module_mp_wsm6.F

References to this file elsewhere.
1 #if ( RWORDSIZE == 4 )
2 #  define VREC vsrec
3 #  define VSQRT vssqrt
4 #else
5 #  define VREC vrec
6 #  define VSQRT vsqrt
7 #endif
8 
9 MODULE module_mp_wsm6
10 !
11 !
12    REAL, PARAMETER, PRIVATE :: dtcldcr     = 120.
13    REAL, PARAMETER, PRIVATE :: n0r = 8.e6
14    REAL, PARAMETER, PRIVATE :: n0g = 4.e6
15    REAL, PARAMETER, PRIVATE :: avtr = 841.9
16    REAL, PARAMETER, PRIVATE :: bvtr = 0.8
17    REAL, PARAMETER, PRIVATE :: r0 = .8e-5 ! 8 microm  in contrast to 10 micro m
18    REAL, PARAMETER, PRIVATE :: peaut = .55   ! collection efficiency
19    REAL, PARAMETER, PRIVATE :: xncr = 3.e8   ! maritime cloud in contrast to 3.e8 in tc80
20    REAL, PARAMETER, PRIVATE :: xmyu = 1.718e-5 ! the dynamic viscosity kgm-1s-1
21    REAL, PARAMETER, PRIVATE :: avts = 11.72
22    REAL, PARAMETER, PRIVATE :: bvts = .41
23    REAL, PARAMETER, PRIVATE :: avtg = 330.
24    REAL, PARAMETER, PRIVATE :: bvtg = 0.8
25    REAL, PARAMETER, PRIVATE :: deng = 500.
26    REAL, PARAMETER, PRIVATE :: n0smax =  1.e11 ! t=-90C unlimited
27    REAL, PARAMETER, PRIVATE :: lamdarmax = 8.e4
28    REAL, PARAMETER, PRIVATE :: lamdasmax = 1.e5
29    REAL, PARAMETER, PRIVATE :: lamdagmax = 6.e4
30    REAL, PARAMETER, PRIVATE :: betai = .6
31    REAL, PARAMETER, PRIVATE :: xn0 = 1.e-2
32    REAL, PARAMETER, PRIVATE :: dicon = 11.9
33    REAL, PARAMETER, PRIVATE :: di0 = 12.9e-6
34    REAL, PARAMETER, PRIVATE :: dimax = 500.e-6
35    REAL, PARAMETER, PRIVATE :: n0s = 2.e6             ! temperature dependent n0s
36    REAL, PARAMETER, PRIVATE :: alpha = .12        ! .122 exponen factor for n0s
37    REAL, PARAMETER, PRIVATE :: pfrz1 = 100.
38    REAL, PARAMETER, PRIVATE :: pfrz2 = 0.66
39    REAL, PARAMETER, PRIVATE :: qcrmin = 1.e-9
40    REAL, PARAMETER, PRIVATE :: t40c = 233.16
41    REAL, PARAMETER, PRIVATE :: eacrc = 1.0
42    REAL, PARAMETER, PRIVATE :: dens  =  100.0
43    REAL, PARAMETER, PRIVATE :: qs0   =  6.e-4   ! pgaut
44    REAL, SAVE ::                                     &
45              qc0, qck1,bvtr1,bvtr2,bvtr3,bvtr4,g1pbr,&
46              g3pbr,g4pbr,g5pbro2,pvtr,eacrr,pacrr,   &
47              bvtr6,g6pbr,                            &
48              precr1,precr2,xm0,xmmax,roqimax,bvts1,  &
49              bvts2,bvts3,bvts4,g1pbs,g3pbs,g4pbs,    &
50              g5pbso2,pvts,pacrs,precs1,precs2,pidn0r,&
51              pidn0s,xlv1,pacrc,                      &
52              bvtg1,bvtg2,bvtg3,bvtg4,g1pbg,          &
53              g3pbg,g4pbg,g5pbgo2,pvtg,pacrg,         &
54              precg1,precg2,pidn0g,                   &
55              rslopermax,rslopesmax,rslopegmax,       &
56              rsloperbmax,rslopesbmax,rslopegbmax,    &
57              rsloper2max,rslopes2max,rslopeg2max,    &
58              rsloper3max,rslopes3max,rslopeg3max
59 CONTAINS
60 !===================================================================
61 !
62   SUBROUTINE wsm6(th, q, qc, qr, qi, qs, qg                        &
63                  ,den, pii, p, delz                                &
64                  ,delt,g, cpd, cpv, rd, rv, t0c                    &
65                  ,ep1, ep2, qmin                                   &
66                  ,XLS, XLV0, XLF0, den0, denr                      &
67                  ,cliq,cice,psat                                   &
68                  ,rain, rainncv                                    &
69                  ,snow, snowncv                                    &
70                  ,graupel, graupelncv                              &
71                  ,sr                                               &
72                  ,ids,ide, jds,jde, kds,kde                        &
73                  ,ims,ime, jms,jme, kms,kme                        &
74                  ,its,ite, jts,jte, kts,kte                        &
75                                                                    )
76 !-------------------------------------------------------------------
77   IMPLICIT NONE
78 !-------------------------------------------------------------------
79 !
80 !  This code is a 6-class GRAUPEL phase microphyiscs scheme (WSM6) of the WRF
81 !  Single-Moment MicroPhyiscs (WSMMP). The WSMMP assumes that ice nuclei
82 !  number concentration is a function of temperature, and seperate assumption
83 !  is developed, in which ice crystal number concentration is a function
84 !  of ice amount. A theoretical background of the ice-microphysics and related
85 !  processes in the WSMMPs are described in Hong et al. (2004).
86 !  All production terms in the WSM6 scheme are described in Hong and Lim (2006).
87 !  All units are in m.k.s. and source/sink terms in kgkg-1s-1.
88 !
89 !  WSM6 cloud scheme
90 !
91 !  Coded by Song-You Hong and Jeong-Ock Jade Lim (Yonsei Univ.)
92 !           Summer 2003
93 !
94 !  Implemented by Song-You Hong (Yonsei Univ.) and Jimy Dudhia (NCAR)
95 !           Summer 2004
96 !
97 !  Reference) Hong, Dudhia, Chen (HDC, 2004) Mon. Wea. Rev. 
98 !             Hong and Lim (HL, 2006) J. Korean Meteor. Soc. 
99 !             Lin, Farley, Orville (LFO, 1983) J. Appl. Meteor.
100 !             Rutledge, Hobbs (RH83, 1983) J. Atmos. Sci.
101 !             Rutledge, Hobbs (RH84, 1984) J. Atmos. Sci.
102 !
103   INTEGER,      INTENT(IN   )    ::   ids,ide, jds,jde, kds,kde , &
104                                       ims,ime, jms,jme, kms,kme , &
105                                       its,ite, jts,jte, kts,kte
106   REAL, DIMENSION( ims:ime , kms:kme , jms:jme ),                 &
107         INTENT(INOUT) ::                                          &
108                                                              th,  &
109                                                               q,  &
110                                                               qc, &
111                                                               qi, &
112                                                               qr, &
113                                                               qs, &
114                                                               qg
115   REAL, DIMENSION( ims:ime , kms:kme , jms:jme ),                 &
116         INTENT(IN   ) ::                                          &
117                                                              den, &
118                                                              pii, &
119                                                                p, &
120                                                             delz
121   REAL, INTENT(IN   ) ::                                    delt, &
122                                                                g, &
123                                                               rd, &
124                                                               rv, &
125                                                              t0c, &
126                                                             den0, &
127                                                              cpd, &
128                                                              cpv, &
129                                                              ep1, &
130                                                              ep2, &
131                                                             qmin, &
132                                                              XLS, &
133                                                             XLV0, &
134                                                             XLF0, &
135                                                             cliq, &
136                                                             cice, &
137                                                             psat, &
138                                                             denr
139   REAL, DIMENSION( ims:ime , jms:jme ),                           &
140         INTENT(INOUT) ::                                    rain, &
141                                                          rainncv, &
142                                                               sr
143 
144   REAL, DIMENSION( ims:ime , jms:jme ), OPTIONAL,                &
145         INTENT(INOUT) ::                                    snow, &
146                                                          snowncv
147 
148   REAL, DIMENSION( ims:ime , jms:jme ), OPTIONAL,                &
149         INTENT(INOUT) ::                                graupel, &
150                                                         graupelncv
151 ! LOCAL VAR
152   REAL, DIMENSION( its:ite , kts:kte ) ::   t
153   REAL, DIMENSION( its:ite , kts:kte, 2 ) ::   qci
154   REAL, DIMENSION( its:ite , kts:kte, 3 ) ::   qrs
155   INTEGER ::               i,j,k
156 !-------------------------------------------------------------------
157       DO j=jts,jte
158          DO k=kts,kte
159          DO i=its,ite
160             t(i,k)=th(i,k,j)*pii(i,k,j)
161             qci(i,k,1) = qc(i,k,j)
162             qci(i,k,2) = qi(i,k,j)
163             qrs(i,k,1) = qr(i,k,j)
164             qrs(i,k,2) = qs(i,k,j)
165             qrs(i,k,3) = qg(i,k,j)
166          ENDDO
167          ENDDO
168          CALL wsm62D(t, q(ims,kms,j), qci, qrs                     &
169                     ,den(ims,kms,j)                                &
170                     ,p(ims,kms,j), delz(ims,kms,j)                 &
171                     ,delt,g, cpd, cpv, rd, rv, t0c                 &
172                     ,ep1, ep2, qmin                                &
173                     ,XLS, XLV0, XLF0, den0, denr                   &
174                     ,cliq,cice,psat                                &
175                     ,j                                             &
176                     ,rain(ims,j),rainncv(ims,j)                    &
177                     ,sr(ims,j)                                     &
178                     ,ids,ide, jds,jde, kds,kde                     &
179                     ,ims,ime, jms,jme, kms,kme                     &
180                     ,its,ite, jts,jte, kts,kte                     &
181                     ,snow(ims,j),snowncv(ims,j)                    &
182                     ,graupel(ims,j),graupelncv(ims,j)              &
183                                                                    )
184          DO K=kts,kte
185          DO I=its,ite
186             th(i,k,j)=t(i,k)/pii(i,k,j)
187             qc(i,k,j) = qci(i,k,1)
188             qi(i,k,j) = qci(i,k,2)
189             qr(i,k,j) = qrs(i,k,1)
190             qs(i,k,j) = qrs(i,k,2)
191             qg(i,k,j) = qrs(i,k,3)
192          ENDDO
193          ENDDO
194       ENDDO
195   END SUBROUTINE wsm6
196 !===================================================================
197 !
