#if ( RWORDSIZE == 4 )
# define VREC vsrec
# define VSQRT vssqrt
#else
# define VREC vrec
# define VSQRT vsqrt
#endif
MODULE module_mp_wdm6 2
!
!
!
REAL, PARAMETER, PRIVATE :: dtcldcr = 120. ! maximum time step for minor loops
REAL, PARAMETER, PRIVATE :: n0r = 8.e6 ! intercept parameter rain
REAL, PARAMETER, PRIVATE :: n0g = 4.e6 ! intercept parameter graupel
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 :: avtg = 330. ! a constant for terminal velocity of graupel
REAL, PARAMETER, PRIVATE :: bvtg = 0.8 ! a constant for terminal velocity of graupel
REAL, PARAMETER, PRIVATE :: deng = 500. ! density of graupel
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 :: dens = 100.0 ! Density of snow
REAL, PARAMETER, PRIVATE :: qs0 = 6.e-4 ! threshold amount for aggretion to occur
!
REAL, PARAMETER, PRIVATE :: satmax = 1.0048 ! maximum saturation value for CCN activation
! 1.008 for maritime /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 = 2000.e-6 ! 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, &
bvtr6,bvtr7, bvtr2o5,bvtr3o5, &
g1pbr,g2pbr,g3pbr,g4pbr,g5pbr,g6pbr,g7pbr, &
g5pbro2,g7pbro2,pi, &
pvtr,pvtrn,eacrr,pacrr,pidn0r,pidnr, &
precr1,precr2,xmmax,roqimax,bvts1,bvts2, &
bvts3,bvts4,g1pbs,g3pbs,g4pbs,g5pbso2, &
pvts,pacrs,precs1,precs2,pidn0s,xlv1,pacrc, &
bvtg1,bvtg2,bvtg3,bvtg4,g1pbg,g3pbg,g4pbg, &
g5pbgo2,pvtg,pacrg,precg1,precg2,pidn0g, &
rslopecmax,rslopec2max,rslopec3max, &
rslopermax,rslopesmax,rslopegmax, &
rsloperbmax,rslopesbmax,rslopegbmax, &
rsloper2max,rslopes2max,rslopeg2max, &
rsloper3max,rslopes3max,rslopeg3max
CONTAINS
!===================================================================
!
SUBROUTINE wdm6(th, q, qc, qr, qi, qs, qg, & 1,1
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, &
graupel, graupelncv, &
itimestep, &
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 6-class GRAUPEL phase
! microphyiscs scheme (WDM6). 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 6-class microphysics (WSM6, Hong and Lim 2006)
! in which theoretical background for WSM ice phase microphysics is
! based on Hong et al. (2004). A new mixed-phase terminal velocity
! for precipitating ice is introduced in WSM6 (Dudhia et al. 2008).
! The WDM scheme is described in Lim and Hong (2010).
! All units are in m.k.s. and source/sink terms in kgkg-1s-1.
!
! WDM6 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, 2010) Mon. Wea. Rev.
! 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, &
qg, &
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
INTEGER, INTENT(IN ) :: itimestep
REAL, DIMENSION( ims:ime , jms:jme ), &
INTENT(INOUT) :: rain, &
rainncv, &
sr
REAL, DIMENSION( ims:ime , jms:jme ), OPTIONAL, &
INTENT(INOUT) :: snow, &
snowncv
REAL, DIMENSION( ims:ime , jms:jme ), OPTIONAL, &
INTENT(INOUT) :: graupel, &
graupelncv
! LOCAL VAR
REAL, DIMENSION( its:ite , kts:kte ) :: t
REAL, DIMENSION( its:ite , kts:kte, 2 ) :: qci
REAL, DIMENSION( its:ite , kts:kte, 3 ) :: qrs, ncr
INTEGER :: i,j,k
!-------------------------------------------------------------------
IF (itimestep .eq. 1) THEN
DO j=jms,jme
DO k=kms,kme
DO i=ims,ime
nn(i,k,j) = ccn0
ENDDO
ENDDO
ENDDO
ENDIF
!
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)
qrs(i,k,3) = qg(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 wdm62D
(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) &
,graupel(ims,j),graupelncv(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)
qg(i,k,j) = qrs(i,k,3)
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
END SUBROUTINE wdm6
!===================================================================
!
SUBROUTINE wdm62D(t, q, qci, qrs, ncr, den, p, delz & 1,8
,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 &
,graupel,graupelncv &
)
!-------------------------------------------------------------------
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
REAL, DIMENSION( its:ite , kts:kte, 3 ), &
INTENT(INOUT) :: &
qrs, &
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
REAL, DIMENSION( ims:ime ), OPTIONAL, &
INTENT(INOUT) :: graupel, &
graupelncv
! LOCAL VAR
REAL, DIMENSION( its:ite , kts:kte , 3) :: &
rh, qs, rslope, rslope2, rslope3, rslopeb, &
falk, fall, work1, qrs_tmp
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 ) :: &
worka,workr
REAL, DIMENSION( its:ite , kts:kte ) :: &
den_tmp, delz_tmp, ncr_tmp
REAL, DIMENSION( its:ite , kts:kte ) :: &
falkc, work1c, work2c, fallc
REAL, DIMENSION( its:ite , kts:kte ) :: &
pcact, prevp, psdep, pgdep, praut, psaut, pgaut, &
pracw, psacw, pgacw, pgacr, pgacs, psaci, pgmlt, praci, &
piacr, pracs, psacr, pgaci, pseml, pgeml, prevp_s
REAL, DIMENSION( its:ite , kts:kte ) :: paacw
REAL, DIMENSION( its:ite , kts:kte ) :: &
nraut, nracw, nrevp, ncevp, nccol, nrcol, &
nsacw, ngacw, niacr, nsacr, ngacr, naacw, &
nseml, ngeml, ncact
REAL, DIMENSION( its:ite , kts:kte ) :: &
pigen, pidep, pcond, xl, cpm, work2, psmlt, psevp, &
denfac, xni, pgevp,n0sfac, qsum, &
denqrs1, denqr1, denqrs2, denqrs3, denncr3, denqci
REAL, DIMENSION( its:ite ) :: &
delqrs1, delqrs2, delqrs3, delncr3, delqi
REAL, DIMENSION( its:ite ) :: tstepsnow, tstepgraup
REAL :: gfac, sfac
! variables for optimization
REAL, DIMENSION( its:ite ) :: tvec1
REAL :: temp
INTEGER, DIMENSION( its:ite ) :: mnstep, numndt
INTEGER, DIMENSION( its:ite ) :: mstep, numdt
LOGICAL, DIMENSION( its:ite ) :: flgcld
REAL :: &
cpmcal, xlcal, lamdac, &
diffus, &
viscos, xka, venfac, conden, diffac, &
x, y, z, a, b, c, d, e, &
ndt, qdt, holdrr, holdrs, holdrg, supcol, supcolt, &
pvt, coeres, supsat, dtcld, xmi, eacrs, satdt, &
qimax, diameter, xni0, roqi0, &
fallsum, fallsum_qsi, fallsum_qg, &
vt2i,vt2r,vt2s,vt2g,acrfac,egs,egi, &
xlwork2, factor, source, value, coecol, &
nfrzdtr, nfrzdtc, &
taucon, lencon, lenconcr, &
xlf, pfrzdtc, pfrzdtr, supice, alpha2, delta2, delta3
REAL :: vt2ave
REAL :: holdc, holdci
!
INTEGER :: i, j, k, mstepmax, &
iprt, latd, lond, loop, loops, ifsat, n, idim, kdim
! Temporaries used for inlining fpvs function
REAL :: dldti, xb, xai, tr, xbi, xa, hvap, cvap, hsub, dldt, ttp
!
!=================================================================
! 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)))
!----------------------------------------------------------------
! diffus: diffusion coefficient of the water vapor
! viscos: kinematic viscosity(m2s-1)
!
diffus(x,y) = 8.794e-5 * exp(log(x)*(1.81)) / y ! 8.794e-5*x**1.81/y
viscos(x,y) = 1.496e-6 * (x*sqrt(x)) /(x+120.)/y ! 1.496e-6*x**1.5/(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))
!
idim = ite-its+1
kdim = kte-kts+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)
qrs(i,k,3) = max(qrs(i,k,3),0.0)
ncr(i,k,1) = max(ncr(i,k,1),0.0)
ncr(i,k,2) = max(ncr(i,k,2),0.0)
ncr(i,k,3) = max(ncr(i,k,3),0.0)
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
do k = kts, kte
do i = its, ite
delz_tmp(i,k) = delz(i,k)
den_tmp(i,k) = den(i,k)
enddo
enddo
!
!----------------------------------------------------------------
! initialize the surface rain, snow, graupel
!
do i = its, ite
rainncv(i) = 0.
if(PRESENT (snowncv) .AND. PRESENT (snow)) snowncv(i) = 0.
if(PRESENT (graupelncv) .AND. PRESENT (graupel)) graupelncv(i) = 0.
sr(i) = 0.
! new local array to catch step snow and graupel
tstepsnow(i) = 0.
tstepgraup(i) = 0.
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
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)
do k = kts, kte
do i = its, ite
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)
rh(i,k,1) = max(q(i,k) / qs(i,k,1),qmin)
tr=ttp/t(i,k)
if(t(i,k).lt.ttp) then
qs(i,k,2)=psat*exp(log(tr)*(xai))*exp(xbi*(1.-tr))
else
qs(i,k,2)=psat*exp(log(tr)*(xa))*exp(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
!
!----------------------------------------------------------------
! initialize the variables for microphysical physics
!
