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sulfate_aer_mod.f90 @ 5310

Last change on this file since 5310 was 5268, checked in by abarral, 2 weeks ago
.f90 <-> .F90 depending on cpp key use
Property svn:keywords set to `Id`
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1	MODULE sulfate_aer_mod
2
3	! microphysical routines based on UPMC aerosol model by Slimane Bekki
4	! adapted for stratospheric sulfate aerosol in LMDZ by Christoph Kleinschmitt
5
6	CONTAINS
7
8	!*******************************************************************
9	SUBROUTINE STRACOMP_KELVIN(sh,t_seri,pplay)
10	!
11	! Aerosol H2SO4 weight fraction as a function of PH2O and temperature
12	! INPUT:
13	! sh: MMR of H2O
14	! t_seri: temperature (K)
15	! pplay: middle layer pression (Pa)
16	!
17	! Modified in modules:
18	! R2SO4: aerosol H2SO4 weight fraction (percent)
19	! R2SO4B: aerosol H2SO4 weight fraction (percent) for each aerosol bin
20	! DENSO4: aerosol density (gr/cm3)
21	! DENSO4B: aerosol density (gr/cm3)for each aerosol bin
22	! f_r_wet: factor for converting dry to wet radius
23	! assuming 'flat surface' composition (does not depend on aerosol size)
24	! f_r_wetB: factor for converting dry to wet radius
25	! assuming 'curved surface' composition (depends on aerosol size)
26
27	USE dimphy, ONLY : klon,klev ! nb of longitude and altitude bands
28	USE infotrac_phy, ONLY : nbtr_bin
29	USE aerophys
30	USE phys_local_var_mod, ONLY: R2SO4, R2SO4B, DENSO4, DENSO4B, f_r_wet, f_r_wetB
31	USE strataer_local_var_mod, ONLY: RRSI
32	! WARNING: in phys_local_var_mod R2SO4B, DENSO4B, f_r_wetB (klon,klev,nbtr_bin)
33	! and dens_aer_dry must be declared somewhere
34
35	IMPLICIT NONE
36
37	REAL,DIMENSION(klon,klev),INTENT(IN) :: t_seri ! Temperature
38	REAL,DIMENSION(klon,klev),INTENT(IN) :: pplay ! pression in the middle of each layer (Pa)
39	REAL,DIMENSION(klon,klev),INTENT(IN) :: sh ! specific humidity (kg h2o/kg air)
40
41	! local variables
42	integer :: ilon,ilev,ik
43	real, parameter :: rath2oair = mAIRmol/mH2Omol
44	real, parameter :: third = 1./3.
45	real :: pph2ogas(klon,klev)
46	real :: temp, wpp, xa, surtens, mvh2o, radwet, fkelvin, pph2okel, r2so4ik, denso4ik
47	!----------------------------------------
48
49	! gas-phase h2o partial pressure (Pa)
50	! vmr=sh*rath2oair
51	pph2ogas(:,:) = pplay(:,:)sh(:,:)rath2oair
52
53	DO ilon=1,klon
54	DO ilev=1,klev
55
56	temp = max(t_seri(ilon,ilev),190.)
57	temp = min(temp,300.)
58
59	! * H2SO4-H2O flat surface *
60	!! equilibrium H2O pressure over pure flat liquid water (Pa)
61	!! pflath2o=psh2o(temp)
62	! h2so4 weight percent(%) = f(P_h2o(Pa),T)
63	R2SO4(ilon,ilev)=wph2so4(pph2ogas(ilon,ilev),temp)
64	! h2so4 mass fraction (0<wpp<1)
65	wpp=R2SO4(ilon,ilev)*1.e-2
66	! mole fraction
67	xa=18.wpp/(18.wpp+98.*(1.-wpp))
68
69	! CHECK:compare h2so4 sat/ pressure (see Marti et al., 97 & reef. therein)
70	! R2SO4(ilon,ilev)=70. temp=298.15
71	! equilibrium h2so4 number density over H2SO4/H2O solution (molec/cm3)
72	! include conversion from molec/cm3 to Pa
73	! ph2so4=solh2so4(temp,xa)(1.38065e-16temp)/10.
74	! print*,' ph2so4=',ph2so4,temp,R2SO4(ilon,ilev)
75	! good match with Martin, et Ayers, not with Gmitro (the famous 0.086)
76
77	! surface tension (mN/m=1.e-3.kg/s2) = f(T,h2so4 mole fraction)
78	surtens=surftension(temp,xa)
79	! molar volume of pure h2o (cm3.mol-1 =1.e-6.m3.mol-1)
80	mvh2o= rmvh2o(temp)
81	! aerosol density (gr/cm3) = f(T,h2so4 mass fraction)
82	DENSO4(ilon,ilev)=density(temp,wpp)
83	! ->x1000., to have it in kg/m3
84	! factor for converting dry to wet radius
85	f_r_wet(ilon,ilev) = (dens_aer_dry/(DENSO4(ilon,ilev)*1.e3)/ &
86	& (R2SO4(ilon,ilev)1.e-2))*third
87	! * End of H2SO4-H2O flat surface *
88
89
90	! Loop on bin radius (RRSI in cm)
91	DO IK=1,nbtr_bin
92
93	! * H2SO4-H2O curved surface - Kelvin effect factor *
94	! wet radius (m) (RRSI(IK) in [cm])
95	if (f_r_wetB(ilon,ilev,IK) .gt. 1.0) then
96	radwet = 1.e-2RRSI(IK)f_r_wetB(ilon,ilev,IK)
97	else
98	! H2SO4-H2O flat surface, only on the first timestep
99	radwet = 1.e-2RRSI(IK)f_r_wet(ilon,ilev)
100	endif
101	! Kelvin factor:
102	! surface tension (mN/m=1.e-3.kg/s2)
103	! molar volume of pure h2o (cm3.mol-1 =1.e-6.m3.mol-1)
104	fkelvin=exp( 2.1.e-3surtens1.e-6mvh2o/ (radwetrgastemp) )
105	! equilibrium: pph2o(gas) = pph2o(liq) = pph2o(liq_flat) * fkelvin
106	! equilibrium: pph2o(liq_flat) = pph2o(gas) / fkelvin
107	! h2o liquid partial pressure before Kelvin effect (Pa)
108	pph2okel = pph2ogas(ilon,ilev) / fkelvin
109	! h2so4 weight percent(%) = f(P_h2o(Pa),temp)
110	r2so4ik=wph2so4(pph2okel,temp)
111	! h2so4 mass fraction (0<wpp<1)
112	wpp=r2so4ik*1.e-2
113	! mole fraction
114	xa=18.wpp/(18.wpp+98.*(1.-wpp))
115	! aerosol density (gr/cm3) = f(T,h2so4 mass fraction)
116	denso4ik=density(temp,wpp)
117	!
