#ifdef _ACCEL
# include "module_mp_wsm5_accel.F"
#else
#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_wsm5
!
!
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 :: lamdarmax = 8.e4 ! 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 :: eacrc = 1.0 ! Snow/cloud-water collection efficiency
REAL, SAVE :: &
qc0, qck1,bvtr1,bvtr2,bvtr3,bvtr4,g1pbr, &
g3pbr,g4pbr,g5pbro2,pvtr,eacrr,pacrr, &
precr1,precr2,xmmax,roqimax,bvts1, &
bvts2,bvts3,bvts4,g1pbs,g3pbs,g4pbs, &
g5pbso2,pvts,pacrs,precs1,precs2,pidn0r, &
pidn0s,xlv1,pacrc,pi, &
rslopermax,rslopesmax,rslopegmax, &
rsloperbmax,rslopesbmax,rslopegbmax, &
rsloper2max,rslopes2max,rslopeg2max, &
rsloper3max,rslopes3max,rslopeg3max
!
! Specifies code-inlining of fpvs function in WSM52D below. JM 20040507
!
CONTAINS
!===================================================================
!
SUBROUTINE wsm5(th, q, qc, qr, qi, qs &
,den, pii, p, delz &
,delt,g, cpd, cpv, 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
!-------------------------------------------------------------------
!
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
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, &
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
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)
ENDDO
ENDDO
! Sending array starting locations of optional variables may cause
! troubles, so we explicitly change the call.
CALL wsm52D(t, q(ims,kms,j), qci, qrs &
,den(ims,kms,j) &
,p(ims,kms,j), delz(ims,kms,j) &
,delt,g, cpd, cpv, 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,snowncv &
)
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)
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 wsm5
!===================================================================
!
SUBROUTINE wsm52D(t, q &
,qci, qrs, den, p, delz &
,delt,g, cpd, cpv, 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
!-------------------------------------------------------------------
!
! This code is a 5-class mixed ice microphyiscs scheme (WSM5) of the
! Single-Moment MicroPhyiscs (WSMMP). The WSMMP assumes that ice nuclei
! number concentration is a function of temperature, and seperate assumption
! is developed, in which ice crystal number concentration is a function
! of ice amount. A theoretical background of the ice-microphysics and related
! processes in the WSMMPs are described in Hong et al. (2004).
! Production terms in the WSM6 scheme are described in Hong and Lim (2006).
! All units are in m.k.s. and source/sink terms in kgkg-1s-1.
!
! WSM5 cloud scheme
!
! Coded by Song-You Hong (Yonsei Univ.)
! Jimy Dudhia (NCAR) and Shu-Hua Chen (UC Davis)
! Summer 2002
!
! Implemented by Song-You Hong (Yonsei Univ.) and Jimy Dudhia (NCAR)
! Summer 2003
!
! Reference) Hong, Dudhia, Chen (HDC, 2004) Mon. Wea. Rev.
! Rutledge, Hobbs (RH83, 1983) J. Atmos. Sci.
! Hong and Lim (HL, 2006) J. Korean Meteor. Soc.
!
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( 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, &
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, jms:jme ), OPTIONAL, &
INTENT(INOUT) :: snow, &
snowncv
! LOCAL VAR
REAL, DIMENSION( its:ite , kts:kte , 2) :: &
rh, &
qs, &
rslope, &
rslope2, &
rslope3, &
rslopeb, &
qrs_tmp, &
falk, &
fall, &
work1
REAL, DIMENSION( its:ite , kts:kte ) :: &
falkc, &
fallc, &
xl, &
cpm, &
denfac, &
xni, &
denqrs1, &
denqrs2, &
denqci, &
n0sfac, &
work2, &
workr, &
works, &
work1c, &
work2c
REAL, DIMENSION( its:ite , kts:kte ) :: &
den_tmp, &
delz_tmp
REAL, DIMENSION( its:ite ) :: &
delqrs1, &
delqrs2, &
delqi
REAL, DIMENSION( its:ite , kts:kte ) :: &
pigen, &
pidep, &
psdep, &
praut, &
psaut, &
prevp, &
psevp, &
pracw, &
psacw, &
psaci, &
pcond, &
psmlt
INTEGER, DIMENSION( its:ite ) :: &
mstep, &
numdt
REAL, DIMENSION(its:ite) :: tstepsnow
REAL, DIMENSION(its:ite) :: rmstep
REAL dtcldden, rdelz, rdtcld
LOGICAL, DIMENSION( its:ite ) :: flgcld
#define WSM_NO_CONDITIONAL_IN_VECTOR
#ifdef WSM_NO_CONDITIONAL_IN_VECTOR
REAL, DIMENSION(its:ite) :: xal, xbl
#endif
REAL :: &
cpmcal, xlcal, diffus, &
viscos, xka, venfac, conden, diffac, &
x, y, z, a, b, c, d, e, &
qdt, holdrr, holdrs, supcol, supcolt, pvt, &
coeres, supsat, dtcld, xmi, eacrs, satdt, &
vt2i,vt2s,acrfac, &
qimax, diameter, xni0, roqi0, &
fallsum, fallsum_qsi, xlwork2, factor, source, &
value, xlf, pfrzdtc, pfrzdtr, supice, holdc, holdci
! variables for optimization
REAL, DIMENSION( its:ite ) :: tvec1
REAL :: temp
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
REAL :: logtr
!
