module_mp_wsm5.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 !Including inline expansion statistical function 
10 MODULE module_mp_wsm5
11 !
12 !
13    REAL, PARAMETER, PRIVATE :: dtcldcr     = 120.
14    REAL, PARAMETER, PRIVATE :: n0r = 8.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 :: n0smax =  1.e11 ! t=-90C unlimited
24    REAL, PARAMETER, PRIVATE :: lamdarmax = 8.e4
25    REAL, PARAMETER, PRIVATE :: lamdasmax = 1.e5
26    REAL, PARAMETER, PRIVATE :: lamdagmax = 6.e4
27    REAL, PARAMETER, PRIVATE :: betai = .6
28    REAL, PARAMETER, PRIVATE :: xn0 = 1.e-2
29    REAL, PARAMETER, PRIVATE :: dicon = 11.9
30    REAL, PARAMETER, PRIVATE :: di0 = 12.9e-6
31    REAL, PARAMETER, PRIVATE :: dimax = 500.e-6
32    REAL, PARAMETER, PRIVATE :: n0s = 2.e6             ! temperature dependent n0s
33    REAL, PARAMETER, PRIVATE :: alpha = .12        ! .122 exponen factor for n0s
34    REAL, PARAMETER, PRIVATE :: pfrz1 = 100.
35    REAL, PARAMETER, PRIVATE :: pfrz2 = 0.66
36    REAL, PARAMETER, PRIVATE :: qcrmin = 1.e-9
37    REAL, PARAMETER, PRIVATE :: t40c = 233.16
38    REAL, PARAMETER, PRIVATE :: eacrc = 1.0
39    REAL, SAVE ::                                     &
40              qc0, qck1,bvtr1,bvtr2,bvtr3,bvtr4,g1pbr,&
41              g3pbr,g4pbr,g5pbro2,pvtr,eacrr,pacrr,   &
42              precr1,precr2,xm0,xmmax,roqimax,bvts1,  &
43              bvts2,bvts3,bvts4,g1pbs,g3pbs,g4pbs,    &
44              g5pbso2,pvts,pacrs,precs1,precs2,pidn0r,&
45              pidn0s,xlv1,pacrc,                      &
46              rslopermax,rslopesmax,rslopegmax,       &
47              rsloperbmax,rslopesbmax,rslopegbmax,    &
48              rsloper2max,rslopes2max,rslopeg2max,    &
49              rsloper3max,rslopes3max,rslopeg3max
50 !
51 ! Specifies code-inlining of fpvs function in WSM52D below. JM 20040507
52 !
53 CONTAINS
54 !===================================================================
55 !
56   SUBROUTINE wsm5(th, q, qc, qr, qi, qs                            &
57                  ,den, pii, p, delz                                &
58                  ,delt,g, cpd, cpv, rd, rv, t0c                    &
59                  ,ep1, ep2, qmin                                   &
60                  ,XLS, XLV0, XLF0, den0, denr                      &
61                  ,cliq,cice,psat                                   &
62                  ,rain, rainncv                                    &
63                  ,snow, snowncv                                    &
64                  ,sr                                               &
65                  ,ids,ide, jds,jde, kds,kde                        &
66                  ,ims,ime, jms,jme, kms,kme                        &
67                  ,its,ite, jts,jte, kts,kte                        &
68                                                                    )
69 !-------------------------------------------------------------------
70   IMPLICIT NONE
71 !-------------------------------------------------------------------
72 !
73 !  This code is a 5-class mixed ice microphyiscs scheme (WSM5) of the WRF
74 !  Single-Moment MicroPhyiscs (WSMMP). The WSMMP assumes that ice nuclei
75 !  number concentration is a function of temperature, and seperate assumption
76 !  is developed, in which ice crystal number concentration is a function
77 !  of ice amount. A theoretical background of the ice-microphysics and related
78 !  processes in the WSMMPs are described in Hong et al. (2004).
79 !  Production terms in the WSM6 scheme are described in Hong and Lim (2006).
80 !  All units are in m.k.s. and source/sink terms in kgkg-1s-1.
81 !
82 !  WSM5 cloud scheme
83 !
84 !  Coded by Song-You Hong (Yonsei Univ.)
85 !             Jimy Dudhia (NCAR) and Shu-Hua Chen (UC Davis)
86 !             Summer 2002
87 !
88 !  Implemented by Song-You Hong (Yonsei Univ.) and Jimy Dudhia (NCAR)
89 !             Summer 2003
90 !
91 !  Reference) Hong, Dudhia, Chen (HDC, 2004) Mon. Wea. Rev.
92 !             Rutledge, Hobbs (RH83, 1983) J. Atmos. Sci.
93 !             Hong and Lim (HL, 2006) J. Korean Meteor. Soc.
94 !
95   INTEGER,      INTENT(IN   )    ::   ids,ide, jds,jde, kds,kde , &
96                                       ims,ime, jms,jme, kms,kme , &
97                                       its,ite, jts,jte, kts,kte
98   REAL, DIMENSION( ims:ime , kms:kme , jms:jme ),                 &
99         INTENT(INOUT) ::                                          &
100                                                              th,  &
101                                                               q,  &
102                                                               qc, &
103                                                               qi, &
104                                                               qr, &
105                                                               qs
106   REAL, DIMENSION( ims:ime , kms:kme , jms:jme ),                 &
107         INTENT(IN   ) ::                                          &
108                                                              den, &
109                                                              pii, &
110                                                                p, &
111                                                             delz
112   REAL, INTENT(IN   ) ::                                    delt, &
113                                                                g, &
114                                                               rd, &
115                                                               rv, &
116                                                              t0c, &
117                                                             den0, &
118                                                              cpd, &
119                                                              cpv, &
120                                                              ep1, &
121                                                              ep2, &
122                                                             qmin, &
123                                                              XLS, &
124                                                             XLV0, &
125                                                             XLF0, &
126                                                             cliq, &
127                                                             cice, &
128                                                             psat, &
129                                                             denr
130   REAL, DIMENSION( ims:ime , jms:jme ),                           &
131         INTENT(INOUT) ::                                    rain, &
132                                                          rainncv, &
133                                                               sr
134 
135   REAL, DIMENSION( ims:ime , jms:jme ), OPTIONAL,                &
136         INTENT(INOUT) ::                                    snow, &
137                                                          snowncv
138 
139 ! LOCAL VAR
140   REAL, DIMENSION( its:ite , kts:kte ) ::   t
141   REAL, DIMENSION( its:ite , kts:kte, 2 ) ::   qci, qrs
142   INTEGER ::               i,j,k
143 !-------------------------------------------------------------------
144       DO j=jts,jte
145          DO k=kts,kte
146          DO i=its,ite
147             t(i,k)=th(i,k,j)*pii(i,k,j)
148             qci(i,k,1) = qc(i,k,j)
149             qci(i,k,2) = qi(i,k,j)
150             qrs(i,k,1) = qr(i,k,j)
151             qrs(i,k,2) = qs(i,k,j)
152          ENDDO
153          ENDDO
154          CALL wsm52D(t, q(ims,kms,j), qci, qrs                     &
155                     ,den(ims,kms,j)                                &
156                     ,p(ims,kms,j), delz(ims,kms,j)                 &
157                     ,delt,g, cpd, cpv, rd, rv, t0c                 &
158                     ,ep1, ep2, qmin                                &
159                     ,XLS, XLV0, XLF0, den0, denr                   &
160                     ,cliq,cice,psat                                &
161                     ,j                                             &
162                     ,rain(ims,j),rainncv(ims,j)                    &
163                     ,sr(ims,j)                                     &
164                     ,ids,ide, jds,jde, kds,kde                     &
165                     ,ims,ime, jms,jme, kms,kme                     &
166                     ,its,ite, jts,jte, kts,kte                     &
167                     ,snow(ims,j),snowncv(ims,j)                    &
168                                                                    )
169          DO K=kts,kte
170          DO I=its,ite
171             th(i,k,j)=t(i,k)/pii(i,k,j)
172             qc(i,k,j) = qci(i,k,1)
173             qi(i,k,j) = qci(i,k,2)
174             qr(i,k,j) = qrs(i,k,1)
175             qs(i,k,j) = qrs(i,k,2)
176          ENDDO
177          ENDDO
178       ENDDO
179   END SUBROUTINE wsm5
180 !===================================================================
181 !
