#ifdef _ACCEL
# include "module_mp_wsm3_accel.F"
#else
#if ( RWORDSIZE == 4 )
# define VREC vsrec
# define VSQRT vssqrt
#else
# define VREC vrec
# define VSQRT vsqrt
#endif
MODULE module_mp_wsm3 2
!
!
REAL, PARAMETER, PRIVATE :: dtcldcr = 120. ! maximum time step for minor loops
REAL, PARAMETER, PRIVATE :: n0r = 8.e6 ! intercept parameter rain
REAL, PARAMETER, PRIVATE :: avtr = 841.9 ! a constant for terminal velocity of rain
REAL, PARAMETER, PRIVATE :: bvtr = 0.8 ! a constant for terminal velocity of rain
REAL, PARAMETER, PRIVATE :: r0 = .8e-5 ! 8 microm in contrast to 10 micro m
REAL, PARAMETER, PRIVATE :: peaut = .55 ! collection efficiency
REAL, PARAMETER, PRIVATE :: xncr = 3.e8 ! maritime cloud in contrast to 3.e8 in tc80
REAL, PARAMETER, PRIVATE :: xmyu = 1.718e-5 ! the dynamic viscosity kgm-1s-1
REAL, PARAMETER, PRIVATE :: avts = 11.72 ! a constant for terminal velocity of snow
REAL, PARAMETER, PRIVATE :: bvts = .41 ! a constant for terminal velocity of snow
REAL, PARAMETER, PRIVATE :: n0smax = 1.e11 ! maximum n0s (t=-90C unlimited)
REAL, PARAMETER, PRIVATE :: 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 :: qcrmin = 1.e-9 ! minimun values for qr, qs, and qg
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,pi, &
rslopermax,rslopesmax,rslopegmax, &
rsloperbmax,rslopesbmax,rslopegbmax, &
rsloper2max,rslopes2max,rslopeg2max, &
rsloper3max,rslopes3max,rslopeg3max
!
! Specifies code-inlining of fpvs function in WSM32D below. JM 20040507
!
CONTAINS
!===================================================================
!
SUBROUTINE wsm3(th, q, qci, qrs & 1,3
, w, 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, &
qci, &
qrs
REAL, DIMENSION( ims:ime , kms:kme , jms:jme ), &
INTENT(IN ) :: w, &
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
REAL, DIMENSION( ims:ime , jms:jme ), OPTIONAL, &
INTENT(INOUT) :: snow, &
snowncv, &
sr
! LOCAL VAR
REAL, DIMENSION( its:ite , kts:kte ) :: t
INTEGER :: i,j,k
!-------------------------------------------------------------------
DO j=jts,jte
DO k=kts,kte
DO i=its,ite
t(i,k)=th(i,k,j)*pii(i,k,j)
ENDDO
ENDDO
CALL wsm32D(t, q(ims,kms,j), qci(ims,kms,j) &
,qrs(ims,kms,j),w(ims,kms,j), 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) &
,snow(ims,j),snowncv(ims,j) &
,sr(ims,j) &
,ids,ide, jds,jde, kds,kde &
,ims,ime, jms,jme, kms,kme &
,its,ite, jts,jte, kts,kte &
)
DO K=kts,kte
DO I=its,ite
th(i,k,j)=t(i,k)/pii(i,k,j)
ENDDO
ENDDO
ENDDO
END SUBROUTINE wsm3
!===================================================================
!
SUBROUTINE wsm32D(t, q & 3,11
,qci, qrs,w, den, p, delz &
,delt,g, cpd, cpv, rd, rv, t0c &
,ep1, ep2, qmin &
,XLS, XLV0, XLF0, den0, denr &
,cliq,cice,psat &
,lat &
,rain, rainncv &
,snow,snowncv &
,sr &
,ids,ide, jds,jde, kds,kde &
,ims,ime, jms,jme, kms,kme &
,its,ite, jts,jte, kts,kte &
)
!-------------------------------------------------------------------
IMPLICIT NONE
!-------------------------------------------------------------------
!
! This code is a 3-class simple ice microphyiscs scheme (WSM3) 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.
!
! WSM3 cloud scheme
!
! Developed 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
!
! History : semi-lagrangian scheme sedimentation(JH), and clean up
! Hong, August 2009
!
