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callsedim_mod.F @ 2214

Last change on this file since 2214 was 2199, checked in by mvals, 6 years ago
Mars GCM: Implementation of a new parametrization of the dust entrainment by slope winds above the sub-grid scale topography. The parametrization is activated with the flag slpwind=.true. (set to "false" by default) in callphys.def. The new parametrization involves the new tracers topdust_mass and topdust_number. MV
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1	MODULE callsedim_mod
2
3	IMPLICIT NONE
4
5	CONTAINS
6
7	SUBROUTINE callsedim(ngrid,nlay,ptimestep,
8	& pplev,zlev,zlay,pt,pdt,
9	& rdust,rstormdust,rtopdust,
10	& rice,rsedcloud,rhocloud,
11	& pq,pdqfi,pdqsed,pdqs_sed,nq,
12	& tau,tauscaling)
13
14	USE ioipsl_getincom, only: getin
15	USE updaterad, only: updaterdust,updaterice_micro,updaterice_typ
16	USE tracer_mod, only: noms, igcm_dust_mass, igcm_dust_number,
17	& rho_dust, rho_q, radius, varian,
18	& igcm_ccn_mass, igcm_ccn_number,
19	& igcm_h2o_ice, nuice_sed, nuice_ref,
20	& igcm_ccnco2_mass,igcm_ccnco2_number,
21	& igcm_co2_ice, igcm_stormdust_mass,
22	& igcm_stormdust_number,igcm_topdust_mass,
23	& igcm_topdust_number
24	USE newsedim_mod, ONLY: newsedim
25	USE comcstfi_h, ONLY: g
26	USE dimradmars_mod, only: naerkind
27	IMPLICIT NONE
28
29	c=======================================================================
30	c Sedimentation of the Martian aerosols
31	c depending on their density and radius
32	c
33	c F.Forget 1999
34	c
35	c Modified by J.-B. Madeleine 2010: Now includes the doubleq
36	c technique in order to have only one call to callsedim in
37	c physiq.F.
38	c
39	c Modified by J. Audouard 09/16: Now includes the co2clouds case
40	c If the co2 microphysics is on, then co2 theice & ccn tracers
41	c are being sedimented in the microtimestep (co2cloud.F), not
42	c in this routine.
43	c
44	c=======================================================================
45
46	c-----------------------------------------------------------------------
47	c declarations:
48	c -------------
49
50	include "callkeys.h"
51
52	c
53	c arguments:
54	c ----------
55
56	integer,intent(in) :: ngrid ! number of horizontal grid points
57	integer,intent(in) :: nlay ! number of atmospheric layers
58	real,intent(in) :: ptimestep ! physics time step (s)
59	real,intent(in) :: pplev(ngrid,nlay+1) ! pressure at inter-layers (Pa)
60	real,intent(in) :: zlev(ngrid,nlay+1) ! altitude at layer boundaries
61	real,intent(in) :: zlay(ngrid,nlay) ! altitude at the middle of the layers
62	real,intent(in) :: pt(ngrid,nlay) ! temperature at mid-layer (K)
63	real,intent(in) :: pdt(ngrid,nlay) ! tendency on temperature, from
