Context Navigation

traccoag_mod.F90 @ 5213

Last change on this file since 5213 was 3677, checked in by oboucher, 5 years ago

Changed the way to initialise nbtr_bin and other dimensions and indices
in the StratAer? module based on infotrac_phy rather than infotrac.

Also added a missing $OMP THREADPRIVATE(nqperes)

Property svn:keywords set to Id

File size: 19.4 KB

Line
1	!
2	! $Id: traccoag_mod.F90 3677 2020-05-06 15:18:32Z evignon $
3	!
4	MODULE traccoag_mod
5	!
6	! This module calculates the concentration of aerosol particles in certain size bins
7	! considering coagulation and sedimentation.
8	!
9	CONTAINS
10
11	SUBROUTINE traccoag(pdtphys, gmtime, debutphy, julien, &
12	presnivs, xlat, xlon, pphis, pphi, &
13	t_seri, pplay, paprs, sh, rh, tr_seri)
14
15	USE phys_local_var_mod, ONLY: mdw, R2SO4, DENSO4, f_r_wet, surf_PM25_sulf, &
16	& budg_emi_ocs, budg_emi_so2, budg_emi_h2so4, budg_emi_part
17
18	USE dimphy
19	USE infotrac_phy
20	USE aerophys
21	USE geometry_mod, ONLY : cell_area, boundslat
22	USE mod_grid_phy_lmdz
23	USE mod_phys_lmdz_mpi_data, ONLY : is_mpi_root
24	USE mod_phys_lmdz_para, only: gather, scatter
25	USE phys_cal_mod
26	USE sulfate_aer_mod
27	USE phys_local_var_mod, ONLY: stratomask
28	USE YOMCST
29	USE print_control_mod, ONLY: lunout
30	USE strataer_mod
31	USE phys_cal_mod, ONLY : year_len
32
33	IMPLICIT NONE
34
35	! Input argument
36	!---------------
37	REAL,INTENT(IN) :: pdtphys ! Pas d'integration pour la physique (seconde)
38	REAL,INTENT(IN) :: gmtime ! Heure courante
39	LOGICAL,INTENT(IN) :: debutphy ! le flag de l'initialisation de la physique
40	INTEGER,INTENT(IN) :: julien ! Jour julien
41
42	REAL,DIMENSION(klev),INTENT(IN) :: presnivs! pressions approximat. des milieux couches (en PA)
43	REAL,DIMENSION(klon),INTENT(IN) :: xlat ! latitudes pour chaque point
44	REAL,DIMENSION(klon),INTENT(IN) :: xlon ! longitudes pour chaque point
45	REAL,DIMENSION(klon),INTENT(IN) :: pphis ! geopotentiel du sol
46	REAL,DIMENSION(klon,klev),INTENT(IN) :: pphi ! geopotentiel de chaque couche
47
48	REAL,DIMENSION(klon,klev),INTENT(IN) :: t_seri ! Temperature
49	REAL,DIMENSION(klon,klev),INTENT(IN) :: pplay ! pression pour le mileu de chaque couche (en Pa)
50	REAL,DIMENSION(klon,klev+1),INTENT(IN) :: paprs ! pression pour chaque inter-couche (en Pa)
51	REAL,DIMENSION(klon,klev),INTENT(IN) :: sh ! humidite specifique
52	REAL,DIMENSION(klon,klev),INTENT(IN) :: rh ! humidite relative
53
54	! Output argument
55	!----------------
56	REAL,DIMENSION(klon,klev,nbtr),INTENT(INOUT) :: tr_seri ! Concentration Traceur [U/KgA]
57
58	! Local variables
59	!----------------
60	REAL :: m_aer_emiss_vol_daily ! daily injection mass emission
61	INTEGER :: it, k, i, ilon, ilev, itime, i_int, ieru
62	LOGICAL,DIMENSION(klon,klev) :: is_strato ! true = above tropopause, false = below
63	REAL,DIMENSION(klon,klev) :: m_air_gridbox ! mass of air in every grid box [kg]
64	REAL,DIMENSION(klon_glo,klev,nbtr) :: tr_seri_glo ! Concentration Traceur [U/KgA]
65	REAL,DIMENSION(klev+1) :: altLMDz ! altitude of layer interfaces in m
66	REAL,DIMENSION(klev) :: f_lay_emiss ! fraction of emission for every vertical layer
67	REAL :: f_lay_sum ! sum of layer emission fractions
68	REAL :: alt ! altitude for integral calculation