! Reference) Hong, Dudhia, Chen (HDC, 2004) Mon. Wea. Rev.
! Dudhia (D89, 1989) J. Atmos. Sci.
! Hong and Lim (HL, 2006) J. Korean Meteor. Soc.
! Juang and Hong (JH, 2010) Mon. Wea. Rev.
!
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( ims:ime , kms:kme ), &
INTENT(INOUT) :: &
q, &
qci, &
qrs
REAL, DIMENSION( ims:ime , kms:kme ), &
INTENT(IN ) :: w, &
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
REAL, DIMENSION( ims:ime ), OPTIONAL, &
INTENT(INOUT) :: snow, &
snowncv, &
sr
! LOCAL VAR
REAL, DIMENSION( its:ite , kts:kte ) :: &
rh, &
qs, &
denfac, &
rslope, &
rslope2, &
rslope3, &
qrs_tmp, &
den_tmp, &
delz_tmp, &
rslopeb
REAL, DIMENSION( its:ite , kts:kte ) :: &
pgen, &
pisd, &
paut, &
pacr, &
pres, &
pcon
REAL, DIMENSION( its:ite , kts:kte ) :: &
fall, &
falk, &
xl, &
cpm, &
work1, &
work2, &
xni, &
qs0, &
denqci, &
denqrs, &
n0sfac, &
falkc, &
work1c, &
work2c, &
fallc
REAL, DIMENSION( its:ite ) :: delqrs,&
delqi
REAL, DIMENSION(its:ite) :: tstepsnow
INTEGER, DIMENSION( its:ite ) :: kwork1,&
kwork2
INTEGER, DIMENSION( its:ite ) :: mstep, &
numdt
LOGICAL, DIMENSION( its:ite ) :: flgcld
REAL :: &
cpmcal, xlcal, diffus, &
viscos, xka, venfac, conden, diffac, &
x, y, z, a, b, c, d, e, &
fallsum, fallsum_qsi, vt2i,vt2s,acrfac, &
qdt, pvt, qik, delq, facq, qrsci, frzmlt, &
snomlt, hold, holdrs, facqci, supcol, coeres, &
supsat, dtcld, xmi, qciik, delqci, eacrs, satdt, &
qimax, diameter, xni0, roqi0, supice,holdc, holdci
INTEGER :: i, j, k, mstepmax, &
iprt, latd, lond, loop, loops, ifsat, kk, n, idim, kdim
! Temporaries used for inlining fpvs function
REAL :: dldti, xb, xai, tr, xbi, xa, hvap, cvap, hsub, dldt, ttp
! variables for optimization
REAL, DIMENSION( its:ite ) :: tvec1
!
!=================================================================
! 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)
! Optimizatin : A**B => exp(log(A)*(B))
!
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) = max(qci(i,k),0.0)
qrs(i,k) = max(qrs(i,k),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) = 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
flgcld(i) = .true.
enddo
!
do k = kts, kte
CALL VREC( tvec1(its), den(its,k), ite-its+1)
do i = its, ite
tvec1(i) = tvec1(i)*den0
enddo
CALL VSQRT( denfac(its,k), tvec1(its), ite-its+1)
enddo
!
! Inline expansion for fpvs
! qs(i,k) = fpvs(t(i,k),1,rd,rv,cpv,cliq,cice,xlv0,xls,psat,t0c)
! qs0(i,k) = fpvs(t(i,k),0,rd,rv,cpv,cliq,cice,xlv0,xls,psat,t0c)
cvap = cpv
hvap=xlv0
hsub=xls
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)
if(t(i,k).lt.ttp) then
qs(i,k) =psat*(exp(log(tr)*(xai)))*exp(xbi*(1.-tr))
else
qs(i,k) =psat*(exp(log(tr)*(xa)))*exp(xb*(1.-tr))
endif
qs0(i,k) =psat*(exp(log(tr)*(xa)))*exp(xb*(1.-tr))
qs0(i,k) = (qs0(i,k)-qs(i,k))/qs(i,k)
qs(i,k) = min(qs(i,k),0.99*p(i,k))
qs(i,k) = ep2 * qs(i,k) / (p(i,k) - qs(i,k))
qs(i,k) = max(qs(i,k),qmin)
rh(i,k) = max(q(i,k) / qs(i,k),qmin)
enddo
enddo
!