!
do k = kts, kte
do i = its, ite
prevp(i,k) = 0.
psdep(i,k) = 0.
pgdep(i,k) = 0.
praut(i,k) = 0.
psaut(i,k) = 0.
pgaut(i,k) = 0.
pracw(i,k) = 0.
praci(i,k) = 0.
piacr(i,k) = 0.
psaci(i,k) = 0.
psacw(i,k) = 0.
pracs(i,k) = 0.
psacr(i,k) = 0.
pgacw(i,k) = 0.
paacw(i,k) = 0.
pgaci(i,k) = 0.
pgacr(i,k) = 0.
pgacs(i,k) = 0.
pigen(i,k) = 0.
pidep(i,k) = 0.
pcond(i,k) = 0.
psmlt(i,k) = 0.
pgmlt(i,k) = 0.
pseml(i,k) = 0.
pgeml(i,k) = 0.
psevp(i,k) = 0.
pgevp(i,k) = 0.
pcact(i,k) = 0.
prevp_s(i,k) = 0.
falk(i,k,1) = 0.
falk(i,k,2) = 0.
falk(i,k,3) = 0.
fall(i,k,1) = 0.
fall(i,k,2) = 0.
fall(i,k,3) = 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.
ngacw(i,k) = 0.
naacw(i,k) = 0.
niacr(i,k) = 0.
nsacr(i,k) = 0.
ngacr(i,k) = 0.
nseml(i,k) = 0.
ngeml(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
do k = kts, kte
do i = its, ite
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
!-------------------------------------------------------------
! Ni: ice crystal number concentraiton [HDC 5c]
!-------------------------------------------------------------
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
!----------------------------------------------------------------
! compute the fallout term:
! first, vertical terminal velosity for minor loops
!----------------------------------------------------------------
do k = kts, kte
do i = its, ite
qrs_tmp(i,k,1) = qrs(i,k,1)
qrs_tmp(i,k,2) = qrs(i,k,2)
qrs_tmp(i,k,3) = qrs(i,k,3)
ncr_tmp(i,k) = ncr(i,k,3)
enddo
enddo
call slope_wdm6(qrs_tmp,ncr_tmp,den_tmp,denfac,t,rslope,rslopeb,rslope2, &
rslope3,work1,workn,its,ite,kts,kte)
!
! vt update for qr and nr
mstepmax = 1
numdt = 1
do k = kte, kts, -1
do i = its, ite
work1(i,k,1) = work1(i,k,1)/delz(i,k)
workn(i,k) = workn(i,k)/delz(i,k)
numdt(i) = max(nint(max(work1(i,k,1),workn(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
falk(i,k,1) = den(i,k)*qrs(i,k,1)*work1(i,k,1)/mstep(i)
falkn(i,k) = ncr(i,k,3)*workn(i,k)/mstep(i)
fall(i,k,1) = fall(i,k,1)+falk(i,k,1)
falln(i,k) = falln(i,k)+falkn(i,k)
qrs(i,k,1) = max(qrs(i,k,1)-falk(i,k,1)*dtcld/den(i,k),0.)
ncr(i,k,3) = max(ncr(i,k,3)-falkn(i,k)*dtcld,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)
falkn(i,k) = ncr(i,k,3)*workn(i,k)/mstep(i)
fall(i,k,1) = fall(i,k,1)+falk(i,k,1)
falln(i,k) = falln(i,k)+falkn(i,k)
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.)
ncr(i,k,3) = max(ncr(i,k,3)-(falkn(i,k)-falkn(i,k+1)*delz(i,k+1) &
/delz(i,k))*dtcld,0.)
endif
enddo
enddo
do k = kts, kte
do i = its, ite
qrs_tmp(i,k,1) = qrs(i,k,1)
ncr_tmp(i,k) = ncr(i,k,3)
enddo
enddo
call slope_rain(qrs_tmp,ncr_tmp,den_tmp,denfac,t,rslope,rslopeb,rslope2, &
rslope3,work1,workn,its,ite,kts,kte)
do k = kte, kts, -1
do i = its, ite
work1(i,k,1) = work1(i,k,1)/delz(i,k)
workn(i,k) = workn(i,k)/delz(i,k)
enddo
enddo
enddo
! for semi
do k = kte, kts, -1
do i = its, ite
qsum(i,k) = max( (qrs(i,k,2)+qrs(i,k,3)), 1.E-15)
if(qsum(i,k) .gt. 1.e-15 ) then
worka(i,k) = (work1(i,k,2)*qrs(i,k,2) + work1(i,k,3)*qrs(i,k,3)) &
/qsum(i,k)
else
worka(i,k) = 0.
endif
denqrs2(i,k) = den(i,k)*qrs(i,k,2)
denqrs3(i,k) = den(i,k)*qrs(i,k,3)
enddo
enddo
call nislfv_rain_plm6(idim,kdim,den_tmp,denfac,t,delz_tmp,worka, &
denqrs2,denqrs3,delqrs2,delqrs3,dtcld,1,1)
do k = kts, kte
do i = its, ite
qrs(i,k,2) = max(denqrs2(i,k)/den(i,k),0.)
qrs(i,k,3) = max(denqrs3(i,k)/den(i,k),0.)
fall(i,k,2) = denqrs2(i,k)*worka(i,k)/delz(i,k)
fall(i,k,3) = denqrs3(i,k)*worka(i,k)/delz(i,k)
enddo
enddo
do i = its, ite
fall(i,1,2) = delqrs2(i)/delz(i,1)/dtcld
fall(i,1,3) = delqrs3(i)/delz(i,1)/dtcld
enddo
do k = kts, kte
do i = its, ite
qrs_tmp(i,k,1) = qrs(i,k,1)
qrs_tmp(i,k,2) = qrs(i,k,2)
qrs_tmp(i,k,3) = qrs(i,k,3)
ncr_tmp(i,k) = ncr(i,k,3)
enddo
enddo
call slope_wdm6(qrs_tmp,ncr_tmp,den_tmp,denfac,t,rslope,rslopeb,rslope2, &
rslope3,work1,workn,its,ite,kts,kte)
!
do k = kte, kts, -1
do i = its, ite
supcol = t0c-t(i,k)
n0sfac(i,k) = max(min(exp(alpha*supcol),n0smax/n0s),1.)
if(t(i,k).gt.t0c) then
!---------------------------------------------------------------
! psmlt: melting of snow [HL A33] [RH83 A25]
! (T>T0: QS->QR)
!---------------------------------------------------------------
xlf = xlf0
work2(i,k) = venfac(p(i,k),t(i,k),den(i,k))
if(qrs(i,k,2).gt.0.) then
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) = 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: melting of snow [LH A27]
! (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
!---------------------------------------------------------------
! pgmlt: melting of graupel [HL A23] [LFO 47]
! (T>T0: QG->QR)
!---------------------------------------------------------------
if(qrs(i,k,3).gt.0.) then
coeres = rslope2(i,k,3)*sqrt(rslope(i,k,3)*rslopeb(i,k,3))
pgmlt(i,k) = xka(t(i,k),den(i,k))/xlf*(t0c-t(i,k))*(precg1 &
*rslope2(i,k,3) + precg2*work2(i,k)*coeres)
pgmlt(i,k) = min(max(pgmlt(i,k)*dtcld/mstep(i), &
-qrs(i,k,3)/mstep(i)),0.)
qrs(i,k,3) = qrs(i,k,3) + pgmlt(i,k)
qrs(i,k,1) = qrs(i,k,1) - pgmlt(i,k)
!-------------------------------------------------------------------
! ngmlt: melting of graupel [LH A28]
! (T>T0: ->NR)
!-------------------------------------------------------------------
if(qrs(i,k,3).gt.qcrmin) then
gfac = rslope(i,k,3)*n0g/qrs(i,k,3)
ncr(i,k,3) = ncr(i,k,3) - gfac*pgmlt(i,k)
endif
t(i,k) = t(i,k) + xlf/cpm(i,k)*pgmlt(i,k)
endif
endif
enddo
enddo
!---------------------------------------------------------------
! Vice [ms-1] : fallout of ice crystal [HDC 5a]
!---------------------------------------------------------------
do k = kte, kts, -1
do i = its, ite
if(qci(i,k,2).le.0.) then
work1c(i,k) = 0.
else
xmi = den(i,k)*qci(i,k,2)/xni(i,k)
diameter = max(min(dicon * sqrt(xmi),dimax), 1.e-25)
work1c(i,k) = 1.49e4*exp(log(diameter)*(1.31))
endif
enddo
enddo
!
! forward semi-laglangian scheme (JH), PCM (piecewise constant), (linear)
!
do k = kte, kts, -1
do i = its, ite
denqci(i,k) = den(i,k)*qci(i,k,2)
enddo
enddo
call nislfv_rain_plmr(idim,kdim,den_tmp,denfac,t,delz_tmp,work1c,denqci,denqci, &
delqi,dtcld,1,0,0)
do k = kts, kte
do i = its, ite
qci(i,k,2) = max(denqci(i,k)/den(i,k),0.)
enddo
enddo
do i = its, ite
fallc(i,1) = delqi(i)/delz(i,1)/dtcld
enddo
!
!----------------------------------------------------------------
! rain (unit is mm/sec;kgm-2s-1: /1000*delt ===> m)==> mm for wrf
!
do i = its, ite
fallsum = fall(i,kts,1)+fall(i,kts,2)+fall(i,kts,3)+fallc(i,kts)
fallsum_qsi = fall(i,kts,2)+fallc(i,kts)
fallsum_qg = fall(i,kts,3)
if(fallsum.gt.0.) then
rainncv(i) = fallsum*delz(i,kts)/denr*dtcld*1000. + rainncv(i)
rain(i) = fallsum*delz(i,kts)/denr*dtcld*1000. + rain(i)
endif
if(fallsum_qsi.gt.0.) then
tstepsnow(i) = fallsum_qsi*delz(i,kts)/denr*dtcld*1000. + tstepsnow(i)
IF ( PRESENT (snowncv) .AND. PRESENT (snow)) THEN
snowncv(i) = fallsum_qsi*delz(i,kts)/denr*dtcld*1000. + snowncv(i)
snow(i) = fallsum_qsi*delz(i,kts)/denr*dtcld*1000. + snow(i)
ENDIF
endif
if(fallsum_qg.gt.0.) then
tstepgraup(i) = fallsum_qg*delz(i,kts)/denr*dtcld*1000. &
+ tstepgraup(i)
IF ( PRESENT (graupelncv) .AND. PRESENT (graupel)) THEN
graupelncv(i) = fallsum_qg*delz(i,kts)/denr*dtcld*1000. &
+ graupelncv(i)
graupel(i) = fallsum_qg*delz(i,kts)/denr*dtcld*1000. + graupel(i)
ENDIF
endif
! if(fallsum.gt.0.) sr(i) = (snowncv(i) + graupelncv(i)) &
if(fallsum.gt.0.) sr(i) = (tstepsnow(i) + tstepgraup(i)) &
/(rainncv(i)+1.e-12)
enddo
!