182   SUBROUTINE wsm52D(t, q, qci, qrs, den, p, delz                   &
183                    ,delt,g, cpd, cpv, rd, rv, t0c                  &
184                    ,ep1, ep2, qmin                                 &
185                    ,XLS, XLV0, XLF0, den0, denr                    &
186                    ,cliq,cice,psat                                 &
187                    ,lat                                            &
188                    ,rain,rainncv                                   &
189                    ,sr                                             &
190                    ,ids,ide, jds,jde, kds,kde                      &
191                    ,ims,ime, jms,jme, kms,kme                      &
192                    ,its,ite, jts,jte, kts,kte                      &
193                    ,snow,snowncv                                   &
194                                                                    )
195 !-------------------------------------------------------------------
196   IMPLICIT NONE
197 !-------------------------------------------------------------------
198   INTEGER,      INTENT(IN   )    ::   ids,ide, jds,jde, kds,kde , &
199                                       ims,ime, jms,jme, kms,kme , &
200                                       its,ite, jts,jte, kts,kte,  &
201                                       lat
202   REAL, DIMENSION( its:ite , kts:kte ),                           &
203         INTENT(INOUT) ::                                          &
204                                                                t
205   REAL, DIMENSION( its:ite , kts:kte, 2 ),                        &
206         INTENT(INOUT) ::                                          &
207                                                              qci, &
208                                                              qrs
209   REAL, DIMENSION( ims:ime , kms:kme ),                           &
210         INTENT(INOUT) ::                                          &
211                                                                q
212   REAL, DIMENSION( ims:ime , kms:kme ),                           &
213         INTENT(IN   ) ::                                          &
214                                                              den, &
215                                                                p, &
216                                                             delz
217   REAL, INTENT(IN   ) ::                                    delt, &
218                                                                g, &
219                                                              cpd, &
220                                                              cpv, &
221                                                              t0c, &
222                                                             den0, &
223                                                               rd, &
224                                                               rv, &
225                                                              ep1, &
226                                                              ep2, &
227                                                             qmin, &
228                                                              XLS, &
229                                                             XLV0, &
230                                                             XLF0, &
231                                                             cliq, &
232                                                             cice, &
233                                                             psat, &
234                                                             denr
235   REAL, DIMENSION( ims:ime ),                                     &
236         INTENT(INOUT) ::                                    rain, &
237                                                          rainncv, &
238                                                               sr
239 
240   REAL, DIMENSION( ims:ime ),     OPTIONAL,                       &
241         INTENT(INOUT) ::                                    snow, &
242                                                          snowncv
243 
244 ! LOCAL VAR
245   REAL, DIMENSION( its:ite , kts:kte , 2) ::                      &
246         rh, qs, rslope, rslope2, rslope3, rslopeb,                &
247         falk, fall, work1
248   REAL, DIMENSION( its:ite , kts:kte ) ::                         &
249               falkc, work1c, work2c, fallc
250   REAL, DIMENSION( its:ite , kts:kte ) ::                         &
251         praut, psaut, prevp, psdep, pracw, psaci, psacw,          &  
252         pigen, pidep, pcond, xl, cpm, work2, psmlt, psevp, denfac, xni,&
253         n0sfac
254 ! variables for optimization
255   REAL, DIMENSION( its:ite )           :: tvec1
256   INTEGER, DIMENSION( its:ite ) :: mstep, numdt
257   REAL, DIMENSION(its:ite) :: rmstep
258   REAL dtcldden, rdelz, rdtcld
259   LOGICAL, DIMENSION( its:ite ) :: flgcld
260   REAL  ::  pi,                                                   &
261             cpmcal, xlcal, lamdar, lamdas, diffus,                &
262             viscos, xka, venfac, conden, diffac,                  &
263             x, y, z, a, b, c, d, e,                               &
264             qdt, holdrr, holdrs, supcol, pvt,                     &
265             coeres, supsat, dtcld, xmi, eacrs, satdt,             &
266             vt2i,vt2s,acrfac,                                     &
267             qimax, diameter, xni0, roqi0,                         &
268             fallsum, fallsum_qsi, xlwork2, factor, source,        &
269             value, xlf, pfrzdtc, pfrzdtr, supice
270   REAL :: temp 
271   REAL  :: holdc, holdci
272   INTEGER :: i, j, k, mstepmax,                                   &
273             iprt, latd, lond, loop, loops, ifsat, n
274 ! Temporaries used for inlining fpvs function
275   REAL  :: dldti, xb, xai, tr, xbi, xa, hvap, cvap, hsub, dldt, ttp
276   REAL  :: logtr
277 !
278 !=================================================================
279 !   compute internal functions
280 !
281       cpmcal(x) = cpd*(1.-max(x,qmin))+max(x,qmin)*cpv
282       xlcal(x) = xlv0-xlv1*(x-t0c)
283 !----------------------------------------------------------------
284 !     size distributions: (x=mixing ratio, y=air density):
285 !     valid for mixing ratio > 1.e-9 kg/kg.
286 !
287 ! Optimizatin : A**B => exp(log(A)*(B))
288       lamdar(x,y)=   sqrt(sqrt(pidn0r/(x*y)))      ! (pidn0r/(x*y))**.25
289       lamdas(x,y,z)= sqrt(sqrt(pidn0s*z/(x*y)))    ! (pidn0s*z/(x*y))**.25
290 !
291 !----------------------------------------------------------------
292 !     diffus: diffusion coefficient of the water vapor
293 !     viscos: kinematic viscosity(m2s-1)
294 !     diffus(x,y) = 8.794e-5 * exp(log(x)*(1.81)) / y        ! 8.794e-5*x**1.81/y
295 !     viscos(x,y) = 1.496e-6 * (x*sqrt(x)) /(x+120.)/y  ! 1.496e-6*x**1.5/(x+120.)/y
296 !     xka(x,y) = 1.414e3*viscos(x,y)*y
297 !     diffac(a,b,c,d,e) = d*a*a/(xka(c,d)*rv*c*c)+1./(e*diffus(c,b))
298 !     venfac(a,b,c) = exp(log((viscos(b,c)/diffus(b,a)))*((.3333333)))    &
299 !                    /sqrt(viscos(b,c))*sqrt(sqrt(den0/c))
300 !     conden(a,b,c,d,e) = (max(b,qmin)-c)/(1.+d*d/(rv*e)*c/(a*a))
301 !
302 !
303       pi = 4. * atan(1.)
304 !
305 !----------------------------------------------------------------
306 !     paddint 0 for negative values generated by dynamics
307 !
308       do k = kts, kte
309         do i = its, ite
310           qci(i,k,1) = max(qci(i,k,1),0.0)
311           qrs(i,k,1) = max(qrs(i,k,1),0.0)
312           qci(i,k,2) = max(qci(i,k,2),0.0)
313           qrs(i,k,2) = max(qrs(i,k,2),0.0)
314         enddo
315       enddo
316 !
317 !----------------------------------------------------------------
318 !     latent heat for phase changes and heat capacity. neglect the
319 !     changes during microphysical process calculation
320 !     emanuel(1994)
321 !
