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lmdz_lscp_tools.f90 @ 5403

Last change on this file since 5403 was 5383, checked in by evignon, 7 days ago
update de la paramétrisation de phase des nuages de Lea et nettoyage associé
File size: 36.6 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
[5007]	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
[5007]	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
[5007]	234
[4562]	235
	236	ENDDO ! klon
	237	RETURN
	238
[3999]	239	END SUBROUTINE ICEFRAC_LSCP
	240	!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
	241
[5383]	242
	243	SUBROUTINE ICEFRAC_LSCP_TURB(klon, dtime, temp, pplay, paprsdn, paprsup, omega, qice_ini, snowcld, qtot_incl, cldfra, tke, &
	244	tke_dissip, qliq, qvap_cld, qice, icefrac, dicefracdT, cldfraliq, sigma2_icefracturb, mean_icefracturb)
[5007]	245	!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
	246	! Compute the liquid, ice and vapour content (+ice fraction) based
[5170]	247	! on turbulence (see Fields 2014, Furtado 2016, Raillard 2025)
[5383]	248	! L.Raillard (23/09/24)
[5007]	249	!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
[3999]	250
	251
[5007]	252	USE lmdz_lscp_ini, ONLY : prt_level, lunout
	253	USE lmdz_lscp_ini, ONLY : RCPD, RLSTT, RLVTT, RLMLT, RVTMP2, RTT, RD, RG, RV, RPI
	254	USE lmdz_lscp_ini, ONLY : seuil_neb, temp_nowater
[5383]	255	USE lmdz_lscp_ini, ONLY : naero5, gamma_snwretro, gamma_taud, capa_crystal
[5007]	256	USE lmdz_lscp_ini, ONLY : eps
	257
	258	IMPLICIT NONE
	259
[5383]	260	INTEGER, INTENT(IN) :: klon !--number of horizontal grid points
	261	REAL, INTENT(IN) :: dtime !--time step [s]
[5007]	262
[5383]	263	REAL, INTENT(IN), DIMENSION(klon) :: temp !--temperature
	264	REAL, INTENT(IN), DIMENSION(klon) :: pplay !--pressure in the middle of the layer [Pa]
	265	REAL, INTENT(IN), DIMENSION(klon) :: paprsdn !--pressure at the bottom interface of the layer [Pa]
	266	REAL, INTENT(IN), DIMENSION(klon) :: paprsup !--pressure at the top interface of the layer [Pa]
	267	REAL, INTENT(IN), DIMENSION(klon) :: omega !--resolved vertical velocity [Pa/s]
	268	REAL, INTENT(IN), DIMENSION(klon) :: qtot_incl !--specific total cloud water in-cloud content [kg/kg]
	269	REAL, INTENT(IN), DIMENSION(klon) :: cldfra !--cloud fraction in gridbox [-]
	270	REAL, INTENT(IN), DIMENSION(klon) :: tke !--turbulent kinetic energy [m2/s2]
	271	REAL, INTENT(IN), DIMENSION(klon) :: tke_dissip !--TKE dissipation [m2/s3]
[5007]	272
[5383]	273	REAL, INTENT(IN), DIMENSION(klon) :: qice_ini !--initial specific ice content gridbox-mean [kg/kg]
[5007]	274	REAL, INTENT(IN), DIMENSION(klon) :: snowcld
[5383]	275	REAL, INTENT(OUT), DIMENSION(klon) :: qliq !--specific liquid content gridbox-mean [kg/kg]
	276	REAL, INTENT(OUT), DIMENSION(klon) :: qvap_cld !--specific cloud vapor content, gridbox-mean [kg/kg]
	277	REAL, INTENT(OUT), DIMENSION(klon) :: qice !--specific ice content gridbox-mean [kg/kg]
	278	REAL, INTENT(OUT), DIMENSION(klon) :: icefrac !--fraction of ice in condensed water [-]
[5007]	279	REAL, INTENT(OUT), DIMENSION(klon) :: dicefracdT
	280
[5383]	281	REAL, INTENT(OUT), DIMENSION(klon) :: cldfraliq !--fraction of cldfra where liquid [-]
	282	REAL, INTENT(OUT), DIMENSION(klon) :: sigma2_icefracturb !--Sigma2 of the ice supersaturation PDF [-]
