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lmdz_lscp_tools.F90 @ 5407

Last change on this file since 5407 was 5202, checked in by Laurent Fairhead, 3 months ago
Updating cirrus branch to trunk revision 5171
File size: 35.4 KB

Rev	Line
[4665]	1	MODULE lmdz_lscp_tools
[3999]	2
	3	IMPLICIT NONE
	4
	5	CONTAINS
	6
	7	!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
	8	SUBROUTINE FALLICE_VELOCITY(klon,iwc,temp,rho,pres,ptconv,velo)
	9
	10	! Ref:
	11	! Stubenrauch, C. J., Bonazzola, M.,
	12	! Protopapadaki, S. E., & Musat, I. (2019).
	13	! New cloud system metrics to assess bulk
	14	! ice cloud schemes in a GCM. Journal of
	15	! Advances in Modeling Earth Systems, 11,
	16	! 3212–3234. https://doi.org/10.1029/2019MS001642
	17
[4665]	18	use lmdz_lscp_ini, only: iflag_vice, ffallv_con, ffallv_lsc
	19	use lmdz_lscp_ini, only: cice_velo, dice_velo
[4535]	20
[3999]	21	IMPLICIT NONE
	22
	23	INTEGER, INTENT(IN) :: klon
	24	REAL, INTENT(IN), DIMENSION(klon) :: iwc ! specific ice water content [kg/m3]
	25	REAL, INTENT(IN), DIMENSION(klon) :: temp ! temperature [K]
	26	REAL, INTENT(IN), DIMENSION(klon) :: rho ! dry air density [kg/m3]
	27	REAL, INTENT(IN), DIMENSION(klon) :: pres ! air pressure [Pa]
	28	LOGICAL, INTENT(IN), DIMENSION(klon) :: ptconv ! convective point [-]
	29
	30	REAL, INTENT(OUT), DIMENSION(klon) :: velo ! fallspeed velocity of crystals [m/s]
	31
	32
	33	INTEGER i
[4559]	34	REAL logvm,iwcg,tempc,phpa,fallv_tun
[3999]	35	REAL m2ice, m2snow, vmice, vmsnow
	36	REAL aice, bice, asnow, bsnow
	37
	38
	39	DO i=1,klon
	40
	41	IF (ptconv(i)) THEN
	42	fallv_tun=ffallv_con
	43	ELSE
	44	fallv_tun=ffallv_lsc
	45	ENDIF
	46
	47	tempc=temp(i)-273.15 ! celcius temp
[4072]	48	iwcg=MAX(iwc(i)*1000.,1E-3) ! iwc in g/m3. We set a minimum value to prevent from division by 0
[3999]	49	phpa=pres(i)/100. ! pressure in hPa
	50
	51	IF (iflag_vice .EQ. 1) THEN
	52	! so-called 'empirical parameterization' in Stubenrauch et al. 2019
	53	if (tempc .GE. -60.0) then
	54
	55	logvm= -0.0000414122tempctempclog(iwcg)-0.00538922tempc*log(iwcg) &
	56	-0.0516344log(iwcg)+0.00216078tempc + 1.9714
	57	velo(i)=exp(logvm)
	58	else
	59	velo(i)=65.0(iwcg0.2)(150./phpa)**0.15
	60	endif
	61
	62	velo(i)=fallv_tun*velo(i)/100.0 ! from cm/s to m/s
	63
	64	ELSE IF (iflag_vice .EQ. 2) THEN
	65	! so called PSDM empirical coherent bulk ice scheme in Stubenrauch et al. 2019
	66	aice=0.587
	67	bice=2.45
	68	asnow=0.0444
	69	bsnow=2.1
	70
	71	m2ice=((iwcg0.001/aice)/(exp(13.6-bice7.76+0.479bice2) &
	72	exp((-0.0361+bice0.0151+0.00149bice*2)tempc))) &
	73	*(1./(0.807+bice0.00581+0.0457bice*2))
	74
[4072]	75	vmice=100.1042.4exp(13.6-(bice+1)7.76+0.479(bice+1.)*2)exp((-0.0361+ &
	76	(bice+1.)0.0151+0.00149(bice+1.)*2)tempc) &
	77	(m2ice(0.807+(bice+1.)0.00581+0.0457(bice+1.)2))/(iwcg0.001/aice)
[3999]	78
	79
	80	vmice=vmice((1000./phpa)*0.2)
	81
	82	m2snow=((iwcg0.001/asnow)/(exp(13.6-bsnow7.76+0.479bsnow2) &
	83	exp((-0.0361+bsnow0.0151+0.00149bsnow*2)tempc))) &
	84	*(1./(0.807+bsnow0.00581+0.0457bsnow*2))
	85
	86
	87	vmsnow=100.14.3exp(13.6-(bsnow+.416)7.76+0.479(bsnow+.416)**2)&
	88	exp((-0.0361+(bsnow+.416)0.0151+0.00149(bsnow+.416)2)tempc)&
	89	(m2snow(0.807+(bsnow+.416)0.00581+0.0457(bsnow+.416)2))/(iwcg0.001/asnow)
	90
	91	vmsnow=vmsnow((1000./phpa)*0.35)
	92	velo(i)=fallv_tun*min(vmsnow,vmice)/100. ! to m/s
	93
	94	ELSE
	95	! By default, fallspeed velocity of ice crystals according to Heymsfield & Donner 1990
[4559]	96	velo(i) = fallv_tuncice_velo((iwcg/1000.)**dice_velo)
[3999]	97	ENDIF
	98	ENDDO
	99
	100	END SUBROUTINE FALLICE_VELOCITY
	101	!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
	102
	103	!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
[4639]	104	SUBROUTINE ICEFRAC_LSCP(klon, temp, iflag_ice_thermo, distcltop, temp_cltop, icefrac, dicefracdT)
[3999]	105	!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
	106
	107	! Compute the ice fraction 1-xliq (see e.g.
	108	! Doutriaux-Boucher & Quaas 2004, section 2.2.)
