#define WSM_NO_CONDITIONAL_IN_VECTOR
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 &
,lon,lat &
,rain,rainncv &
,sr &
,snow,snowncv &
,nx0,nk0,irestrict &
,doit,kts,kte )
!-------------------------------------------------------------------
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 ) :: nx0,nk0,irestrict &
,lon,lat,kts,kte
#define nx CHUNK
#define its 1
#define ite nx
#define ims 1
#define ime nx
#define kms kts
#define kme kte
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 ), OPTIONAL, &
INTENT(INOUT) :: snow, &
snowncv
LOGICAL, INTENT(IN) :: doit ! added for conformity with standalone driver
! LOCAL VAR
REAL, DIMENSION( its:ite , kts:kte , 2) :: &
rh, &
qs, &
falk, &
fall
REAL, DIMENSION( its:ite , 1 , 2) :: &
work1
REAL, DIMENSION( its:ite , 1 ) :: &
work2
REAL, DIMENSION( its:ite , 2) :: &
rslope_v, &
rslope2_v, &
rslope3_v, &
rslopeb_v
REAL, DIMENSION( its:ite , kts:kte ) :: &
falkc, &
fallc, &
xl, &
cpm, &
denfac, &
xni, &
denqrs, &
denqci, &
n0sfac, &
workrs, &
work1c, &
work2c
REAL, DIMENSION( its:ite ) :: &
delqrs
REAL, DIMENSION( its:ite , 1 ) :: &
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
#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, &
xlwork2, factor, source, &
value, xlf, pfrzdtc, pfrzdtr, supice, holdc, holdci
REAL, DIMENSION(CHUNK) :: fallsum, fallsum_qsi ! convert to vector
REAL, DIMENSION(CHUNK) :: supsat_v,satdt_v,coeres_v
! 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, and other vector stuff
REAL :: dldti, xb, xai, xbi, xa, hvap, cvap, hsub, dldt, ttp
REAL :: tr_v(its:ite),logtr_v(its:ite),supcol_v(its:ite),supcolt_v(its:ite),xlf_v(its:ite),temp_v(its:ite)
REAL :: diameter_v(CHUNK),supice_v(CHUNK)
INTEGER :: ifsat_v(CHUNK)
! mask variable
LOGICAL*4 :: lmask(CHUNK)
!
# define LAMDAR(x,y) sqrt(sqrt(pidn0r/((x)*(y))))
# define LAMDAS(x,y,z) sqrt(sqrt(pidn0s*(z)/((x)*(y))))
!
!=================================================================
! compute internal functions
!
#define CPMCAL(x) (cpd*(1.-max(x,qmin))+max(x,qmin)*cpv)
#define XLCAL(x) (xlv0-xlv1*((x)-t0c))
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))
!
!----------------------------------------------------------------
!DIR$ ASSUME_ALIGNED t:64
!DIR$ ASSUME_ALIGNED qci:64
!DIR$ ASSUME_ALIGNED qrs:64
!DIR$ ASSUME_ALIGNED q:64
!DIR$ ASSUME_ALIGNED den:64
!DIR$ ASSUME_ALIGNED p:64
!DIR$ ASSUME_ALIGNED delz:64
!DIR$ ASSUME_ALIGNED rain:64
!DIR$ ASSUME_ALIGNED rainncv:64
!DIR$ ASSUME_ALIGNED sr:64
!DIR$ ASSUME_ALIGNED snow:64
!DIR$ ASSUME_ALIGNED snowncv:64
if ( irestrict .le. 0 .OR. .NOT. doit ) return
idim = ite-its+1
kdim = kte-kts+1
lmask = .FALSE.
do i = its, min(irestrict,ite)
lmask(i) = .TRUE.
enddo
!
!----------------------------------------------------------------
! paddint 0 for negative values generated by dynamics
!
do k = kts, kte
WHERE(lmask)
qci(:,k,1) = max(qci(:,k,1),0.0)
qrs(:,k,1) = max(qrs(:,k,1),0.0)
qci(:,k,2) = max(qci(:,k,2),0.0)
qrs(:,k,2) = max(qrs(:,k,2),0.0)
ENDWHERE
enddo
!
!----------------------------------------------------------------
! latent heat for phase changes and heat capacity. neglect the
! changes during microphysical process calculation
! emanuel(1994)
!
do k = kts, kte
WHERE(lmask)
cpm(:,k) = CPMCAL(q(:,k))
xl(:,k) = XLCAL(t(:,k))
ENDWHERE
enddo
!
!----------------------------------------------------------------
! initialize the surface rain, snow
!
WHERE(lmask)
rainncv(:) = 0.
sr(:) = 0.
tstepsnow(:) = 0.
ENDWHERE
IF(PRESENT (snowncv) .AND. PRESENT (snow)) THEN
WHERE( lmask ) snowncv(:) = 0.
ENDIF
!
!----------------------------------------------------------------
! 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
!
WHERE (lmask)
mstep(:) = 1
flgcld(:) = .true.
ENDWHERE
! this seems to be needed for the standalone version to agree with its reference
do k = kts, kte
CALL VREC( tvec1(its), den(its,k), ite-its+1)
WHERE( lmask )
tvec1(:) = tvec1(:)*den0
ENDWHERE
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
WHERE( lmask )
WHERE(t(:,k).lt.ttp)
xal(:) = xai
xbl(:) = xbi
ELSEWHERE
xal(:) = xa
xbl(:) = xb
ENDWHERE
tr_v=ttp/t(:,k)
logtr_v=log(tr_v)
qs(:,k,1)=psat*exp(logtr_v*(xa)+xb*(1.-tr_v))
qs(:,k,1) = min(qs(:,k,1),0.99*p(:,k))
qs(:,k,1) = ep2 * qs(:,k,1) / (p(:,k) - qs(:,k,1))
qs(:,k,1) = max(qs(:,k,1),qmin)
rh(:,k,1) = max(q(:,k) / qs(:,k,1),qmin)
qs(:,k,2)=psat*exp(logtr_v*(xal(:))+xbl(:)*(1.-tr_v))
qs(:,k,2) = min(qs(:,k,2),0.99*p(:,k))
qs(:,k,2) = ep2 * qs(:,k,2) / (p(:,k) - qs(:,k,2))
qs(:,k,2) = max(qs(:,k,2),qmin)
rh(:,k,2) = max(q(:,k) / qs(:,k,2),qmin)
ENDWHERE
enddo
#else
Bad --- XEON_OPTIMIZED VERSION NEEDS WSM5_NO_CONDITIONAL_IN_VECTOR
#endif
!
!----------------------------------------------------------------
! initialize the variables for microphysical physics
!