!---------------------------------------------------------------
! pimlt: instantaneous melting of cloud ice [HL A47] [RH83 A28]
! (T>T0: QI->QC)
!---------------------------------------------------------------
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 [LH A18]
! (T>T0: ->NC)
!--------------------------------------------------------------
ncr(i,k,2) = ncr(i,k,2) + xni(i,k)
t(i,k) = t(i,k) - xlf/cpm(i,k)*qci(i,k,2)
qci(i,k,2) = 0.
endif
!---------------------------------------------------------------
! pihmf: homogeneous of cloud water below -40c [HL A45]
! (T<-40C: QC->QI)
!---------------------------------------------------------------
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 [LH A17]
! (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 of cloud water [HL A44]
! (T0>T>-40C: QC->QI)
!---------------------------------------------------------------
if(supcol.gt.0. .and. qci(i,k,1).gt.qmin) 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 [LH A16]
! (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
!---------------------------------------------------------------
! pgfrz: freezing of rain water [HL A20] [LFO 45]
! (T<T0, QR->QG)
!---------------------------------------------------------------
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))
!---------------------------------------------------------------
! ngfrz: freezing of rain water [LH A26]
! (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,3) = qrs(i,k,3) + 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
!
!----------------------------------------------------------------
! update the slope parameters for microphysics computation
!
do k = kts, kte
do i = its, ite
qrs_tmp(i,k,1) = qrs(i,k,1)
qrs_tmp(i,k,2) = qrs(i,k,2)
qrs_tmp(i,k,3) = qrs(i,k,3)
ncr_tmp(i,k) = ncr(i,k,3)
enddo
enddo
call slope_wdm6(qrs_tmp,ncr_tmp,den_tmp,denfac,t,rslope,rslopeb,rslope2, &
rslope3,work1,workn,its,ite,kts,kte)
do k = kts, kte
do i = its, ite
!-----------------------------------------------------------------
! compute the mean-volume drop diameter [LH A10]
! 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 [LH A7]
! for cloud-droplet distribution
!--------------------------------------------------------------------
avedia(i,k,1) = rslopec(i,k)
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,2) = diffac(xls,p(i,k),t(i,k),den(i,k),qs(i,k,2))
work2(i,k) = venfac(p(i,k),t(i,k),den(i,k))
enddo
enddo
!
!===============================================================
!
! warm rain processes
!
! - follows the double-moment processes in Lim and Hong
!
!===============================================================
!
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 [LH 9] [CP 17]
! (QC->QR)
!--------------------------------------------------------------
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 [LH A6] [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 [LH 10] [CP 22 & 23]
! (QC->QR)
! nracw: accretion of cloud water by rain [LH A9]
! (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 [LH A8] [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 [LH A21] [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 [HL A41]
! (QV->QR or QR->QV)
!---------------------------------------------------------------
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 [LH A14]
! (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 [LH A15] [KK 23]
! (QR->QC)
!----------------------------------------------------------------
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)
!
!===============================================================
!
do k = kts, kte
do i = its, ite
supcol = t0c-t(i,k)
n0sfac(i,k) = max(min(exp(alpha*supcol),n0smax/n0s),1.)
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))
!
xmi = den(i,k)*qci(i,k,2)/xni(i,k)
diameter = min(dicon * sqrt(xmi),dimax)
vt2i = 1.49e4*diameter**1.31
vt2r=pvtr*rslopeb(i,k,1)*denfac(i,k)
vt2s=pvts*rslopeb(i,k,2)*denfac(i,k)
vt2g=pvtg*rslopeb(i,k,3)*denfac(i,k)
qsum(i,k) = max((qrs(i,k,2)+qrs(i,k,3)),1.e-15)
if(qsum(i,k) .gt. 1.e-15) then
vt2ave=(vt2s*qrs(i,k,2)+vt2g*qrs(i,k,3))/(qsum(i,k))
else
vt2ave=0.
endif
if(supcol.gt.0. .and. qci(i,k,2).gt.qmin) then
if(qrs(i,k,1).gt.qcrmin) then
!-------------------------------------------------------------
! praci: Accretion of cloud ice by rain [HL A15] [LFO 25]
! (T<T0: QI->QR)
!-------------------------------------------------------------
acrfac = 6.*rslope2(i,k,1)+4.*diameter*rslope(i,k,1) + diameter**2
praci(i,k) = pi*qci(i,k,2)*ncr(i,k,3)*abs(vt2r-vt2i)*acrfac/4.
praci(i,k) = min(praci(i,k),qci(i,k,2)/dtcld)
!-------------------------------------------------------------
! piacr: Accretion of rain by cloud ice [HL A19] [LFO 26]
! (T<T0: QR->QS or QR->QG)
!-------------------------------------------------------------
piacr(i,k) = pi*pi*avtr*ncr(i,k,3)*denr*xni(i,k)*denfac(i,k) &
*g7pbr*rslope3(i,k,1)*rslope2(i,k,1)*rslopeb(i,k,1) &
/24./den(i,k)
piacr(i,k) = min(piacr(i,k),qrs(i,k,1)/dtcld)
endif
!-------------------------------------------------------------
! niacr: Accretion of rain by cloud ice [LH A25]
! (T<T0: NR->)
!-------------------------------------------------------------
if(ncr(i,k,3).gt.nrmin) then
niacr(i,k) = pi*avtr*ncr(i,k,3)*xni(i,k)*denfac(i,k)*g4pbr &
*rslope2(i,k,1)*rslopeb(i,k,1)/4.
niacr(i,k) = min(niacr(i,k),ncr(i,k,3)/dtcld)
endif
!-------------------------------------------------------------
! psaci: Accretion of cloud ice by snow [HDC 10]
! (T<T0: QI->QS)
!-------------------------------------------------------------
if(qrs(i,k,2).gt.qcrmin) then
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(vt2ave-vt2i)*acrfac/4.
psaci(i,k) = min(psaci(i,k),qci(i,k,2)/dtcld)
endif
!-------------------------------------------------------------
! pgaci: Accretion of cloud ice by graupel [HL A17] [LFO 41]
! (T<T0: QI->QG)
!-------------------------------------------------------------
if(qrs(i,k,3).gt.qcrmin) then
egi = exp(0.07*(-supcol))
acrfac = 2.*rslope3(i,k,3)+2.*diameter*rslope2(i,k,3) &
+ diameter**2*rslope(i,k,3)
pgaci(i,k) = pi*egi*qci(i,k,2)*n0g*abs(vt2ave-vt2i)*acrfac/4.