69	INTEGER,PARAMETER :: n_int_alt=10 ! number of subintervals for integration over Gaussian emission profile
70	REAL,DIMENSION(nbtr_bin) :: r_bin ! particle radius in size bin [m]
71	REAL,DIMENSION(nbtr_bin) :: r_lower ! particle radius at lower bin boundary [m]
72	REAL,DIMENSION(nbtr_bin) :: r_upper ! particle radius at upper bin boundary [m]
73	REAL,DIMENSION(nbtr_bin) :: m_part_dry ! mass of one dry particle in size bin [kg]
74	REAL :: zrho ! Density of air [kg/m3]
75	REAL :: zdz ! thickness of atm. model layer in m
76	REAL,DIMENSION(klev) :: zdm ! mass of atm. model layer in kg
77	REAL,DIMENSION(klon,klev) :: dens_aer ! density of aerosol particles [kg/m3 aerosol] with default H2SO4 mass fraction
78	REAL :: emission ! emission
79	REAL :: theta_min, theta_max ! for SAI computation between two latitudes
80	REAL :: dlat_loc
81
82	IF (is_mpi_root) THEN
83	WRITE(lunout,*) 'in traccoag: date from phys_cal_mod =',year_cur,'-',mth_cur,'-',day_cur,'-',hour
84	WRITE(lunout,*) 'IN traccoag flag_sulf_emit: ',flag_sulf_emit
85	ENDIF
86
87	DO it=1, nbtr_bin
88	r_bin(it)=mdw(it)/2.
89	ENDDO
90
91	!--set boundaries of size bins
92	DO it=1, nbtr_bin
93	IF (it.EQ.1) THEN
94	r_upper(it)=sqrt(r_bin(it+1)*r_bin(it))
95	r_lower(it)=r_bin(it)**2./r_upper(it)
96	ELSEIF (it.EQ.nbtr_bin) THEN
97	r_lower(it)=sqrt(r_bin(it)*r_bin(it-1))
98	r_upper(it)=r_bin(it)**2./r_lower(it)
99	ELSE
100	r_lower(it)=sqrt(r_bin(it)*r_bin(it-1))
101	r_upper(it)=sqrt(r_bin(it+1)*r_bin(it))
102	ENDIF
103	ENDDO
104
105	IF (debutphy .and. is_mpi_root) THEN
106	DO it=1, nbtr_bin
107	WRITE(lunout,*) 'radius bin', it, ':', r_bin(it), '(from', r_lower(it), 'to', r_upper(it), ')'
108	ENDDO
109	ENDIF
110
111	!--initialising logical is_strato from stratomask
112	is_strato(:,:)=.FALSE.
113	WHERE (stratomask.GT.0.5) is_strato=.TRUE.
114
115	! STRACOMP (H2O, P, t_seri -> aerosol composition (R2SO4))
116	! H2SO4 mass fraction in aerosol (%)
117	CALL stracomp(sh,t_seri,pplay)
118
119	! aerosol density (gr/cm3)
120	CALL denh2sa(t_seri)
121
122	! compute factor for converting dry to wet radius (for every grid box)
123	f_r_wet(:,:) = (dens_aer_dry/(DENSO4(:,:)1000.)/(R2SO4(:,:)/100.))*(1./3.)
124
125	!--calculate mass of air in every grid box
126	DO ilon=1, klon
127	DO ilev=1, klev
128	m_air_gridbox(ilon,ilev)=(paprs(ilon,ilev)-paprs(ilon,ilev+1))/RG*cell_area(ilon)
129	ENDDO
130	ENDDO
131
132	! IF (debutphy) THEN
133	! CALL gather(tr_seri, tr_seri_glo)
134	! IF (MAXVAL(tr_seri_glo).LT.1.e-30) THEN
135	!--initialising tracer concentrations to zero
136	! DO it=1, nbtr
137	! tr_seri(:,:,it)=0.0
138	! ENDDO
139	! ENDIF
140	! ENDIF
141
142	!--initialise emission diagnostics
143	budg_emi_ocs(:)=0.0
144	budg_emi_so2(:)=0.0
145	budg_emi_h2so4(:)=0.0
146	budg_emi_part(:)=0.0
147
148	!--sulfur emission, depending on chosen scenario (flag_sulf_emit)
149	SELECT CASE(flag_sulf_emit)
150
151	CASE(0) ! background aerosol
152	! do nothing (no emission)
153
154	CASE(1) ! volcanic eruption
155	!--only emit on day of eruption
156	! stretch emission over one day of Pinatubo eruption
157	DO ieru=1, nErupt
158	IF (year_cur==year_emit_vol(ieru).AND.mth_cur==mth_emit_vol(ieru).AND.&
159	day_cur>=day_emit_vol(ieru).AND.day_cur<(day_emit_vol(ieru)+injdur)) THEN
160	!