64	! previous processes (K/s)
65	c Aerosol radius provided by the water ice microphysical scheme:
66	real,intent(out) :: rdust(ngrid,nlay) ! Dust geometric mean radius (m)
67	real,intent(out) :: rstormdust(ngrid,nlay) ! Stormdust geometric mean radius (m)
68	real,intent(out) :: rtopdust(ngrid,nlay) ! topdust geometric mean radius (m)
69	real,intent(out) :: rice(ngrid,nlay) ! H2O Ice geometric mean radius (m)
70	c Sedimentation radius of water ice
71	real,intent(in) :: rsedcloud(ngrid,nlay)
72	c Cloud density (kg.m-3)
73	real,intent(inout) :: rhocloud(ngrid,nlay)
74	c Traceurs :
75	real,intent(in) :: pq(ngrid,nlay,nq) ! tracers (kg/kg)
76	real,intent(in) :: pdqfi(ngrid,nlay,nq) ! tendency before sedimentation (kg/kg.s-1)
77	real,intent(out) :: pdqsed(ngrid,nlay,nq) ! tendency due to sedimentation (kg/kg.s-1)
78	real,intent(out) :: pdqs_sed(ngrid,nq) ! flux at surface (kg.m-2.s-1)
79	integer,intent(in) :: nq ! number of tracers
80	real,intent(in) :: tau(ngrid,naerkind) ! dust opacity
81	real,intent(in) :: tauscaling(ngrid)
82
83	c local:
84	c ------
85
86	INTEGER l,ig, iq
87
88	real zqi(ngrid,nlay,nq) ! to locally store tracers
89	real zt(ngrid,nlay) ! to locally store temperature
90	real masse (ngrid,nlay) ! Layer mass (kg.m-2)
91	real epaisseur (ngrid,nlay) ! Layer thickness (m)
92	real wq(ngrid,nlay+1) ! displaced tracer mass (kg.m-2)
93	real r0(ngrid,nlay) ! geometric mean radius used for
94	! sedimentation (m)
95	real r0dust(ngrid,nlay) ! geometric mean radius used for
96	! dust (m)
97	real r0stormdust(ngrid,nlay) ! Geometric mean radius used for stormdust (m)
98	! ! CCNs (m)
99	real r0topdust(ngrid,nlay) ! Geometric mean radius used for topdust (m)
100	! ! CCNs (m)
101	real,save :: beta ! correction for the shape of the ice particles (cf. newsedim)
102	c for ice radius computation
103	REAL Mo,No
104	REAl ccntyp
105
106
107
108	c Discrete size distributions (doubleq)
109	c ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
110	c 1) Parameters used to represent the changes in fall
111	c velocity as a function of particle size;
112	integer ir
113	integer,parameter :: nr=12 !(nr=7) ! number of bins
114	real,save :: rd(nr)
115	real qr(ngrid,nlay,nr)
116	real,save :: rdi(nr+1) ! extreme and intermediate radii
117	real Sq(ngrid,nlay)
118	real,parameter :: rdmin=1.e-8
119	real,parameter :: rdmax=30.e-6
120	real,parameter :: rdimin=1.e-8 ! 1.e-7
121	real,parameter :: rdimax=1.e-4
122
123	c 2) Second size distribution for the log-normal integration
124	c (the mass mixing ratio is computed for each radius)
125
126	integer iint
127	integer,parameter :: ninter=4 ! number of points between each rdi radii
128	real,save :: rr(ninter,nr)
