjm + 1, l) = SUM(aire_2d(:iim, jjm+1) &
215			* teta(:iim, jjm + 1, l)) / apols
216			END forall
217			END IF
218	guez	3
219	guez	33	IF (MOD(itau + 1, iperiod) == 0) THEN
220	guez	40	! Écriture du fichier histoire moyenne:
221	guez	61	CALL writedynav(vcov, ucov, teta, pk, phi, q, masse, ps, phis, &
222			time = itau + 1)
223	guez	40	call bilan_dyn(ps, masse, pk, pbaru, pbarv, teta, phi, ucov, vcov, &
224	guez	57	q(:, :, :, 1))
225	guez	33	ENDIF
226	guez	68
227			IF (MOD(itau + 1, iecri * day_step) == 0) THEN
228	guez	70	CALL geopot(teta, pk, pks, phis, phi)
229	guez	69	CALL writehist(itau, vcov, ucov, teta, phi, q, masse, ps)
230	guez	68	END IF
231	guez	40	end do time_integration
232	guez	3
233	guez	30	CALL dynredem1("restart.nc", vcov, ucov, teta, q, masse, ps, &
234	guez	67	itau = itau_dyn + itaufin)
235	guez	30
236			! Calcul des tendances dynamiques:
237	guez	70	CALL geopot(teta, pk, pks, phis, phi)
238	guez	30	CALL caldyn(itaufin, ucov, vcov, teta, ps, masse, pk, pkf, phis, phi, &
239	guez	47	dudyn, dv, dteta, dp, w, pbaru, pbarv, time_0, &
240	guez	67	conser = MOD(itaufin, iconser) == 0)
241	guez	56
242	guez	3	END SUBROUTINE leapfrog
243
244			end module leapfrog_m