322       do k = kts, kte
323         do i = its, ite
324           cpm(i,k) = cpmcal(q(i,k))
325           xl(i,k) = xlcal(t(i,k))
326         enddo
327       enddo
328 !
329 !----------------------------------------------------------------
330 !     compute the minor time steps.
331 !
332       loops = max(nint(delt/dtcldcr),1)
333       dtcld = delt/loops
334       if(delt.le.dtcldcr) dtcld = delt
335 !
336       do loop = 1,loops
337 !
338 !----------------------------------------------------------------
339 !     initialize the large scale variables
340 !
341       do i = its, ite
342         mstep(i) = 1
343         flgcld(i) = .true.
344       enddo
345 !
346 !     do k = kts, kte
347 !       do i = its, ite
348 !         denfac(i,k) = sqrt(den0/den(i,k))
349 !       enddo
350 !     enddo
351       do k = kts, kte
352         CALL VREC( tvec1(its), den(its,k), ite-its+1)
353         do i = its, ite
354           tvec1(i) = tvec1(i)*den0
355         enddo
356         CALL VSQRT( denfac(its,k), tvec1(its), ite-its+1)
357       enddo
358 !
359 ! Inline expansion for fpvs
360 !         qs(i,k,1) = fpvs(t(i,k),0,rd,rv,cpv,cliq,cice,xlv0,xls,psat,t0c)
361 !         qs(i,k,2) = fpvs(t(i,k),1,rd,rv,cpv,cliq,cice,xlv0,xls,psat,t0c)
362       hsub = xls
363       hvap = xlv0
364       cvap = cpv
365       ttp=t0c+0.01
366       dldt=cvap-cliq
367       xa=-dldt/rv
368       xb=xa+hvap/(rv*ttp)
369       dldti=cvap-cice
370       xai=-dldti/rv
371       xbi=xai+hsub/(rv*ttp)
372       do k = kts, kte
373         do i = its, ite
374           tr=ttp/t(i,k)
375           logtr=log(tr)
376           qs(i,k,1)=psat*exp(logtr*(xa)+xb*(1.-tr))
377           qs(i,k,1) = ep2 * qs(i,k,1) / (p(i,k) - qs(i,k,1))
378           qs(i,k,1) = max(qs(i,k,1),qmin)
379           rh(i,k,1) = max(q(i,k) / qs(i,k,1),qmin)
380           if(t(i,k).lt.ttp) then
381             qs(i,k,2)=psat*exp(logtr*(xai)+xbi*(1.-tr))
382           else
383             qs(i,k,2)=psat*exp(logtr*(xa)+xb*(1.-tr))
384           endif
385           qs(i,k,2) = ep2 * qs(i,k,2) / (p(i,k) - qs(i,k,2))
386           qs(i,k,2) = max(qs(i,k,2),qmin)
387           rh(i,k,2) = max(q(i,k) / qs(i,k,2),qmin)
388         enddo
389       enddo
390 !
391 !----------------------------------------------------------------
392 !     initialize the variables for microphysical physics
393 !
394 !
395       do k = kts, kte
396         do i = its, ite
397           prevp(i,k) = 0.
398           psdep(i,k) = 0.
399           praut(i,k) = 0.
400           psaut(i,k) = 0.
401           pracw(i,k) = 0.
402           psaci(i,k) = 0.
403           psacw(i,k) = 0.
404           pigen(i,k) = 0.
405           pidep(i,k) = 0.
406           pcond(i,k) = 0.
407           psmlt(i,k) = 0.
408           psevp(i,k) = 0.
409           falk(i,k,1) = 0.
410           falk(i,k,2) = 0.
411           fall(i,k,1) = 0.
412           fall(i,k,2) = 0.
413           fallc(i,k) = 0.
414           falkc(i,k) = 0.
415           xni(i,k) = 1.e3
416         enddo
417       enddo
418 !
419 !----------------------------------------------------------------
420 !     compute the fallout term:
421 !     first, vertical terminal velosity for minor loops
422 !
423       do k = kts, kte
424         do i = its, ite
425           supcol = t0c-t(i,k)
426 !---------------------------------------------------------------
427 ! n0s: Intercept parameter for snow [m-4] [HDC 6]
428 !---------------------------------------------------------------
429           n0sfac(i,k) = max(min(exp(alpha*supcol),n0smax/n0s),1.)
430           if(qrs(i,k,1).le.qcrmin)then
431             rslope(i,k,1) = rslopermax
432             rslopeb(i,k,1) = rsloperbmax
433             rslope2(i,k,1) = rsloper2max
434             rslope3(i,k,1) = rsloper3max
435           else
436             rslope(i,k,1) = 1./lamdar(qrs(i,k,1),den(i,k))
437             rslopeb(i,k,1) = exp(log(rslope(i,k,1))*(bvtr))
438             rslope2(i,k,1) = rslope(i,k,1)*rslope(i,k,1)
439             rslope3(i,k,1) = rslope2(i,k,1)*rslope(i,k,1)
440           endif
441           if(qrs(i,k,2).le.qcrmin)then
442             rslope(i,k,2) = rslopesmax
443             rslopeb(i,k,2) = rslopesbmax
444             rslope2(i,k,2) = rslopes2max
445             rslope3(i,k,2) = rslopes3max
446           else
447             rslope(i,k,2) = 1./lamdas(qrs(i,k,2),den(i,k),n0sfac(i,k))
448             rslopeb(i,k,2) = exp(log(rslope(i,k,2))*(bvts))
449             rslope2(i,k,2) = rslope(i,k,2)*rslope(i,k,2)
450             rslope3(i,k,2) = rslope2(i,k,2)*rslope(i,k,2)
451           endif
452 !-------------------------------------------------------------
453 ! Ni: ice crystal number concentraiton   [HDC 5c]
454 !-------------------------------------------------------------
455 !         xni(i,k) = min(max(5.38e7*(den(i,k)                           &
456 !                   *max(qci(i,k,2),qmin))**0.75,1.e3),1.e6)
457           temp = (den(i,k)*max(qci(i,k,2),qmin))
458           temp = sqrt(sqrt(temp*temp*temp))
459           xni(i,k) = min(max(5.38e7*temp,1.e3),1.e6)
460         enddo
461       enddo
462 !
463       mstepmax = 1
464       numdt = 1
465       do k = kte, kts, -1
466         do i = its, ite
467           work1(i,k,1) = pvtr*rslopeb(i,k,1)*denfac(i,k)/delz(i,k)
468           work1(i,k,2) = pvts*rslopeb(i,k,2)*denfac(i,k)/delz(i,k)
469           numdt(i) = max(nint(max(work1(i,k,1),work1(i,k,2))*dtcld+.5),1)
470           if(numdt(i).ge.mstep(i)) mstep(i) = numdt(i)
471         enddo
472       enddo
473       do i = its, ite
474         if(mstepmax.le.mstep(i)) mstepmax = mstep(i)
475         rmstep(i) = 1./mstep(i)
476       enddo
477 !
478       do n = 1, mstepmax
479         k = kte
480         do i = its, ite
481           if(n.le.mstep(i)) then
482 !             falk(i,k,1) = den(i,k)*qrs(i,k,1)*work1(i,k,1)/mstep(i)
483 !             falk(i,k,2) = den(i,k)*qrs(i,k,2)*work1(i,k,2)/mstep(i)
484               falk(i,k,1) = den(i,k)*qrs(i,k,1)*work1(i,k,1)*rmstep(i)
485               falk(i,k,2) = den(i,k)*qrs(i,k,2)*work1(i,k,2)*rmstep(i)
486               fall(i,k,1) = fall(i,k,1)+falk(i,k,1)
487               fall(i,k,2) = fall(i,k,2)+falk(i,k,2)
488 !             qrs(i,k,1) = max(qrs(i,k,1)-falk(i,k,1)*dtcld/den(i,k),0.)