pgaci(i,k) = min(pgaci(i,k),qci(i,k,2)/dtcld)
endif
endif
!-------------------------------------------------------------
! psacw: Accretion of cloud water by snow [HL A7] [LFO 24]
! (T<T0: QC->QS, and T>=T0: QC->QR)
!-------------------------------------------------------------
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)/dtcld)
endif
!-------------------------------------------------------------
! nsacw: Accretion of cloud water by snow [LH A12]
! (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
!-------------------------------------------------------------
! pgacw: Accretion of cloud water by graupel [HL A6] [LFO 40]
! (T<T0: QC->QG, and T>=T0: QC->QR)
!-------------------------------------------------------------
if(qrs(i,k,3).gt.qcrmin .and. qci(i,k,1).gt.qmin) then
pgacw(i,k) = min(pacrg*rslope3(i,k,3)*rslopeb(i,k,3)*qci(i,k,1) &
*denfac(i,k),qci(i,k,1)/dtcld)
endif
!-------------------------------------------------------------
! ngacw: Accretion of cloud water by graupel [LH A13]
! (NC->
!-------------------------------------------------------------
if(qrs(i,k,3).gt.qcrmin .and. ncr(i,k,2).gt.ncmin) then
ngacw(i,k) = min(pacrg*rslope3(i,k,3)*rslopeb(i,k,3)*ncr(i,k,2) &
*denfac(i,k),ncr(i,k,2)/dtcld)
endif
!-------------------------------------------------------------
! paacw: Accretion of cloud water by averaged snow/graupel
! (T<T0: QC->QG or QS, and T>=T0: QC->QR)
!-------------------------------------------------------------
if(qrs(i,k,2).gt.qcrmin .and. qrs(i,k,3).gt.qcrmin) then
paacw(i,k) = (qrs(i,k,2)*psacw(i,k)+qrs(i,k,3)*pgacw(i,k))/(qsum(i,k))
!-------------------------------------------------------------
! naacw: Accretion of cloud water by averaged snow/graupel
! (Nc->)
!-------------------------------------------------------------
naacw(i,k) = (qrs(i,k,2)*nsacw(i,k)+qrs(i,k,3)*ngacw(i,k))/(qsum(i,k))
endif
!-------------------------------------------------------------
! pracs: Accretion of snow by rain [HL A11] [LFO 27]
! (T<T0: QS->QG)
!-------------------------------------------------------------
if(qrs(i,k,2).gt.qcrmin .and. qrs(i,k,1).gt.qcrmin) then
if(supcol.gt.0) then
acrfac = 5.*rslope3(i,k,2)*rslope3(i,k,2) &
+ 4.*rslope3(i,k,2)*rslope2(i,k,2)*rslope(i,k,1) &
+ 1.5*rslope2(i,k,2)*rslope2(i,k,2)*rslope2(i,k,1)
pracs(i,k) = pi*pi*ncr(i,k,3)*n0s*n0sfac(i,k)*abs(vt2r-vt2ave) &
*(dens/den(i,k))*acrfac
pracs(i,k) = min(pracs(i,k),qrs(i,k,2)/dtcld)
endif
!-------------------------------------------------------------
! psacr: Accretion of rain by snow [HL A10] [LFO 28]
! (T<T0:QR->QS or QR->QG) (T>=T0: enhance melting of snow)
!-------------------------------------------------------------
acrfac = 30.*rslope3(i,k,1)*rslope2(i,k,1)*rslope(i,k,2) &
+ 5.*rslope2(i,k,1)*rslope2(i,k,1)*rslope2(i,k,2) &
+ 2.*rslope3(i,k,1)*rslope3(i,k,2)
psacr(i,k) = pi*pi*ncr(i,k,3)*n0s*n0sfac(i,k)*abs(vt2ave-vt2r) &
*(denr/den(i,k))*acrfac
psacr(i,k) = min(psacr(i,k),qrs(i,k,1)/dtcld)
endif
if(qrs(i,k,2).gt.qcrmin .and. ncr(i,k,3).gt.nrmin) then
!-------------------------------------------------------------
! nsacr: Accretion of rain by snow [LH A23]
! (T<T0:NR->)
!-------------------------------------------------------------
acrfac = 1.5*rslope2(i,k,1)*rslope(i,k,2) &
+ 1.0*rslope(i,k,1)*rslope2(i,k,2)+.5*rslope3(i,k,2)
nsacr(i,k) = pi*ncr(i,k,3)*n0s*n0sfac(i,k)*abs(vt2ave-vt2r) &
*acrfac
nsacr(i,k) = min(nsacr(i,k),ncr(i,k,3)/dtcld)
endif
!-------------------------------------------------------------
! pgacr: Accretion of rain by graupel [HL A12] [LFO 42]
! (T<T0: QR->QG) (T>=T0: enhance melting of graupel)
!-------------------------------------------------------------
if(qrs(i,k,3).gt.qcrmin .and. qrs(i,k,1).gt.qcrmin) then
acrfac = 30.*rslope3(i,k,1)*rslope2(i,k,1)*rslope(i,k,3) &
+ 5.*rslope2(i,k,1)*rslope2(i,k,1)*rslope2(i,k,3) &
+ 2.*rslope3(i,k,1)*rslope3(i,k,3)
pgacr(i,k) = pi*pi*ncr(i,k,3)*n0g*abs(vt2ave-vt2r)*(denr/den(i,k)) &
*acrfac
pgacr(i,k) = min(pgacr(i,k),qrs(i,k,1)/dtcld)
endif
!-------------------------------------------------------------
! ngacr: Accretion of rain by graupel [LH A24]
! (T<T0: NR->)
!-------------------------------------------------------------
if(qrs(i,k,3).gt.qcrmin .and. ncr(i,k,3).gt.nrmin) then
acrfac = 1.5*rslope2(i,k,1)*rslope(i,k,3) &
+ 1.0*rslope(i,k,1)*rslope2(i,k,3) + .5*rslope3(i,k,3)
ngacr(i,k) = pi*ncr(i,k,3)*n0g*abs(vt2ave-vt2r)*acrfac
ngacr(i,k) = min(ngacr(i,k),ncr(i,k,3)/dtcld)
endif
!
!-------------------------------------------------------------
! pgacs: Accretion of snow by graupel [HL A13] [LFO 29]
! (QS->QG) : This process is eliminated in V3.0 with the
! new combined snow/graupel fall speeds
!-------------------------------------------------------------
if(qrs(i,k,3).gt.qcrmin .and. qrs(i,k,2).gt.qcrmin) then
pgacs(i,k) = 0.
endif
if(supcol.le.0) then
xlf = xlf0
!-------------------------------------------------------------
! pseml: Enhanced melting of snow by accretion of water [HL A34]
! (T>=T0: QS->QR)
!-------------------------------------------------------------
if(qrs(i,k,2).gt.0.) &
pseml(i,k) = min(max(cliq*supcol*(paacw(i,k)+psacr(i,k)) &
/xlf,-qrs(i,k,2)/dtcld),0.)
!--------------------------------------------------------------
! nseml: Enhanced melting of snow by accretion of water [LH A29]
! (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*pseml(i,k)
endif
!-------------------------------------------------------------
! pgeml: Enhanced melting of graupel by accretion of water [HL A24] [RH84 A21-A22]
! (T>=T0: QG->QR)
!-------------------------------------------------------------
if(qrs(i,k,3).gt.0.) &
pgeml(i,k) = min(max(cliq*supcol*(paacw(i,k)+pgacr(i,k))/xlf &
,-qrs(i,k,3)/dtcld),0.)
!--------------------------------------------------------------
! ngeml: Enhanced melting of graupel by accretion of water [LH A30]
! (T>=T0: -> NR)
!--------------------------------------------------------------
if (qrs(i,k,3).gt.qcrmin) then
gfac = rslope(i,k,3)*n0g/qrs(i,k,3)
ngeml(i,k) = -gfac*pgeml(i,k)
endif
endif
if(supcol.gt.0) then
!-------------------------------------------------------------
! pidep: Deposition/Sublimation rate of ice [HDC 9]
! (T<T0: QV->QI or QI->QV)
!-------------------------------------------------------------
if(qci(i,k,2).gt.0. .and. ifsat.ne.1) then
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)
else
pidep(i,k) = min(min(pidep(i,k),satdt/2),supice)
endif
if(abs(prevp(i,k)+pidep(i,k)).ge.abs(satdt)) ifsat = 1
endif
!-------------------------------------------------------------
! psdep: deposition/sublimation rate of snow [HDC 14]
! (T<T0: QV->QS or QS->QV)
!-------------------------------------------------------------
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)
else
psdep(i,k) = min(min(psdep(i,k),satdt/2),supice)
endif
if(abs(prevp(i,k)+pidep(i,k)+psdep(i,k)).ge.abs(satdt)) ifsat = 1
endif
!-------------------------------------------------------------
! pgdep: deposition/sublimation rate of graupel [HL A21] [LFO 46]
! (T<T0: QV->QG or QG->QV)
!-------------------------------------------------------------
if(qrs(i,k,3).gt.0. .and. ifsat.ne.1) then
coeres = rslope2(i,k,3)*sqrt(rslope(i,k,3)*rslopeb(i,k,3))
pgdep(i,k) = (rh(i,k,2)-1.)*(precg1*rslope2(i,k,3) &
+ precg2*work2(i,k)*coeres)/work1(i,k,2)
supice = satdt-prevp(i,k)-pidep(i,k)-psdep(i,k)
if(pgdep(i,k).lt.0.) then
pgdep(i,k) = max(pgdep(i,k),-qrs(i,k,3)/dtcld)
pgdep(i,k) = max(max(pgdep(i,k),satdt/2),supice)
else
pgdep(i,k) = min(min(pgdep(i,k),satdt/2),supice)
endif
if(abs(prevp(i,k)+pidep(i,k)+psdep(i,k)+pgdep(i,k)).ge. &
abs(satdt)) ifsat = 1
endif
!-------------------------------------------------------------
! pigen: generation(nucleation) of ice from vapor [HL 50] [HDC 7-8]
! (T<T0: QV->QI)
!-------------------------------------------------------------
if(supsat.gt.0. .and. ifsat.ne.1) then
supice = satdt-prevp(i,k)-pidep(i,k)-psdep(i,k)-pgdep(i,k)
xni0 = 1.e3*exp(0.1*supcol)
roqi0 = 4.92e-11*xni0**1.33
pigen(i,k) = max(0.,(roqi0/den(i,k)-max(qci(i,k,2),0.))/dtcld)
pigen(i,k) = min(min(pigen(i,k),satdt),supice)
endif
!
!-------------------------------------------------------------
! psaut: conversion(aggregation) of ice to snow [HDC 12]
! (T<T0: QI->QS)
!-------------------------------------------------------------
if(qci(i,k,2).gt.0.) then
qimax = roqimax/den(i,k)
psaut(i,k) = max(0.,(qci(i,k,2)-qimax)/dtcld)
endif
!
!-------------------------------------------------------------
! pgaut: conversion(aggregation) of snow to graupel [HL A4] [LFO 37]
! (T<T0: QS->QG)
!-------------------------------------------------------------
if(qrs(i,k,2).gt.0.) then
alpha2 = 1.e-3*exp(0.09*(-supcol))
pgaut(i,k) = min(max(0.,alpha2*(qrs(i,k,2)-qs0)),qrs(i,k,2)/dtcld)
endif
endif
!
!-------------------------------------------------------------
! psevp: Evaporation of melting snow [HL A35] [RH83 A27]
! (T>=T0: QS->QV)
!-------------------------------------------------------------
if(supcol.lt.0.) then
if(qrs(i,k,2).gt.0. .and. rh(i,k,1).lt.1.) then
coeres = rslope2(i,k,2)*sqrt(rslope(i,k,2)*rslopeb(i,k,2))
psevp(i,k) = (rh(i,k,1)-1.)*n0sfac(i,k)*(precs1*rslope2(i,k,2) &
+precs2*work2(i,k)*coeres)/work1(i,k,1)
psevp(i,k) = min(max(psevp(i,k),-qrs(i,k,2)/dtcld),0.)
endif
!-------------------------------------------------------------
! pgevp: Evaporation of melting graupel [HL A25] [RH84 A19]
! (T>=T0: QG->QV)
!-------------------------------------------------------------
if(qrs(i,k,3).gt.0. .and. rh(i,k,1).lt.1.) then
coeres = rslope2(i,k,3)*sqrt(rslope(i,k,3)*rslopeb(i,k,3))
pgevp(i,k) = (rh(i,k,1)-1.)*(precg1*rslope2(i,k,3) &
+ precg2*work2(i,k)*coeres)/work1(i,k,1)
pgevp(i,k) = min(max(pgevp(i,k),-qrs(i,k,3)/dtcld),0.)
endif
endif
enddo
enddo
!
