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 !
277 !=================================================================
278 !   compute internal functions
279 !
280       cpmcal(x) = cpd*(1.-max(x,qmin))+max(x,qmin)*cpv
281       xlcal(x) = xlv0-xlv1*(x-t0c)
282 !----------------------------------------------------------------
283 !     size distributions: (x=mixing ratio, y=air density):
284 !     valid for mixing ratio > 1.e-9 kg/kg.
285 !
286 ! Optimizatin : A**B => exp(log(A)*(B))
287       lamdar(x,y)=   sqrt(sqrt(pidn0r/(x*y)))      ! (pidn0r/(x*y))**.25
288       lamdas(x,y,z)= sqrt(sqrt(pidn0s*z/(x*y)))    ! (pidn0s*z/(x*y))**.25
289 !
290 !----------------------------------------------------------------
291 !     diffus: diffusion coefficient of the water vapor
292 !     viscos: kinematic viscosity(m2s-1)
293 !     diffus(x,y) = 8.794e-5 * exp(log(x)*(1.81)) / y        ! 8.794e-5*x**1.81/y
294 !     viscos(x,y) = 1.496e-6 * (x*sqrt(x)) /(x+120.)/y  ! 1.496e-6*x**1.5/(x+120.)/y
295 !     xka(x,y) = 1.414e3*viscos(x,y)*y
296 !     diffac(a,b,c,d,e) = d*a*a/(xka(c,d)*rv*c*c)+1./(e*diffus(c,b))
297 !     venfac(a,b,c) = exp(log((viscos(b,c)/diffus(b,a)))*((.3333333)))    &
298 !                    /sqrt(viscos(b,c))*sqrt(sqrt(den0/c))
299 !     conden(a,b,c,d,e) = (max(b,qmin)-c)/(1.+d*d/(rv*e)*c/(a*a))
300 !
301 !
302       pi = 4. * atan(1.)
303 !
304 !----------------------------------------------------------------
305 !     paddint 0 for negative values generated by dynamics
306 !
307       do k = kts, kte
308         do i = its, ite
309           qci(i,k,1) = max(qci(i,k,1),0.0)
310           qrs(i,k,1) = max(qrs(i,k,1),0.0)
311           qci(i,k,2) = max(qci(i,k,2),0.0)
312           qrs(i,k,2) = max(qrs(i,k,2),0.0)
313         enddo
314       enddo
315 !
316 !----------------------------------------------------------------
317 !     latent heat for phase changes and heat capacity. neglect the
318 !     changes during microphysical process calculation
319 !     emanuel(1994)
320 !
321       do k = kts, kte
322         do i = its, ite
323           cpm(i,k) = cpmcal(q(i,k))
324           xl(i,k) = xlcal(t(i,k))
325         enddo
326       enddo
327 !
328 !----------------------------------------------------------------
329 !     compute the minor time steps.
330 !
331       loops = max(nint(delt/dtcldcr),1)
332       dtcld = delt/loops
333       if(delt.le.dtcldcr) dtcld = delt
334 !
335       do loop = 1,loops
336 !
337 !----------------------------------------------------------------
338 !     initialize the large scale variables
339 !
340       do i = its, ite
341         mstep(i) = 1
342         flgcld(i) = .true.
343       enddo
344 !
345 !     do k = kts, kte
346 !       do i = its, ite
347 !         denfac(i,k) = sqrt(den0/den(i,k))
348 !       enddo
349 !     enddo
350       do k = kts, kte
351         CALL VREC( tvec1(its), den(its,k), ite-its+1)
352         do i = its, ite
353           tvec1(i) = tvec1(i)*den0
354         enddo
355         CALL VSQRT( denfac(its,k), tvec1(its), ite-its+1)
356       enddo
357 !
358 ! Inline expansion for fpvs
359 !         qs(i,k,1) = fpvs(t(i,k),0,rd,rv,cpv,cliq,cice,xlv0,xls,psat,t0c)
360 !         qs(i,k,2) = fpvs(t(i,k),1,rd,rv,cpv,cliq,cice,xlv0,xls,psat,t0c)
361       hsub = xls
362       hvap = xlv0
363       cvap = cpv
364       ttp=t0c+0.01
365       dldt=cvap-cliq
366       xa=-dldt/rv
367       xb=xa+hvap/(rv*ttp)
368       dldti=cvap-cice
369       xai=-dldti/rv
370       xbi=xai+hsub/(rv*ttp)
371       do k = kts, kte
372         do i = its, ite
373           tr=ttp/t(i,k)
374           qs(i,k,1)=psat*exp(log(tr)*(xa))*exp(xb*(1.-tr))
375           qs(i,k,1) = ep2 * qs(i,k,1) / (p(i,k) - qs(i,k,1))
376           qs(i,k,1) = max(qs(i,k,1),qmin)
377           rh(i,k,1) = max(q(i,k) / qs(i,k,1),qmin)
378           tr=ttp/t(i,k)
379           if(t(i,k).lt.ttp) then
380             qs(i,k,2)=psat*exp(log(tr)*(xai))*exp(xbi*(1.-tr))
381           else
382             qs(i,k,2)=psat*exp(log(tr)*(xa))*exp(xb*(1.-tr))
383           endif
384           qs(i,k,2) = ep2 * qs(i,k,2) / (p(i,k) - qs(i,k,2))
385           qs(i,k,2) = max(qs(i,k,2),qmin)
386           rh(i,k,2) = max(q(i,k) / qs(i,k,2),qmin)
387         enddo
388       enddo
389 !
390 !----------------------------------------------------------------
391 !     initialize the variables for microphysical physics
392 !
393 !
394       do k = kts, kte
395         do i = its, ite
396           prevp(i,k) = 0.
397           psdep(i,k) = 0.
398           praut(i,k) = 0.
399           psaut(i,k) = 0.
400           pracw(i,k) = 0.
401           psaci(i,k) = 0.
402           psacw(i,k) = 0.
403           pigen(i,k) = 0.
404           pidep(i,k) = 0.
405           pcond(i,k) = 0.
406           psmlt(i,k) = 0.
407           psevp(i,k) = 0.
408           falk(i,k,1) = 0.
409           falk(i,k,2) = 0.
