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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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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 or 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, pticefracturb, temp, pplay, paprsdn, paprsup, wvel, qice_ini, snowcld, snowfracld, qtot_incl, cldfra, tke, &
244	tke_dissip, sursat_e, invtau_e, 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	! E.Vignon (03/2025) : additional elements for treatment of convective
250	! boundary layer clouds
251	!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
252
253
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
257	USE lmdz_lscp_ini, ONLY : naero5, gamma_snwretro, gamma_taud, capa_crystal, rho_ice
258	USE lmdz_lscp_ini, ONLY : eps, snow_fallspeed
259
260	IMPLICIT NONE
261
262	INTEGER, INTENT(IN) :: klon !--number of horizontal grid points
263	REAL, INTENT(IN) :: dtime !--time step [s]
264	LOGICAL, INTENT(IN), DIMENSION(klon) :: pticefracturb !--grid points concerned by this routine
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]
269	REAL, INTENT(IN), DIMENSION(klon) :: wvel !--vertical velocity [m/s]
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]
274
275	REAL, INTENT(IN), DIMENSION(klon) :: qice_ini !--initial specific ice content gridbox-mean [kg/kg]
276	REAL, INTENT(IN), DIMENSION(klon) :: snowcld !--in-cloud snowfall flux [kg/m2/s]
277	REAL, INTENT(IN), DIMENSION(klon) :: snowfracld !--cloudy precip fraction [-]
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]
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]
283
284	REAL, INTENT(INOUT), DIMENSION(klon) :: icefrac !--fraction of ice in condensed water [-]
285	REAL, INTENT(INOUT), DIMENSION(klon) :: dicefracdT
286
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 [-]
290
291	REAL, DIMENSION(klon) :: qzero, qsatl, dqsatl, qsati, dqsati !--specific humidity saturation values
292	INTEGER :: i
293
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 [-]
298	REAL :: tau_dissipturb
299	REAL :: invtau_phaserelax
300	REAL :: sigma2_pdf
301	REAL :: ai, bi, B0
302	REAL :: sursat_iceliq
303	REAL :: sursat_equ
304	REAL :: liqfra_max
305	REAL :: sursat_iceext
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
309
310	REAL :: cldfra1D
311	REAL :: rho_air
312	REAL :: psati !--saturation vapor pressure wrt ice [Pa]
313
314
315	REAL :: tempvig1, tempvig2
316
317	tempvig1 = -21.06 + RTT
318	tempvig2 = -30.35 + RTT
319	C0 = 10. !--value assumed in Field2014
320	sursat_iceext = -0.1
321	qzero(:) = 0.
322	cldfraliq(:) = 0.
323	qliq(:) = 0.
324	qice(:) = 0.
325	qvap_cld(:) = 0.
326	sigma2_icefracturb(:) = 0.
327	mean_icefracturb(:) = 0.
328
329	!--wrt liquid
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
336	rho_air = pplay(i) / temp(i) / RD
337	! because cldfra is intent in, but can be locally modified due to test
338	cldfra1D = cldfra(i)
339	! activate param for concerned grid points and for cloudy conditions
340	IF ((pticefracturb(i)) .AND. (cldfra(i) .GT. 0.)) THEN
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
363
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
372	ELSE
373
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
383
384	!--1. No preexisting ice and no mixing with environment: if vertical motion, fully liquid
385	!--cloud else fully iced cloud
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
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
402
403
404	!--2. Pre-existing ice and/or mixing with environment:computation of ice properties for
405	!--feedback
406	ELSE
407
408	sursat_iceliq = qsatl(i)/qsati(i) - 1.
409	psati = qsati(i) * pplay(i) / (RD/RV)
410
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
414	!--which is for naero5>0 a function of temperature (DeMott 2010)
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
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.)
437	N0_PSD = nb_crystals * lambda_PSD
438	moment1_PSD = N0_PSD/lambda_PSD**2
439
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 )
450	invtau_phaserelax = bi * B0 * moment1_PSD
451
452	ai = RG / RD / temp(i) * ( RD * RLSTT / RCPD / RV / temp(i) - 1. )
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
456
457	!--2A. No TKE : stationnary binary solution depending on vertical velocity and mixing with env.
458	! If Sequ > Siw liquid cloud, else ice cloud
459	IF ( tke_dissip(i) .LE. eps ) THEN
460	sigma2_icefracturb(i)= 0.