198   SUBROUTINE wsm62D(t, q, qci, qrs, den, p, delz                  &
199                    ,delt,g, cpd, cpv, rd, rv, t0c                 &
200                    ,ep1, ep2, qmin                                &
201                    ,XLS, XLV0, XLF0, den0, denr                   &
202                    ,cliq,cice,psat                                &
203                    ,lat                                           &
204                    ,rain,rainncv                                  &
205                    ,sr                                            &
206                    ,ids,ide, jds,jde, kds,kde                     &
207                    ,ims,ime, jms,jme, kms,kme                     &
208                    ,its,ite, jts,jte, kts,kte                     &
209                    ,snow,snowncv                                  &
210                    ,graupel,graupelncv                            &
211                                                                   )
212 !-------------------------------------------------------------------
213   IMPLICIT NONE
214 !-------------------------------------------------------------------
215   INTEGER,      INTENT(IN   )    ::   ids,ide, jds,jde, kds,kde , &
216                                       ims,ime, jms,jme, kms,kme , &
217                                       its,ite, jts,jte, kts,kte,  &
218                                       lat
219   REAL, DIMENSION( its:ite , kts:kte ),                           &
220         INTENT(INOUT) ::                                          &
221                                                                t
222   REAL, DIMENSION( its:ite , kts:kte, 2 ),                        &
223         INTENT(INOUT) ::                                          &
224                                                              qci
225   REAL, DIMENSION( its:ite , kts:kte, 3 ),                        &
226         INTENT(INOUT) ::                                          &
227                                                              qrs
228   REAL, DIMENSION( ims:ime , kms:kme ),                           &
229         INTENT(INOUT) ::                                          &
230                                                                q
231   REAL, DIMENSION( ims:ime , kms:kme ),                           &
232         INTENT(IN   ) ::                                          &
233                                                              den, &
234                                                                p, &
235                                                             delz
236   REAL, INTENT(IN   ) ::                                    delt, &
237                                                                g, &
238                                                              cpd, &
239                                                              cpv, &
240                                                              t0c, &
241                                                             den0, &
242                                                               rd, &
243                                                               rv, &
244                                                              ep1, &
245                                                              ep2, &
246                                                             qmin, &
247                                                              XLS, &
248                                                             XLV0, &
249                                                             XLF0, &
250                                                             cliq, &
251                                                             cice, &
252                                                             psat, &
253                                                             denr
254   REAL, DIMENSION( ims:ime ),                                     &
255         INTENT(INOUT) ::                                    rain, &
256                                                          rainncv, &
257                                                               sr
258   REAL, DIMENSION( ims:ime ),     OPTIONAL,                       &
259         INTENT(INOUT) ::                                    snow, &
260                                                          snowncv
261 
262   REAL, DIMENSION( ims:ime ),     OPTIONAL,                       &
263         INTENT(INOUT) ::                                 graupel, &
264                                                       graupelncv
265 ! LOCAL VAR
266   REAL, DIMENSION( its:ite , kts:kte , 3) ::                      &
267         rh, qs, rslope, rslope2, rslope3, rslopeb,                &
268         falk, fall, work1
269   REAL, DIMENSION( its:ite , kts:kte , 1) ::                      &
270         worka
271   REAL, DIMENSION( its:ite , kts:kte ) ::                         &
272               falkc, work1c, work2c, fallc
273   REAL, DIMENSION( its:ite , kts:kte ) ::                          &
274         prevp, psdep, pgdep, praut, psaut, pgaut,                 &
275         pracw, psacw, pgacw, pgacr, pgacs, psaci, pgmlt, praci,   &
276         piacr, pracs, psacr, pgaci, pseml, pgeml      
277   REAL, DIMENSION( its:ite , kts:kte) :: qsum
278   REAL, DIMENSION( its:ite , kts:kte ) :: paacw
279   REAL, DIMENSION( its:ite , kts:kte ) ::                         &
280         pigen, pidep, pcond, xl, cpm, work2, psmlt, psevp, denfac,     &
281         xni, pgevp,n0sfac
282 ! variables for optimization
283   REAL, DIMENSION( its:ite )           :: tvec1
284   REAL :: temp
285   INTEGER, DIMENSION( its:ite ) :: mstep, numdt
286   LOGICAL, DIMENSION( its:ite ) :: flgcld
287   REAL  ::  pi,                                                   &
288             cpmcal, xlcal, lamdar, lamdas, lamdag, diffus,        &
289             viscos, xka, venfac, conden, diffac,                  &
290             x, y, z, a, b, c, d, e,                               &
291             qdt, holdrr, holdrs, holdrg, supcol, pvt,             &
292             coeres, supsat, dtcld, xmi, eacrs, satdt,             &
293             qimax, diameter, xni0, roqi0,                         &
294             fallsum, fallsum_qsi, fallsum_qg,                     &
295             vt2i,vt2r,vt2s,vt2g,acrfac,egs,egi,     &
296             xlwork2, factor, source, value,              &
297             xlf, pfrzdtc, pfrzdtr, supice, alpha2, delta2, delta3  
298   REAL  :: vt2ave
299   REAL  :: holdc, holdci
300   INTEGER :: i, j, k, mstepmax,                                   &
301             iprt, latd, lond, loop, loops, ifsat, n
302 ! Temporaries used for inlining fpvs function
303   REAL  :: dldti, xb, xai, tr, xbi, xa, hvap, cvap, hsub, dldt, ttp
304 !
305 !=================================================================
306 !   compute internal functions
307 !
308       cpmcal(x) = cpd*(1.-max(x,qmin))+max(x,qmin)*cpv
309       xlcal(x) = xlv0-xlv1*(x-t0c)
310 !----------------------------------------------------------------
311 !     size distributions: (x=mixing ratio, y=air density):
312 !     valid for mixing ratio > 1.e-9 kg/kg.
313 !
314 ! Optimizatin : A**B => exp(log(A)*(B)) 
315       lamdar(x,y)=   sqrt(sqrt(pidn0r/(x*y)))      ! (pidn0r/(x*y))**.25
316       lamdas(x,y,z)= sqrt(sqrt(pidn0s*z/(x*y)))    ! (pidn0s*z/(x*y))**.25
317       lamdag(x,y)=   sqrt(sqrt(pidn0g/(x*y)))      ! (pidn0g/(x*y))**.25
318 !
319 !----------------------------------------------------------------
320 !     diffus: diffusion coefficient of the water vapor
321 !     viscos: kinematic viscosity(m2s-1)
322 !
323       diffus(x,y) = 8.794e-5 * exp(log(x)*(1.81)) / y        ! 8.794e-5*x**1.81/y
324       viscos(x,y) = 1.496e-6 * (x*sqrt(x)) /(x+120.)/y  ! 1.496e-6*x**1.5/(x+120.)/y
325       xka(x,y) = 1.414e3*viscos(x,y)*y
326       diffac(a,b,c,d,e) = d*a*a/(xka(c,d)*rv*c*c)+1./(e*diffus(c,b))
327       venfac(a,b,c) = exp(log((viscos(b,c)/diffus(b,a)))*((.3333333)))    &
328                      /sqrt(viscos(b,c))*sqrt(sqrt(den0/c))
329       conden(a,b,c,d,e) = (max(b,qmin)-c)/(1.+d*d/(rv*e)*c/(a*a))
330 !
331       pi = 4. * atan(1.)
332 !
333 !
334 !----------------------------------------------------------------
335 !     paddint 0 for negative values generated by dynamics
336 !
337       do k = kts, kte
338         do i = its, ite
339           qci(i,k,1) = max(qci(i,k,1),0.0)
340           qrs(i,k,1) = max(qrs(i,k,1),0.0)
341           qci(i,k,2) = max(qci(i,k,2),0.0)
342           qrs(i,k,2) = max(qrs(i,k,2),0.0)
343           qrs(i,k,3) = max(qrs(i,k,3),0.0)
344         enddo
345       enddo
346 !
347 !----------------------------------------------------------------
348 !     latent heat for phase changes and heat capacity. neglect the
349 !     changes during microphysical process calculation
350 !     emanuel(1994)
351 !
352       do k = kts, kte
353         do i = its, ite
354           cpm(i,k) = cpmcal(q(i,k))
355           xl(i,k) = xlcal(t(i,k))
356         enddo
357       enddo
358 !
359 !----------------------------------------------------------------
360 !     compute the minor time steps.
361 !
362       loops = max(nint(delt/dtcldcr),1)
363       dtcld = delt/loops
364       if(delt.le.dtcldcr) dtcld = delt
365 !
366       do loop = 1,loops
367 !
368 !----------------------------------------------------------------
369 !     initialize the large scale variables
370 !
371       do i = its, ite
372         mstep(i) = 1
373         flgcld(i) = .true.
374       enddo
375 !
376 !     do k = kts, kte
377 !       do i = its, ite
378 !         denfac(i,k) = sqrt(den0/den(i,k))
379 !       enddo
380 !     enddo
381       do k = kts, kte
382         CALL VREC( tvec1(its), den(its,k), ite-its+1)
383         do i = its, ite
384           tvec1(i) = tvec1(i)*den0
385         enddo
386         CALL VSQRT( denfac(its,k), tvec1(its), ite-its+1)
387       enddo
388 !
389 ! Inline expansion for fpvs
390 !         qs(i,k,1) = fpvs(t(i,k),0,rd,rv,cpv,cliq,cice,xlv0,xls,psat,t0c)
391 !         qs(i,k,2) = fpvs(t(i,k),1,rd,rv,cpv,cliq,cice,xlv0,xls,psat,t0c)
392       hsub = xls
393       hvap = xlv0
394       cvap = cpv
395       ttp=t0c+0.01
396       dldt=cvap-cliq
397       xa=-dldt/rv
398       xb=xa+hvap/(rv*ttp)
399       dldti=cvap-cice
400       xai=-dldti/rv
401       xbi=xai+hsub/(rv*ttp)
402       do k = kts, kte
403         do i = its, ite
404           tr=ttp/t(i,k)
405           qs(i,k,1)=psat*exp(log(tr)*(xa))*exp(xb*(1.-tr))
406           qs(i,k,1) = ep2 * qs(i,k,1) / (p(i,k) - qs(i,k,1))
407           qs(i,k,1) = max(qs(i,k,1),qmin)
408           rh(i,k,1) = max(q(i,k) / qs(i,k,1),qmin)
409           tr=ttp/t(i,k)
410           if(t(i,k).lt.ttp) then
411             qs(i,k,2)=psat*exp(log(tr)*(xai))*exp(xbi*(1.-tr))
412           else
413             qs(i,k,2)=psat*exp(log(tr)*(xa))*exp(xb*(1.-tr))
414           endif
415           qs(i,k,2) = ep2 * qs(i,k,2) / (p(i,k) - qs(i,k,2))
416           qs(i,k,2) = max(qs(i,k,2),qmin)
417           rh(i,k,2) = max(q(i,k) / qs(i,k,2),qmin)
418         enddo
419       enddo
420 !
