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lmdz_lscp_tools.f90 @ 5649

Last change on this file since 5649 was 5633, checked in by evignon, 2 months ago
small changes related to mixed phase clouds treatment Etienne and Lea
File size: 39.0 KB

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[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
[5614]	227	! if temperature or temperature of cloud top <-40°C,
[4639]	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
[5633]	243	SUBROUTINE ICEFRAC_LSCP_TURB(klon, dtime, pticefracturb, temp, pplay, paprsdn, paprsup, wvel, qice_ini, snowcld, snowfracld, qtot_incl, cldfra, tke, &
[5614]	244	tke_dissip, sursat_e, invtau_e, 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)
[5614]	249	! E.Vignon (03/2025) : additional elements for treatment of convective
	250	! boundary layer clouds
[5007]	251	!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
[3999]	252
	253
[5007]	254	USE lmdz_lscp_ini, ONLY : prt_level, lunout
	255	USE lmdz_lscp_ini, ONLY : RCPD, RLSTT, RLVTT, RLMLT, RVTMP2, RTT, RD, RG, RV, RPI
	256	USE lmdz_lscp_ini, ONLY : seuil_neb, temp_nowater
[5614]	257	USE lmdz_lscp_ini, ONLY : naero5, gamma_snwretro, gamma_taud, capa_crystal, rho_ice
[5633]	258	USE lmdz_lscp_ini, ONLY : eps, snow_fallspeed
[5007]	259
	260	IMPLICIT NONE
	261
[5383]	262	INTEGER, INTENT(IN) :: klon !--number of horizontal grid points
	263	REAL, INTENT(IN) :: dtime !--time step [s]
[5614]	264	LOGICAL, INTENT(IN), DIMENSION(klon) :: pticefracturb !--grid points concerned by this routine
[5383]	265	REAL, INTENT(IN), DIMENSION(klon) :: temp !--temperature
	266	REAL, INTENT(IN), DIMENSION(klon) :: pplay !--pressure in the middle of the layer [Pa]
	267	REAL, INTENT(IN), DIMENSION(klon) :: paprsdn !--pressure at the bottom interface of the layer [Pa]
	268	REAL, INTENT(IN), DIMENSION(klon) :: paprsup !--pressure at the top interface of the layer [Pa]
[5614]	269	REAL, INTENT(IN), DIMENSION(klon) :: wvel !--vertical velocity [m/s]
[5383]	270	REAL, INTENT(IN), DIMENSION(klon) :: qtot_incl !--specific total cloud water in-cloud content [kg/kg]
	271	REAL, INTENT(IN), DIMENSION(klon) :: cldfra !--cloud fraction in gridbox [-]
	272	REAL, INTENT(IN), DIMENSION(klon) :: tke !--turbulent kinetic energy [m2/s2]
	273	REAL, INTENT(IN), DIMENSION(klon) :: tke_dissip !--TKE dissipation [m2/s3]
[5007]	274
[5383]	275	REAL, INTENT(IN), DIMENSION(klon) :: qice_ini !--initial specific ice content gridbox-mean [kg/kg]
[5614]	276	REAL, INTENT(IN), DIMENSION(klon) :: snowcld !--in-cloud snowfall flux [kg/m2/s]
[5633]	277	REAL, INTENT(IN), DIMENSION(klon) :: snowfracld !--cloudy precip fraction [-]
[5614]	278	REAL, INTENT(IN), DIMENSION(klon) :: sursat_e !--environment supersaturation [-]
	279	REAL, INTENT(IN), DIMENSION(klon) :: invtau_e !--inverse time-scale of mixing with environment [s-1]
[5383]	280	REAL, INTENT(OUT), DIMENSION(klon) :: qliq !--specific liquid content gridbox-mean [kg/kg]
	281	REAL, INTENT(OUT), DIMENSION(klon) :: qvap_cld !--specific cloud vapor content, gridbox-mean [kg/kg]
	282	REAL, INTENT(OUT), DIMENSION(klon) :: qice !--specific ice content gridbox-mean [kg/kg]
[5007]	283
[5614]	284	REAL, INTENT(INOUT), DIMENSION(klon) :: icefrac !--fraction of ice in condensed water [-]
	285	REAL, INTENT(INOUT), DIMENSION(klon) :: dicefracdT
	286
[5383]	287	REAL, INTENT(OUT), DIMENSION(klon) :: cldfraliq !--fraction of cldfra where liquid [-]
	288	REAL, INTENT(OUT), DIMENSION(klon) :: sigma2_icefracturb !--Sigma2 of the ice supersaturation PDF [-]
	289	REAL, INTENT(OUT), DIMENSION(klon) :: mean_icefracturb !--Mean of the ice supersaturation PDF [-]
[5007]	290
[5383]	291	REAL, DIMENSION(klon) :: qzero, qsatl, dqsatl, qsati, dqsati !--specific humidity saturation values
[5007]	292	INTEGER :: i
	293
[5383]	294	REAL :: qvap_incl, qice_incl, qliq_incl, qiceini_incl !--In-cloud specific quantities [kg/kg]