	283	REAL, INTENT(OUT), DIMENSION(klon) :: mean_icefracturb !--Mean of the ice supersaturation PDF [-]
[5007]	284
[5383]	285	REAL, DIMENSION(klon) :: qzero, qsatl, dqsatl, qsati, dqsati !--specific humidity saturation values
[5007]	286	INTEGER :: i
	287
[5383]	288	REAL :: qvap_incl, qice_incl, qliq_incl, qiceini_incl !--In-cloud specific quantities [kg/kg]
	289	REAL :: water_vapor_diff !--Water-vapour diffusion coeff in air (f(T,P)) [m2/s]
	290	REAL :: air_thermal_conduct !--Thermal conductivity of air (f(T)) [J/m/K/s]
	291	REAL :: C0 !--Lagrangian structure function [-]
[5007]	292	REAL :: tau_dissipturb
[5383]	293	REAL :: tau_phaserelax
[5007]	294	REAL :: sigma2_pdf, mean_pdf
	295	REAL :: ai, bi, B0
	296	REAL :: sursat_iceliq
[5383]	297	REAL :: sursat_equ
[5007]	298	REAL :: liqfra_max
	299	REAL :: sursat_iceext
[5383]	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
[5007]	303
[5383]	304	REAL :: rho_ice !--ice density [kg/m3]
[5007]	305	REAL :: cldfra1D
[5383]	306	REAL :: rho_air
	307	REAL :: psati !--saturation vapor pressure wrt ice [Pa]
[5007]	308
[5383]	309	REAL :: vitw !--vertical velocity [m/s]
	310
	311	C0 = 10. !--value assumed in Field2014
[5007]	312	rho_ice = 950.
	313	sursat_iceext = -0.1
	314	qzero(:) = 0.
	315	cldfraliq(:) = 0.
	316	icefrac(:) = 0.
	317	dicefracdT(:) = 0.
	318
	319	sigma2_icefracturb(:) = 0.
[5383]	320	mean_icefracturb(:) = 0.
[5007]	321
[5383]	322	!--wrt liquid
[5007]	323	CALL calc_qsat_ecmwf(klon,temp(:),qzero(:),pplay(:),RTT,1,.false.,qsatl(:),dqsatl(:))
	324	!--wrt ice
	325	CALL calc_qsat_ecmwf(klon,temp(:),qzero(:),pplay(:),RTT,2,.false.,qsati(:),dqsati(:))
	326
	327
	328	DO i=1,klon
	329
[5383]	330	rho_air = pplay(i) / temp(i) / RD
[5007]	331
	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
[5383]	366	!---------------------------------------------------------
	367	!-- MIXED PHASE TEMPERATURE REGIME
	368	!---------------------------------------------------------
	369	!--In the mixed phase regime (-38°C< T <0°C) we distinguish
	370	!--3 possible subcases.
	371	!--1. No pre-existing ice
	372	!--2A. Pre-existing ice and no turbulence
	373	!--2B. Pre-existing ice and turbulence
[5007]	374	ELSE
[5383]	375
	376	vitw = -omega(i) / RG / rho_air
	377	qiceini_incl = qice_ini(i) / cldfra1D + snowcld(i) * RG * dtime / ( paprsdn(i) - paprsup(i) ) / cldfra1D
	378
	379	!--1. No preexisting ice : if vertical motion, fully liquid
	380	!--cloud else fully iced cloud
	381	IF ( qiceini_incl .LT. eps ) THEN
	382	IF ( (vitw .GT. eps) .OR. (tke(i) .GT. eps) ) THEN
	383	qvap_cld(i) = qsatl(i) * cldfra1D
	384	qliq(i) = MAX(0.,qtot_incl(i)-qsatl(i)) * cldfra1D
	385	qice(i) = 0.
	386	cldfraliq(i) = 1.
	387	icefrac(i) = 0.
	388	dicefracdT(i) = 0.
	389	ELSE
	390	qvap_cld(i) = qsati(i) * cldfra1D
	391	qliq(i) = 0.
	392	qice(i) = MAX(0.,qtot_incl(i)-qsati(i)) * cldfra1D
	393	cldfraliq(i) = 0.
	394	icefrac(i) = 1.
	395	dicefracdT(i) = 0.
	396	ENDIF
[5007]	397
	398
[5383]	399	!--2. Pre-existing ice :computation of ice properties for
	400	!--feedback
	401	ELSE
	402	ai = RG / RD / temp(i) * ( RD * RLSTT / RCPD / RV / temp(i) - 1. )
	403
	404	sursat_equ = ai * vitw * tau_phaserelax
	405
[5007]	406	sursat_iceliq = qsatl(i)/qsati(i) - 1.