118	! recalculate Kelvin factor with surface tension and radwet
119	! with new R2SO4B and DENSO4B
120	surtens=surftension(temp,xa)
121	! wet radius (m)
122	radwet = 1.e-2RRSI(IK)(dens_aer_dry/(denso4ik*1.e3)/ &
123	& (r2so4ik1.e-2))*third
124	fkelvin=exp( 2.1.e-3surtens1.e-6mvh2o / (radwetrgastemp) )
125	pph2okel=pph2ogas(ilon,ilev) / fkelvin
126	! h2so4 weight percent(%) = f(P_h2o(Pa),temp)
127	R2SO4B(ilon,ilev,IK)=wph2so4(pph2okel,temp)
128	! h2so4 mass fraction (0<wpp<1)
129	wpp=R2SO4B(ilon,ilev,IK)*1.e-2
130	xa=18.wpp/(18.wpp+98.*(1.-wpp))
131	! aerosol density (gr/cm3) = f(T,h2so4 mass fraction)
132	DENSO4B(ilon,ilev,IK)=density(temp,wpp)
133	! factor for converting dry to wet radius
134	f_r_wetB(ilon,ilev,IK) = (dens_aer_dry/(DENSO4B(ilon,ilev,IK)*1.e3)/ &
135	& (R2SO4B(ilon,ilev,IK)1.e-2))*third
136	!
137	! print*,'R,Rwet(m),kelvin,h2so4(%),ro=',RRSI(ik),radwet,fkelvin, &
138	! & R2SO4B(ilon,ilev,IK),DENSO4B(ilon,ilev,IK)
139	! print*,' equil.h2so4(molec/cm3), &
140	! & sigma',solh2so4(temp,xa),surftension(temp,xa)
141
142	ENDDO
143
144	ENDDO
145	ENDDO
146
147	RETURN
148
149	END SUBROUTINE STRACOMP_KELVIN
150	!********************************************************************
151	SUBROUTINE STRACOMP(sh,t_seri,pplay)
152
153	! AEROSOL H2SO4 WEIGHT FRACTION AS A FUNCTION OF PH2O AND TEMPERATURE
154	! ----------------------------------------------------------------
155	! INPUT:
156	! H2O: VMR of H2O
157	! t_seri: temperature (K)
158	! PMB: pressure (mb)
159	! klon: number of latitude bands in the model domain
160	! klev: number of altitude bands in the model domain
161	! for IFS: perhaps add another dimension for longitude
162	!
163	! OUTPUT:
164	! R2SO4: aerosol H2SO4 weight fraction (percent)
165
166	USE dimphy, ONLY : klon,klev
167	USE aerophys
168	USE phys_local_var_mod, ONLY: R2SO4
169
170	IMPLICIT NONE
171
172	REAL,DIMENSION(klon,klev),INTENT(IN) :: t_seri ! Temperature
173	REAL,DIMENSION(klon,klev),INTENT(IN) :: pplay ! pression pour le mileu de chaque couche (en Pa)
174	REAL,DIMENSION(klon,klev),INTENT(IN) :: sh ! humidite specifique
175
176	REAL PMB(klon,klev), H2O(klon,klev)
177	!
178	! working variables
179	INTEGER I,J,K
180	REAL TP, PH2O, VAL, A, B
181	! local variables to be saved on exit
182	INTEGER INSTEP
183	INTEGER, PARAMETER :: N=16, M=28
184	DATA INSTEP/0/
185	REAL F(N,M)
186	REAL XC(N)
187	REAL YC(M)
188	REAL XC1, XC16, YC1, YC28
189	!
190	SAVE INSTEP,F,XC,YC,XC1,XC16,YC1,YC28
191	!$OMP THREADPRIVATE(INSTEP,F,XC,YC,XC1,XC16,YC1,YC28)
192
193	! convert pplay (in Pa) to PMB (in mb)
194	PMB(:,:)=pplay(:,:)/100.0
195
196	! convert specific humidity sh (in kg/kg) to VMR H2O
197	H2O(:,:)=sh(:,:)*mAIRmol/mH2Omol
198
199	IF(INSTEP.EQ.0) THEN
200
201	INSTEP=1
202	XC(1)=0.01
203	XC(2)=0.1
204	XC(3)=0.5
205	XC(4)=1.0
206	XC(5)=1.5
207	XC(6)=2.0
208	XC(7)=3.0
209	XC(8)=5.0
210	XC(9)=6.0
211	XC(10)=8.0
212	XC(11)=10.0
213	XC(12)=12.0
214	XC(13)=15.0
215	XC(14)=20.0
216	XC(15)=30.0
217	XC(16)=100.0
218	!
219	YC(1)=175.0
220	DO I=2,28
221	YC(I)=YC(I-1)+5.0
222	ENDDO
223
224	! CONVERSION mb IN 1.0E-4mB
225	DO I=1,16
226	XC(I)=XC(I)*1.0E-4
227	ENDDO
228	!