	295	REAL :: water_vapor_diff !--Water-vapour diffusion coeff in air (f(T,P)) [m2/s]
	296	REAL :: air_thermal_conduct !--Thermal conductivity of air (f(T)) [J/m/K/s]
	297	REAL :: C0 !--Lagrangian structure function [-]
[5007]	298	REAL :: tau_dissipturb
[5614]	299	REAL :: invtau_phaserelax
	300	REAL :: sigma2_pdf
[5007]	301	REAL :: ai, bi, B0
	302	REAL :: sursat_iceliq
[5383]	303	REAL :: sursat_equ
[5007]	304	REAL :: liqfra_max
	305	REAL :: sursat_iceext
[5383]	306	REAL :: nb_crystals !--number concentration of ice crystals [#/m3]
	307	REAL :: moment1_PSD !--1st moment of ice PSD
	308	REAL :: N0_PSD, lambda_PSD !--parameters of the exponential PSD
[5007]	309
	310	REAL :: cldfra1D
[5383]	311	REAL :: rho_air
	312	REAL :: psati !--saturation vapor pressure wrt ice [Pa]
[5614]	313
[5383]	314
[5614]	315	REAL :: tempvig1, tempvig2
	316
	317	tempvig1 = -21.06 + RTT
	318	tempvig2 = -30.35 + RTT
[5383]	319	C0 = 10. !--value assumed in Field2014
[5007]	320	sursat_iceext = -0.1
	321	qzero(:) = 0.
	322	cldfraliq(:) = 0.
[5614]	323	qliq(:) = 0.
	324	qice(:) = 0.
	325	qvap_cld(:) = 0.
[5007]	326	sigma2_icefracturb(:) = 0.
[5383]	327	mean_icefracturb(:) = 0.
[5007]	328
[5383]	329	!--wrt liquid
[5007]	330	CALL calc_qsat_ecmwf(klon,temp(:),qzero(:),pplay(:),RTT,1,.false.,qsatl(:),dqsatl(:))
	331	!--wrt ice
	332	CALL calc_qsat_ecmwf(klon,temp(:),qzero(:),pplay(:),RTT,2,.false.,qsati(:),dqsati(:))
	333
	334
	335	DO i=1,klon
[5383]	336	rho_air = pplay(i) / temp(i) / RD
[5007]	337	! because cldfra is intent in, but can be locally modified due to test
	338	cldfra1D = cldfra(i)
[5614]	339	! activate param for concerned grid points and for cloudy conditions
	340	IF ((pticefracturb(i)) .AND. (cldfra(i) .GT. 0.)) THEN
[5007]	341	IF (cldfra(i) .GE. 1.0) THEN
	342	cldfra1D = 1.0
	343	END IF
	344
	345	! T>0°C, no ice allowed
	346	IF ( temp(i) .GE. RTT ) THEN
	347	qvap_cld(i) = qsatl(i) * cldfra1D
	348	qliq(i) = MAX(0.0,qtot_incl(i)-qsatl(i)) * cldfra1D
	349	qice(i) = 0.
	350	cldfraliq(i) = 1.
	351	icefrac(i) = 0.
	352	dicefracdT(i) = 0.
	353
	354	! T<-38°C, no liquid allowed
	355	ELSE IF ( temp(i) .LE. temp_nowater) THEN
	356	qvap_cld(i) = qsati(i) * cldfra1D
	357	qliq(i) = 0.
	358	qice(i) = MAX(0.0,qtot_incl(i)-qsati(i)) * cldfra1D
	359	cldfraliq(i) = 0.
	360	icefrac(i) = 1.
	361	dicefracdT(i) = 0.
	362
[5614]	363
[5383]	364	!---------------------------------------------------------
	365	!-- MIXED PHASE TEMPERATURE REGIME
	366	!---------------------------------------------------------
	367	!--In the mixed phase regime (-38°C< T <0°C) we distinguish
	368	!--3 possible subcases.
	369	!--1. No pre-existing ice
	370	!--2A. Pre-existing ice and no turbulence
	371	!--2B. Pre-existing ice and turbulence
[5007]	372	ELSE
[5383]	373
[5633]	374	! gamma_snwretro controls the contribution of snowflakes to the negative feedback
	375	! note that for reasons related to inetarctions with the condensation iteration in lscp_main
	376	! we consider here the mean snowflake concentration in the mesh (not the in-cloud concentration)
	377	! when poprecip is active, it will be worth testing considering the incloud fraction, dividing
	378	! by snowfracld
	379	! qiceini_incl = qice_ini(i) / cldfra1D + &
	380	! gamma_snwretro * snowcld(i) * RG * dtime / ( paprsdn(i) - paprsup(i) )
	381	! assuming constant snowfall velocity
	382	qiceini_incl = qice_ini(i) / cldfra1D + gamma_snwretro * snowcld(i) / pplay(i) * RD * temp(i) / snow_fallspeed
[5383]	383
[5614]	384	!--1. No preexisting ice and no mixing with environment: if vertical motion, fully liquid
[5383]	385	!--cloud else fully iced cloud
[5614]	386	IF ( (qiceini_incl .LT. eps) .AND. (invtau_e(i) .LT. eps) ) THEN
	387	IF ( (wvel(i) .GT. eps) .OR. (tke(i) .GT. eps) ) THEN
[5383]	388	qvap_cld(i) = qsatl(i) * cldfra1D
	389	qliq(i) = MAX(0.,qtot_incl(i)-qsatl(i)) * cldfra1D
	390	qice(i) = 0.