	407	psati = qsati(i) * pplay(i) / (RD/RV)
[5383]	408
[5007]	409	!--We assume an exponential ice PSD whose parameters
	410	!--are computed following Morrison&Gettelman 2008
	411	!--Ice number density is assumed equals to INP density
	412	!--which is a function of temperature (DeMott 2010)
	413	!--bi and B0 are microphysical function characterizing
	414	!--vapor/ice interactions
	415	!--tau_phase_relax is the typical time of vapor deposition
	416	!--onto ice crystals
	417
[5383]	418	nb_crystals = 1.e3 * 5.94e-5 * ( RTT - temp(i) )*3.33 naero5*(0.0264(RTT-temp(i))+0.0033)
	419	lambda_PSD = ( (RPIrho_icenb_crystals) / (rho_air * qiceini_incl ) ) ** (1./3.)
	420	N0_PSD = nb_crystals * lambda_PSD
	421	moment1_PSD = N0_PSD/lambda_PSD**2
	422
[5007]	423	!--Formulae for air thermal conductivity and water vapor diffusivity
	424	!--comes respectively from Beard and Pruppacher (1971)
	425	!--and Hall and Pruppacher (1976)
	426
	427	air_thermal_conduct = ( 5.69 + 0.017 * ( temp(i) - RTT ) ) * 1.e-3 * 4.184
	428	water_vapor_diff = 2.111e-5 ( temp(i) / RTT )*1.94 ( 101325 / pplay(i) )
	429
	430	bi = 1./((qsati(i)+qsatl(i))/2.) + RLSTT2 / RCPD / RV / temp(i)2
	431	B0 = 4. * RPI * capa_crystal * 1. / ( RLSTT2 / air_thermal_conduct / RV / temp(i)2 &
	432	+ RV * temp(i) / psati / water_vapor_diff )
[5383]	433	tau_phaserelax = 1. / (bi * B0 * moment1_PSD )
	434
	435	ai = RG / RD / temp(i) * ( RD * RLSTT / RCPD / RV / temp(i) - 1. )
[5007]	436
[5383]	437	!--2A. No TKE : stationnary binary solution depending on omega
	438	! If Sequ > Siw liquid cloud, else ice cloud
	439	IF ( tke_dissip(i) .LE. eps ) THEN
	440	IF (sursat_equ .GT. sursat_iceliq) THEN
	441	qvap_cld(i) = qsatl(i) * cldfra1D
	442	qliq(i) = MAX(0.,qtot_incl(i)-qsatl(i)) * cldfra1D
	443	qice(i) = 0.
	444	cldfraliq(i) = 1.
	445	icefrac(i) = 0.
	446	dicefracdT(i) = 0.
	447	ELSE
	448	qvap_cld(i) = qsati(i) * cldfra1D
	449	qliq(i) = 0.
	450	qice(i) = MAX(0.,qtot_incl(i)-qsati(i)) * cldfra1D
	451	cldfraliq(i) = 0.
	452	icefrac(i) = 1.
	453	dicefracdT(i) = 0.
	454	ENDIF
	455
	456	!--2B. TKE and ice : ice supersaturation PDF
	457	!--we compute the cloud liquid properties with a Gaussian PDF
	458	!--of ice supersaturation F(Si) (Field2014, Furtado2016).
	459	!--Parameters of the PDF are function of turbulence and
	460	!--microphysics/existing ice.