!
do k = kts, kte
do i = its, min(irestrict,ite)
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]
!-------------------------------------------------------------
!jm note reuse of tr_v as temporary
do k = kts, kte
WHERE( lmask )
tr_v = (den(:,k)*max(qci(:,k,2),qmin))
tr_v = sqrt(sqrt(tr_v*tr_v*tr_v))
xni(:,k) = min(max(5.38e7*tr_v,1.e3),1.e6)
ENDWHERE
enddo
!
!----------------------------------------------------------------
! compute the fallout term:
! first, vertical terminal velosity for minor loops
!----------------------------------------------------------------
!
#if 1
do k = kts, kte
WHERE(lmask)
!---------------------------------------------------------------
! n0s: Intercept parameter for snow [m-4] [HDC 6]
!---------------------------------------------------------------
WHERE (qrs(:,k,1).le.0.0)
workrs(:,k) = 0.0
ELSEWHERE (qrs(:,k,1).le.qcrmin)
workrs(:,k) = pvtr*rsloperbmax*denfac(:,k)
ELSEWHERE
! (rslopeb ( rslope ) )
workrs(:,k) = pvtr*( exp(log( 1./LAMDAR(qrs(:,k,1),den(:,k)) )*(bvtr)) )*denfac(:,k)
ENDWHERE
ENDWHERE
enddo
qrs(:,:,1) = den*qrs(:,:,1)
call nislfv_rain_plm(idim,kdim,den,denfac,t,delz,workrs,qrs(:,:,1), &
delqrs,dtcld,1,1,irestrict,lon,lat,.true.,1)
fall(:,:,1) = qrs(:,:,1)*workrs/delz
qrs(:,:,1) = max(qrs(:,:,1)/den,0.)
fall(:,1,1) = delqrs/delz(:,1)/dtcld
do k = kts, kte
WHERE(lmask)
WHERE (qrs(:,k,2).le.0.0)
workrs(:,k) = 0.0
ELSEWHERE (qrs(:,k,2).le.qcrmin)
workrs(:,k) = pvts*rslopesbmax*denfac(:,k)
ELSEWHERE
workrs(:,k) = pvts*(exp(log(1./ &
LAMDAS(qrs(:,k,2),den(:,k), max(min(exp(alpha*(t0c-t(:,k))),n0smax/n0s),1.)) &
) *(bvts)))*denfac(:,k)
ENDWHERE
ENDWHERE
enddo
qrs(:,:,2) = den*qrs(:,:,2)
call nislfv_rain_plm(idim,kdim,den,denfac,t,delz,workrs,qrs(:,:,2), &
delqrs,dtcld,2,1,irestrict,lon,lat,.false.,2)
fall(:,:,2) = qrs(:,:,2)*workrs/delz
qrs(:,:,2) = max(qrs(:,:,2)/den,0.)
fall(:,1,2) = delqrs/delz(:,1)/dtcld
#else
WHERE( qrs(:,:,1) .le. 0.0 )
workr = 0.0
ELSEWHERE
workr = work1(:,:,1)
ENDWHERE
denqrs1 = den*qrs(:,:,1)
call nislfv_rain_plm(idim,kdim,den,denfac,t,delz,workr,denqrs1, &
delqrs1,dtcld,1,1,irestrict,lon,lat,.true.,1)
qrs(:,:,1) = max(denqrs1/den,0.)
fall(:,:,1) = denqrs1*workr/delz
fall(:,1,1) = delqrs1/delz(:,1)/dtcld
WHERE( qrs(:,:,2) .le. 0.0 )
works = 0.0
ELSEWHERE
works = work1(:,:,2)
ENDWHERE
denqrs2 = den*qrs(:,:,2)
call nislfv_rain_plm(idim,kdim,den,denfac,t,delz,works,denqrs2, &
delqrs2,dtcld,2,1,irestrict,lon,lat,.false.,2)
qrs(:,:,2) = max(denqrs2/den,0.)
fall(:,:,2) = denqrs2*works/delz
fall(:,1,2) = delqrs2/delz(:,1)/dtcld
#endif
!note reuse of tr_v as temporary for coeres
xlf = xlf0
do k = kte, kts, -1
psmlt = 0.
WHERE(lmask)
supcol_v = t0c-t(:,k)
n0sfac(:,k) = max(min(exp(alpha*supcol_v),n0smax/n0s),1.)
WHERE(qrs(:,k,2).le.qcrmin)
rslope_v(:,2) = rslopesmax
rslopeb_v(:,2) = rslopesbmax
rslope2_v(:,2) = rslopes2max
ELSEWHERE
rslope_v(:,2) = 1./LAMDAS(qrs(:,k,2),den(:,k),max(min(exp(alpha*(t0c-t(:,k))),n0smax/n0s),1.))
rslopeb_v(:,2) = exp(log(rslope_v(:,2))*(bvts))
rslope2_v(:,2) = rslope_v(:,2)*rslope_v(:,2)
ENDWHERE
WHERE (t(:,k).gt.t0c.and.qrs(:,k,2).gt.0.)
!----------------------------------------------------------------
! psmlt: melting of snow [HL A33] [RH83 A25]
! (T>T0: S->R)
!----------------------------------------------------------------
work2(:,1)= (exp(log(((1.496e-6*((t(:,k))*sqrt(t(:,k))) &
/((t(:,k))+120.)/(den(:,k)))/(8.794e-5 &
*exp(log(t(:,k))*(1.81))/p(:,k)))) &
*((.3333333)))/sqrt((1.496e-6*((t(:,k)) &
*sqrt(t(:,k)))/((t(:,k))+120.)/(den(:,k)))) &
*sqrt(sqrt(den0/(den(:,k)))))
tr_v = rslope2_v(:,2)*sqrt(rslope_v(:,2)*rslopeb_v(:,2))
psmlt(:,1) = (1.414e3*(1.496e-6*((t(:,k))*sqrt(t(:,k))) &
/((t(:,k))+120.)/(den(:,k)) )*(den(:,k))) &
/xlf*(t0c-t(:,k))*pi/2. &
*n0sfac(:,k)*(precs1*rslope2_v(:,2)+precs2 &
*work2(:,1)*tr_v)
psmlt(:,1) = min(max(psmlt(:,1)*dtcld/mstep(:), &
-qrs(:,k,2)/mstep(:)),0.)
qrs(:,k,2) = qrs(:,k,2) + psmlt(:,1)
qrs(:,k,1) = qrs(:,k,1) - psmlt(:,1)
t(:,k) = t(:,k) + xlf/cpm(:,k)*psmlt(:,1)
ENDWHERE
ENDWHERE
enddo
!---------------------------------------------------------------
! Vice [ms-1] : fallout of ice crystal [HDC 5a]
!---------------------------------------------------------------
work1c = 0.