229	XC1=XC(1)+1.E-10
230	XC16=XC(16)-1.E-8
231	YC1=YC(1)+1.E-5
232	YC28=YC(28)-1.E-5
233
234	F(6,4)=43.45
235	F(6,5)=53.96
236	F(6,6)=60.62
237	F(6,7)=65.57
238	F(6,8)=69.42
239	F(6,9)=72.56
240	F(6,10)=75.17
241	F(6,11)=77.38
242	F(6,12)=79.3
243	F(6,13)=80.99
244	F(6,14)=82.5
245	F(6,15)=83.92
246	F(6,16)=85.32
247	F(6,17)=86.79
248	F(6,18)=88.32
249	!
250	! ADD FACTOR BECAUSE THE SLOP IS TOO IMPORTANT
251	! NOT FOR THIS ONE BUT THE REST
252	! LOG DOESN'T WORK
253	A=(F(6,5)-F(6,4))/( (YC(5)-YC(4))*2.0)
254	B=-A*YC(4) + F(6,4)
255	F(6,1)=A*YC(1) + B
256	F(6,2)=A*YC(2) + B
257	F(6,3)=A*YC(3) + B
258	!
259	F(7,4)=37.02
260	F(7,5)=49.46
261	F(7,6)=57.51
262	F(7,7)=63.12
263	F(7,8)=67.42
264	F(7,9)=70.85
265	F(7,10)=73.70
266	F(7,11)=76.09
267	F(7,12)=78.15
268	F(7,13)=79.96
269	F(7,14)=81.56
270	F(7,15)=83.02
271	F(7,16)=84.43
272	F(7,17)=85.85
273	F(7,18)=87.33
274	!
275	A=(F(7,5)-F(7,4))/( (YC(5)-YC(4))*2.0)
276	B=-A*YC(4) + F(7,4)
277	F(7,1)=A*YC(1) + B
278	F(7,2)=A*YC(2) + B
279	F(7,3)=A*YC(3) + B
280	!
281	F(8,4)=25.85
282	F(8,5)=42.26
283	F(8,6)=52.78
284	F(8,7)=59.55
285	F(8,8)=64.55
286	F(8,9)=68.45
287	F(8,10)=71.63
288	F(8,11)=74.29
289	F(8,12)=76.56
290	F(8,13)=78.53
291	F(8,14)=80.27
292	F(8,15)=81.83
293	F(8,16)=83.27
294	F(8,17)=84.67
295	F(8,18)=86.10
296	!
297	A=(F(8,5)-F(8,4))/( (YC(5)-YC(4))*2.5 )
298	B=-A*YC(4) + F(8,4)
299	F(8,1)=A*YC(1) + B
300	F(8,2)=A*YC(2) + B
301	F(8,3)=A*YC(3) + B
302	!
303	F(9,4)=15.38
304	F(9,5)=39.35
305	F(9,6)=50.73
306	F(9,7)=58.11
307	F(9,8)=63.41
308	F(9,9)=67.52
309	F(9,10)=70.83
310	F(9,11)=73.6
311	F(9,12)=75.95
312	F(9,13)=77.98
313	F(9,14)=79.77
314	F(9,15)=81.38
315	F(9,16)=82.84
316	F(9,17)=84.25
317	F(9,18)=85.66
318	!
319	A=(F(9,5)-F(9,4))/( (YC(5)-YC(4))*7.0)
320	B=-A*YC(4) + F(9,4)
321	F(9,1)=A*YC(1) + B
322	F(9,2)=A*YC(2) + B
323	F(9,3)=A*YC(3) + B
324	!
325	F(10,4)=0.0
326	F(10,5)=34.02
327	F(10,6)=46.93
328	F(10,7)=55.61
329	F(10,8)=61.47
330	F(10,9)=65.94
331	F(10,10)=69.49
332	F(10,11)=72.44
333	F(10,12)=74.93
334	F(10,13)=77.08
335	F(10,14)=78.96
336	F(10,15)=80.63
337	F(10,16)=82.15
338	F(10,17)=83.57
339	F(10,18)=84.97
340	!
341	A=(F(10,6)-F(10,5))/( (YC(6)-YC(5))*1.5)
342	B=-A*YC(5) + F(10,5)
343	F(10,1)=A*YC(1) + B
344	F(10,2)=A*YC(2) + B
345	F(10,3)=A*YC(3) + B
346	F(10,4)=A*YC(4) + B
347	!
348	F(11,4)=0.0
349	F(11,5)=29.02
350	F(11,6)=43.69
351	F(11,7)=53.44
352	F(11,8)=59.83
353	F(11,9)=64.62
354	F(11,10)=68.39
355	F(11,11)=71.48
356	F(11,12)=74.10
357	F(11,13)=76.33
358	F(11,14)=78.29
359	F(11,15)=80.02
360	F(11,16)=81.58
361	F(11,17)=83.03
362	F(11,18)=84.44
363	!
364	A=(F(11,6)-F(11,5))/( (YC(6)-YC(5))*2.5 )
365	B=-A*YC(5) + F(11,5)
366	F(11,1)=A*YC(1) + B
367	F(11,2)=A*YC(2) + B
368	F(11,3)=A*YC(3) + B
369	F(11,4)=A*YC(4) + B
370	!
371	F(12,4)=0.0
372	F(12,5)=23.13
373	F(12,6)=40.86
374	F(12,7)=51.44
375	F(12,8)=58.38
376	F(12,9)=63.47
377	F(12,10)=67.43
378	F(12,11)=70.66
379	F(12,12)=73.38
380	F(12,13)=75.70
381	F(12,14)=77.72
382	F(12,15)=79.51
383	F(12,16)=81.11
384	F(12,17)=82.58
385	F(12,18)=83.99
386	!