421 !----------------------------------------------------------------
422 !     initialize the variables for microphysical physics
423 !
424 !
425       do k = kts, kte
426         do i = its, ite
427           prevp(i,k) = 0.
428           psdep(i,k) = 0.
429           pgdep(i,k) = 0.
430           praut(i,k) = 0.
431           psaut(i,k) = 0.
432           pgaut(i,k) = 0.
433           pracw(i,k) = 0.
434           praci(i,k) = 0.
435           piacr(i,k) = 0.
436           psaci(i,k) = 0.
437           psacw(i,k) = 0.
438           pracs(i,k) = 0.
439           psacr(i,k) = 0.
440           pgacw(i,k) = 0.
441           paacw(i,k) = 0.
442           pgaci(i,k) = 0.
443           pgacr(i,k) = 0.
444           pgacs(i,k) = 0.
445           pigen(i,k) = 0.
446           pidep(i,k) = 0.
447           pcond(i,k) = 0.
448           psmlt(i,k) = 0.
449           pgmlt(i,k) = 0.
450           pseml(i,k) = 0.
451           pgeml(i,k) = 0.
452           psevp(i,k) = 0.
453           pgevp(i,k) = 0.
454           falk(i,k,1) = 0.
455           falk(i,k,2) = 0.
456           falk(i,k,3) = 0.
457           fall(i,k,1) = 0.
458           fall(i,k,2) = 0.
459           fall(i,k,3) = 0.
460           fallc(i,k) = 0.
461           falkc(i,k) = 0.
462           xni(i,k) = 1.e3
463         enddo
464       enddo
465 !
466 !----------------------------------------------------------------
467 !     compute the fallout term:
468 !     first, vertical terminal velosity for minor loops
469 !
470       do k = kts, kte
471         do i = its, ite
472           supcol = t0c-t(i,k)
473 !---------------------------------------------------------------
474 ! n0s: Intercept parameter for snow [m-4] [HDC 6]
475 !---------------------------------------------------------------
476           n0sfac(i,k) = max(min(exp(alpha*supcol),n0smax/n0s),1.)
477           if(qrs(i,k,1).le.qcrmin)then
478             rslope(i,k,1) = rslopermax
479             rslopeb(i,k,1) = rsloperbmax
480             rslope2(i,k,1) = rsloper2max
481             rslope3(i,k,1) = rsloper3max
482           else
483             rslope(i,k,1) = 1./lamdar(qrs(i,k,1),den(i,k))
484             rslopeb(i,k,1) = rslope(i,k,1)**bvtr
485             rslope2(i,k,1) = rslope(i,k,1)*rslope(i,k,1)
486             rslope3(i,k,1) = rslope2(i,k,1)*rslope(i,k,1)
487           endif
488           if(qrs(i,k,2).le.qcrmin)then
489             rslope(i,k,2) = rslopesmax
490             rslopeb(i,k,2) = rslopesbmax
491             rslope2(i,k,2) = rslopes2max
492             rslope3(i,k,2) = rslopes3max
493           else
494             rslope(i,k,2) = 1./lamdas(qrs(i,k,2),den(i,k),n0sfac(i,k))
495             rslopeb(i,k,2) = rslope(i,k,2)**bvts
496             rslope2(i,k,2) = rslope(i,k,2)*rslope(i,k,2)
497             rslope3(i,k,2) = rslope2(i,k,2)*rslope(i,k,2)
498           endif
499           if(qrs(i,k,3).le.qcrmin)then
500             rslope(i,k,3) = rslopegmax
501             rslopeb(i,k,3) = rslopegbmax
502             rslope2(i,k,3) = rslopeg2max
503             rslope3(i,k,3) = rslopeg3max
504           else
505             rslope(i,k,3) = 1./lamdag(qrs(i,k,3),den(i,k))
506             rslopeb(i,k,3) = rslope(i,k,3)**bvtg
507             rslope2(i,k,3) = rslope(i,k,3)*rslope(i,k,3)
508             rslope3(i,k,3) = rslope2(i,k,3)*rslope(i,k,3)
509           endif
510 !-------------------------------------------------------------
511 ! Ni: ice crystal number concentraiton   [HDC 5c]
512 !-------------------------------------------------------------
513 !         xni(i,k) = min(max(5.38e7*(den(i,k)                           &
514 !                   *max(qci(i,k,2),qmin))**0.75,1.e3),1.e6)
515           temp = (den(i,k)*max(qci(i,k,2),qmin))
516           temp = sqrt(sqrt(temp*temp*temp))
517           xni(i,k) = min(max(5.38e7*temp,1.e3),1.e6)
518         enddo
519       enddo
520 !
521       mstepmax = 1
522       numdt = 1
523       do k = kte, kts, -1
524         do i = its, ite
525           work1(i,k,1) = pvtr*rslopeb(i,k,1)*denfac(i,k)/delz(i,k)
526           work1(i,k,2) = pvts*rslopeb(i,k,2)*denfac(i,k)/delz(i,k)
527           work1(i,k,3) = pvtg*rslopeb(i,k,3)*denfac(i,k)/delz(i,k)
528           qsum(i,k) = qrs(i,k,2)+qrs(i,k,3)
529           if(qsum(i,k) .le. 0) then
530           qsum(i,k) = 1.E-15
531           endif
532           worka(i,k,1) = (pvts*rslopeb(i,k,2)*denfac(i,k)*qrs(i,k,2)      &
533                          +pvtg*rslopeb(i,k,3)*denfac(i,k)*qrs(i,k,3))/qsum(i,k)/delz(i,k)     
534           numdt(i) = max(nint(max(work1(i,k,1),worka(i,k,1)) &
535                     *dtcld+.5),1)
536           if(numdt(i).ge.mstep(i)) mstep(i) = numdt(i)
537         enddo
538       enddo
539       do i = its, ite
540         if(mstepmax.le.mstep(i)) mstepmax = mstep(i)
541       enddo
542 !
543       do n = 1, mstepmax
544         k = kte
545         do i = its, ite
546           if(n.le.mstep(i)) then
547               falk(i,k,1) = den(i,k)*qrs(i,k,1)*work1(i,k,1)/mstep(i)
548               falk(i,k,2) = den(i,k)*qrs(i,k,2)*worka(i,k,1)/mstep(i)
549               falk(i,k,3) = den(i,k)*qrs(i,k,3)*worka(i,k,1)/mstep(i)
550               fall(i,k,1) = fall(i,k,1)+falk(i,k,1)
551               fall(i,k,2) = fall(i,k,2)+falk(i,k,2)
552               fall(i,k,3) = fall(i,k,3)+falk(i,k,3)
553               qrs(i,k,1) = max(qrs(i,k,1)-falk(i,k,1)*dtcld/den(i,k),0.)
554               qrs(i,k,2) = max(qrs(i,k,2)-falk(i,k,2)*dtcld/den(i,k),0.)
555               qrs(i,k,3) = max(qrs(i,k,3)-falk(i,k,3)*dtcld/den(i,k),0.)
556             endif
557           enddo
558         do k = kte-1, kts, -1
559           do i = its, ite
560             if(n.le.mstep(i)) then
561               falk(i,k,1) = den(i,k)*qrs(i,k,1)*work1(i,k,1)/mstep(i)
562               falk(i,k,2) = den(i,k)*qrs(i,k,2)*worka(i,k,1)/mstep(i)
563               falk(i,k,3) = den(i,k)*qrs(i,k,3)*worka(i,k,1)/mstep(i)
564               fall(i,k,1) = fall(i,k,1)+falk(i,k,1)
565               fall(i,k,2) = fall(i,k,2)+falk(i,k,2)
566               fall(i,k,3) = fall(i,k,3)+falk(i,k,3)
567               qrs(i,k,1) = max(qrs(i,k,1)-(falk(i,k,1)-falk(i,k+1,1)    &
568                           *delz(i,k+1)/delz(i,k))*dtcld/den(i,k),0.)
569               qrs(i,k,2) = max(qrs(i,k,2)-(falk(i,k,2)-falk(i,k+1,2)    &
570                           *delz(i,k+1)/delz(i,k))*dtcld/den(i,k),0.)
571               qrs(i,k,3) = max(qrs(i,k,3)-(falk(i,k,3)-falk(i,k+1,3)    &
572                           *delz(i,k+1)/delz(i,k))*dtcld/den(i,k),0.)
573             endif
574           enddo
575         enddo
576         do k = kte, kts, -1
577           do i = its, ite
578             if(n.le.mstep(i).and.t(i,k).gt.t0c) then
579 !---------------------------------------------------------------
580 ! psmlt: melting of snow [HL A33] [RH83 A25]
581 !       (T>T0: S->R)
582 !---------------------------------------------------------------
583               xlf = xlf0
584               work2(i,k) = venfac(p(i,k),t(i,k),den(i,k))
585               if(qrs(i,k,2).gt.0.) then
586                 coeres = rslope2(i,k,2)*sqrt(rslope(i,k,2)*rslopeb(i,k,2))
587                 psmlt(i,k) = xka(t(i,k),den(i,k))/xlf*(t0c-t(i,k))*pi/2. &
588                            *n0sfac(i,k)*(precs1*rslope2(i,k,2)          &
589                            +precs2*work2(i,k)*coeres)
590                 psmlt(i,k) = min(max(psmlt(i,k)*dtcld/mstep(i),           &
591                             -qrs(i,k,2)/mstep(i)),0.)