	391	cldfraliq(i) = 1.
	392	icefrac(i) = 0.
	393	dicefracdT(i) = 0.
	394	ELSE
	395	qvap_cld(i) = qsati(i) * cldfra1D
	396	qliq(i) = 0.
	397	qice(i) = MAX(0.,qtot_incl(i)-qsati(i)) * cldfra1D
	398	cldfraliq(i) = 0.
	399	icefrac(i) = 1.
	400	dicefracdT(i) = 0.
	401	ENDIF
[5007]	402
	403
[5614]	404	!--2. Pre-existing ice and/or mixing with environment:computation of ice properties for
[5383]	405	!--feedback
	406	ELSE
	407
[5007]	408	sursat_iceliq = qsatl(i)/qsati(i) - 1.
	409	psati = qsati(i) * pplay(i) / (RD/RV)
[5383]	410
[5007]	411	!--We assume an exponential ice PSD whose parameters
	412	!--are computed following Morrison&Gettelman 2008
	413	!--Ice number density is assumed equals to INP density
[5614]	414	!--which is for naero5>0 a function of temperature (DeMott 2010)
[5007]	415	!--bi and B0 are microphysical function characterizing
	416	!--vapor/ice interactions
	417	!--tau_phase_relax is the typical time of vapor deposition
	418	!--onto ice crystals
	419
[5614]	420	!--For naero5<=0 INP density is derived from the empirical fit
	421	!--from MARCUS campaign from Vignon 2021
	422	!--/!\ Note that option is very specific and should be use for
	423	!--the Southern Ocean and the Antarctic
	424
	425	IF (naero5 .LE. 0) THEN
	426	IF ( temp(i) .GT. tempvig1 ) THEN
	427	nb_crystals = 1.e3 * 10*(-0.14(temp(i)-tempvig1) - 2.88)
	428	ELSE IF ( temp(i) .GT. tempvig2 ) THEN
	429	nb_crystals = 1.e3 * 10*(-0.31(temp(i)-tempvig1) - 2.88)
	430	ELSE
	431	nb_crystals = 1.e3 * 10**(0.)
	432	ENDIF
	433	ELSE
	434	nb_crystals = 1.e3 * 5.94e-5 * ( RTT - temp(i) )*3.33 naero5*(0.0264(RTT-temp(i))+0.0033)
	435	ENDIF
	436	lambda_PSD = ( (RPIrho_icenb_crystals) / (rho_air * MAX(qiceini_incl , eps) ) ) ** (1./3.)
[5383]	437	N0_PSD = nb_crystals * lambda_PSD
	438	moment1_PSD = N0_PSD/lambda_PSD**2
	439
[5007]	440	!--Formulae for air thermal conductivity and water vapor diffusivity
	441	!--comes respectively from Beard and Pruppacher (1971)
	442	!--and Hall and Pruppacher (1976)
	443
	444	air_thermal_conduct = ( 5.69 + 0.017 * ( temp(i) - RTT ) ) * 1.e-3 * 4.184
	445	water_vapor_diff = 2.111e-5 ( temp(i) / RTT )*1.94 ( 101325 / pplay(i) )
	446
	447	bi = 1./((qsati(i)+qsatl(i))/2.) + RLSTT2 / RCPD / RV / temp(i)2
	448	B0 = 4. * RPI * capa_crystal * 1. / ( RLSTT2 / air_thermal_conduct / RV / temp(i)2 &
	449	+ RV * temp(i) / psati / water_vapor_diff )
[5614]	450	invtau_phaserelax = bi * B0 * moment1_PSD
[5383]	451
	452	ai = RG / RD / temp(i) * ( RD * RLSTT / RCPD / RV / temp(i) - 1. )
[5614]	453	sursat_equ = (ai * wvel(i) + sursat_e(i)*invtau_e(i)) / (invtau_phaserelax + invtau_e(i))
	454	! as sursaturation is by definition lower than -1 and
	455	! because local supersaturation > 1 are never found in the atmosphere
[5007]	456
[5614]	457	!--2A. No TKE : stationnary binary solution depending on vertical velocity and mixing with env.
[5383]	458	! If Sequ > Siw liquid cloud, else ice cloud
	459	IF ( tke_dissip(i) .LE. eps ) THEN
[5614]	460	sigma2_icefracturb(i)= 0.