129	integer radpower
130	real sigma0
131
132	c 3) Other local variables used in doubleq
133
134	INTEGER,SAVE :: idust_mass ! index of tracer containing dust mass
135	! mix. ratio
136	INTEGER,SAVE :: idust_number ! index of tracer containing dust number
137	! mix. ratio
138	INTEGER,SAVE :: iccn_mass ! index of tracer containing CCN mass
139	! mix. ratio
140	INTEGER,SAVE :: iccn_number ! index of tracer containing CCN number
141	! mix. ratio
142	INTEGER,SAVE :: istormdust_mass ! index of tracer containing
143	!stormdust mass mix. ratio
144	INTEGER,SAVE :: istormdust_number ! index of tracer containing
145	!stormdust number mix. ratio
146	INTEGER,SAVE :: itopdust_mass ! index of tracer containing
147	!topdust mass mix. ratio
148	INTEGER,SAVE :: itopdust_number ! index of tracer containing
149	!topdust number mix. ratio
150	INTEGER,SAVE :: iccnco2_number ! index of tracer containing CCN number
151	INTEGER,SAVE :: iccnco2_mass ! index of tracer containing CCN number
152	INTEGER,SAVE :: ico2_ice ! index of tracer containing CCN number
153
154
155	LOGICAL,SAVE :: firstcall=.true.
156
157
158
159	c ** un petit test de coherence
160	c --------------------------
161	! AS: firstcall OK absolute
162	IF (firstcall) THEN
163
164	c Doubleq: initialization
165	IF (doubleq) THEN
166	do ir=1,nr
167	rd(ir)= rdmin(rdmax/rdmin)*(float(ir-1)/float(nr-1))
168	end do
169	rdi(1)=rdimin
170	do ir=2,nr
171	rdi(ir)= sqrt(rd(ir-1)*rd(ir))
172	end do
173	rdi(nr+1)=rdimax
174
175	do ir=1,nr
176	do iint=1,ninter
177	rr(iint,ir)=
178	& rdi(ir)*
179	& (rdi(ir+1)/rdi(ir))**(float(iint-1)/float(ninter-1))
180	c write(,) rr(iint,ir)
181	end do
182	end do
183
184	! identify tracers corresponding to mass mixing ratio and
185	! number mixing ratio
186	idust_mass=0 ! dummy initialization
187	idust_number=0 ! dummy initialization
188
189	do iq=1,nq
190	if (noms(iq).eq."dust_mass") then
191	idust_mass=iq
192	write(,)"callsedim: idust_mass=",idust_mass
193	endif
194	if (noms(iq).eq."dust_number") then
195	idust_number=iq
196	write(,)"callsedim: idust_number=",idust_number
197	endif
198	enddo
199
200	! check that we did find the tracers
201	if ((idust_mass.eq.0).or.(idust_number.eq.0)) then
202	write(,) 'callsedim: error! could not identify'
203	write(,) ' tracers for dust mass and number mixing'
204	write(,) ' ratio and doubleq is activated!'
205	stop
206	endif
207	ENDIF !of if (doubleq)
208
209	IF (microphys) THEN
210	iccn_mass=0
211	iccn_number=0
212	do iq=1,nq
213	if (noms(iq).eq."ccn_mass") then
214	iccn_mass=iq
215	write(,)"callsedim: iccn_mass=",iccn_mass
216	endif
217	if (noms(iq).eq."ccn_number") then
218	iccn_number=iq
219	write(,)"callsedim: iccn_number=",iccn_number
220	endif
221	enddo
222	! check that we did find the tracers
223	if ((iccn_mass.eq.0).or.(iccn_number.eq.0)) then
224	write(,) 'callsedim: error! could not identify'
225	write(,) ' tracers for ccn mass and number mixing'
226	write(,) ' ratio and microphys is activated!'
227	stop
228	endif
229	ENDIF !of if (microphys)
230
231	IF (co2clouds) THEN
232	iccnco2_mass=0
233	iccnco2_number=0
234	ico2_ice=0
235	do iq=1,nq
236	if (noms(iq).eq."ccnco2_mass") then
237	iccnco2_mass=iq
238	write(,)"callsedim: iccnco2_mass=",iccnco2_mass
239	endif
240	if (noms(iq).eq."co2_ice") then
241	ico2_ice=iq
242	write(,)"callsedim: ico2_ice=",ico2_ice
243	endif
244	if (noms(iq).eq."ccnco2_number") then
245	iccnco2_number=iq
246	write(,)"callsedim: iccnco2_number=",iccnco2_number
247	endif
248	enddo
249	! check that we did find the tracers
250	if ((iccnco2_mass.eq.0).or.(iccnco2_number.eq.0)) then
251	write(,) 'callsedim: error! could not identify'
252	write(,) ' tracers for ccn co2 mass and number mixing'
253	write(,) ' ratio and co2clouds are activated!'
254	stop
255	endif
256	ENDIF !of if (co2clouds)
257
258	IF (water) THEN
259	write(,) "correction for the shape of the ice particles ?"
260	beta=0.75 ! default value
261	call getin("ice_shape",beta)
262	write(,) " ice_shape = ",beta
263
264	write(,) "water_param nueff Sedimentation:", nuice_sed
265	IF (activice) THEN
266	write(,) "water_param nueff Radiative:", nuice_ref
267	ENDIF
268	ENDIF
269
270	IF (rdstorm) THEN ! identifying stormdust tracers for sedimentation
271	istormdust_mass=0 ! dummy initialization
272	istormdust_number=0 ! dummy initialization
273
274	do iq=1,nq
275	if (noms(iq).eq."stormdust_mass") then
276	istormdust_mass=iq
277	write(,)"callsedim: istormdust_mass=",istormdust_mass
278	endif
279	if (noms(iq).eq."stormdust_number") then
280	istormdust_number=iq
281	write(,)"callsedim: istormdust_number=",
282	& istormdust_number
283	endif
284	enddo
285
286	! check that we did find the tracers
287	if ((istormdust_mass.eq.0).or.(istormdust_number.eq.0)) then
288	write(,) 'callsedim: error! could not identify'
289	write(,) ' tracers for stormdust mass and number mixing'
290	write(,) ' ratio and rdstorm is activated!'
