#ifdef _ACCEL # include "module_mp_wsm5_accel.F" #else #if ( RWORDSIZE == 4 ) # define VREC vsrec # define VSQRT vssqrt #else # define VREC vrec # define VSQRT vsqrt #endif !Including inline expansion statistical function MODULE module_mp_wsm5 ! ! REAL, PARAMETER, PRIVATE :: dtcldcr = 120. ! maximum time step for minor loops REAL, PARAMETER, PRIVATE :: n0r = 8.e6 ! intercept parameter rain REAL, PARAMETER, PRIVATE :: avtr = 841.9 ! a constant for terminal velocity of rain REAL, PARAMETER, PRIVATE :: bvtr = 0.8 ! a constant for terminal velocity of rain REAL, PARAMETER, PRIVATE :: r0 = .8e-5 ! 8 microm in contrast to 10 micro m REAL, PARAMETER, PRIVATE :: peaut = .55 ! collection efficiency REAL, PARAMETER, PRIVATE :: xncr = 3.e8 ! maritime cloud in contrast to 3.e8 in tc80 REAL, PARAMETER, PRIVATE :: xmyu = 1.718e-5 ! the dynamic viscosity kgm-1s-1 REAL, PARAMETER, PRIVATE :: avts = 11.72 ! a constant for terminal velocity of snow REAL, PARAMETER, PRIVATE :: bvts = .41 ! a constant for terminal velocity of snow REAL, PARAMETER, PRIVATE :: n0smax = 1.e11 ! maximum n0s (t=-90C unlimited) REAL, PARAMETER, PRIVATE :: lamdarmax = 8.e4 ! limited maximum value for slope parameter of rain REAL, PARAMETER, PRIVATE :: lamdasmax = 1.e5 ! limited maximum value for slope parameter of snow REAL, PARAMETER, PRIVATE :: lamdagmax = 6.e4 ! limited maximum value for slope parameter of graupel REAL, PARAMETER, PRIVATE :: dicon = 11.9 ! constant for the cloud-ice diamter REAL, PARAMETER, PRIVATE :: dimax = 500.e-6 ! limited maximum value for the cloud-ice diamter REAL, PARAMETER, PRIVATE :: n0s = 2.e6 ! temperature dependent intercept parameter snow REAL, PARAMETER, PRIVATE :: alpha = .12 ! .122 exponen factor for n0s REAL, PARAMETER, PRIVATE :: pfrz1 = 100. ! constant in Biggs freezing REAL, PARAMETER, PRIVATE :: pfrz2 = 0.66 ! constant in Biggs freezing REAL, PARAMETER, PRIVATE :: qcrmin = 1.e-9 ! minimun values for qr, qs, and qg REAL, PARAMETER, PRIVATE :: eacrc = 1.0 ! Snow/cloud-water collection efficiency REAL, SAVE :: & qc0, qck1,bvtr1,bvtr2,bvtr3,bvtr4,g1pbr, & g3pbr,g4pbr,g5pbro2,pvtr,eacrr,pacrr, & precr1,precr2,xmmax,roqimax,bvts1, & bvts2,bvts3,bvts4,g1pbs,g3pbs,g4pbs, & g5pbso2,pvts,pacrs,precs1,precs2,pidn0r, & pidn0s,xlv1,pacrc,pi, & rslopermax,rslopesmax,rslopegmax, & rsloperbmax,rslopesbmax,rslopegbmax, & rsloper2max,rslopes2max,rslopeg2max, & rsloper3max,rslopes3max,rslopeg3max ! ! Specifies code-inlining of fpvs function in WSM52D below. JM 20040507 ! CONTAINS !=================================================================== ! SUBROUTINE wsm5(th, q, qc, qr, qi, qs & ,den, pii, p, delz & ,delt,g, cpd, cpv, rd, rv, t0c & ,ep1, ep2, qmin & ,XLS, XLV0, XLF0, den0, denr & ,cliq,cice,psat & ,rain, rainncv & ,snow, snowncv & ,sr & ,ids,ide, jds,jde, kds,kde & ,ims,ime, jms,jme, kms,kme & ,its,ite, jts,jte, kts,kte & ) !------------------------------------------------------------------- IMPLICIT NONE !------------------------------------------------------------------- ! INTEGER, INTENT(IN ) :: ids,ide, jds,jde, kds,kde , & ims,ime, jms,jme, kms,kme , & its,ite, jts,jte, kts,kte REAL, DIMENSION( ims:ime , kms:kme , jms:jme ), & INTENT(INOUT) :: & th, & q, & qc, & qi, & qr, & qs REAL, DIMENSION( ims:ime , kms:kme , jms:jme ), & INTENT(IN ) :: & den, & pii, & p, & delz REAL, INTENT(IN ) :: delt, & g, & rd, & rv, & t0c, & den0, & cpd, & cpv, & ep1, & ep2, & qmin, & XLS, & XLV0, & XLF0, & cliq, & cice, & psat, & denr REAL, DIMENSION( ims:ime , jms:jme ), & INTENT(INOUT) :: rain, & rainncv, & sr REAL, DIMENSION( ims:ime , jms:jme ), OPTIONAL, & INTENT(INOUT) :: snow, & snowncv ! LOCAL VAR REAL, DIMENSION( its:ite , kts:kte ) :: t REAL, DIMENSION( its:ite , kts:kte, 2 ) :: qci, qrs CHARACTER*256 :: emess INTEGER :: mkx_test INTEGER :: i,j,k !