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coagulate.F90 @ 5322

Last change on this file since 5322 was 5202, checked in by Laurent Fairhead, 8 weeks ago
Updating cirrus branch to trunk revision 5171
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1	!
2	! $Id: coagulate.F90 5202 2024-09-20 10:32:04Z abarral $
3	!
4	SUBROUTINE COAGULATE(pdtcoag,mdw,tr_seri,t_seri,pplay,dens_aer,is_strato)
5	! -----------------------------------------------------------------------
6	!
7	! Author : Christoph Kleinschmitt (with Olivier Boucher)
8	! ------
9	!
10	! purpose
11	! -------
12	!
13	! interface
14	! ---------
15	! input
16	! pdtphys time step duration [sec]
17	! tr_seri tracer mixing ratios [kg/kg]
18	! mdw # or mass median diameter [m]
19	!
20	! method
21	! ------
22	!
23	! -----------------------------------------------------------------------
24
25	USE dimphy, ONLY : klon,klev
26	USE aerophys
27	USE infotrac_phy
28	USE phys_local_var_mod, ONLY: DENSO4, DENSO4B, f_r_wet, f_r_wetB
29	USE strataer_local_var_mod, ONLY: flag_new_strat_compo
30
31	IMPLICIT NONE
32
33	!--------------------------------------------------------
34
35	! transfer variables when calling this routine
36	REAL,INTENT(IN) :: pdtcoag ! Time step in coagulation routine [s]
37	REAL,DIMENSION(nbtr_bin),INTENT(IN) :: mdw ! aerosol particle diameter in each bin [m]
38	REAL,DIMENSION(klon,klev,nbtr),INTENT(INOUT) :: tr_seri ! Concentration Traceur [U/KgA]
39	REAL,DIMENSION(klon,klev),INTENT(IN) :: t_seri ! Temperature
40	REAL,DIMENSION(klon,klev),INTENT(IN) :: pplay ! pression pour le mileu de chaque couche (en Pa)
41	REAL,DIMENSION(klon,klev) :: dens_aer! density of aerosol [kg/m3 aerosol] with default H2SO4 mass
42	LOGICAL,DIMENSION(klon,klev),INTENT(IN) :: is_strato
43
44	! local variables in coagulation routine
45	INTEGER :: i,j,k,nb,ilon,ilev
46	REAL, DIMENSION(nbtr_bin) :: radiusdry ! dry aerosol particle radius in each bin [m]
47	REAL, DIMENSION(nbtr_bin) :: radiuswet ! wet aerosol particle radius in each bin [m]
48	REAL, DIMENSION(klon,klev,nbtr_bin) :: tr_t ! Concentration Traceur at time t [U/KgA]
49	REAL, DIMENSION(klon,klev,nbtr_bin) :: tr_tp1 ! Concentration Traceur at time t+1 [U/KgA]
50	REAL, DIMENSION(nbtr_bin,nbtr_bin,nbtr_bin) :: ff ! Volume fraction of intermediate particles
51	REAL, DIMENSION(nbtr_bin) :: Vdry ! Volume dry of bins
52	REAL, DIMENSION(nbtr_bin) :: Vwet ! Volume wet of bins
53	REAL, DIMENSION(nbtr_bin,nbtr_bin) :: Vij ! Volume sum of i and j
54	REAL :: eta ! Dynamic viscosity of air
55	REAL, PARAMETER :: mair=4.8097E-26 ! Average mass of an air molecule [kg]
56	REAL :: zrho ! Density of air
57	REAL :: mnfrpth ! Mean free path of air
58	REAL, DIMENSION(nbtr_bin) :: Kn ! Knudsen number of particle i
59	REAL, DIMENSION(nbtr_bin) :: Di ! Particle diffusion coefficient
60	REAL, DIMENSION(nbtr_bin) :: m_par ! Mass of particle i
61	REAL, DIMENSION(nbtr_bin) :: thvelpar! Thermal velocity of particle i
62	REAL, DIMENSION(nbtr_bin) :: mfppar ! Mean free path of particle i
63	REAL, DIMENSION(nbtr_bin) :: delta! delta of particle i (from equation 21)
64	REAL, DIMENSION(nbtr_bin,nbtr_bin) :: beta ! Coagulation kernel from Brownian diffusion
65	REAL :: beta_const ! Constant coagulation kernel (for comparison)
66	REAL :: num
67	REAL :: numi
68	REAL :: denom
69
70	! Additional variables for coagulation enhancement factor due to van der Waals forces
71	! Taken from Chan and Mozurkewich, Measurement of the coagulation rate constant for sulfuric acid
72	! particles as a function of particle size using TDMA, Aerosol Science, 32, 321-339, 2001.