461	mean_icefracturb(i) = sursat_equ
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
488
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
496
497	liqfra_max = MAX(0., (MIN (1.,( qtot_incl(i) - (qice_ini(i) / cldfra1D) - qsati(i) * (1 + sursat_iceext ) ) / ( qsatl(i) - qsati(i) ) ) ) )
498	sigma2_pdf = 1./2. * ( ai*2 ) 2./3. * tke(i) * tau_dissipturb / (invtau_phaserelax + invtau_e(i))
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) ) ) )
501	IF (cldfraliq(i) .GT. liqfra_max) THEN
502	cldfraliq(i) = liqfra_max
503	ENDIF
504
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 )
507
508	sigma2_icefracturb(i)= sigma2_pdf
509	mean_icefracturb(i) = sursat_equ
510
511	!------------ SPECIFIC VAPOR CONTENT AND WATER CONSERVATION ------------
512
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.
522
523	qvap_incl = MAX(qsati(i), ( 1. - cldfraliq(i) ) * (sursat_iceext + 1.) * qsati(i) + cldfraliq(i) * qsatl(i) )
524
525	IF ( qvap_incl .GE. qtot_incl(i) ) THEN
526	qvap_incl = qsati(i)
527	qliq_incl = MAX(0.0,qtot_incl(i) - qvap_incl)
528	qice_incl = 0.
529
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
536
537	qvap_cld(i) = qvap_incl * cldfra1D
538	qliq(i) = qliq_incl * cldfra1D
539	qice(i) = qice_incl * cldfra1D
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
545	dicefracdT(i) = 0.
546
547	END IF ! Enough TKE
548
549	END IF ! End qini
550
551	END IF ! ! MPC temperature
552
553	END IF ! pticefracturb and cldfra
554
555	ENDDO ! klon
556	END SUBROUTINE ICEFRAC_LSCP_TURB
557	!
558	!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
559
560
561	SUBROUTINE CALC_QSAT_ECMWF(klon,temp,qtot,pressure,tref,phase,flagth,qs,dqs)
562	!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
563	! Calculate qsat following ECMWF method
564	!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
565
566
567	USE yoethf_mod_h
568	USE yomcst_mod_h
569	IMPLICIT NONE
570
571
572	include "FCTTRE.h"
573
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
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
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
587
588	REAL delta, cor, cvm5
589	INTEGER i
590
591	DO i=1,klon
592
593	IF (phase .EQ. 1) THEN
594	delta=0.
595	ELSEIF (phase .EQ. 2) THEN
596	delta=1.
597	ELSE
598	delta=MAX(0.,SIGN(1.,tref-temp(i)))
599	ENDIF
600
601	IF (flagth) THEN
602	cvm5=R5LES(1.-delta) + R5IESdelta
603	ELSE
604	cvm5 = R5LESRLVTT(1.-delta) + R5IESRLSTTdelta
605	cvm5 = cvm5 /RCPD/(1.0+RVTMP2*(qtot(i)))
606	ENDIF
607
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)
613
614	END DO
615
616	END SUBROUTINE CALC_QSAT_ECMWF
617	!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
618
619
620	!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
621	SUBROUTINE CALC_GAMMASAT(klon,temp,qtot,pressure,gammasat,dgammasatdt)
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
630	use lmdz_lscp_ini, only: iflag_gammasat, temp_nowater, RTT
631	use lmdz_lscp_ini, only: a_homofreez, b_homofreez, delta_hetfreez
632
633	IMPLICIT NONE
634
635
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
639
640	REAL, INTENT(IN), DIMENSION(klon) :: pressure ! pressure in Pa
641
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
644
645	REAL, DIMENSION(klon) :: qsi,qsl,dqsl,dqsi
646	REAL f_homofreez, fac
647
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)
652
653	DO i = 1, klon
654
655	IF ( temp(i) .GE. RTT ) THEN
656	! warm clouds: condensation at saturation wrt liquid
657	gammasat(i) = 1.
658	dgammasatdt(i) = 0.
659
660	ELSE
661	! cold clouds: qsi > qsl
662
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
681
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
700
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
712	ELSE
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.
717
718	ENDIF
719
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
727	ENDIF
728
729	END DO
730
731
732	END SUBROUTINE CALC_GAMMASAT
733	!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
734
735
736	!++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
737	SUBROUTINE DISTANCE_TO_CLOUD_TOP(klon,klev,k,temp,pplay,paprs,rneb,distcltop1D,temp_cltop)
738	!++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
739
740	USE lmdz_lscp_ini, ONLY : rd,rg,tresh_cl
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
752	REAL, INTENT(OUT), DIMENSION(klon) :: temp_cltop ! temperature of cloud top
753
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
778	k_top = k
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
799	temp_cltop(i) = temp(i,k_top)
800	ENDDO ! klon
801
802	END SUBROUTINE DISTANCE_TO_CLOUD_TOP
803	!++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
804
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
981	END MODULE lmdz_lscp_tools
982
983

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