592                 qrs(i,k,2) = qrs(i,k,2) + psmlt(i,k)
593                 qrs(i,k,1) = qrs(i,k,1) - psmlt(i,k)
594                 t(i,k) = t(i,k) + xlf/cpm(i,k)*psmlt(i,k)
595               endif
596 !---------------------------------------------------------------
597 ! pgmlt: melting of graupel [HL A23]  [LFO 47]
598 !       (T>T0: G->R)
599 !---------------------------------------------------------------
600               if(qrs(i,k,3).gt.0.) then
601                 coeres = rslope2(i,k,3)*sqrt(rslope(i,k,3)*rslopeb(i,k,3))
602                 pgmlt(i,k) = xka(t(i,k),den(i,k))/xlf                    &
603                            *(t0c-t(i,k))*(precg1*rslope2(i,k,3)         &
604                            +precg2*work2(i,k)*coeres)
605                 pgmlt(i,k) = min(max(pgmlt(i,k)*dtcld/mstep(i),           &
606                             -qrs(i,k,3)/mstep(i)),0.)
607                 qrs(i,k,3) = qrs(i,k,3) + pgmlt(i,k)
608                 qrs(i,k,1) = qrs(i,k,1) - pgmlt(i,k)
609                 t(i,k) = t(i,k) + xlf/cpm(i,k)*pgmlt(i,k)
610               endif
611             endif
612           enddo
613         enddo
614       enddo
615 !---------------------------------------------------------------
616 ! Vice [ms-1] : fallout of ice crystal [HDC 5a]
617 !---------------------------------------------------------------
618       mstepmax = 1
619       mstep = 1
620       numdt = 1
621       do k = kte, kts, -1
622         do i = its, ite
623           if(qci(i,k,2).le.0.) then
624             work2c(i,k) = 0.
625           else
626             xmi = den(i,k)*qci(i,k,2)/xni(i,k)
627 !           diameter  = min(dicon * sqrt(xmi),dimax)
628             diameter  = max(min(dicon * sqrt(xmi),dimax), 1.e-25)
629             work1c(i,k) = 1.49e4*diameter**1.31
630             work2c(i,k) = work1c(i,k)/delz(i,k)
631           endif
632           numdt(i) = max(nint(work2c(i,k)*dtcld+.5),1)
633           if(numdt(i).ge.mstep(i)) mstep(i) = numdt(i)
634         enddo
635       enddo
636       do i = its, ite
637         if(mstepmax.le.mstep(i)) mstepmax = mstep(i)
638       enddo
639 !
640       do n = 1, mstepmax
641         k = kte
642         do i = its, ite
643           if(n.le.mstep(i)) then
644             falkc(i,k) = den(i,k)*qci(i,k,2)*work2c(i,k)/mstep(i)
645             holdc = falkc(i,k)
646             fallc(i,k) = fallc(i,k)+falkc(i,k)
647             holdci = qci(i,k,2)
648             qci(i,k,2) = max(qci(i,k,2)-falkc(i,k)*dtcld/den(i,k),0.)
649           endif
650         enddo
651         do k = kte-1, kts, -1
652           do i = its, ite
653             if(n.le.mstep(i)) then
654               falkc(i,k) = den(i,k)*qci(i,k,2)*work2c(i,k)/mstep(i)
655               holdc = falkc(i,k)
656               fallc(i,k) = fallc(i,k)+falkc(i,k)
657               holdci = qci(i,k,2)
658               qci(i,k,2) = max(qci(i,k,2)-(falkc(i,k)-falkc(i,k+1)      &
659                           *delz(i,k+1)/delz(i,k))*dtcld/den(i,k),0.)
660             endif
661           enddo
662         enddo
663       enddo
664 !
665 !----------------------------------------------------------------
666 !      rain (unit is mm/sec;kgm-2s-1: /1000*delt ===> m)==> mm for wrf
667 !
668       do i = its, ite
669         fallsum = fall(i,kts,1)+fall(i,kts,2)+fall(i,kts,3)+fallc(i,kts)
670         fallsum_qsi = fall(i,kts,2)+fallc(i,kts)
671         fallsum_qg = fall(i,kts,3)
672         rainncv(i) = 0.
673         if(fallsum.gt.0.) then
674           rainncv(i) = fallsum*delz(i,kts)/denr*dtcld*1000.
675           rain(i) = fallsum*delz(i,kts)/denr*dtcld*1000. + rain(i)
676         endif
677         IF ( PRESENT (snowncv) .AND. PRESENT (snow)) THEN
678         snowncv(i) = 0.
679         if(fallsum_qsi.gt.0.) then
680           snowncv(i) = fallsum_qsi*delz(i,kts)/denr*dtcld*1000.
681           snow(i) = fallsum_qsi*delz(i,kts)/denr*dtcld*1000. + snow(i)
682         endif
683         ENDIF
684         IF ( PRESENT (graupelncv) .AND. PRESENT (graupel)) THEN
685         graupelncv(i) = 0.
686         if(fallsum_qg.gt.0.) then
687           graupelncv(i) = fallsum_qg*delz(i,kts)/denr*dtcld*1000.
688           graupel(i) = fallsum_qg*delz(i,kts)/denr*dtcld*1000. + graupel(i)
689         endif
690         ENDIF
691         sr(i) = 0.
692         if(fallsum.gt.0.)sr(i)=(fallsum_qsi*delz(i,kts)/denr*dtcld*1000. + &
693                                 fallsum_qg*delz(i,kts)/denr*dtcld*1000.)/(rainncv(i)+1.e-12)
694       enddo
695 !
696 !---------------------------------------------------------------
697 ! pimlt: instantaneous melting of cloud ice [HL A47] [RH83 A28]
698 !       (T>T0: I->C)
699 !---------------------------------------------------------------
700       do k = kts, kte
701         do i = its, ite
702           supcol = t0c-t(i,k)
703           xlf = xls-xl(i,k)
704           if(supcol.lt.0.) xlf = xlf0
705           if(supcol.lt.0.and.qci(i,k,2).gt.0.) then
706             qci(i,k,1) = qci(i,k,1) + qci(i,k,2)
707             t(i,k) = t(i,k) - xlf/cpm(i,k)*qci(i,k,2)
708             qci(i,k,2) = 0.
709           endif
710 !---------------------------------------------------------------
711 ! pihmf: homogeneous freezing of cloud water below -40c [HL A45]
712 !        (T<-40C: C->I)
713 !---------------------------------------------------------------
714           if(supcol.gt.40..and.qci(i,k,1).gt.0.) then
715             qci(i,k,2) = qci(i,k,2) + qci(i,k,1)
716             t(i,k) = t(i,k) + xlf/cpm(i,k)*qci(i,k,1)
717             qci(i,k,1) = 0.
718           endif
719 !---------------------------------------------------------------
720 ! pihtf: heterogeneous freezing of cloud water [HL A44]
721 !        (T0>T>-40C: C->I)
722 !---------------------------------------------------------------
723           if(supcol.gt.0..and.qci(i,k,1).gt.qmin) then
724 !           pfrzdtc = min(pfrz1*(exp(pfrz2*supcol)-1.)                  &
725 !              *den(i,k)/denr/xncr*qci(i,k,1)**2*dtcld,qci(i,k,1))
726             pfrzdtc = min(pfrz1*(exp(pfrz2*supcol)-1.)                  &
727             *den(i,k)/denr/xncr*qci(i,k,1)*qci(i,k,1)*dtcld,qci(i,k,1))
728             qci(i,k,2) = qci(i,k,2) + pfrzdtc
729             t(i,k) = t(i,k) + xlf/cpm(i,k)*pfrzdtc
730             qci(i,k,1) = qci(i,k,1)-pfrzdtc
731           endif
732 !---------------------------------------------------------------
733 ! pgfrz: freezing of rain water [HL A20] [LFO 45]
734 !        (T<T0, R->G)
735 !---------------------------------------------------------------
736           if(supcol.gt.0..and.qrs(i,k,1).gt.0.) then
737 !           pfrzdtr = min(20.*pi**2*pfrz1*n0r*denr/den(i,k)             &
738 !                 *(exp(pfrz2*supcol)-1.)*rslope3(i,k,1)**2             &
739 !                 *rslope(i,k,1)*dtcld,qrs(i,k,1))
740             temp = rslope3(i,k,1)
741             temp = temp*temp*rslope(i,k,1)
742             pfrzdtr = min(20.*(pi*pi)*pfrz1*n0r*denr/den(i,k)           &
743                   *(exp(pfrz2*supcol)-1.)*temp*dtcld,                   &
744                   qrs(i,k,1))
745             qrs(i,k,3) = qrs(i,k,3) + pfrzdtr
746             t(i,k) = t(i,k) + xlf/cpm(i,k)*pfrzdtr
747             qrs(i,k,1) = qrs(i,k,1)-pfrzdtr
748           endif
749         enddo
750       enddo
751 !
752 !
753 !----------------------------------------------------------------
754 !     rsloper: reverse of the slope parameter of the rain(m)
755 !     xka:    thermal conductivity of air(jm-1s-1k-1)
756 !     work1:  the thermodynamic term in the denominator associated with
757 !             heat conduction and vapor diffusion
758 !             (ry88, y93, h85)
759 !     work2: parameter associated with the ventilation effects(y93)
760 !
761       do k = kts, kte
762         do i = its, ite
763           if(qrs(i,k,1).le.qcrmin)then
764             rslope(i,k,1) = rslopermax
765             rslopeb(i,k,1) = rsloperbmax
766             rslope2(i,k,1) = rsloper2max
767             rslope3(i,k,1) = rsloper3max
768           else
769             rslope(i,k,1) = 1./lamdar(qrs(i,k,1),den(i,k))
770             rslopeb(i,k,1) = rslope(i,k,1)**bvtr
771             rslope2(i,k,1) = rslope(i,k,1)*rslope(i,k,1)
772             rslope3(i,k,1) = rslope2(i,k,1)*rslope(i,k,1)
773           endif
774           if(qrs(i,k,2).le.qcrmin)then
775             rslope(i,k,2) = rslopesmax
776             rslopeb(i,k,2) = rslopesbmax
777             rslope2(i,k,2) = rslopes2max
778             rslope3(i,k,2) = rslopes3max
779           else
780             rslope(i,k,2) = 1./lamdas(qrs(i,k,2),den(i,k),n0sfac(i,k))
781             rslopeb(i,k,2) = rslope(i,k,2)**bvts
782             rslope2(i,k,2) = rslope(i,k,2)*rslope(i,k,2)
783             rslope3(i,k,2) = rslope2(i,k,2)*rslope(i,k,2)
784           endif
785           if(qrs(i,k,3).le.qcrmin)then
786             rslope(i,k,3) = rslopegmax
787             rslopeb(i,k,3) = rslopegbmax
788             rslope2(i,k,3) = rslopeg2max
789             rslope3(i,k,3) = rslopeg3max
790           else
791             rslope(i,k,3) = 1./lamdag(qrs(i,k,3),den(i,k))
792             rslopeb(i,k,3) = rslope(i,k,3)**bvtg
793             rslope2(i,k,3) = rslope(i,k,3)*rslope(i,k,3)
794             rslope3(i,k,3) = rslope2(i,k,3)*rslope(i,k,3)
795           endif
796         enddo
797       enddo
798 !