!----------------------------------------------------------------
! initialize the variables for microphysical physics
!
!
do k = kts, kte
do i = its, ite
pres(i,k) = 0.
paut(i,k) = 0.
pacr(i,k) = 0.
pgen(i,k) = 0.
pisd(i,k) = 0.
pcon(i,k) = 0.
fall(i,k) = 0.
falk(i,k) = 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
xni(i,k) = min(max(5.38e7 &
*exp(log((den(i,k)*max(qci(i,k),qmin)))*(0.75)),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) = qrs(i,k)
enddo
enddo
call slope_wsm3(qrs_tmp,den_tmp,denfac,t,rslope,rslopeb,rslope2,rslope3, &
work1,its,ite,kts,kte)
!
!
! forward semi-laglangian scheme (JH), PCM (piecewise constant), (linear)
!
do k = kte, kts, -1
do i = its, ite
denqrs(i,k) = den(i,k)*qrs(i,k)
enddo
enddo
call nislfv_rain_plm(idim,kdim,den_tmp,denfac,t,delz_tmp,work1,denqrs, &
delqrs,dtcld,1,1)
do k = kts, kte
do i = its, ite
qrs(i,k) = max(denqrs(i,k)/den(i,k),0.)
fall(i,k) = denqrs(i,k)*work1(i,k)/delz(i,k)
enddo
enddo
do i = its, ite
fall(i,1) = delqrs(i)/delz(i,1)/dtcld
enddo
!---------------------------------------------------------------
! Vice [ms-1] : fallout of ice crystal [HDC 5a]
!---------------------------------------------------------------
do k = kte, kts, -1
do i = its, ite
if(t(i,k).lt.t0c.and.qci(i,k).gt.0.) then
xmi = den(i,k)*qci(i,k)/xni(i,k)
diameter = max(dicon * sqrt(xmi), 1.e-25)
work1c(i,k) = 1.49e4*exp(log(diameter)*(1.31))
else
work1c(i,k) = 0.
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)
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) = max(denqci(i,k)/den(i,k),0.)
enddo
enddo
do i = its, ite
fallc(i,1) = delqi(i)/delz(i,1)/dtcld
enddo
!
!----------------------------------------------------------------
! compute the freezing/melting term. [D89 B16-B17]
! freezing occurs one layer above the melting level
!
do i = its, ite
mstep(i) = 0
enddo
do k = kts, kte
!
do i = its, ite
if(t(i,k).ge.t0c) then
mstep(i) = k
endif
enddo
enddo
!
do i = its, ite
kwork2(i) = mstep(i)
kwork1(i) = mstep(i)
if(mstep(i).ne.0) then
if (w(i,mstep(i)).gt.0.) then
kwork1(i) = mstep(i) + 1
endif
endif
enddo
!
do i = its, ite
k = kwork1(i)
kk = kwork2(i)
if(k*kk.ge.1) then
qrsci = qrs(i,k) + qci(i,k)
if(qrsci.gt.0..or.fall(i,kk).gt.0.) then
frzmlt = min(max(-w(i,k)*qrsci/delz(i,k),-qrsci/dtcld), &
qrsci/dtcld)
snomlt = min(max(fall(i,kk)/den(i,kk),-qrs(i,k)/dtcld), &
qrs(i,k)/dtcld)
if(k.eq.kk) then
t(i,k) = t(i,k) - xlf0/cpm(i,k)*(frzmlt+snomlt)*dtcld
else
t(i,k) = t(i,k) - xlf0/cpm(i,k)*frzmlt*dtcld
t(i,kk) = t(i,kk) - xlf0/cpm(i,kk)*snomlt*dtcld
endif
endif
endif
enddo
!
!----------------------------------------------------------------
! rain (unit is mm/sec;kgm-2s-1: /1000*delt ===> m)==> mm for wrf
!
do i = its, ite
fallsum = fall(i,1)
fallsum_qsi = 0.
if((t0c-t(i,1)).gt.0) then
fallsum = fallsum+fallc(i,1)
fallsum_qsi = fall(i,1)+fallc(i,1)
endif
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) = fallsum_qsi*delz(i,kts)/denr*dtcld*1000. + snowncv(i)
snow(i) = fallsum_qsi*delz(i,kts)/denr*dtcld*1000. + snow(i)
ENDIF
endif
! if(fallsum.gt.0.) sr(i) = snowncv(i)/(rainncv(i)+1.e-12)
if(fallsum.gt.0.) sr(i) = tstepsnow(i)/(rainncv(i)+1.e-12)
enddo
!