489 !             qrs(i,k,2) = max(qrs(i,k,2)-falk(i,k,2)*dtcld/den(i,k),0.)
490               dtcldden = dtcld/den(i,k)
491               qrs(i,k,1) = max(qrs(i,k,1)-falk(i,k,1)*dtcldden,0.)
492               qrs(i,k,2) = max(qrs(i,k,2)-falk(i,k,2)*dtcldden,0.)
493             endif
494           enddo
495         do k = kte-1, kts, -1
496           do i = its, ite
497             if(n.le.mstep(i)) then
498 !             falk(i,k,1) = den(i,k)*qrs(i,k,1)*work1(i,k,1)/mstep(i)
499 !             falk(i,k,2) = den(i,k)*qrs(i,k,2)*work1(i,k,2)/mstep(i)
500               falk(i,k,1) = den(i,k)*qrs(i,k,1)*work1(i,k,1)*rmstep(i)
501               falk(i,k,2) = den(i,k)*qrs(i,k,2)*work1(i,k,2)*rmstep(i)
502               fall(i,k,1) = fall(i,k,1)+falk(i,k,1)
503               fall(i,k,2) = fall(i,k,2)+falk(i,k,2)
504 !             qrs(i,k,1) = max(qrs(i,k,1)-(falk(i,k,1)-falk(i,k+1,1)    &
505 !                         *delz(i,k+1)/delz(i,k))*dtcld/den(i,k),0.)
506 !             qrs(i,k,2) = max(qrs(i,k,2)-(falk(i,k,2)-falk(i,k+1,2)    &
507 !                         *delz(i,k+1)/delz(i,k))*dtcld/den(i,k),0.)
508               dtcldden = dtcld/den(i,k)
509               rdelz = 1./delz(i,k)
510               qrs(i,k,1) = max(qrs(i,k,1)-(falk(i,k,1)-falk(i,k+1,1)    &
511                           *delz(i,k+1)*rdelz)*dtcldden,0.)
512               qrs(i,k,2) = max(qrs(i,k,2)-(falk(i,k,2)-falk(i,k+1,2)    &
513                           *delz(i,k+1)*rdelz)*dtcldden,0.)
514             endif
515           enddo
516         enddo
517         do k = kte, kts, -1
518           do i = its, ite
519             if(n.le.mstep(i)) then
520               if(t(i,k).gt.t0c.and.qrs(i,k,2).gt.0.) then
521 !----------------------------------------------------------------
522 ! psmlt: melting of snow [HL A33] [RH83 A25]
523 !       (T>T0: S->R)
524 !----------------------------------------------------------------
525                 xlf = xlf0
526 !               work2(i,k)= venfac(p(i,k),t(i,k),den(i,k))
527                 work2(i,k)= (exp(log(((1.496e-6*((t(i,k))*sqrt(t(i,k))) &
528                             /((t(i,k))+120.)/(den(i,k)))/(8.794e-5      &
529                             *exp(log(t(i,k))*(1.81))/p(i,k))))          &
530                             *((.3333333)))/sqrt((1.496e-6*((t(i,k))     &
531                             *sqrt(t(i,k)))/((t(i,k))+120.)/(den(i,k)))) &
532                             *sqrt(sqrt(den0/(den(i,k)))))
533                 coeres = rslope2(i,k,2)*sqrt(rslope(i,k,2)*rslopeb(i,k,2))
534 !               psmlt(i,k) = xka(t(i,k),den(i,k))/xlf*(t0c-t(i,k))*pi/2. &
535 !                           *n0sfac(i,k)*(precs1*rslope2(i,k,2)+precs2  &
536 !                           *work2(i,k)*coeres)
537                 psmlt(i,k) = &
538 (1.414e3*(1.496e-6 * ((t(i,k))*sqrt(t(i,k))) /((t(i,k))+120.)/(den(i,k)) )*(den(i,k)))&
539                             /xlf*(t0c-t(i,k))*pi/2.                     &
540                             *n0sfac(i,k)*(precs1*rslope2(i,k,2)+precs2  &
541                             *work2(i,k)*coeres)
542                 psmlt(i,k) = min(max(psmlt(i,k)*dtcld/mstep(i),           &
543                             -qrs(i,k,2)/mstep(i)),0.)
544                 qrs(i,k,2) = qrs(i,k,2) + psmlt(i,k)
545                 qrs(i,k,1) = qrs(i,k,1) - psmlt(i,k)
546                 t(i,k) = t(i,k) + xlf/cpm(i,k)*psmlt(i,k)
547               endif
548             endif
549           enddo
550         enddo
551       enddo
552 !---------------------------------------------------------------
553 ! Vice [ms-1] : fallout of ice crystal [HDC 5a]
554 !---------------------------------------------------------------
555       mstepmax = 1
556       mstep = 1
557       numdt = 1
558       do k = kte, kts, -1
559         do i = its, ite
560           if(qci(i,k,2).le.0.) then
561             work2c(i,k) = 0.
562           else
563             xmi = den(i,k)*qci(i,k,2)/xni(i,k)
564 !           diameter  = min(dicon * sqrt(xmi),dimax)
565             diameter  = max(min(dicon * sqrt(xmi),dimax), 1.e-25)
566             work1c(i,k) = 1.49e4*exp(log(diameter)*(1.31))
567             work2c(i,k) = work1c(i,k)/delz(i,k)
568           endif
569           numdt(i) = max(nint(work2c(i,k)*dtcld+.5),1)
570           if(numdt(i).ge.mstep(i)) mstep(i) = numdt(i)
571         enddo
572       enddo
573       do i = its, ite
574         if(mstepmax.le.mstep(i)) mstepmax = mstep(i)
575       enddo
576 !
577       do n = 1, mstepmax
578         k = kte
579         do i = its, ite
580           if(n.le.mstep(i)) then
581             falkc(i,k) = den(i,k)*qci(i,k,2)*work2c(i,k)/mstep(i)
582             holdc = falkc(i,k)
583             fallc(i,k) = fallc(i,k)+falkc(i,k)
584             holdci = qci(i,k,2)
585             qci(i,k,2) = max(qci(i,k,2)-falkc(i,k)*dtcld/den(i,k),0.)
586           endif
587         enddo
588         do k = kte-1, kts, -1
589           do i = its, ite
590             if(n.le.mstep(i)) then
591               falkc(i,k) = den(i,k)*qci(i,k,2)*work2c(i,k)/mstep(i)
592               holdc = falkc(i,k)
593               fallc(i,k) = fallc(i,k)+falkc(i,k)
594               holdci = qci(i,k,2)
595               qci(i,k,2) = max(qci(i,k,2)-(falkc(i,k)-falkc(i,k+1)      &
596                           *delz(i,k+1)/delz(i,k))*dtcld/den(i,k),0.)
597             endif
598           enddo
599         enddo
600       enddo
601 !
602 !
603 !----------------------------------------------------------------
604 !      rain (unit is mm/sec;kgm-2s-1: /1000*delt ===> m)==> mm for wrf
605 !
606       do i = its, ite
607         fallsum = fall(i,1,1)+fall(i,1,2)+fallc(i,1)
608         fallsum_qsi = fall(i,1,2)+fallc(i,1)
609         rainncv(i) = 0.
610         if(fallsum.gt.0.) then
611           rainncv(i) = fallsum*delz(i,1)/denr*dtcld*1000.
612           rain(i) = fallsum*delz(i,1)/denr*dtcld*1000. + rain(i)
613         endif
614         IF ( PRESENT (snowncv) .AND. PRESENT (snow)) THEN
615         snowncv(i) = 0.
616         if(fallsum_qsi.gt.0.) then
617           snowncv(i) = fallsum_qsi*delz(i,kts)/denr*dtcld*1000.