73	!--ok_vdw is 0 for no vdW forces, 1 for E(0), 2 for E(infinity)
74	INTEGER, PARAMETER :: ok_vdw = 0
75	REAL, PARAMETER :: avdW1 = 0.0757
76	REAL, PARAMETER :: avdW3 = 0.0015
77	REAL, PARAMETER :: bvdW0 = 0.0151
78	REAL, PARAMETER :: bvdW1 = -0.186
79	REAL, PARAMETER :: bvdW3 = -0.0163
80	REAL, PARAMETER :: AvdW = 6.4e-20 !Hamaker constant in J = 1e7 erg
81	REAL :: AvdWi
82	REAL :: xvdW
83	REAL :: EvdW
84
85	include "YOMCST.h"
86
87	! ff(i,j,k): Volume fraction of Vi,j that is partitioned to each model bin k
88	! just need to be calculated in model initialization because mdw(:) size is fixed
89	! no need to recalculate radius, Vdry, Vij, and ff every timestep because it is for
90	! dry aerosols
91	DO i=1, nbtr_bin
92	radiusdry(i)=mdw(i)/2.
93	Vdry(i)=radiusdry(i)*3. !neglecting factor 4RPI/3
94	Vwet(i)=0.0
95	ENDDO
96
97	DO j=1, nbtr_bin
98	DO i=1, nbtr_bin
99	Vij(i,j)= Vdry(i)+Vdry(j)
100	ENDDO
101	ENDDO
102
103	!--pre-compute the f(i,j,k) from Jacobson equation 13
104	ff=0.0
105	DO k=1, nbtr_bin
106	DO j=1, nbtr_bin
107	DO i=1, nbtr_bin
108	IF (k.EQ.1) THEN
109	ff(i,j,k)= 0.0
110	ELSEIF (k.GT.1.AND.Vdry(k-1).LT.Vij(i,j).AND.Vij(i,j).LT.Vdry(k)) THEN
111	ff(i,j,k)= 1.-ff(i,j,k-1)
112	ELSEIF (k.EQ.nbtr_bin) THEN
113	IF (Vij(i,j).GE.Vdry(k)) THEN
114	ff(i,j,k)= 1.
115	ELSE
116	ff(i,j,k)= 0.0
117	ENDIF
118	ELSEIF (k.LE.(nbtr_bin-1).AND.Vdry(k).LE.Vij(i,j).AND.Vij(i,j).LT.Vdry(k+1)) THEN
119	ff(i,j,k)= Vdry(k)/Vij(i,j)*(Vdry(k+1)-Vij(i,j))/(Vdry(k+1)-Vdry(k))
120	ENDIF
121	ENDDO
122	ENDDO
123	ENDDO
124	! End of just need to be calculated at initialization because mdw(:) size is fixed
125
126	DO ilon=1, klon
127	DO ilev=1, klev
128	!only in the stratosphere
129	IF (is_strato(ilon,ilev)) THEN
130	!compute actual wet particle radius & volume for every grid box
131	IF(flag_new_strat_compo) THEN
132	DO i=1, nbtr_bin
133	radiuswet(i)=f_r_wetB(ilon,ilev,i)*mdw(i)/2.
134	Vwet(i)= radiuswet(i)*3. !neglecting factor 4RPI/3
135	!! Vwet(i)= Vdry(i)(f_r_wetB(ilon,ilev,i)*3)
136	ENDDO
137	ELSE
138	DO i=1, nbtr_bin
139	radiuswet(i)=f_r_wet(ilon,ilev)*mdw(i)/2.