!----------------------------------------------------------------
! update the slope parameters for microphysics computation
!
do k = kts, kte
do i = its, ite
qrs_tmp(i,k) = qrs(i,k)
enddo
enddo
call slope_wsm3(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
! work2: parameter associated with the ventilation effects(y93)
!
do k = kts, kte
do i = its, ite
if(t(i,k).ge.t0c) then
work1(i,k) = diffac(xl(i,k),p(i,k),t(i,k),den(i,k),qs(i,k))
else
work1(i,k) = diffac(xls,p(i,k),t(i,k),den(i,k),qs(i,k))
endif
work2(i,k) = venfac(p(i,k),t(i,k),den(i,k))
enddo
enddo
!
do k = kts, kte
do i = its, ite
supsat = max(q(i,k),qmin)-qs(i,k)
satdt = supsat/dtcld
if(t(i,k).ge.t0c) then
!
!===============================================================
!
! warm rain processes
!
! - follows the processes in RH83 and LFO except for autoconcersion
!
!===============================================================
!---------------------------------------------------------------
! praut: auto conversion rate from cloud to rain [HDC 16]
! (C->R)
!---------------------------------------------------------------
if(qci(i,k).gt.qc0) then
! paut(i,k) = qck1*qci(i,k)**(7./3.)
paut(i,k) = qck1*exp(log(qci(i,k))*((7./3.)))
paut(i,k) = min(paut(i,k),qci(i,k)/dtcld)
endif
!---------------------------------------------------------------
! pracw: accretion of cloud water by rain [HL A40] [D89 B15]
! (C->R)
!---------------------------------------------------------------
if(qrs(i,k).gt.qcrmin.and.qci(i,k).gt.qmin) then
pacr(i,k) = min(pacrr*rslope3(i,k)*rslopeb(i,k) &
*qci(i,k)*denfac(i,k),qci(i,k)/dtcld)
endif
!---------------------------------------------------------------
! prevp: evaporation/condensation rate of rain [HDC 14]
! (V->R or R->V)
!---------------------------------------------------------------
if(qrs(i,k).gt.0.) then
coeres = rslope2(i,k)*sqrt(rslope(i,k)*rslopeb(i,k))
pres(i,k) = (rh(i,k)-1.)*(precr1*rslope2(i,k) &
+precr2*work2(i,k)*coeres)/work1(i,k)
if(pres(i,k).lt.0.) then
pres(i,k) = max(pres(i,k),-qrs(i,k)/dtcld)
pres(i,k) = max(pres(i,k),satdt/2)
else
pres(i,k) = min(pres(i,k),satdt/2)
endif
endif
else
!
!===============================================================
!
! cold rain processes
!
! - follows the revised ice microphysics processes in HDC
! - the processes same as in RH83 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)
!
!===============================================================
!
supcol = t0c-t(i,k)
n0sfac(i,k) = max(min(exp(alpha*supcol),n0smax/n0s),1.)