	461	mean_icefracturb(i) = sursat_equ
[5383]	462	IF (sursat_equ .GT. sursat_iceliq) THEN
	463	qvap_cld(i) = qsatl(i) * cldfra1D
	464	qliq(i) = MAX(0.,qtot_incl(i)-qsatl(i)) * cldfra1D
	465	qice(i) = 0.
	466	cldfraliq(i) = 1.
	467	icefrac(i) = 0.
	468	dicefracdT(i) = 0.
	469	ELSE
	470	qvap_cld(i) = qsati(i) * cldfra1D
	471	qliq(i) = 0.
	472	qice(i) = MAX(0.,qtot_incl(i)-qsati(i)) * cldfra1D
	473	cldfraliq(i) = 0.
	474	icefrac(i) = 1.
	475	dicefracdT(i) = 0.
	476	ENDIF
	477
	478	!--2B. TKE and ice : ice supersaturation PDF
	479	!--we compute the cloud liquid properties with a Gaussian PDF
	480	!--of ice supersaturation F(Si) (Field2014, Furtado2016).
	481	!--Parameters of the PDF are function of turbulence and
	482	!--microphysics/existing ice.
	483	ELSE
	484
	485	!--Tau_dissipturb is the time needed for turbulence to decay
	486	!--due to viscosity
	487	tau_dissipturb = gamma_taud * 2. * 2./3. * tke(i) / tke_dissip(i) / C0
[5007]	488
[5383]	489	!--------------------- PDF COMPUTATIONS ---------------------
	490	!--Formulae for sigma2_pdf (variance), mean of PDF in Raillard2025
	491	!--cloud liquid fraction and in-cloud liquid content are given
	492	!--by integrating resp. F(Si) and Si*F(Si)
	493	!--Liquid is limited by the available water vapor trough a
	494	!--maximal liquid fraction
	495	!--qice_ini(i) / cldfra1D = qiceincld without precip
[5007]	496
[5383]	497	liqfra_max = MAX(0., (MIN (1.,( qtot_incl(i) - (qice_ini(i) / cldfra1D) - qsati(i) * (1 + sursat_iceext ) ) / ( qsatl(i) - qsati(i) ) ) ) )
[5633]	498	sigma2_pdf = 1./2. * ( ai*2 ) 2./3. * tke(i) * tau_dissipturb / (invtau_phaserelax + invtau_e(i))
[5614]	499	! sursat ranges between -1 and 1, so we prevent sigma2 so exceed 1
	500	cldfraliq(i) = 0.5 * (1. - erf( ( sursat_iceliq - sursat_equ) / (SQRT(2.* sigma2_pdf) ) ) )
[5383]	501	IF (cldfraliq(i) .GT. liqfra_max) THEN
	502	cldfraliq(i) = liqfra_max
	503	ENDIF
	504
[5614]	505	qliq_incl = qsati(i) * SQRT(sigma2_pdf) / SQRT(2.RPI) EXP( -1.(sursat_iceliq - sursat_equ)2. / (2.sigma2_pdf) ) &
	506	- qsati(i) * cldfraliq(i) * (sursat_iceliq - sursat_equ )
[5383]	507
	508	sigma2_icefracturb(i)= sigma2_pdf
[5614]	509	mean_icefracturb(i) = sursat_equ
[5170]	510
[5383]	511	!------------ SPECIFIC VAPOR CONTENT AND WATER CONSERVATION ------------
[5007]	512
[5383]	513	IF ( (qliq_incl .LE. eps) .OR. (cldfraliq(i) .LE. eps) ) THEN
	514	qliq_incl = 0.
	515	cldfraliq(i) = 0.
	516	END IF
	517
	518	!--Specific humidity is the max between qsati and the weighted mean between
	519	!--qv in MPC patches and qv in ice-only parts. We assume that MPC parts are
	520	!--always at qsatl and ice-only parts slightly subsaturated (qsati*sursat_iceext+1)
	521	!--The whole cloud can therefore be supersaturated but never subsaturated.
[5170]	522
[5383]	523	qvap_incl = MAX(qsati(i), ( 1. - cldfraliq(i) ) * (sursat_iceext + 1.) * qsati(i) + cldfraliq(i) * qsatl(i) )
[5170]	524
[5383]	525	IF ( qvap_incl .GE. qtot_incl(i) ) THEN
	526	qvap_incl = qsati(i)
[5614]	527	qliq_incl = MAX(0.0,qtot_incl(i) - qvap_incl)
[5383]	528	qice_incl = 0.
[5170]	529
[5383]	530	ELSEIF ( (qvap_incl + qliq_incl) .GE. qtot_incl(i) ) THEN
	531	qliq_incl = MAX(0.0,qtot_incl(i) - qvap_incl)
	532	qice_incl = 0.
