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coagulate.F90 @ 5409

Last change on this file since 5409 was 5117, checked in by abarral, 5 months ago
rename modules properly lmdz_* move some unused files to obsolete/ (lint) uppercase fortran keywords
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1
2	! $Id: coagulate.F90 5117 2024-07-24 14:23:34Z evignon $
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	USE lmdz_yomcst
31
32	IMPLICIT NONE
33
34	!--------------------------------------------------------
35
36	! transfer variables when calling this routine
37	REAL,INTENT(IN) :: pdtcoag ! Time step in coagulation routine [s]
38	REAL,DIMENSION(nbtr_bin),INTENT(IN) :: mdw ! aerosol particle diameter in each bin [m]
39	REAL,DIMENSION(klon,klev,nbtr),INTENT(INOUT) :: tr_seri ! Concentration Traceur [U/KgA]
40	REAL,DIMENSION(klon,klev),INTENT(IN) :: t_seri ! Temperature
41	REAL,DIMENSION(klon,klev),INTENT(IN) :: pplay ! pression pour le mileu de chaque couche (en Pa)
42	REAL,DIMENSION(klon,klev) :: dens_aer! density of aerosol [kg/m3 aerosol] with default H2SO4 mass
43	LOGICAL,DIMENSION(klon,klev),INTENT(IN) :: is_strato
44
45	! local variables in coagulation routine
46	INTEGER :: i,j,k,nb,ilon,ilev
47	REAL, DIMENSION(nbtr_bin) :: radiusdry ! dry aerosol particle radius in each bin [m]
48	REAL, DIMENSION(nbtr_bin) :: radiuswet ! wet aerosol particle radius in each bin [m]
49	REAL, DIMENSION(klon,klev,nbtr_bin) :: tr_t ! Concentration Traceur at time t [U/KgA]
50	REAL, DIMENSION(klon,klev,nbtr_bin) :: tr_tp1 ! Concentration Traceur at time t+1 [U/KgA]
51	REAL, DIMENSION(nbtr_bin,nbtr_bin,nbtr_bin) :: ff ! Volume fraction of intermediate particles
52	REAL, DIMENSION(nbtr_bin) :: Vdry ! Volume dry of bins
53	REAL, DIMENSION(nbtr_bin) :: Vwet ! Volume wet of bins
54	REAL, DIMENSION(nbtr_bin,nbtr_bin) :: Vij ! Volume sum of i and j
55	REAL :: eta ! Dynamic viscosity of air
56	REAL, PARAMETER :: mair=4.8097E-26 ! Average mass of an air molecule [kg]
57	REAL :: zrho ! Density of air
58	REAL :: mnfrpth ! Mean free path of air
59	REAL, DIMENSION(nbtr_bin) :: Kn ! Knudsen number of particle i
60	REAL, DIMENSION(nbtr_bin) :: Di ! Particle diffusion coefficient
61	REAL, DIMENSION(nbtr_bin) :: m_par ! Mass of particle i
62	REAL, DIMENSION(nbtr_bin) :: thvelpar! Thermal velocity of particle i
63	REAL, DIMENSION(nbtr_bin) :: mfppar ! Mean free path of particle i
64	REAL, DIMENSION(nbtr_bin) :: delta! delta of particle i (from equation 21)
65	REAL, DIMENSION(nbtr_bin,nbtr_bin) :: beta ! Coagulation kernel from Brownian diffusion
66	REAL :: beta_const ! Constant coagulation kernel (for comparison)
67	REAL :: num
68	REAL :: numi
69	REAL :: denom
70
71	! Additional variables for coagulation enhancement factor due to van der Waals forces
72	! Taken from Chan and Mozurkewich, Measurement of the coagulation rate constant for sulfuric acid
73	! particles as a function of particle size using TDMA, Aerosol Science, 32, 321-339, 2001.