799       do k = kts, kte
800         do i = its, ite
801           work1(i,k,1) = diffac(xl(i,k),p(i,k),t(i,k),den(i,k),qs(i,k,1))
802           work1(i,k,2) = diffac(xls,p(i,k),t(i,k),den(i,k),qs(i,k,2))
803           work2(i,k) = venfac(p(i,k),t(i,k),den(i,k))
804         enddo
805       enddo
806 !
807 !===============================================================
808 !
809 ! warm rain processes
810 !
811 ! - follows the processes in RH83 and LFO except for autoconcersion
812 !
813 !===============================================================
814 !
815       do k = kts, kte
816         do i = its, ite
817           supsat = max(q(i,k),qmin)-qs(i,k,1)
818           satdt = supsat/dtcld
819 !---------------------------------------------------------------
820 ! praut: auto conversion rate from cloud to rain [HDC 16]
821 !        (C->R)
822 !---------------------------------------------------------------
823           if(qci(i,k,1).gt.qc0) then
824             praut(i,k) = qck1*qci(i,k,1)**(7./3.)
825             praut(i,k) = min(praut(i,k),qci(i,k,1)/dtcld)
826           endif
827 !---------------------------------------------------------------
828 ! pracw: accretion of cloud water by rain [HL A40] [LFO 51]
829 !        (C->R)
830 !---------------------------------------------------------------
831           if(qrs(i,k,1).gt.qcrmin.and.qci(i,k,1).gt.qmin) then
832             pracw(i,k) = min(pacrr*rslope3(i,k,1)*rslopeb(i,k,1)        &
833                         *qci(i,k,1)*denfac(i,k),qci(i,k,1)/dtcld)
834           endif
835 !---------------------------------------------------------------
836 ! prevp: evaporation/condensation rate of rain [HDC 14]
837 !        (V->R or R->V)
838 !---------------------------------------------------------------
839           if(qrs(i,k,1).gt.0.) then
840             coeres = rslope2(i,k,1)*sqrt(rslope(i,k,1)*rslopeb(i,k,1))
841             prevp(i,k) = (rh(i,k,1)-1.)*(precr1*rslope2(i,k,1)         &
842                          +precr2*work2(i,k)*coeres)/work1(i,k,1)
843             if(prevp(i,k).lt.0.) then
844               prevp(i,k) = max(prevp(i,k),-qrs(i,k,1)/dtcld)
845               prevp(i,k) = max(prevp(i,k),satdt/2)
846             else
847               prevp(i,k) = min(prevp(i,k),satdt/2)
848             endif
849           endif
850         enddo
851       enddo
852 !
853 !===============================================================
854 !
855 ! cold rain processes
856 !
857 ! - follows the revised ice microphysics processes in HDC
858 ! - the processes same as in RH83 and RH84  and LFO behave
859 !   following ice crystal hapits defined in HDC, inclduing
860 !   intercept parameter for snow (n0s), ice crystal number
861 !   concentration (ni), ice nuclei number concentration
862 !   (n0i), ice diameter (d)
863 !
864 !===============================================================
865 !
866       do k = kts, kte
867         do i = its, ite
868           supcol = t0c-t(i,k)
869           supsat = max(q(i,k),qmin)-qs(i,k,2)
870           satdt = supsat/dtcld
871           ifsat = 0
872 !-------------------------------------------------------------
873 ! Ni: ice crystal number concentraiton   [HDC 5c]
874 !-------------------------------------------------------------
875 !         xni(i,k) = min(max(5.38e7*(den(i,k)                           &
876 !                      *max(qci(i,k,2),qmin))**0.75,1.e3),1.e6)
877           temp = (den(i,k)*max(qci(i,k,2),qmin))
878           temp = sqrt(sqrt(temp*temp*temp))
879           xni(i,k) = min(max(5.38e7*temp,1.e3),1.e6)
880           eacrs = exp(0.07*(-supcol))
881 !
882           xmi = den(i,k)*qci(i,k,2)/xni(i,k)
883           diameter  = min(dicon * sqrt(xmi),dimax)
884           vt2i = 1.49e4*diameter**1.31
885           vt2r=pvtr*rslopeb(i,k,1)*denfac(i,k)
886           vt2s=pvts*rslopeb(i,k,2)*denfac(i,k)
887           vt2g=pvtg*rslopeb(i,k,3)*denfac(i,k)
888           qsum(i,k) = qrs(i,k,2)+qrs(i,k,3)
889           if(qsum(i,k) .le. 0) then
890           qsum(i,k) = 1.E-15
891           endif
892           vt2ave=(vt2s*qrs(i,k,2)+vt2g*qrs(i,k,3))/(qsum(i,k))
893           if(supcol.gt.0.and.qci(i,k,2).gt.qmin) then
894             if(qrs(i,k,1).gt.qcrmin) then
895 !-------------------------------------------------------------
896 ! praci: Accretion of cloud ice by rain [HL A15] [LFO 25]
897 !        (T<T0: I->R)
898 !-------------------------------------------------------------
899               acrfac = 2.*rslope3(i,k,1)+2.*diameter*rslope2(i,k,1)     &
900                       +diameter**2*rslope(i,k,1)
901               praci(i,k) = pi*qci(i,k,2)*n0r*abs(vt2r-vt2i)*acrfac/4.
902               praci(i,k) = min(praci(i,k),qci(i,k,2)/dtcld)
903 !-------------------------------------------------------------
904 ! piacr: Accretion of rain by cloud ice [HL A19] [LFO 26]
905 !        (T<T0: R->S or R->G)
906 !-------------------------------------------------------------
907               piacr(i,k) = pi**2*avtr*n0r*denr*xni(i,k)*denfac(i,k)     &
908                           *g6pbr*rslope3(i,k,1)*rslope3(i,k,1)          &
909                           *rslopeb(i,k,1)/24./den(i,k)
910               piacr(i,k) = min(piacr(i,k),qrs(i,k,1)/dtcld)
911             endif
912 !-------------------------------------------------------------
913 ! psaci: Accretion of cloud ice by snow [HDC 10]
914 !        (T<T0: I->S)
915 !-------------------------------------------------------------
916             if(qrs(i,k,2).gt.qcrmin) then
917               acrfac = 2.*rslope3(i,k,2)+2.*diameter*rslope2(i,k,2)     &
918                       +diameter**2*rslope(i,k,2)
919               psaci(i,k) = pi*qci(i,k,2)*eacrs*n0s*n0sfac(i,k)          &
920                           *abs(vt2ave-vt2i)*acrfac/4.
921               psaci(i,k) = min(psaci(i,k),qci(i,k,2)/dtcld)
922             endif
923 !-------------------------------------------------------------
924 ! pgaci: Accretion of cloud ice by graupel [HL A17] [LFO 41]
925 !        (T<T0: I->G)
926 !-------------------------------------------------------------
927             if(qrs(i,k,3).gt.qcrmin) then
928               egi = exp(0.07*(-supcol))
929               acrfac = 2.*rslope3(i,k,3)+2.*diameter*rslope2(i,k,3)     &
930                       +diameter**2*rslope(i,k,3)
931               pgaci(i,k) = pi*egi*qci(i,k,2)*n0g*abs(vt2ave-vt2i)*acrfac/4.
932               pgaci(i,k) = min(pgaci(i,k),qci(i,k,2)/dtcld)
933             endif
934           endif
935 !-------------------------------------------------------------
936 ! psacw: Accretion of cloud water by snow  [HL A7] [LFO 24]
937 !        (T<T0: C->S, and T>=T0: C->R)
938 !-------------------------------------------------------------
939           if(qrs(i,k,2).gt.qcrmin.and.qci(i,k,1).gt.qmin) then
940             psacw(i,k) = min(pacrc*n0sfac(i,k)*rslope3(i,k,2)           &
941                         *rslopeb(i,k,2)*qci(i,k,1)*denfac(i,k)          &
942                         ,qci(i,k,1)/dtcld)
943           endif
944 !-------------------------------------------------------------
945 ! pgacw: Accretion of cloud water by graupel [HL A6] [LFO 40]
946 !        (T<T0: C->G, and T>=T0: C->R)
947 !-------------------------------------------------------------
948           if(qrs(i,k,3).gt.qcrmin.and.qci(i,k,1).gt.qmin) then
949             pgacw(i,k) = min(pacrg*rslope3(i,k,3)*rslopeb(i,k,3)        &
950                         *qci(i,k,1)*denfac(i,k),qci(i,k,1)/dtcld)
951           endif
952 !-------------------------------------------------------------
953 ! paacw: Accretion of cloud water by averaged snow/graupel 
954 !        (T<T0: C->G or S, and T>=T0: C->R) 
955 !-------------------------------------------------------------
956           if(qrs(i,k,2).gt.qcrmin.and.qrs(i,k,3).gt.qcrmin) then
957             paacw(i,k) = (qrs(i,k,2)*psacw(i,k)+qrs(i,k,3)*pgacw(i,k))/(qsum(i,k))
958            endif      
959 !-------------------------------------------------------------
960 ! pracs: Accretion of snow by rain [HL A11] [LFO 27]
961 !         (T<T0: S->G)
962 !-------------------------------------------------------------
963           if(qrs(i,k,2).gt.qcrmin.and.qrs(i,k,1).gt.qcrmin) then
964             if(supcol.gt.0) then
965               acrfac = 5.*rslope3(i,k,2)*rslope3(i,k,2)*rslope(i,k,1)   &
966                       +2.*rslope3(i,k,2)*rslope2(i,k,2)*rslope2(i,k,1)  &
967                       +.5*rslope2(i,k,2)*rslope2(i,k,2)*rslope3(i,k,1)
968               pracs(i,k) = pi**2*n0r*n0s*n0sfac(i,k)*abs(vt2r-vt2ave)     &
969                           *(dens/den(i,k))*acrfac
970               pracs(i,k) = min(pracs(i,k),qrs(i,k,2)/dtcld)
971             endif
972 !-------------------------------------------------------------
973 ! psacr: Accretion of rain by snow [HL A10] [LFO 28]
974 !         (T<T0:R->S or R->G) (T>=T0: enhance melting of snow)
975 !-------------------------------------------------------------
976             acrfac = 5.*rslope3(i,k,1)*rslope3(i,k,1)*rslope(i,k,2)     &
977                     +2.*rslope3(i,k,1)*rslope2(i,k,1)*rslope2(i,k,2)    &
978                     +.5*rslope2(i,k,1)*rslope2(i,k,1)*rslope3(i,k,2)
979             psacr(i,k) = pi**2*n0r*n0s*n0sfac(i,k)*abs(vt2ave-vt2r)       &
980                         *(denr/den(i,k))*acrfac
981             psacr(i,k) = min(psacr(i,k),qrs(i,k,1)/dtcld)
982           endif
983 !-------------------------------------------------------------
984 ! pgacr: Accretion of rain by graupel [HL A12] [LFO 42]
985 !         (T<T0: R->G) (T>=T0: enhance melting of graupel)
986 !-------------------------------------------------------------
987           if(qrs(i,k,3).gt.qcrmin.and.qrs(i,k,1).gt.qcrmin) then
988             acrfac = 5.*rslope3(i,k,1)*rslope3(i,k,1)*rslope(i,k,3)     &
989                     +2.*rslope3(i,k,1)*rslope2(i,k,1)*rslope2(i,k,3)    &
990                     +.5*rslope2(i,k,1)*rslope2(i,k,1)*rslope3(i,k,3)
991             pgacr(i,k) = pi**2*n0r*n0g*abs(vt2ave-vt2r)*(denr/den(i,k))   &
992                         *acrfac
993             pgacr(i,k) = min(pgacr(i,k),qrs(i,k,1)/dtcld)
994           endif
995 !