410           fall(i,k,1) = 0.
411           fall(i,k,2) = 0.
412           fallc(i,k) = 0.
413           falkc(i,k) = 0.
414           xni(i,k) = 1.e3
415         enddo
416       enddo
417 !
418 !----------------------------------------------------------------
419 !     compute the fallout term:
420 !     first, vertical terminal velosity for minor loops
421 !
422       do k = kts, kte
423         do i = its, ite
424           supcol = t0c-t(i,k)
425 !---------------------------------------------------------------
426 ! n0s: Intercept parameter for snow [m-4] [HDC 6]
427 !---------------------------------------------------------------
428           n0sfac(i,k) = max(min(exp(alpha*supcol),n0smax/n0s),1.)
429           if(qrs(i,k,1).le.qcrmin)then
430             rslope(i,k,1) = rslopermax
431             rslopeb(i,k,1) = rsloperbmax
432             rslope2(i,k,1) = rsloper2max
433             rslope3(i,k,1) = rsloper3max
434           else
435             rslope(i,k,1) = 1./lamdar(qrs(i,k,1),den(i,k))
436             rslopeb(i,k,1) = exp(log(rslope(i,k,1))*(bvtr))
437             rslope2(i,k,1) = rslope(i,k,1)*rslope(i,k,1)
438             rslope3(i,k,1) = rslope2(i,k,1)*rslope(i,k,1)
439           endif
440           if(qrs(i,k,2).le.qcrmin)then
441             rslope(i,k,2) = rslopesmax
442             rslopeb(i,k,2) = rslopesbmax
443             rslope2(i,k,2) = rslopes2max
444             rslope3(i,k,2) = rslopes3max
445           else
446             rslope(i,k,2) = 1./lamdas(qrs(i,k,2),den(i,k),n0sfac(i,k))
447             rslopeb(i,k,2) = exp(log(rslope(i,k,2))*(bvts))
448             rslope2(i,k,2) = rslope(i,k,2)*rslope(i,k,2)
449             rslope3(i,k,2) = rslope2(i,k,2)*rslope(i,k,2)
450           endif
451 !-------------------------------------------------------------
452 ! Ni: ice crystal number concentraiton   [HDC 5c]
453 !-------------------------------------------------------------
454 !         xni(i,k) = min(max(5.38e7*(den(i,k)                           &
455 !                   *max(qci(i,k,2),qmin))**0.75,1.e3),1.e6)
456           temp = (den(i,k)*max(qci(i,k,2),qmin))
457           temp = sqrt(sqrt(temp*temp*temp))
458           xni(i,k) = min(max(5.38e7*temp,1.e3),1.e6)
459         enddo
460       enddo
461 !
462       mstepmax = 1
463       numdt = 1
464       do k = kte, kts, -1
465         do i = its, ite
466           work1(i,k,1) = pvtr*rslopeb(i,k,1)*denfac(i,k)/delz(i,k)
467           work1(i,k,2) = pvts*rslopeb(i,k,2)*denfac(i,k)/delz(i,k)
468           numdt(i) = max(nint(max(work1(i,k,1),work1(i,k,2))*dtcld+.5),1)
469           if(numdt(i).ge.mstep(i)) mstep(i) = numdt(i)
470         enddo
471       enddo
472       do i = its, ite
473         if(mstepmax.le.mstep(i)) mstepmax = mstep(i)
474         rmstep(i) = 1./mstep(i)
475       enddo
476 !
477       do n = 1, mstepmax
478         k = kte
479         do i = its, ite
480           if(n.le.mstep(i)) then
481 !             falk(i,k,1) = den(i,k)*qrs(i,k,1)*work1(i,k,1)/mstep(i)
482 !             falk(i,k,2) = den(i,k)*qrs(i,k,2)*work1(i,k,2)/mstep(i)
483               falk(i,k,1) = den(i,k)*qrs(i,k,1)*work1(i,k,1)*rmstep(i)
484               falk(i,k,2) = den(i,k)*qrs(i,k,2)*work1(i,k,2)*rmstep(i)
485               fall(i,k,1) = fall(i,k,1)+falk(i,k,1)
486               fall(i,k,2) = fall(i,k,2)+falk(i,k,2)
487 !             qrs(i,k,1) = max(qrs(i,k,1)-falk(i,k,1)*dtcld/den(i,k),0.)
488 !             qrs(i,k,2) = max(qrs(i,k,2)-falk(i,k,2)*dtcld/den(i,k),0.)
489               dtcldden = dtcld/den(i,k)
490               qrs(i,k,1) = max(qrs(i,k,1)-falk(i,k,1)*dtcldden,0.)
491               qrs(i,k,2) = max(qrs(i,k,2)-falk(i,k,2)*dtcldden,0.)
492             endif
493           enddo
494         do k = kte-1, kts, -1
495           do i = its, ite
496             if(n.le.mstep(i)) then
497 !             falk(i,k,1) = den(i,k)*qrs(i,k,1)*work1(i,k,1)/mstep(i)
498 !             falk(i,k,2) = den(i,k)*qrs(i,k,2)*work1(i,k,2)/mstep(i)
499               falk(i,k,1) = den(i,k)*qrs(i,k,1)*work1(i,k,1)*rmstep(i)
500               falk(i,k,2) = den(i,k)*qrs(i,k,2)*work1(i,k,2)*rmstep(i)
501               fall(i,k,1) = fall(i,k,1)+falk(i,k,1)
502               fall(i,k,2) = fall(i,k,2)+falk(i,k,2)
503 !             qrs(i,k,1) = max(qrs(i,k,1)-(falk(i,k,1)-falk(i,k+1,1)    &
504 !                         *delz(i,k+1)/delz(i,k))*dtcld/den(i,k),0.)
505 !             qrs(i,k,2) = max(qrs(i,k,2)-(falk(i,k,2)-falk(i,k+1,2)    &
506 !                         *delz(i,k+1)/delz(i,k))*dtcld/den(i,k),0.)
507               dtcldden = dtcld/den(i,k)
508               rdelz = 1./delz(i,k)
509               qrs(i,k,1) = max(qrs(i,k,1)-(falk(i,k,1)-falk(i,k+1,1)    &
510                           *delz(i,k+1)*rdelz)*dtcldden,0.)