------------------------------------------------------------------- #ifndef RUN_ON_GPU DO j=jts,jte DO k=kts,kte DO i=its,ite t(i,k)=th(i,k,j)*pii(i,k,j) qci(i,k,1) = qc(i,k,j) qci(i,k,2) = qi(i,k,j) qrs(i,k,1) = qr(i,k,j) qrs(i,k,2) = qs(i,k,j) ENDDO ENDDO ! Sending array starting locations of optional variables may cause ! troubles, so we explicitly change the call. CALL wsm52D(t, q(ims,kms,j), qci, qrs & ,den(ims,kms,j) & ,p(ims,kms,j), delz(ims,kms,j) & ,delt,g, cpd, cpv, rd, rv, t0c & ,ep1, ep2, qmin & ,XLS, XLV0, XLF0, den0, denr & ,cliq,cice,psat & ,j & ,rain(ims,j),rainncv(ims,j) & ,sr(ims,j) & ,ids,ide, jds,jde, kds,kde & ,ims,ime, jms,jme, kms,kme & ,its,ite, jts,jte, kts,kte & ,snow,snowncv & ) DO K=kts,kte DO I=its,ite th(i,k,j)=t(i,k)/pii(i,k,j) qc(i,k,j) = qci(i,k,1) qi(i,k,j) = qci(i,k,2) qr(i,k,j) = qrs(i,k,1) qs(i,k,j) = qrs(i,k,2) ENDDO ENDDO ENDDO #else CALL get_wsm5_gpu_levels ( mkx_test ) IF ( mkx_test .LT. kte ) THEN WRITE(emess,*)'Number of levels compiled for GPU WSM5 too small. ', & mkx_test,' < ',kte CALL wrf_error_fatal(emess) ENDIF CALL wsm5_host ( & th(its:ite,kts:kte,jts:jte), pii(its:ite,kts:kte,jts:jte) & ,q(its:ite,kts:kte,jts:jte), qc(its:ite,kts:kte,jts:jte) & ,qi(its:ite,kts:kte,jts:jte), qr(its:ite,kts:kte,jts:jte) & ,qs(its:ite,kts:kte,jts:jte), den(its:ite,kts:kte,jts:jte) & ,p(its:ite,kts:kte,jts:jte), delz(its:ite,kts:kte,jts:jte) & ,delt & ,rain(its:ite,jts:jte),rainncv(its:ite,jts:jte) & ,snow(its:ite,jts:jte),snowncv(its:ite,jts:jte) & ,sr(its:ite,jts:jte) & ,its, ite, jts, jte, kts, kte & ,its, ite, jts, jte, kts, kte & ,its, ite, jts, jte, kts, kte & ) #endif END SUBROUTINE wsm5 !=================================================================== ! SUBROUTINE wsm52D(t, q & ,qci, qrs, den, p, delz & ,delt,g, cpd, cpv, rd, rv, t0c & ,ep1, ep2, qmin & ,XLS, XLV0, XLF0, den0, denr & ,cliq,cice,psat & ,lat & ,rain,rainncv & ,sr & ,ids,ide, jds,jde, kds,kde & ,ims,ime, jms,jme, kms,kme & ,its,ite, jts,jte, kts,kte & ,snow,snowncv & ) !------------------------------------------------------------------- IMPLICIT NONE !------------------------------------------------------------------- ! ! This code is a 5-class mixed ice microphyiscs scheme (WSM5) of the ! Single-Moment MicroPhyiscs (WSMMP). The WSMMP assumes that ice nuclei ! number concentration is a function of temperature, and seperate assumption ! is developed, in which ice crystal number concentration is a function ! of ice amount. A theoretical background of the ice-microphysics and related ! processes in the WSMMPs are described in Hong et al. (2004). ! Production terms in the WSM6 scheme are described in Hong and Lim (2006). ! All units are in m.k.s. and source/sink terms in kgkg-1s-1. ! ! WSM5 cloud scheme ! ! Coded by Song-You Hong (Yonsei Univ.) ! Jimy Dudhia (NCAR) and Shu-Hua Chen (UC Davis) ! Summer 2002 ! ! Implemented by Song-You Hong (Yonsei Univ.) and Jimy Dudhia (NCAR) ! Summer 2003 ! ! Reference) Hong, Dudhia, Chen (HDC, 2004) Mon. Wea. Rev. ! Rutledge, Hobbs (RH83, 1983) J. Atmos. Sci. ! Hong and Lim (HL, 2006) J. Korean Meteor. Soc. ! INTEGER, INTENT(IN ) :: ids,ide, jds,jde, kds,kde , & ims,ime, jms,jme, kms,kme , & its,ite, jts,jte, kts,kte, & lat REAL, DIMENSION( its:ite , kts:kte ), & INTENT(INOUT) :: & t REAL, DIMENSION( its:ite , kts:kte, 2 ), & INTENT(INOUT) :: & qci, & qrs REAL, DIMENSION( ims:ime , kms:kme ), & INTENT(INOUT) :: & q REAL, DIMENSION( ims:ime , kms:kme ), & INTENT(IN ) :: & den, & p, & delz REAL, INTENT(IN ) :: delt, & g, & cpd, & cpv, & t0c, & den0, & rd, & rv, & ep1, & ep2, & qmin, & XLS, & XLV0, & XLF0, & cliq, & cice, & psat, & denr REAL, DIMENSION( ims:ime ), & INTENT(INOUT) :: rain, & rainncv, & sr REAL, DIMENSION( ims:ime, jms:jme ), OPTIONAL, & INTENT(INOUT) :: snow, & snowncv ! LOCAL VAR REAL, DIMENSION( its:ite , kts:kte , 