ifsat = 0
!-------------------------------------------------------------
! Ni: ice crystal number concentraiton [HDC 5c]
!-------------------------------------------------------------
xni(i,k) = min(max(5.38e7 &
*exp(log((den(i,k)*max(qci(i,k),qmin)))*(0.75)),1.e3),1.e6)
eacrs = exp(0.07*(-supcol))
if(qrs(i,k).gt.qcrmin.and.qci(i,k).gt.qmin) then
xmi = den(i,k)*qci(i,k)/xni(i,k)
diameter = min(dicon * sqrt(xmi),dimax)
vt2i = 1.49e4*diameter**1.31
vt2s = pvts*rslopeb(i,k)*denfac(i,k)
!-------------------------------------------------------------
! praci: Accretion of cloud ice by rain [HL A15] [LFO 25]
! (T<T0: I->R)
!-------------------------------------------------------------
acrfac = 2.*rslope3(i,k)+2.*diameter*rslope2(i,k) &
+diameter**2*rslope(i,k)
pacr(i,k) = min(pi*qci(i,k)*eacrs*n0s*n0sfac(i,k) &
*abs(vt2s-vt2i)*acrfac/4.,qci(i,k)/dtcld)
endif
!-------------------------------------------------------------
! pidep: Deposition/Sublimation rate of ice [HDC 9]
! (T<T0: V->I or I->V)
!-------------------------------------------------------------
if(qci(i,k).gt.0.) then
xmi = den(i,k)*qci(i,k)/xni(i,k)
diameter = dicon * sqrt(xmi)
pisd(i,k) = 4.*diameter*xni(i,k)*(rh(i,k)-1.)/work1(i,k)
if(pisd(i,k).lt.0.) then
pisd(i,k) = max(pisd(i,k),satdt/2)
pisd(i,k) = max(pisd(i,k),-qci(i,k)/dtcld)
else
pisd(i,k) = min(pisd(i,k),satdt/2)
endif
if(abs(pisd(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).gt.0..and.ifsat.ne.1) then
coeres = rslope2(i,k)*sqrt(rslope(i,k)*rslopeb(i,k))
pres(i,k) = (rh(i,k)-1.)*n0sfac(i,k)*(precs1*rslope2(i,k) &
+precs2*work2(i,k)*coeres)/work1(i,k)
supice = satdt-pisd(i,k)
if(pres(i,k).lt.0.) then
pres(i,k) = max(pres(i,k),-qrs(i,k)/dtcld)
pres(i,k) = max(max(pres(i,k),satdt/2),supice)
else
pres(i,k) = min(min(pres(i,k),satdt/2),supice)
endif
if(abs(pisd(i,k)+pres(i,k)).ge.abs(satdt)) ifsat = 1
endif
!-------------------------------------------------------------
! pigen: generation(nucleation) of ice from vapor [HDC 7-8]
! (T<T0: V->I)
!-------------------------------------------------------------
if(supsat.gt.0.and.ifsat.ne.1) then
supice = satdt-pisd(i,k)-pres(i,k)
xni0 = 1.e3*exp(0.1*supcol)
roqi0 = 4.92e-11*exp(log(xni0)*(1.33))
pgen(i,k) = max(0.,(roqi0/den(i,k)-max(qci(i,k),0.))/dtcld)
pgen(i,k) = min(min(pgen(i,k),satdt),supice)
endif
!-------------------------------------------------------------
! psaut: conversion(aggregation) of ice to snow [HDC 12]
! (T<T0: I->S)
!-------------------------------------------------------------
if(qci(i,k).gt.0.) then
qimax = roqimax/den(i,k)
paut(i,k) = max(0.,(qci(i,k)-qimax)/dtcld)
endif
endif
enddo
enddo
!
!----------------------------------------------------------------
! check mass conservation of generation terms and feedback to the
! large scale
!
do k = kts, kte
do i = its, ite
qciik = max(qmin,qci(i,k))
delqci = (paut(i,k)+pacr(i,k)-pgen(i,k)-pisd(i,k))*dtcld
if(delqci.ge.qciik) then
facqci = qciik/delqci
paut(i,k) = paut(i,k)*facqci
pacr(i,k) = pacr(i,k)*facqci
pgen(i,k) = pgen(i,k)*facqci
pisd(i,k) = pisd(i,k)*facqci
endif
qik = max(qmin,q(i,k))
delq = (pres(i,k)+pgen(i,k)+pisd(i,k))*dtcld
if(delq.ge.qik) then
facq = qik/delq
pres(i,k) = pres(i,k)*facq
pgen(i,k) = pgen(i,k)*facq
pisd(i,k) = pisd(i,k)*facq
endif
work2(i,k) = -pres(i,k)-pgen(i,k)-pisd(i,k)
q(i,k) = q(i,k)+work2(i,k)*dtcld
qci(i,k) = max(qci(i,k)-(paut(i,k)+pacr(i,k)-pgen(i,k)-pisd(i,k)) &
*dtcld,0.)
qrs(i,k) = max(qrs(i,k)+(paut(i,k)+pacr(i,k)+pres(i,k))*dtcld,0.)
if(t(i,k).lt.t0c) then
t(i,k) = t(i,k)-xls*work2(i,k)/cpm(i,k)*dtcld
else
t(i,k) = t(i,k)-xl(i,k)*work2(i,k)/cpm(i,k)*dtcld
endif
enddo
enddo
!