996 !-------------------------------------------------------------
997 ! pgacs: Accretion of snow by graupel [HL A13] [LFO 29]
998 !        (S->G)
999 !-------------------------------------------------------------
1000           if(qrs(i,k,3).gt.qcrmin.and.qrs(i,k,2).gt.qcrmin) then
1001             acrfac = 5.*rslope3(i,k,2)*rslope3(i,k,2)*rslope(i,k,3)     &
1002                     +2.*rslope3(i,k,2)*rslope2(i,k,2)*rslope2(i,k,3)    &
1003                     +.5*rslope2(i,k,2)*rslope2(i,k,2)*rslope3(i,k,3)
1004             if(supcol.gt.0) then
1005               egs = exp(-0.09*supcol)
1006             else
1007               egs = 1.
1008             endif
1009             pgacs(i,k) = pi**2*egs*n0s*n0sfac(i,k)*n0g*abs(vt2ave-vt2ave)   &
1010                         *(dens/den(i,k))*acrfac
1011             pgacs(i,k) = min(pgacs(i,k),qrs(i,k,2)/dtcld)
1012           endif
1013           if(supcol.le.0) then
1014             xlf = xlf0
1015 !-------------------------------------------------------------
1016 ! pseml: Enhanced melting of snow by accretion of water [HL A34]
1017 !        (T>=T0: S->R)
1018 !-------------------------------------------------------------
1019             if(qrs(i,k,2).gt.0.)                                        &
1020               pseml(i,k) = min(max(cliq*supcol*(paacw(i,k)+psacr(i,k))  &
1021                           /xlf,-qrs(i,k,2)/dtcld),0.)
1022 !-------------------------------------------------------------
1023 ! pgeml: Enhanced melting of graupel by accretion of water [HL A24] [RH84 A21-A22]
1024 !        (T>=T0: G->R)
1025 !-------------------------------------------------------------
1026             if(qrs(i,k,3).gt.0.)                                        &
1027               pgeml(i,k) = min(max(cliq*supcol*(paacw(i,k)+pgacr(i,k))  &
1028                           /xlf,-qrs(i,k,3)/dtcld),0.)
1029           endif
1030           if(supcol.gt.0) then
1031 !-------------------------------------------------------------
1032 ! pidep: Deposition/Sublimation rate of ice [HDC 9]
1033 !       (T<T0: V->I or I->V)
1034 !-------------------------------------------------------------
1035             if(qci(i,k,2).gt.0.and.ifsat.ne.1) then
1036               pidep(i,k) = 4.*diameter*xni(i,k)*(rh(i,k,2)-1.)/work1(i,k,2)
1037               supice = satdt-prevp(i,k)
1038               if(pidep(i,k).lt.0.) then
1039                 pidep(i,k) = max(max(pidep(i,k),satdt/2),supice)
1040                 pidep(i,k) = max(pidep(i,k),-qci(i,k,2)/dtcld)
1041               else
1042                 pidep(i,k) = min(min(pidep(i,k),satdt/2),supice)
1043               endif
1044               if(abs(prevp(i,k)+pidep(i,k)).ge.abs(satdt)) ifsat = 1
1045             endif
1046 !-------------------------------------------------------------
1047 ! psdep: deposition/sublimation rate of snow [HDC 14]
1048 !        (T<T0: V->S or S->V)
1049 !-------------------------------------------------------------
1050             if(qrs(i,k,2).gt.0..and.ifsat.ne.1) then
1051               coeres = rslope2(i,k,2)*sqrt(rslope(i,k,2)*rslopeb(i,k,2))
1052               psdep(i,k) = (rh(i,k,2)-1.)*n0sfac(i,k)*(precs1          &
1053                            *rslope2(i,k,2)+precs2*work2(i,k)            &
1054                            *coeres)/work1(i,k,2)
1055               supice = satdt-prevp(i,k)-pidep(i,k)
1056               if(psdep(i,k).lt.0.) then
1057                 psdep(i,k) = max(psdep(i,k),-qrs(i,k,2)/dtcld)
1058                 psdep(i,k) = max(max(psdep(i,k),satdt/2),supice)
1059               else
1060                 psdep(i,k) = min(min(psdep(i,k),satdt/2),supice)
1061               endif
1062               if(abs(prevp(i,k)+pidep(i,k)+psdep(i,k)).ge.abs(satdt))  &
1063                 ifsat = 1
1064             endif
1065 !-------------------------------------------------------------
1066 ! pgdep: deposition/sublimation rate of graupel [HL A21] [LFO 46]
1067 !        (T<T0: V->G or G->V)
1068 !-------------------------------------------------------------
1069             if(qrs(i,k,3).gt.0..and.ifsat.ne.1) then
1070               coeres = rslope2(i,k,3)*sqrt(rslope(i,k,3)*rslopeb(i,k,3))
1071               pgdep(i,k) = (rh(i,k,2)-1.)*(precg1*rslope2(i,k,3)       &
1072                               +precg2*work2(i,k)*coeres)/work1(i,k,2)
1073               supice = satdt-prevp(i,k)-pidep(i,k)-psdep(i,k)
1074               if(pgdep(i,k).lt.0.) then
1075                 pgdep(i,k) = max(pgdep(i,k),-qrs(i,k,3)/dtcld)
1076                 pgdep(i,k) = max(max(pgdep(i,k),satdt/2),supice)
1077               else
1078                 pgdep(i,k) = min(min(pgdep(i,k),satdt/2),supice)
1079               endif
1080               if(abs(prevp(i,k)+pidep(i,k)+psdep(i,k)+pgdep(i,k)).ge. &
1081                 abs(satdt)) ifsat = 1
1082             endif
1083 !-------------------------------------------------------------
1084 ! pigen: generation(nucleation) of ice from vapor [HL 50] [HDC 7-8]
1085 !       (T<T0: V->I)
1086 !-------------------------------------------------------------
1087             if(supsat.gt.0.and.ifsat.ne.1) then
1088               supice = satdt-prevp(i,k)-pidep(i,k)-psdep(i,k)-pgdep(i,k)
1089               xni0 = 1.e3*exp(0.1*supcol)
1090               roqi0 = 4.92e-11*xni0**1.33
1091               pigen(i,k) = max(0.,(roqi0/den(i,k)-max(qci(i,k,2),0.))    &
1092                          /dtcld)
1093               pigen(i,k) = min(min(pigen(i,k),satdt),supice)
1094             endif
1095 !
1096 !-------------------------------------------------------------
1097 ! psaut: conversion(aggregation) of ice to snow [HDC 12]
1098 !        (T<T0: I->S)
1099 !-------------------------------------------------------------
1100             if(qci(i,k,2).gt.0.) then
1101               qimax = roqimax/den(i,k)
1102               psaut(i,k) = max(0.,(qci(i,k,2)-qimax)/dtcld)
1103             endif
1104 !
1105 !-------------------------------------------------------------
1106 ! pgaut: conversion(aggregation) of snow to graupel [HL A4] [LFO 37]
1107 !        (T<T0: S->G)
1108 !-------------------------------------------------------------
1109             if(qrs(i,k,2).gt.0.) then
1110               alpha2 = 1.e-3*exp(0.09*(-supcol))
1111               pgaut(i,k) = min(max(0.,alpha2*(qrs(i,k,2)-qs0))         &
1112                            ,qrs(i,k,2)/dtcld)
1113             endif
1114           endif
1115 !
1116 !-------------------------------------------------------------
1117 ! psevp: Evaporation of melting snow [HL A35] [RH83 A27]
1118 !       (T>=T0: S->V)
1119 !-------------------------------------------------------------
1120           if(supcol.lt.0.) then
1121             if(qrs(i,k,2).gt.0..and.rh(i,k,1).lt.1.) then
1122               coeres = rslope2(i,k,2)*sqrt(rslope(i,k,2)*rslopeb(i,k,2))
1123               psevp(i,k) = (rh(i,k,1)-1.)*n0sfac(i,k)*(precs1            &
1124                            *rslope2(i,k,2)+precs2*work2(i,k)            &
1125                            *coeres)/work1(i,k,1)
1126               psevp(i,k) = min(max(psevp(i,k),-qrs(i,k,2)/dtcld),0.)
