#if ( RWORDSIZE == 4 )
# define VREC vsrec
# define VSQRT vssqrt
#else
# define VREC vrec
# define VSQRT vsqrt
#endif
!Including inline expansion statistical function
MODULE module_mp_wdm5 
(docs) 2
!
REAL, PARAMETER, PRIVATE :: dtcldcr = 120. ! maximum time step for minor loops
REAL, PARAMETER, PRIVATE :: n0r = 8.e6 ! intercept parameter rain
REAL, PARAMETER, PRIVATE :: avtr = 841.9 ! a constant for terminal velocity of rain
REAL, PARAMETER, PRIVATE :: bvtr = 0.8 ! a constant for terminal velocity of rain
REAL, PARAMETER, PRIVATE :: r0 = .8e-5 ! 8 microm in contrast to 10 micro m
REAL, PARAMETER, PRIVATE :: peaut = .55 ! collection efficiency
REAL, PARAMETER, PRIVATE :: xncr = 3.e8 ! maritime cloud in contrast to 3.e8 in tc80
REAL, PARAMETER, PRIVATE :: xmyu = 1.718e-5 ! the dynamic viscosity kgm-1s-1
REAL, PARAMETER, PRIVATE :: avts = 11.72 ! a constant for terminal velocity of snow
REAL, PARAMETER, PRIVATE :: bvts = .41 ! a constant for terminal velocity of snow
REAL, PARAMETER, PRIVATE :: n0smax = 1.e11 ! maximum n0s (t=-90C unlimited)
REAL, PARAMETER, PRIVATE :: lamdacmax = 1.e10 ! limited maximum value for slope parameter of cloud water
REAL, PARAMETER, PRIVATE :: lamdarmax = 1.e8 ! limited maximum value for slope parameter of rain
REAL, PARAMETER, PRIVATE :: lamdasmax = 1.e5 ! limited maximum value for slope parameter of snow
REAL, PARAMETER, PRIVATE :: lamdagmax = 6.e4 ! limited maximum value for slope parameter of graupel
REAL, PARAMETER, PRIVATE :: dicon = 11.9 ! constant for the cloud-ice diamter
REAL, PARAMETER, PRIVATE :: dimax = 500.e-6 ! limited maximum value for the cloud-ice diamter
REAL, PARAMETER, PRIVATE :: n0s = 2.e6 ! temperature dependent intercept parameter snow
REAL, PARAMETER, PRIVATE :: alpha = .12 ! .122 exponen factor for n0s
REAL, PARAMETER, PRIVATE :: pfrz1 = 100. ! constant in Biggs freezing
REAL, PARAMETER, PRIVATE :: pfrz2 = 0.66 ! constant in Biggs freezing
REAL, PARAMETER, PRIVATE :: qcrmin = 1.e-9 ! minimun values for qr, qs, and qg
REAL, PARAMETER, PRIVATE :: ncmin = 1.e1 ! minimum value for Nc
REAL, PARAMETER, PRIVATE :: nrmin = 1.e-2 ! minimum value for Nr
REAL, PARAMETER, PRIVATE :: eacrc = 1.0 ! Snow/cloud-water collection efficiency
!
REAL, PARAMETER, PRIVATE :: satmax = 1.0048 ! maximum saturation value for CCN activation
! 1.008 for maritime air mass /1.0048 for conti
REAL, PARAMETER, PRIVATE :: actk = 0.6 ! parameter for the CCN activation
REAL, PARAMETER, PRIVATE :: actr = 1.5 ! radius of activated CCN drops
REAL, PARAMETER, PRIVATE :: ncrk1 = 3.03e3 ! Long's collection kernel coefficient
REAL, PARAMETER, PRIVATE :: ncrk2 = 2.59e15 ! Long's collection kernel coefficient
REAL, PARAMETER, PRIVATE :: di100 = 1.e-4 ! parameter related with accretion and collection of cloud drops
REAL, PARAMETER, PRIVATE :: di600 = 6.e-4 ! parameter related with accretion and collection of cloud drops
REAL, PARAMETER, PRIVATE :: di2000 = 20.e-4 ! parameter related with accretion and collection of cloud drops
REAL, PARAMETER, PRIVATE :: di82 = 82.e-6 ! dimater related with raindrops evaporation
REAL, PARAMETER, PRIVATE :: di15 = 15.e-6 ! auto conversion takes place beyond this diameter
REAL, SAVE :: &
qc0, qck1,pidnc,bvtr1,bvtr2,bvtr3,bvtr4, &
bvtr5,bvtr7,bvtr2o5,bvtr3o5,g1pbr,g2pbr, &
g3pbr,g4pbr,g5pbr,g7pbr,g5pbro2,g7pbro2, &
pvtr,pvtrn,eacrr,pacrr, &
precr1,precr2,xmmax,roqimax,bvts1, &
bvts2,bvts3,bvts4,g1pbs,g3pbs,g4pbs, &
g5pbso2,pvts,pacrs,precs1,precs2,pidn0r, &
pidn0s,pidnr,xlv1,pacrc, &
rslopecmax,rslopec2max,rslopec3max, &
rslopermax,rslopesmax,rslopegmax, &
rsloperbmax,rslopesbmax,rslopegbmax, &
rsloper2max,rslopes2max,rslopeg2max, &
rsloper3max,rslopes3max,rslopeg3max
!
! Specifies code-inlining of fpvs function in WDM52D below. JM 20040507
!
CONTAINS
!===================================================================
!
SUBROUTINE wdm5 (docs) (th, q, qc, qr, qi, qs & 1,2
,nn, nc, nr &
,den, pii, p, delz &
,delt,g, cpd, cpv, ccn0, rd, rv, t0c &
,ep1, ep2, qmin &
,XLS, XLV0, XLF0, den0, denr &
,cliq,cice,psat &
,rain, rainncv &
,snow, snowncv &
,sr &
,ids,ide, jds,jde, kds,kde &
,ims,ime, jms,jme, kms,kme &
,its,ite, jts,jte, kts,kte &
)
!-------------------------------------------------------------------
IMPLICIT NONE
!-------------------------------------------------------------------
!
! This code is a WRF double-moment 5-class mixed ice
! microphyiscs scheme (WDM5). The WDM microphysics scheme predicts
! number concentrations for warm rain species including clouds and
! rain. cloud condensation nuclei (CCN) is also predicted.
! The cold rain species including ice, snow, graupel follow the
! WRF single-moment 5-class microphysics (WSM5)
! in which theoretical background for WSM ice phase microphysics is
! based on Hong et al. (2004).
! The WDM scheme is described in Lim and Hong (2009).
! All units are in m.k.s. and source/sink terms in kgkg-1s-1.
!
! WDM5 cloud scheme
!
! Coded by Kyo-Sun Lim and Song-You Hong (Yonsei Univ.) Fall 2008
!
! Implemented by Kyo-Sun Lim and Jimy Dudhia (NCAR) Winter 2008
!
! Reference) Lim and Hong (LH, 2009) Manuscript in preperation
! Hong, Dudhia, Chen (HDC, 2004) Mon. Wea. Rev.
! Hong and Lim (HL, 2006) J. Korean Meteor. Soc.
! Cohard and Pinty (CP, 2000) Quart. J. Roy. Meteor. Soc.
! Khairoutdinov and Kogan (KK, 2000) Mon. Wea. Rev.
! Dudhia, Hong and Lim (DHL, 2008) J. Meteor. Soc. Japan
!
! Lin, Farley, Orville (LFO, 1983) J. Appl. Meteor.
! Rutledge, Hobbs (RH83, 1983) J. Atmos. Sci.
! Rutledge, Hobbs (RH84, 1984) J. Atmos. Sci.
!
INTEGER, INTENT(IN ) :: ids,ide, jds,jde, kds,kde , &
ims,ime, jms,jme, kms,kme , &
its,ite, jts,jte, kts,kte
REAL, DIMENSION( ims:ime , kms:kme , jms:jme ), &
INTENT(INOUT) :: &
th, &
q, &
qc, &
qi, &
qr, &
qs, &
nn, &
nc, &
nr
REAL, DIMENSION( ims:ime , kms:kme , jms:jme ), &
INTENT(IN ) :: &
den, &
pii, &
p, &
delz
REAL, INTENT(IN ) :: delt, &
g, &
rd, &
rv, &
t0c, &
den0, &
cpd, &
cpv, &
ccn0, &
ep1, &
ep2, &
qmin, &
XLS, &
XLV0, &
XLF0, &
cliq, &
cice, &
psat, &
denr
REAL, DIMENSION( ims:ime , jms:jme ), &
INTENT(INOUT) :: rain, &
rainncv, &
sr
REAL, DIMENSION( ims:ime , jms:jme ), OPTIONAL, &
INTENT(INOUT) :: snow, &
snowncv
! LOCAL VAR
REAL, DIMENSION( its:ite , kts:kte ) :: t
REAL, DIMENSION( its:ite , kts:kte, 2 ) :: qci, qrs
REAL, DIMENSION( its:ite , kts:kte, 3 ) :: ncr
CHARACTER*256 :: emess
INTEGER :: mkx_test
INTEGER :: i,j,k
!-------------------------------------------------------------------
#ifndef RUN_ON_GPU
DO j=jts,jte
DO k=kts,kte
DO i=its,ite
t(i,k)=th(i,k,j)*pii(i,k,j)
qci(i,k,1) = qc(i,k,j)
qci(i,k,2) = qi(i,k,j)
qrs(i,k,1) = qr(i,k,j)
qrs(i,k,2) = qs(i,k,j)
ncr(i,k,1) = nn(i,k,j)
ncr(i,k,2) = nc(i,k,j)
ncr(i,k,3) = nr(i,k,j)
ENDDO
ENDDO
! Sending array starting locations of optional variables may cause
! troubles, so we explicitly change the call.