291	stop
292	endif
293	ENDIF !of if (rdstorm)
294
295	IF (slpwind) THEN ! identifying topdust tracers for sedimentation
296	itopdust_mass=0 ! dummy initialization
297	itopdust_number=0 ! dummy initialization
298
299	do iq=1,nq
300	if (noms(iq).eq."topdust_mass") then
301	itopdust_mass=iq
302	write(,)"callsedim: itopdust_mass=",itopdust_mass
303	endif
304	if (noms(iq).eq."topdust_number") then
305	itopdust_number=iq
306	write(,)"callsedim: itopdust_number=",
307	& itopdust_number
308	endif
309	enddo
310
311	! check that we did find the tracers
312	if ((itopdust_mass.eq.0).or.(itopdust_number.eq.0)) then
313	write(,) 'callsedim: error! could not identify'
314	write(,) ' tracers for topdust mass and number mixing'
315	write(,) ' ratio and slpwind is activated!'
316	stop
317	endif
318	ENDIF !of if (slpwind)
319
320	firstcall=.false.
321	ENDIF ! of IF (firstcall)
322
323	c-----------------------------------------------------------------------
324	c 1. Initialization
325	c -----------------
326
327	! zqi(1:ngrid,1:nlay,1:nqmx) = 0.
328	c Update the mass mixing ratio and temperature with the tendencies coming
329	c from other parameterizations:
330	c ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
331	zqi(1:ngrid,1:nlay,1:nq)=pq(1:ngrid,1:nlay,1:nq)
332	& +pdqfi(1:ngrid,1:nlay,1:nq)*ptimestep
333	zt(1:ngrid,1:nlay)=pt(1:ngrid,1:nlay)
334	& +pdt(1:ngrid,1:nlay)*ptimestep
335
336	c Computing the different layer properties
337	c ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
338	c Mass (kg.m-2), thickness(m), crossing time (s) etc.
339
340	do l=1,nlay
341	do ig=1, ngrid
342	masse(ig,l)=(pplev(ig,l) - pplev(ig,l+1)) /g
343	epaisseur(ig,l)= zlev(ig,l+1) - zlev(ig,l)
344	end do
345	end do
346
347	c =================================================================
348	c Compute the geometric mean radius used for sedimentation
349
350	if (doubleq) then
351	do l=1,nlay
352	do ig=1, ngrid
353
354	call updaterdust(zqi(ig,l,igcm_dust_mass),
355	& zqi(ig,l,igcm_dust_number),r0dust(ig,l),
356	& tauscaling(ig))
357
358	end do
359	end do
360	endif
361	c rocket dust storm
362	if (rdstorm) then
363	do l=1,nlay
364	do ig=1, ngrid
365
366	call updaterdust(zqi(ig,l,igcm_stormdust_mass),
367	& zqi(ig,l,igcm_stormdust_number),r0stormdust(ig,l),
368	& tauscaling(ig))
369
370	end do
371	end do
372	endif
373	c entrainment by slope wind
374	if (slpwind) then
375	do l=1,nlay
376	do ig=1, ngrid
377
378	call updaterdust(zqi(ig,l,igcm_topdust_mass),
379	& zqi(ig,l,igcm_topdust_number),r0topdust(ig,l),
380	& tauscaling(ig))
381
382	end do
383	end do
384	endif
385	c =================================================================
386	do iq=1,nq
387	if(radius(iq).gt.1.e-9 .and.(iq.ne.ico2_ice) .and.
388	& (iq .ne. iccnco2_mass) .and. (iq .ne.
389	& iccnco2_number)) then ! no sedim for gaz or CO2 clouds (done in microtimestep)
390
391	c -----------------------------------------------------------------
392	c DOUBLEQ CASE
393	c -----------------------------------------------------------------
394	if ( doubleq.and.
395	& ((iq.eq.idust_mass).or.(iq.eq.idust_number).or.