161	! daily injection mass emission - NL
162	m_aer_emiss_vol_daily = m_aer_emiss_vol(ieru)/(REAL(injdur)*REAL(ponde_lonlat_vol(ieru)))
163	WRITE(lunout,*) 'IN traccoag DD m_aer_emiss_vol(ieru)=',m_aer_emiss_vol(ieru), &
164	'ponde_lonlat_vol(ieru)=',ponde_lonlat_vol(ieru),'(injdur*ponde_lonlat_vol(ieru))', &
165	(injdur*ponde_lonlat_vol(ieru)),'m_aer_emiss_vol_daily=',m_aer_emiss_vol_daily,'ieru=',ieru
166	WRITE(lunout,*) 'IN traccoag, dlon=',dlon
167	DO i=1,klon
168	!Pinatubo eruption at 15.14N, 120.35E
169	dlat_loc=180./RPI/2.*(boundslat(i,1)-boundslat(i,3)) ! dlat = half difference of boundary latitudes
170	WRITE(lunout,*) 'IN traccoag, dlat=',dlat_loc
171	IF ( xlat(i).GE.xlat_min_vol(ieru)-dlat_loc .AND. xlat(i).LT.xlat_max_vol(ieru)+dlat_loc .AND. &
172	xlon(i).GE.xlon_min_vol(ieru)-dlon .AND. xlon(i).LT.xlon_max_vol(ieru)+dlon ) THEN
173	!
174	WRITE(lunout,*) 'coordinates of volcanic injection point=',xlat(i),xlon(i),day_cur,mth_cur,year_cur
175	WRITE(lunout,*) 'DD m_aer_emiss_vol_daily=',m_aer_emiss_vol_daily
176	! compute altLMDz
177	altLMDz(:)=0.0
178	DO k=1, klev
179	zrho=pplay(i,k)/t_seri(i,k)/RD !air density in kg/m3
180	zdm(k)=(paprs(i,k)-paprs(i,k+1))/RG !mass of layer in kg
181	zdz=zdm(k)/zrho !thickness of layer in m
182	altLMDz(k+1)=altLMDz(k)+zdz !altitude of interface
183	ENDDO
184
185	SELECT CASE(flag_sulf_emit_distrib)
186
187	CASE(0) ! Gaussian distribution
188	!compute distribution of emission to vertical model layers (based on Gaussian peak in altitude)
189	f_lay_sum=0.0
190	DO k=1, klev
191	f_lay_emiss(k)=0.0
192	DO i_int=1, n_int_alt
193	alt=altLMDz(k)+float(i_int)*(altLMDz(k+1)-altLMDz(k))/float(n_int_alt)
194	f_lay_emiss(k)=f_lay_emiss(k)+1./(sqrt(2.RPI)sigma_alt_vol(ieru))* &
195	& exp(-0.5((alt-altemiss_vol(ieru))/sigma_alt_vol(ieru))2.) &
196	& (altLMDz(k+1)-altLMDz(k))/float(n_int_alt)
197	ENDDO
198	f_lay_sum=f_lay_sum+f_lay_emiss(k)
199	ENDDO
200
201	CASE(1) ! Uniform distribution
202	! In this case, parameter sigma_alt_vol(ieru) is considered to be half the
203	! height of the injection, centered around altemiss_vol(ieru)
204	DO k=1, klev
205	f_lay_emiss(k)=max(min(altemiss_vol(ieru)+sigma_alt_vol(ieru),altLMDz(k+1))- &
206	& max(altemiss_vol(ieru)-sigma_alt_vol(ieru),altLMDz(k)),0.)/(2.*sigma_alt_vol(ieru))
207	f_lay_sum=f_lay_sum+f_lay_emiss(k)
208	ENDDO
209
210	END SELECT ! End CASE over flag_sulf_emit_distrib)
211
212	WRITE(lunout,*) "IN traccoag m_aer_emiss_vol=",m_aer_emiss_vol(ieru)
213	WRITE(lunout,*) "IN traccoag f_lay_emiss=",f_lay_emiss
214	!correct for step integration error
215	f_lay_emiss(:)=f_lay_emiss(:)/f_lay_sum
216	!emission as SO2 gas (with m(SO2)=64/32*m_aer_emiss)
217	!vertically distributed emission