WHERE (qci(:,:,2).gt.0.)
work1c = &
1.49e4*exp( &
log( &
max(min(dicon * sqrt(den*qci(:,:,2)/xni),dimax), 1.e-25) &
)*(1.31) &
)
ENDWHERE
denqci = den*qci(:,:,2)
call nislfv_rain_plm(idim,kdim,den,denfac,t,delz,work1c,denqci, &
delqrs,dtcld,1,0,irestrict,lon,lat,.false.,3)
do k = kts, kte
WHERE(lmask)
qci(:,k,2) = max(denqci(:,k)/den(:,k),0.)
ENDWHERE
enddo
WHERE(lmask)
fallc(:,1) = delqrs(:)/delz(:,1)/dtcld
ENDWHERE
!
!----------------------------------------------------------------
! rain (unit is mm/sec;kgm-2s-1: /1000*delt ===> m)==> mm for wrf
!
fallsum = fall(:,1,1)+fall(:,1,2)+fallc(:,1)
fallsum_qsi = fall(:,1,2)+fallc(:,1)
WHERE (lmask .and. fallsum.gt.0.)
rainncv = fallsum*delz(:,1)/denr*dtcld*1000. + rainncv
rain = fallsum*delz(:,1)/denr*dtcld*1000. + rain
ENDWHERE
WHERE (lmask .and. fallsum_qsi.gt.0.)
tstepsnow = fallsum_qsi*delz(:,kts)/denr*dtcld*1000. &
+tstepsnow
snowncv = fallsum_qsi*delz(:,kts)/denr*dtcld*1000. &
+snowncv
snow = fallsum_qsi*delz(:,kts)/denr*dtcld*1000. + snow
ENDWHERE
WHERE (lmask.and.fallsum.gt.0.)sr=tstepsnow/(rainncv+1.e-12)
!
!---------------------------------------------------------------
! pimlt: instantaneous melting of cloud ice [HL A47] [RH83 A28]
! (T>T0: I->C)
!---------------------------------------------------------------
do k = kts, kte
WHERE(lmask)
supcol_v = t0c-t(:,k)
xlf_v = xlf0
WHERE(supcol_v.ge.0.) xlf_v = xls-xl(:,k)
WHERE(supcol_v.lt.0..and.qci(:,k,2).gt.0.)
qci(:,k,1) = qci(:,k,1) + qci(:,k,2)
t(:,k) = t(:,k) - xlf_v/cpm(:,k)*qci(:,k,2)
qci(:,k,2) = 0.
ENDWHERE
!---------------------------------------------------------------
! pihmf: homogeneous freezing of cloud water below -40c [HL A45]
! (T<-40C: C->I)
!---------------------------------------------------------------
WHERE(supcol_v.gt.40..and.qci(:,k,1).gt.0.)
qci(:,k,2) = qci(:,k,2) + qci(:,k,1)
t(:,k) = t(:,k) + xlf_v/cpm(:,k)*qci(:,k,1)
qci(:,k,1) = 0.
ENDWHERE
!---------------------------------------------------------------
! pihtf: heterogeneous freezing of cloud water [HL A44]
! (T0>T>-40C: C->I)
!---------------------------------------------------------------
!jm note use of tr_v for temporary
WHERE(supcol_v.gt.0..and.qci(:,k,1).gt.0)
supcolt_v=min(supcol_v,50.)
tr_v = min(pfrz1*(exp(pfrz2*supcolt_v)-1.) &
*den(:,k)/denr/xncr*qci(:,k,1)*qci(:,k,1)*dtcld,qci(:,k,1))
qci(:,k,2) = qci(:,k,2) + tr_v
t(:,k) = t(:,k) + xlf_v/cpm(:,k)*tr_v
qci(:,k,1) = qci(:,k,1)-tr_v
ENDWHERE
!---------------------------------------------------------------
! psfrz: freezing of rain water [HL A20] [LFO 45]
! (T<T0, R->S)
!---------------------------------------------------------------
!jm note use of tr_v
WHERE(supcol_v.gt.0..and.qrs(:,k,1).gt.0)
supcolt_v=min(supcol_v,50.)
WHERE ( qrs(:,k,1).le.qcrmin)
temp_v = (rslopermax)
ELSEWHERE
temp_v = (1./LAMDAR(qrs(:,k,1),den(:,k)))
ENDWHERE
temp_v = temp_v*temp_v*temp_v*temp_v*temp_v*temp_v*temp_v
tr_v = min(20.*(pi*pi)*pfrz1*n0r*denr/den(:,k) &
*(exp(pfrz2*supcolt_v)-1.)*temp_v*dtcld, &
qrs(:,k,1))
qrs(:,k,2) = qrs(:,k,2) + tr_v
t(:,k) = t(:,k) + xlf_v/cpm(:,k)*tr_v
qrs(:,k,1) = qrs(:,k,1)-tr_v
ENDWHERE
ENDWHERE
enddo
!
!----------------------------------------------------------------
! update the slope parameters for microphysics computation
!
!------------------------------------------------------------------
! 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)
!
rdtcld = 1./dtcld
! big fused k-loop
do k = kts, kte
do i = its, min(irestrict,ite)
prevp(i,1) = 0.
psdep(i,1) = 0.
praut(i,1) = 0.
psaut(i,1) = 0.
pracw(i,1) = 0.
psaci(i,1) = 0.
psacw(i,1) = 0.
pigen(i,1) = 0.
pidep(i,1) = 0.
pcond(i,1) = 0.
psevp(i,1) = 0.
enddo
WHERE(lmask)
work1(:,1,1) = (((((den(:,k))*(xl(:,k))*(xl(:,k)))*((t(:,k))+120.) & ! was work1
*(den(:,k)))/(1.414e3*(1.496e-6*((t(:,k))*sqrt(t(:,k)))) &
*(den(:,k))*(rv*(t(:,k))*(t(:,k))))) &
+p(:,k)/((qs(:,k,1))*(8.794e-5*exp(log(t(:,k))*(1.81)))))
work1(:,1,2) = ((((den(:,k))*(xls)*(xls))*((t(:,k))+120.)*(den(:,k)))&
/(1.414e3*(1.496e-6*((t(:,k))*sqrt(t(:,k))))*(den(:,k)) &
*(rv*(t(:,k))*(t(:,k)))) &
+ p(:,k)/(qs(:,k,2)*(8.794e-5*exp(log(t(:,k))*(1.81)))))
work2(:,1) = (exp(.3333333*log(((1.496e-6 * ((t(:,k))*sqrt(t(:,k)))) &
*p(:,k))/(((t(:,k))+120.)*den(:,k)*(8.794e-5 &
*exp(log(t(:,k))*(1.81))))))*sqrt(sqrt(den0/(den(:,k))))) &
/sqrt((1.496e-6*((t(:,k))*sqrt(t(:,k)))) &
/(((t(:,k))+120.)*den(:,k)))
ENDWHERE
!
