#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. REAL, PARAMETER, PRIVATE :: n0r = 8.e6 REAL, PARAMETER, PRIVATE :: avtr = 841.9 REAL, PARAMETER, PRIVATE :: bvtr = 0.8 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 REAL, PARAMETER, PRIVATE :: bvts = .41 REAL, PARAMETER, PRIVATE :: n0smax = 1.e11 ! t=-90C unlimited REAL, PARAMETER, PRIVATE :: lamdarmax = 8.e4 REAL, PARAMETER, PRIVATE :: lamdasmax = 1.e5 REAL, PARAMETER, PRIVATE :: lamdagmax = 6.e4 REAL, PARAMETER, PRIVATE :: betai = .6 REAL, PARAMETER, PRIVATE :: xn0 = 1.e-2 REAL, PARAMETER, PRIVATE :: dicon = 11.9 REAL, PARAMETER, PRIVATE :: di0 = 12.9e-6 REAL, PARAMETER, PRIVATE :: dimax = 500.e-6 REAL, PARAMETER, PRIVATE :: n0s = 2.e6 ! temperature dependent n0s REAL, PARAMETER, PRIVATE :: alpha = .12 ! .122 exponen factor for n0s REAL, PARAMETER, PRIVATE :: pfrz1 = 100. REAL, PARAMETER, PRIVATE :: pfrz2 = 0.66 REAL, PARAMETER, PRIVATE :: qcrmin = 1.e-9 REAL, PARAMETER, PRIVATE :: t40c = 233.16 REAL, PARAMETER, PRIVATE :: eacrc = 1.0 REAL, SAVE :: & qc0, qck1,bvtr1,bvtr2,bvtr3,bvtr4,g1pbr,& g3pbr,g4pbr,g5pbro2,pvtr,eacrr,pacrr, & precr1,precr2,xm0,xmmax,roqimax,bvts1, & bvts2,bvts3,bvts4,g1pbs,g3pbs,g4pbs, & g5pbso2,pvts,pacrs,precs1,precs2,pidn0r,& pidn0s,xlv1,pacrc, & 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 !------------------------------------------------------------------- ! ! This code is a 5-class mixed ice microphyiscs scheme (WSM5) of the WRF ! 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 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 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) 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 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(ims,j),snowncv(ims,j) & ) DO K=kts,kte DO I=its,ite th(i,k,j)=t(i,k)/pii(i,k,j) qc(i,k,j) = qci(i,k,1) qi(i,k,j) = qci(i,k,2) qr(i,k,j) = qrs(i,k,1) qs(i,k,j) = qrs(i,k,2) ENDDO ENDDO ENDDO 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 !------------------------------------------------------------------- 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 ), OPTIONAL, & INTENT(INOUT) :: snow, & snowncv ! LOCAL VAR REAL, DIMENSION( its:ite , kts:kte , 2) :: & rh, qs, rslope, rslope2, rslope3, rslopeb, & falk, fall, work1 REAL, DIMENSION( its:ite , kts:kte ) :: & falkc, work1c, work2c, fallc REAL, DIMENSION( its:ite , kts:kte ) :: & praut, psaut, prevp, psdep, pracw, psaci, psacw, & pigen, pidep, pcond, xl, cpm, work2, psmlt, psevp, denfac, xni,& n0sfac ! variables for optimization REAL, DIMENSION( its:ite ) :: tvec1 INTEGER, DIMENSION( its:ite ) :: mstep, numdt REAL, DIMENSION(its:ite) :: rmstep REAL dtcldden, rdelz, rdtcld LOGICAL, DIMENSION( its:ite ) :: flgcld REAL :: pi, & cpmcal, xlcal, lamdar, lamdas, diffus, & viscos, xka, venfac, conden, diffac, & x, y, z, a, b, c, d, e, & qdt, holdrr, holdrs, supcol, 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 REAL :: temp REAL :: holdc, holdci INTEGER :: i, j, k, mstepmax, & iprt, latd, lond, loop, loops, ifsat, n ! Temporaries used for inlining fpvs function REAL :: dldti, xb, xai, tr, xbi, xa, hvap, cvap, hsub, dldt, ttp ! !================================================================= ! compute internal functions ! cpmcal(x) = cpd*(1.