511               qrs(i,k,2) = max(qrs(i,k,2)-(falk(i,k,2)-falk(i,k+1,2)    &
512                           *delz(i,k+1)*rdelz)*dtcldden,0.)
513             endif
514           enddo
515         enddo
516         do k = kte, kts, -1
517           do i = its, ite
518             if(n.le.mstep(i)) then
519               if(t(i,k).gt.t0c.and.qrs(i,k,2).gt.0.) then
520 !----------------------------------------------------------------
521 ! psmlt: melting of snow [HL A33] [RH83 A25]
522 !       (T>T0: S->R)
523 !----------------------------------------------------------------
524                 xlf = xlf0
525 !               work2(i,k)= venfac(p(i,k),t(i,k),den(i,k))
526                 work2(i,k)= (exp(log(((1.496e-6*((t(i,k))*sqrt(t(i,k))) &
527                             /((t(i,k))+120.)/(den(i,k)))/(8.794e-5      &
528                             *exp(log(t(i,k))*(1.81))/p(i,k))))          &
529                             *((.3333333)))/sqrt((1.496e-6*((t(i,k))     &
530                             *sqrt(t(i,k)))/((t(i,k))+120.)/(den(i,k)))) &
531                             *sqrt(sqrt(den0/(den(i,k)))))
532                 coeres = rslope2(i,k,2)*sqrt(rslope(i,k,2)*rslopeb(i,k,2))
533 !               psmlt(i,k) = xka(t(i,k),den(i,k))/xlf*(t0c-t(i,k))*pi/2. &
534 !                           *n0sfac(i,k)*(precs1*rslope2(i,k,2)+precs2  &
535 !                           *work2(i,k)*coeres)
536                 psmlt(i,k) = &
537 (1.414e3*(1.496e-6 * ((t(i,k))*sqrt(t(i,k))) /((t(i,k))+120.)/(den(i,k)) )*(den(i,k)))&
538                             /xlf*(t0c-t(i,k))*pi/2.                     &
539                             *n0sfac(i,k)*(precs1*rslope2(i,k,2)+precs2  &
540                             *work2(i,k)*coeres)
541                 psmlt(i,k) = min(max(psmlt(i,k)*dtcld/mstep(i),           &
542                             -qrs(i,k,2)/mstep(i)),0.)
543                 qrs(i,k,2) = qrs(i,k,2) + psmlt(i,k)
544                 qrs(i,k,1) = qrs(i,k,1) - psmlt(i,k)
545                 t(i,k) = t(i,k) + xlf/cpm(i,k)*psmlt(i,k)
546               endif
547             endif
548           enddo
549         enddo
550       enddo
551 !---------------------------------------------------------------
552 ! Vice [ms-1] : fallout of ice crystal [HDC 5a]
553 !---------------------------------------------------------------
554       mstepmax = 1
555       mstep = 1
556       numdt = 1
557       do k = kte, kts, -1
558         do i = its, ite
559           if(qci(i,k,2).le.0.) then
560             work2c(i,k) = 0.
561           else
562             xmi = den(i,k)*qci(i,k,2)/xni(i,k)
563 !           diameter  = min(dicon * sqrt(xmi),dimax)
564             diameter  = max(min(dicon * sqrt(xmi),dimax), 1.e-25)
565             work1c(i,k) = 1.49e4*exp(log(diameter)*(1.31))
566             work2c(i,k) = work1c(i,k)/delz(i,k)
567           endif
568           numdt(i) = max(nint(work2c(i,k)*dtcld+.5),1)
569           if(numdt(i).ge.mstep(i)) mstep(i) = numdt(i)
570         enddo
571       enddo
572       do i = its, ite
573         if(mstepmax.le.mstep(i)) mstepmax = mstep(i)
574       enddo
575 !
576       do n = 1, mstepmax
577         k = kte
578         do i = its, ite
579           if(n.le.mstep(i)) then
580             falkc(i,k) = den(i,k)*qci(i,k,2)*work2c(i,k)/mstep(i)
581             holdc = falkc(i,k)
582             fallc(i,k) = fallc(i,k)+falkc(i,k)
583             holdci = qci(i,k,2)
584             qci(i,k,2) = max(qci(i,k,2)-falkc(i,k)*dtcld/den(i,k),0.)
585           endif
586         enddo
587         do k = kte-1, kts, -1
588           do i = its, ite
589             if(n.le.mstep(i)) then
590               falkc(i,k) = den(i,k)*qci(i,k,2)*work2c(i,k)/mstep(i)
591               holdc = falkc(i,k)
592               fallc(i,k) = fallc(i,k)+falkc(i,k)
593               holdci = qci(i,k,2)
594               qci(i,k,2) = max(qci(i,k,2)-(falkc(i,k)-falkc(i,k+1)      &
595                           *delz(i,k+1)/delz(i,k))*dtcld/den(i,k),0.)
596             endif
597           enddo
598         enddo
599       enddo
600 !
601 !
602 !----------------------------------------------------------------
603 !      rain (unit is mm/sec;kgm-2s-1: /1000*delt ===> m)==> mm for wrf
604 !
605       do i = its, ite
606         fallsum = fall(i,1,1)+fall(i,1,2)+fallc(i,1)
607         fallsum_qsi = fall(i,1,2)+fallc(i,1)
608         rainncv(i) = 0.
609         if(fallsum.gt.0.) then
610           rainncv(i) = fallsum*delz(i,1)/denr*dtcld*1000.
611           rain(i) = fallsum*delz(i,1)/denr*dtcld*1000. + rain(i)
612         endif
613         IF ( PRESENT (snowncv) .AND. PRESENT (snow)) THEN
614         snowncv(i) = 0.
615         if(fallsum_qsi.gt.0.) then
616           snowncv(i) = fallsum_qsi*delz(i,kts)/denr*dtcld*1000.
617           snow(i) = fallsum_qsi*delz(i,kts)/denr*dtcld*1000. + snow(i)
618         endif
619         ENDIF
620         sr(i) = 0.
621         if(fallsum.gt.0.)sr(i)=fallsum_qsi*delz(i,kts)/denr*dtcld*1000./(rainncv(i)+1.e-12)
622       enddo
623 !