!
!----------------------------------------------------------------
! check mass conservation of generation terms and feedback to the
! large scale
!
do k = kts, kte
do i = its, ite
!
delta2=0.
delta3=0.
if(qrs(i,k,1).lt.1.e-4 .and. qrs(i,k,2).lt.1.e-4) delta2=1.
if(qrs(i,k,1).lt.1.e-4) delta3=1.
if(t(i,k).le.t0c) then
!
! cloud water
!
value = max(qmin,qci(i,k,1))
source = (praut(i,k)+pracw(i,k)+paacw(i,k)+paacw(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
paacw(i,k) = paacw(i,k)*factor
prevp_s(i,k) = prevp_s(i,k)*factor
endif
!
! cloud ice
!
value = max(qmin,qci(i,k,2))
source = (psaut(i,k)-pigen(i,k)-pidep(i,k)+praci(i,k)+psaci(i,k) &
+pgaci(i,k))*dtcld
if (source.gt.value) then
factor = value/source
psaut(i,k) = psaut(i,k)*factor
pigen(i,k) = pigen(i,k)*factor
pidep(i,k) = pidep(i,k)*factor
praci(i,k) = praci(i,k)*factor
psaci(i,k) = psaci(i,k)*factor
pgaci(i,k) = pgaci(i,k)*factor
endif
!
! rain
!
value = max(qmin,qrs(i,k,1))
source = (-praut(i,k)-prevp(i,k)-pracw(i,k)+piacr(i,k) &
+prevp_s(i,k)+psacr(i,k)+pgacr(i,k))*dtcld
if (source.gt.value) then
factor = value/source
praut(i,k) = praut(i,k)*factor
prevp(i,k) = prevp(i,k)*factor
pracw(i,k) = pracw(i,k)*factor
piacr(i,k) = piacr(i,k)*factor
psacr(i,k) = psacr(i,k)*factor
pgacr(i,k) = pgacr(i,k)*factor
prevp_s(i,k) = prevp_s(i,k)*factor
endif
!
! snow
!
value = max(qmin,qrs(i,k,2))
source = -(psdep(i,k)+psaut(i,k)-pgaut(i,k)+paacw(i,k) &
+piacr(i,k)*delta3+praci(i,k)*delta3 &
-pracs(i,k)*(1.-delta2)+psacr(i,k)*delta2 &
+psaci(i,k)-pgacs(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
pgaut(i,k) = pgaut(i,k)*factor
paacw(i,k) = paacw(i,k)*factor
piacr(i,k) = piacr(i,k)*factor
praci(i,k) = praci(i,k)*factor
psaci(i,k) = psaci(i,k)*factor
pracs(i,k) = pracs(i,k)*factor
psacr(i,k) = psacr(i,k)*factor
pgacs(i,k) = pgacs(i,k)*factor
endif
!
! graupel
!
value = max(qmin,qrs(i,k,3))
source = -(pgdep(i,k)+pgaut(i,k) &
+piacr(i,k)*(1.-delta3)+praci(i,k)*(1.-delta3) &
+psacr(i,k)*(1.-delta2)+pracs(i,k)*(1.-delta2) &
+pgaci(i,k)+paacw(i,k)+pgacr(i,k)+pgacs(i,k))*dtcld
if (source.gt.value) then
factor = value/source
pgdep(i,k) = pgdep(i,k)*factor
pgaut(i,k) = pgaut(i,k)*factor
piacr(i,k) = piacr(i,k)*factor
praci(i,k) = praci(i,k)*factor
psacr(i,k) = psacr(i,k)*factor
pracs(i,k) = pracs(i,k)*factor
paacw(i,k) = paacw(i,k)*factor
pgaci(i,k) = pgaci(i,k)*factor
pgacr(i,k) = pgacr(i,k)*factor
pgacs(i,k) = pgacs(i,k)*factor
endif
!
! cloud
!
value = max(ncmin,ncr(i,k,2))
source = (nraut(i,k)+nccol(i,k)+nracw(i,k) &
+naacw(i,k)+naacw(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
naacw(i,k) = naacw(i,k)*factor
nrevp(i,k) = nrevp(i,k)*factor
endif
!
! rain
!
value = max(nrmin,ncr(i,k,3))
source = (-nraut(i,k)+nrcol(i,k)+niacr(i,k)+nsacr(i,k)+ngacr(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
niacr(i,k) = niacr(i,k)*factor
nsacr(i,k) = nsacr(i,k)*factor
ngacr(i,k) = ngacr(i,k)*factor
nrevp(i,k) = nrevp(i,k)*factor
endif
!
work2(i,k)=-(prevp(i,k)+psdep(i,k)+pgdep(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) &
+paacw(i,k)+paacw(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)-piacr(i,k)-pgacr(i,k) &
-psacr(i,k)-prevp_s(i,k))*dtcld,0.)
qci(i,k,2) = max(qci(i,k,2)-(psaut(i,k)+praci(i,k) &
+psaci(i,k)+pgaci(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)+paacw(i,k) &
-pgaut(i,k)+piacr(i,k)*delta3 &
+praci(i,k)*delta3+psaci(i,k)-pgacs(i,k) &
-pracs(i,k)*(1.-delta2)+psacr(i,k)*delta2) &
*dtcld,0.)
qrs(i,k,3) = max(qrs(i,k,3)+(pgdep(i,k)+pgaut(i,k) &
+piacr(i,k)*(1.-delta3) &
+praci(i,k)*(1.-delta3)+psacr(i,k)*(1.-delta2) &
+pracs(i,k)*(1.-delta2)+pgaci(i,k)+paacw(i,k) &
+pgacr(i,k)+pgacs(i,k))*dtcld,0.)
ncr(i,k,2) = max(ncr(i,k,2)+(-nraut(i,k)-nccol(i,k)-nracw(i,k) &
-naacw(i,k)-naacw(i,k)+nrevp(i,k))*dtcld,0.)
ncr(i,k,3) = max(ncr(i,k,3)+(nraut(i,k)-nrcol(i,k)-niacr(i,k) &
-nsacr(i,k)-ngacr(i,k)-nrevp(i,k))*dtcld,0.)
xlf = xls-xl(i,k)
xlwork2 = -xls*(psdep(i,k)+pgdep(i,k)+pidep(i,k)+pigen(i,k)) &
-xl(i,k)*prevp(i,k)-xlf*(piacr(i,k)+paacw(i,k) &
+paacw(i,k)+pgacr(i,k)+psacr(i,k))
t(i,k) = t(i,k)-xlwork2/cpm(i,k)*dtcld
else
!
! cloud water
!
value = max(qmin,qci(i,k,1))
source= (praut(i,k)+pracw(i,k)+paacw(i,k)+paacw(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
paacw(i,k) = paacw(i,k)*factor
prevp_s(i,k) = prevp_s(i,k)*factor
endif
!
! rain
!
value = max(qmin,qrs(i,k,1))
source = (-paacw(i,k)-praut(i,k)+pseml(i,k)+pgeml(i,k) &
+prevp_s(i,k)-pracw(i,k)-paacw(i,k)-prevp(i,k))*dtcld
if (source.gt.value) then
factor = value/source
praut(i,k) = praut(i,k)*factor
prevp(i,k) = prevp(i,k)*factor
pracw(i,k) = pracw(i,k)*factor
paacw(i,k) = paacw(i,k)*factor
pseml(i,k) = pseml(i,k)*factor
pgeml(i,k) = pgeml(i,k)*factor
prevp_s(i,k) = prevp_s(i,k)*factor
endif
!
! snow
!
value = max(qcrmin,qrs(i,k,2))
source=(pgacs(i,k)-pseml(i,k)-psevp(i,k))*dtcld
if (source.gt.value) then
factor = value/source
pgacs(i,k) = pgacs(i,k)*factor
psevp(i,k) = psevp(i,k)*factor
pseml(i,k) = pseml(i,k)*factor
endif
!
! graupel
!
value = max(qcrmin,qrs(i,k,3))
source=-(pgacs(i,k)+pgevp(i,k)+pgeml(i,k))*dtcld
if (source.gt.value) then
factor = value/source
pgacs(i,k) = pgacs(i,k)*factor
pgevp(i,k) = pgevp(i,k)*factor
pgeml(i,k) = pgeml(i,k)*factor
endif
!
! cloud
!
value = max(ncmin,ncr(i,k,2))
source = (+nraut(i,k)+nccol(i,k)+nracw(i,k)+naacw(i,k) &
+naacw(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
naacw(i,k) = naacw(i,k)*factor
nrevp(i,k) = nrevp(i,k)*factor
endif
!
! rain
!
value = max(nrmin,ncr(i,k,3))
source = (-nraut(i,k)+nrcol(i,k)-nseml(i,k)-ngeml(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
nseml(i,k) = nseml(i,k)*factor
ngeml(i,k) = ngeml(i,k)*factor
endif
!
work2(i,k)=-(prevp(i,k)+psevp(i,k)+pgevp(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) &
+prevp_s(i,k)+paacw(i,k)+paacw(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)+paacw(i,k)+paacw(i,k)-pseml(i,k) &
-pgeml(i,k))*dtcld,0.)
qrs(i,k,2) = max(qrs(i,k,2)+(psevp(i,k)-pgacs(i,k) &
+pseml(i,k))*dtcld,0.)
qrs(i,k,3) = max(qrs(i,k,3)+(pgacs(i,k)+pgevp(i,k) &
+pgeml(i,k))*dtcld,0.)
ncr(i,k,2) = max(ncr(i,k,2)+(-nraut(i,k)-nccol(i,k)-nracw(i,k) &
-naacw(i,k)-naacw(i,k)+nrevp(i,k))*dtcld,0.)
ncr(i,k,3) = max(ncr(i,k,3)+(nraut(i,k)-nrcol(i,k)+nseml(i,k) &
+ngeml(i,k)-nrevp(i,k))*dtcld,0.)
xlf = xls-xl(i,k)
xlwork2 = -xl(i,k)*(prevp(i,k)+psevp(i,k)+pgevp(i,k)) &
-xlf*(pseml(i,k)+pgeml(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)
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)
tr=ttp/t(i,k)
if(t(i,k).lt.ttp) then
qs(i,k,2)=psat*exp(log(tr)*(xai))*exp(xbi*(1.-tr))
else
qs(i,k,2)=psat*exp(log(tr)*(xa))*exp(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,1) = max(q(i,k) / qs(i,k,1),qmin)
enddo
enddo
!
do k = kts, kte
do i = its, ite
!---------------------------------------------------------------
! rate of change of cloud drop concentration due to CCN activation
! pcact: QV -> QC [LH 8] [KK 14]
! ncact: NCCN -> NC [LH A2] [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
! (QV->QC or QC->QV)
!---------------------------------------------------------------
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) = conden(t(i,k),q(i,k),qs(i,k,1),xl(i,k),cpm(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 [LH A3]
! (NC->NCCN)
!----------------------------------------------------------------
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 wdm62d
! ...................................................................