CALL wdm52D
(t, q(ims,kms,j), qci, qrs, ncr &
,den(ims,kms,j) &
,p(ims,kms,j), delz(ims,kms,j) &
,delt,g, cpd, cpv, ccn0, rd, rv, t0c &
,ep1, ep2, qmin &
,XLS, XLV0, XLF0, den0, denr &
,cliq,cice,psat &
,j &
,rain(ims,j),rainncv(ims,j) &
,sr(ims,j) &
,ids,ide, jds,jde, kds,kde &
,ims,ime, jms,jme, kms,kme &
,its,ite, jts,jte, kts,kte &
,snow(ims,j),snowncv(ims,j) &
)
DO K=kts,kte
DO I=its,ite
th(i,k,j)=t(i,k)/pii(i,k,j)
qc(i,k,j) = qci(i,k,1)
qi(i,k,j) = qci(i,k,2)
qr(i,k,j) = qrs(i,k,1)
qs(i,k,j) = qrs(i,k,2)
nn(i,k,j) = ncr(i,k,1)
nc(i,k,j) = ncr(i,k,2)
nr(i,k,j) = ncr(i,k,3)
ENDDO
ENDDO
ENDDO
#else
CALL get_wsm5_gpu_levels ( mkx_test )
IF ( mkx_test .LT. kte ) THEN
WRITE(emess,*)'Number of levels compiled for GPU WSM5 too small. ', &
mkx_test,' < ',kte
CALL wrf_error_fatal(emess)
ENDIF
CALL wsm5_host ( &
th(its:ite,kts:kte,jts:jte), pii(its:ite,kts:kte,jts:jte) &
,q(its:ite,kts:kte,jts:jte), qc(its:ite,kts:kte,jts:jte) &
,qi(its:ite,kts:kte,jts:jte), qr(its:ite,kts:kte,jts:jte) &
,qs(its:ite,kts:kte,jts:jte), den(its:ite,kts:kte,jts:jte) &
,p(its:ite,kts:kte,jts:jte), delz(its:ite,kts:kte,jts:jte) &
,delt &
,rain(its:ite,jts:jte),rainncv(its:ite,jts:jte) &
,snow(its:ite,jts:jte),snowncv(its:ite,jts:jte) &
,sr(its:ite,jts:jte) &
,its, ite, jts, jte, kts, kte &
,its, ite, jts, jte, kts, kte &
,its, ite, jts, jte, kts, kte &
)
#endif
END SUBROUTINE wdm5
!===================================================================
!
SUBROUTINE wdm52D (docs) (t, q, qci, qrs, ncr, den, p, delz & 1,2
,delt,g, cpd, cpv, ccn0, rd, rv, t0c &
,ep1, ep2, qmin &
,XLS, XLV0, XLF0, den0, denr &
,cliq,cice,psat &
,lat &
,rain,rainncv &
,sr &
,ids,ide, jds,jde, kds,kde &
,ims,ime, jms,jme, kms,kme &
,its,ite, jts,jte, kts,kte &
,snow,snowncv &
)
!-------------------------------------------------------------------
IMPLICIT NONE
!-------------------------------------------------------------------
INTEGER, INTENT(IN ) :: ids,ide, jds,jde, kds,kde , &
ims,ime, jms,jme, kms,kme , &
its,ite, jts,jte, kts,kte, &
lat
REAL, DIMENSION( its:ite , kts:kte ), &
INTENT(INOUT) :: &
t
REAL, DIMENSION( its:ite , kts:kte, 2 ), &
INTENT(INOUT) :: &
qci, &
qrs
REAL, DIMENSION( its:ite , kts:kte, 3 ), &
INTENT(INOUT) :: &
ncr
REAL, DIMENSION( ims:ime , kms:kme ), &
INTENT(INOUT) :: &
q
REAL, DIMENSION( ims:ime , kms:kme ), &
INTENT(IN ) :: &
den, &
p, &
delz
REAL, INTENT(IN ) :: delt, &
g, &
cpd, &
cpv, &
ccn0, &
t0c, &
den0, &
rd, &
rv, &
ep1, &
ep2, &
qmin, &
XLS, &
XLV0, &
XLF0, &
cliq, &
cice, &
psat, &
denr
REAL, DIMENSION( ims:ime ), &
INTENT(INOUT) :: rain, &
rainncv, &
sr
REAL, DIMENSION( ims:ime ), OPTIONAL, &
INTENT(INOUT) :: snow, &
snowncv
! LOCAL VAR
REAL, DIMENSION( its:ite , kts:kte , 2) :: &
rh, qs, rslope, rslope2, rslope3, rslopeb, &
falk, fall, work1
REAL, DIMENSION( its:ite , kts:kte ) :: &
rslopec, rslopec2,rslopec3
REAL, DIMENSION( its:ite , kts:kte, 2) :: &
avedia
REAL, DIMENSION( its:ite , kts:kte ) :: &
workn,falln,falkn
REAL, DIMENSION( its:ite , kts:kte ) :: &
falkc, work1c, work2c, fallc
REAL, DIMENSION( its:ite , kts:kte ) :: &
pcact, praut, psaut, prevp, psdep, pracw, psaci, psacw, &
pigen, pidep, pcond, prevp_s, &
xl, cpm, work2, psmlt, psevp, denfac, xni, &
n0sfac
REAL, DIMENSION( its:ite , kts:kte ) :: &
nraut, nracw, nrevp, ncevp, nccol, nrcol, &
nsacw, nseml, ncact
REAL :: ifac, sfac
!
#define WSM_NO_CONDITIONAL_IN_VECTOR
#ifdef WSM_NO_CONDITIONAL_IN_VECTOR
REAL, DIMENSION(its:ite) :: xal, xbl
#endif
! variables for optimization
REAL, DIMENSION( its:ite ) :: tvec1
INTEGER, DIMENSION( its:ite ) :: mnstep, numndt
INTEGER, DIMENSION( its:ite ) :: mstep, numdt
REAL, DIMENSION(its:ite) :: rmstep
REAL dtcldden, rdelz, rdtcld
LOGICAL, DIMENSION( its:ite ) :: flgcld
REAL :: pi, &
cpmcal, xlcal, lamdac, lamdar, lamdas, diffus, &
viscos, xka, venfac, conden, diffac, &
x, y, z, a, b, c, d, e, &
ndt, qdt, holdrr, holdrs, supcol, supcolt, pvt, &
coeres, supsat, dtcld, xmi, eacrs, satdt, &
vt2i,vt2s,acrfac, coecol, &
nfrzdtr, nfrzdtc, &
taucon, lencon, lenconcr, &
qimax, diameter, xni0, roqi0, &
fallsum, fallsum_qsi, xlwork2, factor, source, &
value, xlf, pfrzdtc, pfrzdtr, supice
REAL :: temp
REAL :: holdc, holdci
INTEGER :: i, j, k, mstepmax, &
iprt, latd, lond, loop, loops, ifsat, n
! Temporaries used for inlining fpvs function
REAL :: dldti, xb, xai, tr, xbi, xa, hvap, cvap, hsub, dldt, ttp
REAL :: logtr
!
!=================================================================
! compute internal functions
!
cpmcal(x) = cpd*(1.-max(x,qmin))+max(x,qmin)*cpv
xlcal(x) = xlv0-xlv1*(x-t0c)
!----------------------------------------------------------------
! size distributions: (x=mixing ratio, y=air density):
! valid for mixing ratio > 1.e-9 kg/kg.
!
! Optimizatin : A**B => exp(log(A)*(B))
lamdac(x,y,z)= exp(log(((pidnc*z)/(x*y)))*((.33333333)))
lamdar(x,y,z)= exp(log(((pidnr*z)/(x*y)))*((.33333333)))
lamdas(x,y,z)= sqrt(sqrt(pidn0s*z/(x*y))) ! (pidn0s*z/(x*y))**.25
!
!----------------------------------------------------------------
! diffus: diffusion coefficient of the water vapor
! viscos: kinematic viscosity(m2s-1)
! diffus(x,y) = 8.794e-5 * exp(log(x)*(1.81)) / y
! viscos(x,y) = 1.496e-6 * (x*sqrt(x)) /(x+120.)/y
! xka(x,y) = 1.414e3*viscos(x,y)*y
! diffac(a,b,c,d,e) = d*a*a/(xka(c,d)*rv*c*c)+1./(e*diffus(c,b))
! venfac(a,b,c) = exp(log((viscos(b,c)/diffus(b,a)))*((.3333333))) &
! /sqrt(viscos(b,c))*sqrt(sqrt(den0/c))
! conden(a,b,c,d,e) = (max(b,qmin)-c)/(1.+d*d/(rv*e)*c/(a*a))
!
!
pi = 4. * atan(1.)
!
!----------------------------------------------------------------
! paddint 0 for negative values generated by dynamics
!
do k = kts, kte
do i = its, ite
qci(i,k,1) = max(qci(i,k,1),0.0)
qrs(i,k,1) = max(qrs(i,k,1),0.0)
qci(i,k,2) = max(qci(i,k,2),0.0)
qrs(i,k,2) = max(qrs(i,k,2),0.0)
ncr(i,k,1) = max(ncr(i,k,1),0.)
ncr(i,k,2) = max(ncr(i,k,2),0.)
ncr(i,k,3) = max(ncr(i,k,3),0.)
enddo
enddo
!
! latent heat for phase changes and heat capacity. neglect the
! changes during microphysical process calculation
! emanuel(1994)
!
do k = kts, kte
do i = its, ite
cpm(i,k) = cpmcal(q(i,k))
xl(i,k) = xlcal(t(i,k))
enddo
enddo
!