	461	ELSE
	462
	463	!--Tau_dissipturb is the time needed for turbulence to decay
	464	!--due to viscosity
	465	tau_dissipturb = gamma_taud * 2. * 2./3. * tke(i) / tke_dissip(i) / C0
[5007]	466
[5383]	467	!--------------------- PDF COMPUTATIONS ---------------------
	468	!--Formulae for sigma2_pdf (variance), mean of PDF in Raillard2025
	469	!--cloud liquid fraction and in-cloud liquid content are given
	470	!--by integrating resp. F(Si) and Si*F(Si)
	471	!--Liquid is limited by the available water vapor trough a
	472	!--maximal liquid fraction
	473	!--qice_ini(i) / cldfra1D = qiceincld without precip
[5007]	474
[5383]	475	liqfra_max = MAX(0., (MIN (1.,( qtot_incl(i) - (qice_ini(i) / cldfra1D) - qsati(i) * (1 + sursat_iceext ) ) / ( qsatl(i) - qsati(i) ) ) ) )
	476	sigma2_pdf = 1./2. * ( ai*2 ) 2./3. * tke(i) * tau_dissipturb * tau_phaserelax
	477
	478	mean_pdf = ai * vitw * tau_phaserelax
	479
	480	cldfraliq(i) = 0.5 * (1. - erf( ( sursat_iceliq - mean_pdf) / (SQRT(2.* sigma2_pdf) ) ) )
	481	IF (cldfraliq(i) .GT. liqfra_max) THEN
	482	cldfraliq(i) = liqfra_max
	483	ENDIF
	484
	485	qliq_incl = qsati(i) * SQRT(sigma2_pdf) / SQRT(2.RPI) EXP( -1.(sursat_iceliq - mean_pdf)2. / (2.sigma2_pdf) ) &
	486	- qsati(i) * cldfraliq(i) * (sursat_iceliq - mean_pdf )
	487
	488	sigma2_icefracturb(i)= sigma2_pdf
	489	mean_icefracturb(i) = mean_pdf
[5170]	490
[5383]	491	!------------ SPECIFIC VAPOR CONTENT AND WATER CONSERVATION ------------
[5007]	492
[5383]	493	IF ( (qliq_incl .LE. eps) .OR. (cldfraliq(i) .LE. eps) ) THEN
	494	qliq_incl = 0.
	495	cldfraliq(i) = 0.
	496	END IF
	497
	498	!--Specific humidity is the max between qsati and the weighted mean between
	499	!--qv in MPC patches and qv in ice-only parts. We assume that MPC parts are
	500	!--always at qsatl and ice-only parts slightly subsaturated (qsati*sursat_iceext+1)
	501	!--The whole cloud can therefore be supersaturated but never subsaturated.
[5170]	502
[5383]	503	qvap_incl = MAX(qsati(i), ( 1. - cldfraliq(i) ) * (sursat_iceext + 1.) * qsati(i) + cldfraliq(i) * qsatl(i) )
[5170]	504
[5383]	505	IF ( qvap_incl .GE. qtot_incl(i) ) THEN
	506	qvap_incl = qsati(i)
	507	qliq_incl = qtot_incl(i) - qvap_incl
	508	qice_incl = 0.
[5170]	509
[5383]	510	ELSEIF ( (qvap_incl + qliq_incl) .GE. qtot_incl(i) ) THEN
	511	qliq_incl = MAX(0.0,qtot_incl(i) - qvap_incl)
	512	qice_incl = 0.
	513	ELSE
	514	qice_incl = qtot_incl(i) - qvap_incl - qliq_incl
	515	END IF
[5007]	516
[5383]	517	qvap_cld(i) = qvap_incl * cldfra1D
	518	qliq(i) = qliq_incl * cldfra1D
	519	qice(i) = qice_incl * cldfra1D
	520	icefrac(i) = qice(i) / ( qice(i) + qliq(i) )
	521	dicefracdT(i) = 0.
[5007]	522
[5383]	523	END IF ! Enough TKE
	524
	525	END IF ! End qini
[5007]	526
	527	END IF ! ! MPC temperature
	528
	529	END IF ! cldfra
	530
	531	ENDDO ! klon
	532	END SUBROUTINE ICEFRAC_LSCP_TURB
[5383]	533	!
[5007]	534	!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
	535
	536
[4072]	537	SUBROUTINE CALC_QSAT_ECMWF(klon,temp,qtot,pressure,tref,phase,flagth,qs,dqs)
[3999]	538	!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
	539	! Calculate qsat following ECMWF method
	540	!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
	541
[4072]	542
[5284]	543	USE yoethf_mod_h
[5285]	544	USE yomcst_mod_h
[5274]	545	IMPLICIT NONE
[3999]	546
[5274]	547
[3999]	548	include "FCTTRE.h"
	549
[4072]	550	INTEGER, INTENT(IN) :: klon ! number of horizontal grid points
	551	REAL, INTENT(IN), DIMENSION(klon) :: temp ! temperature in K
	552	REAL, INTENT(IN), DIMENSION(klon) :: qtot ! total specific water in kg/kg
	553	REAL, INTENT(IN), DIMENSION(klon) :: pressure ! pressure in Pa
	554	REAL, INTENT(IN) :: tref ! reference temperature in K
[3999]	555	LOGICAL, INTENT(IN) :: flagth ! flag for qsat calculation for thermals
	556	INTEGER, INTENT(IN) :: phase
	557	! phase: 0=depend on temperature sign (temp>tref -> liquid, temp<tref, solid)
	558	! 1=liquid
	559	! 2=solid
	560
[4072]	561	REAL, INTENT(OUT), DIMENSION(klon) :: qs ! saturation specific humidity [kg/kg]
	562	REAL, INTENT(OUT), DIMENSION(klon) :: dqs ! derivation of saturation specific humidity wrt T
[3999]	563
	564	REAL delta, cor, cvm5
[4072]	565	INTEGER i
	566
	567	DO i=1,klon
	568
[3999]	569	IF (phase .EQ. 1) THEN
	570	delta=0.