REAL FUNCTION rgmma(x) 74
!-------------------------------------------------------------------
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(t,ice,rd,rv,cvap,cliq,cice,hvap,hsub,psat,t0c) 9
!--------------------------------------------------------------------------
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*(tr**xai)*exp(xbi*(1.-tr))
else
fpvs=psat*(tr**xa)*exp(xb*(1.-tr))
endif
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
END FUNCTION fpvs
!-------------------------------------------------------------------
SUBROUTINE wdm6init(den0,denr,dens,cl,cpv, ccn0, allowed_to_read) 1,17
!-------------------------------------------------------------------
IMPLICIT NONE
!-------------------------------------------------------------------
!.... constants which may not be tunable
REAL, INTENT(IN) :: den0,denr,dens,cl,cpv,ccn0
LOGICAL, INTENT(IN) :: allowed_to_read
!
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
bvtr6 = 6.+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)
g6pbr = rgmma(bvtr6)
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
!
bvtg1 = 1.+bvtg
bvtg2 = 2.5+.5*bvtg
bvtg3 = 3.+bvtg
bvtg4 = 4.+bvtg
g1pbg = rgmma(bvtg1)
g3pbg = rgmma(bvtg3)
g4pbg = rgmma(bvtg4)
g5pbgo2 = rgmma(bvtg2)
pacrg = pi*n0g*avtg*g3pbg*.25
pvtg = avtg*g4pbg/6.
precg1 = 2.*pi*n0g*.78
precg2 = 2.*pi*n0g*.31*avtg**.5*g5pbgo2
pidn0g = pi*deng*n0g
!
rslopecmax = 1./lamdacmax
rslopermax = 1./lamdarmax
rslopesmax = 1./lamdasmax
rslopegmax = 1./lamdagmax
rsloperbmax = rslopermax ** bvtr
rslopesbmax = rslopesmax ** bvts
rslopegbmax = rslopegmax ** bvtg
rslopec2max = rslopecmax * rslopecmax
rsloper2max = rslopermax * rslopermax
rslopes2max = rslopesmax * rslopesmax
rslopeg2max = rslopegmax * rslopegmax
rslopec3max = rslopec2max * rslopecmax
rsloper3max = rsloper2max * rslopermax
rslopes3max = rslopes2max * rslopesmax
rslopeg3max = rslopeg2max * rslopegmax
!
END SUBROUTINE wdm6init
!------------------------------------------------------------------------------
subroutine slope_wdm6(qrs,ncr,den,denfac,t,rslope,rslopeb,rslope2,rslope3, & 3
vt,vtn,its,ite,kts,kte)
IMPLICIT NONE
INTEGER :: its,ite, jts,jte, kts,kte
REAL, DIMENSION( its:ite , kts:kte,3) :: &
qrs, &
rslope, &
rslopeb, &
rslope2, &
rslope3, &
vt
REAL, DIMENSION( its:ite , kts:kte) :: &
ncr, &
vtn, &
den, &
denfac, &
t
REAL, PARAMETER :: t0c = 273.15
REAL, DIMENSION( its:ite , kts:kte ) :: &
n0sfac
REAL :: lamdar, lamdas, lamdag, x, y, z, supcol
integer :: i, j, k
!----------------------------------------------------------------
! size distributions: (x=mixing ratio, y=air density):
! valid for mixing ratio > 1.e-9 kg/kg.
!
! Optimizatin : A**B => exp(log(A)*(B))
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
lamdag(x,y)= sqrt(sqrt(pidn0g/(x*y))) ! (pidn0g/(x*y))**.25
!
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).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) = min(1./lamdar(qrs(i,k,1),den(i,k),ncr(i,k)),1.e-3)
rslopeb(i,k,1) = 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(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) = 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
if(qrs(i,k,3).le.qcrmin) then
rslope(i,k,3) = rslopegmax
rslopeb(i,k,3) = rslopegbmax
rslope2(i,k,3) = rslopeg2max
rslope3(i,k,3) = rslopeg3max
else
rslope(i,k,3) = 1./lamdag(qrs(i,k,3),den(i,k))
rslopeb(i,k,3) = rslope(i,k,3)**bvtg
rslope2(i,k,3) = rslope(i,k,3)*rslope(i,k,3)
rslope3(i,k,3) = rslope2(i,k,3)*rslope(i,k,3)
endif
vt(i,k,1) = pvtr*rslopeb(i,k,1)*denfac(i,k)
vt(i,k,2) = pvts*rslopeb(i,k,2)*denfac(i,k)
vt(i,k,3) = pvtg*rslopeb(i,k,3)*denfac(i,k)
vtn(i,k) = pvtrn*rslopeb(i,k,1)*denfac(i,k)
if(qrs(i,k,1).le.0.0) vt(i,k,1) = 0.0
if(qrs(i,k,2).le.0.0) vt(i,k,2) = 0.0
if(qrs(i,k,3).le.0.0) vt(i,k,3) = 0.0
if(ncr(i,k).le.0.0) vtn(i,k) = 0.0
enddo
enddo
END subroutine slope_wdm6
!-----------------------------------------------------------------------------
subroutine slope_rain(qrs,ncr,den,denfac,t,rslope,rslopeb,rslope2,rslope3, & 6
vt,vtn,its,ite,kts,kte)
IMPLICIT NONE
INTEGER :: its,ite, jts,jte, kts,kte
REAL, DIMENSION( its:ite , kts:kte) :: &
qrs, &
ncr, &
rslope, &
rslopeb, &
rslope2, &
rslope3, &
vt, &
vtn, &
den, &
denfac, &
t
REAL, PARAMETER :: t0c = 273.15
REAL, DIMENSION( its:ite , kts:kte ) :: &
n0sfac
REAL :: lamdar, x, y, z, supcol
integer :: i, j, k
!----------------------------------------------------------------
! size distributions: (x=mixing ratio, y=air density):
! valid for mixing ratio > 1.e-9 kg/kg.
lamdar(x,y,z)= exp(log(((pidnr*z)/(x*y)))*((.33333333)))
!
do k = kts, kte
do i = its, ite
if(qrs(i,k).le.qcrmin .or. ncr(i,k).le.nrmin) then
rslope(i,k) = rslopermax
rslopeb(i,k) = rsloperbmax
rslope2(i,k) = rsloper2max
rslope3(i,k) = rsloper3max
else
rslope(i,k) = min(1./lamdar(qrs(i,k),den(i,k),ncr(i,k)),1.e-3)
rslopeb(i,k) = rslope(i,k)**bvtr
rslope2(i,k) = rslope(i,k)*rslope(i,k)
rslope3(i,k) = rslope2(i,k)*rslope(i,k)
endif
vt(i,k) = pvtr*rslopeb(i,k)*denfac(i,k)
vtn(i,k) = pvtrn*rslopeb(i,k)*denfac(i,k)
if(qrs(i,k).le.0.0) vt(i,k) = 0.0
if(ncr(i,k).le.0.0) vtn(i,k) = 0.0
enddo
enddo
END subroutine slope_rain
!------------------------------------------------------------------------------
subroutine slope_snow(qrs,den,denfac,t,rslope,rslopeb,rslope2,rslope3, & 4
vt,its,ite,kts,kte)
IMPLICIT NONE
INTEGER :: its,ite, jts,jte, kts,kte
REAL, DIMENSION( its:ite , kts:kte) :: &
qrs, &
rslope, &
rslopeb, &
rslope2, &
rslope3, &
vt, &
den, &
denfac, &
t
REAL, PARAMETER :: t0c = 273.15
REAL, DIMENSION( its:ite , kts:kte ) :: &
n0sfac
REAL :: lamdas, x, y, z, supcol
integer :: i, j, k
!----------------------------------------------------------------
! size distributions: (x=mixing ratio, y=air density):
! valid for mixing ratio > 1.e-9 kg/kg.
lamdas(x,y,z)= sqrt(sqrt(pidn0s*z/(x*y))) ! (pidn0s*z/(x*y))**.25
!