!----------------------------------------------------------------
! compute the minor time steps.
!
loops = max(nint(delt/dtcldcr),1)
dtcld = delt/loops
if(delt.le.dtcldcr) dtcld = delt
!
do loop = 1,loops
!
!----------------------------------------------------------------
! initialize the large scale variables
!
do i = its, ite
mstep(i) = 1
mnstep(i) = 1
flgcld(i) = .true.
enddo
!
! do k = kts, kte
! do i = its, ite
! denfac(i,k) = sqrt(den0/den(i,k))
! enddo
! enddo
do k = kts, kte
CALL VREC( tvec1(its), den(its,k), ite-its+1)
do i = its, ite
tvec1(i) = tvec1(i)*den0
enddo
CALL VSQRT( denfac(its,k), tvec1(its), ite-its+1)
enddo
!
! Inline expansion for fpvs
! qs(i,k,1) = fpvs(t(i,k),0,rd,rv,cpv,cliq,cice,xlv0,xls,psat,t0c)
! qs(i,k,2) = fpvs(t(i,k),1,rd,rv,cpv,cliq,cice,xlv0,xls,psat,t0c)
hsub = xls
hvap = xlv0
cvap = cpv
ttp=t0c+0.01
dldt=cvap-cliq
xa=-dldt/rv
xb=xa+hvap/(rv*ttp)
dldti=cvap-cice
xai=-dldti/rv
xbi=xai+hsub/(rv*ttp)
! this is for compilers where the conditional inhibits vectorization
#ifdef WSM_NO_CONDITIONAL_IN_VECTOR
do k = kts, kte
do i = its, ite
if(t(i,k).lt.ttp) then
xal(i) = xai
xbl(i) = xbi
else
xal(i) = xa
xbl(i) = xb
endif
enddo
do i = its, ite
tr=ttp/t(i,k)
logtr=log(tr)
qs(i,k,1)=psat*exp(logtr*(xa)+xb*(1.-tr))
qs(i,k,1) = ep2 * qs(i,k,1) / (p(i,k) - qs(i,k,1))
qs(i,k,1) = max(qs(i,k,1),qmin)
rh(i,k,1) = max(q(i,k) / qs(i,k,1),qmin)
qs(i,k,2)=psat*exp(logtr*(xal(i))+xbl(i)*(1.-tr))
qs(i,k,2) = ep2 * qs(i,k,2) / (p(i,k) - qs(i,k,2))
qs(i,k,2) = max(qs(i,k,2),qmin)
rh(i,k,2) = max(q(i,k) / qs(i,k,2),qmin)
enddo
enddo
#else
do k = kts, kte
do i = its, ite
tr=ttp/t(i,k)
logtr=log(tr)
qs(i,k,1)=psat*exp(logtr*(xa)+xb*(1.-tr))
qs(i,k,1) = ep2 * qs(i,k,1) / (p(i,k) - qs(i,k,1))
qs(i,k,1) = max(qs(i,k,1),qmin)
rh(i,k,1) = max(q(i,k) / qs(i,k,1),qmin)
if(t(i,k).lt.ttp) then
qs(i,k,2)=psat*exp(logtr*(xai)+xbi*(1.-tr))
else
qs(i,k,2)=psat*exp(logtr*(xa)+xb*(1.-tr))
endif
qs(i,k,2) = ep2 * qs(i,k,2) / (p(i,k) - qs(i,k,2))
qs(i,k,2) = max(qs(i,k,2),qmin)
rh(i,k,2) = max(q(i,k) / qs(i,k,2),qmin)
enddo
enddo
#endif
!
!----------------------------------------------------------------
! initialize the variables for microphysical physics
!
do k = kts, kte
do i = its, ite
prevp(i,k) = 0.
psdep(i,k) = 0.
praut(i,k) = 0.
psaut(i,k) = 0.
pracw(i,k) = 0.
psaci(i,k) = 0.
psacw(i,k) = 0.
pigen(i,k) = 0.
pidep(i,k) = 0.
pcond(i,k) = 0.
psmlt(i,k) = 0.
psevp(i,k) = 0.
pcact(i,k) = 0.
prevp_s(i,k) = 0.
falk(i,k,1) = 0.
falk(i,k,2) = 0.
fall(i,k,1) = 0.
fall(i,k,2) = 0.
fallc(i,k) = 0.
falkc(i,k) = 0.
falln(i,k) = 0.
falkn(i,k) = 0.
xni(i,k) = 1.e3
nsacw(i,k) = 0.
nseml(i,k) = 0.
nracw(i,k) = 0.
nccol(i,k) = 0.
nrcol(i,k) = 0.
ncact(i,k) = 0.
nraut(i,k) = 0.
nrevp(i,k) = 0.
ncevp(i,k) = 0.
enddo
enddo
!
!----------------------------------------------------------------
! compute the fallout term:
! first, vertical terminal velosity for minor loops
!
do k = kts, kte
do i = its, ite
supcol = t0c-t(i,k)
!---------------------------------------------------------------
! n0s: Intercept parameter for snow [m-4] [HDC 6]
!---------------------------------------------------------------
n0sfac(i,k) = max(min(exp(alpha*supcol),n0smax/n0s),1.)
if(qrs(i,k,1).le.qcrmin .or. ncr(i,k,3).le.nrmin)then
rslope(i,k,1) = rslopermax
rslopeb(i,k,1) = rsloperbmax
rslope2(i,k,1) = rsloper2max
rslope3(i,k,1) = rsloper3max
else
rslope(i,k,1) = 1./lamdar(qrs(i,k,1),den(i,k),ncr(i,k,3))
rslopeb(i,k,1) = exp(log(rslope(i,k,1))*(bvtr))
rslope2(i,k,1) = rslope(i,k,1)*rslope(i,k,1)
rslope3(i,k,1) = rslope2(i,k,1)*rslope(i,k,1)
endif
if(qci(i,k,1).le.qmin .or. ncr(i,k,2).le.ncmin)then
rslopec(i,k) = rslopecmax
rslopec2(i,k) = rslopec2max
rslopec3(i,k) = rslopec3max
else
rslopec(i,k) = 1./lamdac(qci(i,k,1),den(i,k),ncr(i,k,2))
rslopec2(i,k) = rslopec(i,k)*rslopec(i,k)
rslopec3(i,k) = rslopec2(i,k)*rslopec(i,k)
endif
if(qrs(i,k,2).le.qcrmin)then
rslope(i,k,2) = rslopesmax
rslopeb(i,k,2) = rslopesbmax
rslope2(i,k,2) = rslopes2max
rslope3(i,k,2) = rslopes3max
else
rslope(i,k,2) = 1./lamdas(qrs(i,k,2),den(i,k),n0sfac(i,k))
rslopeb(i,k,2) = exp(log(rslope(i,k,2))*(bvts))
rslope2(i,k,2) = rslope(i,k,2)*rslope(i,k,2)
rslope3(i,k,2) = rslope2(i,k,2)*rslope(i,k,2)
endif
!-------------------------------------------------------------
! Ni: ice crystal number concentraiton [HDC 5c]
!-------------------------------------------------------------
! xni(i,k) = min(max(5.38e7*(den(i,k) &
! *max(qci(i,k,2),qmin))**0.75,1.e3),1.e6)
temp = (den(i,k)*max(qci(i,k,2),qmin))
temp = sqrt(sqrt(temp*temp*temp))
xni(i,k) = min(max(5.38e7*temp,1.e3),1.e6)
enddo
enddo
!
mstepmax = 1
numndt = 1
do k = kte, kts, -1
do i = its, ite
workn(i,k) = pvtrn*rslopeb(i,k,1)*denfac(i,k)/delz(i,k)
numndt(i) = max(nint(workn(i,k)*dtcld+.5),1)
if(numndt(i).ge.mnstep(i)) mnstep(i) = numndt(i)
enddo
enddo
do i = its, ite
if(mstepmax.le.mnstep(i)) mstepmax = mnstep(i)
enddo
!
do n = 1, mstepmax
k = kte
do i = its, ite
if(n.le.mnstep(i)) then
falkn(i,k) = den(i,k)*ncr(i,k,3)*workn(i,k)/mnstep(i)
falln(i,k) = falln(i,k)+falkn(i,k)
ncr(i,k,3) = max(ncr(i,k,3)-falkn(i,k) &
*dtcld/den(i,k),0.)
endif
enddo
do k = kte-1, kts, -1
do i = its, ite
if(n.le.mnstep(i)) then
falkn(i,k) = den(i,k)*ncr(i,k,3)*workn(i,k)/mnstep(i)
falln(i,k) = falln(i,k)+falkn(i,k)
ncr(i,k,3) = max(ncr(i,k,3)-(falkn(i,k)-falkn(i,k+1) &
*delz(i,k+1)/delz(i,k))*dtcld/den(i,k),0.)
endif
enddo
enddo
enddo
!
mstepmax = 1
numdt = 1
do k = kte, kts, -1
do i = its, ite
work1(i,k,1) = pvtr*rslopeb(i,k,1)*denfac(i,k)/delz(i,k)
work1(i,k,2) = pvts*rslopeb(i,k,2)*denfac(i,k)/delz(i,k)
numdt(i) = max(nint(max(work1(i,k,1),work1(i,k,2))*dtcld+.5),1)
if(numdt(i).ge.mstep(i)) mstep(i) = numdt(i)
enddo
enddo
do i = its, ite
if(mstepmax.le.mstep(i)) mstepmax = mstep(i)
rmstep(i) = 1./mstep(i)
enddo
!
do n = 1, mstepmax
k = kte
do i = its, ite
if(n.le.mstep(i)) then
! falk(i,k,1) = den(i,k)*qrs(i,k,1)*work1(i,k,1)/mstep(i)
! falk(i,k,2) = den(i,k)*qrs(i,k,2)*work1(i,k,2)/mstep(i)
falk(i,k,1) = den(i,k)*qrs(i,k,1)*work1(i,k,1)*rmstep(i)
falk(i,k,2) = den(i,k)*qrs(i,k,2)*work1(i,k,2)*rmstep(i)
fall(i,k,1) = fall(i,k,1)+falk(i,k,1)
fall(i,k,2) = fall(i,k,2)+falk(i,k,2)
! qrs(i,k,1) = max(qrs(i,k,1)-falk(i,k,1)*dtcld/den(i,k),0.)