618           snow(i) = fallsum_qsi*delz(i,kts)/denr*dtcld*1000. + snow(i)
619         endif
620         ENDIF
621         sr(i) = 0.
622         if(fallsum.gt.0.)sr(i)=fallsum_qsi*delz(i,kts)/denr*dtcld*1000./(rainncv(i)+1.e-12)
623       enddo
624 !
625 !---------------------------------------------------------------
626 ! pimlt: instantaneous melting of cloud ice [HL A47] [RH83 A28]
627 !       (T>T0: I->C)
628 !---------------------------------------------------------------
629       do k = kts, kte
630         do i = its, ite
631           supcol = t0c-t(i,k)
632           xlf = xls-xl(i,k)
633           if(supcol.lt.0.) xlf = xlf0
634           if(supcol.lt.0.and.qci(i,k,2).gt.0.) then
635             qci(i,k,1) = qci(i,k,1) + qci(i,k,2)
636             t(i,k) = t(i,k) - xlf/cpm(i,k)*qci(i,k,2)
637             qci(i,k,2) = 0.
638           endif
639 !---------------------------------------------------------------
640 ! pihmf: homogeneous freezing of cloud water below -40c [HL A45]
641 !        (T<-40C: C->I)
642 !---------------------------------------------------------------
643           if(supcol.gt.40..and.qci(i,k,1).gt.0.) then
644             qci(i,k,2) = qci(i,k,2) + qci(i,k,1)
645             t(i,k) = t(i,k) + xlf/cpm(i,k)*qci(i,k,1)
646             qci(i,k,1) = 0.
647           endif
648 !---------------------------------------------------------------
649 ! pihtf: heterogeneous freezing of cloud water [HL A44]
650 !        (T0>T>-40C: C->I)
651 !---------------------------------------------------------------
652           if(supcol.gt.0..and.qci(i,k,1).gt.0.) then
653 !           pfrzdtc = min(pfrz1*(exp(pfrz2*supcol)-1.)                  &
654 !              *den(i,k)/denr/xncr*qci(i,k,1)**2*dtcld,qci(i,k,1))
655             pfrzdtc = min(pfrz1*(exp(pfrz2*supcol)-1.)                  &
656             *den(i,k)/denr/xncr*qci(i,k,1)*qci(i,k,1)*dtcld,qci(i,k,1))
657             qci(i,k,2) = qci(i,k,2) + pfrzdtc
658             t(i,k) = t(i,k) + xlf/cpm(i,k)*pfrzdtc
659             qci(i,k,1) = qci(i,k,1)-pfrzdtc
660           endif
661 !---------------------------------------------------------------
662 ! psfrz: freezing of rain water [HL A20] [LFO 45]
663 !        (T<T0, R->S)
664 !---------------------------------------------------------------
665           if(supcol.gt.0..and.qrs(i,k,1).gt.0.) then
666 !           pfrzdtr = min(20.*pi**2*pfrz1*n0r*denr/den(i,k)             &
667 !                 *(exp(pfrz2*supcol)-1.)*rslope(i,k,1)**7*dtcld,       &
668 !                 qrs(i,k,1))
669             temp = rslope(i,k,1)
670             temp = temp*temp*temp*temp*temp*temp*temp
671             pfrzdtr = min(20.*(pi*pi)*pfrz1*n0r*denr/den(i,k)             &
672                   *(exp(pfrz2*supcol)-1.)*temp*dtcld,                   &
673                   qrs(i,k,1))
674             qrs(i,k,2) = qrs(i,k,2) + pfrzdtr
675             t(i,k) = t(i,k) + xlf/cpm(i,k)*pfrzdtr
676             qrs(i,k,1) = qrs(i,k,1)-pfrzdtr
677           endif
678         enddo
679       enddo
680 !
681 !----------------------------------------------------------------
682 !     rsloper: reverse of the slope parameter of the rain(m)
683 !     xka:    thermal conductivity of air(jm-1s-1k-1)
684 !     work1:  the thermodynamic term in the denominator associated with
685 !             heat conduction and vapor diffusion
686 !             (ry88, y93, h85)
687 !     work2: parameter associated with the ventilation effects(y93)
688 !
689       do k = kts, kte
690         do i = its, ite
691           if(qrs(i,k,1).le.qcrmin)then
692             rslope(i,k,1) = rslopermax
693             rslopeb(i,k,1) = rsloperbmax
694             rslope2(i,k,1) = rsloper2max
695             rslope3(i,k,1) = rsloper3max
696           else
697 !           rslope(i,k,1) = 1./lamdar(qrs(i,k,1),den(i,k))
698             rslope(i,k,1) = 1./(sqrt(sqrt(pidn0r/((qrs(i,k,1))*(den(i,k))))))
699             rslopeb(i,k,1) = exp(log(rslope(i,k,1))*(bvtr))
700             rslope2(i,k,1) = rslope(i,k,1)*rslope(i,k,1)
701             rslope3(i,k,1) = rslope2(i,k,1)*rslope(i,k,1)
702           endif
703           if(qrs(i,k,2).le.qcrmin)then
704             rslope(i,k,2) = rslopesmax
705             rslopeb(i,k,2) = rslopesbmax
706             rslope2(i,k,2) = rslopes2max
707             rslope3(i,k,2) = rslopes3max
708           else
709 !            rslope(i,k,2) = 1./lamdas(qrs(i,k,2),den(i,k),n0sfac(i,k))
710             rslope(i,k,2) = 1./(sqrt(sqrt(pidn0s*(n0sfac(i,k))/((qrs(i,k,2))*(den(i,k))))))
711             rslopeb(i,k,2) = exp(log(rslope(i,k,2))*(bvts))
712             rslope2(i,k,2) = rslope(i,k,2)*rslope(i,k,2)
713             rslope3(i,k,2) = rslope2(i,k,2)*rslope(i,k,2)
714           endif
715         enddo
716       enddo
717 !
718       do k = kts, kte
719         do i = its, ite
720 !         work1(i,k,1) = diffac(xl(i,k),p(i,k),t(i,k),den(i,k),qs(i,k,1))
721           work1(i,k,1) =                                                     &
722         ((((den(i,k))*(xl(i,k))*(xl(i,k))) * ((t(i,k))+120.) * (den(i,k)))   &
723            /                                                                 &
724          ( 1.414e3 * (1.496e-6 * ((t(i,k))*sqrt(t(i,k)))) * (den(i,k)) *     &
725                                                    (rv*(t(i,k))*(t(i,k)))))  &
726         +                                                                    &
727         p(i,k) / ( (qs(i,k,1)) * ( 8.794e-5 * exp(log(t(i,k))*(1.81)) ) )
728 !         work1(i,k,2) = diffac(xls,p(i,k),t(i,k),den(i,k),qs(i,k,2))
729           work1(i,k,2) =                                                     &
730         (                                                                    &
731          (((den(i,k))*(xls)*(xls))*((t(i,k))+120.)*(den(i,k)))               &
732            /                                                                 &
733           (                                                                  &
734          1.414e3 * (1.496e-6 * ((t(i,k))*sqrt(t(i,k)))) * (den(i,k)) *       &
735                                                    (rv*(t(i,k))*(t(i,k)))    &
736           )                                                                  &
737           +                                                                  &
738          p(i,k)                                                              &
739           /                                                                  &
740          ( qs(i,k,2) * (8.794e-5 * exp(log(t(i,k))*(1.81))))                 &
741         )
742 !         work2(i,k) = venfac(p(i,k),t(i,k),den(i,k))
743           work2(i,k) =                                                       &
744         (                                                                    &
745          exp(.3333333*log(                                                   &
746              ((1.496e-6 * ((t(i,k))*sqrt(t(i,k))))*p(i,k))                   &
747                 /                                                            &
748              (((t(i,k))+120.)*den(i,k)*(8.794e-5 * exp(log(t(i,k))*(1.81)))) &
749            ))                                                                &
750            *                                                                 &
751            sqrt(sqrt(den0/(den(i,k))))                                       &
752         )                                                                    &
753         /                                                                    &
754         sqrt(                                                                &
755            (1.496e-6 * ((t(i,k))*sqrt(t(i,k))))                              &
756              /                                                               &
757            (                                                                 &
758             ((t(i,k))+120.) * den(i,k)                                       &
759            )                                                                 &
760         )
761         ENDDO
762       ENDDO
763 !