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).le.qcrmin)then
rslope(i,k) = rslopesmax
rslopeb(i,k) = rslopesbmax
rslope2(i,k) = rslopes2max
rslope3(i,k) = rslopes3max
else
rslope(i,k) = 1./lamdas(qrs(i,k),den(i,k),n0sfac(i,k))
rslopeb(i,k) = rslope(i,k)**bvts
rslope2(i,k) = rslope(i,k)*rslope(i,k)
rslope3(i,k) = rslope2(i,k)*rslope(i,k)
endif
vt(i,k) = pvts*rslopeb(i,k)*denfac(i,k)
if(qrs(i,k).le.0.0) vt(i,k) = 0.0
enddo
enddo
END subroutine slope_snow
!----------------------------------------------------------------------------------
subroutine slope_graup(qrs,den,denfac,t,rslope,rslopeb,rslope2,rslope3, & 2
vt,its,ite,kts,kte)
IMPLICIT NONE
INTEGER :: its,ite, jts,jte, kts,kte
REAL, DIMENSION( its:ite , kts:kte) :: &
qrs, &
rslope, &
rslopeb, &
rslope2, &
rslope3, &
vt, &
den, &
denfac, &
t
REAL, PARAMETER :: t0c = 273.15
REAL, DIMENSION( its:ite , kts:kte ) :: &
n0sfac
REAL :: lamdag, x, y, z, supcol
integer :: i, j, k
!----------------------------------------------------------------
! size distributions: (x=mixing ratio, y=air density):
! valid for mixing ratio > 1.e-9 kg/kg.
lamdag(x,y)= sqrt(sqrt(pidn0g/(x*y))) ! (pidn0g/(x*y))**.25
!
do k = kts, kte
do i = its, ite
!---------------------------------------------------------------
! n0s: Intercept parameter for snow [m-4] [HDC 6]
!---------------------------------------------------------------
if(qrs(i,k).le.qcrmin)then
rslope(i,k) = rslopegmax
rslopeb(i,k) = rslopegbmax
rslope2(i,k) = rslopeg2max
rslope3(i,k) = rslopeg3max
else
rslope(i,k) = 1./lamdag(qrs(i,k),den(i,k))
rslopeb(i,k) = rslope(i,k)**bvtg
rslope2(i,k) = rslope(i,k)*rslope(i,k)
rslope3(i,k) = rslope2(i,k)*rslope(i,k)
endif
vt(i,k) = pvtg*rslopeb(i,k)*denfac(i,k)
if(qrs(i,k).le.0.0) vt(i,k) = 0.0
enddo
enddo
END subroutine slope_graup
!---------------------------------------------------------------------------------
!-------------------------------------------------------------------
SUBROUTINE nislfv_rain_plmr(im,km,denl,denfacl,tkl,dzl,wwl,rql,rnl,precip,dt,id,iter,rid) 1,2
!-------------------------------------------------------------------
!
! for non-iteration semi-Lagrangain forward advection for cloud
! with mass conservation and positive definite advection
! 2nd order interpolation with monotonic piecewise linear method
! this routine is under assumption of decfl < 1 for semi_Lagrangian
!
! dzl depth of model layer in meter
! wwl terminal velocity at model layer m/s
! rql cloud density*mixing ration
! precip precipitation
! dt time step
! id kind of precip: 0 test case; 1 raindrop
! iter how many time to guess mean terminal velocity: 0 pure forward.
! 0 : use departure wind for advection
! 1 : use mean wind for advection
! > 1 : use mean wind after iter-1 iterations
! rid : 1 for number 0 for mixing ratio
!
! author: hann-ming henry juang <henry.juang@noaa.gov>
! implemented by song-you hong
!
implicit none
integer im,km,id
real dt
real dzl(im,km),wwl(im,km),rql(im,km),rnl(im,km),precip(im)
real denl(im,km),denfacl(im,km),tkl(im,km)
!
integer i,k,n,m,kk,kb,kt,iter,rid
real tl,tl2,qql,dql,qqd
real th,th2,qqh,dqh
real zsum,qsum,dim,dip,c1,con1,fa1,fa2
real allold, allnew, zz, dzamin, cflmax, decfl
real dz(km), ww(km), qq(km), nr(km), wd(km), wa(km), wa2(km), was(km)
real den(km), denfac(km), tk(km)
real wi(km+1), zi(km+1), za(km+1)
real qn(km), qr(km),tmp(km),tmp1(km),tmp2(km),tmp3(km)
real dza(km+1), qa(km+1), qmi(km+1), qpi(km+1)
!
precip(:) = 0.0
!
i_loop : do i=1,im
! -----------------------------------
dz(:) = dzl(i,:)
qq(:) = rql(i,:)
nr(:) = rnl(i,:)
if(rid .eq. 1) nr(:) = rnl(i,:)/denl(i,:)
ww(:) = wwl(i,:)
den(:) = denl(i,:)
denfac(:) = denfacl(i,:)
tk(:) = tkl(i,:)
! skip for no precipitation for all layers
allold = 0.0
do k=1,km
allold = allold + qq(k)
enddo
if(allold.le.0.0) then
cycle i_loop
endif
!
! compute interface values
zi(1)=0.0
do k=1,km
zi(k+1) = zi(k)+dz(k)
enddo
!
! save departure wind
wd(:) = ww(:)
n=1
100 continue
! plm is 2nd order, we can use 2nd order wi or 3rd order wi
! 2nd order interpolation to get wi
wi(1) = ww(1)
wi(km+1) = ww(km)
do k=2,km
wi(k) = (ww(k)*dz(k-1)+ww(k-1)*dz(k))/(dz(k-1)+dz(k))
enddo
! 3rd order interpolation to get wi
fa1 = 9./16.
fa2 = 1./16.
wi(1) = ww(1)
wi(2) = 0.5*(ww(2)+ww(1))
do k=3,km-1
wi(k) = fa1*(ww(k)+ww(k-1))-fa2*(ww(k+1)+ww(k-2))
enddo
wi(km) = 0.5*(ww(km)+ww(km-1))
wi(km+1) = ww(km)
!
! terminate of top of raingroup
do k=2,km
if( ww(k).eq.0.0 ) wi(k)=ww(k-1)
enddo
!
! diffusivity of wi
con1 = 0.05
do k=km,1,-1
decfl = (wi(k+1)-wi(k))*dt/dz(k)
if( decfl .gt. con1 ) then
wi(k) = wi(k+1) - con1*dz(k)/dt
endif
enddo
! compute arrival point
do k=1,km+1
za(k) = zi(k) - wi(k)*dt
enddo
!
do k=1,km
dza(k) = za(k+1)-za(k)
enddo
dza(km+1) = zi(km+1) - za(km+1)
!
! computer deformation at arrival point
do k=1,km
qa(k) = qq(k)*dz(k)/dza(k)
qr(k) = qa(k)/den(k)
if(rid .eq. 1) qr(k) = qa(K)
enddo
qa(km+1) = 0.0
! call maxmin(km,1,qa,' arrival points ')
!
! compute arrival terminal velocity, and estimate mean terminal velocity
! then back to use mean terminal velocity
if( n.le.iter ) then
if(rid.eq.1) then
call slope_rain(nr,qr,den,denfac,tk,tmp,tmp1,tmp2,tmp3,wa,wa2,1,1,1,km)
else
call slope_rain(qr,nr,den,denfac,tk,tmp,tmp1,tmp2,tmp3,wa,wa2,1,1,1,km)
endif
if(rid.eq.1) wa(:) = wa2(:)
if( n.ge.2 ) wa(1:km)=0.5*(wa(1:km)+was(1:km))
do k=1,km
!#ifdef DEBUG
! print*,' slope_wsm3 ',qr(k)*1000.,den(k),denfac(k),tk(k),tmp(k),tmp1(k),tmp2(k),ww(k),wa(k)
!#endif
! mean wind is average of departure and new arrival winds
ww(k) = 0.5* ( wd(k)+wa(k) )
enddo
was(:) = wa(:)
n=n+1
go to 100
endif
!
! estimate values at arrival cell interface with monotone
do k=2,km
dip=(qa(k+1)-qa(k))/(dza(k+1)+dza(k))
dim=(qa(k)-qa(k-1))/(dza(k-1)+dza(k))
if( dip*dim.le.0.0 ) then
qmi(k)=qa(k)
qpi(k)=qa(k)
else
qpi(k)=qa(k)+0.5*(dip+dim)*dza(k)
qmi(k)=2.0*qa(k)-qpi(k)
if( qpi(k).lt.0.0 .or. qmi(k).lt.0.0 ) then
qpi(k) = qa(k)
qmi(k) = qa(k)
endif
endif
enddo
qpi(1)=qa(1)
qmi(1)=qa(1)
qmi(km+1)=qa(km+1)
qpi(km+1)=qa(km+1)
!
! interpolation to regular point
qn = 0.0
kb=1
kt=1
intp : do k=1,km
kb=max(kb-1,1)
kt=max(kt-1,1)
! find kb and kt
if( zi(k).ge.za(km+1) ) then
exit intp
else
find_kb : do kk=kb,km
if( zi(k).le.za(kk+1) ) then
kb = kk
exit find_kb
else
cycle find_kb
endif
enddo find_kb
find_kt : do kk=kt,km
if( zi(k+1).le.za(kk) ) then
kt = kk
exit find_kt
else
cycle find_kt
endif
enddo find_kt
kt = kt - 1
! compute q with piecewise constant method
if( kt.eq.kb ) then
tl=(zi(k)-za(kb))/dza(kb)
th=(zi(k+1)-za(kb))/dza(kb)
tl2=tl*tl
th2=th*th
qqd=0.5*(qpi(kb)-qmi(kb))
qqh=qqd*th2+qmi(kb)*th
qql=qqd*tl2+qmi(kb)*tl
qn(k) = (qqh-qql)/(th-tl)
else if( kt.gt.kb ) then
tl=(zi(k)-za(kb))/dza(kb)
tl2=tl*tl
qqd=0.5*(qpi(kb)-qmi(kb))
qql=qqd*tl2+qmi(kb)*tl
dql = qa(kb)-qql
zsum = (1.-tl)*dza(kb)
qsum = dql*dza(kb)
if( kt-kb.gt.1 ) then
do m=kb+1,kt-1
zsum = zsum + dza(m)
qsum = qsum + qa(m) * dza(m)
enddo
endif
th=(zi(k+1)-za(kt))/dza(kt)
th2=th*th
qqd=0.5*(qpi(kt)-qmi(kt))
dqh=qqd*th2+qmi(kt)*th
zsum = zsum + th*dza(kt)
qsum = qsum + dqh*dza(kt)
qn(k) = qsum/zsum
endif
cycle intp
endif
!
enddo intp
!