624 !---------------------------------------------------------------
625 ! pimlt: instantaneous melting of cloud ice [HL A47] [RH83 A28]
626 !       (T>T0: I->C)
627 !---------------------------------------------------------------
628       do k = kts, kte
629         do i = its, ite
630           supcol = t0c-t(i,k)
631           xlf = xls-xl(i,k)
632           if(supcol.lt.0.) xlf = xlf0
633           if(supcol.lt.0.and.qci(i,k,2).gt.0.) then
634             qci(i,k,1) = qci(i,k,1) + qci(i,k,2)
635             t(i,k) = t(i,k) - xlf/cpm(i,k)*qci(i,k,2)
636             qci(i,k,2) = 0.
637           endif
638 !---------------------------------------------------------------
639 ! pihmf: homogeneous freezing of cloud water below -40c [HL A45]
640 !        (T<-40C: C->I)
641 !---------------------------------------------------------------
642           if(supcol.gt.40..and.qci(i,k,1).gt.0.) then
643             qci(i,k,2) = qci(i,k,2) + qci(i,k,1)
644             t(i,k) = t(i,k) + xlf/cpm(i,k)*qci(i,k,1)
645             qci(i,k,1) = 0.
646           endif
647 !---------------------------------------------------------------
648 ! pihtf: heterogeneous freezing of cloud water [HL A44]
649 !        (T0>T>-40C: C->I)
650 !---------------------------------------------------------------
651           if(supcol.gt.0..and.qci(i,k,1).gt.0.) then
652 !           pfrzdtc = min(pfrz1*(exp(pfrz2*supcol)-1.)                  &
653 !              *den(i,k)/denr/xncr*qci(i,k,1)**2*dtcld,qci(i,k,1))
654             pfrzdtc = min(pfrz1*(exp(pfrz2*supcol)-1.)                  &
655             *den(i,k)/denr/xncr*qci(i,k,1)*qci(i,k,1)*dtcld,qci(i,k,1))
656             qci(i,k,2) = qci(i,k,2) + pfrzdtc
657             t(i,k) = t(i,k) + xlf/cpm(i,k)*pfrzdtc
658             qci(i,k,1) = qci(i,k,1)-pfrzdtc
659           endif
660 !---------------------------------------------------------------
661 ! psfrz: freezing of rain water [HL A20] [LFO 45]
662 !        (T<T0, R->S)
663 !---------------------------------------------------------------
664           if(supcol.gt.0..and.qrs(i,k,1).gt.0.) then
665 !           pfrzdtr = min(20.*pi**2*pfrz1*n0r*denr/den(i,k)             &
666 !                 *(exp(pfrz2*supcol)-1.)*rslope(i,k,1)**7*dtcld,       &
667 !                 qrs(i,k,1))
668             temp = rslope(i,k,1)
669             temp = temp*temp*temp*temp*temp*temp*temp
670             pfrzdtr = min(20.*(pi*pi)*pfrz1*n0r*denr/den(i,k)             &
671                   *(exp(pfrz2*supcol)-1.)*temp*dtcld,                   &
672                   qrs(i,k,1))
673             qrs(i,k,2) = qrs(i,k,2) + pfrzdtr
674             t(i,k) = t(i,k) + xlf/cpm(i,k)*pfrzdtr
675             qrs(i,k,1) = qrs(i,k,1)-pfrzdtr
676           endif
677         enddo
678       enddo
679 !
680 !----------------------------------------------------------------
681 !     rsloper: reverse of the slope parameter of the rain(m)
682 !     xka:    thermal conductivity of air(jm-1s-1k-1)
683 !     work1:  the thermodynamic term in the denominator associated with
684 !             heat conduction and vapor diffusion
685 !             (ry88, y93, h85)
686 !     work2: parameter associated with the ventilation effects(y93)
687 !
688       do k = kts, kte
689         do i = its, ite
690           if(qrs(i,k,1).le.qcrmin)then
691             rslope(i,k,1) = rslopermax
692             rslopeb(i,k,1) = rsloperbmax
693             rslope2(i,k,1) = rsloper2max
694             rslope3(i,k,1) = rsloper3max
695           else
696 !           rslope(i,k,1) = 1./lamdar(qrs(i,k,1),den(i,k))
697             rslope(i,k,1) = 1./(sqrt(sqrt(pidn0r/((qrs(i,k,1))*(den(i,k))))))
698             rslopeb(i,k,1) = exp(log(rslope(i,k,1))*(bvtr))
699             rslope2(i,k,1) = rslope(i,k,1)*rslope(i,k,1)
700             rslope3(i,k,1) = rslope2(i,k,1)*rslope(i,k,1)
701           endif
702           if(qrs(i,k,2).le.qcrmin)then
703             rslope(i,k,2) = rslopesmax
704             rslopeb(i,k,2) = rslopesbmax
705             rslope2(i,k,2) = rslopes2max
706             rslope3(i,k,2) = rslopes3max
707           else
708 !            rslope(i,k,2) = 1./lamdas(qrs(i,k,2),den(i,k),n0sfac(i,k))
709             rslope(i,k,2) = 1./(sqrt(sqrt(pidn0s*(n0sfac(i,k))/((qrs(i,k,2))*(den(i,k))))))
710             rslopeb(i,k,2) = exp(log(rslope(i,k,2))*(bvts))
711             rslope2(i,k,2) = rslope(i,k,2)*rslope(i,k,2)
712             rslope3(i,k,2) = rslope2(i,k,2)*rslope(i,k,2)
713           endif
714         enddo
715       enddo
716 !