387	A=(F(12,6)-F(12,5))/( (YC(6)-YC(5))*3.5 )
388	B=-A*YC(5) + F(12,5)
389	F(12,1)=A*YC(1) + B
390	F(12,2)=A*YC(2) + B
391	F(12,3)=A*YC(3) + B
392	F(12,4)=A*YC(4) + B
393	!
394	F(13,4)=0.0
395	F(13,5)=0.0
396	F(13,6)=36.89
397	F(13,7)=48.63
398	F(13,8)=56.46
399	F(13,9)=61.96
400	F(13,10)=66.19
401	F(13,11)=69.6
402	F(13,12)=72.45
403	F(13,13)=74.89
404	F(13,14)=76.99
405	F(13,15)=78.85
406	F(13,16)=80.50
407	F(13,17)=82.02
408	F(13,18)=83.44
409	!
410	A=(F(13,7)-F(13,6))/( (YC(7)-YC(6))*2.0)
411	B=-A*YC(6) + F(13,6)
412	F(13,1)=A*YC(1) + B
413	F(13,2)=A*YC(2) + B
414	F(13,3)=A*YC(3) + B
415	F(13,4)=A*YC(4) + B
416	F(13,5)=A*YC(5) + B
417	!
418	F(14,4)=0.0
419	F(14,5)=0.0
420	F(14,6)=30.82
421	F(14,7)=44.49
422	F(14,8)=53.69
423	F(14,9)=59.83
424	F(14,10)=64.47
425	F(14,11)=68.15
426	F(14,12)=71.19
427	F(14,13)=73.77
428	F(14,14)=76.0
429	F(14,15)=77.95
430	F(14,16)=79.69
431	F(14,17)=81.26
432	F(14,18)=82.72
433	!
434	A=(F(14,7)-F(14,6))/( (YC(7)-YC(6))*2.5 )
435	B=-A*YC(6) + F(14,6)
436	F(14,1)=A*YC(1) + B
437	F(14,2)=A*YC(2) + B
438	F(14,3)=A*YC(3) + B
439	F(14,4)=A*YC(4) + B
440	F(14,5)=A*YC(5) + B
441	!
442	F(15,4)=0.0
443	F(15,5)=0.0
444	F(15,6)=0.0
445	F(15,7)=37.71
446	F(15,8)=48.49
447	F(15,9)=56.40
448	F(15,10)=61.75
449	F(15,11)=65.89
450	F(15,12)=69.25
451	F(15,13)=72.07
452	F(15,14)=74.49
453	F(15,15)=76.59
454	F(15,16)=78.45
455	F(15,17)=80.12
456	F(15,18)=81.64
457	!
458	A=(F(15,8)-F(15,7))/( (YC(8)-YC(7))*1.5)
459	B=-A*YC(7) + F(15,7)
460	F(15,1)=A*YC(1) + B
461	F(15,2)=A*YC(2) + B
462	F(15,3)=A*YC(3) + B
463	F(15,4)=A*YC(4) + B
464	F(15,5)=A*YC(5) + B
465	F(15,6)=A*YC(6) + B
466
467	! SUPPOSE THAT AT GIVEN AND PH2O<2mB,
468	! %H2SO4 = A *LOG(PH2O) +B
469	! XC(1-5) :EXTENSION LEFT (LOW H2O)
470	DO J=1,18
471	A=(F(6,J)-F(7,J))/(LOG(XC(6))-LOG(XC(7)))
472	B=-A*LOG(XC(6)) + F(6,J)
473	DO K=1,5
474	F(K,J)=A*LOG(XC(K)) + B
475	ENDDO
476	ENDDO
477
478	! XC(16) :EXTENSION RIGHT (HIGH H2O)
479	DO J=1,18
480	A=(F(15,J)-F(14,J))/(XC(15)-XC(14))
481	B=-A*XC(15) + F(15,J)
482	F(16,J)=A*XC(16) + B
483	! F(16,2)=1.0
484	ENDDO
485
486	! YC(16-25) :EXTENSION DOWN (HIGH T)
487	DO I=1,16
488	A=(F(I,18)-F(I,17))/(YC(18)-YC(17))
489	B=-A*YC(18) + F(I,18)
490	DO K=19,28
491	F(I,K)=A*YC(K) + B
492	ENDDO
493	ENDDO
494
495	! MANUAL CORRECTIONS
496	DO J=1,10
497	F(1,J)=94.0
498	ENDDO
499
500	DO J=1,6
501	F(2,J)=77.0 +REAL(J)
502	ENDDO
503
504	DO J=1,7
505	F(16,J)=9.0
506	ENDDO
507
508	DO I=1,16
509	DO J=1,28
510	IF (F(I,J).LT.9.0) F(I,J)=30.0
511	IF (F(I,J).GT.99.99) F(I,J)=99.99
512	ENDDO
513	ENDDO
514
515	ENDIF
516
517	DO I=1,klon
518	DO J=1,klev
519	TP=t_seri(I,J)
520	IF (TP.LT.175.1) TP=175.1
521	! Partial pressure of H2O (mb)
522	PH2O =PMB(I,J)*H2O(I,J)
523	IF (PH2O.LT.XC1) THEN
524	R2SO4(I,J)=99.99
525	! PH2O=XC(1)+1.0E-10
526	ELSE
527	IF (PH2O.GT.XC16) PH2O=XC16
528	! SIMPLE LINEAR INTERPOLATIONS
529	CALL FIND(PH2O,TP,XC,YC,F,VAL,N,M)
530	IF (PMB(I,J).GE.10.0.AND.VAL.LT.60.0) VAL=60.0
531	R2SO4(I,J)=VAL
532	ENDIF
533	ENDDO
534	ENDDO
535
536	END SUBROUTINE
537
538	!****************************************************************
539	SUBROUTINE STRAACT(ACTSO4)
540
541	! H2SO4 ACTIVITY (GIAUQUE) AS A FUNCTION OF H2SO4 WP
542	! ----------------------------------------
543	! INPUT:
544	! H2SO4: VMR of H2SO4
545	! klon: number of latitude bands in the model domain
546	! klev: number of altitude bands in the model domain
547	! for IFS: perhaps add another dimension for longitude
548	!