! qrs(i,k,2) = max(qrs(i,k,2)-falk(i,k,2)*dtcld/den(i,k),0.)
dtcldden = dtcld/den(i,k)
qrs(i,k,1) = max(qrs(i,k,1)-falk(i,k,1)*dtcldden,0.)
qrs(i,k,2) = max(qrs(i,k,2)-falk(i,k,2)*dtcldden,0.)
endif
enddo
do k = kte-1, kts, -1
do i = its, ite
if(n.le.mstep(i)) then
! falk(i,k,1) = den(i,k)*qrs(i,k,1)*work1(i,k,1)/mstep(i)
! falk(i,k,2) = den(i,k)*qrs(i,k,2)*work1(i,k,2)/mstep(i)
falk(i,k,1) = den(i,k)*qrs(i,k,1)*work1(i,k,1)*rmstep(i)
falk(i,k,2) = den(i,k)*qrs(i,k,2)*work1(i,k,2)*rmstep(i)
fall(i,k,1) = fall(i,k,1)+falk(i,k,1)
fall(i,k,2) = fall(i,k,2)+falk(i,k,2)
! qrs(i,k,1) = max(qrs(i,k,1)-(falk(i,k,1)-falk(i,k+1,1) &
! *delz(i,k+1)/delz(i,k))*dtcld/den(i,k),0.)
! qrs(i,k,2) = max(qrs(i,k,2)-(falk(i,k,2)-falk(i,k+1,2) &
! *delz(i,k+1)/delz(i,k))*dtcld/den(i,k),0.)
dtcldden = dtcld/den(i,k)
rdelz = 1./delz(i,k)
qrs(i,k,1) = max(qrs(i,k,1)-(falk(i,k,1)-falk(i,k+1,1) &
*delz(i,k+1)*rdelz)*dtcldden,0.)
qrs(i,k,2) = max(qrs(i,k,2)-(falk(i,k,2)-falk(i,k+1,2) &
*delz(i,k+1)*rdelz)*dtcldden,0.)
endif
enddo
enddo
do k = kte, kts, -1
do i = its, ite
if(n.le.mstep(i)) then
if(t(i,k).gt.t0c .and. qrs(i,k,2).gt.0.) then
!----------------------------------------------------------------
! psmlt: melting of snow [HL A33] [RH83 A25]
! (T>T0: S->R)
!----------------------------------------------------------------
xlf = xlf0
! work2(i,k)= venfac(p(i,k),t(i,k),den(i,k))
work2(i,k)= (exp(log(((1.496e-6*((t(i,k))*sqrt(t(i,k))) &
/((t(i,k))+120.)/(den(i,k)))/(8.794e-5 &
*exp(log(t(i,k))*(1.81))/p(i,k)))) &
*((.3333333)))/sqrt((1.496e-6*((t(i,k)) &
*sqrt(t(i,k)))/((t(i,k))+120.)/(den(i,k)))) &
*sqrt(sqrt(den0/(den(i,k)))))
coeres = rslope2(i,k,2)*sqrt(rslope(i,k,2)*rslopeb(i,k,2))
! psmlt(i,k) = xka(t(i,k),den(i,k))/xlf*(t0c-t(i,k))*pi/2. &
! *n0sfac(i,k)*(precs1*rslope2(i,k,2)+precs2 &
! *work2(i,k)*coeres)
psmlt(i,k) = (1.414e3*(1.496e-6 * ((t(i,k))*sqrt(t(i,k))) &
/((t(i,k))+120.)/(den(i,k)))*(den(i,k)))/xlf &
*(t0c-t(i,k))*pi/2.*n0sfac(i,k) &
*(precs1*rslope2(i,k,2)+precs2*work2(i,k)*coeres)
psmlt(i,k) = min(max(psmlt(i,k)*dtcld/mstep(i),-qrs(i,k,2) &
/mstep(i)),0.)
qrs(i,k,2) = qrs(i,k,2) + psmlt(i,k)
qrs(i,k,1) = qrs(i,k,1) - psmlt(i,k)
!-------------------------------------------------------------------
! nsmlt: melgin of snow
! (T>T0: ->NR)
!-------------------------------------------------------------------
if(qrs(i,k,2).gt.qcrmin) then
sfac = rslope(i,k,2)*n0s*n0sfac(i,k)/qrs(i,k,2)
ncr(i,k,3) = ncr(i,k,3) - sfac*psmlt(i,k)
endif
t(i,k) = t(i,k) + xlf/cpm(i,k)*psmlt(i,k)
endif
endif
enddo
enddo
enddo
!---------------------------------------------------------------
! Vice [ms-1] : fallout of ice crystal [HDC 5a]
!---------------------------------------------------------------
mstepmax = 1
mstep = 1
numdt = 1
do k = kte, kts, -1
do i = its, ite
if(qci(i,k,2).le.0.) then
work2c(i,k) = 0.
else
xmi = den(i,k)*qci(i,k,2)/xni(i,k)
! diameter = min(dicon * sqrt(xmi),dimax)
diameter = max(min(dicon * sqrt(xmi),dimax), 1.e-25)
work1c(i,k) = 1.49e4*exp(log(diameter)*(1.31))
work2c(i,k) = work1c(i,k)/delz(i,k)
endif
numdt(i) = max(nint(work2c(i,k)*dtcld+.5),1)
if(numdt(i).ge.mstep(i)) mstep(i) = numdt(i)
enddo
enddo
do i = its, ite
if(mstepmax.le.mstep(i)) mstepmax = mstep(i)
enddo
!
do n = 1, mstepmax
k = kte
do i = its, ite
if(n.le.mstep(i)) then
falkc(i,k) = den(i,k)*qci(i,k,2)*work2c(i,k)/mstep(i)
holdc = falkc(i,k)
fallc(i,k) = fallc(i,k)+falkc(i,k)
holdci = qci(i,k,2)
qci(i,k,2) = max(qci(i,k,2)-falkc(i,k)*dtcld/den(i,k),0.)
endif
enddo
do k = kte-1, kts, -1
do i = its, ite
if(n.le.mstep(i)) then
falkc(i,k) = den(i,k)*qci(i,k,2)*work2c(i,k)/mstep(i)
holdc = falkc(i,k)
fallc(i,k) = fallc(i,k)+falkc(i,k)
holdci = qci(i,k,2)
qci(i,k,2) = max(qci(i,k,2)-(falkc(i,k)-falkc(i,k+1)*delz(i,k+1) &
/delz(i,k))*dtcld/den(i,k),0.)
endif
enddo
enddo
enddo
!
!
!----------------------------------------------------------------
! rain (unit is mm/sec;kgm-2s-1: /1000*delt ===> m)==> mm for wrf
!
do i = its, ite
fallsum = fall(i,1,1)+fall(i,1,2)+fallc(i,1)
fallsum_qsi = fall(i,1,2)+fallc(i,1)
rainncv(i) = 0.
if(fallsum.gt.0.) then
rainncv(i) = fallsum*delz(i,1)/denr*dtcld*1000.
rain(i) = fallsum*delz(i,1)/denr*dtcld*1000.+rain(i)
endif
if (PRESENT (snowncv) .and. PRESENT (snow)) then
snowncv(i) = 0.
if(fallsum_qsi.gt.0.) then
snowncv(i) = fallsum_qsi*delz(i,kts)/denr*dtcld*1000.
snow(i) = fallsum_qsi*delz(i,kts)/denr*dtcld*1000.+snow(i)
endif
endif
sr(i) = 0.
if(fallsum.gt.0.)sr(i)=fallsum_qsi*delz(i,kts)/denr*dtcld*1000. &
/(rainncv(i)+1.e-12)
enddo
!