717       do k = kts, kte
718         do i = its, ite
719 !         work1(i,k,1) = diffac(xl(i,k),p(i,k),t(i,k),den(i,k),qs(i,k,1))
720           work1(i,k,1) =                                                     &
721         ((((den(i,k))*(xl(i,k))*(xl(i,k))) * ((t(i,k))+120.) * (den(i,k)))   &
722            /                                                                 &
723          ( 1.414e3 * (1.496e-6 * ((t(i,k))*sqrt(t(i,k)))) * (den(i,k)) *     &
724                                                    (rv*(t(i,k))*(t(i,k)))))  &
725         +                                                                    &
726         p(i,k) / ( (qs(i,k,1)) * ( 8.794e-5 * exp(log(t(i,k))*(1.81)) ) )
727 !         work1(i,k,2) = diffac(xls,p(i,k),t(i,k),den(i,k),qs(i,k,2))
728           work1(i,k,2) =                                                     &
729         (                                                                    &
730          (((den(i,k))*(xls)*(xls))*((t(i,k))+120.)*(den(i,k)))               &
731            /                                                                 &
732           (                                                                  &
733          1.414e3 * (1.496e-6 * ((t(i,k))*sqrt(t(i,k)))) * (den(i,k)) *       &
734                                                    (rv*(t(i,k))*(t(i,k)))    &
735           )                                                                  &
736           +                                                                  &
737          p(i,k)                                                              &
738           /                                                                  &
739          ( qs(i,k,2) * (8.794e-5 * exp(log(t(i,k))*(1.81))))                 &
740         )
741 !         work2(i,k) = venfac(p(i,k),t(i,k),den(i,k))
742           work2(i,k) =                                                       &
743         (                                                                    &
744          exp(.3333333*log(                                                   &
745              ((1.496e-6 * ((t(i,k))*sqrt(t(i,k))))*p(i,k))                   &
746                 /                                                            &
747              (((t(i,k))+120.)*den(i,k)*(8.794e-5 * exp(log(t(i,k))*(1.81)))) &
748            ))                                                                &
749            *                                                                 &
750            sqrt(sqrt(den0/(den(i,k))))                                       &
751         )                                                                    &
752         /                                                                    &
753         sqrt(                                                                &
754            (1.496e-6 * ((t(i,k))*sqrt(t(i,k))))                              &
755              /                                                               &
756            (                                                                 &
757             ((t(i,k))+120.) * den(i,k)                                       &
758            )                                                                 &
759         )
760         ENDDO
761       ENDDO
762 !
763 !===============================================================
764 !
765 ! warm rain processes
766 !
767 ! - follows the processes in RH83 and LFO except for autoconcersion
768 !
769 !===============================================================
770 !
771       do k = kts, kte
772         do i = its, ite
773           supsat = max(q(i,k),qmin)-qs(i,k,1)
774           satdt = supsat/dtcld
775 !---------------------------------------------------------------
776 ! praut: auto conversion rate from cloud to rain [HDC 16]
777 !        (C->R)
778 !---------------------------------------------------------------
779           if(qci(i,k,1).gt.qc0) then
780             praut(i,k) = qck1*exp(log(qci(i,k,1))*((7./3.)))
781             praut(i,k) = min(praut(i,k),qci(i,k,1)/dtcld)
782           endif
783 !---------------------------------------------------------------
784 ! pracw: accretion of cloud water by rain [HL A40] [LFO 51]
785 !        (C->R)
786 !---------------------------------------------------------------
787           if(qrs(i,k,1).gt.qcrmin.and.qci(i,k,1).gt.qmin) then
788             pracw(i,k) = min(pacrr*rslope3(i,k,1)*rslopeb(i,k,1)       &
789                          *qci(i,k,1)*denfac(i,k),qci(i,k,1)/dtcld)
790           endif
791 !---------------------------------------------------------------
792 ! prevp: evaporation/condensation rate of rain [HDC 14]
793 !        (V->R or R->V)
794 !---------------------------------------------------------------
795           if(qrs(i,k,1).gt.0.) then
796             coeres = rslope2(i,k,1)*sqrt(rslope(i,k,1)*rslopeb(i,k,1))
797             prevp(i,k) = (rh(i,k,1)-1.)*(precr1*rslope2(i,k,1)         &
798                          +precr2*work2(i,k)*coeres)/work1(i,k,1)
799             if(prevp(i,k).lt.0.) then
800               prevp(i,k) = max(prevp(i,k),-qrs(i,k,1)/dtcld)
801               prevp(i,k) = max(prevp(i,k),satdt/2)
802             else
803               prevp(i,k) = min(prevp(i,k),satdt/2)
804             endif
805           endif
806         enddo
807       enddo
808 !
809 !===============================================================
810 !
811 ! cold rain processes
812 !
813 ! - follows the revised ice microphysics processes in HDC
814 ! - the processes same as in RH83 and RH84  and LFO behave
815 !   following ice crystal hapits defined in HDC, inclduing
816 !   intercept parameter for snow (n0s), ice crystal number
817 !   concentration (ni), ice nuclei number concentration
818 !   (n0i), ice diameter (d)
819 !
820 !===============================================================
821 !
822       rdtcld = 1./dtcld
823       do k = kts, kte
824         do i = its, ite
825           supcol = t0c-t(i,k)
826           supsat = max(q(i,k),qmin)-qs(i,k,2)
827           satdt = supsat/dtcld
828           ifsat = 0
829 !-------------------------------------------------------------
830 ! Ni: ice crystal number concentraiton   [HDC 5c]
831 !-------------------------------------------------------------
832 !         xni(i,k) = min(max(5.38e7*(den(i,k)                           &
833 !                      *max(qci(i,k,2),qmin))**0.75,1.e3),1.e6)
834           temp = (den(i,k)*max(qci(i,k,2),qmin))
835           temp = sqrt(sqrt(temp*temp*temp))
836           xni(i,k) = min(max(5.38e7*temp,1.e3),1.e6)
837           eacrs = exp(0.07*(-supcol))
838 !
839           if(supcol.gt.0) then
840             if(qrs(i,k,2).gt.qcrmin.and.qci(i,k,2).gt.qmin) then
841               xmi = den(i,k)*qci(i,k,2)/xni(i,k)
842               diameter  = min(dicon * sqrt(xmi),dimax)
843               vt2i = 1.49e4*diameter**1.31
844               vt2s = pvts*rslopeb(i,k,2)*denfac(i,k)
845 !-------------------------------------------------------------
846 ! psaci: Accretion of cloud ice by rain [HDC 10]
847 !        (T<T0: I->S)
848 !-------------------------------------------------------------
849               acrfac = 2.*rslope3(i,k,2)+2.*diameter*rslope2(i,k,2)     &
850                       +diameter**2*rslope(i,k,2)
851               psaci(i,k) = pi*qci(i,k,2)*eacrs*n0s*n0sfac(i,k)         &
852                            *abs(vt2s-vt2i)*acrfac/4.