cvap = cpv
hvap = xlv0
hsub = xls
ttp=t0c+0.01
dldt=cvap-cliq
xa=-dldt/rv
xb=xa+hvap/(rv*ttp)
dldti=cvap-cice
xai=-dldti/rv
xbi=xai+hsub/(rv*ttp)
do k = kts, kte
do i = its, ite
tr=ttp/t(i,k)
qs(i,k)=psat*(exp(log(tr)*(xa)))*exp(xb*(1.-tr))
qs(i,k) = min(qs(i,k),0.99*p(i,k))
qs(i,k) = ep2 * qs(i,k) / (p(i,k) - qs(i,k))
qs(i,k) = max(qs(i,k),qmin)
denfac(i,k) = sqrt(den0/den(i,k))
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) = conden(t(i,k),q(i,k),qs(i,k),xl(i,k),cpm(i,k))
work2(i,k) = qci(i,k)+work1(i,k)
pcon(i,k) = min(max(work1(i,k),0.),max(q(i,k),0.))/dtcld
if(qci(i,k).gt.0..and.work1(i,k).lt.0.and.t(i,k).gt.t0c) &
pcon(i,k) = max(work1(i,k),-qci(i,k))/dtcld
q(i,k) = q(i,k)-pcon(i,k)*dtcld
qci(i,k) = max(qci(i,k)+pcon(i,k)*dtcld,0.)
t(i,k) = t(i,k)+pcon(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).le.qmin) qci(i,k) = 0.0
if(qrs(i,k).le.qcrmin) qrs(i,k) = 0.0
enddo
enddo
!
enddo ! big loops
END SUBROUTINE wsm32D
! ...................................................................
REAL FUNCTION rgmma(x) 74
!-------------------------------------------------------------------
IMPLICIT NONE
!-------------------------------------------------------------------
! rgmma function: use infinite product form
REAL :: euler
PARAMETER (euler=0.577215664901532)
REAL :: x, y
INTEGER :: i
if(x.eq.1.)then
rgmma=0.
else
rgmma=x*exp(euler*x)
do i=1,10000
y=float(i)
rgmma=rgmma*(1.000+x/y)*exp(-x/y)
enddo
rgmma=1./rgmma
endif
END FUNCTION rgmma
!
!--------------------------------------------------------------------------
REAL FUNCTION fpvs(t,ice,rd,rv,cvap,cliq,cice,hvap,hsub,psat,t0c) 9
!--------------------------------------------------------------------------
IMPLICIT NONE
!--------------------------------------------------------------------------
REAL t,rd,rv,cvap,cliq,cice,hvap,hsub,psat,t0c,dldt,xa,xb,dldti, &
xai,xbi,ttp,tr
INTEGER ice
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
ttp=t0c+0.01
dldt=cvap-cliq
xa=-dldt/rv
xb=xa+hvap/(rv*ttp)
dldti=cvap-cice
xai=-dldti/rv
xbi=xai+hsub/(rv*ttp)
tr=ttp/t
if(t.lt.ttp.and.ice.eq.1) then
fpvs=psat*(tr**xai)*exp(xbi*(1.-tr))
else
fpvs=psat*(tr**xa)*exp(xb*(1.-tr))
endif
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
END FUNCTION fpvs
!-------------------------------------------------------------------
SUBROUTINE wsm3init(den0,denr,dens,cl,cpv,allowed_to_read) 1,16
!-------------------------------------------------------------------
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
!
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 wsm3init
!
subroutine slope_wsm3(qrs,den,denfac,t,rslope,rslopeb,rslope2,rslope3,vt,its,ite,kts,kte) 4
IMPLICIT NONE
INTEGER :: its,ite, jts,jte, kts,kte
REAL, DIMENSION( its:ite , kts:kte ) :: &
qrs, &
den, &
denfac, &
t, &
rslope, &
rslopeb, &
rslope2, &
rslope3, &
vt
REAL, PARAMETER :: t0c = 273.15
REAL, DIMENSION( its:ite , kts:kte ) :: &
n0sfac
REAL :: lamdar,lamdas,x, y, z, supcol, pvt
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
if(t(i,k).ge.t0c) then
pvt = pvtr
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) = exp(log(rslope(i,k))*(bvtr))
rslope2(i,k) = rslope(i,k)*rslope(i,k)
rslope3(i,k) = rslope2(i,k)*rslope(i,k)
endif
else
supcol = t0c-t(i,k)
n0sfac(i,k) = max(min(exp(alpha*supcol),n0smax/n0s),1.)