764 !===============================================================
765 !
766 ! warm rain processes
767 !
768 ! - follows the processes in RH83 and LFO except for autoconcersion
769 !
770 !===============================================================
771 !
772       do k = kts, kte
773         do i = its, ite
774           supsat = max(q(i,k),qmin)-qs(i,k,1)
775           satdt = supsat/dtcld
776 !---------------------------------------------------------------
777 ! praut: auto conversion rate from cloud to rain [HDC 16]
778 !        (C->R)
779 !---------------------------------------------------------------
780           if(qci(i,k,1).gt.qc0) then
781             praut(i,k) = qck1*exp(log(qci(i,k,1))*((7./3.)))
782             praut(i,k) = min(praut(i,k),qci(i,k,1)/dtcld)
783           endif
784 !---------------------------------------------------------------
785 ! pracw: accretion of cloud water by rain [HL A40] [LFO 51]
786 !        (C->R)
787 !---------------------------------------------------------------
788           if(qrs(i,k,1).gt.qcrmin.and.qci(i,k,1).gt.qmin) then
789             pracw(i,k) = min(pacrr*rslope3(i,k,1)*rslopeb(i,k,1)       &
790                          *qci(i,k,1)*denfac(i,k),qci(i,k,1)/dtcld)
791           endif
792 !---------------------------------------------------------------
793 ! prevp: evaporation/condensation rate of rain [HDC 14]
794 !        (V->R or R->V)
795 !---------------------------------------------------------------
796           if(qrs(i,k,1).gt.0.) then
797             coeres = rslope2(i,k,1)*sqrt(rslope(i,k,1)*rslopeb(i,k,1))
798             prevp(i,k) = (rh(i,k,1)-1.)*(precr1*rslope2(i,k,1)         &
799                          +precr2*work2(i,k)*coeres)/work1(i,k,1)
800             if(prevp(i,k).lt.0.) then
801               prevp(i,k) = max(prevp(i,k),-qrs(i,k,1)/dtcld)
802               prevp(i,k) = max(prevp(i,k),satdt/2)
803             else
804               prevp(i,k) = min(prevp(i,k),satdt/2)
805             endif
806           endif
807         enddo
808       enddo
809 !
810 !===============================================================
811 !
812 ! cold rain processes
813 !
814 ! - follows the revised ice microphysics processes in HDC
815 ! - the processes same as in RH83 and RH84  and LFO behave
816 !   following ice crystal hapits defined in HDC, inclduing
817 !   intercept parameter for snow (n0s), ice crystal number
818 !   concentration (ni), ice nuclei number concentration
819 !   (n0i), ice diameter (d)
820 !
821 !===============================================================
822 !
823       rdtcld = 1./dtcld
824       do k = kts, kte
825         do i = its, ite
826           supcol = t0c-t(i,k)
827           supsat = max(q(i,k),qmin)-qs(i,k,2)
828           satdt = supsat/dtcld
829           ifsat = 0
830 !-------------------------------------------------------------
831 ! Ni: ice crystal number concentraiton   [HDC 5c]
832 !-------------------------------------------------------------
833 !         xni(i,k) = min(max(5.38e7*(den(i,k)                           &
834 !                      *max(qci(i,k,2),qmin))**0.75,1.e3),1.e6)
835           temp = (den(i,k)*max(qci(i,k,2),qmin))
836           temp = sqrt(sqrt(temp*temp*temp))
837           xni(i,k) = min(max(5.38e7*temp,1.e3),1.e6)
838           eacrs = exp(0.07*(-supcol))
839 !
840           if(supcol.gt.0) then
841             if(qrs(i,k,2).gt.qcrmin.and.qci(i,k,2).gt.qmin) then
842               xmi = den(i,k)*qci(i,k,2)/xni(i,k)
843               diameter  = min(dicon * sqrt(xmi),dimax)
844               vt2i = 1.49e4*diameter**1.31
845               vt2s = pvts*rslopeb(i,k,2)*denfac(i,k)
846 !-------------------------------------------------------------
847 ! psaci: Accretion of cloud ice by rain [HDC 10]
848 !        (T<T0: I->S)
849 !-------------------------------------------------------------
850               acrfac = 2.*rslope3(i,k,2)+2.*diameter*rslope2(i,k,2)     &
851                       +diameter**2*rslope(i,k,2)
852               psaci(i,k) = pi*qci(i,k,2)*eacrs*n0s*n0sfac(i,k)         &
853                            *abs(vt2s-vt2i)*acrfac/4.
854             endif
855 !-------------------------------------------------------------
856 ! psacw: Accretion of cloud water by snow  [HL A7] [LFO 24]
857 !        (T<T0: C->S, and T>=T0: C->R)
858 !-------------------------------------------------------------
859             if(qrs(i,k,2).gt.qcrmin.and.qci(i,k,1).gt.qmin) then
860               psacw(i,k) = min(pacrc*n0sfac(i,k)*rslope3(i,k,2)        &
861                            *rslopeb(i,k,2)*qci(i,k,1)*denfac(i,k)       &
862 !                          ,qci(i,k,1)/dtcld)
863                            ,qci(i,k,1)*rdtcld)
864             endif
865 !-------------------------------------------------------------
866 ! pidep: Deposition/Sublimation rate of ice [HDC 9]
867 !       (T<T0: V->I or I->V)
868 !-------------------------------------------------------------
869             if(qci(i,k,2).gt.0.and.ifsat.ne.1) then
870               xmi = den(i,k)*qci(i,k,2)/xni(i,k)
871               diameter = dicon * sqrt(xmi)
872               pidep(i,k) = 4.*diameter*xni(i,k)*(rh(i,k,2)-1.)/work1(i,k,2)
873               supice = satdt-prevp(i,k)
874               if(pidep(i,k).lt.0.) then
875 !               pidep(i,k) = max(max(pidep(i,k),satdt/2),supice)
876 !               pidep(i,k) = max(pidep(i,k),-qci(i,k,2)/dtcld)
877                 pidep(i,k) = max(max(pidep(i,k),satdt*.5),supice)
878                 pidep(i,k) = max(pidep(i,k),-qci(i,k,2)*rdtcld)
879               else
880 !               pidep(i,k) = min(min(pidep(i,k),satdt/2),supice)
881                 pidep(i,k) = min(min(pidep(i,k),satdt*.5),supice)
882               endif
883               if(abs(prevp(i,k)+pidep(i,k)).ge.abs(satdt)) ifsat = 1
884             endif
885           endif
886 !-------------------------------------------------------------
887 ! psdep: deposition/sublimation rate of snow [HDC 14]
888 !        (V->S or S->V)
889 !-------------------------------------------------------------
890           if(qrs(i,k,2).gt.0..and.ifsat.ne.1) then
891             coeres = rslope2(i,k,2)*sqrt(rslope(i,k,2)*rslopeb(i,k,2))
892             psdep(i,k) = (rh(i,k,2)-1.)*n0sfac(i,k)                    &
893                          *(precs1*rslope2(i,k,2)+precs2                 &
894                          *work2(i,k)*coeres)/work1(i,k,2)
895             supice = satdt-prevp(i,k)-pidep(i,k)
896             if(psdep(i,k).lt.0.) then
897 !             psdep(i,k) = max(psdep(i,k),-qrs(i,k,2)/dtcld)
898 !             psdep(i,k) = max(max(psdep(i,k),satdt/2),supice)
899               psdep(i,k) = max(psdep(i,k),-qrs(i,k,2)*rdtcld)
900               psdep(i,k) = max(max(psdep(i,k),satdt*.5),supice)
901             else
902 !             psdep(i,k) = min(min(psdep(i,k),satdt/2),supice)
903               psdep(i,k) = min(min(psdep(i,k),satdt*.5),supice)
904             endif
905             if(abs(prevp(i,k)+pidep(i,k)+psdep(i,k)).ge.abs(satdt))    &
906               ifsat = 1
907           endif
908 !-------------------------------------------------------------
909 ! pigen: generation(nucleation) of ice from vapor [HL A50] [HDC 7-8]
910 !       (T<T0: V->I)
911 !-------------------------------------------------------------
912           if(supcol.gt.0) then
913             if(supsat.gt.0.and.ifsat.ne.1) then
914               supice = satdt-prevp(i,k)-pidep(i,k)-psdep(i,k)
915               xni0 = 1.e3*exp(0.1*supcol)
916               roqi0 = 4.92e-11*exp(log(xni0)*(1.33))
917               pigen(i,k) = max(0.,(roqi0/den(i,k)-max(qci(i,k,2),0.))    &
918 !                        /dtcld)
919                          *rdtcld)
920               pigen(i,k) = min(min(pigen(i,k),satdt),supice)
921             endif
922 !