	571	ELSEIF (phase .EQ. 2) THEN
	572	delta=1.
	573	ELSE
[4072]	574	delta=MAX(0.,SIGN(1.,tref-temp(i)))
[3999]	575	ENDIF
	576
	577	IF (flagth) THEN
	578	cvm5=R5LES(1.-delta) + R5IESdelta
	579	ELSE
	580	cvm5 = R5LESRLVTT(1.-delta) + R5IESRLSTTdelta
[4072]	581	cvm5 = cvm5 /RCPD/(1.0+RVTMP2*(qtot(i)))
[3999]	582	ENDIF
	583
[4072]	584	qs(i)= R2ES*FOEEW(temp(i),delta)/pressure(i)
	585	qs(i)=MIN(0.5,qs(i))
	586	cor=1./(1.-RETV*qs(i))
	587	qs(i)=qs(i)*cor
	588	dqs(i)= FOEDE(temp(i),delta,cvm5,qs(i),cor)
[3999]	589
[4072]	590	END DO
	591
[3999]	592	END SUBROUTINE CALC_QSAT_ECMWF
	593	!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
	594
	595
	596	!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
[4072]	597	SUBROUTINE CALC_GAMMASAT(klon,temp,qtot,pressure,gammasat,dgammasatdt)
[3999]	598
	599	!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
	600	! programme that calculates the gammasat parameter that determines the
	601	! homogeneous condensation thresholds for cold (<0oC) clouds
	602	! condensation at q>gammasat*qsat
	603	! Etienne Vignon, March 2021
	604	!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
	605
[5204]	606	use lmdz_lscp_ini, only: iflag_gammasat, temp_nowater, RTT
	607	use lmdz_lscp_ini, only: a_homofreez, b_homofreez, delta_hetfreez
[3999]	608
[4059]	609	IMPLICIT NONE
[3999]	610
	611
[4072]	612	INTEGER, INTENT(IN) :: klon ! number of horizontal grid points
	613	REAL, INTENT(IN), DIMENSION(klon) :: temp ! temperature in K
	614	REAL, INTENT(IN), DIMENSION(klon) :: qtot ! total specific water in kg/kg
[3999]	615
[4072]	616	REAL, INTENT(IN), DIMENSION(klon) :: pressure ! pressure in Pa
[3999]	617
[4072]	618	REAL, INTENT(OUT), DIMENSION(klon) :: gammasat ! coefficient to multiply qsat with to calculate saturation
	619	REAL, INTENT(OUT), DIMENSION(klon) :: dgammasatdt ! derivative of gammasat wrt temperature
[3999]	620
[4072]	621	REAL, DIMENSION(klon) :: qsi,qsl,dqsl,dqsi
[5204]	622	REAL f_homofreez, fac
[3999]	623
[4072]	624	INTEGER i
	625
	626	CALL CALC_QSAT_ECMWF(klon,temp,qtot,pressure,RTT,1,.false.,qsl,dqsl)
	627	CALL CALC_QSAT_ECMWF(klon,temp,qtot,pressure,RTT,2,.false.,qsi,dqsi)
[3999]	628
[5204]	629	DO i = 1, klon
[3999]	630
[5204]	631	IF ( temp(i) .GE. RTT ) THEN
[3999]	632	! warm clouds: condensation at saturation wrt liquid
[5204]	633	gammasat(i) = 1.
	634	dgammasatdt(i) = 0.