	109	! as a function of temperature
	110	! see also Fig 3 of Madeleine et al. 2020, JAMES
	111	!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
	112
	113
	114	USE print_control_mod, ONLY: lunout, prt_level
[4665]	115	USE lmdz_lscp_ini, ONLY: t_glace_min, t_glace_max, exposant_glace, iflag_t_glace
	116	USE lmdz_lscp_ini, ONLY : RTT, dist_liq, temp_nowater
[3999]	117
[4059]	118	IMPLICIT NONE
[3999]	119
	120
[4639]	121	INTEGER, INTENT(IN) :: klon ! number of horizontal grid points
	122	REAL, INTENT(IN), DIMENSION(klon) :: temp ! temperature
	123	REAL, INTENT(IN), DIMENSION(klon) :: distcltop ! distance to cloud top
	124	REAL, INTENT(IN), DIMENSION(klon) :: temp_cltop ! temperature of cloud top
[4535]	125	INTEGER, INTENT(IN) :: iflag_ice_thermo
[3999]	126	REAL, INTENT(OUT), DIMENSION(klon) :: icefrac
	127	REAL, INTENT(OUT), DIMENSION(klon) :: dicefracdT
	128
	129
	130	INTEGER i
[4562]	131	REAL liqfrac_tmp, dicefrac_tmp
[3999]	132	REAL Dv, denomdep,beta,qsi,dqsidt
	133	LOGICAL ice_thermo
	134
[4562]	135	CHARACTER (len = 20) :: modname = 'lscp_tools'
	136	CHARACTER (len = 80) :: abort_message
	137
[5202]	138	IF ((iflag_t_glace.LT.2)) THEN !.OR. (iflag_t_glace.GT.6)) THEN
[4562]	139	abort_message = 'lscp cannot be used if iflag_t_glace<2 or >6'
	140	CALL abort_physic(modname,abort_message,1)
[3999]	141	ENDIF
	142
[4562]	143	IF (.NOT.((iflag_ice_thermo .EQ. 1).OR.(iflag_ice_thermo .GE. 3))) THEN
	144	abort_message = 'lscp cannot be used without ice thermodynamics'
	145	CALL abort_physic(modname,abort_message,1)
	146	ENDIF
[3999]	147
	148
	149	DO i=1,klon
[4562]	150
	151	! old function with sole dependence upon temperature
	152	IF (iflag_t_glace .EQ. 2) THEN
	153	liqfrac_tmp = (temp(i)-t_glace_min) / (t_glace_max-t_glace_min)
	154	liqfrac_tmp = MIN(MAX(liqfrac_tmp,0.0),1.0)
[3999]	155	icefrac(i) = (1.0-liqfrac_tmp)**exposant_glace
	156	IF (icefrac(i) .GT.0.) THEN
	157	dicefracdT(i)= exposant_glace * (icefrac(i)**(exposant_glace-1.)) &
	158	/ (t_glace_min - t_glace_max)
	159	ENDIF
	160
	161	IF ((icefrac(i).EQ.0).OR.(icefrac(i).EQ.1)) THEN
	162	dicefracdT(i)=0.
	163	ENDIF
	164
[4562]	165	ENDIF
[3999]	166
[4562]	167	! function of temperature used in CMIP6 physics
	168	IF (iflag_t_glace .EQ. 3) THEN
	169	liqfrac_tmp = (temp(i)-t_glace_min) / (t_glace_max-t_glace_min)
	170	liqfrac_tmp = MIN(MAX(liqfrac_tmp,0.0),1.0)
	171	icefrac(i) = 1.0-liqfrac_tmp**exposant_glace
	172	IF ((icefrac(i) .GT.0.) .AND. (liqfrac_tmp .GT. 0.)) THEN
	173	dicefracdT(i)= exposant_glace * ((liqfrac_tmp)**(exposant_glace-1.)) &
	174	/ (t_glace_min - t_glace_max)
	175	ELSE
	176	dicefracdT(i)=0.
	177	ENDIF
	178	ENDIF
[4072]	179
[4562]	180	! for iflag_t_glace .GE. 4, the liquid fraction depends upon temperature at cloud top
	181	! and then decreases with decreasing height
[3999]	182
[4562]	183	!with linear function of temperature at cloud top
	184	IF (iflag_t_glace .EQ. 4) THEN
	185	liqfrac_tmp = (temp(i)-t_glace_min) / (t_glace_max-t_glace_min)
	186	liqfrac_tmp = MIN(MAX(liqfrac_tmp,0.0),1.0)
	187	icefrac(i) = MAX(MIN(1.,1.0 - liqfrac_tmp*exp(-distcltop(i)/dist_liq)),0.)
	188	dicefrac_tmp = - temp(i)/(t_glace_max-t_glace_min)
	189	dicefracdT(i) = dicefrac_tmp*exp(-distcltop(i)/dist_liq)
	190	IF ((liqfrac_tmp .LE.0) .OR. (liqfrac_tmp .GE. 1)) THEN
	191	dicefracdT(i) = 0.
	192	ENDIF
	193	ENDIF
	194
	195	! with CMIP6 function of temperature at cloud top
[5202]	196	IF ((iflag_t_glace .EQ. 5) .OR. (iflag_t_glace .EQ. 7)) THEN
[4562]	197	liqfrac_tmp = (temp(i)-t_glace_min) / (t_glace_max-t_glace_min)
	198	liqfrac_tmp = MIN(MAX(liqfrac_tmp,0.0),1.0)
	199	liqfrac_tmp = liqfrac_tmp**exposant_glace
	200	icefrac(i) = MAX(MIN(1.,1.0 - liqfrac_tmp*exp(-distcltop(i)/dist_liq)),0.)
	201	IF ((liqfrac_tmp .LE.0) .OR. (liqfrac_tmp .GE. 1)) THEN
	202	dicefracdT(i) = 0.
	203	ELSE
	204	dicefracdT(i) = exposant_glace((liqfrac_tmp)*(exposant_glace-1.))/(t_glace_min- t_glace_max) &
	205	*exp(-distcltop(i)/dist_liq)
	206	ENDIF
	207	ENDIF
	208
	209	! with modified function of temperature at cloud top
	210	! to get largere values around 260 K, works well with t_glace_min = 241K
	211	IF (iflag_t_glace .EQ. 6) THEN
	212	IF (temp(i) .GT. t_glace_max) THEN
	213	liqfrac_tmp = 1.
