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