[3999]	635
[5204]	636	ELSE
	637	! cold clouds: qsi > qsl
[3999]	638
[5204]	639	! homogeneous freezing of aerosols, according to
	640	! Koop, 2000 and Ren and MacKenzie, 2005 (QJRMS)
	641	! 'Cirrus regime'
	642	! if f_homofreez > qsl / qsi, liquid nucleation
	643	! if f_homofreez < qsl / qsi, homogeneous freezing of aerosols
	644	! Note: f_homofreez = qsl / qsi for temp ~= -38degC
	645	f_homofreez = a_homofreez - temp(i) / b_homofreez
	646
	647	IF ( iflag_gammasat .GE. 3 ) THEN
	648	! condensation at homogeneous freezing threshold for temp < -38 degC
	649	! condensation at liquid saturation for temp > -38 degC
	650	IF ( f_homofreez .LE. qsl(i) / qsi(i) ) THEN
	651	gammasat(i) = f_homofreez
	652	dgammasatdt(i) = - 1. / b_homofreez
	653	ELSE
	654	gammasat(i) = qsl(i) / qsi(i)
	655	dgammasatdt(i) = ( dqsl(i) * qsi(i) - dqsi(i) * qsl(i) ) / qsi(i) / qsi(i)
	656	ENDIF
[3999]	657
[5204]	658	ELSEIF ( iflag_gammasat .EQ. 2 ) THEN
	659	! condensation at homogeneous freezing threshold for temp < -38 degC
	660	! condensation at a threshold linearly decreasing between homogeneous
	661	! freezing and ice saturation for -38 degC < temp < temp_nowater
	662	! condensation at ice saturation for temp > temp_nowater
	663	! If temp_nowater = 235.15 K, this is equivalent to iflag_gammasat = 1
	664	IF ( f_homofreez .LE. qsl(i) / qsi(i) ) THEN
	665	gammasat(i) = f_homofreez
	666	dgammasatdt(i) = - 1. / b_homofreez
	667	ELSEIF ( temp(i) .LE. temp_nowater ) THEN
	668	! Here, we assume that f_homofreez = qsl / qsi for temp = -38 degC = 235.15 K
	669	dgammasatdt(i) = ( a_homofreez - 235.15 / b_homofreez - 1. ) &
	670	/ ( 235.15 - temp_nowater )
	671	gammasat(i) = dgammasatdt(i) * ( temp(i) - temp_nowater ) + 1.
	672	ELSE
	673	gammasat(i) = 1.
	674	dgammasatdt(i) = 0.
	675	ENDIF
[3999]	676
[5204]	677	ELSEIF ( iflag_gammasat .EQ. 1 ) THEN
	678	! condensation at homogeneous freezing threshold for temp < -38 degC
	679	! condensation at ice saturation for temp > -38 degC
	680	IF ( f_homofreez .LE. qsl(i) / qsi(i) ) THEN
	681	gammasat(i) = f_homofreez
	682	dgammasatdt(i) = - 1. / b_homofreez
	683	ELSE
	684	gammasat(i) = 1.
	685	dgammasatdt(i) = 0.
	686	ENDIF
	687
[3999]	688	ELSE
[5204]	689	! condensation at ice saturation for temp < -38 degC
	690	! condensation at ice saturation for temp > -38 degC
	691	gammasat(i) = 1.
	692	dgammasatdt(i) = 0.
[3999]	693
	694	ENDIF
	695
[5204]	696	! Note that the delta_hetfreez parameter allows to linearly decrease the
	697	! condensation threshold between the calculated threshold and the ice saturation
	698	! for delta_hetfreez = 1, the threshold is the calculated condensation threshold
	699	! for delta_hetfreez = 0, the threshold is the ice saturation
	700	gammasat(i) = ( 1. - delta_hetfreez ) + delta_hetfreez * gammasat(i)
	701	dgammasatdt(i) = delta_hetfreez * dgammasatdt(i)
	702
[3999]	703	ENDIF
	704
[4072]	705	END DO
	706
	707
[3999]	708	END SUBROUTINE CALC_GAMMASAT
[4562]	709	!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
[3999]	710
	711
[4562]	712	!++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
[4639]	713	SUBROUTINE DISTANCE_TO_CLOUD_TOP(klon,klev,k,temp,pplay,paprs,rneb,distcltop1D,temp_cltop)
[4562]	714	!++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
	715
[4665]	716	USE lmdz_lscp_ini, ONLY : rd,rg,tresh_cl
[4562]	717
	718	IMPLICIT NONE
	719
	720	INTEGER, INTENT(IN) :: klon,klev !number of horizontal and vertical grid points