!===============================================================
!
! warm rain processes
!
! - follows the processes in RH83 and LFO except for autoconcersion
!
!===============================================================
!
! do k = kts, kte
WHERE(lmask)
WHERE(qrs(:,k,1).le.qcrmin)
rslope_v(:,1) = rslopermax
rslopeb_v(:,1) = rsloperbmax
rslope2_v(:,1) = rsloper2max
rslope3_v(:,1) = rsloper3max
ELSEWHERE
rslope_v(:,1) = 1./LAMDAR(qrs(:,k,1),den(:,k))
rslopeb_v(:,1) = exp(log(rslope_v(:,1))*(bvtr))
rslope2_v(:,1) = rslope_v(:,1)*rslope_v(:,1)
rslope3_v(:,1) = rslope2_v(:,1)*rslope_v(:,1)
ENDWHERE
supsat_v = max(q(:,k),qmin)-qs(:,k,1)
satdt_v = supsat_v/dtcld
!---------------------------------------------------------------
! praut: auto conversion rate from cloud to rain [HDC 16]
! (C->R)
!---------------------------------------------------------------
WHERE (qci(:,k,1).gt.qc0)
praut(:,1) = qck1*exp(log(qci(:,k,1))*((7./3.)))
praut(:,1) = min(praut(:,1),qci(:,k,1)/dtcld)
ENDWHERE
!---------------------------------------------------------------
! pracw: accretion of cloud water by rain [HL A40] [LFO 51]
! (C->R)
!---------------------------------------------------------------
WHERE (qrs(:,k,1).gt.qcrmin.and.qci(:,k,1).gt.qmin)
pracw(:,1) = min(pacrr*rslope3_v(:,1)*rslopeb_v(:,1) &
*qci(:,k,1)*denfac(:,k),qci(:,k,1)/dtcld)
ENDWHERE
!---------------------------------------------------------------
! prevp: evaporation/condensation rate of rain [HDC 14]
! (V->R or R->V)
!---------------------------------------------------------------
WHERE(qrs(:,k,1).gt.0.)
coeres_v = rslope2_v(:,1)*sqrt(rslope_v(:,1)*rslopeb_v(:,1))
prevp(:,1) = (rh(:,k,1)-1.)*(precr1*rslope2_v(:,1) &
+precr2*work2(:,1)*coeres_v)/work1(:,1,1)
WHERE(prevp(:,1).lt.0.)
prevp(:,1) = max(prevp(:,1),-qrs(:,k,1)/dtcld)
prevp(:,1) = max(prevp(:,1),satdt_v/2)
ELSEWHERE
prevp(:,1) = min(prevp(:,1),satdt_v/2)
ENDWHERE
ENDWHERE
ENDWHERE
!jm fused-K 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)
!
!===============================================================
!
!jm fused-K do k = kts, kte
WHERE(lmask)
!---------------------------------------------------------------
! n0s: Intercept parameter for snow [m-4] [HDC 6]
!---------------------------------------------------------------
WHERE(qrs(:,k,2).le.qcrmin)
rslope_v(:,2) = rslopesmax
rslopeb_v(:,2) = rslopesbmax
rslope2_v(:,2) = rslopes2max
rslope3_v(:,2) = rslopes3max
ELSEWHERE
rslope_v(:,2) = 1./LAMDAS(qrs(:,k,2),den(:,k),max(min(exp(alpha*(t0c-t(:,k))),n0smax/n0s),1.))
rslopeb_v(:,2) = exp(log(rslope_v(:,2))*(bvts))
rslope2_v(:,2) = rslope_v(:,2)*rslope_v(:,2)
rslope3_v(:,2) = rslope2_v(:,2)*rslope_v(:,2)
ENDWHERE
ENDWHERE
WHERE(lmask)
supcol_v = t0c-t(:,k)
n0sfac(:,1) = max(min(exp(alpha*supcol_v),n0smax/n0s),1.)
supsat_v = max(q(:,k),qmin)-qs(:,k,2)
satdt_v = supsat_v/dtcld
ifsat_v(:) = 0
!-------------------------------------------------------------
! Ni: ice crystal number concentraiton [HDC 5c]
!-------------------------------------------------------------
temp_v = (den(:,k)*max(qci(:,k,2),qmin))
temp_v = sqrt(sqrt(temp_v*temp_v*temp_v))
xni(:,1) = min(max(5.38e7*temp_v,1.e3),1.e6)
!
psaci(:,1) = 0.
psacw(:,1) = 0.
WHERE( supcol_v .gt. 0 )
WHERE(qrs(:,k,2).gt.qcrmin.and.qci(:,k,2).gt.qmin)
diameter_v = min(dicon * sqrt(den(:,k)*qci(:,k,2)/xni(:,1)),dimax)
!-------------------------------------------------------------
! psaci: Accretion of cloud ice by rain [HDC 10]
! (T<T0: I->S)
!-------------------------------------------------------------
psaci(:,1) = pi*qci(:,k,2)*(exp(0.07*(-supcol_v)))*n0s*n0sfac(:,1) &
*abs((pvts*rslopeb_v(:,2)*denfac(:,k)) &
-(1.49e4*diameter_v**1.31))*(2.*rslope3_v(:,2)+2. &
*diameter_v*rslope2_v(:,2) &
+diameter_v*diameter_v*rslope_v(:,2))/4.
ENDWHERE
ENDWHERE
!-------------------------------------------------------------
! psacw: Accretion of cloud water by snow [HL A7] [LFO 24]
! (T<T0: C->S, and T>=T0: C->R)
!-------------------------------------------------------------
WHERE(qrs(:,k,2).gt.qcrmin.and.qci(:,k,1).gt.qmin)
psacw(:,1) = min(pacrc*n0sfac(:,1)*rslope3_v(:,2) &
*rslopeb_v(:,2)*qci(:,k,1)*denfac(:,k) &
,qci(:,k,1)*rdtcld)
ENDWHERE
pidep(:,1) = 0.
psdep(:,1) = 0.