853             endif
854 !-------------------------------------------------------------
855 ! psacw: Accretion of cloud water by snow  [HL A7] [LFO 24]
856 !        (T<T0: C->S, and T>=T0: C->R)
857 !-------------------------------------------------------------
858             if(qrs(i,k,2).gt.qcrmin.and.qci(i,k,1).gt.qmin) then
859               psacw(i,k) = min(pacrc*n0sfac(i,k)*rslope3(i,k,2)        &
860                            *rslopeb(i,k,2)*qci(i,k,1)*denfac(i,k)       &
861 !                          ,qci(i,k,1)/dtcld)
862                            ,qci(i,k,1)*rdtcld)
863             endif
864 !-------------------------------------------------------------
865 ! pidep: Deposition/Sublimation rate of ice [HDC 9]
866 !       (T<T0: V->I or I->V)
867 !-------------------------------------------------------------
868             if(qci(i,k,2).gt.0.and.ifsat.ne.1) then
869               xmi = den(i,k)*qci(i,k,2)/xni(i,k)
870               diameter = dicon * sqrt(xmi)
871               pidep(i,k) = 4.*diameter*xni(i,k)*(rh(i,k,2)-1.)/work1(i,k,2)
872               supice = satdt-prevp(i,k)
873               if(pidep(i,k).lt.0.) then
874 !               pidep(i,k) = max(max(pidep(i,k),satdt/2),supice)
875 !               pidep(i,k) = max(pidep(i,k),-qci(i,k,2)/dtcld)
876                 pidep(i,k) = max(max(pidep(i,k),satdt*.5),supice)
877                 pidep(i,k) = max(pidep(i,k),-qci(i,k,2)*rdtcld)
878               else
879 !               pidep(i,k) = min(min(pidep(i,k),satdt/2),supice)
880                 pidep(i,k) = min(min(pidep(i,k),satdt*.5),supice)
881               endif
882               if(abs(prevp(i,k)+pidep(i,k)).ge.abs(satdt)) ifsat = 1
883             endif
884           endif
885 !-------------------------------------------------------------
886 ! psdep: deposition/sublimation rate of snow [HDC 14]
887 !        (V->S or S->V)
888 !-------------------------------------------------------------
889           if(qrs(i,k,2).gt.0..and.ifsat.ne.1) then
890             coeres = rslope2(i,k,2)*sqrt(rslope(i,k,2)*rslopeb(i,k,2))
891             psdep(i,k) = (rh(i,k,2)-1.)*n0sfac(i,k)                    &
892                          *(precs1*rslope2(i,k,2)+precs2                 &
893                          *work2(i,k)*coeres)/work1(i,k,2)
894             supice = satdt-prevp(i,k)-pidep(i,k)
895             if(psdep(i,k).lt.0.) then
896 !             psdep(i,k) = max(psdep(i,k),-qrs(i,k,2)/dtcld)
897 !             psdep(i,k) = max(max(psdep(i,k),satdt/2),supice)
898               psdep(i,k) = max(psdep(i,k),-qrs(i,k,2)*rdtcld)
899               psdep(i,k) = max(max(psdep(i,k),satdt*.5),supice)
900             else
901 !             psdep(i,k) = min(min(psdep(i,k),satdt/2),supice)
902               psdep(i,k) = min(min(psdep(i,k),satdt*.5),supice)
903             endif
904             if(abs(prevp(i,k)+pidep(i,k)+psdep(i,k)).ge.abs(satdt))    &
905               ifsat = 1
906           endif
907 !-------------------------------------------------------------
908 ! pigen: generation(nucleation) of ice from vapor [HL A50] [HDC 7-8]
909 !       (T<T0: V->I)
910 !-------------------------------------------------------------
911           if(supcol.gt.0) then
912             if(supsat.gt.0.and.ifsat.ne.1) then
913               supice = satdt-prevp(i,k)-pidep(i,k)-psdep(i,k)
914               xni0 = 1.e3*exp(0.1*supcol)
915               roqi0 = 4.92e-11*exp(log(xni0)*(1.33))
916               pigen(i,k) = max(0.,(roqi0/den(i,k)-max(qci(i,k,2),0.))    &
917 !                        /dtcld)
918                          *rdtcld)
919               pigen(i,k) = min(min(pigen(i,k),satdt),supice)
920             endif
921 !
922 !-------------------------------------------------------------
923 ! psaut: conversion(aggregation) of ice to snow [HDC 12]
924 !       (T<T0: I->S)
925 !-------------------------------------------------------------
926             if(qci(i,k,2).gt.0.) then
927               qimax = roqimax/den(i,k)
928 !             psaut(i,k) = max(0.,(qci(i,k,2)-qimax)/dtcld)
929               psaut(i,k) = max(0.,(qci(i,k,2)-qimax)*rdtcld)
930             endif
931           endif
932 !-------------------------------------------------------------
933 ! psevp: Evaporation of melting snow [HL A35] [RH83 A27]
934 !       (T>T0: S->V)
935 !-------------------------------------------------------------
936           if(supcol.lt.0.) then
937             if(qrs(i,k,2).gt.0..and.rh(i,k,1).lt.1.)                    &
938               psevp(i,k) = psdep(i,k)*work1(i,k,2)/work1(i,k,1)
939 !              psevp(i,k) = min(max(psevp(i,k),-qrs(i,k,2)/dtcld),0.)
940               psevp(i,k) = min(max(psevp(i,k),-qrs(i,k,2)*rdtcld),0.)
941           endif
942         enddo
943       enddo
944 !
945 !
946 !----------------------------------------------------------------
947 !     check mass conservation of generation terms and feedback to the
948 !     large scale
949 !
950       do k = kts, kte
951         do i = its, ite
952           if(t(i,k).le.t0c) then
953 !
954 !     cloud water
955 !
956             value = max(qmin,qci(i,k,1))
957             source = (praut(i,k)+pracw(i,k)+psacw(i,k))*dtcld
958             if (source.gt.value) then
959               factor = value/source
960               praut(i,k) = praut(i,k)*factor
961               pracw(i,k) = pracw(i,k)*factor
962               psacw(i,k) = psacw(i,k)*factor
963             endif
964 !