1127             endif
1128 !-------------------------------------------------------------
1129 ! pgevp: Evaporation of melting graupel [HL A25] [RH84 A19]
1130 !       (T>=T0: G->V)
1131 !-------------------------------------------------------------
1132             if(qrs(i,k,3).gt.0..and.rh(i,k,1).lt.1.) then
1133               coeres = rslope2(i,k,3)*sqrt(rslope(i,k,3)*rslopeb(i,k,3))
1134               pgevp(i,k) = (rh(i,k,1)-1.)*(precg1*rslope2(i,k,3)         &
1135                          +precg2*work2(i,k)*coeres)/work1(i,k,1)
1136               pgevp(i,k) = min(max(pgevp(i,k),-qrs(i,k,3)/dtcld),0.)
1137             endif
1138           endif
1139         enddo
1140       enddo
1141 !
1142 !
1143 !----------------------------------------------------------------
1144 !     check mass conservation of generation terms and feedback to the
1145 !     large scale
1146 !
1147       do k = kts, kte
1148         do i = its, ite
1149 !
1150           delta2=0.
1151           delta3=0.
1152           if(qrs(i,k,1).lt.1.e-4.and.qrs(i,k,2).lt.1.e-4) delta2=1.
1153           if(qrs(i,k,1).lt.1.e-4) delta3=1.
1154           if(t(i,k).le.t0c) then
1155 !
1156 !     cloud water
1157 !
1158             value = max(qmin,qci(i,k,1))
1159             source = (praut(i,k)+pracw(i,k)+paacw(i,k)+paacw(i,k))*dtcld
1160             if (source.gt.value) then
1161               factor = value/source
1162               praut(i,k) = praut(i,k)*factor
1163               pracw(i,k) = pracw(i,k)*factor
1164               paacw(i,k) = paacw(i,k)*factor
1165             endif
1166 !
1167 !     cloud ice
1168 !
1169             value = max(qmin,qci(i,k,2))
1170             source = (psaut(i,k)-pigen(i,k)-pidep(i,k)+praci(i,k)        &
1171                     +psaci(i,k)+pgaci(i,k))*dtcld
1172             if (source.gt.value) then
1173               factor = value/source
1174               psaut(i,k) = psaut(i,k)*factor
1175               pigen(i,k) = pigen(i,k)*factor
1176               pidep(i,k) = pidep(i,k)*factor
1177               praci(i,k) = praci(i,k)*factor
1178               psaci(i,k) = psaci(i,k)*factor
1179               pgaci(i,k) = pgaci(i,k)*factor
1180             endif
1181 !
1182 !     rain
1183 !
1184             value = max(qmin,qrs(i,k,1))
1185             source = (-praut(i,k)-prevp(i,k)-pracw(i,k)+piacr(i,k)    &
1186                     +psacr(i,k)+pgacr(i,k))*dtcld
1187             if (source.gt.value) then
1188               factor = value/source
1189               praut(i,k) = praut(i,k)*factor
1190               prevp(i,k) = prevp(i,k)*factor
1191               pracw(i,k) = pracw(i,k)*factor
1192               piacr(i,k) = piacr(i,k)*factor
1193               psacr(i,k) = psacr(i,k)*factor
1194               pgacr(i,k) = pgacr(i,k)*factor
1195             endif
1196 !
1197 !     snow
1198 !
1199             value = max(qmin,qrs(i,k,2))
1200             source = -(psdep(i,k)+psaut(i,k)-pgaut(i,k)+paacw(i,k)      &
1201                      +piacr(i,k)*delta3+praci(i,k)*delta3               &
1202                      -pracs(i,k)*(1.-delta2)+psacr(i,k)*delta2          &
1203                      +psaci(i,k)-pgacs(i,k) )*dtcld
1204             if (source.gt.value) then
1205               factor = value/source
1206               psdep(i,k) = psdep(i,k)*factor
1207               psaut(i,k) = psaut(i,k)*factor
1208               pgaut(i,k) = pgaut(i,k)*factor
1209               paacw(i,k) = paacw(i,k)*factor
1210               piacr(i,k) = piacr(i,k)*factor
1211               praci(i,k) = praci(i,k)*factor
1212               psaci(i,k) = psaci(i,k)*factor
1213               pracs(i,k) = pracs(i,k)*factor
1214               psacr(i,k) = psacr(i,k)*factor
1215               pgacs(i,k) = pgacs(i,k)*factor
1216             endif
1217 !
1218 !     graupel
1219 !
1220             value = max(qmin,qrs(i,k,3))
1221             source = -(pgdep(i,k)+pgaut(i,k)               &
1222                      +piacr(i,k)*(1.-delta3)+praci(i,k)*(1.-delta3)     &
1223                      +psacr(i,k)*(1.-delta2)+pracs(i,k)*(1.-delta2)     &
1224                      +pgaci(i,k)+paacw(i,k)+pgacr(i,k)+pgacs(i,k))*dtcld
1225             if (source.gt.value) then
1226               factor = value/source
1227               pgdep(i,k) = pgdep(i,k)*factor
1228               pgaut(i,k) = pgaut(i,k)*factor
1229               piacr(i,k) = piacr(i,k)*factor
1230               praci(i,k) = praci(i,k)*factor
1231               psacr(i,k) = psacr(i,k)*factor
1232               pracs(i,k) = pracs(i,k)*factor
1233               paacw(i,k) = paacw(i,k)*factor
1234               pgaci(i,k) = pgaci(i,k)*factor
1235               pgacr(i,k) = pgacr(i,k)*factor
1236               pgacs(i,k) = pgacs(i,k)*factor
1237             endif
1238 !
1239             work2(i,k)=-(prevp(i,k)+psdep(i,k)+pgdep(i,k)+pigen(i,k)   &
1240                        +pidep(i,k))
1241 !     update
1242             q(i,k) = q(i,k)+work2(i,k)*dtcld
1243             qci(i,k,1) = max(qci(i,k,1)-(praut(i,k)+pracw(i,k)          &
1244                            +paacw(i,k)+paacw(i,k))*dtcld,0.)
1245             qrs(i,k,1) = max(qrs(i,k,1)+(praut(i,k)+pracw(i,k)          &
1246                            +prevp(i,k)-piacr(i,k)-pgacr(i,k)            &
1247                            -psacr(i,k))*dtcld,0.)
1248             qci(i,k,2) = max(qci(i,k,2)-(psaut(i,k)+praci(i,k)          &
1249                            +psaci(i,k)+pgaci(i,k)-pigen(i,k)-pidep(i,k))   &
1250                            *dtcld,0.)
1251             qrs(i,k,2) = max(qrs(i,k,2)+(psdep(i,k)+psaut(i,k)+paacw(i,k)  &
1252                            -pgaut(i,k)+piacr(i,k)*delta3                &
1253                            +praci(i,k)*delta3+psaci(i,k)-pgacs(i,k)      &
1254                            -pracs(i,k)*(1.-delta2)+psacr(i,k)*delta2)    &
1255                            *dtcld,0.)
1256             qrs(i,k,3) = max(qrs(i,k,3)+(pgdep(i,k)+pgaut(i,k)         &
1257                            +piacr(i,k)*(1.-delta3)            &
1258                            +praci(i,k)*(1.-delta3)+psacr(i,k)*(1.-delta2)&
1259                            +pracs(i,k)*(1.-delta2)+pgaci(i,k)+paacw(i,k) &
1260                            +pgacr(i,k)+pgacs(i,k))*dtcld,0.)
1261             xlf = xls-xl(i,k)
1262             xlwork2 = -xls*(psdep(i,k)+pgdep(i,k)+pidep(i,k)+pigen(i,k)) &
1263                       -xl(i,k)*prevp(i,k)-xlf*(piacr(i,k)+paacw(i,k)    &
1264                       +paacw(i,k)+pgacr(i,k)+psacr(i,k))
1265             t(i,k) = t(i,k)-xlwork2/cpm(i,k)*dtcld
1266           else
1267 !
1268 !     cloud water
1269 !
1270             value = max(qmin,qci(i,k,1))
1271             source=(praut(i,k)+pracw(i,k)+paacw(i,k)+paacw(i,k))*dtcld
1272             if (source.gt.value) then
1273               factor = value/source
1274               praut(i,k) = praut(i,k)*factor
1275               pracw(i,k) = pracw(i,k)*factor
1276               paacw(i,k) = paacw(i,k)*factor
1277             endif
1278 !
1279 !     rain
1280 !
1281             value = max(qmin,qrs(i,k,1))
1282             source = (-paacw(i,k)-praut(i,k)+pseml(i,k)+pgeml(i,k)     &
1283                      -pracw(i,k)-paacw(i,k)-prevp(i,k))*dtcld
1284             if (source.gt.value) then
1285               factor = value/source
1286               praut(i,k) = praut(i,k)*factor
1287               prevp(i,k) = prevp(i,k)*factor
1288               pracw(i,k) = pracw(i,k)*factor
1289               paacw(i,k) = paacw(i,k)*factor
1290               pseml(i,k) = pseml(i,k)*factor
1291               pgeml(i,k) = pgeml(i,k)*factor
1292             endif
1293 !
1294 !     snow
1295 !
1296             value = max(qcrmin,qrs(i,k,2))
1297             source=(pgacs(i,k)-pseml(i,k)-psevp(i,k))*dtcld
1298             if (source.gt.value) then
1299               factor = value/source
1300               pgacs(i,k) = pgacs(i,k)*factor
1301               psevp(i,k) = psevp(i,k)*factor
1302               pseml(i,k) = pseml(i,k)*factor
1303             endif
1304 !
1305 !     graupel
1306 !
1307             value = max(qcrmin,qrs(i,k,3))
1308             source=-(pgacs(i,k)+pgevp(i,k)+pgeml(i,k))*dtcld
1309             if (source.gt.value) then
1310               factor = value/source
1311               pgacs(i,k) = pgacs(i,k)*factor
1312               pgevp(i,k) = pgevp(i,k)*factor
1313               pgeml(i,k) = pgeml(i,k)*factor
1314             endif
1315             work2(i,k)=-(prevp(i,k)+psevp(i,k)+pgevp(i,k))
1316 !     update
1317             q(i,k) = q(i,k)+work2(i,k)*dtcld
1318             qci(i,k,1) = max(qci(i,k,1)-(praut(i,k)+pracw(i,k)         &
1319                     +paacw(i,k)+paacw(i,k))*dtcld,0.)
