Sources/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 com_io_dyn, ONLY: histaveid
    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, &
         periodav
    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 logic, ONLY: iflag_phys, ok_guide
    USE paramet_m, ONLY: ip1jmp1
    USE pressure_var, ONLY: p3d
    USE temps, ONLY: itau_dyn

    ! Variables dynamiques:
    REAL, intent(inout):: ucov(ip1jmp1, 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(ip1jmp1, llm) ! masse d'air
    REAL phis(ip1jmp1) ! 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(ip1jmp1) ! exner au sol
    REAL pk(iim + 1, jjm + 1, llm) ! exner au milieu des couches
    REAL pkf(ip1jmp1, llm) ! exner filt.au milieu des couches
    REAL phi(iim + 1, jjm + 1, llm) ! geopotential
    REAL w(ip1jmp1, llm) ! vitesse verticale

    ! variables dynamiques intermediaire pour le transport
    REAL pbaru(ip1jmp1, llm), pbarv((iim + 1) * jjm, llm) !flux de masse

    ! variables dynamiques au pas - 1
    REAL vcovm1((iim + 1) * jjm, llm), ucovm1(ip1jmp1, llm)
    REAL tetam1(iim + 1, jjm + 1, llm), psm1(iim + 1, jjm + 1)
    REAL massem1(ip1jmp1, llm)

    ! tendances dynamiques
    REAL dv((iim + 1) * jjm, llm), dudyn(ip1jmp1, llm)
    REAL dteta(iim + 1, jjm + 1, llm), dq(ip1jmp1, llm, nqmx), dp(ip1jmp1)

    ! tendances de la dissipation
    REAL dvdis((iim + 1) * jjm, llm), dudis(ip1jmp1, llm)
    REAL dtetadis(iim + 1, jjm + 1, llm)

    ! tendances physiques
    REAL dvfi((iim + 1) * jjm, llm), dufi(ip1jmp1, llm)
    REAL dtetafi(iim + 1, jjm + 1, llm), dqfi(ip1jmp1, llm, nqmx), dpfi(ip1jmp1)

    ! 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(ip1jmp1, 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 dtetaecdt(iim + 1, jjm + 1, llm)
    ! tendance de la température potentielle due à la tansformation
    ! d'énergie cinétique en énergie thermique créée par la dissipation

    REAL vcont((iim + 1) * jjm, llm), ucont(ip1jmp1, llm)
    logical leapf
    real dt

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

    print *, "Call sequence information: leapfrog"

    itaufin = nday * day_step
    ! "day_step" is a multiple of "iperiod", therefore "itaufin" is one too

    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., 1)
       end if

       ! Calcul des tendances dynamiques:
       CALL geopot(ip1jmp1, 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(ip1jmp1, 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 echelles:

          ! calcul de l'energie cinetique 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 rajoute la tendance due à la transformation Ec -> E
          ! thermique créée lors de la dissipation
          call covcont(llm, ucov, vcov, ucont, vcont)
          call enercin(vcov, ucov, vcont, ucont, ecin)
          dtetaecdt= (ecin0 - ecin) / pk
          dtetadis=dtetadis + dtetaecdt
          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(histaveid, nqmx, itau + 1, vcov, ucov, teta, pk, &
               phi, q, masse, ps, phis)
          call bilan_dyn(ps, masse, pk, pbaru, pbarv, teta, phi, ucov, vcov, &
               q(:, :, :, 1), dt_app = dtvr * iperiod, &
               dt_cum = dtvr * day_step * periodav)
       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(ip1jmp1, 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 com_io_dyn, ONLY: histaveid
19			USE comconst, ONLY: daysec, dtphys, dtvr
20	guez	29	USE comgeom, ONLY: aire_2d, apoln, apols
21	guez	26	USE comvert, ONLY: ap, bp
22	guez	27	USE conf_gcm_m, ONLY: day_step, iconser, iperiod, iphysiq, nday, offline, &
23			periodav
24	guez	29	USE dimens_m, ONLY: iim, jjm, llm, nqmx
25	guez	47	use dissip_m, only: dissip
26	guez	26	USE dynetat0_m, ONLY: day_ini
27	guez	27	use dynredem1_m, only: dynredem1
28	guez	26	USE exner_hyb_m, ONLY: exner_hyb
29	guez	27	use filtreg_m, only: filtreg
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	26	USE logic, ONLY: iflag_phys, ok_guide
35	guez	29	USE paramet_m, ONLY: ip1jmp1
36	guez	26	USE pressure_var, ONLY: p3d
37	guez	28	USE temps, ONLY: itau_dyn
38	guez	3
39	guez	10	! Variables dynamiques:
40	guez	36	REAL, intent(inout):: ucov(ip1jmp1, llm) ! vent covariant
41	guez	32	REAL, intent(inout):: vcov((iim + 1) * jjm, llm) ! vent covariant
42	guez	43
43			REAL, intent(inout):: teta(:, :, :) ! (iim + 1, jjm + 1, llm)
44			! potential temperature
45
46	guez	45	REAL, intent(inout):: ps(:, :) ! (iim + 1, jjm + 1) pression au sol, en Pa
47	guez	10	REAL masse(ip1jmp1, llm) ! masse d'air
48			REAL phis(ip1jmp1) ! geopotentiel au sol
49	guez	40
50			REAL, intent(inout):: q(:, :, :, :) ! (iim + 1, jjm + 1, llm, nqmx)
51			! mass fractions of advected fields
52
53	guez	24	REAL, intent(in):: time_0
54	guez	10
55			! Variables local to the procedure:
56
57			! Variables dynamiques:
58
59	guez	3	REAL pks(ip1jmp1) ! exner au sol
60	guez	29	REAL pk(iim + 1, jjm + 1, llm) ! exner au milieu des couches
61	guez	3	REAL pkf(ip1jmp1, llm) ! exner filt.au milieu des couches
62	guez	47	REAL phi(iim + 1, jjm + 1, llm) ! geopotential
63	guez	3	REAL w(ip1jmp1, llm) ! vitesse verticale
64
65			! variables dynamiques intermediaire pour le transport
66	guez	29	REAL pbaru(ip1jmp1, llm), pbarv((iim + 1) * jjm, llm) !flux de masse
67	guez	3
68			! variables dynamiques au pas - 1
69	guez	29	REAL vcovm1((iim + 1) * jjm, llm), ucovm1(ip1jmp1, llm)
70			REAL tetam1(iim + 1, jjm + 1, llm), psm1(iim + 1, jjm + 1)
71	guez	3	REAL massem1(ip1jmp1, llm)
72
73			! tendances dynamiques
74	guez	47	REAL dv((iim + 1) * jjm, llm), dudyn(ip1jmp1, llm)
75	guez	44	REAL dteta(iim + 1, jjm + 1, llm), dq(ip1jmp1, llm, nqmx), dp(ip1jmp1)
76	guez	3
77			! tendances de la dissipation
78	guez	29	REAL dvdis((iim + 1) * jjm, llm), dudis(ip1jmp1, llm)
79			REAL dtetadis(iim + 1, jjm + 1, llm)