WHERE(supcol_v .gt. 0)
!-------------------------------------------------------------
! pidep: Deposition/Sublimation rate of ice [HDC 9]
! (T<T0: V->I or I->V)
!-------------------------------------------------------------
WHERE(qci(:,k,2).gt.0.and.ifsat_v(:).ne.1)
diameter_v = dicon * sqrt(den(:,k)*qci(:,k,2)/xni(:,1))
pidep(:,1) = 4.*diameter_v*xni(:,1)*(rh(:,k,2)-1.)/work1(:,1,2)
supice_v = satdt_v-prevp(:,1)
WHERE(pidep(:,1).lt.0.)
pidep(:,1) = max(max(pidep(:,1),satdt_v*.5),supice_v)
pidep(:,1) = max(pidep(:,1),-qci(:,k,2)*rdtcld)
ELSEWHERE
pidep(:,1) = min(min(pidep(:,1),satdt_v*.5),supice_v)
ENDWHERE
WHERE(abs(prevp(:,1)+pidep(:,1)).ge.abs(satdt_v)) ifsat_v(:) = 1
ENDWHERE
!-------------------------------------------------------------
! psdep: deposition/sublimation rate of snow [HDC 14]
! (V->S or S->V)
!-------------------------------------------------------------
WHERE(qrs(:,k,2).gt.0..and.ifsat_v(:).ne.1)
psdep(:,1) = (rh(:,k,2)-1.)*n0sfac(:,1) &
*(precs1*rslope2_v(:,2)+precs2 &
*work2(:,1)*(rslope2_v(:,2)*sqrt(rslope_v(:,2)*rslopeb_v(:,2))))/work1(:,1,2)
supice_v = satdt_v-prevp(:,1)-pidep(:,1)
WHERE(psdep(:,1).lt.0.)
psdep(:,1) = max(psdep(:,1),-qrs(:,k,2)*rdtcld)
psdep(:,1) = max(max(psdep(:,1),satdt_v*.5),supice_v)
ELSEWHERE
psdep(:,1) = min(min(psdep(:,1),satdt_v*.5),supice_v)
ENDWHERE
WHERE(abs(prevp(:,1)+pidep(:,1)+psdep(:,1)).ge.abs(satdt_v)) &
ifsat_v(:) = 1
ENDWHERE
!-------------------------------------------------------------
! pigen: generation(nucleation) of ice from vapor [HL A50] [HDC 7-8]
! (T<T0: V->I)
!-------------------------------------------------------------
pigen(:,1) = 0.
WHERE(supsat_v.gt.0.and.ifsat_v(:).ne.1)
supice_v = satdt_v-prevp(:,1)-pidep(:,1)-psdep(:,1)
pigen(:,1) = max(0.,((4.92e-11*exp(log(1.e3*exp(0.1*supcol_v)) &
*(1.33)))/den(:,k)-max(qci(:,k,2),0.)) &
*rdtcld)
pigen(:,1) = min(min(pigen(:,1),satdt_v),supice_v)
ENDWHERE
!
!-------------------------------------------------------------
! psaut: conversion(aggregation) of ice to snow [HDC 12]
! (T<T0: I->S)
!-------------------------------------------------------------
psaut(:,1) = 0.
WHERE(qci(:,k,2).gt.0.)
psaut(:,1) = max(0.,(qci(:,k,2)-(roqimax/den(:,k)))*rdtcld)
ENDWHERE
ENDWHERE
!-------------------------------------------------------------
! psevp: Evaporation of melting snow [HL A35] [RH83 A27]
! (T>T0: S->V)
!-------------------------------------------------------------
psevp(:,1) = 0.
WHERE(supcol_v.lt.0.)
WHERE(qrs(:,k,2).gt.0..and.rh(:,k,1).lt.1.)
psevp(:,1) = psdep(:,1)*work1(:,1,2)/work1(:,1,1)
ENDWHERE
psevp(:,1) = min(max(psevp(:,1),-qrs(:,k,2)*rdtcld),0.)
ENDWHERE
ENDWHERE
!JM fuse-K enddo
!
!
!----------------------------------------------------------------
! check mass conservation of generation terms and feedback to the
! large scale
!
!JM fuse-K do k = kts, kte
do i = its, min(irestrict,ite)
if(t(i,k).le.t0c) then
!
! cloud water
!
value = max(qmin,qci(i,k,1))
source = (praut(i,1)+pracw(i,1)+psacw(i,1))*dtcld
if (source.gt.value) then
factor = value/source
praut(i,1) = praut(i,1)*factor
pracw(i,1) = pracw(i,1)*factor
psacw(i,1) = psacw(i,1)*factor
endif
!
! cloud ice
!
value = max(qmin,qci(i,k,2))
source = (psaut(i,1)+psaci(i,1)-pigen(i,1)-pidep(i,1))*dtcld
if (source.gt.value) then
factor = value/source
psaut(i,1) = psaut(i,1)*factor
psaci(i,1) = psaci(i,1)*factor
pigen(i,1) = pigen(i,1)*factor
pidep(i,1) = pidep(i,1)*factor
endif
!
! rain
!
!
value = max(qmin,qrs(i,k,1))
source = (-praut(i,1)-pracw(i,1)-prevp(i,1))*dtcld
if (source.gt.value) then
factor = value/source
praut(i,1) = praut(i,1)*factor
pracw(i,1) = pracw(i,1)*factor
prevp(i,1) = prevp(i,1)*factor
endif
!
! snow
!
value = max(qmin,qrs(i,k,2))
source = (-psdep(i,1)-psaut(i,1)-psaci(i,1)-psacw(i,1))*dtcld
if (source.gt.value) then
factor = value/source
psdep(i,1) = psdep(i,1)*factor
psaut(i,1) = psaut(i,1)*factor
psaci(i,1) = psaci(i,1)*factor
psacw(i,1) = psacw(i,1)*factor
endif
!
work2(i,1)=-(prevp(i,1)+psdep(i,1)+pigen(i,1)+pidep(i,1))
! update
q(i,k) = q(i,k)+work2(i,1)*dtcld
qci(i,k,1) = max(qci(i,k,1)-(praut(i,1)+pracw(i,1) &
+psacw(i,1))*dtcld,0.)
qrs(i,k,1) = max(qrs(i,k,1)+(praut(i,1)+pracw(i,1) &
+prevp(i,1))*dtcld,0.)
qci(i,k,2) = max(qci(i,k,2)-(psaut(i,1)+psaci(i,1) &
-pigen(i,1)-pidep(i,1))*dtcld,0.)
qrs(i,k,2) = max(qrs(i,k,2)+(psdep(i,1)+psaut(i,1) &
+psaci(i,1)+psacw(i,1))*dtcld,0.)
xlf = xls-xl(i,k)
xlwork2 = -xls*(psdep(i,1)+pidep(i,1)+pigen(i,1)) &
-xl(i,k)*prevp(i,1)-xlf*psacw(i,1)
t(i,k) = t(i,k)-xlwork2/cpm(i,k)*dtcld
else
!
! cloud water
!
value = max(qmin,qci(i,k,1))
source=(praut(i,1)+pracw(i,1)+psacw(i,1))*dtcld
if (source.gt.value) then
factor = value/source
praut(i,1) = praut(i,1)*factor
pracw(i,1) = pracw(i,1)*factor
psacw(i,1) = psacw(i,1)*factor
endif
!