2) :: & rh, & qs, & rslope, & rslope2, & rslope3, & rslopeb, & qrs_tmp, & falk, & fall, & work1 REAL, DIMENSION( its:ite , kts:kte ) :: & falkc, & fallc, & xl, & cpm, & denfac, & xni, & denqrs1, & denqrs2, & denqci, & n0sfac, & work2, & workr, & works, & work1c, & work2c REAL, DIMENSION( its:ite , kts:kte ) :: & den_tmp, & delz_tmp REAL, DIMENSION( its:ite ) :: & delqrs1, & delqrs2, & delqi REAL, DIMENSION( its:ite , kts:kte ) :: & pigen, & pidep, & psdep, & praut, & psaut, & prevp, & psevp, & pracw, & psacw, & psaci, & pcond, & psmlt INTEGER, DIMENSION( its:ite ) :: & mstep, & numdt REAL, DIMENSION(its:ite) :: tstepsnow REAL, DIMENSION(its:ite) :: rmstep REAL dtcldden, rdelz, rdtcld LOGICAL, DIMENSION( its:ite ) :: flgcld #define WSM_NO_CONDITIONAL_IN_VECTOR #ifdef WSM_NO_CONDITIONAL_IN_VECTOR REAL, DIMENSION(its:ite) :: xal, xbl #endif REAL :: & cpmcal, xlcal, diffus, & viscos, xka, venfac, conden, diffac, & x, y, z, a, b, c, d, e, & qdt, holdrr, holdrs, supcol, supcolt, pvt, & coeres, supsat, dtcld, xmi, eacrs, satdt, & vt2i,vt2s,acrfac, & qimax, diameter, xni0, roqi0, & fallsum, fallsum_qsi, xlwork2, factor, source, & value, xlf, pfrzdtc, pfrzdtr, supice, holdc, holdci ! variables for optimization REAL, DIMENSION( its:ite ) :: tvec1 REAL :: temp INTEGER :: i, j, k, mstepmax, & iprt, latd, lond, loop, loops, ifsat, n, idim, kdim ! Temporaries used for inlining fpvs function REAL :: dldti, xb, xai, tr, xbi, xa, hvap, cvap, hsub, dldt, ttp REAL :: logtr ! !================================================================= ! compute internal functions ! cpmcal(x) = cpd*(1.-max(x,qmin))+max(x,qmin)*cpv xlcal(x) = xlv0-xlv1*(x-t0c) !---------------------------------------------------------------- ! diffus: diffusion coefficient of the water vapor ! viscos: kinematic viscosity(m2s-1) ! diffus(x,y) = 8.794e-5 * exp(log(x)*(1.81)) / y ! 8.794e-5*x**1.81/y ! viscos(x,y) = 1.496e-6 * (x*sqrt(x)) /(x+120.)/y ! 1.496e-6*x**1.5/(x+120.)/y ! xka(x,y) = 1.414e3*viscos(x,y)*y ! diffac(a,b,c,d,e) = d*a*a/(xka(c,d)*rv*c*c)+1./(e*diffus(c,b)) ! venfac(a,b,c) = exp(log((viscos(b,c)/diffus(b,a)))*((.3333333))) & ! /sqrt(viscos(b,c))*sqrt(sqrt(den0/c)) ! conden(a,b,c,d,e) = (max(b,qmin)-c)/(1.+d*d/(rv*e)*c/(a*a)) ! !---------------------------------------------------------------- idim = ite-its+1 kdim = kte-kts+1 ! !---------------------------------------------------------------- ! paddint 0 for negative values generated by dynamics ! do k = kts, kte do i = its, ite qci(i,k,1) = max(qci(i,k,1),0.0) qrs(i,k,1) = max(qrs(i,k,1),0.0) qci(i,k,2) = max(qci(i,k,2),0.0) qrs(i,k,2) = max(qrs(i,k,2),0.0) enddo enddo ! !---------------------------------------------------------------- ! latent heat for phase changes and heat capacity. neglect the ! changes during microphysical process calculation ! emanuel(1994) ! do k = kts, kte do i = its, ite cpm(i,k) = cpmcal(q(i,k)) xl(i,k) = xlcal(t(i,k)) enddo enddo do k = kts, kte do i = its, ite delz_tmp(i,k) = delz(i,k) den_tmp(i,k) = den(i,k) enddo enddo ! !---------------------------------------------------------------- ! initialize the surface rain, snow ! do i = its, ite rainncv(i) = 0. if(PRESENT (snowncv) .AND. PRESENT (snow)) snowncv(i,lat) = 0. sr(i) = 0. ! new local array to catch step snow tstepsnow(i) = 0. enddo ! !---------------------------------------------------------------- ! compute the minor time steps. ! loops = max(nint(delt/dtcldcr),1) dtcld = delt/loops if(delt.le.dtcldcr) dtcld = delt ! do loop = 1,loops ! !