-max(x,qmin))+max(x,qmin)*cpv xlcal(x) = xlv0-xlv1*(x-t0c) !---------------------------------------------------------------- ! size distributions: (x=mixing ratio, y=air density): ! valid for mixing ratio > 1.e-9 kg/kg. ! ! Optimizatin : A**B => exp(log(A)*(B)) 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 ! !---------------------------------------------------------------- ! 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)) ! ! pi = 4. * atan(1.) ! !---------------------------------------------------------------- ! paddint 0 for negative values generated by dynamics ! do k = kts, kte do i = its, ite qci(i,k,1) = max(qci(i,k,1),0.0) qrs(i,k,1) = max(qrs(i,k,1),0.0) qci(i,k,2) = max(qci(i,k,2),0.0) qrs(i,k,2) = max(qrs(i,k,2),0.0) enddo enddo ! !---------------------------------------------------------------- ! latent heat for phase changes and heat capacity. neglect the ! changes during microphysical process calculation ! emanuel(1994) ! do k = kts, kte do i = its, ite cpm(i,k) = cpmcal(q(i,k)) xl(i,k) = xlcal(t(i,k)) enddo enddo ! !---------------------------------------------------------------- ! compute the minor time steps. ! loops = max(nint(delt/dtcldcr),1) dtcld = delt/loops if(delt.le.dtcldcr) dtcld = delt ! do loop = 1,loops ! !---------------------------------------------------------------- ! initialize the large scale variables ! do i = its, ite mstep(i) = 1 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) do k = kts, kte do i = its, ite tr=ttp/t(i,k) qs(i,k,1)=psat*exp(log(tr)*(xa))*exp(xb*(1.-tr)) qs(i,k,1) = ep2 * qs(i,k,1) / (p(i,k) - qs(i,k,1)) qs(i,k,1) = max(qs(i,k,1),qmin) rh(i,k,1) = max(q(i,k) / qs(i,k,1),qmin) tr=ttp/t(i,k) if(t(i,k).lt.ttp) then qs(i,k,2)=psat*exp(log(tr)*(xai))*exp(xbi*(1.-tr)) else qs(i,k,2)=psat*exp(log(tr)*(xa))*exp(xb*(1.-tr)) endif qs(i,k,2) = ep2 * qs(i,k,2) / (p(i,k) - qs(i,k,2)) qs(i,k,2) = max(qs(i,k,2),qmin) rh(i,k,2) = max(q(i,k) / qs(i,k,2),qmin) enddo enddo ! !---------------------------------------------------------------- ! initialize the variables for microphysical physics ! ! do k = kts, kte do i = its, ite prevp(i,k) = 0. psdep(i,k) = 0. 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 ! !---------------------------------------------------------------- ! compute the fallout term: ! first, vertical terminal velosity for minor loops ! do k = kts, kte do i = its, ite supcol = t0c-t(i,k) !--------------------------------------------------------------- ! n0s: Intercept parameter for snow [m-4] [HDC 6] !--------------------------------------------------------------- n0sfac(i,k) = max(min(exp(alpha*supcol),n0smax/n0s),1.) if(qrs(i,k,1).le.qcrmin)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 !------------------------------------------------------------- ! Ni: ice crystal number concentraiton [HDC 5c] !