	721	INTEGER, INTENT(IN) :: k ! vertical index
	722	REAL, INTENT(IN), DIMENSION(klon,klev) :: temp ! temperature in K
	723	REAL, INTENT(IN), DIMENSION(klon,klev) :: pplay ! pressure middle layer in Pa
	724	REAL, INTENT(IN), DIMENSION(klon,klev+1) :: paprs ! pressure interfaces in Pa
	725	REAL, INTENT(IN), DIMENSION(klon,klev) :: rneb ! cloud fraction
	726
	727	REAL, INTENT(OUT), DIMENSION(klon) :: distcltop1D ! distance from cloud top
[4639]	728	REAL, INTENT(OUT), DIMENSION(klon) :: temp_cltop ! temperature of cloud top
	729
[4562]	730	REAL dzlay(klon,klev)
	731	REAL zlay(klon,klev)
	732	REAL dzinterf
	733	INTEGER i,k_top, kvert
	734	LOGICAL bool_cl
	735
	736
	737	DO i=1,klon
	738	! Initialization height middle of first layer
	739	dzlay(i,1) = Rd * temp(i,1) / rg * log(paprs(i,1)/paprs(i,2))
	740	zlay(i,1) = dzlay(i,1)/2
	741
	742	DO kvert=2,klev
	743	IF (kvert.EQ.klev) THEN
	744	dzlay(i,kvert) = 2(rd temp(i,kvert) / rg * log(paprs(i,kvert)/pplay(i,kvert)))
	745	ELSE
	746	dzlay(i,kvert) = rd * temp(i,kvert) / rg * log(paprs(i,kvert)/paprs(i,kvert+1))
	747	ENDIF
	748	dzinterf = rd * temp(i,kvert) / rg * log(pplay(i,kvert-1)/pplay(i,kvert))
	749	zlay(i,kvert) = zlay(i,kvert-1) + dzinterf
	750	ENDDO
	751	ENDDO
	752
	753	DO i=1,klon
[4639]	754	k_top = k
[4562]	755	IF (rneb(i,k) .LE. tresh_cl) THEN
	756	bool_cl = .FALSE.
	757	ELSE
	758	bool_cl = .TRUE.
	759	ENDIF
	760
	761	DO WHILE ((bool_cl) .AND. (k_top .LE. klev))
	762	! find cloud top
	763	IF (rneb(i,k_top) .GT. tresh_cl) THEN
	764	k_top = k_top + 1
	765	ELSE
	766	bool_cl = .FALSE.
	767	k_top = k_top - 1
	768	ENDIF
	769	ENDDO
	770	k_top=min(k_top,klev)
	771
	772	!dist to top is dist between current layer and layer of cloud top (from middle to middle) + dist middle to
	773	!interf for layer of cloud top
	774	distcltop1D(i) = zlay(i,k_top) - zlay(i,k) + dzlay(i,k_top)/2
[4639]	775	temp_cltop(i) = temp(i,k_top)
[4562]	776	ENDDO ! klon
	777
	778	END SUBROUTINE DISTANCE_TO_CLOUD_TOP
[3999]	779	!++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
	780
[5204]	781	!++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
	782	FUNCTION GAMMAINC ( p, x )
	783
	784	!*****************************************************************************80
	785	!
	786	!! GAMMAINC computes the regularized lower incomplete Gamma Integral
	787	!
	788	! Modified:
	789	!
	790	! 20 January 2008
	791	!
	792	! Author:
	793	!
	794	! Original FORTRAN77 version by B Shea.
	795	! FORTRAN90 version by John Burkardt.
	796	!
	797	! Reference:
	798	!
	799	! B Shea,
	800	! Algorithm AS 239:
	801	! Chi-squared and Incomplete Gamma Integral,
	802	! Applied Statistics,
	803	! Volume 37, Number 3, 1988, pages 466-473.
	804	!
	805	! Parameters:
	806	!
	807	! Input, real X, P, the parameters of the incomplete
	808	! gamma ratio. 0 <= X, and 0 < P.
	809	!
	810	! Output, real GAMMAINC, the value of the incomplete
	811	! Gamma integral.
	812	!
	813	IMPLICIT NONE
	814
	815	REAL A
	816	REAL AN
	817	REAL ARG
	818	REAL B
	819	REAL C
	820	REAL, PARAMETER :: ELIMIT = - 88.0E+00
	821	REAL GAMMAINC
	822	REAL, PARAMETER :: OFLO = 1.0E+37
	823	REAL P
	824	REAL, PARAMETER :: PLIMIT = 1000.0E+00
	825	REAL PN1
	826	REAL PN2
	827	REAL PN3
	828	REAL PN4
	829	REAL PN5
	830	REAL PN6
	831	REAL RN
	832	REAL, PARAMETER :: TOL = 1.0E-14
	833	REAL X
	834	REAL, PARAMETER :: XBIG = 1.0E+08
	835
	836	GAMMAINC = 0.0E+00
	837
	838	IF ( X == 0.0E+00 ) THEN
	839	GAMMAINC = 0.0E+00
	840	RETURN
	841	END IF
	842	!