---------------------------------------------------------------- ! initialize the large scale variables ! do i = its, ite mstep(i) = 1 flgcld(i) = .true. enddo ! ! do k = kts, kte ! do i = its, ite ! denfac(i,k) = sqrt(den0/den(i,k)) ! enddo ! enddo do k = kts, kte CALL VREC( tvec1(its), den(its,k), ite-its+1) do i = its, ite tvec1(i) = tvec1(i)*den0 enddo CALL VSQRT( denfac(its,k), tvec1(its), ite-its+1) enddo ! ! Inline expansion for fpvs ! qs(i,k,1) = fpvs(t(i,k),0,rd,rv,cpv,cliq,cice,xlv0,xls,psat,t0c) ! qs(i,k,2) = fpvs(t(i,k),1,rd,rv,cpv,cliq,cice,xlv0,xls,psat,t0c) hsub = xls hvap = xlv0 cvap = cpv ttp=t0c+0.01 dldt=cvap-cliq xa=-dldt/rv xb=xa+hvap/(rv*ttp) dldti=cvap-cice xai=-dldti/rv xbi=xai+hsub/(rv*ttp) ! this is for compilers where the conditional inhibits vectorization #ifdef WSM_NO_CONDITIONAL_IN_VECTOR do k = kts, kte do i = its, ite if(t(i,k).lt.ttp) then xal(i) = xai xbl(i) = xbi else xal(i) = xa xbl(i) = xb endif enddo do i = its, ite tr=ttp/t(i,k) logtr=log(tr) qs(i,k,1)=psat*exp(logtr*(xa)+xb*(1.-tr)) qs(i,k,1) = min(qs(i,k,1),0.99*p(i,k)) qs(i,k,1) = ep2 * qs(i,k,1) / (p(i,k) - qs(i,k,1)) qs(i,k,1) = max(qs(i,k,1),qmin) rh(i,k,1) = max(q(i,k) / qs(i,k,1),qmin) qs(i,k,2)=psat*exp(logtr*(xal(i))+xbl(i)*(1.-tr)) qs(i,k,2) = min(qs(i,k,2),0.99*p(i,k)) qs(i,k,2) = ep2 * qs(i,k,2) / (p(i,k) - qs(i,k,2)) qs(i,k,2) = max(qs(i,k,2),qmin) rh(i,k,2) = max(q(i,k) / qs(i,k,2),qmin) #else do k = kts, kte do i = its, ite tr=ttp/t(i,k) logtr=log(tr) qs(i,k,1)=psat*exp(logtr*(xa)+xb*(1.-tr)) qs(i,k,1) = min(qs(i,k,1),0.99*p(i,k)) qs(i,k,1) = ep2 * qs(i,k,1) / (p(i,k) - qs(i,k,1)) qs(i,k,1) = max(qs(i,k,1),qmin) rh(i,k,1) = max(q(i,k) / qs(i,k,1),qmin) if(t(i,k).lt.ttp) then qs(i,k,2)=psat*exp(logtr*(xai)+xbi*(1.-tr)) else qs(i,k,2)=psat*exp(logtr*(xa)+xb*(1.-tr)) endif qs(i,k,2) = min(qs(i,k,2),0.99*p(i,k)) qs(i,k,2) = ep2 * qs(i,k,2) / (p(i,k) - qs(i,k,2)) qs(i,k,2) = max(qs(i,k,2),qmin) rh(i,k,2) = max(q(i,k) / qs(i,k,2),qmin) enddo enddo #endif enddo enddo ! !---------------------------------------------------------------- ! initialize the variables for microphysical physics ! ! do k = kts, kte do i = its, ite prevp(i,k) = 0. psdep(i,k) = 0. praut(i,k) = 0. psaut(i,k) = 0. pracw(i,k) = 0. psaci(i,k) = 0. psacw(i,k) = 0. pigen(i,k) = 0. pidep(i,k) = 0. pcond(i,k) = 0. psmlt(i,k) = 0. psevp(i,k) = 0. falk(i,k,1) = 0. falk(i,k,2) = 0. fall(i,k,1) = 0. fall(i,k,2) = 0. fallc(i,k) = 0. falkc(i,k) = 0. xni(i,k) = 1.e3 enddo enddo !------------------------------------------------------------- ! Ni: ice crystal number concentraiton [HDC 5c] !------------------------------------------------------------- do k = kts, kte do i = its, ite temp = (den(i,k)*max(qci(i,k,2),qmin)) temp = sqrt(sqrt(temp*temp*temp)) xni(i,k) = min(max(5.38e7*temp,1.e3),1.e6) enddo enddo ! !---------------------------------------------------------------- ! compute the fallout term: ! first, vertical terminal velosity for minor loops !---------------------------------------------------------------- do k = kts, kte do i = its, ite qrs_tmp(i,k,1) = qrs(i,k,1) qrs_tmp(i,k,2) = qrs(i,k,2) enddo enddo call slope_wsm5(qrs_tmp,den_tmp,denfac,t,rslope,rslopeb,rslope2,rslope3, & work1,its,ite,kts,kte) ! do k = kte, kts, -1 do i = its, ite workr(i,k) = work1(i,k,1) works(i,k) = work1(i,k,2) denqrs1(i,k) = den(i,k)*qrs(i,k,1) denqrs2(i,k) = den(i,k)*qrs(i,k,2) if(qrs(i,k,1).le.0.0) workr(i,k) = 0.0 if(qrs(i,k,2).le.0.0) works(i,k) = 0.0 enddo enddo call nislfv_rain_plm(idim,kdim,den_tmp,denfac,t,delz_tmp,workr,denqrs1, & delqrs1,dtcld,1,1) call nislfv_rain_plm(idim,kdim,den_tmp,denfac,t,delz_tmp,works,denqrs2, & delqrs2,dtcld,2,1) do k = kts, kte do i = its, ite qrs(i,k,1) = max(denqrs1(i,k)/den(i,k),0.) qrs(i,k,2) = max(denqrs2(i,k)/den(i,k),0.) fall(i,k,1) = denqrs1(i,k)*workr(i,k)/delz(i,k) fall(i,k,2) = denqrs2(i,k)*works(i,k)/delz(i,k) enddo enddo do i = its, ite fall(i,1,1) = delqrs1(i)/delz(i,1)/dtcld fall(i,1,2) = delqrs2(i)/delz(i,1)/dtcld enddo do k = kts, kte do i = its, ite qrs_tmp(i,k,1) = qrs(i,k,1) qrs_tmp(i,k,2) = qrs(i,k,2) enddo enddo call slope_wsm5(qrs_tmp,den_tmp,denfac,t,rslope,rslopeb,rslope2,rslope3, & work1,its,ite,kts,kte) do k = kte, kts, -1 do i = its, ite supcol = t0c-t(i,k) n0sfac(i,k) = max(min(exp(alpha*supcol),n0smax/n0s),1.) if(t(i,k).gt.t0c.and.qrs(i,k,2).gt.0.) then !