1320             qrs(i,k,1) = max(qrs(i,k,1)+(praut(i,k)+pracw(i,k)         &
1321                     +prevp(i,k)+paacw(i,k)+paacw(i,k)-pseml(i,k)       &
1322                     -pgeml(i,k))*dtcld,0.)
1323             qrs(i,k,2) = max(qrs(i,k,2)+(psevp(i,k)-pgacs(i,k)           &
1324                     +pseml(i,k))*dtcld,0.)
1325             qrs(i,k,3) = max(qrs(i,k,3)+(pgacs(i,k)+pgevp(i,k)           &
1326                     +pgeml(i,k))*dtcld,0.)
1327             xlf = xls-xl(i,k)
1328             xlwork2 = -xl(i,k)*(prevp(i,k)+psevp(i,k)+pgevp(i,k))        &
1329                       -xlf*(pseml(i,k)+pgeml(i,k))
1330             t(i,k) = t(i,k)-xlwork2/cpm(i,k)*dtcld
1331           endif
1332         enddo
1333       enddo
1334 !
1335 ! Inline expansion for fpvs
1336 !         qs(i,k,1) = fpvs(t(i,k),0,rd,rv,cpv,cliq,cice,xlv0,xls,psat,t0c)
1337 !         qs(i,k,2) = fpvs(t(i,k),1,rd,rv,cpv,cliq,cice,xlv0,xls,psat,t0c)
1338       hsub = xls
1339       hvap = xlv0
1340       cvap = cpv
1341       ttp=t0c+0.01
1342       dldt=cvap-cliq
1343       xa=-dldt/rv
1344       xb=xa+hvap/(rv*ttp)
1345       dldti=cvap-cice
1346       xai=-dldti/rv
1347       xbi=xai+hsub/(rv*ttp)
1348       do k = kts, kte
1349         do i = its, ite
1350           tr=ttp/t(i,k)
1351           qs(i,k,1)=psat*exp(log(tr)*(xa))*exp(xb*(1.-tr))
1352           qs(i,k,1) = ep2 * qs(i,k,1) / (p(i,k) - qs(i,k,1))
1353           qs(i,k,1) = max(qs(i,k,1),qmin)
1354           tr=ttp/t(i,k)
1355           if(t(i,k).lt.ttp) then
1356             qs(i,k,2)=psat*exp(log(tr)*(xai))*exp(xbi*(1.-tr))
1357           else
1358             qs(i,k,2)=psat*exp(log(tr)*(xa))*exp(xb*(1.-tr))
1359           endif
1360           qs(i,k,2) = ep2 * qs(i,k,2) / (p(i,k) - qs(i,k,2))
1361           qs(i,k,2) = max(qs(i,k,2),qmin)
1362         enddo
1363       enddo
1364 !
1365 !----------------------------------------------------------------
1366 !  pcond: condensational/evaporational rate of cloud water [HL A46] [RH83 A6]
1367 !     if there exists additional water vapor condensated/if
1368 !     evaporation of cloud water is not enough to remove subsaturation
1369 !
1370       do k = kts, kte
1371         do i = its, ite
1372           work1(i,k,1) = conden(t(i,k),q(i,k),qs(i,k,1),xl(i,k),cpm(i,k))
1373           work2(i,k) = qci(i,k,1)+work1(i,k,1)
1374           pcond(i,k) = min(max(work1(i,k,1)/dtcld,0.),max(q(i,k),0.)/dtcld)
1375           if(qci(i,k,1).gt.0..and.work1(i,k,1).lt.0.)                   &
1376             pcond(i,k) = max(work1(i,k,1),-qci(i,k,1))/dtcld
1377           q(i,k) = q(i,k)-pcond(i,k)*dtcld
1378           qci(i,k,1) = max(qci(i,k,1)+pcond(i,k)*dtcld,0.)
1379           t(i,k) = t(i,k)+pcond(i,k)*xl(i,k)/cpm(i,k)*dtcld
1380         enddo
1381       enddo
1382 !
1383 !
1384 !----------------------------------------------------------------
1385 !     padding for small values
1386 !
1387       do k = kts, kte
1388         do i = its, ite
1389           if(qci(i,k,1).le.qmin) qci(i,k,1) = 0.0
1390           if(qci(i,k,2).le.qmin) qci(i,k,2) = 0.0
1391         enddo
1392       enddo
1393       enddo                  ! big loops
1394   END SUBROUTINE wsm62d
1395 ! ...................................................................
1396       REAL FUNCTION rgmma(x)
1397 !-------------------------------------------------------------------
1398   IMPLICIT NONE
1399 !-------------------------------------------------------------------
1400 !     rgmma function:  use infinite product form
1401       REAL :: euler
1402       PARAMETER (euler=0.577215664901532)
1403       REAL :: x, y
1404       INTEGER :: i
1405       if(x.eq.1.)then
1406         rgmma=0.
1407           else
1408         rgmma=x*exp(euler*x)
1409         do i=1,10000
1410           y=float(i)
1411           rgmma=rgmma*(1.000+x/y)*exp(-x/y)
1412         enddo
1413         rgmma=1./rgmma
1414       endif
1415       END FUNCTION rgmma
1416 !
1417 !--------------------------------------------------------------------------
1418       REAL FUNCTION fpvs(t,ice,rd,rv,cvap,cliq,cice,hvap,hsub,psat,t0c)
1419 !--------------------------------------------------------------------------
1420       IMPLICIT NONE
1421 !--------------------------------------------------------------------------
1422       REAL t,rd,rv,cvap,cliq,cice,hvap,hsub,psat,t0c,dldt,xa,xb,dldti,  &
1423            xai,xbi,ttp,tr
1424       INTEGER ice
1425 ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
1426       ttp=t0c+0.01
1427       dldt=cvap-cliq
1428       xa=-dldt/rv
1429       xb=xa+hvap/(rv*ttp)
1430       dldti=cvap-cice
1431       xai=-dldti/rv
1432       xbi=xai+hsub/(rv*ttp)
1433       tr=ttp/t
1434       if(t.lt.ttp.and.ice.eq.1) then
1435         fpvs=psat*(tr**xai)*exp(xbi*(1.-tr))
1436       else
1437         fpvs=psat*(tr**xa)*exp(xb*(1.-tr))
1438       endif
1439 ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
1440       END FUNCTION fpvs
1441 !-------------------------------------------------------------------
1442   SUBROUTINE wsm6init(den0,denr,dens,cl,cpv,allowed_to_read)
1443 !-------------------------------------------------------------------
1444   IMPLICIT NONE
1445 !-------------------------------------------------------------------
1446 !.... constants which may not be tunable
1447    REAL, INTENT(IN) :: den0,denr,dens,cl,cpv
1448    LOGICAL, INTENT(IN) :: allowed_to_read
1449    REAL :: pi
1450 !
1451    pi = 4.*atan(1.)
1452    xlv1 = cl-cpv
1453 !
1454    qc0  = 4./3.*pi*denr*r0**3*xncr/den0  ! 0.419e-3 -- .61e-3
1455    qck1 = .104*9.8*peaut/(xncr*denr)**(1./3.)/xmyu*den0**(4./3.) ! 7.03
1456 !
1457    bvtr1 = 1.+bvtr
1458    bvtr2 = 2.5+.5*bvtr
1459    bvtr3 = 3.+bvtr
1460    bvtr4 = 4.+bvtr
1461    bvtr6 = 6.+bvtr
1462    g1pbr = rgmma(bvtr1)
1463    g3pbr = rgmma(bvtr3)
1464    g4pbr = rgmma(bvtr4)            ! 17.837825
1465    g6pbr = rgmma(bvtr6)
1466    g5pbro2 = rgmma(bvtr2)          ! 1.8273
1467    pvtr = avtr*g4pbr/6.
1468    eacrr = 1.0
1469    pacrr = pi*n0r*avtr*g3pbr*.25*eacrr
1470    precr1 = 2.*pi*n0r*.78
1471    precr2 = 2.*pi*n0r*.31*avtr**.5*g5pbro2
1472    xm0  = (di0/dicon)**2
1473    xmmax = (dimax/dicon)**2
1474    roqimax = 2.08e22*dimax**8
1475 !
1476    bvts1 = 1.+bvts
1477    bvts2 = 2.5+.5*bvts
1478    bvts3 = 3.+bvts
1479    bvts4 = 4.+bvts
1480    g1pbs = rgmma(bvts1)    !.8875
1481    g3pbs = rgmma(bvts3)
1482    g4pbs = rgmma(bvts4)    ! 12.0786
1483    g5pbso2 = rgmma(bvts2)
1484    pvts = avts*g4pbs/6.
1485    pacrs = pi*n0s*avts*g3pbs*.25
1486    precs1 = 4.*n0s*.65
1487    precs2 = 4.*n0s*.44*avts**.5*g5pbso2
1488    pidn0r =  pi*denr*n0r
1489    pidn0s =  pi*dens*n0s
1490 !
1491    pacrc = pi*n0s*avts*g3pbs*.25*eacrc
1492 !
1493    bvtg1 = 1.+bvtg
1494    bvtg2 = 2.5+.5*bvtg
1495    bvtg3 = 3.+bvtg
1496    bvtg4 = 4.+bvtg
1497    g1pbg = rgmma(bvtg1)
1498    g3pbg = rgmma(bvtg3)
1499    g4pbg = rgmma(bvtg4)
1500    pacrg = pi*n0g*avtg*g3pbg*.25
1501    g5pbgo2 = rgmma(bvtg2)
1502    pvtg = avtg*g4pbg/6.
1503    precg1 = 2.*pi*n0g*.78
1504    precg2 = 2.*pi*n0g*.31*avtg**.5*g5pbgo2
1505    pidn0g =  pi*deng*n0g
1506 !
1507    rslopermax = 1./lamdarmax
1508    rslopesmax = 1./lamdasmax
1509    rslopegmax = 1./lamdagmax
1510    rsloperbmax = rslopermax ** bvtr
1511    rslopesbmax = rslopesmax ** bvts
1512    rslopegbmax = rslopegmax ** bvtg
1513    rsloper2max = rslopermax * rslopermax
1514    rslopes2max = rslopesmax * rslopesmax
1515    rslopeg2max = rslopegmax * rslopegmax
1516    rsloper3max = rsloper2max * rslopermax
1517    rslopes3max = rslopes2max * rslopesmax
1518    rslopeg3max = rslopeg2max * rslopegmax
1519 !
1520   END SUBROUTINE wsm6init
1521 END MODULE module_mp_wsm6