	533	ELSE
	534	qice_incl = qtot_incl(i) - qvap_incl - qliq_incl
	535	END IF
[5007]	536
[5383]	537	qvap_cld(i) = qvap_incl * cldfra1D
	538	qliq(i) = qliq_incl * cldfra1D
	539	qice(i) = qice_incl * cldfra1D
[5614]	540	IF ((qice(i)+qliq(i)) .GT. 0.) THEN
	541	icefrac(i) = qice(i) / ( qice(i) + qliq(i) )
	542	ELSE
	543	icefrac(i) = 1. ! to keep computation of qsat wrt ice in condensation loop in lmdz_lscp_main
	544	ENDIF
[5383]	545	dicefracdT(i) = 0.
[5007]	546
[5383]	547	END IF ! Enough TKE
	548
	549	END IF ! End qini
[5007]	550
	551	END IF ! ! MPC temperature
	552
[5614]	553	END IF ! pticefracturb and cldfra
[5007]	554
	555	ENDDO ! klon
	556	END SUBROUTINE ICEFRAC_LSCP_TURB
[5383]	557	!
[5007]	558	!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
	559
	560
[4072]	561	SUBROUTINE CALC_QSAT_ECMWF(klon,temp,qtot,pressure,tref,phase,flagth,qs,dqs)
[3999]	562	!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
	563	! Calculate qsat following ECMWF method
	564	!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
	565
[4072]	566
[5284]	567	USE yoethf_mod_h
[5285]	568	USE yomcst_mod_h
[5274]	569	IMPLICIT NONE
[3999]	570
[5274]	571
[3999]	572	include "FCTTRE.h"
	573
[4072]	574	INTEGER, INTENT(IN) :: klon ! number of horizontal grid points
	575	REAL, INTENT(IN), DIMENSION(klon) :: temp ! temperature in K
	576	REAL, INTENT(IN), DIMENSION(klon) :: qtot ! total specific water in kg/kg
	577	REAL, INTENT(IN), DIMENSION(klon) :: pressure ! pressure in Pa
	578	REAL, INTENT(IN) :: tref ! reference temperature in K
[3999]	579	LOGICAL, INTENT(IN) :: flagth ! flag for qsat calculation for thermals
	580	INTEGER, INTENT(IN) :: phase
	581	! phase: 0=depend on temperature sign (temp>tref -> liquid, temp<tref, solid)
	582	! 1=liquid
	583	! 2=solid
	584
[4072]	585	REAL, INTENT(OUT), DIMENSION(klon) :: qs ! saturation specific humidity [kg/kg]
	586	REAL, INTENT(OUT), DIMENSION(klon) :: dqs ! derivation of saturation specific humidity wrt T
[3999]	587
	588	REAL delta, cor, cvm5
[4072]	589	INTEGER i
	590
	591	DO i=1,klon
	592
[3999]	593	IF (phase .EQ. 1) THEN
	594	delta=0.
	595	ELSEIF (phase .EQ. 2) THEN
	596	delta=1.
	597	ELSE
[4072]	598	delta=MAX(0.,SIGN(1.,tref-temp(i)))
[3999]	599	ENDIF
	600
	601	IF (flagth) THEN
	602	cvm5=R5LES(1.-delta) + R5IESdelta
	603	ELSE
	604	cvm5 = R5LESRLVTT(1.-delta) + R5IESRLSTTdelta
[4072]	605	cvm5 = cvm5 /RCPD/(1.0+RVTMP2*(qtot(i)))
[3999]	606	ENDIF
	607
[4072]	608	qs(i)= R2ES*FOEEW(temp(i),delta)/pressure(i)
	609	qs(i)=MIN(0.5,qs(i))
	610	cor=1./(1.-RETV*qs(i))
	611	qs(i)=qs(i)*cor
	612	dqs(i)= FOEDE(temp(i),delta,cvm5,qs(i),cor)
[3999]	613
[4072]	614	END DO
	615
[3999]	616	END SUBROUTINE CALC_QSAT_ECMWF
	617	!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
	618
	619
	620	!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
[4072]	621	SUBROUTINE CALC_GAMMASAT(klon,temp,qtot,pressure,gammasat,dgammasatdt)
[3999]	622
	623	!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
	624	! programme that calculates the gammasat parameter that determines the
	625	! homogeneous condensation thresholds for cold (<0oC) clouds
	626	! condensation at q>gammasat*qsat
	627	! Etienne Vignon, March 2021
	628	!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
	629
[5204]	630	use lmdz_lscp_ini, only: iflag_gammasat, temp_nowater, RTT
	631	use lmdz_lscp_ini, only: a_homofreez, b_homofreez, delta_hetfreez
[3999]	632
[4059]	633	IMPLICIT NONE
[3999]	634
	635
[4072]	636	INTEGER, INTENT(IN) :: klon ! number of horizontal grid points
	637	REAL, INTENT(IN), DIMENSION(klon) :: temp ! temperature in K
	638	REAL, INTENT(IN), DIMENSION(klon) :: qtot ! total specific water in kg/kg
[3999]	639
[4072]	640	REAL, INTENT(IN), DIMENSION(klon) :: pressure ! pressure in Pa
[3999]	641
[4072]	642	REAL, INTENT(OUT), DIMENSION(klon) :: gammasat ! coefficient to multiply qsat with to calculate saturation
	643	REAL, INTENT(OUT), DIMENSION(klon) :: dgammasatdt ! derivative of gammasat wrt temperature
[3999]	644
[4072]	645	REAL, DIMENSION(klon) :: qsi,qsl,dqsl,dqsi
[5204]	646	REAL f_homofreez, fac
[3999]	647
[4072]	648	INTEGER i
	649
	650	CALL CALC_QSAT_ECMWF(klon,temp,qtot,pressure,RTT,1,.false.,qsl,dqsl)
	651	CALL CALC_QSAT_ECMWF(klon,temp,qtot,pressure,RTT,2,.false.,qsi,dqsi)
[3999]	652
[5204]	653	DO i = 1, klon
[3999]	654
[5204]	655	IF ( temp(i) .GE. RTT ) THEN
[3999]	656	! warm clouds: condensation at saturation wrt liquid
[5204]	657	gammasat(i) = 1.