! rain
!
value = max(qmin,qrs(i,k,1))
source = (-praut(i,1)-pracw(i,1)-prevp(i,1)-psacw(i,1))*dtcld
if (source.gt.value) then
factor = value/source
praut(i,1) = praut(i,1)*factor
pracw(i,1) = pracw(i,1)*factor
prevp(i,1) = prevp(i,1)*factor
psacw(i,1) = psacw(i,1)*factor
endif
!
! snow
!
value = max(qcrmin,qrs(i,k,2))
source=(-psevp(i,1))*dtcld
if (source.gt.value) then
factor = value/source
psevp(i,1) = psevp(i,1)*factor
endif
work2(i,1)=-(prevp(i,1)+psevp(i,1))
! update
q(i,k) = q(i,k)+work2(i,1)*dtcld
qci(i,k,1) = max(qci(i,k,1)-(praut(i,1)+pracw(i,1) &
+psacw(i,1))*dtcld,0.)
qrs(i,k,1) = max(qrs(i,k,1)+(praut(i,1)+pracw(i,1) &
+prevp(i,1) +psacw(i,1))*dtcld,0.)
qrs(i,k,2) = max(qrs(i,k,2)+psevp(i,1)*dtcld,0.)
xlf = xls-xl(i,k)
xlwork2 = -xl(i,k)*(prevp(i,1)+psevp(i,1))
t(i,k) = t(i,k)-xlwork2/cpm(i,k)*dtcld
endif
enddo
enddo ! fuse K
!
! 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
WHERE(lmask)
tr_v=ttp/t(:,k)
logtr_v = log(tr_v)
qs(:,k,1)=psat*exp(logtr_v*(xa)+xb*(1.-tr_v))
qs(:,k,1) = min(qs(:,k,1),0.99*p(:,k))
qs(:,k,1) = ep2 * qs(:,k,1) / (p(:,k) - qs(:,k,1))
qs(:,k,1) = max(qs(:,k,1),qmin)
ENDWHERE
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, min(irestrict,ite)
work1(i,1,1) = ((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)))))
pcond(i,1) = min(max(work1(i,1,1)/dtcld,0.),max(q(i,k),0.)/dtcld)
if(qci(i,k,1).gt.0..and.work1(i,1,1).lt.0.) &
pcond(i,1) = max(work1(i,1,1),-qci(i,k,1))/dtcld
q(i,k) = q(i,k)-pcond(i,1)*dtcld
qci(i,k,1) = max(qci(i,k,1)+pcond(i,1)*dtcld,0.)
t(i,k) = t(i,k)+pcond(i,1)*xl(i,k)/cpm(i,k)*dtcld
enddo
enddo
!
!
!----------------------------------------------------------------
! padding for small values
!
do k = kts, kte
do i = its, min(irestrict,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
!------------------------------------------------------------------------------
#if 0
SUBROUTINE slope_wsm5(qrs,den,denfac,t,rslope,rslopeb,rslope2,rslope3, &
vt,irestrict,kts,kte,lmask)
IMPLICIT NONE
INTEGER :: irestrict,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
REAL :: supcol_v(CHUNK)
integer :: i, j, k
LOGICAL*4 lmask(CHUNK)
!----------------------------------------------------------------
! 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
#define LAMDAR(x,y) sqrt(sqrt(pidn0r/((x)*(y))))
#define LAMDAS(x,y,z) sqrt(sqrt(pidn0s*(z)/((x)*(y))))
!
do k = kts, kte
WHERE(lmask)
supcol_v = t0c-t(:,k)
!---------------------------------------------------------------
! n0s: Intercept parameter for snow [m-4] [HDC 6]
!---------------------------------------------------------------
n0sfac(:,k) = max(min(exp(alpha*supcol_v),n0smax/n0s),1.)
WHERE(qrs(:,k,1).le.qcrmin)
rslope(:,k,1) = rslopermax
rslopeb(:,k,1) = rsloperbmax
rslope2(:,k,1) = rsloper2max
rslope3(:,k,1) = rsloper3max
ELSEWHERE
rslope(:,k,1) = 1./LAMDAR(qrs(:,k,1),den(:,k))
rslopeb(:,k,1) = exp(log(rslope(:,k,1))*(bvtr))
rslope2(:,k,1) = rslope(:,k,1)*rslope(:,k,1)
rslope3(:,k,1) = rslope2(:,k,1)*rslope(:,k,1)
ENDWHERE
WHERE(qrs(:,k,2).le.qcrmin)
rslope(:,k,2) = rslopesmax
rslopeb(:,k,2) = rslopesbmax
rslope2(:,k,2) = rslopes2max
rslope3(:,k,2) = rslopes3max
ELSEWHERE
rslope(:,k,2) = 1./LAMDAS(qrs(:,k,2),den(:,k),n0sfac(:,k))
rslopeb(:,k,2) = exp(log(rslope(:,k,2))*(bvts))
rslope2(:,k,2) = rslope(:,k,2)*rslope(:,k,2)
rslope3(:,k,2) = rslope2(:,k,2)*rslope(:,k,2)
ENDWHERE
WHERE (qrs(:,k,1).le.0.0)
vt(:,k,1) = 0.0
ELSEWHERE
vt(:,k,1) = pvtr*rslopeb(:,k,1)*denfac(:,k)
ENDWHERE
WHERE (qrs(:,k,2).le.0.0)
vt(:,k,2) = 0.0
ELSEWHERE
vt(:,k,2) = pvts*rslopeb(:,k,2)*denfac(:,k)
ENDWHERE
ENDWHERE
enddo
#undef LAMDAR
#undef LAMDAS
END SUBROUTINE slope_wsm5
#endif
#if 0
#undef nx
#undef nk
#undef its
#undef ite
#undef ims
#undef ime
#undef kms
#undef kme
#undef im
#undef km
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(im0,km,den, denfac, tk, dz, ww0,qq0,precip0,dt,id,iter,irestrict,lon,lat,doit,call)
SUBROUTINE nislfv_rain_plm(im, km,denl,denfacl,tkl,dzl,wwl,rql,precip ,dt,id,iter, &
irestrict, lon, lat, doit, call )
!-------------------------------------------------------------------
!