!---------------------------------------------------------------
! pimlt: instantaneous melting of cloud ice [HL A47] [RH83 A28]
! (T>T0: I->C)
!---------------------------------------------------------------
do k = kts, kte
do i = its, ite
supcol = t0c-t(i,k)
xlf = xls-xl(i,k)
if(supcol.lt.0.) xlf = xlf0
if(supcol.lt.0 .and. qci(i,k,2).gt.0.) then
qci(i,k,1) = qci(i,k,1)+qci(i,k,2)
!---------------------------------------------------------------
! nimlt: instantaneous melting of cloud ice
! (T>T0: ->NC)
!--------------------------------------------------------------
if(qci(i,k,2).gt.qmin) then
ifac = xni(i,k)/qci(i,k,2)
ncr(i,k,2) = ncr(i,k,2)+ifac*qci(i,k,2)
endif
t(i,k) = t(i,k) - xlf/cpm(i,k)*qci(i,k,2)
qci(i,k,2) = 0.
endif
!---------------------------------------------------------------
! pihmf: homogeneous freezing of cloud water below -40c [HL A45]
! (T<-40C: C->I)
!---------------------------------------------------------------
if(supcol.gt.40. .and. qci(i,k,1).gt.0.) then
qci(i,k,2) = qci(i,k,2) + qci(i,k,1)
!---------------------------------------------------------------
! nihmf: homogeneous of cloud water below -40c [HL A45]
! (T<-40C: NC->)
!---------------------------------------------------------------
if(ncr(i,k,2).gt.0.) ncr(i,k,2) = 0.
t(i,k) = t(i,k) + xlf/cpm(i,k)*qci(i,k,1)
qci(i,k,1) = 0.
endif
!---------------------------------------------------------------
! pihtf: heterogeneous freezing of cloud water [HL A44]
! (T0>T>-40C: C->I)
!---------------------------------------------------------------
if(supcol.gt.0. .and. qci(i,k,1).gt.0.) then
supcolt=min(supcol,70.)
pfrzdtc = min(pi*pi*pfrz1*(exp(pfrz2*supcolt)-1.)*denr/den(i,k) &
*ncr(i,k,2)*rslopec3(i,k)*rslopec3(i,k)/18.*dtcld,qci(i,k,1))
!---------------------------------------------------------------
! nihtf: heterogeneous of cloud water
! (T0>T>-40C: NC->)
!---------------------------------------------------------------
if(ncr(i,k,2).gt.ncmin) then
nfrzdtc = min(pi*pfrz1*(exp(pfrz2*supcolt)-1.)*ncr(i,k,2) &
*rslopec3(i,k)/6.*dtcld,ncr(i,k,2))
ncr(i,k,2) = ncr(i,k,2) - nfrzdtc
endif
qci(i,k,2) = qci(i,k,2) + pfrzdtc
t(i,k) = t(i,k) + xlf/cpm(i,k)*pfrzdtc
qci(i,k,1) = qci(i,k,1)-pfrzdtc
endif
!---------------------------------------------------------------
! psfrz: freezing of rain water [HL A20] [LFO 45]
! (T<T0, R->S)
!---------------------------------------------------------------
if(supcol.gt.0. .and. qrs(i,k,1).gt.0.) then
supcolt=min(supcol,70.)
pfrzdtr = min(140.*(pi*pi)*pfrz1*ncr(i,k,3)*denr/den(i,k) &
*(exp(pfrz2*supcolt)-1.)*rslope3(i,k,1)*rslope3(i,k,1) &
*dtcld,qrs(i,k,1))
!---------------------------------------------------------------
! nsfrz: freezing of rain water
! (T<T0, NR-> )
!---------------------------------------------------------------
if(ncr(i,k,3).gt.nrmin) then
nfrzdtr = min(4.*pi*pfrz1*ncr(i,k,3)*(exp(pfrz2*supcolt)-1.) &
*rslope3(i,k,1)*dtcld,ncr(i,k,3))
ncr(i,k,3) = ncr(i,k,3)-nfrzdtr
endif
qrs(i,k,2) = qrs(i,k,2) + pfrzdtr
t(i,k) = t(i,k) + xlf/cpm(i,k)*pfrzdtr
qrs(i,k,1) = qrs(i,k,1)-pfrzdtr
endif
enddo
enddo
!
do k = kts, kte
do i = its, ite
ncr(i,k,2) = max(ncr(i,k,2),0.0)
ncr(i,k,3) = max(ncr(i,k,3),0.0)
enddo
enddo
!
!----------------------------------------------------------------
! rsloper: reverse of the slope parameter of the rain(m)
! xka: thermal conductivity of air(jm-1s-1k-1)
! work1: the thermodynamic term in the denominator associated with
! heat conduction and vapor diffusion
! (ry88, y93, h85)
! work2: parameter associated with the ventilation effects(y93)
!
do k = kts, kte
do i = its, ite
if(qrs(i,k,1).le.qcrmin .or. ncr(i,k,3).le.nrmin)then
rslope(i,k,1) = rslopermax
rslopeb(i,k,1) = rsloperbmax
rslope2(i,k,1) = rsloper2max
rslope3(i,k,1) = rsloper3max
else
rslope(i,k,1) = 1./lamdar(qrs(i,k,1),den(i,k),ncr(i,k,3))
rslopeb(i,k,1) = exp(log(rslope(i,k,1))*(bvtr))
rslope2(i,k,1) = rslope(i,k,1)*rslope(i,k,1)
rslope3(i,k,1) = rslope2(i,k,1)*rslope(i,k,1)
endif
!
! compute the mean-volume drop diameter for raindrop distribution
avedia(i,k,2) = rslope(i,k,1)*((24.)**(.3333333))
!
if(qci(i,k,1).le.qmin .or. ncr(i,k,2).le.ncmin)then
rslopec(i,k) = rslopecmax
rslopec2(i,k) = rslopec2max
rslopec3(i,k) = rslopec3max
else
rslopec(i,k) = 1./lamdac(qci(i,k,1),den(i,k),ncr(i,k,2))
rslopec2(i,k) = rslopec(i,k)*rslopec(i,k)
rslopec3(i,k) = rslopec2(i,k)*rslopec(i,k)
endif
!
! compute the mean-volume drop diameter for cloud-droplet distribution
avedia(i,k,1) = rslopec(i,k)
!
if(qrs(i,k,2).le.qcrmin)then
rslope(i,k,2) = rslopesmax
rslopeb(i,k,2) = rslopesbmax
rslope2(i,k,2) = rslopes2max
rslope3(i,k,2) = rslopes3max
else
! rslope(i,k,2) = 1./lamdas(qrs(i,k,2),den(i,k),n0sfac(i,k))
rslope(i,k,2) = 1./(sqrt(sqrt(pidn0s*(n0sfac(i,k))/((qrs(i,k,2)) &
*(den(i,k))))))
rslopeb(i,k,2) = exp(log(rslope(i,k,2))*(bvts))
rslope2(i,k,2) = rslope(i,k,2)*rslope(i,k,2)
rslope3(i,k,2) = rslope2(i,k,2)*rslope(i,k,2)
endif
enddo
enddo
!
do k = kts, kte
do i = its, ite
! work1(i,k,1) = diffac(xl(i,k),p(i,k),t(i,k),den(i,k),qs(i,k,1))
work1(i,k,1) = ((((den(i,k))*(xl(i,k))*(xl(i,k)))*((t(i,k))+120.) &
*(den(i,k)))/(1.414e3*(1.496e-6*((t(i,k))*sqrt(t(i,k))))&
*(den(i,k))*(rv*(t(i,k))*(t(i,k))))) &
+ p(i,k)/((qs(i,k,1))*(8.794e-5*exp(log(t(i,k))*(1.81))))
! work1(i,k,2) = diffac(xls,p(i,k),t(i,k),den(i,k),qs(i,k,2))
work1(i,k,2) = ((((den(i,k))*(xls)*(xls))*((t(i,k))+120.)*(den(i,k)))&
/(1.414e3*(1.496e-6*((t(i,k))*sqrt(t(i,k))))*(den(i,k)) &
*(rv*(t(i,k))*(t(i,k)))) &
+ p(i,k)/(qs(i,k,2)*(8.794e-5*exp(log(t(i,k))*(1.81)))))
! work2(i,k) = venfac(p(i,k),t(i,k),den(i,k))
work2(i,k) = (exp(.3333333*log(((1.496e-6 * ((t(i,k))*sqrt(t(i,k)))) &
*p(i,k))/(((t(i,k))+120.)*den(i,k)*(8.794e-5 &
*exp(log(t(i,k))*(1.81))))))*sqrt(sqrt(den0/(den(i,k))))) &
/sqrt((1.496e-6*((t(i,k))*sqrt(t(i,k)))) &
/(((t(i,k))+120.)*den(i,k)))
enddo
enddo
!
!===============================================================
!
! warm rain processes
!
! - follows the processes in RH83 and LFO except for autoconcersion
!
!===============================================================
!