------------------------------------------------------------- ! xni(i,k) = min(max(5.38e7*(den(i,k) & ! *max(qci(i,k,2),qmin))**0.75,1.e3),1.e6) temp = (den(i,k)*max(qci(i,k,2),qmin)) temp = sqrt(sqrt(temp*temp*temp)) xni(i,k) = min(max(5.38e7*temp,1.e3),1.e6) enddo enddo ! mstepmax = 1 numdt = 1 do k = kte, kts, -1 do i = its, ite work1(i,k,1) = pvtr*rslopeb(i,k,1)*denfac(i,k)/delz(i,k) work1(i,k,2) = pvts*rslopeb(i,k,2)*denfac(i,k)/delz(i,k) numdt(i) = max(nint(max(work1(i,k,1),work1(i,k,2))*dtcld+.5),1) if(numdt(i).ge.mstep(i)) mstep(i) = numdt(i) enddo enddo do i = its, ite if(mstepmax.le.mstep(i)) mstepmax = mstep(i) rmstep(i) = 1./mstep(i) enddo ! do n = 1, mstepmax k = kte do i = its, ite if(n.le.mstep(i)) then ! falk(i,k,1) = den(i,k)*qrs(i,k,1)*work1(i,k,1)/mstep(i) ! falk(i,k,2) = den(i,k)*qrs(i,k,2)*work1(i,k,2)/mstep(i) falk(i,k,1) = den(i,k)*qrs(i,k,1)*work1(i,k,1)*rmstep(i) falk(i,k,2) = den(i,k)*qrs(i,k,2)*work1(i,k,2)*rmstep(i) fall(i,k,1) = fall(i,k,1)+falk(i,k,1) fall(i,k,2) = fall(i,k,2)+falk(i,k,2) ! qrs(i,k,1) = max(qrs(i,k,1)-falk(i,k,1)*dtcld/den(i,k),0.) ! qrs(i,k,2) = max(qrs(i,k,2)-falk(i,k,2)*dtcld/den(i,k),0.) dtcldden = dtcld/den(i,k) qrs(i,k,1) = max(qrs(i,k,1)-falk(i,k,1)*dtcldden,0.) qrs(i,k,2) = max(qrs(i,k,2)-falk(i,k,2)*dtcldden,0.) endif enddo do k = kte-1, kts, -1 do i = its, ite if(n.le.mstep(i)) then ! falk(i,k,1) = den(i,k)*qrs(i,k,1)*work1(i,k,1)/mstep(i) ! falk(i,k,2) = den(i,k)*qrs(i,k,2)*work1(i,k,2)/mstep(i) falk(i,k,1) = den(i,k)*qrs(i,k,1)*work1(i,k,1)*rmstep(i) falk(i,k,2) = den(i,k)*qrs(i,k,2)*work1(i,k,2)*rmstep(i) fall(i,k,1) = fall(i,k,1)+falk(i,k,1) fall(i,k,2) = fall(i,k,2)+falk(i,k,2) ! qrs(i,k,1) = max(qrs(i,k,1)-(falk(i,k,1)-falk(i,k+1,1) & ! *delz(i,k+1)/delz(i,k))*dtcld/den(i,k),0.) ! qrs(i,k,2) = max(qrs(i,k,2)-(falk(i,k,2)-falk(i,k+1,2) & ! *delz(i,k+1)/delz(i,k))*dtcld/den(i,k),0.) dtcldden = dtcld/den(i,k) rdelz = 1./delz(i,k) qrs(i,k,1) = max(qrs(i,k,1)-(falk(i,k,1)-falk(i,k+1,1) & *delz(i,k+1)*rdelz)*dtcldden,0.) qrs(i,k,2) = max(qrs(i,k,2)-(falk(i,k,2)-falk(i,k+1,2) & *delz(i,k+1)*rdelz)*dtcldden,0.) endif enddo enddo do k = kte, kts, -1 do i = its, ite if(n.le.mstep(i)) then if(t(i,k).gt.t0c.and.qrs(i,k,2).gt.0.) then !---------------------------------------------------------------- ! psmlt: melting of snow [HL A33] [RH83 A25] ! (T>T0: S->R) !---------------------------------------------------------------- xlf = xlf0 ! work2(i,k)= venfac(p(i,k),t(i,k),den(i,k)) work2(i,k)= (exp(log(((1.496e-6*((t(i,k))*sqrt(t(i,k))) & /((t(i,k))+120.)/(den(i,k)))/(8.794e-5 & *exp(log(t(i,k))*(1.81))/p(i,k)))) & *((.3333333)))/sqrt((1.496e-6*((t(i,k)) & *sqrt(t(i,k)))/((t(i,k))+120.)/(den(i,k)))) & *sqrt(sqrt(den0/(den(i,k))))) coeres = rslope2(i,k,2)*sqrt(rslope(i,k,2)*rslopeb(i,k,2)) ! psmlt(i,k) = xka(t(i,k),den(i,k))/xlf*(t0c-t(i,k))*pi/2. & ! *n0sfac(i,k)*(precs1*rslope2(i,k,2)+precs2 & ! *work2(i,k)*coeres) psmlt(i,k) = & (1.414e3*(1.496e-6 * ((t(i,k))*sqrt(t(i,k))) /((t(i,k))+120.)/(den(i,k)) )*(den(i,k)))& /xlf*(t0c-t(i,k))*pi/2. & *n0sfac(i,k)*(precs1*rslope2(i,k,2)+precs2 & *work2(i,k)*coeres) psmlt(i,k) = min(max(psmlt(i,k)*dtcld/mstep(i), & -qrs(i,k,2)/mstep(i)),0.) qrs(i,k,2) = qrs(i,k,2) + psmlt(i,k) qrs(i,k,1) = qrs(i,k,1) - psmlt(i,k) t(i,k) = t(i,k) + xlf/cpm(i,k)*psmlt(i,k) endif endif enddo enddo enddo !--------------------------------------------------------------- ! Vice [ms-1] : fallout of ice crystal [HDC 5a] !