549	! OUTPUT:
550	! ACTSO4: H2SO4 activity (percent)
551
552	USE dimphy, ONLY : klon,klev
553	USE phys_local_var_mod, ONLY: R2SO4
554
555	IMPLICIT NONE
556
557	REAL ACTSO4(klon,klev)
558
559	! Working variables
560	INTEGER NN,I,J,JX,JX1
561	REAL TC,TB,TA,XT
562	PARAMETER (NN=109)
563	REAL XC(NN), X(NN)
564
565	! H2SO4 activity
566	DATA X/ &
567	& 0.0,0.25,0.78,1.437,2.19,3.07,4.03,5.04,6.08 &
568	& ,7.13,8.18,14.33,18.59,28.59,39.17,49.49 &
569	& ,102.4,157.8,215.7,276.9,341.6,409.8,481.5,556.6 &
570	& ,635.5,719.,808.,902.,1000.,1103.,1211.,1322.,1437.,1555. &
571	& ,1677.,1800.,1926.,2054.,2183.,2312.,2442.,2572.,2701.,2829. &
572	& ,2955.,3080.,3203.,3325.,3446.,3564.,3681.,3796.,3910.,4022. &
573	& ,4134.,4351.,4564.,4771.,4974.,5171.,5364.,5551.,5732.,5908. &
574	& ,6079.,6244.,6404.,6559.,6709.,6854.,6994.,7131.,7264.,7393. &
575	& ,7520.,7821.,8105.,8373.,8627.,8867.,9093.,9308.,9511.,9703. &
576	& ,9885.,10060.,10225.,10535.,10819.,11079.,11318.,11537. &
577	& ,11740.,12097.,12407.,12676.,12915.,13126.,13564.,13910. &
578	& ,14191.,14423.,14617.,14786.,10568.,15299.,15491.,15654. &
579	& ,15811./
580	! H2SO4 weight fraction (percent)
581	DATA XC/ &
582	& 100.0,99.982,99.963,99.945,99.927,99.908,99.890,99.872 &
583	& ,99.853,99.835,99.817,99.725,99.634,99.452,99.270 &
584	& ,99.090,98.196,97.319,96.457,95.610,94.777,93.959,93.156 &
585	& ,92.365,91.588,90.824,90.073,89.334,88.607,87.892,87.188 &
586	& ,86.495,85.814,85.143,84.482,83.832,83.191,82.560,81.939 &
587	& ,81.327,80.724,80.130,79.545,78.968,78.399,77.839,77.286 &
588	& ,76.741,76.204,75.675,75.152,74.637,74.129,73.628,73.133 &
589	& ,72.164,71.220,70.300,69.404,68.530,67.678,66.847,66.037 &
590	& ,65.245,64.472,63.718,62.981,62.261,61.557,60.868,60.195 &
591	& ,59.537,58.893,58.263,57.646,56.159,54.747,53.405,52.126 &
592	& ,50.908,49.745,48.634,47.572,46.555,45.580,44.646,43.749 &
593	& ,42.059,40.495,39.043,37.691,36.430,35.251,33.107,31.209 &
594	& ,29.517,27.999,26.629,23.728,21.397,19.482,17.882,16.525 &
595	& ,15.360,13.461,11.980,10.792,9.819,8.932/
596
597	DO I=1,klon
598	DO J=1,klev
599	! HERE LINEAR INTERPOLATIONS
600	XT=R2SO4(I,J)
601	CALL POSACT(XT,XC,NN,JX)
602	JX1=JX+1
603	IF(JX.EQ.0) THEN
604	ACTSO4(I,J)=0.0
605	ELSE IF(JX.GE.NN) THEN
606	ACTSO4(I,J)=15811.0
607	ELSE
608	TC=XT -XC(JX)
609	TB=X(JX1) -X(JX)
610	TA=XC(JX1) -XC(JX)
611	TA=TB/TA
612	ACTSO4(I,J)=X(JX) + TA*TC
613	ENDIF
614	ENDDO
615	ENDDO
616
617	END SUBROUTINE
618
619	!****************************************************************
620	SUBROUTINE DENH2SA(t_seri)
621
622	! AERSOL DENSITY AS A FUNCTION OF H2SO4 WEIGHT PERCENT AND T
623	! ---------------------------------------------
624	! VERY ROUGH APPROXIMATION (SEE FOR WATER IN HANDBOOK
625	! LINEAR 2% FOR 30 DEGREES with RESPECT TO WATER)
626	!
627	! INPUT:
628	! R2SO4: aerosol H2SO4 weight fraction (percent)
629	! t_seri: temperature (K)
630	! klon: number of latitude bands in the model domain
631	! klev: number of altitude bands in the model domain
632	! for IFS: perhaps add another dimension for longitude
633	!
634	! OUTPUT:
635	! DENSO4: aerosol mass density (gr/cm3 = aerosol mass/aerosol volume)
636	!
637	USE dimphy, ONLY : klon,klev
638	USE phys_local_var_mod, ONLY: R2SO4, DENSO4
639
640	IMPLICIT NONE
641
642	REAL,DIMENSION(klon,klev),INTENT(IN) :: t_seri ! Temperature
643
644	INTEGER I,J
645
646	! Loop on model domain (2 dimension for UPMC model; 3 for IFS)
647	DO I=1,klon
648	DO J=1,klev
649	! RO AT 20C
650	DENSO4(I,J)=0.78681252E-5R2SO4(I,J)R2SO4(I,J)+ 0.82185978E-2*R2SO4(I,J)+0.97968381
651	DENSO4(I,J)=DENSO4(I,J)* ( 1.0 - (t_seri(I,J)-293.0)*0.02/30.0 )
652	ENDDO
653	ENDDO
654
655	END SUBROUTINE
656
657	!***********************************************************
658	SUBROUTINE FIND(X,Y,XC,YC,F,VAL,N,M)
659	!