	214	ELSE
	215	liqfrac_tmp = -((temp(i)-t_glace_max) / (t_glace_max-t_glace_min))**2+1.
	216	ENDIF
	217	liqfrac_tmp = MIN(MAX(liqfrac_tmp,0.0),1.0)
	218	icefrac(i) = MAX(MIN(1.,1.0 - liqfrac_tmp*exp(-distcltop(i)/dist_liq)),0.)
	219	IF ((liqfrac_tmp .LE.0) .OR. (liqfrac_tmp .GE. 1)) THEN
	220	dicefracdT(i) = 0.
	221	ELSE
	222	dicefracdT(i) = 2*((temp(i)-t_glace_max) / (t_glace_max-t_glace_min))/(t_glace_max-t_glace_min) &
	223	*exp(-distcltop(i)/dist_liq)
	224	ENDIF
	225	ENDIF
	226
[4639]	227	! if temperature of cloud top <-40°C,
	228	IF (iflag_t_glace .GE. 4) THEN
	229	IF ((temp_cltop(i) .LE. temp_nowater) .AND. (temp(i) .LE. t_glace_max)) THEN
	230	icefrac(i) = 1.
	231	dicefracdT(i) = 0.
	232	ENDIF
	233	ENDIF
[5202]	234
[4562]	235
	236	ENDDO ! klon
	237	RETURN
	238
[3999]	239	END SUBROUTINE ICEFRAC_LSCP
	240	!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
	241
[5202]	242	SUBROUTINE ICEFRAC_LSCP_TURB(klon, dtime, temp, pplay, paprsdn, paprsup, qice_ini, snowcld, qtot_incl, cldfra, tke, tke_dissip, qliq, qvap_cld, qice, icefrac, dicefracdT, cldfraliq, sigma2_icefracturb, mean_icefracturb)
	243	!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
	244	! Compute the liquid, ice and vapour content (+ice fraction) based
	245	! on turbulence (see Fields 2014, Furtado 2016, Raillard 2025)
	246	! L.Raillard (30/08/24)
	247	!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
[3999]	248
	249
[5202]	250	USE lmdz_lscp_ini, ONLY : prt_level, lunout
	251	USE lmdz_lscp_ini, ONLY : RCPD, RLSTT, RLVTT, RLMLT, RVTMP2, RTT, RD, RG, RV, RPI
	252	USE lmdz_lscp_ini, ONLY : seuil_neb, temp_nowater
	253	USE lmdz_lscp_ini, ONLY : tau_mixenv, lmix_mpc, naero5, gamma_snwretro, gamma_taud, capa_crystal
	254	USE lmdz_lscp_ini, ONLY : eps
	255
	256	IMPLICIT NONE
	257
	258	INTEGER, INTENT(IN) :: klon !--number of horizontal grid points
	259	REAL, INTENT(IN) :: dtime !--time step [s]
	260
	261	REAL, INTENT(IN), DIMENSION(klon) :: temp !--temperature
	262	REAL, INTENT(IN), DIMENSION(klon) :: pplay !--pressure in the middle of the layer [Pa]
	263	REAL, INTENT(IN), DIMENSION(klon) :: paprsdn !--pressure at the bottom interface of the layer [Pa]
	264	REAL, INTENT(IN), DIMENSION(klon) :: paprsup !--pressure at the top interface of the layer [Pa]
	265	REAL, INTENT(IN), DIMENSION(klon) :: qtot_incl !--specific total cloud water content, in-cloud content [kg/kg]
	266	REAL, INTENT(IN), DIMENSION(klon) :: cldfra !--cloud fraction in gridbox [-]
	267	REAL, INTENT(IN), DIMENSION(klon) :: tke !--turbulent kinetic energy [m2/s2]
	268	REAL, INTENT(IN), DIMENSION(klon) :: tke_dissip !--TKE dissipation [m2/s3]
	269
	270	REAL, INTENT(IN), DIMENSION(klon) :: qice_ini !--initial specific ice content gridbox-mean [kg/kg]
	271	REAL, INTENT(IN), DIMENSION(klon) :: snowcld
	272	REAL, INTENT(OUT), DIMENSION(klon) :: qliq !--specific liquid content gridbox-mean [kg/kg]
	273	REAL, INTENT(OUT), DIMENSION(klon) :: qvap_cld !--specific cloud vapor content, gridbox-mean [kg/kg]
	274	REAL, INTENT(OUT), DIMENSION(klon) :: qice !--specific ice content gridbox-mean [kg/kg]
	275	REAL, INTENT(OUT), DIMENSION(klon) :: icefrac !--fraction of ice in condensed water [-]
	276	REAL, INTENT(OUT), DIMENSION(klon) :: dicefracdT
	277
	278	REAL, INTENT(OUT), DIMENSION(klon) :: cldfraliq !--fraction of cldfra which is liquid only
	279	REAL, INTENT(OUT), DIMENSION(klon) :: sigma2_icefracturb !--Temporary
	280	REAL, INTENT(OUT), DIMENSION(klon) :: mean_icefracturb !--Temporary
	281
	282	REAL, DIMENSION(klon) :: qzero, qsatl, dqsatl, qsati, dqsati !--specific humidity saturation values
	283	INTEGER :: i
	284
	285	REAL :: qvap_incl, qice_incl, qliq_incl, qiceini_incl !--In-cloud specific quantities [kg/kg]
	286	REAL :: qsnowcld_incl
	287	!REAL :: capa_crystal !--Capacitance of ice crystals [-]
	288	REAL :: water_vapor_diff !--Water-vapour diffusion coefficient in air [m2/s] (function of T&P)
	289	REAL :: air_thermal_conduct !--Thermal conductivity of air [J/m/K/s] (function of T)
	290	REAL :: C0 !--Lagrangian structure function [-]
	291	REAL :: tau_mixingenv
	292	REAL :: tau_dissipturb
	293	REAL :: invtau_phaserelax
	294	REAL :: sigma2_pdf, mean_pdf
	295	REAL :: ai, bi, B0
	296	REAL :: sursat_iceliq
	297	REAL :: sursat_env
	298	REAL :: liqfra_max
	299	REAL :: sursat_iceext
	300	REAL :: nb_crystals !--number concentration of ice crystals [#/m3]
	301	REAL :: moment1_PSD !--1st moment of ice PSD
	302	REAL :: N0_PSD, lambda_PSD !--parameters of the exponential PSD
	303
	304	REAL :: rho_ice !--ice density [kg/m3]
	305	REAL :: cldfra1D
	306	REAL :: deltaz, rho_air
	307	REAL :: psati !--saturation vapor pressure wrt i [Pa]
	308
	309	C0 = 10. !--value assumed in Field2014
	310	rho_ice = 950.