923 !-------------------------------------------------------------
924 ! psaut: conversion(aggregation) of ice to snow [HDC 12]
925 !       (T<T0: I->S)
926 !-------------------------------------------------------------
927             if(qci(i,k,2).gt.0.) then
928               qimax = roqimax/den(i,k)
929 !             psaut(i,k) = max(0.,(qci(i,k,2)-qimax)/dtcld)
930               psaut(i,k) = max(0.,(qci(i,k,2)-qimax)*rdtcld)
931             endif
932           endif
933 !-------------------------------------------------------------
934 ! psevp: Evaporation of melting snow [HL A35] [RH83 A27]
935 !       (T>T0: S->V)
936 !-------------------------------------------------------------
937           if(supcol.lt.0.) then
938             if(qrs(i,k,2).gt.0..and.rh(i,k,1).lt.1.)                    &
939               psevp(i,k) = psdep(i,k)*work1(i,k,2)/work1(i,k,1)
940 !              psevp(i,k) = min(max(psevp(i,k),-qrs(i,k,2)/dtcld),0.)
941               psevp(i,k) = min(max(psevp(i,k),-qrs(i,k,2)*rdtcld),0.)
942           endif
943         enddo
944       enddo
945 !
946 !
947 !----------------------------------------------------------------
948 !     check mass conservation of generation terms and feedback to the
949 !     large scale
950 !
951       do k = kts, kte
952         do i = its, ite
953           if(t(i,k).le.t0c) then
954 !
955 !     cloud water
956 !
957             value = max(qmin,qci(i,k,1))
958             source = (praut(i,k)+pracw(i,k)+psacw(i,k))*dtcld
959             if (source.gt.value) then
960               factor = value/source
961               praut(i,k) = praut(i,k)*factor
962               pracw(i,k) = pracw(i,k)*factor
963               psacw(i,k) = psacw(i,k)*factor
964             endif
965 !
966 !     cloud ice
967 !
968             value = max(qmin,qci(i,k,2))
969             source = (psaut(i,k)+psaci(i,k)-pigen(i,k)-pidep(i,k))*dtcld
970             if (source.gt.value) then
971               factor = value/source
972               psaut(i,k) = psaut(i,k)*factor
973               psaci(i,k) = psaci(i,k)*factor
974               pigen(i,k) = pigen(i,k)*factor
975               pidep(i,k) = pidep(i,k)*factor
976             endif
977 !
978             work2(i,k)=-(prevp(i,k)+psdep(i,k)+pigen(i,k)+pidep(i,k))
979 !     update
980             q(i,k) = q(i,k)+work2(i,k)*dtcld
981             qci(i,k,1) = max(qci(i,k,1)-(praut(i,k)+pracw(i,k)         &
982                         +psacw(i,k))*dtcld,0.)
983             qrs(i,k,1) = max(qrs(i,k,1)+(praut(i,k)+pracw(i,k)         &
984                         +prevp(i,k))*dtcld,0.)
985             qci(i,k,2) = max(qci(i,k,2)-(psaut(i,k)+psaci(i,k)         &
986                         -pigen(i,k)-pidep(i,k))*dtcld,0.)
987             qrs(i,k,2) = max(qrs(i,k,2)+(psdep(i,k)+psaut(i,k)         &
988                         +psaci(i,k)+psacw(i,k))*dtcld,0.)
989             xlf = xls-xl(i,k)
990             xlwork2 = -xls*(psdep(i,k)+pidep(i,k)+pigen(i,k))             &
991                       -xl(i,k)*prevp(i,k)-xlf*psacw(i,k)
992             t(i,k) = t(i,k)-xlwork2/cpm(i,k)*dtcld
993           else
994 !
995 !     cloud water
996 !
997             value = max(qmin,qci(i,k,1))
998             source=(praut(i,k)+pracw(i,k)+psacw(i,k))*dtcld
999             if (source.gt.value) then
1000               factor = value/source
1001               praut(i,k) = praut(i,k)*factor
1002               pracw(i,k) = pracw(i,k)*factor
1003               psacw(i,k) = psacw(i,k)*factor
1004             endif
1005 !
1006 !     snow
1007 !
1008             value = max(qcrmin,qrs(i,k,2))
1009             source=(-psevp(i,k))*dtcld
1010             if (source.gt.value) then
1011               factor = value/source
1012               psevp(i,k) = psevp(i,k)*factor
1013             endif
1014             work2(i,k)=-(prevp(i,k)+psevp(i,k))
1015 !     update
1016             q(i,k) = q(i,k)+work2(i,k)*dtcld
1017             qci(i,k,1) = max(qci(i,k,1)-(praut(i,k)+pracw(i,k)        &
1018                         +psacw(i,k))*dtcld,0.)
1019             qrs(i,k,1) = max(qrs(i,k,1)+(praut(i,k)+pracw(i,k)        &
1020                         +prevp(i,k) +psacw(i,k))*dtcld,0.)
1021             qrs(i,k,2) = max(qrs(i,k,2)+psevp(i,k)*dtcld,0.)
1022             xlf = xls-xl(i,k)
1023             xlwork2 = -xl(i,k)*(prevp(i,k)+psevp(i,k))
1024             t(i,k) = t(i,k)-xlwork2/cpm(i,k)*dtcld
1025           endif
1026         enddo
1027       enddo
1028 !
1029 ! Inline expansion for fpvs
1030 !         qs(i,k,1) = fpvs(t(i,k),0,rd,rv,cpv,cliq,cice,xlv0,xls,psat,t0c)
1031 !         qs(i,k,2) = fpvs(t(i,k),1,rd,rv,cpv,cliq,cice,xlv0,xls,psat,t0c)
1032       hsub = xls
1033       hvap = xlv0
1034       cvap = cpv
1035       ttp=t0c+0.01
1036       dldt=cvap-cliq
1037       xa=-dldt/rv
1038       xb=xa+hvap/(rv*ttp)
1039       dldti=cvap-cice
1040       xai=-dldti/rv
1041       xbi=xai+hsub/(rv*ttp)
1042       do k = kts, kte
1043       do i = its, ite
1044           tr=ttp/t(i,k)
1045           logtr = log(tr)
1046           qs(i,k,1)=psat*exp(logtr*(xa)+xb*(1.-tr))
1047           qs(i,k,1) = ep2 * qs(i,k,1) / (p(i,k) - qs(i,k,1))
1048           qs(i,k,1) = max(qs(i,k,1),qmin)
1049           if(t(i,k).lt.ttp) then
1050             qs(i,k,2)=psat*exp(logtr*(xai)+xbi*(1.-tr))
1051           else
1052             qs(i,k,2)=psat*exp(logtr*(xa)+xb*(1.-tr))
1053           endif
1054           qs(i,k,2) = ep2 * qs(i,k,2) / (p(i,k) - qs(i,k,2))
1055           qs(i,k,2) = max(qs(i,k,2),qmin)
1056         enddo
1057       enddo
1058 !