---------------------------------------------------------------- ! psmlt: melting of snow [HL A33] [RH83 A25] ! (T>T0: S->R) !---------------------------------------------------------------- xlf = xlf0 ! work2(i,k)= venfac(p(i,k),t(i,k),den(i,k)) work2(i,k)= (exp(log(((1.496e-6*((t(i,k))*sqrt(t(i,k))) & /((t(i,k))+120.)/(den(i,k)))/(8.794e-5 & *exp(log(t(i,k))*(1.81))/p(i,k)))) & *((.3333333)))/sqrt((1.496e-6*((t(i,k)) & *sqrt(t(i,k)))/((t(i,k))+120.)/(den(i,k)))) & *sqrt(sqrt(den0/(den(i,k))))) coeres = rslope2(i,k,2)*sqrt(rslope(i,k,2)*rslopeb(i,k,2)) psmlt(i,k) = (1.414e3*(1.496e-6*((t(i,k))*sqrt(t(i,k))) & /((t(i,k))+120.)/(den(i,k)) )*(den(i,k))) & /xlf*(t0c-t(i,k))*pi/2. & *n0sfac(i,k)*(precs1*rslope2(i,k,2)+precs2 & *work2(i,k)*coeres) psmlt(i,k) = min(max(psmlt(i,k)*dtcld/mstep(i), & -qrs(i,k,2)/mstep(i)),0.) qrs(i,k,2) = qrs(i,k,2) + psmlt(i,k) qrs(i,k,1) = qrs(i,k,1) - psmlt(i,k) t(i,k) = t(i,k) + xlf/cpm(i,k)*psmlt(i,k) endif enddo enddo !--------------------------------------------------------------- ! Vice [ms-1] : fallout of ice crystal [HDC 5a] !--------------------------------------------------------------- do k = kte, kts, -1 do i = its, ite if(qci(i,k,2).le.0.) then work1c(i,k) = 0. else xmi = den(i,k)*qci(i,k,2)/xni(i,k) diameter = max(min(dicon * sqrt(xmi),dimax), 1.e-25) work1c(i,k) = 1.49e4*exp(log(diameter)*(1.31)) endif enddo enddo ! ! forward semi-laglangian scheme (JH), PCM (piecewise constant), (linear) ! do k = kte, kts, -1 do i = its, ite denqci(i,k) = den(i,k)*qci(i,k,2) enddo enddo call nislfv_rain_plm(idim,kdim,den_tmp,denfac,t,delz_tmp,work1c,denqci, & delqi,dtcld,1,0) do k = kts, kte do i = its, ite qci(i,k,2) = max(denqci(i,k)/den(i,k),0.) enddo enddo do i = its, ite fallc(i,1) = delqi(i)/delz(i,1)/dtcld enddo ! !---------------------------------------------------------------- ! rain (unit is mm/sec;kgm-2s-1: /1000*delt ===> m)==> mm for wrf ! do i = its, ite fallsum = fall(i,1,1)+fall(i,1,2)+fallc(i,1) fallsum_qsi = fall(i,1,2)+fallc(i,1) if(fallsum.gt.0.) then rainncv(i) = fallsum*delz(i,1)/denr*dtcld*1000. + rainncv(i) rain(i) = fallsum*delz(i,1)/denr*dtcld*1000. + rain(i) endif if(fallsum_qsi.gt.0.) then tstepsnow(i) = fallsum_qsi*delz(i,kts)/denr*dtcld*1000. & +tstepsnow(i) IF ( PRESENT (snowncv) .AND. PRESENT (snow)) THEN snowncv(i,lat) = fallsum_qsi*delz(i,kts)/denr*dtcld*1000. & +snowncv(i,lat) snow(i,lat) = fallsum_qsi*delz(i,kts)/denr*dtcld*1000. + snow(i,lat) ENDIF endif ! if(fallsum.gt.0.)sr(i)=snowncv(i,lat)/(rainncv(i)+1.e-12) if(fallsum.gt.0.)sr(i)=tstepsnow(i)/(rainncv(i)+1.e-12) enddo ! !--------------------------------------------------------------- ! pimlt: instantaneous melting of cloud ice [HL A47] [RH83 A28] ! (T>T0: I->C) !--------------------------------------------------------------- do k = kts, kte do i = its, ite supcol = t0c-t(i,k) xlf = xls-xl(i,k) if(supcol.lt.0.) xlf = xlf0 if(supcol.lt.0.and.qci(i,k,2).gt.0.) then qci(i,k,1) = qci(i,k,1) + qci(i,k,2) t(i,k) = t(i,k) - xlf/cpm(i,k)*qci(i,k,2) qci(i,k,2) = 0. endif !--------------------------------------------------------------- ! pihmf: homogeneous freezing of cloud water below -40c [HL A45] ! (T<-40C: C->I) !--------------------------------------------------------------- if(supcol.gt.40..and.qci(i,k,1).gt.0.) then qci(i,k,2) = qci(i,k,2) + qci(i,k,1) t(i,k) = t(i,k) + xlf/cpm(i,k)*qci(i,k,1) qci(i,k,1) = 0. endif !--------------------------------------------------------------- ! pihtf: heterogeneous freezing of cloud water [HL A44] ! (T0>T>-40C: C->I) !