218	DO k=1, klev
219	! stretch emission over one day of Pinatubo eruption
220	emission=m_aer_emiss_vol_daily(mSO2mol/mSatom)/m_air_gridbox(i,k)f_lay_emiss(k)/1./(86400.-pdtphys)
221	tr_seri(i,k,id_SO2_strat)=tr_seri(i,k,id_SO2_strat)+emission*pdtphys
222	budg_emi_so2(i)=budg_emi_so2(i)+emissionzdm(k)mSatom/mSO2mol
223	ENDDO
224	ENDIF ! emission grid cell
225	ENDDO ! klon loop
226	WRITE(lunout,*) "IN traccoag (ieru=",ieru,") m_aer_emiss_vol_daily=",m_aer_emiss_vol_daily
227	ENDIF ! emission period
228	ENDDO ! eruption number
229
230	CASE(2) ! stratospheric aerosol injections (SAI)
231	!
232	DO i=1,klon
233	! SAI standard scenario with continuous emission from 1 grid point at the equator
234	! SAI emission on single month
235	! SAI continuous emission o
236	dlat_loc=180./RPI/2.*(boundslat(i,1)-boundslat(i,3)) ! dlat = half difference of boundary latitudes
237	IF ( xlat(i).GE.xlat_sai-dlat_loc .AND. xlat(i).LT.xlat_sai+dlat_loc .AND. &
238	& xlon(i).GE.xlon_sai-dlon .AND. xlon(i).LT.xlon_sai+dlon ) THEN
239	!
240	! compute altLMDz
241	altLMDz(:)=0.0
242	DO k=1, klev
243	zrho=pplay(i,k)/t_seri(i,k)/RD !air density in kg/m3
244	zdm(k)=(paprs(i,k)-paprs(i,k+1))/RG !mass of layer in kg
245	zdz=zdm(k)/zrho !thickness of layer in m
246	altLMDz(k+1)=altLMDz(k)+zdz !altitude of interface
247	ENDDO
248
249	SELECT CASE(flag_sulf_emit_distrib)
250
251	CASE(0) ! Gaussian distribution
252	!compute distribution of emission to vertical model layers (based on Gaussian peak in altitude)
253	f_lay_sum=0.0
254	DO k=1, klev
255	f_lay_emiss(k)=0.0
256	DO i_int=1, n_int_alt
257	alt=altLMDz(k)+float(i_int)*(altLMDz(k+1)-altLMDz(k))/float(n_int_alt)
258	f_lay_emiss(k)=f_lay_emiss(k)+1./(sqrt(2.RPI)sigma_alt_sai)* &
259	& exp(-0.5((alt-altemiss_sai)/sigma_alt_sai)2.) &
260	& (altLMDz(k+1)-altLMDz(k))/float(n_int_alt)
261	ENDDO
262	f_lay_sum=f_lay_sum+f_lay_emiss(k)
263	ENDDO
264
265	CASE(1) ! Uniform distribution
266	f_lay_sum=0.0
267	! In this case, parameter sigma_alt_vol(ieru) is considered to be half
268	! the height of the injection, centered around altemiss_sai
269	DO k=1, klev
270	f_lay_emiss(k)=max(min(altemiss_sai+sigma_alt_sai,altLMDz(k+1))- &
271	& max(altemiss_sai-sigma_alt_sai,altLMDz(k)),0.)/(2.*sigma_alt_sai)
272	f_lay_sum=f_lay_sum+f_lay_emiss(k)
273	ENDDO
274
275	END SELECT ! Gaussian or uniform distribution
276
277	!correct for step integration error
278	f_lay_emiss(:)=f_lay_emiss(:)/f_lay_sum
279	!emission as SO2 gas (with m(SO2)=64/32*m_aer_emiss)
280	!vertically distributed emission
281	DO k=1, klev
282	! stretch emission over whole year (360d)
283	emission=m_aer_emiss_sai(mSO2mol/mSatom)/m_air_gridbox(i,k)f_lay_emiss(k)/FLOAT(year_len)/86400.