	311	sursat_iceext = -0.1
	312	!capa_crystal = 1. !r_ice
	313	qzero(:) = 0.
	314	cldfraliq(:) = 0.
	315	icefrac(:) = 0.
	316	dicefracdT(:) = 0.
	317
	318	sigma2_icefracturb(:) = 0.
	319	mean_icefracturb(:) = 0.
	320
	321	!--wrt liquid water
	322	CALL calc_qsat_ecmwf(klon,temp(:),qzero(:),pplay(:),RTT,1,.false.,qsatl(:),dqsatl(:))
	323	!--wrt ice
	324	CALL calc_qsat_ecmwf(klon,temp(:),qzero(:),pplay(:),RTT,2,.false.,qsati(:),dqsati(:))
	325
	326
	327	DO i=1,klon
	328
	329
	330	rho_air = pplay(i) / temp(i) / RD
	331	!deltaz = ( paprsdn(i) - paprsup(i) ) / RG / rho_air(i)
	332	! because cldfra is intent in, but can be locally modified due to test
	333	cldfra1D = cldfra(i)
	334	IF (cldfra(i) .LE. 0.) THEN
	335	qvap_cld(i) = 0.
	336	qliq(i) = 0.
	337	qice(i) = 0.
	338	cldfraliq(i) = 0.
	339	icefrac(i) = 0.
	340	dicefracdT(i) = 0.
	341
	342	! If there is a cloud
	343	ELSE
	344	IF (cldfra(i) .GE. 1.0) THEN
	345	cldfra1D = 1.0
	346	END IF
	347
	348	! T>0°C, no ice allowed
	349	IF ( temp(i) .GE. RTT ) THEN
	350	qvap_cld(i) = qsatl(i) * cldfra1D
	351	qliq(i) = MAX(0.0,qtot_incl(i)-qsatl(i)) * cldfra1D
	352	qice(i) = 0.
	353	cldfraliq(i) = 1.
	354	icefrac(i) = 0.
	355	dicefracdT(i) = 0.
	356
	357	! T<-38°C, no liquid allowed
	358	ELSE IF ( temp(i) .LE. temp_nowater) THEN
	359	qvap_cld(i) = qsati(i) * cldfra1D
	360	qliq(i) = 0.
	361	qice(i) = MAX(0.0,qtot_incl(i)-qsati(i)) * cldfra1D
	362	cldfraliq(i) = 0.
	363	icefrac(i) = 1.
	364	dicefracdT(i) = 0.
	365
	366	! MPC temperature
	367	ELSE
	368	! Not enough TKE
	369	IF ( tke_dissip(i) .LE. eps ) THEN
	370	qvap_cld(i) = qsati(i) * cldfra1D
	371	qliq(i) = 0.
	372	qice(i) = MAX(0.,qtot_incl(i)-qsati(i)) * cldfra1D
	373	cldfraliq(i) = 0.
	374	icefrac(i) = 1.
	375	dicefracdT(i) = 0.
	376
	377	! Enough TKE
	378	ELSE
	379	print*,"MOUCHOIRACTIVE"
	380	!---------------------------------------------------------
	381	!-- ICE SUPERSATURATION PDF
	382	!---------------------------------------------------------
	383	!--If -38°C< T <0°C and there is enough turbulence,
	384	!--we compute the cloud liquid properties with a Gaussian PDF
	385	!--of ice supersaturation F(Si) (Field2014, Furtado2016).
	386	!--Parameters of the PDF are function of turbulence and
	387	!--microphysics/existing ice.
	388
	389	sursat_iceliq = qsatl(i)/qsati(i) - 1.
	390	psati = qsati(i) * pplay(i) / (RD/RV)
	391
	392	!-------------- MICROPHYSICAL TERMS --------------
	393	!--We assume an exponential ice PSD whose parameters
	394	!--are computed following Morrison&Gettelman 2008
	395	!--Ice number density is assumed equals to INP density
	396	!--which is a function of temperature (DeMott 2010)
	397	!--bi and B0 are microphysical function characterizing
	398	!--vapor/ice interactions
	399	!--tau_phase_relax is the typical time of vapor deposition
	400	!--onto ice crystals
	401
	402	qiceini_incl = qice_ini(i) / cldfra1D
	403	qsnowcld_incl = snowcld(i) * RG * dtime / ( paprsdn(i) - paprsup(i) ) / cldfra1D
	404	sursat_env = max(0., (qtot_incl(i) - qiceini_incl)/qsati(i) - 1.)
	405	IF ( qiceini_incl .GT. eps ) THEN
	406	nb_crystals = 1.e3 * 5.94e-5 * ( RTT - temp(i) )*3.33 naero5*(0.0264(RTT-temp(i))+0.0033)
	407	lambda_PSD = ( (RPIrho_icenb_crystals) / (rho_air(qiceini_incl + gamma_snwretro qsnowcld_incl)) ) ** (1./3.)
	408	N0_PSD = nb_crystals * lambda_PSD
	409	moment1_PSD = N0_PSD/lambda_PSD**2
	410	ELSE
	411	moment1_PSD = 0.