660	! BI-LINEAR INTERPOLATION
661
662	! INPUT:
663	! X: Partial pressure of H2O (mb)
664	! Y: temperature (K)
665	! XC: Table partial pressure of H2O (mb)
666	! YC: Table temperature (K)
667	! F: Table aerosol H2SO4 weight fraction=f(XC,YC) (percent)
668	!
669	! OUTPUT:
670	! VAL: aerosol H2SO4 weight fraction (percent)
671
672	IMPLICIT NONE
673
674	INTEGER N,M
675	REAL X,Y,XC(N),YC(M),F(N,M),VAL
676	!
677	! working variables
678	INTEGER IERX,IERY,JX,JY,JXP1,JYP1
679	REAL SXY,SX1Y,SX1Y1,SXY1,TA,TB,T,UA,UB,U
680
681	IERX=0
682	IERY=0
683	CALL POSITION(XC,X,N,JX,IERX)
684	CALL POSITION(YC,Y,M,JY,IERY)
685
686	IF(JX.EQ.0.OR.IERY.EQ.1) THEN
687	VAL=99.99
688	RETURN
689	ENDIF
690
691	IF(JY.EQ.0.OR.IERX.EQ.1) THEN
692	VAL=9.0
693	RETURN
694	ENDIF
695
696	JXP1=JX+1
697	JYP1=JY+1
698	SXY=F(JX, JY )
699	SX1Y=F(JXP1,JY )
700	SX1Y1=F(JXP1,JYP1)
701	SXY1=F(JX, JYP1)
702
703	! x-slope.
704	TA=X -XC(JX)
705	TB=XC(JXP1)-XC(JX)
706	T=TA/TB
707
708	! y-slope.
709	UA=Y -YC(JY)
710	UB=YC(JYP1)-YC(JY)
711	U=UA/UB
712
713	! Use bilinear interpolation to determine function at point X,Y.
714	VAL=(1.-T)(1.-U)SXY + T(1.0-U)SX1Y + TUSX1Y1 + (1.0-T)USXY1
715
716	IF(VAL.LT.9.0) VAL=9.0
717	IF(VAL.GT.99.99) VAL=99.99
718
719	RETURN
720	END SUBROUTINE
721	!****************************************************************
722	SUBROUTINE POSITION(XC,X,N,JX,IER)
723
724	IMPLICIT NONE
725
726	INTEGER N,JX,IER,I
727	REAL X,XC(N)
728
729	IER=0
730	IF(X.LT.XC(1)) THEN
731	JX=0
732	ELSE
733	DO 10 I=1,N
734	IF (X.LT.XC(I)) GO TO 20
735	10 CONTINUE
736	IER=1
737	20 JX=I-1
738	ENDIF
739
740	RETURN
741	END SUBROUTINE
742	!********************************************************************
743	SUBROUTINE POSACT(XT,X,N,JX)
744
745	! POSITION OF XT IN THE ARRAY X
746	! -----------------------------------------------
747
748	IMPLICIT NONE
749
750	INTEGER N
751	REAL XT,X(N)
752	! Working variables
753	INTEGER JX,I
754
755	IF(XT.GT.X(1)) THEN
756	JX=0
757	ELSE
758	DO 10 I=1,N
759	IF (XT.GT.X(I)) GO TO 20
760	10 CONTINUE
761	20 JX=I
762	ENDIF
763
764	RETURN
765	END SUBROUTINE
766	!********************************************************************
767	!-----------------------------------------------------------------------
768	real function psh2so4(T) result(psh2so4_out)
769	! equilibrium H2SO4 pressure over pure H2SO4 solution (Pa)
770	!
771	!---->Ayers et.al. (1980), GRL (7) pp 433-436
772	! plus corrections for lower temperatures by Kulmala and Laaksonen (1990)
773	! and Noppel et al. (1990)
774
775	implicit none
776	real, intent(in) :: T
777	real, parameter :: &
778	& b1=1.01325e5, &
779	& b2=11.5, &
780	& b3=1.0156e4, &
781	& b4=0.38/545., &
782	& tref=360.15
783
784	! saturation vapor pressure ( N/m2 = Pa = kg/(m.s2) )
785	psh2so4_out=b1exp( -b2 +b3( 1./tref-1./T &
786	& +b4*(1.+log(tref/T)-tref/T) ) )
787
788	return
789	end function psh2so4
790	!-----------------------------------------------------------------------
791	real function ndsh2so4(T) result(ndsh2so4_out)
792	! equilibrium H2SO4 number density over pure H2SO4 (molec/cm3)
793
794	implicit none
795	real, intent(in) :: T
796	real :: presat
797
798	! Boltzmann constant ( 1.38065e-23 J/K = m2⋅kg/(s2⋅K) )
799	! akb idem in cm2⋅g/(s2⋅K)
800	real, parameter :: akb=1.38065e-16
801
802	! pure h2so4 saturation vapor pressure (Pa)
803	presat=psh2so4(T)
804	! saturation number density (1/cm3) - (molec/cm3)
805	ndsh2so4_out=presat10./(akbT)
806
807	return
808	end function ndsh2so4
809	!-----------------------------------------------------------------------
810	real function psh2o(T) result(psh2o_out)
811	! equilibrium H2O pressure over pure liquid water (Pa)
812	!