284	tr_seri(i,k,id_SO2_strat)=tr_seri(i,k,id_SO2_strat)+emission*pdtphys
285	budg_emi_so2(i)=budg_emi_so2(i)+emissionzdm(k)mSatom/mSO2mol
286	ENDDO
287
288	! !emission as monodisperse particles with 0.1um dry radius (BIN21)
289	! !vertically distributed emission
290	! DO k=1, klev
291	! ! stretch emission over whole year (360d)
292	! emission=m_aer_emiss(mH2SO4mol/mSatom)/m_part_dry(21)/m_air_gridbox(i,k)f_lay_emiss(k)/FLOAT(year_len)/86400.
293	! tr_seri(i,k,id_BIN01_strat+20)=tr_seri(i,k,id_BIN01_strat+20)+emission*pdtphys
294	! budg_emi_part(i)=budg_emi_part(i)+emissionzdm(k)mSatom/mH2SO4mol
295	! ENDDO
296	ENDIF ! emission grid cell
297	ENDDO ! klon loop
298
299	CASE(3) ! --- SAI injection over a single band of longitude and between
300	! lat_min and lat_max
301
302	DO i=1,klon
303	! SAI scenario with continuous emission
304	dlat_loc=180./RPI/2.*(boundslat(i,1)-boundslat(i,3)) ! dlat = half difference of boundary latitudes
305	theta_min = max(xlat(i)-dlat_loc,xlat_min_sai)
306	theta_max = min(xlat(i)+dlat_loc,xlat_max_sai)
307	IF ( xlat(i).GE.xlat_min_sai-dlat_loc .AND. xlat(i).LT.xlat_max_sai+dlat_loc .AND. &
308	& xlon(i).GE.xlon_sai-dlon .AND. xlon(i).LT.xlon_sai+dlon ) THEN
309	!
310	! compute altLMDz
311	altLMDz(:)=0.0
312	DO k=1, klev
313	zrho=pplay(i,k)/t_seri(i,k)/RD !air density in kg/m3
314	zdm(k)=(paprs(i,k)-paprs(i,k+1))/RG !mass of layer in kg
315	zdz=zdm(k)/zrho !thickness of layer in m
316	altLMDz(k+1)=altLMDz(k)+zdz !altitude of interface
317	ENDDO
318
319	SELECT CASE(flag_sulf_emit_distrib)
320
321	CASE(0) ! Gaussian distribution
322	!compute distribution of emission to vertical model layers (based on
323	!Gaussian peak in altitude)
324	f_lay_sum=0.0
325	DO k=1, klev
326	f_lay_emiss(k)=0.0
327	DO i_int=1, n_int_alt
328	alt=altLMDz(k)+float(i_int)*(altLMDz(k+1)-altLMDz(k))/float(n_int_alt)
329	f_lay_emiss(k)=f_lay_emiss(k)+1./(sqrt(2.RPI)sigma_alt_sai)* &
330	& exp(-0.5((alt-altemiss_sai)/sigma_alt_sai)2.) &
331	& (altLMDz(k+1)-altLMDz(k))/float(n_int_alt)
332	ENDDO
333	f_lay_sum=f_lay_sum+f_lay_emiss(k)
334	ENDDO
335
336	CASE(1) ! Uniform distribution
337	f_lay_sum=0.0
338	! In this case, parameter sigma_alt_vol(ieru) is considered to be half
339	! the height of the injection, centered around altemiss_sai
340	DO k=1, klev
341	f_lay_emiss(k)=max(min(altemiss_sai+sigma_alt_sai,altLMDz(k+1))- &
342	& max(altemiss_sai-sigma_alt_sai,altLMDz(k)),0.)/(2.*sigma_alt_sai)
343	f_lay_sum=f_lay_sum+f_lay_emiss(k)
344	ENDDO
345
346	END SELECT ! Gaussian or uniform distribution
347
348	!correct for step integration error
349	f_lay_emiss(:)=f_lay_emiss(:)/f_lay_sum
350	!emission as SO2 gas (with m(SO2)=64/32*m_aer_emiss)
351	!vertically distributed emission
352	DO k=1, klev