	412	ENDIF
	413
	414	!--Formulae for air thermal conductivity and water vapor diffusivity
	415	!--comes respectively from Beard and Pruppacher (1971)
	416	!--and Hall and Pruppacher (1976)
	417
	418	air_thermal_conduct = ( 5.69 + 0.017 * ( temp(i) - RTT ) ) * 1.e-3 * 4.184
	419	water_vapor_diff = 2.111e-5 ( temp(i) / RTT )*1.94 ( 101325 / pplay(i) )
	420
	421	bi = 1./((qsati(i)+qsatl(i))/2.) + RLSTT2 / RCPD / RV / temp(i)2
	422	B0 = 4. * RPI * capa_crystal * 1. / ( RLSTT2 / air_thermal_conduct / RV / temp(i)2 &
	423	+ RV * temp(i) / psati / water_vapor_diff )
	424
	425	invtau_phaserelax = (bi * B0 * moment1_PSD )
	426
	427	! Old way of estimating moment1 : spherical crystals + monodisperse PSD
	428	! nb_crystals = rho_air * qiceini_incl / ( 4. / 3. * RPI * r_ice*3. rho_ice )
	429	! moment1_PSD = nb_crystals * r_ice
	430
	431	!----------------- TURBULENT SOURCE/SINK TERMS -----------------
	432	!--Tau_mixingenv is the time needed to homogeneize the parcel
	433	!--with its environment by turbulent diffusion over the parcel
	434	!--length scale
	435	!--if lmix_mpc <0, tau_mixigenv value is prescribed
	436	!--else tau_mixigenv value is derived from tke_dissip and lmix_mpc
	437	!--Tau_dissipturb is the time needed turbulence to decay due to
	438	!--viscosity
	439
	440	ai = RG / RD / temp(i) * ( RD * RLSTT / RCPD / RV / temp(i) - 1. )
	441	IF ( lmix_mpc .GT. 0 ) THEN
	442	tau_mixingenv = ( lmix_mpc2. / tke_dissip(i) )(1./3.)
	443	ELSE
	444	tau_mixingenv = tau_mixenv
	445	ENDIF
	446
	447	tau_dissipturb = gamma_taud * 2. * 2./3. * tke(i) / tke_dissip(i) / C0
	448
	449	!--------------------- PDF COMPUTATIONS ---------------------
	450	!--Formulae for sigma2_pdf (variance), mean of PDF in Furtado2016
	451	!--cloud liquid fraction and in-cloud liquid content are given
	452	!--by integrating resp. F(Si) and Si*F(Si)
	453	!--Liquid is limited by the available water vapor trough a
	454	!--maximal liquid fraction
	455
	456	liqfra_max = MAX(0., (MIN (1.,( qtot_incl(i) - qiceini_incl - qsati(i) * (1 + sursat_iceext ) ) / ( qsatl(i) - qsati(i) ) ) ) )
	457	sigma2_pdf = 1./2. * ( ai*2 ) 2./3. * tke(i) * tau_dissipturb / ( invtau_phaserelax + 1./tau_mixingenv )
	458	mean_pdf = sursat_env * 1./tau_mixingenv / ( invtau_phaserelax + 1./tau_mixingenv )
	459	cldfraliq(i) = 0.5 * (1. - erf( ( sursat_iceliq - mean_pdf) / (SQRT(2.* sigma2_pdf) ) ) )
	460	IF (cldfraliq(i) .GT. liqfra_max) THEN
	461	cldfraliq(i) = liqfra_max
	462	ENDIF
	463
	464	qliq_incl = qsati(i) * SQRT(sigma2_pdf) / SQRT(2.RPI) EXP( -1.(sursat_iceliq - mean_pdf)2. / (2.sigma2_pdf) ) &
	465	- qsati(i) * cldfraliq(i) * (sursat_iceliq - mean_pdf )
	466
	467	sigma2_icefracturb(i)= sigma2_pdf
	468	mean_icefracturb(i) = mean_pdf
	469
	470	!------------ SPECIFIC VAPOR CONTENT AND WATER CONSERVATION ------------
	471
	472	IF ( (qliq_incl .LE. eps) .OR. (cldfraliq(i) .LE. eps) ) THEN
	473	qliq_incl = 0.
	474	cldfraliq(i) = 0.
	475	END IF
	476
	477	!--Specific humidity is the max between qsati and the weighted mean between
	478	!--qv in MPC patches and qv in ice-only parts. We assume that MPC parts are
	479	!--always at qsatl and ice-only parts slightly subsaturated (qsati*sursat_iceext+1)
	480	!--The whole cloud can therefore be supersaturated but never subsaturated.
	481
	482	qvap_incl = MAX(qsati(i), ( 1. - cldfraliq(i) ) * (sursat_iceext + 1.) * qsati(i) + cldfraliq(i) * qsatl(i) )
	483
	484
	485	IF ( qvap_incl .GE. qtot_incl(i) ) THEN
	486	qvap_incl = qsati(i)
	487	qliq_incl = qtot_incl(i) - qvap_incl
	488	qice_incl = 0.
	489
	490	ELSEIF ( (qvap_incl + qliq_incl) .GE. qtot_incl(i) ) THEN
	491	qliq_incl = MAX(0.0,qtot_incl(i) - qvap_incl)
	492	qice_incl = 0.
	493	ELSE
	494	qice_incl = qtot_incl(i) - qvap_incl - qliq_incl
	495	END IF
	496
	497	qvap_cld(i) = qvap_incl * cldfra1D
	498	qliq(i) = qliq_incl * cldfra1D
	499	qice(i) = qice_incl * cldfra1D
	500	icefrac(i) = qice(i) / ( qice(i) + qliq(i) )
	501	dicefracdT(i) = 0.