813	implicit none
814	real, intent(in) :: T
815
816	if(T.gt.229.) then
817	! Preining et al., 1981 (from Kulmala et al., 1998)
818	! saturation vapor pressure (N/m2 = 1 Pa = 1 kg/(m·s2))
819	psh2o_out=exp( 77.34491296 -7235.424651/T &
820	& -8.2log(T) + 5.7133e-3T )
821	else
822	! Tabazadeh et al., 1997, parameterization for 185<T<260
823	! saturation water vapor partial pressure (mb = hPa =1.E2 kg/(m·s2))
824	! or from Clegg and Brimblecombe , J. Chem. Eng., p43, 1995.
825	;
826	psh2o_out=18.452406985 -3505.1578807/T &
827	& -330918.55082/(T*T) &
828	& +12725068.262/(TTT)
829	! in Pa
830	psh2o_out=100.*exp(psh2o_out)
831	end if
832	! print*,psh2o_out
833
834	return
835	end function psh2o
836	!-----------------------------------------------------------------------
837	real function density(T,so4mfrac) result(density_out)
838	! calculation of particle density (gr/cm3)
839
840	! requires Temperature (T) and acid mass fraction (so4mfrac)
841	!---->Vehkamaeki et al. (2002)
842
843	implicit none
844	real, intent(in) :: T, so4mfrac
845	real, parameter :: &
846	& a1= 0.7681724,&
847	& a2= 2.184714, &
848	& a3= 7.163002, &
849	& a4=-44.31447, &
850	& a5= 88.74606, &
851	& a6=-75.73729, &
852	& a7= 23.43228
853	real, parameter :: &
854	& b1= 1.808225e-3, &
855	& b2=-9.294656e-3, &
856	& b3=-3.742148e-2, &
857	& b4= 2.565321e-1, &
858	& b5=-5.362872e-1, &
859	& b6= 4.857736e-1, &
860	& b7=-1.629592e-1
861	real, parameter :: &
862	& c1=-3.478524e-6, &
863	& c2= 1.335867e-5, &
864	& c3= 5.195706e-5, &
865	& c4=-3.717636e-4, &
866	& c5= 7.990811e-4, &
867	& c6=-7.458060e-4, &
868	& c7= 2.581390e-4
869	real :: a,b,c,so4m2,so4m3,so4m4,so4m5,so4m6
870
871	so4m2=so4mfrac*so4mfrac
872	so4m3=so4mfrac*so4m2
873	so4m4=so4mfrac*so4m3
874	so4m5=so4mfrac*so4m4
875	so4m6=so4mfrac*so4m5
876
877	a=+a1+a2so4mfrac+a3so4m2+a4*so4m3 &
878	& +a5so4m4+a6so4m5+a7*so4m6
879	b=+b1+b2so4mfrac+b3so4m2+b4*so4m3 &
880	& +b5so4m4+b6so4m5+b7*so4m6
881	c=+c1+c2so4mfrac+c3so4m2+c4*so4m3 &
882	& +c5so4m4+c6so4m5+c7*so4m6
883	density_out=(a+bT+cTT) ! units are gm/cm*3
884
885	return
886	end function density
887	!-----------------------------------------------------------------------
888	real function surftension(T,so4frac) result(surftension_out)
889	! calculation of surface tension (mN/meter)
890	! requires Temperature (T) and acid mole fraction (so4frac)
891	!---->Vehkamaeki et al. (2002)
892
893	implicit none
894	real,intent(in) :: T, so4frac
895	real :: a,b,so4mfrac,so4m2,so4m3,so4m4,so4m5,so4sig
896	real, parameter :: &
897	& a1= 0.11864, &
898	& a2=-0.11651, &
899	& a3= 0.76852, &
900	& a4=-2.40909, &
901	& a5= 2.95434, &
902	& a6=-1.25852
903	real, parameter :: &
904	& b1=-1.5709e-4, &
905	& b2= 4.0102e-4, &
906	& b3=-2.3995e-3, &
907	& b4= 7.611235e-3, &
908	& b5=-9.37386e-3, &
909	& b6= 3.89722e-3
910	real, parameter :: convfac=1.e3 ! convert from newton/m to dyne/cm
911	real, parameter :: Mw=18.01528, Ma=98.079
912
913	! so4 mass fraction
914	so4mfrac=Maso4frac/( Maso4frac+Mw*(1.-so4frac) )
915	so4m2=so4mfrac*so4mfrac
916	so4m3=so4mfrac*so4m2
917	so4m4=so4mfrac*so4m3
918	so4m5=so4mfrac*so4m4
919
920	a=+a1+a2so4mfrac+a3so4m2+a4so4m3+a5so4m4+a6*so4m5
921	b=+b1+b2so4mfrac+b3so4m2+b4so4m3+b5so4m4+b6*so4m5
922	so4sig=a+b*T
923	surftension_out=so4sig*convfac
924
925	return
926	end function surftension
927	!-----------------------------------------------------------------------
928	real function wph2so4(pph2o,T) result(wph2so4_out)
929	! Calculates the equilibrium composition of h2so4 aerosols
930	! as a function of temperature and H2O pressure, using
931	! the parameterization of Tabazadeh et al., GRL, p1931, 1997.
932	!
933	! Parameters
934	!
935	! input:
936	! T.....temperature (K)
937	! pph2o..... amhbiant 2o pressure (Pa)
938	!
939	! output:
940	! wph2so4......sulfuric acid composition (weight percent wt % h2so4)
941	! = h2so4 mass fraction*100.
942	!