965 !     cloud ice
966 !
967             value = max(qmin,qci(i,k,2))
968             source = (psaut(i,k)+psaci(i,k)-pigen(i,k)-pidep(i,k))*dtcld
969             if (source.gt.value) then
970               factor = value/source
971               psaut(i,k) = psaut(i,k)*factor
972               psaci(i,k) = psaci(i,k)*factor
973               pigen(i,k) = pigen(i,k)*factor
974               pidep(i,k) = pidep(i,k)*factor
975             endif
976 !
977             work2(i,k)=-(prevp(i,k)+psdep(i,k)+pigen(i,k)+pidep(i,k))
978 !     update
979             q(i,k) = q(i,k)+work2(i,k)*dtcld
980             qci(i,k,1) = max(qci(i,k,1)-(praut(i,k)+pracw(i,k)         &
981                         +psacw(i,k))*dtcld,0.)
982             qrs(i,k,1) = max(qrs(i,k,1)+(praut(i,k)+pracw(i,k)         &
983                         +prevp(i,k))*dtcld,0.)
984             qci(i,k,2) = max(qci(i,k,2)-(psaut(i,k)+psaci(i,k)         &
985                         -pigen(i,k)-pidep(i,k))*dtcld,0.)
986             qrs(i,k,2) = max(qrs(i,k,2)+(psdep(i,k)+psaut(i,k)         &
987                         +psaci(i,k)+psacw(i,k))*dtcld,0.)
988             xlf = xls-xl(i,k)
989             xlwork2 = -xls*(psdep(i,k)+pidep(i,k)+pigen(i,k))             &
990                       -xl(i,k)*prevp(i,k)-xlf*psacw(i,k)
991             t(i,k) = t(i,k)-xlwork2/cpm(i,k)*dtcld
992           else
993 !
994 !     cloud water
995 !
996             value = max(qmin,qci(i,k,1))
997             source=(praut(i,k)+pracw(i,k)+psacw(i,k))*dtcld
998             if (source.gt.value) then
999               factor = value/source
1000               praut(i,k) = praut(i,k)*factor
1001               pracw(i,k) = pracw(i,k)*factor
1002               psacw(i,k) = psacw(i,k)*factor
1003             endif
1004 !
1005 !     snow
1006 !
1007             value = max(qcrmin,qrs(i,k,2))
1008             source=(-psevp(i,k))*dtcld
1009             if (source.gt.value) then
1010               factor = value/source
1011               psevp(i,k) = psevp(i,k)*factor
1012             endif
1013             work2(i,k)=-(prevp(i,k)+psevp(i,k))
1014 !     update
1015             q(i,k) = q(i,k)+work2(i,k)*dtcld
1016             qci(i,k,1) = max(qci(i,k,1)-(praut(i,k)+pracw(i,k)        &
1017                         +psacw(i,k))*dtcld,0.)
1018             qrs(i,k,1) = max(qrs(i,k,1)+(praut(i,k)+pracw(i,k)        &
1019                         +prevp(i,k) +psacw(i,k))*dtcld,0.)
1020             qrs(i,k,2) = max(qrs(i,k,2)+psevp(i,k)*dtcld,0.)
1021             xlf = xls-xl(i,k)
1022             xlwork2 = -xl(i,k)*(prevp(i,k)+psevp(i,k))
1023             t(i,k) = t(i,k)-xlwork2/cpm(i,k)*dtcld
1024           endif
1025         enddo
1026       enddo
1027 !
1028 ! Inline expansion for fpvs
1029 !         qs(i,k,1) = fpvs(t(i,k),0,rd,rv,cpv,cliq,cice,xlv0,xls,psat,t0c)
1030 !         qs(i,k,2) = fpvs(t(i,k),1,rd,rv,cpv,cliq,cice,xlv0,xls,psat,t0c)
1031       hsub = xls
1032       hvap = xlv0
1033       cvap = cpv
1034       ttp=t0c+0.01
1035       dldt=cvap-cliq
1036       xa=-dldt/rv
1037       xb=xa+hvap/(rv*ttp)
1038       dldti=cvap-cice
1039       xai=-dldti/rv
1040       xbi=xai+hsub/(rv*ttp)
1041       do k = kts, kte
1042         do i = its, ite
1043           tr=ttp/t(i,k)
1044           qs(i,k,1)=psat*exp(log(tr)*(xa))*exp(xb*(1.-tr))
1045           qs(i,k,1) = ep2 * qs(i,k,1) / (p(i,k) - qs(i,k,1))
1046           qs(i,k,1) = max(qs(i,k,1),qmin)
1047           tr=ttp/t(i,k)
1048           if(t(i,k).lt.ttp) then
1049             qs(i,k,2)=psat*exp(log(tr)*(xai))*exp(xbi*(1.-tr))
1050           else
1051             qs(i,k,2)=psat*exp(log(tr)*(xa))*exp(xb*(1.-tr))
1052           endif
1053           qs(i,k,2) = ep2 * qs(i,k,2) / (p(i,k) - qs(i,k,2))
1054           qs(i,k,2) = max(qs(i,k,2),qmin)
1055         enddo
1056       enddo
1057 !
1058 !----------------------------------------------------------------
1059 !  pcond: condensational/evaporational rate of cloud water [HL A46] [RH83 A6]
1060 !     if there exists additional water vapor condensated/if
1061 !     evaporation of cloud water is not enough to remove subsaturation
1062 !
1063       do k = kts, kte
1064         do i = its, ite
1065 !         work1(i,k,1) = conden(t(i,k),q(i,k),qs(i,k,1),xl(i,k),cpm(i,k))
1066           work1(i,k,1) = ((max(q(i,k),qmin)-(qs(i,k,1)))/              & 
1067           (1.+(xl(i,k))*(xl(i,k))/(rv*(cpm(i,k)))*(qs(i,k,1))/((t(i,k))*(t(i,k)))))
1068           work2(i,k) = qci(i,k,1)+work1(i,k,1)
1069           pcond(i,k) = min(max(work1(i,k,1)/dtcld,0.),max(q(i,k),0.)/dtcld)
1070           if(qci(i,k,1).gt.0..and.work1(i,k,1).lt.0.)                   &
1071             pcond(i,k) = max(work1(i,k,1),-qci(i,k,1))/dtcld
1072           q(i,k) = q(i,k)-pcond(i,k)*dtcld
1073           qci(i,k,1) = max(qci(i,k,1)+pcond(i,k)*dtcld,0.)