	502	!print*,'MPC turb'
	503
	504	END IF ! Enough TKE
	505
	506	END IF ! ! MPC temperature
	507
	508	END IF ! cldfra
	509
	510	ENDDO ! klon
	511	END SUBROUTINE ICEFRAC_LSCP_TURB
	512	!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
	513
	514
[4072]	515	SUBROUTINE CALC_QSAT_ECMWF(klon,temp,qtot,pressure,tref,phase,flagth,qs,dqs)
[3999]	516	!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
	517	! Calculate qsat following ECMWF method
	518	!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
	519
[4072]	520
[4059]	521	IMPLICIT NONE
[3999]	522
	523	include "YOMCST.h"
	524	include "YOETHF.h"
	525	include "FCTTRE.h"
	526
[4072]	527	INTEGER, INTENT(IN) :: klon ! number of horizontal grid points
	528	REAL, INTENT(IN), DIMENSION(klon) :: temp ! temperature in K
	529	REAL, INTENT(IN), DIMENSION(klon) :: qtot ! total specific water in kg/kg
	530	REAL, INTENT(IN), DIMENSION(klon) :: pressure ! pressure in Pa
	531	REAL, INTENT(IN) :: tref ! reference temperature in K
[3999]	532	LOGICAL, INTENT(IN) :: flagth ! flag for qsat calculation for thermals
	533	INTEGER, INTENT(IN) :: phase
	534	! phase: 0=depend on temperature sign (temp>tref -> liquid, temp<tref, solid)
	535	! 1=liquid
	536	! 2=solid
	537
[4072]	538	REAL, INTENT(OUT), DIMENSION(klon) :: qs ! saturation specific humidity [kg/kg]
	539	REAL, INTENT(OUT), DIMENSION(klon) :: dqs ! derivation of saturation specific humidity wrt T
[3999]	540
	541	REAL delta, cor, cvm5
[4072]	542	INTEGER i
	543
	544	DO i=1,klon
	545
[3999]	546	IF (phase .EQ. 1) THEN
	547	delta=0.
	548	ELSEIF (phase .EQ. 2) THEN
	549	delta=1.
	550	ELSE
[4072]	551	delta=MAX(0.,SIGN(1.,tref-temp(i)))
[3999]	552	ENDIF
	553
	554	IF (flagth) THEN
	555	cvm5=R5LES(1.-delta) + R5IESdelta
	556	ELSE
	557	cvm5 = R5LESRLVTT(1.-delta) + R5IESRLSTTdelta
[4072]	558	cvm5 = cvm5 /RCPD/(1.0+RVTMP2*(qtot(i)))
[3999]	559	ENDIF
	560
[4072]	561	qs(i)= R2ES*FOEEW(temp(i),delta)/pressure(i)
	562	qs(i)=MIN(0.5,qs(i))
	563	cor=1./(1.-RETV*qs(i))
	564	qs(i)=qs(i)*cor
	565	dqs(i)= FOEDE(temp(i),delta,cvm5,qs(i),cor)
[3999]	566
[4072]	567	END DO
	568
[3999]	569	END SUBROUTINE CALC_QSAT_ECMWF
	570	!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
	571
	572
	573	!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
[4072]	574	SUBROUTINE CALC_GAMMASAT(klon,temp,qtot,pressure,gammasat,dgammasatdt)
[3999]	575
	576	!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
	577	! programme that calculates the gammasat parameter that determines the
	578	! homogeneous condensation thresholds for cold (<0oC) clouds
	579	! condensation at q>gammasat*qsat
	580	! Etienne Vignon, March 2021
	581	!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
	582
[4951]	583	use lmdz_lscp_ini, only: iflag_gammasat, temp_nowater, RTT
	584	use lmdz_lscp_ini, only: a_homofreez, b_homofreez, delta_hetfreez
[3999]	585
[4059]	586	IMPLICIT NONE
[3999]	587
	588
[4072]	589	INTEGER, INTENT(IN) :: klon ! number of horizontal grid points
	590	REAL, INTENT(IN), DIMENSION(klon) :: temp ! temperature in K
	591	REAL, INTENT(IN), DIMENSION(klon) :: qtot ! total specific water in kg/kg
[3999]	592
[4072]	593	REAL, INTENT(IN), DIMENSION(klon) :: pressure ! pressure in Pa
[3999]	594
[4072]	595	REAL, INTENT(OUT), DIMENSION(klon) :: gammasat ! coefficient to multiply qsat with to calculate saturation
	596	REAL, INTENT(OUT), DIMENSION(klon) :: dgammasatdt ! derivative of gammasat wrt temperature
[3999]	597
[4072]	598	REAL, DIMENSION(klon) :: qsi,qsl,dqsl,dqsi
[4951]	599	REAL f_homofreez, fac
[3999]	600
[4072]	601	INTEGER i
	602
	603	CALL CALC_QSAT_ECMWF(klon,temp,qtot,pressure,RTT,1,.false.,qsl,dqsl)
	604	CALL CALC_QSAT_ECMWF(klon,temp,qtot,pressure,RTT,2,.false.,qsi,dqsi)
[3999]	605
[5019]	606	DO i = 1, klon
[3999]	607
[5019]	608	IF ( temp(i) .GE. RTT ) THEN
[3999]	609	! warm clouds: condensation at saturation wrt liquid
[5019]	610	gammasat(i) = 1.
	611	dgammasatdt(i) = 0.
[3999]	612
[5019]	613	ELSE
	614	! cold clouds: qsi > qsl
[3999]	615
[5019]	616	! homogeneous freezing of aerosols, according to
	617	! Koop, 2000 and Ren and MacKenzie, 2005 (QJRMS)
	618	! 'Cirrus regime'
	619	! if f_homofreez > qsl / qsi, liquid nucleation
	620	! if f_homofreez < qsl / qsi, homogeneous freezing of aerosols
	621	! Note: f_homofreez = qsl / qsi for temp ~= -38degC
	622	f_homofreez = a_homofreez - temp(i) / b_homofreez
	623
	624	IF ( iflag_gammasat .GE. 3 ) THEN
	625	! condensation at homogeneous freezing threshold for temp < -38 degC
	626	! condensation at liquid saturation for temp > -38 degC
	627	IF ( f_homofreez .LE. qsl(i) / qsi(i) ) THEN
	628	gammasat(i) = f_homofreez
	629	dgammasatdt(i) = - 1. / b_homofreez
	630	ELSE
	631	gammasat(i) = qsl(i) / qsi(i)
	632	dgammasatdt(i) = ( dqsl(i) * qsi(i) - dqsi(i) * qsl(i) ) / qsi(i) / qsi(i)
	633	ENDIF
[3999]	634
[5019]	635	ELSEIF ( iflag_gammasat .EQ. 2 ) THEN
	636	! condensation at homogeneous freezing threshold for temp < -38 degC
	637	! condensation at a threshold linearly decreasing between homogeneous
	638	! freezing and ice saturation for -38 degC < temp < temp_nowater
	639	! condensation at ice saturation for temp > temp_nowater
	640	! If temp_nowater = 235.15 K, this is equivalent to iflag_gammasat = 1
	641	IF ( f_homofreez .LE. qsl(i) / qsi(i) ) THEN
	642	gammasat(i) = f_homofreez
	643	dgammasatdt(i) = - 1. / b_homofreez
	644	ELSEIF ( temp(i) .LE. temp_nowater ) THEN
	645	! Here, we assume that f_homofreez = qsl / qsi for temp = -38 degC = 235.15 K
	646	dgammasatdt(i) = ( a_homofreez - 235.15 / b_homofreez - 1. ) &
	647	/ ( 235.15 - temp_nowater )
	648	gammasat(i) = dgammasatdt(i) * ( temp(i) - temp_nowater ) + 1.