74	!--ok_vdw is 0 for no vdW forces, 1 for E(0), 2 for E(infinity)
75	INTEGER, PARAMETER :: ok_vdw = 0
76	REAL, PARAMETER :: avdW1 = 0.0757
77	REAL, PARAMETER :: avdW3 = 0.0015
78	REAL, PARAMETER :: bvdW0 = 0.0151
79	REAL, PARAMETER :: bvdW1 = -0.186
80	REAL, PARAMETER :: bvdW3 = -0.0163
81	REAL, PARAMETER :: AvdW = 6.4e-20 !Hamaker constant in J = 1e7 erg
82	REAL :: AvdWi
83	REAL :: xvdW
84	REAL :: EvdW
85
86	! ff(i,j,k): Volume fraction of Vi,j that is partitioned to each model bin k
87	! just need to be calculated in model initialization because mdw(:) size is fixed
88	! no need to recalculate radius, Vdry, Vij, and ff every timestep because it is for
89	! dry aerosols
90	DO i=1, nbtr_bin
91	radiusdry(i)=mdw(i)/2.
92	Vdry(i)=radiusdry(i)*3. !neglecting factor 4RPI/3
93	Vwet(i)=0.0
94	ENDDO
95
96	DO j=1, nbtr_bin
97	DO i=1, nbtr_bin
98	Vij(i,j)= Vdry(i)+Vdry(j)
99	ENDDO
100	ENDDO
101
102	!--pre-compute the f(i,j,k) from Jacobson equation 13
103	ff=0.0
104	DO k=1, nbtr_bin
105	DO j=1, nbtr_bin
106	DO i=1, nbtr_bin
107	IF (k==1) THEN
108	ff(i,j,k)= 0.0
109	ELSEIF (k>1.AND.Vdry(k-1)<Vij(i,j).AND.Vij(i,j)<Vdry(k)) THEN
110	ff(i,j,k)= 1.-ff(i,j,k-1)
111	ELSEIF (k==nbtr_bin) THEN
112	IF (Vij(i,j)>=Vdry(k)) THEN
113	ff(i,j,k)= 1.
114	ELSE
115	ff(i,j,k)= 0.0
116	ENDIF
117	ELSEIF (k<=(nbtr_bin-1).AND.Vdry(k)<=Vij(i,j).AND.Vij(i,j)<Vdry(k+1)) THEN
118	ff(i,j,k)= Vdry(k)/Vij(i,j)*(Vdry(k+1)-Vij(i,j))/(Vdry(k+1)-Vdry(k))
119	ENDIF
120	ENDDO
121	ENDDO
122	ENDDO
123	! End of just need to be calculated at initialization because mdw(:) size is fixed
124
125	DO ilon=1, klon
126	DO ilev=1, klev
127	!only in the stratosphere
128	IF (is_strato(ilon,ilev)) THEN
129	!compute actual wet particle radius & volume for every grid box
130	IF(flag_new_strat_compo) THEN
131	DO i=1, nbtr_bin
132	radiuswet(i)=f_r_wetB(ilon,ilev,i)*mdw(i)/2.
133	Vwet(i)= radiuswet(i)*3. !neglecting factor 4RPI/3
134	!! Vwet(i)= Vdry(i)(f_r_wetB(ilon,ilev,i)*3)
135	ENDDO
136	ELSE
137	DO i=1, nbtr_bin
138	radiuswet(i)=f_r_wet(ilon,ilev)*mdw(i)/2.