140	Vwet(i)= radiuswet(i)*3. !neglecting factor 4RPI/3
141	!! Vwet(i)= Vdry(i)(f_r_wet(ilon,ilev)*3)
142	ENDDO
143	ENDIF
144
145	!--Calculations for the coagulation kernel---------------------------------------------------------
146
147	zrho=pplay(ilon,ilev)/t_seri(ilon,ilev)/RD
148
149	!--initialize the tracer at time t and convert from [number/KgA] to [number/m3]
150	DO i=1, nbtr_bin
151	tr_t(ilon,ilev,i) = tr_seri(ilon,ilev,i+nbtr_sulgas) * zrho
152	ENDDO
153
154	! mean free path of air (Pruppacher and Klett, 2010, p.417) [m]
155	mnfrpth=6.6E-8(1.01325E+5/pplay(ilon,ilev))(t_seri(ilon,ilev)/293.15)
156	! mnfrpth=2.eta/(zrhothvelair)
157	! mean free path of air (Prupp. Klett) in [10^-6 m]
158	! ZLAIR = 0.066 (1.01325E+5/PPLAY)(T_SERI/293.15)*1.E-06
159
160	! dynamic viscosity of air (Pruppacher and Klett, 2010, p.417) [kg/(m*s)]
161	IF (t_seri(ilon,ilev).GE.273.15) THEN
162	eta=(1.718+0.0049(t_seri(ilon,ilev)-273.15))1.E-5
163	ELSE
164	eta=(1.718+0.0049(t_seri(ilon,ilev)-273.15)-1.2E-5(t_seri(ilon,ilev)-273.15)*2)1.E-5
165	ENDIF
166
167	!--pre-compute the particle diffusion coefficient Di(i) from equation 18
168	Di=0.0
169	DO i=1, nbtr_bin
170	Kn(i)=mnfrpth/radiuswet(i)
171	Di(i)=RKBOLt_seri(ilon,ilev)/(6.RPIradiuswet(i)eta)(1.+Kn(i)(1.249+0.42*exp(-0.87/Kn(i))))
172	ENDDO
173
174	!--pre-compute the thermal velocity of a particle thvelpar(i) from equation 20
175	thvelpar=0.0
176	IF(flag_new_strat_compo) THEN
177	DO i=1, nbtr_bin
178	m_par(i)=4./3.RPIradiuswet(i)*3.DENSO4B(ilon,ilev,i)*1000.
179	thvelpar(i)=sqrt(8.RKBOLt_seri(ilon,ilev)/(RPI*m_par(i)))
180	ENDDO
181	ELSE
182	DO i=1, nbtr_bin
183	m_par(i)=4./3.RPIradiuswet(i)*3.DENSO4(ilon,ilev)*1000.
184	thvelpar(i)=sqrt(8.RKBOLt_seri(ilon,ilev)/(RPI*m_par(i)))
185	ENDDO
186	ENDIF
187
188	!--pre-compute the particle mean free path mfppar(i) from equation 22
189	mfppar=0.0
190	DO i=1, nbtr_bin
191	mfppar(i)=8.Di(i)/(RPIthvelpar(i))
192	ENDDO
193
194	!--pre-compute the mean distance delta(i) from the center of a sphere reached by particles
195	!--leaving the surface of the sphere and traveling a distance of particle mfppar(i) from equation 21
196	delta=0.0
197	DO i=1, nbtr_bin
198	delta(i)=((2.radiuswet(i)+mfppar(i))3.-(4.radiuswet(i)2.+mfppar(i)2.)**1.5)/ &
199	& (6.radiuswet(i)mfppar(i))-2.*radiuswet(i)
200	ENDDO
201
202	! beta(i,j): coagulation kernel (rate coefficient) of 2 colliding particles i,j
203	!--pre-compute the beta(i,j) from equation 17 in Jacobson
204	num=0.0
205	DO j=1, nbtr_bin
206	DO i=1, nbtr_bin
207	!
208	num=4.RPI(radiuswet(i)+radiuswet(j))*(Di(i)+Di(j))
209	denom=(radiuswet(i)+radiuswet(j))/(radiuswet(i)+radiuswet(j)+sqrt(delta(i)2.+delta(j)2.))+ &
210	& 4.(Di(i)+Di(j))/(sqrt(thvelpar(i)2.+thvelpar(j)2.)(radiuswet(i)+radiuswet(j)))
211	beta(i,j)=num/denom
212	!