! 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 irestrict,lon,lat,call
logical doit
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,irestrict !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
#else
SUBROUTINE slope_rain(qrs,den,denfac,t,rslope,rslopeb, &
vt,irestrict,kts,kte,lmask)
IMPLICIT NONE
INTEGER :: irestrict,kts,kte
REAL, DIMENSION( its:ite , kts:kte) :: &
qrs, &
vt, &
den, &
denfac, &
t
REAL, DIMENSION( its:ite ) :: &
rslope, &
rslopeb
REAL, PARAMETER :: t0c = 273.15
REAL :: lamdar, x, y, z
LOGICAL*4 :: lmask(its:ite)
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
#define LAMDAR(x,y) sqrt(sqrt(pidn0r/((x)*(y))))
!
do k = kts, kte
WHERE(lmask)
WHERE(qrs(:,k).le.qcrmin)
rslope(:) = rslopermax
rslopeb(:) = rsloperbmax
ELSEWHERE
rslope(:) = 1./LAMDAR(qrs(:,k),den(:,k))
rslopeb(:) = rslope(:)**bvtr
! rslopeb(:) = exp(log(rslope(:))*(bvtr))
ENDWHERE
WHERE(qrs(:,k).le.0.0)
vt(:,k) = 0.0
ELSEWHERE
vt(:,k) = pvtr*rslopeb(:)*denfac(:,k)
ENDWHERE
ENDWHERE
enddo
#undef LAMDAR
END SUBROUTINE slope_rain
!------------------------------------------------------------------------------
SUBROUTINE slope_snow(qrs,den,denfac,t,rslope,rslopeb, &
vt,irestrict,kts,kte,lmask)
IMPLICIT NONE
INTEGER :: irestrict,kts,kte
REAL, DIMENSION( its:ite , kts:kte) :: &
qrs, &
vt, &
den, &
denfac, &
t
REAL, DIMENSION( its:ite ) :: &
rslope, &
rslopeb
REAL, PARAMETER :: t0c = 273.15
integer :: i, j, k
LOGICAL*4 lmask(CHUNK)
!----------------------------------------------------------------
! size distributions: (x=mixing ratio, y=air density):
! valid for mixing ratio > 1.e-9 kg/kg.
#define LAMDAS(x,y,z) sqrt(sqrt(pidn0s*(z)/((x)*(y))))
!
do k = kts, kte
WHERE(lmask)
!---------------------------------------------------------------
! n0s: Intercept parameter for snow [m-4] [HDC 6]
!---------------------------------------------------------------
WHERE(qrs(:,k).le.qcrmin)
rslope(:) = rslopesmax
rslopeb(:) = rslopesbmax
ELSEWHERE
rslope(:) = 1./LAMDAS(qrs(:,k),den(:,k),(max(min(exp(alpha*(t0c-t(:,k))),n0smax/n0s),1.)))
rslopeb(:) = rslope(:)**bvts
! rslopeb(:) = exp(log(rslope(:))*(bvts))
ENDWHERE
WHERE(qrs(:,k).le.0.0)
vt(:,k) = 0.0
ELSEWHERE
vt(:,k) = pvts*rslopeb(:)*denfac(:,k)
ENDWHERE
ENDWHERE
enddo
#undef LAMDAS
END SUBROUTINE slope_snow
!-------------------------------------------------------------------
! SUBROUTINE nislfv_rain_plm(im,km,denl,denfacl,tkl,dzl,wwl,rql,precip,dt,id,iter)
SUBROUTINE nislfv_rain_plm(im0,km,den,denfac,tk,dz,ww0,qq0,precip0,dt,id,iter,irestrict,lon,lat,doit,call)
!-------------------------------------------------------------------
!
! 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
!
#define im nx
!#define km nk
implicit none
integer,intent(in ) :: im0,km,id,irestrict
real, intent(in ) :: den(im,km)
real, intent(in ) :: denfac(im,km)
real, intent(in ) :: tk(im,km)
real, intent(in ) :: dz(im,km)
real, intent(in ) :: ww0(im,km)
real, intent( out) :: precip0(im)
real, intent(inout) :: qq0(im,km)
real, intent(in ) :: dt
logical, intent(in) :: doit
integer :: call
!
integer i,k,m,kk,iter
integer n
real dim(im),dip(im),c1,con1,fa1,fa2
real allold(im), allnew(im), zz(im), dzamin(im), cflmax(im), decfl(im)
real qq(im,km), ww(im,km),precip(im)
real wd(im,km), wa(im,km), was(im,km)
real wi(im,km+1), zi(im,km+1), za(im,km+1)
real qn(im,km),qr(im,km),tmp(im,km),tmp1(im,km),tmp2(im,km),tmp3(im,km)
real dza(im,km+1), qa(im,km+1), qmi(im,km+1), qpi(im,km+1)
logical*4 lmask(im)
INTEGER minkb, minkt
LOGICAL, DIMENSION(CHUNK) :: intp_mask, tmask
INTEGER, DIMENSION(CHUNK) :: kb, kt
REAL, DIMENSION(CHUNK) :: tl,tl2,th,th2,qqd,qqh,qql,zsum,qsum,dql,dqh
REAL, DIMENSION(CHUNK) :: za_gath_t,za_gath_b
REAL, DIMENSION(CHUNK) :: qa_gath_b
REAL, DIMENSION(CHUNK) :: dza_gath_t,dza_gath_b
REAL, DIMENSION(CHUNK) :: qpi_gath_t,qpi_gath_b
REAL, DIMENSION(CHUNK) :: qmi_gath_t,qmi_gath_b
integer, intent(in) :: lat,lon
!
precip = 0.0
! -----------------------------------
qq = qq0
ww = ww0
! skip for no precipitation for all layers
lmask = .false.
do i = 1,min( irestrict, im )
lmask(i) = .true.
enddo
allold = 0.0
do k=1,km
where(lmask)allold = allold + qq(:,k)
enddo
lmask = lmask .and. ( allold .gt. 0.0 )
IF ( .NOT. ANY(lmask) ) THEN
precip0 = precip
RETURN
ENDIF
!
! compute interface values
zi(:,1)=0.0
do k=1,km
where(lmask) zi(:,k+1) = zi(:,k)+dz(:,k)
enddo
!
! save departure wind
wd = ww
DO n = 0, iter
where(lmask)
! 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)
endwhere
do k=2,km
where(lmask)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.
where(lmask)
wi(:,1) = ww(:,1)
wi(:,2) = 0.5*(ww(:,2)+ww(:,1))
endwhere
do k=3,km-1
where(lmask)wi(:,k) = fa1*(ww(:,k)+ww(:,k-1))-fa2*(ww(:,k+1)+ww(:,k-2))
enddo
where(lmask)
wi(:,km) = 0.5*(ww(:,km)+ww(:,km-1))
wi(:,km+1) = ww(:,km)
endwhere
!
! terminate of top of raingroup
do k=2,km
where(lmask .and. ww(:,k).eq.0.0 ) wi(:,k)=ww(:,k-1)
enddo
!
! diffusivity of wi
con1 = 0.05
do k=km,1,-1
where (lmask)
decfl = (wi(:,k+1)-wi(:,k))*dt/dz(:,k)
elsewhere
decfl = 0.
endwhere
where (lmask )
where (decfl .gt. con1 )
wi(:,k) = wi(:,k+1) - con1*dz(:,k)/dt
endwhere
endwhere
enddo
! compute arrival point
do k=1,km+1
where (lmask) za(:,k) = zi(:,k) - wi(:,k)*dt
enddo
!
do k=1,km
where (lmask) dza(:,k) = za(:,k+1)-za(:,k)
enddo
where (lmask) dza(:,km+1) = zi(:,km+1) - za(:,km+1)
!