do k = kts, kte
do i = its, ite
supsat = max(q(i,k),qmin)-qs(i,k,1)
satdt = supsat/dtcld
!---------------------------------------------------------------
! praut: auto conversion rate from cloud to rain [CP 17]
! (C->R)
!---------------------------------------------------------------
lencon = 2.7e-2*den(i,k)*qci(i,k,1)*(1.e20/16.*rslopec2(i,k) &
*rslopec2(i,k)-0.4)
lenconcr = max(1.2*lencon,qcrmin)
if(avedia(i,k,1).gt.di15) then
taucon = 3.7/den(i,k)/qci(i,k,1)/(0.5e6*rslopec(i,k)-7.5)
praut(i,k) = lencon/taucon
praut(i,k) = min(max(praut(i,k),0.),qci(i,k,1)/dtcld)
!---------------------------------------------------------------
! nraut: auto conversion rate from cloud to rain [CP 18 & 19]
! (NC->NR)
!---------------------------------------------------------------
nraut(i,k) = 3.5e9*den(i,k)*praut(i,k)
if(qrs(i,k,1).gt.lenconcr) &
nraut(i,k) = ncr(i,k,3)/qrs(i,k,1)*praut(i,k)
nraut(i,k) = min(nraut(i,k),ncr(i,k,2)/dtcld)
endif
!---------------------------------------------------------------
! pracw: accretion of cloud water by rain [CP 22 & 23]
! (C->R)
! nracw: accretion of cloud water by rain
! (NC->)
!---------------------------------------------------------------
if(qrs(i,k,1).ge.lenconcr) then
if(avedia(i,k,2).ge.di100) then
nracw(i,k) = min(ncrk1*ncr(i,k,2)*ncr(i,k,3)*(rslopec3(i,k) &
+ 24.*rslope3(i,k,1)),ncr(i,k,2)/dtcld)
pracw(i,k) = min(pi/6.*(denr/den(i,k))*ncrk1*ncr(i,k,2) &
*ncr(i,k,3)*rslopec3(i,k)*(2.*rslopec3(i,k) &
+ 24.*rslope3(i,k,1)),qci(i,k,1)/dtcld)
else
nracw(i,k) = min(ncrk2*ncr(i,k,2)*ncr(i,k,3)*(2.*rslopec3(i,k) &
*rslopec3(i,k)+5040.*rslope3(i,k,1) &
*rslope3(i,k,1)),ncr(i,k,2)/dtcld)
pracw(i,k) = min(pi/6.*(denr/den(i,k))*ncrk2*ncr(i,k,2) &
*ncr(i,k,3)*rslopec3(i,k)*(6.*rslopec3(i,k) &
*rslopec3(i,k)+5040.*rslope3(i,k,1) &
*rslope3(i,k,1)),qci(i,k,1)/dtcld)
endif
endif
!----------------------------------------------------------------
! nccol: self collection of cloud water [CP 24 & 25]
! (NC->)
!----------------------------------------------------------------
if(avedia(i,k,1).ge.di100) then
nccol(i,k) = ncrk1*ncr(i,k,2)*ncr(i,k,2)*rslopec3(i,k)
else
nccol(i,k) = 2.*ncrk2*ncr(i,k,2)*ncr(i,k,2)*rslopec3(i,k) &
*rslopec3(i,k)
endif
!----------------------------------------------------------------
! nrcol: self collection of rain-drops and break-up [CP 24 & 25]
! (NR->)
!----------------------------------------------------------------
if(qrs(i,k,1).ge.lenconcr) then
if(avedia(i,k,2).lt.di100) then
nrcol(i,k) = 5040.*ncrk2*ncr(i,k,3)*ncr(i,k,3)*rslope3(i,k,1) &
*rslope3(i,k,1)
elseif(avedia(i,k,2).ge.di100 .and. avedia(i,k,2).lt.di600) then
nrcol(i,k) = 24.*ncrk1*ncr(i,k,3)*ncr(i,k,3)*rslope3(i,k,1)
elseif(avedia(i,k,2).ge.di600 .and. avedia(i,k,2).lt.di2000) then
coecol = -2.5e3*(avedia(i,k,2)-di600)
nrcol(i,k) = 24.*exp(coecol)*ncrk1*ncr(i,k,3)*ncr(i,k,3) &
*rslope3(i,k,1)
else
nrcol(i,k) = 0.
endif
endif
!---------------------------------------------------------------
! prevp: evaporation/condensation rate of rain
! (V->R or R->V)
!---------------------------------------------------------------
if(qrs(i,k,1).gt.0.) then
coeres = rslope(i,k,1)*sqrt(rslope(i,k,1)*rslopeb(i,k,1))
prevp(i,k) = (rh(i,k,1)-1.)*ncr(i,k,3)*(precr1*rslope(i,k,1) &
+precr2*work2(i,k)*coeres)/work1(i,k,1)
if(prevp(i,k).lt.0.) then
prevp(i,k) = max(prevp(i,k),-qrs(i,k,1)/dtcld)
prevp(i,k) = max(prevp(i,k),satdt/2)
!----------------------------------------------------------------
! Nrevp: evaporation/condensation rate of rain [CP ]
! (NR->NC)
!----------------------------------------------------------------
if(avedia(i,k,2).le.di82) then
nrevp(i,k) = ncr(i,k,3)/dtcld
!----------------------------------------------------------------
! Prevp_s: evaporation/condensation rate of rain [KK 23]
! (R->C)
!----------------------------------------------------------------
prevp_s(i,k) = qrs(i,k,1)/dtcld
endif
else
!
prevp(i,k) = min(prevp(i,k),satdt/2)
endif
endif
enddo
enddo
!
!===============================================================
!
! cold rain processes
!
! - follows the revised ice microphysics processes in HDC
! - the processes same as in RH83 and RH84 and LFO behave
! following ice crystal hapits defined in HDC, inclduing
! intercept parameter for snow (n0s), ice crystal number
! concentration (ni), ice nuclei number concentration
! (n0i), ice diameter (d)
!
!===============================================================
!
rdtcld = 1./dtcld
do k = kts, kte
do i = its, ite
supcol = t0c-t(i,k)
supsat = max(q(i,k),qmin)-qs(i,k,2)
satdt = supsat/dtcld
ifsat = 0
!-------------------------------------------------------------
! Ni: ice crystal number concentraiton [HDC 5c]
!-------------------------------------------------------------
! xni(i,k) = min(max(5.38e7*(den(i,k) &
! *max(qci(i,k,2),qmin))**0.75,1.e3),1.e6)
temp = (den(i,k)*max(qci(i,k,2),qmin))
temp = sqrt(sqrt(temp*temp*temp))
xni(i,k) = min(max(5.38e7*temp,1.e3),1.e6)
eacrs = exp(0.07*(-supcol))
!
if(supcol.gt.0) then
if(qrs(i,k,2).gt.qcrmin .and. qci(i,k,2).gt.qmin) then
xmi = den(i,k)*qci(i,k,2)/xni(i,k)
diameter = min(dicon * sqrt(xmi),dimax)
vt2i = 1.49e4*diameter**1.31
vt2s = pvts*rslopeb(i,k,2)*denfac(i,k)
!-------------------------------------------------------------
! psaci: Accretion of cloud ice by rain [HDC 10]
! (T<T0: I->S)
!-------------------------------------------------------------
acrfac = 2.*rslope3(i,k,2)+2.*diameter*rslope2(i,k,2) &
+ diameter**2*rslope(i,k,2)
psaci(i,k) = pi*qci(i,k,2)*eacrs*n0s*n0sfac(i,k)*abs(vt2s-vt2i) &
*acrfac/4.
endif
endif
!-------------------------------------------------------------
! psacw: Accretion of cloud water by snow [HL A7] [LFO 24]
! (T<T0: C->S, and T>=T0: C->R)
!-------------------------------------------------------------
if(qrs(i,k,2).gt.qcrmin .and. qci(i,k,1).gt.qmin) then
psacw(i,k) = min(pacrc*n0sfac(i,k)*rslope3(i,k,2)*rslopeb(i,k,2) &
*qci(i,k,1)*denfac(i,k),qci(i,k,1)*rdtcld)
endif
!-------------------------------------------------------------
! nsacw: Accretion of cloud water by snow
! (NC ->)
!-------------------------------------------------------------
if(qrs(i,k,2).gt.qcrmin .and. ncr(i,k,2).gt.ncmin) then
nsacw(i,k) = min(pacrc*n0sfac(i,k)*rslope3(i,k,2)*rslopeb(i,k,2) &
*ncr(i,k,2)*denfac(i,k),ncr(i,k,2)/dtcld)
endif
if(supcol.le.0) then
xlf = xlf0
!--------------------------------------------------------------
! nseml: Enhanced melting of snow by accretion of water
! (T>=T0: ->NR)
!--------------------------------------------------------------
if (qrs(i,k,2).gt.qcrmin) then
sfac = rslope(i,k,2)*n0s*n0sfac(i,k)/qrs(i,k,2)
nseml(i,k) = -sfac*min(max(cliq*supcol*(psacw(i,k))/xlf &
,-qrs(i,k,2)/dtcld),0.)
endif
endif
if(supcol.gt.0) then
!-------------------------------------------------------------
! pidep: Deposition/Sublimation rate of ice [HDC 9]
! (T<T0: V->I or I->V)
!-------------------------------------------------------------
if(qci(i,k,2).gt.0 .and. ifsat.ne.1) then
xmi = den(i,k)*qci(i,k,2)/xni(i,k)
diameter = dicon * sqrt(xmi)
pidep(i,k) = 4.*diameter*xni(i,k)*(rh(i,k,2)-1.)/work1(i,k,2)
supice = satdt-prevp(i,k)
if(pidep(i,k).lt.0.) then
! pidep(i,k) = max(max(pidep(i,k),satdt/2),supice)
! pidep(i,k) = max(pidep(i,k),-qci(i,k,2)/dtcld)
pidep(i,k) = max(max(pidep(i,k),satdt*.5),supice)
pidep(i,k) = max(pidep(i,k),-qci(i,k,2)*rdtcld)
else
! pidep(i,k) = min(min(pidep(i,k),satdt/2),supice)
pidep(i,k) = min(min(pidep(i,k),satdt*.5),supice)
endif
if(abs(prevp(i,k)+pidep(i,k)).ge.abs(satdt)) ifsat = 1
endif
!-------------------------------------------------------------
! psdep: deposition/sublimation rate of snow [HDC 14]
! (V->S or S->V)
!-------------------------------------------------------------
if(qrs(i,k,2).gt.0. .and. ifsat.ne.1) then
coeres = rslope2(i,k,2)*sqrt(rslope(i,k,2)*rslopeb(i,k,2))
psdep(i,k) = (rh(i,k,2)-1.)*n0sfac(i,k)*(precs1*rslope2(i,k,2) &
+ precs2*work2(i,k)*coeres)/work1(i,k,2)
supice = satdt-prevp(i,k)-pidep(i,k)
if(psdep(i,k).lt.0.) then
! psdep(i,k) = max(psdep(i,k),-qrs(i,k,2)/dtcld)
! psdep(i,k) = max(max(psdep(i,k),satdt/2),supice)
psdep(i,k) = max(psdep(i,k),-qrs(i,k,2)*rdtcld)
psdep(i,k) = max(max(psdep(i,k),satdt*.5),supice)
else
! psdep(i,k) = min(min(psdep(i,k),satdt/2),supice)
psdep(i,k) = min(min(psdep(i,k),satdt*.5),supice)
endif
if(abs(prevp(i,k)+pidep(i,k)+psdep(i,k)).ge.abs(satdt)) ifsat = 1
endif
!-------------------------------------------------------------
! pigen: generation(nucleation) of ice from vapor [HL A50] [HDC 7-8]
! (T<T0: V->I)
!-------------------------------------------------------------
if(supsat.gt.0 .and. ifsat.ne.1) then
supice = satdt-prevp(i,k)-pidep(i,k)-psdep(i,k)
xni0 = 1.e3*exp(0.1*supcol)
roqi0 = 4.92e-11*exp(log(xni0)*(1.33))
pigen(i,k) = max(0.,(roqi0/den(i,k)-max(qci(i,k,2),0.))*rdtcld)
pigen(i,k) = min(min(pigen(i,k),satdt),supice)
endif
!