213	!--compute enhancement factor due to van der Waals forces
214	IF (ok_vdw .EQ. 0) THEN !--no enhancement factor
215	Evdw=1.0
216	ELSEIF (ok_vdw .EQ. 1) THEN !--E(0) case
217	AvdWi = AvdW/(RKBOLt_seri(ilon,ilev))(4.radiuswet(i)radiuswet(j))/(radiuswet(i)+radiuswet(j))**2.
218	xvdW = LOG(1.+AvdWi)
219	EvdW = 1. + avdW1xvdW + avdW3xvdW**3
220	ELSEIF (ok_vdw .EQ. 2) THEN !--E(infinity) case
221	AvdWi = AvdW/(RKBOLt_seri(ilon,ilev))(4.radiuswet(i)radiuswet(j))/(radiuswet(i)+radiuswet(j))**2.
222	xvdW = LOG(1.+AvdWi)
223	EvdW = 1. + SQRT(AvdWi/3.)/(1.+bvdW0SQRT(AvdWi)) + bvdW1xvdW + bvdW3xvdW*3.
224	ENDIF
225	!
226	beta(i,j)=beta(i,j)*EvdW
227
228	ENDDO
229	ENDDO
230
231	!--external loop for equation 14
232	DO k=1, nbtr_bin
233
234	!--calculating denominator sum
235	denom=0.0
236	DO j=1, nbtr_bin
237	! fraction of coagulation of k and j that is not giving k
238	denom=denom+(1.-ff(k,j,k))beta(k,j)tr_t(ilon,ilev,j)
239	ENDDO
240
241	IF (k.EQ.1) THEN
242	!--calculate new concentration of smallest bin
243	tr_tp1(ilon,ilev,k)=tr_t(ilon,ilev,k)/(1.+pdtcoag*denom)
244	ELSE
245	!--calculating double sum terms in numerator of eq 14
246	num=0.0
247	DO j=1, k
248	numi=0.0
249	DO i=1, k-1
250	!
251	! see Jacobson: " In order to conserve volume and volume concentration (which
252	! coagulation physically does) while giving up some accuracy in number concentration"
253	!
254	! Coagulation of i and j giving k
255	! with V(i) and then V(j) because it considers i,j and j,i with the double loop
256	!
257	! BUT WHY WET VOLUME V(i) in old STRATAER? tracers are already dry aerosols and coagulation
258	! kernel beta(i,j) accounts for wet aerosols -> reply below
259	!
260	! numi=numi+ff(i,j,k)beta(i,j)V(i)tr_tp1(ilon,ilev,i)tr_t(ilon,ilev,j)
261	numi=numi+ff(i,j,k)beta(i,j)Vdry(i)tr_tp1(ilon,ilev,i)tr_t(ilon,ilev,j)
262	ENDDO
263	num=num+numi
264	ENDDO
265
266	!--calculate new concentration of other bins
267	! tr_tp1(ilon,ilev,k)=(V(k)tr_t(ilon,ilev,k)+pdtcoagnum)/( (1.+pdtcoagdenom)V(k) )
268	tr_tp1(ilon,ilev,k)=(Vdry(k)tr_t(ilon,ilev,k)+pdtcoagnum)/( (1.+pdtcoagdenom)Vdry(k) )
269	!
270	! In constant composition (no dependency on aerosol size because no kelvin effect)
271	! V(l)= (f_r_wet(ilon,ilev)*3)((mdw(l)/2.)3) = (f_r_wet(ilon,ilev)3)*Vdry(i)
272	! so numi and num are proportional (f_r_wet(ilon,ilev)**3)
273	! and so
274	! tr_tp1(ilon,ilev,k)=(V(k)tr_t(ilon,ilev,k)+pdtcoagnum)/( (1.+pdtcoagdenom)V(k) )
275	! =(Vdry(k)tr_t(ilon,ilev,k)+pdtcoagnum_dry)/( (1.+pdtcoagdenom)Vdry(k) )
276	! with num_dry=...beta(i,j)Vdry(i)....
277	! so in old STRATAER (.not.flag_new_strat_compo), it was correct
278	ENDIF
279
280	ENDDO !--end of loop k
281
282	!--convert tracer concentration back from [number/m3] to [number/KgA] and write into tr_seri
283	DO i=1, nbtr_bin
284	tr_seri(ilon,ilev,i+nbtr_sulgas) = tr_tp1(ilon,ilev,i) / zrho
285	ENDDO
286
287	ENDIF ! IF IN STRATOSPHERE
288	ENDDO !--end of loop klev
289	ENDDO !--end of loop klon
290	! *********************************************
291
292	END SUBROUTINE COAGULATE

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