--------------------------------------------------------------- mstepmax = 1 mstep = 1 numdt = 1 do k = kte, kts, -1 do i = its, ite if(qci(i,k,2).le.0.) then work2c(i,k) = 0. else xmi = den(i,k)*qci(i,k,2)/xni(i,k) ! diameter = min(dicon * sqrt(xmi),dimax) diameter = max(min(dicon * sqrt(xmi),dimax), 1.e-25) work1c(i,k) = 1.49e4*exp(log(diameter)*(1.31)) work2c(i,k) = work1c(i,k)/delz(i,k) endif numdt(i) = max(nint(work2c(i,k)*dtcld+.5),1) if(numdt(i).ge.mstep(i)) mstep(i) = numdt(i) enddo enddo do i = its, ite if(mstepmax.le.mstep(i)) mstepmax = mstep(i) enddo ! do n = 1, mstepmax k = kte do i = its, ite if(n.le.mstep(i)) then falkc(i,k) = den(i,k)*qci(i,k,2)*work2c(i,k)/mstep(i) holdc = falkc(i,k) fallc(i,k) = fallc(i,k)+falkc(i,k) holdci = qci(i,k,2) qci(i,k,2) = max(qci(i,k,2)-falkc(i,k)*dtcld/den(i,k),0.) endif enddo do k = kte-1, kts, -1 do i = its, ite if(n.le.mstep(i)) then falkc(i,k) = den(i,k)*qci(i,k,2)*work2c(i,k)/mstep(i) holdc = falkc(i,k) fallc(i,k) = fallc(i,k)+falkc(i,k) holdci = qci(i,k,2) qci(i,k,2) = max(qci(i,k,2)-(falkc(i,k)-falkc(i,k+1) & *delz(i,k+1)/delz(i,k))*dtcld/den(i,k),0.) endif enddo enddo enddo ! ! !---------------------------------------------------------------- ! rain (unit is mm/sec;kgm-2s-1: /1000*delt ===> m)==> mm for wrf ! do i = its, ite fallsum = fall(i,1,1)+fall(i,1,2)+fallc(i,1) fallsum_qsi = fall(i,1,2)+fallc(i,1) rainncv(i) = 0. if(fallsum.gt.0.) then rainncv(i) = fallsum*delz(i,1)/denr*dtcld*1000. rain(i) = fallsum*delz(i,1)/denr*dtcld*1000. + rain(i) endif IF ( PRESENT (snowncv) .AND. PRESENT (snow)) THEN snowncv(i) = 0. if(fallsum_qsi.gt.0.) then snowncv(i) = fallsum_qsi*delz(i,kts)/denr*dtcld*1000. snow(i) = fallsum_qsi*delz(i,kts)/denr*dtcld*1000. + snow(i) endif ENDIF sr(i) = 0. if(fallsum.gt.0.)sr(i)=fallsum_qsi*delz(i,kts)/denr*dtcld*1000./(rainncv(i)+1.e-12) enddo ! !--------------------------------------------------------------- ! pimlt: instantaneous melting of cloud ice [HL A47] [RH83 A28] ! (T>T0: I->C) !--------------------------------------------------------------- do k = kts, kte do i = its, ite supcol = t0c-t(i,k) xlf = xls-xl(i,k) if(supcol.lt.0.) xlf = xlf0 if(supcol.lt.0.and.qci(i,k,2).gt.0.) then qci(i,k,1) = qci(i,k,1) + qci(i,k,2) 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 ! 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*supcol)-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] ! (TS) !--------------------------------------------------------------- if(supcol.gt.0..and.qrs(i,k,1).gt.0.) then ! 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*supcol)-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 ! !---------------------------------------------------------------- ! rsloper: reverse of the slope parameter of the rain(m) ! xka: thermal conductivity of air(jm-1s-1k-1) ! work1: the thermodynamic term in the denominator associated with ! heat conduction and vapor diffusion ! (ry88, y93, h85) ! work2: parameter associated with the ventilation effects(y93) ! do k = kts, kte do i = its, ite if(qrs(i,k,1).le.qcrmin)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)) rslope(i,k,1) = 1./(sqrt(sqrt(pidn0r/((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)) rslope(i,k,2) = 1./(sqrt(sqrt(pidn0s*(n0sfac(i,k))/((qrs(i,k,2))*(den(i,k)))))) rslopeb(i,k,2) = exp(log(rslope(i,k,2))*(bvts)) rslope2(i,k,2) = rslope(i,k,2)*rslope(i,k,2) rslope3(i,k,2) = rslope2(i,k,2)*rslope(i,k,2) endif