	658	dgammasatdt(i) = 0.
[3999]	659
[5204]	660	ELSE
	661	! cold clouds: qsi > qsl
[3999]	662
[5204]	663	! homogeneous freezing of aerosols, according to
	664	! Koop, 2000 and Ren and MacKenzie, 2005 (QJRMS)
	665	! 'Cirrus regime'
	666	! if f_homofreez > qsl / qsi, liquid nucleation
	667	! if f_homofreez < qsl / qsi, homogeneous freezing of aerosols
	668	! Note: f_homofreez = qsl / qsi for temp ~= -38degC
	669	f_homofreez = a_homofreez - temp(i) / b_homofreez
	670
	671	IF ( iflag_gammasat .GE. 3 ) THEN
	672	! condensation at homogeneous freezing threshold for temp < -38 degC
	673	! condensation at liquid saturation for temp > -38 degC
	674	IF ( f_homofreez .LE. qsl(i) / qsi(i) ) THEN
	675	gammasat(i) = f_homofreez
	676	dgammasatdt(i) = - 1. / b_homofreez
	677	ELSE
	678	gammasat(i) = qsl(i) / qsi(i)
	679	dgammasatdt(i) = ( dqsl(i) * qsi(i) - dqsi(i) * qsl(i) ) / qsi(i) / qsi(i)
	680	ENDIF
[3999]	681
[5204]	682	ELSEIF ( iflag_gammasat .EQ. 2 ) THEN
	683	! condensation at homogeneous freezing threshold for temp < -38 degC
	684	! condensation at a threshold linearly decreasing between homogeneous
	685	! freezing and ice saturation for -38 degC < temp < temp_nowater
	686	! condensation at ice saturation for temp > temp_nowater
	687	! If temp_nowater = 235.15 K, this is equivalent to iflag_gammasat = 1
	688	IF ( f_homofreez .LE. qsl(i) / qsi(i) ) THEN
	689	gammasat(i) = f_homofreez
	690	dgammasatdt(i) = - 1. / b_homofreez
	691	ELSEIF ( temp(i) .LE. temp_nowater ) THEN
	692	! Here, we assume that f_homofreez = qsl / qsi for temp = -38 degC = 235.15 K
	693	dgammasatdt(i) = ( a_homofreez - 235.15 / b_homofreez - 1. ) &
	694	/ ( 235.15 - temp_nowater )
	695	gammasat(i) = dgammasatdt(i) * ( temp(i) - temp_nowater ) + 1.
	696	ELSE
	697	gammasat(i) = 1.
	698	dgammasatdt(i) = 0.
	699	ENDIF
[3999]	700
[5204]	701	ELSEIF ( iflag_gammasat .EQ. 1 ) THEN
	702	! condensation at homogeneous freezing threshold for temp < -38 degC
	703	! condensation at ice saturation for temp > -38 degC
	704	IF ( f_homofreez .LE. qsl(i) / qsi(i) ) THEN
	705	gammasat(i) = f_homofreez
	706	dgammasatdt(i) = - 1. / b_homofreez
	707	ELSE
	708	gammasat(i) = 1.
	709	dgammasatdt(i) = 0.
	710	ENDIF
	711
[3999]	712	ELSE
[5204]	713	! condensation at ice saturation for temp < -38 degC
	714	! condensation at ice saturation for temp > -38 degC
	715	gammasat(i) = 1.
	716	dgammasatdt(i) = 0.