! compute deformation at arrival point
do k=1,km
where (lmask) qa(:,k) = qq(:,k)*dz(:,k)/dza(:,k)
where (lmask) qr(:,k) = qa(:,k)/den(:,k)
enddo
where (lmask) qa(:,km+1) = 0.0
! compute arrival terminal velocity, and estimate mean terminal velocity
! then back to use mean terminal velocity
if( n.le.iter-1 ) then
if (id.eq.1) then
call slope_rain(qr,den,denfac,tk,tmp,tmp1,wa,irestrict,1,km,lmask)
else
call slope_snow(qr,den,denfac,tk,tmp,tmp1,wa,irestrict,1,km,lmask)
endif
do k=1,km
if( n.ge.1 ) where (lmask) wa(:,k)=0.5*(wa(:,k)+was(:,k))
where (lmask ) ww(:,k) = 0.5* ( wd(:,k)+wa(:,k) )
enddo
was = wa
endif
ENDDO ! n loop
!
! estimate values at arrival cell interface with monotone
do k=2,km
where (lmask )
dip=(qa(:,k+1)-qa(:,k))/(dza(:,k+1)+dza(:,k))
dim=(qa(:,k)-qa(:,k-1))/(dza(:,k-1)+dza(:,k))
where( dip*dim.le.0.0 )
qmi(:,k)=qa(:,k)
qpi(:,k)=qa(:,k)
elsewhere
qpi(:,k)=qa(:,k)+0.5*(dip+dim)*dza(:,k)
qmi(:,k)=2.0*qa(:,k)-qpi(:,k)
where( qpi(:,k).lt.0.0 .or. qmi(:,k).lt.0.0 )
qpi(:,k) = qa(:,k)
qmi(:,k) = qa(:,k)
endwhere
endwhere
endwhere
enddo
where (lmask )
qpi(:,1)=qa(:,1)
qmi(:,1)=qa(:,1)
qmi(:,km+1)=qa(:,km+1)
qpi(:,km+1)=qa(:,km+1)
endwhere
!
! interpolation to regular point
qn = 0.0
kb=1 ! kb is a vector
kt=1 ! kt is a vector
INTP : do k=1,km
kb=max(kb-1,1)
kt=max(kt-1,1)
! find kb and kt
intp_mask = ( zi(:,k).lt.za(:,km+1) .AND. lmask )
tmask = intp_mask
minkb = 999
minkt = 999
DO i=1,CHUNK
IF ( tmask(i) .AND. kb(i) .lt. minkb ) minkb = kb(i)
IF ( tmask(i) .AND. kt(i) .lt. minkt ) minkt = kt(i)
ENDDO
find_kb : do kk=minkb,km
WHERE ( tmask .AND. zi(:,k).le.za(:,kk+1) )
kb = kk
tmask = .FALSE.
END WHERE
enddo find_kb
tmask = intp_mask
find_kt : do kk=minkt,km
WHERE ( tmask .AND. zi(:,k+1).le.za(:,kk) )
kt = kk
tmask = .FALSE.
END WHERE
enddo find_kt
kt = max(kt - 1,1)
!#define RANGE_CHECKING
#ifndef RANGE_CHECKING
# define DX1 (i+(kb(i)-1)*im),1
# define DX2 (i+(kt(i)-1)*im),1
#else
# define DX1 i,kb(i)
# define DX2 i,kt(i)
#endif
!DEC$ SIMD
DO i = 1, CHUNK
qa_gath_b(i) = qa(DX1)
za_gath_b(i) = za(DX1)
dza_gath_b(i) = dza(DX1)
qpi_gath_b(i) = qpi(DX1)
qmi_gath_b(i) = qmi(DX1)
ENDDO
!DEC$ SIMD
DO i = 1, CHUNK
za_gath_t(i) = za(DX2)
dza_gath_t(i) = dza(DX2)
qpi_gath_t(i) = qpi(DX2)
qmi_gath_t(i) = qmi(DX2)
ENDDO
WHERE ( kt .eq. kb .AND. intp_mask )
tl=(zi(:,k)-za_gath_b)/dza_gath_b
th=(zi(:,k+1)-za_gath_b)/dza_gath_b
tl2 = tl*tl
th2 = th*th
qqd=0.5*(qpi_gath_b-qmi_gath_b)
qqh=qqd*th2+qmi_gath_b*th
qql=qqd*tl2+qmi_gath_b*tl
qn(:,k) = (qqh-qql)/(th-tl)
ELSE WHERE ( kt .gt. kb .AND. intp_mask )
tl=(zi(:,k)-za_gath_b)/dza_gath_b
tl2=tl*tl
qqd=0.5*(qpi_gath_b-qmi_gath_b)
qql=qqd*tl2+qmi_gath_b*tl
dql = qa_gath_b-qql
zsum = (1.-tl)*dza_gath_b
qsum = dql*dza_gath_b
END WHERE
DO i = 1, CHUNK
if( kt(i)-kb(i).gt.1 .AND. intp_mask(i) ) then
do m=kb(i)+1,kt(i)-1
zsum(i) = zsum(i) + dza(i,m)
qsum(i) = qsum(i) + qa(i,m) * dza(i,m)
enddo
endif
enddo
WHERE ( kt .gt. kb .AND. intp_mask )
th=(zi(:,k+1)-za_gath_t)/dza_gath_t
th2 = th*th
qqd=0.5*(qpi_gath_t-qmi_gath_t)
dqh=qqd*th2+qmi_gath_t*th
zsum = zsum + th*dza_gath_t
qsum = qsum + dqh*dza_gath_t
qn(:,k) = qsum/zsum
END WHERE
ENDDO intp
!
! rain out
intp_mask = lmask
sum_precip: do k=1,km
WHERE ( za(:,k).lt.0.0 .and. za(:,k+1).lt.0.0 .AND. intp_mask )
precip = precip + qa(:,k)*dza(:,k)
ELSE WHERE ( za(:,k).lt.0.0 .and. za(:,k+1).ge.0.0 .AND. intp_mask)
precip = precip + qa(:,k)*(0.0-za(:,k))
intp_mask = .FALSE.
END WHERE
enddo sum_precip
! ENDDO ! i loop
!
! replace the new values
do k = 1,km
where(lmask) qq0(:,k) = qn(:,k)
enddo
precip0 = 0.
where (lmask) precip0 = precip
!
! ----------------------------------
! enddo i_loop
!
END SUBROUTINE nislfv_rain_plm
#undef nx
#undef nk
#undef its
#undef ite
#undef ims
#undef ime
#undef kms
#undef kme
#undef im
#undef km
#endif