enddo enddo ! do k = kts, kte do i = its, ite ! work1(i,k,1) = diffac(xl(i,k),p(i,k),t(i,k),den(i,k),qs(i,k,1)) work1(i,k,1) = & ((((den(i,k))*(xl(i,k))*(xl(i,k))) * ((t(i,k))+120.) * (den(i,k))) & / & ( 1.414e3 * (1.496e-6 * ((t(i,k))*sqrt(t(i,k)))) * (den(i,k)) * & (rv*(t(i,k))*(t(i,k))))) & + & p(i,k) / ( (qs(i,k,1)) * ( 8.794e-5 * exp(log(t(i,k))*(1.81)) ) ) ! work1(i,k,2) = diffac(xls,p(i,k),t(i,k),den(i,k),qs(i,k,2)) work1(i,k,2) = & ( & (((den(i,k))*(xls)*(xls))*((t(i,k))+120.)*(den(i,k))) & / & ( & 1.414e3 * (1.496e-6 * ((t(i,k))*sqrt(t(i,k)))) * (den(i,k)) * & (rv*(t(i,k))*(t(i,k))) & ) & + & p(i,k) & / & ( qs(i,k,2) * (8.794e-5 * exp(log(t(i,k))*(1.81)))) & ) ! work2(i,k) = venfac(p(i,k),t(i,k),den(i,k)) work2(i,k) = & ( & exp(.3333333*log( & ((1.496e-6 * ((t(i,k))*sqrt(t(i,k))))*p(i,k)) & / & (((t(i,k))+120.)*den(i,k)*(8.794e-5 * exp(log(t(i,k))*(1.81)))) & )) & * & sqrt(sqrt(den0/(den(i,k)))) & ) & / & sqrt( & (1.496e-6 * ((t(i,k))*sqrt(t(i,k)))) & / & ( & ((t(i,k))+120.) * den(i,k) & ) & ) ENDDO ENDDO ! !=============================================================== ! ! warm rain processes ! ! - follows the processes in RH83 and LFO except for autoconcersion ! !=============================================================== ! do k = kts, kte do i = its, ite supsat = max(q(i,k),qmin)-qs(i,k,1) satdt = supsat/dtcld !--------------------------------------------------------------- ! praut: auto conversion rate from cloud to rain [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) 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] ! (TS) !------------------------------------------------------------- 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 !------------------------------------------------------------- ! psacw: Accretion of cloud water by snow [HL A7] [LFO 24] ! (TS, 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 !------------------------------------------------------------- ! pidep: Deposition/Sublimation rate of ice [HDC 9] ! (TI 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 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] ! (TI) !------------------------------------------------------------- if(supcol.gt.0) then 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] ! (TS) !------------------------------------------------------------- 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 ! 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 ! ! 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) qs(i,k,1)=psat*exp(log(tr)*(xa))*exp(xb*(1.-tr)) qs(i,k,1) = ep2 * qs(i,k,1) / (p(i,k) - qs(i,k,1)) qs(i,k,1) = max(qs(i,k,1),qmin) tr=ttp/t(i,k) if(t(i,k).lt.ttp) then qs(i,k,2)=psat*exp(log(tr)*(xai))*exp(xbi*(1.-tr)) else qs(i,k,2)=psat*exp(log(tr)*(xa))*exp(xb*(1.-tr)) endif qs(i,k,2) = ep2 * qs(i,k,2) / (p(i,k) - qs(i,k,2)) qs(i,k,2) = max(qs(i,k,2),qmin) 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 REAL :: pi ! pi = 4.*atan(1.) xlv1 = cl-cpv ! qc0 = 4./3.*pi*denr*r0**3*xncr/den0 ! 0.419e-3 -- .61e-3 qck1 = .104*9.8*peaut/(xncr*denr)**(1./3.)/xmyu*den0**(4./3.) ! 7.03 ! 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 xm0 = (di0/dicon)**2 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 END MODULE module_mp_wsm5