	649	ELSE
	650	gammasat(i) = 1.
	651	dgammasatdt(i) = 0.
	652	ENDIF
[3999]	653
[5019]	654	ELSEIF ( iflag_gammasat .EQ. 1 ) THEN
	655	! condensation at homogeneous freezing threshold for temp < -38 degC
	656	! condensation at ice saturation for temp > -38 degC
	657	IF ( f_homofreez .LE. qsl(i) / qsi(i) ) THEN
	658	gammasat(i) = f_homofreez
	659	dgammasatdt(i) = - 1. / b_homofreez
	660	ELSE
	661	gammasat(i) = 1.
	662	dgammasatdt(i) = 0.
	663	ENDIF
	664
[3999]	665	ELSE
[5019]	666	! condensation at ice saturation for temp < -38 degC
	667	! condensation at ice saturation for temp > -38 degC
	668	gammasat(i) = 1.
	669	dgammasatdt(i) = 0.
[3999]	670
	671	ENDIF
	672
[5019]	673	! Note that the delta_hetfreez parameter allows to linearly decrease the
	674	! condensation threshold between the calculated threshold and the ice saturation
	675	! for delta_hetfreez = 1, the threshold is the calculated condensation threshold
	676	! for delta_hetfreez = 0, the threshold is the ice saturation
	677	gammasat(i) = ( 1. - delta_hetfreez ) + delta_hetfreez * gammasat(i)
	678	dgammasatdt(i) = delta_hetfreez * dgammasatdt(i)
	679
[3999]	680	ENDIF
	681
[4072]	682	END DO
	683
	684
[3999]	685	END SUBROUTINE CALC_GAMMASAT
[4562]	686	!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
[3999]	687
	688
[4562]	689	!++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
[4639]	690	SUBROUTINE DISTANCE_TO_CLOUD_TOP(klon,klev,k,temp,pplay,paprs,rneb,distcltop1D,temp_cltop)
[4562]	691	!++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
	692
[4665]	693	USE lmdz_lscp_ini, ONLY : rd,rg,tresh_cl
[4562]	694
	695	IMPLICIT NONE
	696
	697	INTEGER, INTENT(IN) :: klon,klev !number of horizontal and vertical grid points
	698	INTEGER, INTENT(IN) :: k ! vertical index
	699	REAL, INTENT(IN), DIMENSION(klon,klev) :: temp ! temperature in K
	700	REAL, INTENT(IN), DIMENSION(klon,klev) :: pplay ! pressure middle layer in Pa
	701	REAL, INTENT(IN), DIMENSION(klon,klev+1) :: paprs ! pressure interfaces in Pa
	702	REAL, INTENT(IN), DIMENSION(klon,klev) :: rneb ! cloud fraction
	703
	704	REAL, INTENT(OUT), DIMENSION(klon) :: distcltop1D ! distance from cloud top
[4639]	705	REAL, INTENT(OUT), DIMENSION(klon) :: temp_cltop ! temperature of cloud top
	706
[4562]	707	REAL dzlay(klon,klev)
	708	REAL zlay(klon,klev)
	709	REAL dzinterf
	710	INTEGER i,k_top, kvert
	711	LOGICAL bool_cl
	712
	713
	714	DO i=1,klon
	715	! Initialization height middle of first layer
	716	dzlay(i,1) = Rd * temp(i,1) / rg * log(paprs(i,1)/paprs(i,2))
	717	zlay(i,1) = dzlay(i,1)/2
	718
	719	DO kvert=2,klev
	720	IF (kvert.EQ.klev) THEN
	721	dzlay(i,kvert) = 2(rd temp(i,kvert) / rg * log(paprs(i,kvert)/pplay(i,kvert)))
	722	ELSE
	723	dzlay(i,kvert) = rd * temp(i,kvert) / rg * log(paprs(i,kvert)/paprs(i,kvert+1))
	724	ENDIF
	725	dzinterf = rd * temp(i,kvert) / rg * log(pplay(i,kvert-1)/pplay(i,kvert))
	726	zlay(i,kvert) = zlay(i,kvert-1) + dzinterf
	727	ENDDO
	728	ENDDO
	729
	730	DO i=1,klon
[4639]	731	k_top = k
[4562]	732	IF (rneb(i,k) .LE. tresh_cl) THEN
	733	bool_cl = .FALSE.
	734	ELSE
	735	bool_cl = .TRUE.
	736	ENDIF
	737
	738	DO WHILE ((bool_cl) .AND. (k_top .LE. klev))
	739	! find cloud top
	740	IF (rneb(i,k_top) .GT. tresh_cl) THEN
	741	k_top = k_top + 1
	742	ELSE
	743	bool_cl = .FALSE.
	744	k_top = k_top - 1
	745	ENDIF
	746	ENDDO
	747	k_top=min(k_top,klev)
	748
	749	!dist to top is dist between current layer and layer of cloud top (from middle to middle) + dist middle to
	750	!interf for layer of cloud top
	751	distcltop1D(i) = zlay(i,k_top) - zlay(i,k) + dzlay(i,k_top)/2
[4639]	752	temp_cltop(i) = temp(i,k_top)
[4562]	753	ENDDO ! klon
	754
	755	END SUBROUTINE DISTANCE_TO_CLOUD_TOP
[3999]	756	!++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
	757
[4951]	758	!++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
	759	FUNCTION GAMMAINC ( p, x )
	760
	761	!*****************************************************************************80
	762	!