!=================================================================
! compute internal functions
!
cpmcal(x) = cpd*(1.-max(x,qmin))+max(x,qmin)*cpv
xlcal(x) = xlv0-xlv1*(x-t0c)
!----------------------------------------------------------------
! 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)
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
!
do i = its, ite
rainncv(i) = 0.
if(PRESENT (snowncv) .AND. PRESENT (snow)) snowncv(i,lat) = 0.
sr(i) = 0.
! new local array to catch step snow
tstepsnow(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
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) = min(qs(i,k,1),0.99*p(i,k))
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) = min(qs(i,k,2),0.99*p(i,k))
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)
#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) = min(qs(i,k,1),0.99*p(i,k))
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) = min(qs(i,k,2),0.99*p(i,k))
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
enddo
enddo
!
!----------------------------------------------------------------
! 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.
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.
xni(i,k) = 1.e3
enddo
enddo
!-------------------------------------------------------------
! Ni: ice crystal number concentraiton [HDC 5c]
!-------------------------------------------------------------
do k = kts, kte
do i = its, ite
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)
enddo
enddo
call slope_wsm5(qrs_tmp,den_tmp,denfac,t,rslope,rslopeb,rslope2,rslope3, &
work1,its,ite,kts,kte)
!
do k = kte, kts, -1
do i = its, ite
workr(i,k) = work1(i,k,1)
works(i,k) = work1(i,k,2)
denqrs1(i,k) = den(i,k)*qrs(i,k,1)
denqrs2(i,k) = den(i,k)*qrs(i,k,2)
if(qrs(i,k,1).le.0.0) workr(i,k) = 0.0
if(qrs(i,k,2).le.0.0) works(i,k) = 0.0
enddo
enddo
call nislfv_rain_plm(idim,kdim,den_tmp,denfac,t,delz_tmp,workr,denqrs1, &
delqrs1,dtcld,1,1)
call nislfv_rain_plm(idim,kdim,den_tmp,denfac,t,delz_tmp,works,denqrs2, &
delqrs2,dtcld,2,1)
do k = kts, kte
do i = its, ite
qrs(i,k,1) = max(denqrs1(i,k)/den(i,k),0.)
qrs(i,k,2) = max(denqrs2(i,k)/den(i,k),0.)
fall(i,k,1) = denqrs1(i,k)*workr(i,k)/delz(i,k)
fall(i,k,2) = denqrs2(i,k)*works(i,k)/delz(i,k)
enddo
enddo
do i = its, ite
fall(i,1,1) = delqrs1(i)/delz(i,1)/dtcld
fall(i,1,2) = delqrs2(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)
enddo
enddo
call slope_wsm5(qrs_tmp,den_tmp,denfac,t,rslope,rslopeb,rslope2,rslope3, &
work1,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.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) = (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)
t(i,k) = t(i,k) + xlf/cpm(i,k)*psmlt(i,k)
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_plm(idim,kdim,den_tmp,denfac,t,delz_tmp,work1c,denqci, &
delqi,dtcld,1,0)
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,1,1)+fall(i,1,2)+fallc(i,1)
fallsum_qsi = fall(i,1,2)+fallc(i,1)
if(fallsum.gt.0.) then
rainncv(i) = fallsum*delz(i,1)/denr*dtcld*1000. + rainncv(i)
rain(i) = fallsum*delz(i,1)/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,lat) = fallsum_qsi*delz(i,kts)/denr*dtcld*1000. &
+snowncv(i,lat)
snow(i,lat) = fallsum_qsi*delz(i,kts)/denr*dtcld*1000. + snow(i,lat)
ENDIF
endif
! if(fallsum.gt.0.)sr(i)=snowncv(i,lat)/(rainncv(i)+1.e-12)
if(fallsum.gt.0.)sr(i)=tstepsnow(i)/(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)
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)
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,50.)