! rain out
sum_precip: do k=1,km
if( za(k).lt.0.0 .and. za(k+1).lt.0.0 ) then
precip(i) = precip(i) + qa(k)*dza(k)
cycle sum_precip
else if ( za(k).lt.0.0 .and. za(k+1).ge.0.0 ) then
precip(i) = precip(i) + qa(k)*(0.0-za(k))
exit sum_precip
endif
exit sum_precip
enddo sum_precip
!
! replace the new values
rql(i,:) = qn(:)
!
! ----------------------------------
enddo i_loop
!
END SUBROUTINE nislfv_rain_plmr
!-------------------------------------------------------------------
SUBROUTINE nislfv_rain_plm6(im,km,denl,denfacl,tkl,dzl,wwl,rql,rql2, precip1, precip2,dt,id,iter) 2,4
!-------------------------------------------------------------------
!
! for non-iteration semi-Lagrangain forward advection for cloud
! with mass conservation and positive definite advection
! 2nd order interpolation with monotonic piecewise linear method
! this routine is under assumption of decfl < 1 for semi_Lagrangian
!
! dzl depth of model layer in meter
! wwl terminal velocity at model layer m/s
! rql cloud density*mixing ration
! precip precipitation
! dt time step
! id kind of precip: 0 test case; 1 raindrop
! iter how many time to guess mean terminal velocity: 0 pure forward.
! 0 : use departure wind for advection
! 1 : use mean wind for advection
! > 1 : use mean wind after iter-1 iterations
!
! author: hann-ming henry juang <henry.juang@noaa.gov>
! implemented by song-you hong
!
implicit none
integer im,km,id
real dt
real dzl(im,km),wwl(im,km),rql(im,km),rql2(im,km),precip(im),precip1(im),precip2(im)
real denl(im,km),denfacl(im,km),tkl(im,km)
!
integer i,k,n,m,kk,kb,kt,iter,ist
real tl,tl2,qql,dql,qqd
real th,th2,qqh,dqh
real zsum,qsum,dim,dip,c1,con1,fa1,fa2
real allold, allnew, zz, dzamin, cflmax, decfl
real dz(km), ww(km), qq(km), qq2(km), wd(km), wa(km), wa2(km), was(km)
real den(km), denfac(km), tk(km)
real wi(km+1), zi(km+1), za(km+1)
real qn(km), qr(km),qr2(km),tmp(km),tmp1(km),tmp2(km),tmp3(km)
real dza(km+1), qa(km+1), qa2(km+1),qmi(km+1), qpi(km+1)
!
precip(:) = 0.0
precip1(:) = 0.0
precip2(:) = 0.0
!
i_loop : do i=1,im
! -----------------------------------
dz(:) = dzl(i,:)
qq(:) = rql(i,:)
qq2(:) = rql2(i,:)
ww(:) = wwl(i,:)
den(:) = denl(i,:)
denfac(:) = denfacl(i,:)
tk(:) = tkl(i,:)
! skip for no precipitation for all layers
allold = 0.0
do k=1,km
allold = allold + qq(k)
enddo
if(allold.le.0.0) then
cycle i_loop
endif
!
! compute interface values
zi(1)=0.0
do k=1,km
zi(k+1) = zi(k)+dz(k)
enddo
!
! save departure wind
wd(:) = ww(:)
n=1
100 continue
! plm is 2nd order, we can use 2nd order wi or 3rd order wi
! 2nd order interpolation to get wi
wi(1) = ww(1)
wi(km+1) = ww(km)
do k=2,km
wi(k) = (ww(k)*dz(k-1)+ww(k-1)*dz(k))/(dz(k-1)+dz(k))
enddo
! 3rd order interpolation to get wi
fa1 = 9./16.
fa2 = 1./16.
wi(1) = ww(1)
wi(2) = 0.5*(ww(2)+ww(1))
do k=3,km-1
wi(k) = fa1*(ww(k)+ww(k-1))-fa2*(ww(k+1)+ww(k-2))
enddo
wi(km) = 0.5*(ww(km)+ww(km-1))
wi(km+1) = ww(km)
!
! terminate of top of raingroup
do k=2,km
if( ww(k).eq.0.0 ) wi(k)=ww(k-1)
enddo
!
! diffusivity of wi
con1 = 0.05
do k=km,1,-1
decfl = (wi(k+1)-wi(k))*dt/dz(k)
if( decfl .gt. con1 ) then
wi(k) = wi(k+1) - con1*dz(k)/dt
endif
enddo
! compute arrival point
do k=1,km+1
za(k) = zi(k) - wi(k)*dt
enddo
!
do k=1,km
dza(k) = za(k+1)-za(k)
enddo
dza(km+1) = zi(km+1) - za(km+1)
!
! computer deformation at arrival point
do k=1,km
qa(k) = qq(k)*dz(k)/dza(k)
qa2(k) = qq2(k)*dz(k)/dza(k)
qr(k) = qa(k)/den(k)
qr2(k) = qa2(k)/den(k)
enddo
qa(km+1) = 0.0
qa2(km+1) = 0.0
! call maxmin(km,1,qa,' arrival points ')
!
! compute arrival terminal velocity, and estimate mean terminal velocity
! then back to use mean terminal velocity
if( n.le.iter ) then
call slope_snow(qr,den,denfac,tk,tmp,tmp1,tmp2,tmp3,wa,1,1,1,km)
call slope_graup(qr2,den,denfac,tk,tmp,tmp1,tmp2,tmp3,wa2,1,1,1,km)
do k = 1, km
tmp(k) = max((qr(k)+qr2(k)), 1.E-15)
IF ( tmp(k) .gt. 1.e-15 ) THEN
wa(k) = (wa(k)*qr(k) + wa2(k)*qr2(k))/tmp(k)
ELSE
wa(k) = 0.
ENDIF
enddo
if( n.ge.2 ) wa(1:km)=0.5*(wa(1:km)+was(1:km))
do k=1,km
!#ifdef DEBUG
! print*,' slope_wsm3 ',qr(k)*1000.,den(k),denfac(k),tk(k),tmp(k),tmp1(k),tmp2(k), &
! ww(k),wa(k)
!#endif
! mean wind is average of departure and new arrival winds
ww(k) = 0.5* ( wd(k)+wa(k) )
enddo
was(:) = wa(:)
n=n+1
go to 100
endif
ist_loop : do ist = 1, 2
if (ist.eq.2) then
qa(:) = qa2(:)
endif
!
precip(i) = 0.
!
! estimate values at arrival cell interface with monotone
do k=2,km
dip=(qa(k+1)-qa(k))/(dza(k+1)+dza(k))
dim=(qa(k)-qa(k-1))/(dza(k-1)+dza(k))
if( dip*dim.le.0.0 ) then
qmi(k)=qa(k)
qpi(k)=qa(k)
else
qpi(k)=qa(k)+0.5*(dip+dim)*dza(k)
qmi(k)=2.0*qa(k)-qpi(k)
if( qpi(k).lt.0.0 .or. qmi(k).lt.0.0 ) then
qpi(k) = qa(k)
qmi(k) = qa(k)
endif
endif
enddo
qpi(1)=qa(1)
qmi(1)=qa(1)
qmi(km+1)=qa(km+1)
qpi(km+1)=qa(km+1)
!
! interpolation to regular point
qn = 0.0
kb=1
kt=1
intp : do k=1,km
kb=max(kb-1,1)
kt=max(kt-1,1)
! find kb and kt
if( zi(k).ge.za(km+1) ) then
exit intp
else
find_kb : do kk=kb,km
if( zi(k).le.za(kk+1) ) then
kb = kk
exit find_kb
else
cycle find_kb
endif
enddo find_kb
find_kt : do kk=kt,km
if( zi(k+1).le.za(kk) ) then
kt = kk
exit find_kt
else
cycle find_kt
endif
enddo find_kt
kt = kt - 1
! compute q with piecewise constant method
if( kt.eq.kb ) then
tl=(zi(k)-za(kb))/dza(kb)
th=(zi(k+1)-za(kb))/dza(kb)
tl2=tl*tl
th2=th*th
qqd=0.5*(qpi(kb)-qmi(kb))
qqh=qqd*th2+qmi(kb)*th
qql=qqd*tl2+qmi(kb)*tl
qn(k) = (qqh-qql)/(th-tl)
else if( kt.gt.kb ) then
tl=(zi(k)-za(kb))/dza(kb)
tl2=tl*tl
qqd=0.5*(qpi(kb)-qmi(kb))
qql=qqd*tl2+qmi(kb)*tl
dql = qa(kb)-qql
zsum = (1.-tl)*dza(kb)
qsum = dql*dza(kb)
if( kt-kb.gt.1 ) then
do m=kb+1,kt-1
zsum = zsum + dza(m)
qsum = qsum + qa(m) * dza(m)
enddo
endif
th=(zi(k+1)-za(kt))/dza(kt)
th2=th*th
qqd=0.5*(qpi(kt)-qmi(kt))
dqh=qqd*th2+qmi(kt)*th
zsum = zsum + th*dza(kt)
qsum = qsum + dqh*dza(kt)
qn(k) = qsum/zsum
endif
cycle intp
endif
!
enddo intp
!
! rain out
sum_precip: do k=1,km
if( za(k).lt.0.0 .and. za(k+1).lt.0.0 ) then
precip(i) = precip(i) + qa(k)*dza(k)
cycle sum_precip
else if ( za(k).lt.0.0 .and. za(k+1).ge.0.0 ) then
precip(i) = precip(i) + qa(k)*(0.0-za(k))
exit sum_precip
endif
exit sum_precip
enddo sum_precip
!
! replace the new values
if(ist.eq.1) then
rql(i,:) = qn(:)
precip1(i) = precip(i)
else
rql2(i,:) = qn(:)
precip2(i) = precip(i)
endif
enddo ist_loop
!
! ----------------------------------
enddo i_loop
!
END SUBROUTINE nislfv_rain_plm6
END MODULE module_mp_wdm6