--------------------------------------------------------------- if(supcol.gt.0..and.qci(i,k,1).gt.0.) then supcolt=min(supcol,50.) ! pfrzdtc = min(pfrz1*(exp(pfrz2*supcol)-1.) & ! *den(i,k)/denr/xncr*qci(i,k,1)**2*dtcld,qci(i,k,1)) pfrzdtc = min(pfrz1*(exp(pfrz2*supcolt)-1.) & *den(i,k)/denr/xncr*qci(i,k,1)*qci(i,k,1)*dtcld,qci(i,k,1)) qci(i,k,2) = qci(i,k,2) + pfrzdtc t(i,k) = t(i,k) + xlf/cpm(i,k)*pfrzdtc qci(i,k,1) = qci(i,k,1)-pfrzdtc endif !--------------------------------------------------------------- ! psfrz: freezing of rain water [HL A20] [LFO 45] ! (TS) !--------------------------------------------------------------- if(supcol.gt.0..and.qrs(i,k,1).gt.0.) then supcolt=min(supcol,50.) ! pfrzdtr = min(20.*pi**2*pfrz1*n0r*denr/den(i,k) & ! *(exp(pfrz2*supcol)-1.)*rslope(i,k,1)**7*dtcld, & ! qrs(i,k,1)) temp = rslope(i,k,1) temp = temp*temp*temp*temp*temp*temp*temp pfrzdtr = min(20.*(pi*pi)*pfrz1*n0r*denr/den(i,k) & *(exp(pfrz2*supcolt)-1.)*temp*dtcld, & qrs(i,k,1)) qrs(i,k,2) = qrs(i,k,2) + pfrzdtr t(i,k) = t(i,k) + xlf/cpm(i,k)*pfrzdtr qrs(i,k,1) = qrs(i,k,1)-pfrzdtr endif enddo enddo ! !---------------------------------------------------------------- ! update the slope parameters for microphysics computation ! do k = kts, kte do i = its, ite qrs_tmp(i,k,1) = qrs(i,k,1) qrs_tmp(i,k,2) = qrs(i,k,2) enddo enddo call slope_wsm5(qrs_tmp,den_tmp,denfac,t,rslope,rslopeb,rslope2,rslope3, & work1,its,ite,kts,kte) !------------------------------------------------------------------ ! work1: the thermodynamic term in the denominator associated with ! heat conduction and vapor diffusion ! (ry88, y93, h85) ! work2: parameter associated with the ventilation effects(y93) ! do k = kts, kte do i = its, ite ! work1(i,k,1) = diffac(xl(i,k),p(i,k),t(i,k),den(i,k),qs(i,k,1)) work1(i,k,1) = ((((den(i,k))*(xl(i,k))*(xl(i,k)))*((t(i,k))+120.) & *(den(i,k)))/(1.414e3*(1.496e-6*((t(i,k))*sqrt(t(i,k))))& *(den(i,k))*(rv*(t(i,k))*(t(i,k))))) & + p(i,k)/((qs(i,k,1))*(8.794e-5*exp(log(t(i,k))*(1.81)))) ! work1(i,k,2) = diffac(xls,p(i,k),t(i,k),den(i,k),qs(i,k,2)) work1(i,k,2) = ((((den(i,k))*(xls)*(xls))*((t(i,k))+120.)*(den(i,k)))& /(1.414e3*(1.496e-6*((t(i,k))*sqrt(t(i,k))))*(den(i,k)) & *(rv*(t(i,k))*(t(i,k)))) & + p(i,k)/(qs(i,k,2)*(8.794e-5*exp(log(t(i,k))*(1.81))))) ! work2(i,k) = venfac(p(i,k),t(i,k),den(i,k)) work2(i,k) = (exp(.3333333*log(((1.496e-6 * ((t(i,k))*sqrt(t(i,k)))) & *p(i,k))/(((t(i,k))+120.)*den(i,k)*(8.794e-5 & *exp(log(t(i,k))*(1.81))))))*sqrt(sqrt(den0/(den(i,k))))) & /sqrt((1.496e-6*((t(i,k))*sqrt(t(i,k)))) & /(((t(i,k))+120.)*den(i,k))) enddo enddo ! !=============================================================== ! ! warm rain processes ! ! - follows the processes in RH83 and LFO except for autoconcersion ! !=============================================================== ! do k = kts, kte do i = its, ite supsat = max(q(i,k),qmin)-qs(i,k,1) satdt = supsat/dtcld !--------------------------------------------------------------- ! praut: auto conversion rate from cloud to rain [HDC 16] ! (C->R) !--------------------------------------------------------------- if(qci(i,k,1).gt.qc0) then praut(i,k) = qck1*exp(log(qci(i,k,1))*((7./3.))) praut(i,k) = min(praut(i,k),qci(i,k,1)/dtcld) endif !--------------------------------------------------------------- ! pracw: accretion of cloud water by rain [HL A40] [LFO 51] ! (C->R) !--------------------------------------------------------------- if(qrs(i,k,1).gt.qcrmin.and.qci(i,k,1).gt.qmin) then pracw(i,k) = min(pacrr*rslope3(i,k,1)*rslopeb(i,k,1) & *qci(i,k,1)*denfac(i,k),qci(i,k,1)/dtcld) endif !--------------------------------------------------------------- ! prevp: evaporation/condensation rate of rain [HDC 14] ! (V->R or R->V) !--------------------------------------------------------------- if(qrs(i,k,1).gt.0.) then coeres = rslope2(i,k,1)*sqrt(rslope(i,k,1)*rslopeb(i,k,1)) prevp(i,k) = (rh(i,k,1)-1.)