! pfrzdtc = min(pfrz1*(exp(pfrz2*supcol)-1.) &
! *den(i,k)/denr/xncr*qci(i,k,1)**2*dtcld,qci(i,k,1))
pfrzdtc = min(pfrz1*(exp(pfrz2*supcolt)-1.) &
*den(i,k)/denr/xncr*qci(i,k,1)*qci(i,k,1)*dtcld,qci(i,k,1))
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,50.)
! pfrzdtr = min(20.*pi**2*pfrz1*n0r*denr/den(i,k) &
! *(exp(pfrz2*supcol)-1.)*rslope(i,k,1)**7*dtcld, &
! qrs(i,k,1))
temp = rslope(i,k,1)
temp = temp*temp*temp*temp*temp*temp*temp
pfrzdtr = min(20.*(pi*pi)*pfrz1*n0r*denr/den(i,k) &
*(exp(pfrz2*supcolt)-1.)*temp*dtcld, &
qrs(i,k,1))
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
!
!----------------------------------------------------------------
! 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)
enddo
enddo
call slope_wsm5(qrs_tmp,den_tmp,denfac,t,rslope,rslopeb,rslope2,rslope3, &
work1,its,ite,kts,kte)
!------------------------------------------------------------------
! 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
! 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 [HDC 16]
! (C->R)
!---------------------------------------------------------------
if(qci(i,k,1).gt.qc0) then
praut(i,k) = qck1*exp(log(qci(i,k,1))*((7./3.)))
praut(i,k) = min(praut(i,k),qci(i,k,1)/dtcld)
endif
!---------------------------------------------------------------
! pracw: accretion of cloud water by rain [HL A40] [LFO 51]
! (C->R)
!---------------------------------------------------------------
if(qrs(i,k,1).gt.qcrmin.and.qci(i,k,1).gt.qmin) then
pracw(i,k) = min(pacrr*rslope3(i,k,1)*rslopeb(i,k,1) &
*qci(i,k,1)*denfac(i,k),qci(i,k,1)/dtcld)
endif
!---------------------------------------------------------------
! prevp: evaporation/condensation rate of rain [HDC 14]
! (V->R or R->V)
!---------------------------------------------------------------
if(qrs(i,k,1).gt.0.) then
coeres = rslope2(i,k,1)*sqrt(rslope(i,k,1)*rslopeb(i,k,1))
prevp(i,k) = (rh(i,k,1)-1.)*(precr1*rslope2(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)
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)
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))
!
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)/dtcld)
,qci(i,k,1)*rdtcld)
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.)) &
! /dtcld)
*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
!
! cloud water
!
value = max(qmin,qci(i,k,1))
source = (praut(i,k)+pracw(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
psacw(i,k) = psacw(i,k)*factor
endif
!
! 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
!
! rain
!
!
value = max(qmin,qrs(i,k,1))
source = (-praut(i,k)-pracw(i,k)-prevp(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
endif
!
! 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
!
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))*dtcld,0.)
qrs(i,k,1) = max(qrs(i,k,1)+(praut(i,k)+pracw(i,k) &
+prevp(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.)
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
!
! cloud water
!
value = max(qmin,qci(i,k,1))
source=(praut(i,k)+pracw(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
psacw(i,k) = psacw(i,k)*factor
endif
!
! rain
!
value = max(qmin,qrs(i,k,1))
source = (-praut(i,k)-pracw(i,k)-prevp(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
endif
!
! 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
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))*dtcld,0.)
qrs(i,k,1) = max(qrs(i,k,1)+(praut(i,k)+pracw(i,k) &
+prevp(i,k) +psacw(i,k))*dtcld,0.)
qrs(i,k,2) = max(qrs(i,k,2)+psevp(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) = min(qs(i,k,1),0.99*p(i,k))
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)
enddo
enddo
!
!----------------------------------------------------------------
! 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
!
do k = kts, kte
do i = its, ite
! work1(i,k,1) = conden(t(i,k),q(i,k),qs(i,k,1),xl(i,k),cpm(i,k))
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
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 wsm52d
! ...................................................................