1074           t(i,k) = t(i,k)+pcond(i,k)*xl(i,k)/cpm(i,k)*dtcld
1075         enddo
1076       enddo
1077 !
1078 !
1079 !----------------------------------------------------------------
1080 !     padding for small values
1081 !
1082       do k = kts, kte
1083         do i = its, ite
1084           if(qci(i,k,1).le.qmin) qci(i,k,1) = 0.0
1085           if(qci(i,k,2).le.qmin) qci(i,k,2) = 0.0
1086         enddo
1087       enddo
1088       enddo                  ! big loops
1089   END SUBROUTINE wsm52d
1090 ! ...................................................................
1091       REAL FUNCTION rgmma(x)
1092 !-------------------------------------------------------------------
1093   IMPLICIT NONE
1094 !-------------------------------------------------------------------
1095 !     rgmma function:  use infinite product form
1096       REAL :: euler
1097       PARAMETER (euler=0.577215664901532)
1098       REAL :: x, y
1099       INTEGER :: i
1100       if(x.eq.1.)then
1101         rgmma=0.
1102           else
1103         rgmma=x*exp(euler*x)
1104         do i=1,10000
1105           y=float(i)
1106           rgmma=rgmma*(1.000+x/y)*exp(-x/y)
1107         enddo
1108         rgmma=1./rgmma
1109       endif
1110       END FUNCTION rgmma
1111 !
1112 !--------------------------------------------------------------------------
1113       REAL FUNCTION fpvs(t,ice,rd,rv,cvap,cliq,cice,hvap,hsub,psat,t0c)
1114 !--------------------------------------------------------------------------
1115       IMPLICIT NONE
1116 !--------------------------------------------------------------------------
1117       REAL t,rd,rv,cvap,cliq,cice,hvap,hsub,psat,t0c,dldt,xa,xb,dldti,   &
1118            xai,xbi,ttp,tr
1119       INTEGER ice
1120 ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
1121       ttp=t0c+0.01
1122       dldt=cvap-cliq
1123       xa=-dldt/rv
1124       xb=xa+hvap/(rv*ttp)
1125       dldti=cvap-cice
1126       xai=-dldti/rv
1127       xbi=xai+hsub/(rv*ttp)
1128       tr=ttp/t
1129       if(t.lt.ttp.and.ice.eq.1) then
1130         fpvs=psat*exp(log(tr)*(xai))*exp(xbi*(1.-tr))
1131       else
1132         fpvs=psat*exp(log(tr)*(xa))*exp(xb*(1.-tr))
1133       endif
1134 ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
1135       END FUNCTION fpvs
1136 !-------------------------------------------------------------------
1137   SUBROUTINE wsm5init(den0,denr,dens,cl,cpv,allowed_to_read)
1138 !-------------------------------------------------------------------
1139   IMPLICIT NONE
1140 !-------------------------------------------------------------------
1141 !.... constants which may not be tunable
1142    REAL, INTENT(IN) :: den0,denr,dens,cl,cpv
1143    LOGICAL, INTENT(IN) :: allowed_to_read
1144    REAL :: pi
1145 !
1146    pi = 4.*atan(1.)
1147    xlv1 = cl-cpv
1148 !
1149    qc0  = 4./3.*pi*denr*r0**3*xncr/den0  ! 0.419e-3 -- .61e-3
1150    qck1 = .104*9.8*peaut/(xncr*denr)**(1./3.)/xmyu*den0**(4./3.) ! 7.03
1151 !
1152    bvtr1 = 1.+bvtr
1153    bvtr2 = 2.5+.5*bvtr
1154    bvtr3 = 3.+bvtr
1155    bvtr4 = 4.+bvtr
1156    g1pbr = rgmma(bvtr1)
1157    g3pbr = rgmma(bvtr3)
1158    g4pbr = rgmma(bvtr4)            ! 17.837825
1159    g5pbro2 = rgmma(bvtr2)          ! 1.8273
1160    pvtr = avtr*g4pbr/6.
1161    eacrr = 1.0
1162    pacrr = pi*n0r*avtr*g3pbr*.25*eacrr
1163    precr1 = 2.*pi*n0r*.78
1164    precr2 = 2.*pi*n0r*.31*avtr**.5*g5pbro2
1165    xm0  = (di0/dicon)**2
1166    xmmax = (dimax/dicon)**2
1167    roqimax = 2.08e22*dimax**8
1168 !
1169    bvts1 = 1.+bvts
1170    bvts2 = 2.5+.5*bvts
1171    bvts3 = 3.+bvts
1172    bvts4 = 4.+bvts
1173    g1pbs = rgmma(bvts1)    !.8875
1174    g3pbs = rgmma(bvts3)
1175    g4pbs = rgmma(bvts4)    ! 12.0786
1176    g5pbso2 = rgmma(bvts2)
1177    pvts = avts*g4pbs/6.
1178    pacrs = pi*n0s*avts*g3pbs*.25
1179    precs1 = 4.*n0s*.65
1180    precs2 = 4.*n0s*.44*avts**.5*g5pbso2
1181    pidn0r =  pi*denr*n0r
1182    pidn0s =  pi*dens*n0s
1183    pacrc = pi*n0s*avts*g3pbs*.25*eacrc
1184 !
1185    rslopermax = 1./lamdarmax
1186    rslopesmax = 1./lamdasmax
1187    rsloperbmax = rslopermax ** bvtr
1188    rslopesbmax = rslopesmax ** bvts
1189    rsloper2max = rslopermax * rslopermax
1190    rslopes2max = rslopesmax * rslopesmax
1191    rsloper3max = rsloper2max * rslopermax
1192    rslopes3max = rslopes2max * rslopesmax
1193 !
1194   END SUBROUTINE wsm5init
1195 END MODULE module_mp_wsm5