pvt = pvts
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) = exp(log(rslope(i,k))*(bvts))
rslope2(i,k) = rslope(i,k)*rslope(i,k)
rslope3(i,k) = rslope2(i,k)*rslope(i,k)
endif
endif
vt(i,k) = pvt*rslopeb(i,k)*denfac(i,k)
if(qrs(i,k).le.0.0) vt(i,k) = 0.0
enddo
enddo
END subroutine slope_wsm3
!-------------------------------------------------------------------
SUBROUTINE nislfv_rain_pcm(im,km,denl,denfacl,tkl,dzl,wwl,rql,precip,dt,id,iter),1
!-------------------------------------------------------------------
!
! for non-iteration semi-Lagrangain forward advection for cloud
! with mass conservation and positive definite advection
! 2nd order interpolation with monotonic piecewise linear method
! this routine is under assumption of decfl < 1 for semi_Lagrangian
!
! dzl depth of model layer in meter
! wwl terminal velocity at model layer m/s
! rql cloud density*mixing ration
! precip precipitation
! dt time step
! id kind of precip: 0 test case; 1 raindrop
! iter how many time to guess mean terminal velocity: 0 pure forward.
! 0 : use departure wind for advection
! 1 : use mean wind for advection
! > 1 : use mean wind after iter-1 iterations
!
! author: hann-ming henry juang <henry.juang@noaa.gov>
! implemented by song-you hong
!
implicit none
integer im,km,id
real dt
real dzl(im,km),wwl(im,km),rql(im,km),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 zsumt,qsumt,zsumb,qsumb
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
! pcm is 1st order, we should use 2nd order wi
! 2nd order interpolation to get wi
wi(1) = ww(1)
do k=2,km
wi(k) = (ww(k)*dz(k-1)+ww(k-1)*dz(k))/(dz(k-1)+dz(k))
enddo
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
call slope_wsm3(qr,den,denfac,tk,tmp,tmp1,tmp2,tmp3,wa,1,1,1,km)
if( n.eq.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
!
!
! 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
! compute q with piecewise constant method
if( kt-kb.eq.1 ) then
qn(k) = qa(kb)
else if( kt-kb.ge.2 ) then
zsumb = za(kb+1)-zi(k)
qsumb = qa(kb) * zsumb
zsumt = zi(k+1)-za(kt-1)
qsumt = qa(kt-1) * zsumt
qsum = 0.0
zsum = 0.0
if( kt-kb.ge.3 ) then
do m=kb+1,kt-2
qsum = qsum + qa(m) * dza(m)
zsum = zsum + dza(m)
enddo
endif
qn(k) = (qsumb+qsum+qsumt)/(zsumb+zsum+zsumt)
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_pcm
!-------------------------------------------------------------------
SUBROUTINE nislfv_rain_plm(im,km,denl,denfacl,tkl,dzl,wwl,rql,precip,dt,id,iter) 9,5
!-------------------------------------------------------------------
!
! for non-iteration semi-Lagrangain forward advection for cloud
! with mass conservation and positive definite advection
! 2nd order interpolation with monotonic piecewise linear method
! this routine is under assumption of decfl < 1 for semi_Lagrangian
!
! dzl depth of model layer in meter
! wwl terminal velocity at model layer m/s
! rql cloud density*mixing ration
! precip precipitation
! dt time step
! id kind of precip: 0 test case; 1 raindrop
! iter how many time to guess mean terminal velocity: 0 pure forward.
! 0 : use departure wind for advection
! 1 : use mean wind for advection
! > 1 : use mean wind after iter-1 iterations
!
! author: hann-ming henry juang <henry.juang@noaa.gov>
! implemented by song-you hong
!
implicit none
integer im,km,id
real dt
real dzl(im,km),wwl(im,km),rql(im,km),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
call slope_wsm3(qr,den,denfac,tk,tmp,tmp1,tmp2,tmp3,wa,1,1,1,km)
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_wsm3
#endif