*(precr1*rslope2(i,k,1) & +precr2*work2(i,k)*coeres)/work1(i,k,1) if(prevp(i,k).lt.0.) then prevp(i,k) = max(prevp(i,k),-qrs(i,k,1)/dtcld) prevp(i,k) = max(prevp(i,k),satdt/2) else prevp(i,k) = min(prevp(i,k),satdt/2) endif endif enddo enddo ! !=============================================================== ! ! cold rain processes ! ! - follows the revised ice microphysics processes in HDC ! - the processes same as in RH83 and RH84 and LFO behave ! following ice crystal hapits defined in HDC, inclduing ! intercept parameter for snow (n0s), ice crystal number ! concentration (ni), ice nuclei number concentration ! (n0i), ice diameter (d) ! !=============================================================== ! rdtcld = 1./dtcld do k = kts, kte do i = its, ite supcol = t0c-t(i,k) n0sfac(i,k) = max(min(exp(alpha*supcol),n0smax/n0s),1.) supsat = max(q(i,k),qmin)-qs(i,k,2) satdt = supsat/dtcld ifsat = 0 !------------------------------------------------------------- ! Ni: ice crystal number concentraiton [HDC 5c] !------------------------------------------------------------- ! xni(i,k) = min(max(5.38e7*(den(i,k) & ! *max(qci(i,k,2),qmin))**0.75,1.e3),1.e6) temp = (den(i,k)*max(qci(i,k,2),qmin)) temp = sqrt(sqrt(temp*temp*temp)) xni(i,k) = min(max(5.38e7*temp,1.e3),1.e6) eacrs = exp(0.07*(-supcol)) ! if(supcol.gt.0) then if(qrs(i,k,2).gt.qcrmin.and.qci(i,k,2).gt.qmin) then xmi = den(i,k)*qci(i,k,2)/xni(i,k) diameter = min(dicon * sqrt(xmi),dimax) vt2i = 1.49e4*diameter**1.31 vt2s = pvts*rslopeb(i,k,2)*denfac(i,k) !------------------------------------------------------------- ! psaci: Accretion of cloud ice by rain [HDC 10] ! (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 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 if(supcol .gt. 0) then !------------------------------------------------------------- ! 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 !------------------------------------------------------------- ! 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(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 ! ! rain ! ! value = max(qmin,qrs(i,k,1)) source = (-praut(i,k)-pracw(i,k)-prevp(i,k))*dtcld if (source.gt.value) then factor = value/source praut(i,k) = praut(i,k)*factor pracw(i,k) = pracw(i,k)*factor prevp(i,k) = prevp(i,k)*factor endif ! ! snow ! value = max(qmin,qrs(i,k,2)) source = (-psdep(i,k)-psaut(i,k)-psaci(i,k)-psacw(i,k))*dtcld if (source.gt.value) then factor = value/source psdep(i,k) = psdep(i,k)*factor psaut(i,k) = psaut(i,k)*factor psaci(i,k) = psaci(i,k)*factor psacw(i,k) = psacw(i,k)*factor endif ! work2(i,k)=-(prevp(i,k)+psdep(i,k)+pigen(i,k)+pidep(i,k)) ! update q(i,k) = q(i,k)+work2(i,k)*dtcld qci(i,k,1) = max(qci(i,k,1)-(praut(i,k)+pracw(i,k) & +psacw(i,k))*dtcld,0.) qrs(i,k,1) = max(qrs(i,k,1)+(praut(i,k)+pracw(i,k) & +prevp(i,k))*dtcld,0.) qci(i,k,2) = max(qci(i,k,2)-(psaut(i,k)+psaci(i,k) & -pigen(i,k)-pidep(i,k))*dtcld,0.) qrs(i,k,2) = max(qrs(i,k,2)+(psdep(i,k)+psaut(i,k) & +psaci(i,k)+psacw(i,k))*dtcld,0.) xlf = xls-xl(i,k) xlwork2 = -xls*(psdep(i,k)+pidep(i,k)+pigen(i,k)) & -xl(i,k)*prevp(i,k)-xlf*psacw(i,k) t(i,k) = t(i,k)-xlwork2/cpm(i,k)*dtcld else ! ! cloud water ! value = max(qmin,qci(i,k,1)) source=(praut(i,k)+pracw(i,k)+psacw(i,k))*dtcld if (source.gt.value) then factor = value/source praut(i,k) = praut(i,k)*factor pracw(i,k) = pracw(i,k)*factor psacw(i,k) = psacw(i,k)*factor endif ! ! rain ! value = max(qmin,qrs(i,k,1)) source = (-praut(i,k)-pracw(i,k)-prevp(i,k)-psacw(i,k))*dtcld if (source.gt.value) then factor = value/source praut(i,k) = praut(i,k)*factor pracw(i,k) = pracw(i,k)*factor prevp(i,k) = prevp(i,k)*factor psacw(i,k) = psacw(i,k)*factor endif ! ! snow ! value = max(qcrmin,qrs(i,k,2)) source=(-psevp(i,k))*dtcld if (source.gt.value) then factor = value/source psevp(i,k) = psevp(i,k)*factor endif work2(i,k)=-(prevp(i,k)+psevp(i,k)) ! update q(i,k) = q(i,k)+work2(i,k)*dtcld