139	Vwet(i)= radiuswet(i)*3. !neglecting factor 4RPI/3
140	!! Vwet(i)= Vdry(i)(f_r_wet(ilon,ilev)*3)
141	ENDDO
142	ENDIF
143
144	!--Calculations for the coagulation kernel---------------------------------------------------------
145
146	zrho=pplay(ilon,ilev)/t_seri(ilon,ilev)/RD
147
148	!--initialize the tracer at time t and convert from [number/KgA] to [number/m3]
149	DO i=1, nbtr_bin
150	tr_t(ilon,ilev,i) = tr_seri(ilon,ilev,i+nbtr_sulgas) * zrho
151	ENDDO
152
153	! mean free path of air (Pruppacher and Klett, 2010, p.417) [m]
154	mnfrpth=6.6E-8(1.01325E+5/pplay(ilon,ilev))(t_seri(ilon,ilev)/293.15)
155	! mnfrpth=2.eta/(zrhothvelair)
156	! mean free path of air (Prupp. Klett) in [10^-6 m]
157	! ZLAIR = 0.066 (1.01325E+5/PPLAY)(T_SERI/293.15)*1.E-06
158
159	! dynamic viscosity of air (Pruppacher and Klett, 2010, p.417) [kg/(m*s)]
160	IF (t_seri(ilon,ilev)>=273.15) THEN
161	eta=(1.718+0.0049(t_seri(ilon,ilev)-273.15))1.E-5
162	ELSE
163	eta=(1.718+0.0049(t_seri(ilon,ilev)-273.15)-1.2E-5(t_seri(ilon,ilev)-273.15)*2)1.E-5
164	ENDIF
165
166	!--pre-compute the particle diffusion coefficient Di(i) from equation 18
167	Di=0.0
168	DO i=1, nbtr_bin
169	Kn(i)=mnfrpth/radiuswet(i)
170	Di(i)=RKBOLt_seri(ilon,ilev)/(6.RPIradiuswet(i)eta)(1.+Kn(i)(1.249+0.42*exp(-0.87/Kn(i))))
171	ENDDO
172
173	!--pre-compute the thermal velocity of a particle thvelpar(i) from equation 20
174	thvelpar=0.0
175	IF(flag_new_strat_compo) THEN
176	DO i=1, nbtr_bin
177	m_par(i)=4./3.RPIradiuswet(i)*3.DENSO4B(ilon,ilev,i)*1000.
178	thvelpar(i)=sqrt(8.RKBOLt_seri(ilon,ilev)/(RPI*m_par(i)))
179	ENDDO
180	ELSE
181	DO i=1, nbtr_bin
182	m_par(i)=4./3.RPIradiuswet(i)*3.DENSO4(ilon,ilev)*1000.
183	thvelpar(i)=sqrt(8.RKBOLt_seri(ilon,ilev)/(RPI*m_par(i)))
184	ENDDO
185	ENDIF
186
187	!--pre-compute the particle mean free path mfppar(i) from equation 22
188	mfppar=0.0
189	DO i=1, nbtr_bin
190	mfppar(i)=8.Di(i)/(RPIthvelpar(i))
191	ENDDO
192
193	!--pre-compute the mean distance delta(i) from the center of a sphere reached by particles
194	!--leaving the surface of the sphere and traveling a distance of particle mfppar(i) from equation 21
195	delta=0.0
196	DO i=1, nbtr_bin
197	delta(i)=((2.radiuswet(i)+mfppar(i))3.-(4.radiuswet(i)2.+mfppar(i)2.)**1.5)/ &
198	(6.radiuswet(i)mfppar(i))-2.*radiuswet(i)
199	ENDDO
200
201	! beta(i,j): coagulation kernel (rate coefficient) of 2 colliding particles i,j
202	!--pre-compute the beta(i,j) from equation 17 in Jacobson
203	num=0.0
204	DO j=1, nbtr_bin
205	DO i=1, nbtr_bin
206
207	num=4.RPI(radiuswet(i)+radiuswet(j))*(Di(i)+Di(j))
208	denom=(radiuswet(i)+radiuswet(j))/(radiuswet(i)+radiuswet(j)+sqrt(delta(i)2.+delta(j)2.))+ &
209	4.(Di(i)+Di(j))/(sqrt(thvelpar(i)2.+thvelpar(j)2.)(radiuswet(i)+radiuswet(j)))