1059 !----------------------------------------------------------------
1060 !  pcond: condensational/evaporational rate of cloud water [HL A46] [RH83 A6]
1061 !     if there exists additional water vapor condensated/if
1062 !     evaporation of cloud water is not enough to remove subsaturation
1063 !
1064       do k = kts, kte
1065         do i = its, ite
1066 !         work1(i,k,1) = conden(t(i,k),q(i,k),qs(i,k,1),xl(i,k),cpm(i,k))
1067           work1(i,k,1) = ((max(q(i,k),qmin)-(qs(i,k,1)))/              & 
1068           (1.+(xl(i,k))*(xl(i,k))/(rv*(cpm(i,k)))*(qs(i,k,1))/((t(i,k))*(t(i,k)))))
1069           work2(i,k) = qci(i,k,1)+work1(i,k,1)
1070           pcond(i,k) = min(max(work1(i,k,1)/dtcld,0.),max(q(i,k),0.)/dtcld)
1071           if(qci(i,k,1).gt.0..and.work1(i,k,1).lt.0.)                   &
1072             pcond(i,k) = max(work1(i,k,1),-qci(i,k,1))/dtcld
1073           q(i,k) = q(i,k)-pcond(i,k)*dtcld
1074           qci(i,k,1) = max(qci(i,k,1)+pcond(i,k)*dtcld,0.)
1075           t(i,k) = t(i,k)+pcond(i,k)*xl(i,k)/cpm(i,k)*dtcld
1076         enddo
1077       enddo
1078 !
1079 !
1080 !----------------------------------------------------------------
1081 !     padding for small values
1082 !
1083       do k = kts, kte
1084         do i = its, ite
1085           if(qci(i,k,1).le.qmin) qci(i,k,1) = 0.0
1086           if(qci(i,k,2).le.qmin) qci(i,k,2) = 0.0
1087         enddo
1088       enddo
1089       enddo                  ! big loops
1090   END SUBROUTINE wsm52d
1091 ! ...................................................................
1092       REAL FUNCTION rgmma(x)
1093 !-------------------------------------------------------------------
1094   IMPLICIT NONE
1095 !-------------------------------------------------------------------
1096 !     rgmma function:  use infinite product form
1097       REAL :: euler
1098       PARAMETER (euler=0.577215664901532)
1099       REAL :: x, y
1100       INTEGER :: i
1101       if(x.eq.1.)then
1102         rgmma=0.
1103           else
1104         rgmma=x*exp(euler*x)
1105         do i=1,10000
1106           y=float(i)
1107           rgmma=rgmma*(1.000+x/y)*exp(-x/y)
1108         enddo
1109         rgmma=1./rgmma
1110       endif
1111       END FUNCTION rgmma
1112 !
1113 !--------------------------------------------------------------------------
1114       REAL FUNCTION fpvs(t,ice,rd,rv,cvap,cliq,cice,hvap,hsub,psat,t0c)
1115 !--------------------------------------------------------------------------
1116       IMPLICIT NONE
1117 !--------------------------------------------------------------------------
1118       REAL t,rd,rv,cvap,cliq,cice,hvap,hsub,psat,t0c,dldt,xa,xb,dldti,   &
1119            xai,xbi,ttp,tr
1120       INTEGER ice
1121 ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
1122       ttp=t0c+0.01
1123       dldt=cvap-cliq
1124       xa=-dldt/rv
1125       xb=xa+hvap/(rv*ttp)
1126       dldti=cvap-cice
1127       xai=-dldti/rv
1128       xbi=xai+hsub/(rv*ttp)
1129       tr=ttp/t
1130       if(t.lt.ttp.and.ice.eq.1) then
1131         fpvs=psat*exp(log(tr)*(xai))*exp(xbi*(1.-tr))
1132       else
1133         fpvs=psat*exp(log(tr)*(xa))*exp(xb*(1.-tr))
1134       endif
1135 ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
1136       END FUNCTION fpvs
1137 !-------------------------------------------------------------------
1138   SUBROUTINE wsm5init(den0,denr,dens,cl,cpv,allowed_to_read)
1139 !-------------------------------------------------------------------
1140   IMPLICIT NONE
1141 !-------------------------------------------------------------------
1142 !.... constants which may not be tunable
1143    REAL, INTENT(IN) :: den0,denr,dens,cl,cpv
1144    LOGICAL, INTENT(IN) :: allowed_to_read
1145    REAL :: pi
1146 !
1147    pi = 4.*atan(1.)
1148    xlv1 = cl-cpv
1149 !
1150    qc0  = 4./3.*pi*denr*r0**3*xncr/den0  ! 0.419e-3 -- .61e-3
1151    qck1 = .104*9.8*peaut/(xncr*denr)**(1./3.)/xmyu*den0**(4./3.) ! 7.03
1152 !
1153    bvtr1 = 1.+bvtr
1154    bvtr2 = 2.5+.5*bvtr
1155    bvtr3 = 3.+bvtr
1156    bvtr4 = 4.+bvtr
1157    g1pbr = rgmma(bvtr1)
1158    g3pbr = rgmma(bvtr3)
1159    g4pbr = rgmma(bvtr4)            ! 17.837825
1160    g5pbro2 = rgmma(bvtr2)          ! 1.8273
1161    pvtr = avtr*g4pbr/6.
1162    eacrr = 1.0
1163    pacrr = pi*n0r*avtr*g3pbr*.25*eacrr
1164    precr1 = 2.*pi*n0r*.78
1165    precr2 = 2.*pi*n0r*.31*avtr**.5*g5pbro2
1166    xm0  = (di0/dicon)**2
1167    xmmax = (dimax/dicon)**2
1168    roqimax = 2.08e22*dimax**8
1169 !
1170    bvts1 = 1.+bvts
1171    bvts2 = 2.5+.5*bvts
1172    bvts3 = 3.+bvts
1173    bvts4 = 4.+bvts
1174    g1pbs = rgmma(bvts1)    !.8875
1175    g3pbs = rgmma(bvts3)
1176    g4pbs = rgmma(bvts4)    ! 12.0786
1177    g5pbso2 = rgmma(bvts2)
1178    pvts = avts*g4pbs/6.
1179    pacrs = pi*n0s*avts*g3pbs*.25
1180    precs1 = 4.*n0s*.65
1181    precs2 = 4.*n0s*.44*avts**.5*g5pbso2
1182    pidn0r =  pi*denr*n0r
1183    pidn0s =  pi*dens*n0s
1184    pacrc = pi*n0s*avts*g3pbs*.25*eacrc
1185 !
1186    rslopermax = 1./lamdarmax
1187    rslopesmax = 1./lamdasmax
1188    rsloperbmax = rslopermax ** bvtr
1189    rslopesbmax = rslopesmax ** bvts
1190    rsloper2max = rslopermax * rslopermax
1191    rslopes2max = rslopesmax * rslopesmax
1192    rsloper3max = rsloper2max * rslopermax
1193    rslopes3max = rslopes2max * rslopesmax
1194 !
1195   END SUBROUTINE wsm5init
1196 END MODULE module_mp_wsm5