REAL FUNCTION rgmma(x)
!-------------------------------------------------------------------
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)
!--------------------------------------------------------------------------
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 wsm5init(den0,denr,dens,cl,cpv,allowed_to_read)
!-------------------------------------------------------------------
IMPLICIT NONE
!-------------------------------------------------------------------
!.... constants which may not be tunable
REAL, INTENT(IN) :: den0,denr,dens,cl,cpv
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
!
bvtr1 = 1.+bvtr
bvtr2 = 2.5+.5*bvtr
bvtr3 = 3.+bvtr
bvtr4 = 4.+bvtr
g1pbr = rgmma(bvtr1)
g3pbr = rgmma(bvtr3)
g4pbr = rgmma(bvtr4) ! 17.837825
g5pbro2 = rgmma(bvtr2) ! 1.8273
pvtr = avtr*g4pbr/6.
eacrr = 1.0
pacrr = pi*n0r*avtr*g3pbr*.25*eacrr
precr1 = 2.*pi*n0r*.78
precr2 = 2.*pi*n0r*.31*avtr**.5*g5pbro2
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
pidn0r = pi*denr*n0r
pidn0s = pi*dens*n0s
pacrc = pi*n0s*avts*g3pbs*.25*eacrc
!
rslopermax = 1./lamdarmax
rslopesmax = 1./lamdasmax
rsloperbmax = rslopermax ** bvtr
rslopesbmax = rslopesmax ** bvts
rsloper2max = rslopermax * rslopermax
rslopes2max = rslopesmax * rslopesmax
rsloper3max = rsloper2max * rslopermax
rslopes3max = rslopes2max * rslopesmax
!
END SUBROUTINE wsm5init
!------------------------------------------------------------------------------
subroutine slope_wsm5(qrs,den,denfac,t,rslope,rslopeb,rslope2,rslope3, &
vt,its,ite,kts,kte)
IMPLICIT NONE
INTEGER :: its,ite, jts,jte, kts,kte
REAL, DIMENSION( its:ite , kts:kte,2) :: &
qrs, &
rslope, &
rslopeb, &
rslope2, &
rslope3, &
vt
REAL, DIMENSION( its:ite , kts:kte) :: &
den, &
denfac, &
t
REAL, PARAMETER :: t0c = 273.15
REAL, DIMENSION( its:ite , kts:kte ) :: &
n0sfac
REAL :: lamdar, 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.
lamdar(x,y)= sqrt(sqrt(pidn0r/(x*y))) ! (pidn0r/(x*y))**.25
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,1).le.qcrmin)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))
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(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
vt(i,k,1) = pvtr*rslopeb(i,k,1)*denfac(i,k)
vt(i,k,2) = pvts*rslopeb(i,k,2)*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
enddo
enddo
END subroutine slope_wsm5
!-----------------------------------------------------------------------------
subroutine slope_rain(qrs,den,denfac,t,rslope,rslopeb,rslope2,rslope3, &
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 :: 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)= sqrt(sqrt(pidn0r/(x*y))) ! (pidn0r/(x*y))**.25
!
do k = kts, kte
do i = its, ite
if(qrs(i,k).le.qcrmin)then
rslope(i,k) = rslopermax
rslopeb(i,k) = rsloperbmax
rslope2(i,k) = rsloper2max
rslope3(i,k) = rsloper3max
else
rslope(i,k) = 1./lamdar(qrs(i,k),den(i,k))
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)
if(qrs(i,k).le.0.0) vt(i,k) = 0.0
enddo
enddo
END subroutine slope_rain
!------------------------------------------------------------------------------
subroutine slope_snow(qrs,den,denfac,t,rslope,rslopeb,rslope2,rslope3, &
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 nislfv_rain_plm(im,km,denl,denfacl,tkl,dzl,wwl,rql,precip,dt,id,iter)
!-------------------------------------------------------------------
!
! 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 2: snow
! 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),precip(im)
real denl(im,km),denfacl(im,km),tkl(im,km)
!
integer i,k,n,m,kk,kb,kt,iter
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), wd(km), wa(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,:)
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)
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 (id.eq.1) then
call slope_rain(qr,den,denfac,tk,tmp,tmp1,tmp2,tmp3,wa,1,1,1,km)
else
call slope_snow(qr,den,denfac,tk,tmp,tmp1,tmp2,tmp3,wa,1,1,1,km)
endif
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_plm
END MODULE module_mp_wsm5
#endif