[3999]	717
	718	ENDIF
	719
[5204]	720	! Note that the delta_hetfreez parameter allows to linearly decrease the
	721	! condensation threshold between the calculated threshold and the ice saturation
	722	! for delta_hetfreez = 1, the threshold is the calculated condensation threshold
	723	! for delta_hetfreez = 0, the threshold is the ice saturation
	724	gammasat(i) = ( 1. - delta_hetfreez ) + delta_hetfreez * gammasat(i)
	725	dgammasatdt(i) = delta_hetfreez * dgammasatdt(i)
	726
[3999]	727	ENDIF
	728
[4072]	729	END DO
	730
	731
[3999]	732	END SUBROUTINE CALC_GAMMASAT
[4562]	733	!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
[3999]	734
	735
[4562]	736	!++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
[4639]	737	SUBROUTINE DISTANCE_TO_CLOUD_TOP(klon,klev,k,temp,pplay,paprs,rneb,distcltop1D,temp_cltop)
[4562]	738	!++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
	739
[4665]	740	USE lmdz_lscp_ini, ONLY : rd,rg,tresh_cl
[4562]	741
	742	IMPLICIT NONE
	743
	744	INTEGER, INTENT(IN) :: klon,klev !number of horizontal and vertical grid points
	745	INTEGER, INTENT(IN) :: k ! vertical index
	746	REAL, INTENT(IN), DIMENSION(klon,klev) :: temp ! temperature in K
	747	REAL, INTENT(IN), DIMENSION(klon,klev) :: pplay ! pressure middle layer in Pa
	748	REAL, INTENT(IN), DIMENSION(klon,klev+1) :: paprs ! pressure interfaces in Pa
	749	REAL, INTENT(IN), DIMENSION(klon,klev) :: rneb ! cloud fraction
	750
	751	REAL, INTENT(OUT), DIMENSION(klon) :: distcltop1D ! distance from cloud top
[4639]	752	REAL, INTENT(OUT), DIMENSION(klon) :: temp_cltop ! temperature of cloud top
	753
[4562]	754	REAL dzlay(klon,klev)
	755	REAL zlay(klon,klev)
	756	REAL dzinterf
	757	INTEGER i,k_top, kvert
	758	LOGICAL bool_cl
	759
	760
	761	DO i=1,klon
	762	! Initialization height middle of first layer
	763	dzlay(i,1) = Rd * temp(i,1) / rg * log(paprs(i,1)/paprs(i,2))
	764	zlay(i,1) = dzlay(i,1)/2
	765
	766	DO kvert=2,klev
	767	IF (kvert.EQ.klev) THEN
	768	dzlay(i,kvert) = 2(rd temp(i,kvert) / rg * log(paprs(i,kvert)/pplay(i,kvert)))
	769	ELSE
	770	dzlay(i,kvert) = rd * temp(i,kvert) / rg * log(paprs(i,kvert)/paprs(i,kvert+1))
	771	ENDIF
	772	dzinterf = rd * temp(i,kvert) / rg * log(pplay(i,kvert-1)/pplay(i,kvert))
	773	zlay(i,kvert) = zlay(i,kvert-1) + dzinterf
	774	ENDDO
	775	ENDDO
	776
	777	DO i=1,klon
[4639]	778	k_top = k
[4562]	779	IF (rneb(i,k) .LE. tresh_cl) THEN
	780	bool_cl = .FALSE.
	781	ELSE
	782	bool_cl = .TRUE.
	783	ENDIF
	784
	785	DO WHILE ((bool_cl) .AND. (k_top .LE. klev))
	786	! find cloud top
	787	IF (rneb(i,k_top) .GT. tresh_cl) THEN
	788	k_top = k_top + 1
	789	ELSE
	790	bool_cl = .FALSE.
	791	k_top = k_top - 1
	792	ENDIF
	793	ENDDO
	794	k_top=min(k_top,klev)
	795
	796	!dist to top is dist between current layer and layer of cloud top (from middle to middle) + dist middle to
	797	!interf for layer of cloud top
	798	distcltop1D(i) = zlay(i,k_top) - zlay(i,k) + dzlay(i,k_top)/2
[4639]	799	temp_cltop(i) = temp(i,k_top)
[4562]	800	ENDDO ! klon
	801
	802	END SUBROUTINE DISTANCE_TO_CLOUD_TOP
[3999]	803	!++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
	804
[5204]	805	!++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
	806	FUNCTION GAMMAINC ( p, x )
	807
	808	!*****************************************************************************80
	809	!
	810	!! GAMMAINC computes the regularized lower incomplete Gamma Integral
	811	!
	812	! Modified:
	813	!
	814	! 20 January 2008
	815	!
	816	! Author:
	817	!
	818	! Original FORTRAN77 version by B Shea.
	819	! FORTRAN90 version by John Burkardt.
	820	!
	821	! Reference:
	822	!
	823	! B Shea,
	824	! Algorithm AS 239:
	825	! Chi-squared and Incomplete Gamma Integral,
	826	! Applied Statistics,
	827	! Volume 37, Number 3, 1988, pages 466-473.
	828	!
	829	! Parameters:
	830	!
	831	! Input, real X, P, the parameters of the incomplete
	832	! gamma ratio. 0 <= X, and 0 < P.
	833	!
	834	! Output, real GAMMAINC, the value of the incomplete
	835	! Gamma integral.
	836	!
