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lmdz_lscp_tools.f90 @ 5441

Last change on this file since 5441 was 5383, checked in by evignon, 2 weeks ago
update de la paramétrisation de phase des nuages de Lea et nettoyage associé
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1	MODULE lmdz_lscp_tools
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
18	use lmdz_lscp_ini, only: iflag_vice, ffallv_con, ffallv_lsc
19	use lmdz_lscp_ini, only: cice_velo, dice_velo
20
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
34	REAL logvm,iwcg,tempc,phpa,fallv_tun
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
48	iwcg=MAX(iwc(i)*1000.,1E-3) ! iwc in g/m3. We set a minimum value to prevent from division by 0
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
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)
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
96	velo(i) = fallv_tuncice_velo((iwcg/1000.)**dice_velo)
97	ENDIF
98	ENDDO
99
100	END SUBROUTINE FALLICE_VELOCITY
101	!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
102
103	!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
104	SUBROUTINE ICEFRAC_LSCP(klon, temp, iflag_ice_thermo, distcltop, temp_cltop, icefrac, dicefracdT)
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
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
117
118	IMPLICIT NONE
119
120
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
125	INTEGER, INTENT(IN) :: iflag_ice_thermo
126	REAL, INTENT(OUT), DIMENSION(klon) :: icefrac
127	REAL, INTENT(OUT), DIMENSION(klon) :: dicefracdT
128
129
130	INTEGER i
131	REAL liqfrac_tmp, dicefrac_tmp
132	REAL Dv, denomdep,beta,qsi,dqsidt
133	LOGICAL ice_thermo
134
135	CHARACTER (len = 20) :: modname = 'lscp_tools'
136	CHARACTER (len = 80) :: abort_message
137
138	IF ((iflag_t_glace.LT.2)) THEN !.OR. (iflag_t_glace.GT.6)) THEN
139	abort_message = 'lscp cannot be used if iflag_t_glace<2 or >6'
140	CALL abort_physic(modname,abort_message,1)
141	ENDIF
142
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
147
148
149	DO i=1,klon
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)
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
165	ENDIF
166
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
179
180	! for iflag_t_glace .GE. 4, the liquid fraction depends upon temperature at cloud top
181	! and then decreases with decreasing height
182
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
196	IF ((iflag_t_glace .EQ. 5) .OR. (iflag_t_glace .EQ. 7)) THEN
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
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
234
235
236	ENDDO ! klon
237	RETURN
238
239	END SUBROUTINE ICEFRAC_LSCP
240	!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
241
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)
245	!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
246	! Compute the liquid, ice and vapour content (+ice fraction) based
247	! on turbulence (see Fields 2014, Furtado 2016, Raillard 2025)
248	! L.Raillard (23/09/24)
249	!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
250
251
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
255	USE lmdz_lscp_ini, ONLY : naero5, gamma_snwretro, gamma_taud, capa_crystal
256	USE lmdz_lscp_ini, ONLY : eps
257
258	IMPLICIT NONE
259
260	INTEGER, INTENT(IN) :: klon !--number of horizontal grid points
261	REAL, INTENT(IN) :: dtime !--time step [s]
262
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]
272
273	REAL, INTENT(IN), DIMENSION(klon) :: qice_ini !--initial specific ice content gridbox-mean [kg/kg]
274	REAL, INTENT(IN), DIMENSION(klon) :: snowcld
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 [-]
279	REAL, INTENT(OUT), DIMENSION(klon) :: dicefracdT
280
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 [-]
284
285	REAL, DIMENSION(klon) :: qzero, qsatl, dqsatl, qsati, dqsati !--specific humidity saturation values
286	INTEGER :: i
287
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 [-]
292	REAL :: tau_dissipturb
293	REAL :: tau_phaserelax
294	REAL :: sigma2_pdf, mean_pdf
295	REAL :: ai, bi, B0
296	REAL :: sursat_iceliq
297	REAL :: sursat_equ
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 :: rho_air
307	REAL :: psati !--saturation vapor pressure wrt ice [Pa]
308
309	REAL :: vitw !--vertical velocity [m/s]
310
311	C0 = 10. !--value assumed in Field2014
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.
320	mean_icefracturb(:) = 0.