943	implicit none
944	real, intent(in) :: pph2o, T
945
946	real :: aw, rh, y1, y2, sulfmolal
947
948	! psh2o(T): equilibrium H2O pressure over pure liquid water (Pa)
949	! relative humidity
950	rh=pph2o/psh2o(T)
951	! water activity
952	! aw=min( 0.999,max(1.e-3,rh) )
953	aw=min( 0.999999999,max(1.e-8,rh) )
954
955	! composition
956	! calculation of h2so4 molality
957	if(aw .le. 0.05 .and. aw .gt. 0.) then
958	y1=12.372089320aw*(-0.16125516114) &
959	& -30.490657554*aw -2.1133114241
960	y2=13.455394705aw*(-0.19213122550) &
961	& -34.285174607*aw -1.7620073078
962	else if(aw .le. 0.85 .and. aw .gt. 0.05) then
963	y1=11.820654354aw*(-0.20786404244) &
964	& -4.8073063730*aw -5.1727540348
965	y2=12.891938068aw*(-0.23233847708) &
966	& -6.4261237757*aw -4.9005471319
967	else
968	y1=-180.06541028aw*(-0.38601102592) &
969	& -93.317846778*aw +273.88132245
970	y2=-176.95814097aw*(-0.36257048154) &
971	& -90.469744201*aw +267.45509988
972	end if
973	! h2so4 molality (m=moles of h2so4 (solute)/ kg of h2o(solvent))
974	sulfmolal = y1+((T-190.)*(y2-y1)/70.)
975
976	! for a solution containing mh2so4 and mh2o:
977	! sulfmolal = (mh2so4(gr)/h2so4_molar_mass(gr/mole)) / (mh2o(gr)*1.e-3)
978	! mh2o=1.e3(mh2so4/Mh2so4)/sulfmolal=1.e3mh2so4/(Mh2so4*sulfmolal)
979	! h2so4_mass_fraction = mfh2so4 = mh2so4/(mh2o + mh2so4)
980	! mh2o=mh2so4*(1-mfh2so4)/mfh2so4
981	! combining the 2 equations
982	! 1.e3mh2so4/(Mh2so4sulfmolal) = mh2so4*(1-mfh2so4)/mfh2so4
983	! 1.e3/(Mh2so4*sulfmolal) = (1-mfh2so4)/mfh2so4
984	! 1000mfh2so4 = (1-mfh2so4)Mh2so4*sulfmolal
985	! mfh2so4(1000.+Mh2so4sulfmolal) = Mh2so4*sulfmolal
986	! mfh2so4 = Mh2so4sulfmolal / (1000.+Mh2so4sulfmolal)
987	! wph2so4 (% mass fraction)= 100.Mh2so4sulfmolal / (1000.+Mh2so4*sulfmolal)
988	! recall activity of i = a_i = P_i/P_pure_i and
989	! activity coefficient of i = gamma_i = a_i/X_i (X_i: mole fraction of i)
990	! so P_i = gamma_iX_iP_pure_i
991	! if ideal solution, gamma_i=1, P_i = X_i*P_pure_i
992
993	! h2so4 weight precent
994	wph2so4_out = 9800.sulfmolal/(98.sulfmolal+1000.)
995	! print*,rh,pph2o,psh2o(T),vpice(T)
996	! print*,T,aw,sulfmolal,wph2so4_out
997	wph2so4_out = max(wph2so4_out,15.)
998	wph2so4_out = min(wph2so4_out,99.999)
999
1000	return
1001	end function wph2so4
1002	!-----------------------------------------------------------------------
1003	real function solh2so4(T,xa) result(solh2so4_out)
1004	! equilibrium h2so4 number density over H2SO4/H2O solution (molec/cm3)
1005
1006	implicit none
1007	real, intent(in) :: T, xa ! T(K) xa(H2SO4 mass fraction)
1008
1009	real :: xw, a12,b12, cacta, presat
1010
1011	xw=1.0-xa
1012
1013	! pure h2so4 saturation number density (molec/cm3)
1014	presat=ndsh2so4(T)
1015	! compute activity of acid
1016	a12=5.672E3 -4.074E6/T +4.421E8/(T*T)
1017	b12=1./0.527
1018	cacta=10.*(a12xwxw/(xw+b12xa)**2/T)
1019	! h2so4 saturation number density over H2SO4/H2O solution (molec/cm3)
1020	solh2so4_out=cactaxapresat
1021
1022	return
1023	end function solh2so4
1024	!-----------------------------------------------------------------------
1025	real function rpmvh2so4(T,ws) result(rpmvh2so4_out)
1026	! partial molar volume of h2so4 in h2so4/h2o solution (cm3/mole)
1027
1028	implicit none
1029	real, intent(in) :: T, ws
1030	real, dimension(22),parameter :: x=(/ &
1031	& 2.393284E-02,-4.359335E-05,7.961181E-08,0.0,-0.198716351, &
1032	& 1.39564574E-03,-2.020633E-06,0.51684706,-3.0539E-03,4.505475E-06, &
1033	& -0.30119511,1.840408E-03,-2.7221253742E-06,-0.11331674116, &
1034	& 8.47763E-04,-1.22336185E-06,0.3455282,-2.2111E-03,3.503768245E-06, &
1035	& -0.2315332,1.60074E-03,-2.5827835E-06/)
1036
1037	real :: w
1038
1039	w=ws*0.01
1040	rpmvh2so4_out=x(5)+x(6)T+x(7)TT+(x(8)+x(9)T+x(10)TT)*w &
1041	+(x(11)+x(12)T+x(13)TT)w*w
1042	! h2so4 partial molar volume in h2so4/h2o solution (cm3/mole)
1043	rpmvh2so4_out=rpmvh2so4_out*1000.
1044
1045	return
1046	end function rpmvh2so4
1047	!-----------------------------------------------------------------------
1048	real function rmvh2o(T) result(rmvh2o_out)
1049	! molar volume of pure h2o (cm3/mole)
1050
1051	implicit none
1052	real, intent(in) :: T
1053	real, parameter :: x1=2.393284E-02,x2=-4.359335E-05,x3=7.961181E-08
1054
1055	! 1000: L/mole -> cm3/mole
1056	! pure h2o molar volume (cm3/mole)
1057	rmvh2o_out=(x1+x2T+x3TT)1000.
1058
1059	return
1060	end function rmvh2o
1061	!
1062	END MODULE sulfate_aer_mod

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