!-------------------------------------------------------------
! psaut: conversion(aggregation) of ice to snow [HDC 12]
! (T<T0: I->S)
!-------------------------------------------------------------
if(qci(i,k,2).gt.0.) then
qimax = roqimax/den(i,k)
! psaut(i,k) = max(0.,(qci(i,k,2)-qimax)/dtcld)
psaut(i,k) = max(0.,(qci(i,k,2)-qimax)*rdtcld)
endif
endif
!-------------------------------------------------------------
! psevp: Evaporation of melting snow [HL A35] [RH83 A27]
! (T>T0: S->V)
!-------------------------------------------------------------
if(supcol.lt.0.) then
if(qrs(i,k,2).gt.0. .and. rh(i,k,1).lt.1.) &
psevp(i,k) = psdep(i,k)*work1(i,k,2)/work1(i,k,1)
! psevp(i,k) = min(max(psevp(i,k),-qrs(i,k,2)/dtcld),0.)
psevp(i,k) = min(max(psevp(i,k),-qrs(i,k,2)*rdtcld),0.)
endif
enddo
enddo
!
!
!----------------------------------------------------------------
! check mass conservation of generation terms and feedback to the
! large scale
!
do k = kts, kte
do i = its, ite
if(t(i,k).le.t0c) then
!
! Q_cloud water
!
value = max(qmin,qci(i,k,1))
source = (praut(i,k)+pracw(i,k)+psacw(i,k)-prevp_s(i,k))*dtcld
if (source.gt.value) then
factor = value/source
praut(i,k) = praut(i,k)*factor
pracw(i,k) = pracw(i,k)*factor
psacw(i,k) = psacw(i,k)*factor
prevp_s(i,k) = prevp_s(i,k)*factor
endif
!
! Q_cloud ice
!
value = max(qmin,qci(i,k,2))
source = (psaut(i,k)+psaci(i,k)-pigen(i,k)-pidep(i,k))*dtcld
if (source.gt.value) then
factor = value/source
psaut(i,k) = psaut(i,k)*factor
psaci(i,k) = psaci(i,k)*factor
pigen(i,k) = pigen(i,k)*factor
pidep(i,k) = pidep(i,k)*factor
endif
!
! Q_rain
!
!
value = max(qmin,qrs(i,k,1))
source = (-praut(i,k)-pracw(i,k)-prevp(i,k)+prevp_s(i,k))*dtcld
if (source.gt.value) then
factor = value/source
praut(i,k) = praut(i,k)*factor
pracw(i,k) = pracw(i,k)*factor
prevp(i,k) = prevp(i,k)*factor
prevp_s(i,k) = prevp_s(i,k)*factor
endif
!
! Q_snow
!
value = max(qmin,qrs(i,k,2))
source = (-psdep(i,k)-psaut(i,k)-psaci(i,k)-psacw(i,k))*dtcld
if (source.gt.value) then
factor = value/source
psdep(i,k) = psdep(i,k)*factor
psaut(i,k) = psaut(i,k)*factor
psaci(i,k) = psaci(i,k)*factor
psacw(i,k) = psacw(i,k)*factor
endif
!
! N_cloud
!
value = max(ncmin,ncr(i,k,2))
source = (+nraut(i,k)+nccol(i,k)+nracw(i,k)+nsacw(i,k) &
-nrevp(i,k))*dtcld
if (source.gt.value) then
factor = value/source
nraut(i,k) = nraut(i,k)*factor
nccol(i,k) = nccol(i,k)*factor
nracw(i,k) = nracw(i,k)*factor
nsacw(i,k) = nsacw(i,k)*factor
nrevp(i,k) = nrevp(i,k)*factor
endif
!
! N_rain
!
value = max(nrmin,ncr(i,k,3))
source = (-nraut(i,k)+nrcol(i,k)+nrevp(i,k))*dtcld
if (source.gt.value) then
factor = value/source
nraut(i,k) = nraut(i,k)*factor
nrcol(i,k) = nrcol(i,k)*factor
nrevp(i,k) = nrevp(i,k)*factor
endif
!
work2(i,k)=-(prevp(i,k)+psdep(i,k)+pigen(i,k)+pidep(i,k))
! update
q(i,k) = q(i,k)+work2(i,k)*dtcld
qci(i,k,1) = max(qci(i,k,1)-(praut(i,k)+pracw(i,k)+psacw(i,k) &
+prevp_s(i,k))*dtcld,0.)
qrs(i,k,1) = max(qrs(i,k,1)+(praut(i,k)+pracw(i,k)+prevp(i,k) &
-prevp_s(i,k))*dtcld,0.)
qci(i,k,2) = max(qci(i,k,2)-(psaut(i,k)+psaci(i,k)-pigen(i,k) &
-pidep(i,k))*dtcld,0.)
qrs(i,k,2) = max(qrs(i,k,2)+(psdep(i,k)+psaut(i,k)+psaci(i,k) &
+psacw(i,k))*dtcld,0.)
ncr(i,k,2) = max(ncr(i,k,2)+(-nraut(i,k)-nccol(i,k)-nracw(i,k) &
-nsacw(i,k)+nrevp(i,k))*dtcld,0.)
ncr(i,k,3) = max(ncr(i,k,3)+(nraut(i,k)-nrcol(i,k)-nrevp(i,k)) &
*dtcld,0.)
xlf = xls-xl(i,k)
xlwork2 = -xls*(psdep(i,k)+pidep(i,k)+pigen(i,k)) &
-xl(i,k)*prevp(i,k)-xlf*psacw(i,k)
t(i,k) = t(i,k)-xlwork2/cpm(i,k)*dtcld
else
!
! Q_cloud water
!
value = max(qmin,qci(i,k,1))
source=(praut(i,k)+pracw(i,k)+psacw(i,k)-prevp_s(i,k))*dtcld
if (source.gt.value) then
factor = value/source
praut(i,k) = praut(i,k)*factor
pracw(i,k) = pracw(i,k)*factor
psacw(i,k) = psacw(i,k)*factor
prevp_s(i,k) = prevp_s(i,k)*factor
endif
!
! Q_rain
!
value = max(qmin,qrs(i,k,1))
source = (-praut(i,k)-pracw(i,k)-prevp(i,k)+prevp_s(i,k) &
-psacw(i,k))*dtcld
if (source.gt.value) then
factor = value/source
praut(i,k) = praut(i,k)*factor
pracw(i,k) = pracw(i,k)*factor
prevp(i,k) = prevp(i,k)*factor
psacw(i,k) = psacw(i,k)*factor
prevp_s(i,k) = prevp_s(i,k)*factor
endif
!
! Q_snow
!
value = max(qcrmin,qrs(i,k,2))
source=(-psevp(i,k))*dtcld
if (source.gt.value) then
factor = value/source
psevp(i,k) = psevp(i,k)*factor
endif
!
! N_cloud
!
value = max(ncmin,ncr(i,k,2))
source = (+nraut(i,k)+nccol(i,k)+nracw(i,k)+nsacw(i,k) &
-nrevp(i,k))*dtcld
if (source.gt.value) then
factor = value/source
nraut(i,k) = nraut(i,k)*factor
nccol(i,k) = nccol(i,k)*factor
nracw(i,k) = nracw(i,k)*factor
nsacw(i,k) = nsacw(i,k)*factor
nrevp(i,k) = nrevp(i,k)*factor
endif
!
! N_rain
!
value = max(nrmin,ncr(i,k,3))
source = (-nraut(i,k)-nseml(i,k)+nrcol(i,k)+nrevp(i,k))*dtcld
if (source.gt.value) then
factor = value/source
nraut(i,k) = nraut(i,k)*factor
nseml(i,k) = nseml(i,k)*factor
nrcol(i,k) = nrcol(i,k)*factor
nrevp(i,k) = nrevp(i,k)*factor
endif
work2(i,k)=-(prevp(i,k)+psevp(i,k))
! update
q(i,k) = q(i,k)+work2(i,k)*dtcld
qci(i,k,1) = max(qci(i,k,1)-(praut(i,k)+pracw(i,k)+psacw(i,k) &
+prevp_s(i,k))*dtcld,0.)
qrs(i,k,1) = max(qrs(i,k,1)+(praut(i,k)+pracw(i,k)+prevp(i,k) &
+psacw(i,k)-prevp_s(i,k))*dtcld,0.)
qrs(i,k,2) = max(qrs(i,k,2)+psevp(i,k)*dtcld,0.)
ncr(i,k,2) = max(ncr(i,k,2)+(-nraut(i,k)-nccol(i,k)-nracw(i,k) &
-nsacw(i,k)+nrevp(i,k))*dtcld,0.)
ncr(i,k,3) = max(ncr(i,k,3)+(nraut(i,k)+nseml(i,k)-nrcol(i,k) &
-nrevp(i,k))*dtcld,0.)
xlf = xls-xl(i,k)
xlwork2 = -xl(i,k)*(prevp(i,k)+psevp(i,k))
t(i,k) = t(i,k)-xlwork2/cpm(i,k)*dtcld
endif
enddo
enddo
!