210	beta(i,j)=num/denom
211
212	!--compute enhancement factor due to van der Waals forces
213	IF (ok_vdw == 0) THEN !--no enhancement factor
214	Evdw=1.0
215	ELSEIF (ok_vdw == 1) THEN !--E(0) case
216	AvdWi = AvdW/(RKBOLt_seri(ilon,ilev))(4.radiuswet(i)radiuswet(j))/(radiuswet(i)+radiuswet(j))**2.
217	xvdW = LOG(1.+AvdWi)
218	EvdW = 1. + avdW1xvdW + avdW3xvdW**3
219	ELSEIF (ok_vdw == 2) THEN !--E(infinity) case
220	AvdWi = AvdW/(RKBOLt_seri(ilon,ilev))(4.radiuswet(i)radiuswet(j))/(radiuswet(i)+radiuswet(j))**2.
221	xvdW = LOG(1.+AvdWi)
222	EvdW = 1. + SQRT(AvdWi/3.)/(1.+bvdW0SQRT(AvdWi)) + bvdW1xvdW + bvdW3xvdW*3.
223	ENDIF
224
225	beta(i,j)=beta(i,j)*EvdW
226
227	ENDDO
228	ENDDO
229
230	!--external loop for equation 14
231	DO k=1, nbtr_bin
232
233	!--calculating denominator sum
234	denom=0.0
235	DO j=1, nbtr_bin
236	! fraction of coagulation of k and j that is not giving k
237	denom=denom+(1.-ff(k,j,k))beta(k,j)tr_t(ilon,ilev,j)
238	ENDDO
239
240	IF (k==1) THEN
241	!--calculate new concentration of smallest bin
242	tr_tp1(ilon,ilev,k)=tr_t(ilon,ilev,k)/(1.+pdtcoag*denom)
243	ELSE
244	!--calculating double sum terms in numerator of eq 14
245	num=0.0
246	DO j=1, k
247	numi=0.0
248	DO i=1, k-1
249
250	! see Jacobson: " In order to conserve volume and volume concentration (which
251	! coagulation physically does) while giving up some accuracy in number concentration"
252
253	! Coagulation of i and j giving k
254	! with V(i) and then V(j) because it considers i,j and j,i with the double loop
255
256	! BUT WHY WET VOLUME V(i) in old STRATAER? tracers are already dry aerosols and coagulation
257	! kernel beta(i,j) accounts for wet aerosols -> reply below
258
259	! numi=numi+ff(i,j,k)beta(i,j)V(i)tr_tp1(ilon,ilev,i)tr_t(ilon,ilev,j)
260	numi=numi+ff(i,j,k)beta(i,j)Vdry(i)tr_tp1(ilon,ilev,i)tr_t(ilon,ilev,j)
261	ENDDO
262	num=num+numi
263	ENDDO
264
265	!--calculate new concentration of other bins
266	! tr_tp1(ilon,ilev,k)=(V(k)tr_t(ilon,ilev,k)+pdtcoagnum)/( (1.+pdtcoagdenom)V(k) )
267	tr_tp1(ilon,ilev,k)=(Vdry(k)tr_t(ilon,ilev,k)+pdtcoagnum)/( (1.+pdtcoagdenom)Vdry(k) )
268
269	! In constant composition (no dependency on aerosol size because no kelvin effect)
270	! V(l)= (f_r_wet(ilon,ilev)*3)((mdw(l)/2.)3) = (f_r_wet(ilon,ilev)3)*Vdry(i)
271	! so numi and num are proportional (f_r_wet(ilon,ilev)**3)
272	! and so
273	! tr_tp1(ilon,ilev,k)=(V(k)tr_t(ilon,ilev,k)+pdtcoagnum)/( (1.+pdtcoagdenom)V(k) )
274	! =(Vdry(k)tr_t(ilon,ilev,k)+pdtcoagnum_dry)/( (1.+pdtcoagdenom)Vdry(k) )
275	! with num_dry=...beta(i,j)Vdry(i)....
276	! so in old STRATAER (.NOT.flag_new_strat_compo), it was correct
277	ENDIF
278
279	ENDDO !--end of loop k
280
281	!--convert tracer concentration back from [number/m3] to [number/KgA] and write into tr_seri
282	DO i=1, nbtr_bin
283	tr_seri(ilon,ilev,i+nbtr_sulgas) = tr_tp1(ilon,ilev,i) / zrho
284	ENDDO
285
286	ENDIF ! IF IN STRATOSPHERE
287	ENDDO !--end of loop klev
288	ENDDO !--end of loop klon
289	! *********************************************
290
291	END SUBROUTINE COAGULATE

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