321
322	!--wrt liquid
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
330	rho_air = pplay(i) / temp(i) / RD
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
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
374	ELSE
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
397
398
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
406	sursat_iceliq = qsatl(i)/qsati(i) - 1.
407	psati = qsati(i) * pplay(i) / (RD/RV)
408
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
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
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 )
433	tau_phaserelax = 1. / (bi * B0 * moment1_PSD )
434
435	ai = RG / RD / temp(i) * ( RD * RLSTT / RCPD / RV / temp(i) - 1. )
436
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
466
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
474
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
490
491	!------------ SPECIFIC VAPOR CONTENT AND WATER CONSERVATION ------------
492
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.
502
503	qvap_incl = MAX(qsati(i), ( 1. - cldfraliq(i) ) * (sursat_iceext + 1.) * qsati(i) + cldfraliq(i) * qsatl(i) )
504
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.
509
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
516
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.
522
523	END IF ! Enough TKE
524
525	END IF ! End qini
526
527	END IF ! ! MPC temperature
528
529	END IF ! cldfra
530
531	ENDDO ! klon
532	END SUBROUTINE ICEFRAC_LSCP_TURB
533	!
534	!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
535
536
537	SUBROUTINE CALC_QSAT_ECMWF(klon,temp,qtot,pressure,tref,phase,flagth,qs,dqs)
538	!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
539	! Calculate qsat following ECMWF method
540	!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
541
542
543	USE yoethf_mod_h
544	USE yomcst_mod_h
545	IMPLICIT NONE
546
547
548	include "FCTTRE.h"
549
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
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
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
563
564	REAL delta, cor, cvm5
565	INTEGER i
566
567	DO i=1,klon
568
569	IF (phase .EQ. 1) THEN
570	delta=0.
571	ELSEIF (phase .EQ. 2) THEN
572	delta=1.
573	ELSE
574	delta=MAX(0.,SIGN(1.,tref-temp(i)))
575	ENDIF
576
577	IF (flagth) THEN
578	cvm5=R5LES(1.-delta) + R5IESdelta
579	ELSE
580	cvm5 = R5LESRLVTT(1.-delta) + R5IESRLSTTdelta
581	cvm5 = cvm5 /RCPD/(1.0+RVTMP2*(qtot(i)))
582	ENDIF
583
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)
589
590	END DO
591
592	END SUBROUTINE CALC_QSAT_ECMWF
593	!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
594
595
596	!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
597	SUBROUTINE CALC_GAMMASAT(klon,temp,qtot,pressure,gammasat,dgammasatdt)
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
606	use lmdz_lscp_ini, only: iflag_gammasat, temp_nowater, RTT
607	use lmdz_lscp_ini, only: a_homofreez, b_homofreez, delta_hetfreez
608
609	IMPLICIT NONE
610
611
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
615
616	REAL, INTENT(IN), DIMENSION(klon) :: pressure ! pressure in Pa
617
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
620
621	REAL, DIMENSION(klon) :: qsi,qsl,dqsl,dqsi
622	REAL f_homofreez, fac
623
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)
628
629	DO i = 1, klon
630
631	IF ( temp(i) .GE. RTT ) THEN
632	! warm clouds: condensation at saturation wrt liquid
633	gammasat(i) = 1.
634	dgammasatdt(i) = 0.
635
636	ELSE
637	! cold clouds: qsi > qsl
638
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
657
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
676
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
688	ELSE
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.
693
694	ENDIF
695
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
703	ENDIF
704
705	END DO
706
707
708	END SUBROUTINE CALC_GAMMASAT
709	!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
710
711
712	!++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
713	SUBROUTINE DISTANCE_TO_CLOUD_TOP(klon,klev,k,temp,pplay,paprs,rneb,distcltop1D,temp_cltop)
714	!++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
715
716	USE lmdz_lscp_ini, ONLY : rd,rg,tresh_cl
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
728	REAL, INTENT(OUT), DIMENSION(klon) :: temp_cltop ! temperature of cloud top
729
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
754	k_top = k
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
775	temp_cltop(i) = temp(i,k_top)
776	ENDDO ! klon
777
778	END SUBROUTINE DISTANCE_TO_CLOUD_TOP
779	!++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
780
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
957	END MODULE lmdz_lscp_tools
958
959

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