! Inline expansion for fpvs
! qs(i,k,1) = fpvs(t(i,k),0,rd,rv,cpv,cliq,cice,xlv0,xls,psat,t0c)
! qs(i,k,2) = fpvs(t(i,k),1,rd,rv,cpv,cliq,cice,xlv0,xls,psat,t0c)
hsub = xls
hvap = xlv0
cvap = cpv
ttp=t0c+0.01
dldt=cvap-cliq
xa=-dldt/rv
xb=xa+hvap/(rv*ttp)
dldti=cvap-cice
xai=-dldti/rv
xbi=xai+hsub/(rv*ttp)
do k = kts, kte
do i = its, ite
tr=ttp/t(i,k)
logtr = log(tr)
qs(i,k,1)=psat*exp(logtr*(xa)+xb*(1.-tr))
qs(i,k,1) = ep2 * qs(i,k,1) / (p(i,k) - qs(i,k,1))
qs(i,k,1) = max(qs(i,k,1),qmin)
rh(i,k,1) = max(q(i,k) / qs(i,k,1),qmin)
enddo
enddo
!
do k = kts, kte
do i = its, ite
!---------------------------------------------------------------
! put the inital CCN number concentration
!
if(ncr(i,k,1).eq.0.) ncr(i,k,1) = ccn0
!---------------------------------------------------------------
! rate of change of cloud drop concentration due to CCN activation
! pcact: V -> C [KK 14]
! ncact: NCCN -> NC [KK 12]
if(rh(i,k,1).gt.1.) then
ncact(i,k) = max(0.,((ncr(i,k,1)+ncr(i,k,2)) &
*min(1.,(rh(i,k,1)/satmax)**actk) - ncr(i,k,2)))/dtcld
ncact(i,k) =min(ncact(i,k),max(ncr(i,k,1),0.)/dtcld)
pcact(i,k) = min(4.*pi*denr*(actr*1.E-6)**3*ncact(i,k)/ &
(3.*den(i,k)),max(q(i,k),0.)/dtcld)
q(i,k) = max(q(i,k)-pcact(i,k)*dtcld,0.)
qci(i,k,1) = max(qci(i,k,1)+pcact(i,k)*dtcld,0.)
ncr(i,k,1) = max(ncr(i,k,1)-ncact(i,k)*dtcld,0.)
ncr(i,k,2) = max(ncr(i,k,2)+ncact(i,k)*dtcld,0.)
t(i,k) = t(i,k)+pcact(i,k)*xl(i,k)/cpm(i,k)*dtcld
endif
!----------------------------------------------------------------
! pcond: condensational/evaporational rate of cloud water [HL A46] [RH83 A6]
! if there exists additional water vapor condensated/if
! evaporation of cloud water is not enough to remove subsaturation
tr=ttp/t(i,k)
qs(i,k,1)=psat*exp(log(tr)*(xa))*exp(xb*(1.-tr))
qs(i,k,1) = ep2 * qs(i,k,1) / (p(i,k) - qs(i,k,1))
qs(i,k,1) = max(qs(i,k,1),qmin)
work1(i,k,1) = ((max(q(i,k),qmin)-(qs(i,k,1)))/(1.+(xl(i,k)) &
*(xl(i,k))/(rv*(cpm(i,k)))*(qs(i,k,1))/((t(i,k)) &
*(t(i,k)))))
work2(i,k) = qci(i,k,1)+work1(i,k,1)
pcond(i,k) = min(max(work1(i,k,1)/dtcld,0.),max(q(i,k),0.)/dtcld)
if(qci(i,k,1).gt.0. .and. work1(i,k,1).lt.0.) &
pcond(i,k) = max(work1(i,k,1),-qci(i,k,1))/dtcld
!---------------------------------------------------------------
! ncevp: evpration of Cloud number concentration
!
if(pcond(i,k).eq.-qci(i,k,1)/dtcld) then
ncr(i,k,2) = 0.
ncr(i,k,1) = ncr(i,k,1)+ncr(i,k,2)
endif
!
q(i,k) = q(i,k)-pcond(i,k)*dtcld
qci(i,k,1) = max(qci(i,k,1)+pcond(i,k)*dtcld,0.)
t(i,k) = t(i,k)+pcond(i,k)*xl(i,k)/cpm(i,k)*dtcld
enddo
enddo
!
!----------------------------------------------------------------
! padding for small values
!
do k = kts, kte
do i = its, ite
if(qci(i,k,1).le.qmin) qci(i,k,1) = 0.0
if(qci(i,k,2).le.qmin) qci(i,k,2) = 0.0
enddo
enddo
enddo ! big loops
END SUBROUTINE wdm52d
! ...................................................................
REAL FUNCTION rgmma (docs) (x) 58
!-------------------------------------------------------------------
IMPLICIT NONE
!-------------------------------------------------------------------
! rgmma function: use infinite product form
REAL :: euler
PARAMETER (euler=0.577215664901532)
REAL :: x, y
INTEGER :: i
if(x.eq.1.)then
rgmma=0.
else
rgmma=x*exp(euler*x)
do i=1,10000
y=float(i)
rgmma=rgmma*(1.000+x/y)*exp(-x/y)
enddo
rgmma=1./rgmma
endif
END FUNCTION rgmma
!
!--------------------------------------------------------------------------
REAL FUNCTION fpvs (docs) (t,ice,rd,rv,cvap,cliq,cice,hvap,hsub,psat,t0c) 6
!--------------------------------------------------------------------------
IMPLICIT NONE
!--------------------------------------------------------------------------
REAL t,rd,rv,cvap,cliq,cice,hvap,hsub,psat,t0c,dldt,xa,xb,dldti, &
xai,xbi,ttp,tr
INTEGER ice
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
ttp=t0c+0.01
dldt=cvap-cliq
xa=-dldt/rv
xb=xa+hvap/(rv*ttp)
dldti=cvap-cice
xai=-dldti/rv
xbi=xai+hsub/(rv*ttp)
tr=ttp/t
if(t.lt.ttp .and. ice.eq.1) then
fpvs=psat*exp(log(tr)*(xai))*exp(xbi*(1.-tr))
else
fpvs=psat*exp(log(tr)*(xa))*exp(xb*(1.-tr))
endif
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
END FUNCTION fpvs
!-------------------------------------------------------------------
SUBROUTINE wdm5init (docs) (den0,denr,dens,cl,cpv,ccn0,allowed_to_read) 1,12
!-------------------------------------------------------------------
IMPLICIT NONE
!-------------------------------------------------------------------
!.... constants which may not be tunable
REAL, INTENT(IN) :: den0,denr,dens,cl,cpv,ccn0
LOGICAL, INTENT(IN) :: allowed_to_read
REAL :: pi
!
pi = 4.*atan(1.)
xlv1 = cl-cpv
!
qc0 = 4./3.*pi*denr*r0**3*xncr/den0 ! 0.419e-3 -- .61e-3
qck1 = .104*9.8*peaut/(xncr*denr)**(1./3.)/xmyu*den0**(4./3.) ! 7.03
pidnc = pi*denr/6.
!
bvtr1 = 1.+bvtr
bvtr2 = 2.+bvtr
bvtr3 = 3.+bvtr
bvtr4 = 4.+bvtr
bvtr5 = 5.+bvtr
bvtr7 = 7.+bvtr
bvtr2o5 = 2.5+.5*bvtr
bvtr3o5 = 3.5+.5*bvtr
g1pbr = rgmma(bvtr1)
g2pbr = rgmma(bvtr2)
g3pbr = rgmma(bvtr3)
g4pbr = rgmma(bvtr4) ! 17.837825
g5pbr = rgmma(bvtr5)
g7pbr = rgmma(bvtr7)
g5pbro2 = rgmma(bvtr2o5)
g7pbro2 = rgmma(bvtr3o5)
pvtr = avtr*g5pbr/24.
pvtrn = avtr*g2pbr
eacrr = 1.0
pacrr = pi*n0r*avtr*g3pbr*.25*eacrr
precr1 = 2.*pi*1.56
precr2 = 2.*pi*.31*avtr**.5*g7pbro2
pidn0r = pi*denr*n0r
pidnr = 4.*pi*denr
xmmax = (dimax/dicon)**2
roqimax = 2.08e22*dimax**8
!
bvts1 = 1.+bvts
bvts2 = 2.5+.5*bvts
bvts3 = 3.+bvts
bvts4 = 4.+bvts
g1pbs = rgmma(bvts1) !.8875
g3pbs = rgmma(bvts3)
g4pbs = rgmma(bvts4) ! 12.0786
g5pbso2 = rgmma(bvts2)
pvts = avts*g4pbs/6.
pacrs = pi*n0s*avts*g3pbs*.25
precs1 = 4.*n0s*.65
precs2 = 4.*n0s*.44*avts**.5*g5pbso2
pidn0s = pi*dens*n0s
pacrc = pi*n0s*avts*g3pbs*.25*eacrc
!
rslopecmax = 1./lamdacmax
rslopermax = 1./lamdarmax
rslopesmax = 1./lamdasmax
rsloperbmax = rslopermax ** bvtr
rslopesbmax = rslopesmax ** bvts
rslopec2max = rslopecmax * rslopecmax
rsloper2max = rslopermax * rslopermax
rslopes2max = rslopesmax * rslopesmax
rslopec3max = rslopec2max * rslopecmax
rsloper3max = rsloper2max * rslopermax
rslopes3max = rslopes2max * rslopesmax
!
END SUBROUTINE wdm5init
END MODULE module_mp_wdm5