396	& (iq.eq.istormdust_mass).or.(iq.eq.istormdust_number).or.
397	& (iq.eq.itopdust_mass).or.(iq.eq.itopdust_number)) ) then
398
399	c Computing size distribution:
400	c ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
401
402	if ((iq.eq.idust_mass).or.(iq.eq.idust_number)) then
403	do l=1,nlay
404	do ig=1, ngrid
405	r0(ig,l)=r0dust(ig,l)
406	end do
407	end do
408	else if ((iq.eq.istormdust_mass).or.
409	& (iq.eq.istormdust_number)) then
410	do l=1,nlay
411	do ig=1, ngrid
412	r0(ig,l)=r0stormdust(ig,l)
413	end do
414	end do
415	else if ((iq.eq.itopdust_mass).or.
416	& (iq.eq.itopdust_number)) then
417	do l=1,nlay
418	do ig=1, ngrid
419	r0(ig,l)=r0topdust(ig,l)
420	end do
421	end do
422	endif
423	sigma0 = varian
424
425	c Computing mass mixing ratio for each particle size
426	c ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
427	IF ((iq.EQ.idust_mass).or.(iq.EQ.istormdust_mass)
428	& .or.(iq.EQ.itopdust_mass)) then
429	radpower = 2
430	ELSE ! number
431	radpower = -1
432	ENDIF
433	Sq(1:ngrid,1:nlay) = 0.
434	do ir=1,nr
435	do l=1,nlay
436	do ig=1,ngrid
437	c ****************
438	c Size distribution integration
439	c (Trapezoid Integration Method)
440	qr(ig,l,ir)=0.5(rr(2,ir)-rr(1,ir))
441	& (rr(1,ir)*radpower)
442	& exp(-(log(rr(1,ir)/r0(ig,l)))*2/(2sigma0**2))
443	do iint=2,ninter-1
444	qr(ig,l,ir)=qr(ig,l,ir) +
445	& 0.5(rr(iint+1,ir)-rr(iint-1,ir))
446	& (rr(iint,ir)*radpower)
447	& exp(-(log(rr(iint,ir)/r0(ig,l)))**2/
448	& (2sigma0*2))
449	end do
450	qr(ig,l,ir)=qr(ig,l,ir) +
451	& 0.5(rr(ninter,ir)-rr(ninter-1,ir))
452	& (rr(ninter,ir)*radpower)
453	& exp(-(log(rr(ninter,ir)/r0(ig,l)))**2/
454	& (2sigma0*2))
455
456	c **************** old method (not recommended!)
457	c qr(ig,l,ir)=(rd(ir)*(5-3iq))*
458	c & exp( -(log(rd(ir)/r0(ig,l)))*2 / (2sigma0**2) )
459	c ******************************
460
461	Sq(ig,l)=Sq(ig,l)+qr(ig,l,ir)
462	enddo
463	enddo
464	enddo
465
466	do ir=1,nr
467	do l=1,nlay
468	do ig=1,ngrid
469	qr(ig,l,ir) = zqi(ig,l,iq)*qr(ig,l,ir)/Sq(ig,l)
470	enddo
471	enddo
472	enddo
473
474	c Computing sedimentation for each tracer
475	c ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
476
477	zqi(1:ngrid,1:nlay,iq) = 0.
478	pdqs_sed(1:ngrid,iq) = 0.