	837	IMPLICIT NONE
	838
	839	REAL A
	840	REAL AN
	841	REAL ARG
	842	REAL B
	843	REAL C
	844	REAL, PARAMETER :: ELIMIT = - 88.0E+00
	845	REAL GAMMAINC
	846	REAL, PARAMETER :: OFLO = 1.0E+37
	847	REAL P
	848	REAL, PARAMETER :: PLIMIT = 1000.0E+00
	849	REAL PN1
	850	REAL PN2
	851	REAL PN3
	852	REAL PN4
	853	REAL PN5
	854	REAL PN6
	855	REAL RN
	856	REAL, PARAMETER :: TOL = 1.0E-14
	857	REAL X
	858	REAL, PARAMETER :: XBIG = 1.0E+08
	859
	860	GAMMAINC = 0.0E+00
	861
	862	IF ( X == 0.0E+00 ) THEN
	863	GAMMAINC = 0.0E+00
	864	RETURN
	865	END IF
	866	!
	867	! IF P IS LARGE, USE A NORMAL APPROXIMATION.
	868	!
	869	IF ( PLIMIT < P ) THEN
	870
	871	PN1 = 3.0E+00 * SQRT ( P ) * ( ( X / P )**( 1.0E+00 / 3.0E+00 ) &
	872	+ 1.0E+00 / ( 9.0E+00 * P ) - 1.0E+00 )
	873
	874	GAMMAINC = 0.5E+00 * ( 1. + ERF ( PN1 ) )
	875	RETURN
	876
	877	END IF
	878	!
	879	! IF X IS LARGE SET GAMMAD = 1.
	880	!
	881	IF ( XBIG < X ) THEN
	882	GAMMAINC = 1.0E+00
	883	RETURN
	884	END IF
	885	!
	886	! USE PEARSON'S SERIES EXPANSION.
	887	! (NOTE THAT P IS NOT LARGE ENOUGH TO FORCE OVERFLOW IN ALOGAM).
	888	!
	889	IF ( X <= 1.0E+00 .OR. X < P ) THEN
	890
	891	ARG = P * LOG ( X ) - X - LOG_GAMMA ( P + 1.0E+00 )
	892	C = 1.0E+00
	893	GAMMAINC = 1.0E+00
	894	A = P
	895
	896	DO
	897
	898	A = A + 1.0E+00
	899	C = C * X / A
	900	GAMMAINC = GAMMAINC + C
	901
	902	IF ( C <= TOL ) THEN
	903	EXIT
	904	END IF
	905
	906	END DO
	907
	908	ARG = ARG + LOG ( GAMMAINC )
	909
	910	IF ( ELIMIT <= ARG ) THEN
	911	GAMMAINC = EXP ( ARG )
	912	ELSE
	913	GAMMAINC = 0.0E+00
	914	END IF
	915	!
	916	! USE A CONTINUED FRACTION EXPANSION.
	917	!
	918	ELSE
	919
	920	ARG = P * LOG ( X ) - X - LOG_GAMMA ( P )
	921	A = 1.0E+00 - P
	922	B = A + X + 1.0E+00
	923	C = 0.0E+00
	924	PN1 = 1.0E+00
	925	PN2 = X
	926	PN3 = X + 1.0E+00
	927	PN4 = X * B
	928	GAMMAINC = PN3 / PN4
	929
	930	DO
	931
	932	A = A + 1.0E+00
	933	B = B + 2.0E+00
	934	C = C + 1.0E+00
	935	AN = A * C
	936	PN5 = B * PN3 - AN * PN1
	937	PN6 = B * PN4 - AN * PN2
	938
	939	IF ( PN6 /= 0.0E+00 ) THEN
	940
	941	RN = PN5 / PN6
	942
	943	IF ( ABS ( GAMMAINC - RN ) <= MIN ( TOL, TOL * RN ) ) THEN
	944	EXIT
	945	END IF
	946
	947	GAMMAINC = RN
	948
	949	END IF
	950
	951	PN1 = PN3
	952	PN2 = PN4
	953	PN3 = PN5
	954	PN4 = PN6
	955	!
	956	! RE-SCALE TERMS IN CONTINUED FRACTION IF TERMS ARE LARGE.
	957	!
	958	IF ( OFLO <= ABS ( PN5 ) ) THEN
	959	PN1 = PN1 / OFLO
	960	PN2 = PN2 / OFLO
	961	PN3 = PN3 / OFLO
	962	PN4 = PN4 / OFLO
	963	END IF
	964
	965	END DO
	966
	967	ARG = ARG + LOG ( GAMMAINC )
	968
	969	IF ( ELIMIT <= ARG ) THEN
	970	GAMMAINC = 1.0E+00 - EXP ( ARG )
	971	ELSE
	972	GAMMAINC = 1.0E+00
	973	END IF
	974
	975	END IF
	976
	977	RETURN
	978	END FUNCTION GAMMAINC
	979	!++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
	980
[4665]	981	END MODULE lmdz_lscp_tools
[3999]	982
	983

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