80	guez	3
81			! tendances physiques
82	guez	29	REAL dvfi((iim + 1) * jjm, llm), dufi(ip1jmp1, llm)
83	guez	44	REAL dtetafi(iim + 1, jjm + 1, llm), dqfi(ip1jmp1, llm, nqmx), dpfi(ip1jmp1)
84	guez	3
85			! variables pour le fichier histoire
86
87	guez	22	INTEGER itau ! index of the time step of the dynamics, starts at 0
88	guez	27	INTEGER itaufin
89	guez	20	REAL time ! time of day, as a fraction of day length
90	guez	10	real finvmaold(ip1jmp1, llm)
91	guez	33	INTEGER l
92	guez	3	REAL rdayvrai, rdaym_ini
93
94	guez	24	! Variables test conservation energie
95	guez	29	REAL ecin(iim + 1, jjm + 1, llm), ecin0(iim + 1, jjm + 1, llm)
96	guez	43
97	guez	29	REAL dtetaecdt(iim + 1, jjm + 1, llm)
98	guez	43	! tendance de la température potentielle due à la tansformation
99			! d'énergie cinétique en énergie thermique créée par la dissipation
100
101	guez	29	REAL vcont((iim + 1) * jjm, llm), ucont(ip1jmp1, llm)
102	guez	33	logical leapf
103			real dt
104	guez	3
105			!---------------------------------------------------
106
107			print *, "Call sequence information: leapfrog"
108
109			itaufin = nday * day_step
110	guez	30	! "day_step" is a multiple of "iperiod", therefore "itaufin" is one too
111
112	guez	24	dq = 0.
113	guez	33
114	guez	3	! On initialise la pression et la fonction d'Exner :
115	guez	37	forall (l = 1: llm + 1) p3d(:, :, l) = ap(l) + bp(l) * ps
116	guez	10	CALL exner_hyb(ps, p3d, pks, pk, pkf)
117	guez	3
118	guez	40	time_integration: do itau = 0, itaufin - 1
119	guez	33	leapf = mod(itau, iperiod) /= 0
120			if (leapf) then
121			dt = 2 * dtvr
122			else
123			! Matsuno
124			dt = dtvr
125			if (ok_guide .and. (itaufin - itau - 1) * dtvr > 21600.) &
126			call guide(itau, ucov, vcov, teta, q, masse, ps)
127			vcovm1 = vcov
128			ucovm1 = ucov
129			tetam1 = teta
130			massem1 = masse
131			psm1 = ps
132			finvmaold = masse
133			CALL filtreg(finvmaold, jjm + 1, llm, - 2, 2, .TRUE., 1)
134			end if
135	guez	30
136			! Calcul des tendances dynamiques:
137			CALL geopot(ip1jmp1, teta, pk, pks, phis, phi)
138			CALL caldyn(itau, ucov, vcov, teta, ps, masse, pk, pkf, phis, phi, &
139	guez	47	dudyn, dv, dteta, dp, w, pbaru, pbarv, time_0, &
140			conser=MOD(itau, iconser)==0)
141	guez	30
142			! Calcul des tendances advection des traceurs (dont l'humidité)
143			CALL caladvtrac(q, pbaru, pbarv, p3d, masse, dq, teta, pk)
144	guez	33
145	guez	30	! Stokage du flux de masse pour traceurs offline:
146			IF (offline) CALL fluxstokenc(pbaru, pbarv, masse, teta, phi, phis, &
147			dtvr, itau)
148
149	guez	46	! Integrations dynamique et traceurs:
150	guez	47	CALL integrd(vcovm1, ucovm1, tetam1, psm1, massem1, dv, dudyn, dteta, &
151			dp, vcov, ucov, teta, q(:, :, :, :2), ps, masse, finvmaold, dt, &
152			leapf)
153	guez	30
154	guez	33	if (.not. leapf) then
155			! Matsuno backward
156	guez	37	forall (l = 1: llm + 1) p3d(:, :, l) = ap(l) + bp(l) * ps
157	guez	33	CALL exner_hyb(ps, p3d, pks, pk, pkf)
158	guez	30
159	guez	27	! Calcul des tendances dynamiques:
160	guez	3	CALL geopot(ip1jmp1, teta, pk, pks, phis, phi)
161	guez	33	CALL caldyn(itau + 1, ucov, vcov, teta, ps, masse, pk, pkf, phis, &
162	guez	47	phi, dudyn, dv, dteta, dp, w, pbaru, pbarv, time_0, &
163			conser=.false.)
164	guez	3
165			! integrations dynamique et traceurs:
166	guez	47	CALL integrd(vcovm1, ucovm1, tetam1, psm1, massem1, dv, dudyn, &
167			dteta, dp, vcov, ucov, teta, q(:, :, :, :2), ps, masse, &
168			finvmaold, dtvr, leapf=.false.)
169	guez	33	end if
170	guez	3
171	guez	33	IF (MOD(itau + 1, iphysiq) == 0 .AND. iflag_phys /= 0) THEN
172			! calcul des tendances physiques:
173	guez	3
174	guez	37	forall (l = 1: llm + 1) p3d(:, :, l) = ap(l) + bp(l) * ps
175	guez	33	CALL exner_hyb(ps, p3d, pks, pk, pkf)
176	guez	3
177	guez	33	rdaym_ini = itau * dtvr / daysec
178			rdayvrai = rdaym_ini + day_ini
179			time = REAL(mod(itau, day_step)) / day_step + time_0
180			IF (time > 1.) time = time - 1.
181	guez	3
182	guez	37	CALL calfis(rdayvrai, time, ucov, vcov, teta, q, masse, ps, pk, &
183	guez	47	phis, phi, dudyn, dv, dq, w, dufi, dvfi, dtetafi, dqfi, dpfi, &
184	guez	44	lafin=itau+1==itaufin)
185	guez	3
186	guez	33	! ajout des tendances physiques:
187			CALL addfi(nqmx, dtphys, ucov, vcov, teta, q, ps, dufi, dvfi, &
188			dtetafi, dqfi, dpfi)
189			ENDIF
190	guez	3
191	guez	37	forall (l = 1: llm + 1) p3d(:, :, l) = ap(l) + bp(l) * ps
192	guez	33	CALL exner_hyb(ps, p3d, pks, pk, pkf)
193	guez	3
194	guez	33	IF (MOD(itau + 1, idissip) == 0) THEN
195			! dissipation horizontale et verticale des petites echelles:
196	guez	3
197	guez	33	! calcul de l'energie cinetique avant dissipation
198			call covcont(llm, ucov, vcov, ucont, vcont)
199			call enercin(vcov, ucov, vcont, ucont, ecin0)
200	guez	3
201	guez	33	! dissipation
202			CALL dissip(vcov, ucov, teta, p3d, dvdis, dudis, dtetadis)
203			ucov=ucov + dudis
204			vcov=vcov + dvdis
205	guez	3
206	guez	33	! On rajoute la tendance due à la transformation Ec -> E
207			! thermique créée lors de la dissipation
208			call covcont(llm, ucov, vcov, ucont, vcont)
209			call enercin(vcov, ucov, vcont, ucont, ecin)
210			dtetaecdt= (ecin0 - ecin) / pk
211			dtetadis=dtetadis + dtetaecdt
212			teta=teta + dtetadis
213	guez	3
214	guez	33	! Calcul de la valeur moyenne aux pôles :
215			forall (l = 1: llm)
216			teta(:, 1, l) = SUM(aire_2d(:iim, 1) * teta(:iim, 1, l)) &
217			/ apoln
218			teta(:, jjm + 1, l) = SUM(aire_2d(:iim, jjm+1) &
219			* teta(:iim, jjm + 1, l)) / apols
220			END forall
221	guez	3
222	guez	33	ps(:, 1) = SUM(aire_2d(:iim, 1) * ps(:iim, 1)) / apoln
223			ps(:, jjm + 1) = SUM(aire_2d(:iim, jjm+1) * ps(:iim, jjm + 1)) &
224			/ apols
225			END IF
226	guez	3
227	guez	33	IF (MOD(itau + 1, iperiod) == 0) THEN
228	guez	40	! Écriture du fichier histoire moyenne:
229	guez	33	CALL writedynav(histaveid, nqmx, itau + 1, vcov, ucov, teta, pk, &
230			phi, q, masse, ps, phis)
231	guez	40	call bilan_dyn(ps, masse, pk, pbaru, pbarv, teta, phi, ucov, vcov, &
232			q(:, :, :, 1), dt_app = dtvr * iperiod, &
233			dt_cum = dtvr * day_step * periodav)
234	guez	33	ENDIF
235	guez	40	end do time_integration
236	guez	3
237	guez	30	CALL dynredem1("restart.nc", vcov, ucov, teta, q, masse, ps, &
238			itau=itau_dyn+itaufin)
239
240			! Calcul des tendances dynamiques:
241			CALL geopot(ip1jmp1, teta, pk, pks, phis, phi)
242			CALL caldyn(itaufin, ucov, vcov, teta, ps, masse, pk, pkf, phis, phi, &
243	guez	47	dudyn, dv, dteta, dp, w, pbaru, pbarv, time_0, &
244			conser=MOD(itaufin, iconser)==0)
245	guez	3	END SUBROUTINE leapfrog
246
247			end module leapfrog_m