479
480	do ir=1,nr
481	call newsedim(ngrid,nlay,1,1,ptimestep,
482	& pplev,masse,epaisseur,zt,rd(ir),(/rho_dust/),qr(1,1,ir),
483	& wq,0.5)
484
485	c Tendencies
486	c ~~~~~~~~~~
487	do ig=1,ngrid
488	pdqs_sed(ig,iq) = pdqs_sed(ig,iq)
489	& + wq(ig,1)/ptimestep
490	end do
491	DO l = 1, nlay
492	DO ig=1,ngrid
493	zqi(ig,l,iq)=zqi(ig,l,iq)+qr(ig,l,ir)
494	ENDDO
495	ENDDO
496	enddo ! of do ir=1,nr
497	c -----------------------------------------------------------------
498	c WATER CYCLE CASE
499	c -----------------------------------------------------------------
500	else if ((iq .eq. iccn_mass) .or. (iq .eq. iccn_number)
501	& .or. (iq .eq. igcm_h2o_ice)) then
502	if (microphys) then
503	! water ice sedimentation
504	call newsedim(ngrid,nlay,ngridnlay,ngridnlay,
505	& ptimestep,pplev,masse,epaisseur,zt,rsedcloud,rhocloud,
506	& zqi(1,1,iq),wq,beta)
507	else
508	! water ice sedimentation
509	call newsedim(ngrid,nlay,ngrid*nlay,1,
510	& ptimestep,pplev,masse,epaisseur,zt,rsedcloud,rho_q(iq),
511	& zqi(1,1,iq),wq,beta)
512	endif ! of if (microphys)
513	c Tendencies
514	c ~~~~~~~~~~
515	do ig=1,ngrid
516	pdqs_sed(ig,iq)=wq(ig,1)/ptimestep
517	end do
518	c -----------------------------------------------------------------
519	c GENERAL CASE
520	c -----------------------------------------------------------------
521	else
522	call newsedim(ngrid,nlay,1,1,ptimestep,
523	& pplev,masse,epaisseur,zt,radius(iq),rho_q(iq),
524	& zqi(1,1,iq),wq,1.0)
525	c Tendencies
526	c ~~~~~~~~~~
527	do ig=1,ngrid
528	pdqs_sed(ig,iq)=wq(ig,1)/ptimestep
529	end do
530	endif ! of if doubleq and if water
531	c -----------------------------------------------------------------
532
533	c Compute the final tendency:
534	c ---------------------------
535	DO l = 1, nlay
536	DO ig=1,ngrid
537	pdqsed(ig,l,iq)=(zqi(ig,l,iq)-
538	$ (pq(ig,l,iq) + pdqfi(ig,l,iq)*ptimestep))/ptimestep
539	ENDDO
540	ENDDO
541
542	endif ! of if(radius(iq).gt.1.e-9)
543	c =================================================================
544	enddo ! of do iq=1,nq
545
546	c Update the dust particle size "rdust"
547	c -------------------------------------
548	if (doubleq) then
549	DO l = 1, nlay
550	DO ig=1,ngrid
551
552
553	call updaterdust(zqi(ig,l,igcm_dust_mass),
554	& zqi(ig,l,igcm_dust_number),rdust(ig,l),
555	& tauscaling(ig))
556
557
558	ENDDO
559	ENDDO
560	endif ! of if (doubleq)
561
562	if (rdstorm) then
563	DO l = 1, nlay
564	DO ig=1,ngrid
565	call updaterdust(zqi(ig,l,igcm_stormdust_mass),
566	& zqi(ig,l,igcm_stormdust_number),rstormdust(ig,l),
567	& tauscaling(ig))
568	ENDDO
569	ENDDO
570	endif ! of if (rdstorm)
571
572	if (slpwind) then
573	DO l = 1, nlay
574	DO ig=1,ngrid
575	call updaterdust(zqi(ig,l,igcm_topdust_mass),
576	& zqi(ig,l,igcm_topdust_number),rtopdust(ig,l),
577	& tauscaling(ig))
578	ENDDO
579	ENDDO
580	endif ! of if (slpwind)
581
582	c Update the ice particle size "rice"
583	c -------------------------------------
584	if (water) then
585	IF(microphys) THEN
586
587
588	DO l = 1, nlay
589	DO ig=1,ngrid
590
591	call updaterice_micro(zqi(ig,l,igcm_h2o_ice),
592	& zqi(ig,l,igcm_ccn_mass),zqi(ig,l,igcm_ccn_number),
593	& tauscaling(ig),rice(ig,l),rhocloud(ig,l))
594
595	ENDDO
596	ENDDO
597
598	ELSE
599
600	DO l = 1, nlay
601	DO ig=1,ngrid
602
603	call updaterice_typ(zqi(ig,l,igcm_h2o_ice),
604	& tau(ig,1),zlay(ig,l),rice(ig,l))
605
606	ENDDO
607	ENDDO
608	ENDIF ! of IF(microphys)
609	endif ! of if (water)
610
611	END SUBROUTINE callsedim
612
613	END MODULE callsedim_mod
614

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