353	! stretch emission over whole year (360d)
354	emission=m_aer_emiss_sai(mSO2mol/mSatom)/m_air_gridbox(i,k)f_lay_emiss(k)/ &
355	& FLOAT(year_len)/86400.(sin(theta_max/180.RPI)-sin(theta_min/180.*RPI))/ &
356	& (sin(xlat_max_sai/180.RPI)-sin(xlat_min_sai/180.RPI))
357	tr_seri(i,k,id_SO2_strat)=tr_seri(i,k,id_SO2_strat)+emission*pdtphys
358	budg_emi_so2(i)=budg_emi_so2(i)+emissionzdm(k)mSatom/mSO2mol
359	ENDDO
360
361	! !emission as monodisperse particles with 0.1um dry radius (BIN21)
362	! !vertically distributed emission
363	! DO k=1, klev
364	! ! stretch emission over whole year (360d)
365	! emission=m_aer_emiss(mH2SO4mol/mSatom)/m_part_dry(21)/m_air_gridbox(i,k)f_lay_emiss(k)/year_len/86400
366	! tr_seri(i,k,id_BIN01_strat+20)=tr_seri(i,k,id_BIN01_strat+20)+emission*pdtphys
367	! budg_emi_part(i)=budg_emi_part(i)+emissionzdm(k)mSatom/mH2SO4mol
368	! ENDDO
369	ENDIF ! emission grid cell
370	ENDDO ! klon loop
371
372	END SELECT ! emission scenario (flag_sulf_emit)
373
374	!--read background concentrations of OCS and SO2 and lifetimes from input file
375	!--update the variables defined in phys_local_var_mod
376	CALL interp_sulf_input(debutphy,pdtphys,paprs,tr_seri)
377
378	!--convert OCS to SO2 in the stratosphere
379	CALL ocs_to_so2(pdtphys,tr_seri,t_seri,pplay,paprs,is_strato)
380
381	!--convert SO2 to H2SO4
382	CALL so2_to_h2so4(pdtphys,tr_seri,t_seri,pplay,paprs,is_strato)
383
384	!--common routine for nucleation and condensation/evaporation with adaptive timestep
385	CALL micphy_tstep(pdtphys,tr_seri,t_seri,pplay,paprs,rh,is_strato)
386
387	!--call coagulation routine
388	CALL coagulate(pdtphys,mdw,tr_seri,t_seri,pplay,dens_aer,is_strato)
389
390	!--call sedimentation routine
391	CALL aer_sedimnt(pdtphys, t_seri, pplay, paprs, tr_seri, dens_aer)
392
393	!--compute mass concentration of PM2.5 sulfate particles (wet diameter and mass) at the surface for health studies
394	surf_PM25_sulf(:)=0.0
395	DO i=1,klon
396	DO it=1, nbtr_bin
397	IF (mdw(it) .LT. 2.5e-6) THEN
398	!surf_PM25_sulf(i)=surf_PM25_sulf(i)+tr_seri(i,1,it+nbtr_sulgas)*m_part(i,1,it) &
399	!assume that particles consist of ammonium sulfate at the surface (132g/mol)
400	!and are dry at T = 20 deg. C and 50 perc. humidity
401	surf_PM25_sulf(i)=surf_PM25_sulf(i)+tr_seri(i,1,it+nbtr_sulgas) &
402	& 132./98.dens_aer_dry4./3.RPI(mdw(it)/2.)*3 &
403	& pplay(i,1)/t_seri(i,1)/RD1.e9
404	ENDIF
405	ENDDO
406	ENDDO
407
408	! CALL minmaxsimple(tr_seri(:,:,id_SO2_strat),0.0,0.0,'fin SO2')
409	! DO it=1, nbtr_bin
410	! CALL minmaxsimple(tr_seri(:,:,nbtr_sulgas+it),0.0,0.0,'fin bin ')
411	! ENDDO
412
413	END SUBROUTINE traccoag
414
415	END MODULE traccoag_mod

Note: See TracBrowser for help on using the repository browser.

Download in other formats:

Original Format