	763	!! GAMMAINC computes the regularized lower incomplete Gamma Integral
	764	!
	765	! Modified:
	766	!
	767	! 20 January 2008
	768	!
	769	! Author:
	770	!
	771	! Original FORTRAN77 version by B Shea.
	772	! FORTRAN90 version by John Burkardt.
	773	!
	774	! Reference:
	775	!
	776	! B Shea,
	777	! Algorithm AS 239:
	778	! Chi-squared and Incomplete Gamma Integral,
	779	! Applied Statistics,
	780	! Volume 37, Number 3, 1988, pages 466-473.
	781	!
	782	! Parameters:
	783	!
	784	! Input, real X, P, the parameters of the incomplete
	785	! gamma ratio. 0 <= X, and 0 < P.
	786	!
	787	! Output, real GAMMAINC, the value of the incomplete
	788	! Gamma integral.
	789	!
	790	IMPLICIT NONE
	791
	792	REAL A
	793	REAL AN
	794	REAL ARG
	795	REAL B
	796	REAL C
	797	REAL, PARAMETER :: ELIMIT = - 88.0E+00
	798	REAL GAMMAINC
	799	REAL, PARAMETER :: OFLO = 1.0E+37
	800	REAL P
	801	REAL, PARAMETER :: PLIMIT = 1000.0E+00
	802	REAL PN1
	803	REAL PN2
	804	REAL PN3
	805	REAL PN4
	806	REAL PN5
	807	REAL PN6
	808	REAL RN
	809	REAL, PARAMETER :: TOL = 1.0E-14
	810	REAL X
	811	REAL, PARAMETER :: XBIG = 1.0E+08
	812
	813	GAMMAINC = 0.0E+00
	814
	815	IF ( X == 0.0E+00 ) THEN
	816	GAMMAINC = 0.0E+00
	817	RETURN
	818	END IF
	819	!
	820	! IF P IS LARGE, USE A NORMAL APPROXIMATION.
	821	!
	822	IF ( PLIMIT < P ) THEN
	823
	824	PN1 = 3.0E+00 * SQRT ( P ) * ( ( X / P )**( 1.0E+00 / 3.0E+00 ) &
	825	+ 1.0E+00 / ( 9.0E+00 * P ) - 1.0E+00 )
	826
	827	GAMMAINC = 0.5E+00 * ( 1. + ERF ( PN1 ) )
	828	RETURN
	829
	830	END IF
	831	!
	832	! IF X IS LARGE SET GAMMAD = 1.
	833	!
	834	IF ( XBIG < X ) THEN
	835	GAMMAINC = 1.0E+00
	836	RETURN
	837	END IF
	838	!
	839	! USE PEARSON'S SERIES EXPANSION.
	840	! (NOTE THAT P IS NOT LARGE ENOUGH TO FORCE OVERFLOW IN ALOGAM).
	841	!
	842	IF ( X <= 1.0E+00 .OR. X < P ) THEN
	843
	844	ARG = P * LOG ( X ) - X - LOG_GAMMA ( P + 1.0E+00 )
	845	C = 1.0E+00
	846	GAMMAINC = 1.0E+00
	847	A = P
	848
	849	DO
	850
	851	A = A + 1.0E+00
	852	C = C * X / A
	853	GAMMAINC = GAMMAINC + C
	854
	855	IF ( C <= TOL ) THEN
	856	EXIT
	857	END IF
	858
	859	END DO
	860
	861	ARG = ARG + LOG ( GAMMAINC )
	862
	863	IF ( ELIMIT <= ARG ) THEN
	864	GAMMAINC = EXP ( ARG )
	865	ELSE
	866	GAMMAINC = 0.0E+00
	867	END IF
	868	!
	869	! USE A CONTINUED FRACTION EXPANSION.
	870	!
	871	ELSE
	872
	873	ARG = P * LOG ( X ) - X - LOG_GAMMA ( P )
	874	A = 1.0E+00 - P
	875	B = A + X + 1.0E+00
	876	C = 0.0E+00
	877	PN1 = 1.0E+00
	878	PN2 = X
	879	PN3 = X + 1.0E+00
	880	PN4 = X * B
	881	GAMMAINC = PN3 / PN4
	882
	883	DO
	884
	885	A = A + 1.0E+00
	886	B = B + 2.0E+00
	887	C = C + 1.0E+00
	888	AN = A * C
	889	PN5 = B * PN3 - AN * PN1
	890	PN6 = B * PN4 - AN * PN2
	891
	892	IF ( PN6 /= 0.0E+00 ) THEN
	893
	894	RN = PN5 / PN6
	895
	896	IF ( ABS ( GAMMAINC - RN ) <= MIN ( TOL, TOL * RN ) ) THEN
	897	EXIT
	898	END IF
	899
	900	GAMMAINC = RN
	901
	902	END IF
	903
	904	PN1 = PN3
	905	PN2 = PN4
	906	PN3 = PN5
	907	PN4 = PN6
	908	!
	909	! RE-SCALE TERMS IN CONTINUED FRACTION IF TERMS ARE LARGE.
	910	!
	911	IF ( OFLO <= ABS ( PN5 ) ) THEN
	912	PN1 = PN1 / OFLO
	913	PN2 = PN2 / OFLO
	914	PN3 = PN3 / OFLO
	915	PN4 = PN4 / OFLO
	916	END IF
	917
	918	END DO
	919
	920	ARG = ARG + LOG ( GAMMAINC )
	921
	922	IF ( ELIMIT <= ARG ) THEN
	923	GAMMAINC = 1.0E+00 - EXP ( ARG )
	924	ELSE
	925	GAMMAINC = 1.0E+00
	926	END IF
	927
	928	END IF
	929
	930	RETURN
	931	END FUNCTION GAMMAINC
	932	!++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
	933
[4665]	934	END MODULE lmdz_lscp_tools
[3999]	935
	936

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