	843	! IF P IS LARGE, USE A NORMAL APPROXIMATION.
	844	!
	845	IF ( PLIMIT < P ) THEN
	846
	847	PN1 = 3.0E+00 * SQRT ( P ) * ( ( X / P )**( 1.0E+00 / 3.0E+00 ) &
	848	+ 1.0E+00 / ( 9.0E+00 * P ) - 1.0E+00 )
	849
	850	GAMMAINC = 0.5E+00 * ( 1. + ERF ( PN1 ) )
	851	RETURN
	852
	853	END IF
	854	!
	855	! IF X IS LARGE SET GAMMAD = 1.
	856	!
	857	IF ( XBIG < X ) THEN
	858	GAMMAINC = 1.0E+00
	859	RETURN
	860	END IF
	861	!
	862	! USE PEARSON'S SERIES EXPANSION.
	863	! (NOTE THAT P IS NOT LARGE ENOUGH TO FORCE OVERFLOW IN ALOGAM).
	864	!
	865	IF ( X <= 1.0E+00 .OR. X < P ) THEN
	866
	867	ARG = P * LOG ( X ) - X - LOG_GAMMA ( P + 1.0E+00 )
	868	C = 1.0E+00
	869	GAMMAINC = 1.0E+00
	870	A = P
	871
	872	DO
	873
	874	A = A + 1.0E+00
	875	C = C * X / A
	876	GAMMAINC = GAMMAINC + C
	877
	878	IF ( C <= TOL ) THEN
	879	EXIT
	880	END IF
	881
	882	END DO
	883
	884	ARG = ARG + LOG ( GAMMAINC )
	885
	886	IF ( ELIMIT <= ARG ) THEN
	887	GAMMAINC = EXP ( ARG )
	888	ELSE
	889	GAMMAINC = 0.0E+00
	890	END IF
	891	!
	892	! USE A CONTINUED FRACTION EXPANSION.
	893	!
	894	ELSE
	895
	896	ARG = P * LOG ( X ) - X - LOG_GAMMA ( P )
	897	A = 1.0E+00 - P
	898	B = A + X + 1.0E+00
	899	C = 0.0E+00
	900	PN1 = 1.0E+00
	901	PN2 = X
	902	PN3 = X + 1.0E+00
	903	PN4 = X * B
	904	GAMMAINC = PN3 / PN4
	905
	906	DO
	907
	908	A = A + 1.0E+00
	909	B = B + 2.0E+00
	910	C = C + 1.0E+00
	911	AN = A * C
	912	PN5 = B * PN3 - AN * PN1
	913	PN6 = B * PN4 - AN * PN2
	914
	915	IF ( PN6 /= 0.0E+00 ) THEN
	916
	917	RN = PN5 / PN6
	918
	919	IF ( ABS ( GAMMAINC - RN ) <= MIN ( TOL, TOL * RN ) ) THEN
	920	EXIT
	921	END IF
	922
	923	GAMMAINC = RN
	924
	925	END IF
	926
	927	PN1 = PN3
	928	PN2 = PN4
	929	PN3 = PN5
	930	PN4 = PN6
	931	!
	932	! RE-SCALE TERMS IN CONTINUED FRACTION IF TERMS ARE LARGE.
	933	!
	934	IF ( OFLO <= ABS ( PN5 ) ) THEN
	935	PN1 = PN1 / OFLO
	936	PN2 = PN2 / OFLO
	937	PN3 = PN3 / OFLO
	938	PN4 = PN4 / OFLO
	939	END IF
	940
	941	END DO
	942
	943	ARG = ARG + LOG ( GAMMAINC )
	944
	945	IF ( ELIMIT <= ARG ) THEN
	946	GAMMAINC = 1.0E+00 - EXP ( ARG )
	947	ELSE
	948	GAMMAINC = 1.0E+00
	949	END IF
	950
	951	END IF
	952
	953	RETURN
	954	END FUNCTION GAMMAINC
	955	!++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
	956
[4665]	957	END MODULE lmdz_lscp_tools
[3999]	958
	959

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