qci(i,k,1) = max(qci(i,k,1)-(praut(i,k)+pracw(i,k) & +psacw(i,k))*dtcld,0.) qrs(i,k,1) = max(qrs(i,k,1)+(praut(i,k)+pracw(i,k) & +prevp(i,k) +psacw(i,k))*dtcld,0.) qrs(i,k,2) = max(qrs(i,k,2)+psevp(i,k)*dtcld,0.) xlf = xls-xl(i,k) xlwork2 = -xl(i,k)*(prevp(i,k)+psevp(i,k)) t(i,k) = t(i,k)-xlwork2/cpm(i,k)*dtcld endif enddo enddo ! ! Inline expansion for fpvs ! qs(i,k,1) = fpvs(t(i,k),0,rd,rv,cpv,cliq,cice,xlv0,xls,psat,t0c) ! qs(i,k,2) = fpvs(t(i,k),1,rd,rv,cpv,cliq,cice,xlv0,xls,psat,t0c) hsub = xls hvap = xlv0 cvap = cpv ttp=t0c+0.01 dldt=cvap-cliq xa=-dldt/rv xb=xa+hvap/(rv*ttp) dldti=cvap-cice xai=-dldti/rv xbi=xai+hsub/(rv*ttp) do k = kts, kte do i = its, ite tr=ttp/t(i,k) logtr = log(tr) qs(i,k,1)=psat*exp(logtr*(xa)+xb*(1.-tr)) qs(i,k,1) = min(qs(i,k,1),0.99*p(i,k)) qs(i,k,1) = ep2 * qs(i,k,1) / (p(i,k) - qs(i,k,1)) qs(i,k,1) = max(qs(i,k,1),qmin) enddo enddo ! !---------------------------------------------------------------- ! pcond: condensational/evaporational rate of cloud water [HL A46] [RH83 A6] ! if there exists additional water vapor condensated/if ! evaporation of cloud water is not enough to remove subsaturation ! do k = kts, kte do i = its, ite ! work1(i,k,1) = conden(t(i,k),q(i,k),qs(i,k,1),xl(i,k),cpm(i,k)) work1(i,k,1) = ((max(q(i,k),qmin)-(qs(i,k,1)))/(1.+(xl(i,k)) & *(xl(i,k))/(rv*(cpm(i,k)))*(qs(i,k,1)) & /((t(i,k))*(t(i,k))))) work2(i,k) = qci(i,k,1)+work1(i,k,1) pcond(i,k) = min(max(work1(i,k,1)/dtcld,0.),max(q(i,k),0.)/dtcld) if(qci(i,k,1).gt.0..and.work1(i,k,1).lt.0.) & pcond(i,k) = max(work1(i,k,1),-qci(i,k,1))/dtcld q(i,k) = q(i,k)-pcond(i,k)*dtcld qci(i,k,1) = max(qci(i,k,1)+pcond(i,k)*dtcld,0.) t(i,k) = t(i,k)+pcond(i,k)*xl(i,k)/cpm(i,k)*dtcld enddo enddo ! ! !---------------------------------------------------------------- ! padding for small values ! do k = kts, kte do i = its, ite if(qci(i,k,1).le.qmin) qci(i,k,1) = 0.0 if(qci(i,k,2).le.qmin) qci(i,k,2) = 0.0 enddo enddo enddo ! big loops END SUBROUTINE wsm52d ! ................................................................... REAL FUNCTION rgmma(x) !------------------------------------------------------------------- IMPLICIT NONE !------------------------------------------------------------------- ! rgmma function: use infinite product form REAL :: euler PARAMETER (euler=0.577215664901532) REAL :: x, y INTEGER :: i if(x.eq.1.)then rgmma=0. else rgmma=x*exp(euler*x) do i=1,10000 y=float(i) rgmma=rgmma*(1.000+x/y)*exp(-x/y) enddo rgmma=1./rgmma endif END FUNCTION rgmma ! !-------------------------------------------------------------------------- REAL FUNCTION fpvs(t,ice,rd,rv,cvap,cliq,cice,hvap,hsub,psat,t0c) !-------------------------------------------------------------------------- IMPLICIT NONE !-------------------------------------------------------------------------- REAL t,rd,rv,cvap,cliq,cice,hvap,hsub,psat,t0c,dldt,xa,xb,dldti, & xai,xbi,ttp,tr INTEGER ice ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ttp=t0c+0.01 dldt=cvap-cliq xa=-dldt/rv xb=xa+hvap/(rv*ttp) dldti=cvap-cice xai=-dldti/rv xbi=xai+hsub/(rv*ttp) tr=ttp/t if(t.lt.ttp.and.ice.eq.1) then fpvs=psat*exp(log(tr)*(xai))*exp(xbi*(1.-tr)) else fpvs=psat*exp(log(tr)*(xa))*exp(xb*(1.-tr)) endif ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - END FUNCTION fpvs !------------------------------------------------------------------- SUBROUTINE wsm5init(den0,denr,dens,cl,cpv,allowed_to_read) !------------------------------------------------------------------- IMPLICIT NONE !------------------------------------------------------------------- !.... constants which may not be tunable REAL, INTENT(IN) :: den0,denr,dens,cl,cpv LOGICAL, INTENT(IN) :: allowed_to_read ! pi = 4.*atan(1.) xlv1 = cl-cpv ! qc0 = 4./3.*pi*denr*r0**3*xncr/den0 ! 0.419e-3 -- .61e-3 qck1 = .104*9.8*peaut/(xncr*denr)**(1./3.)/xmyu*den0**(4./3.) ! 7.03 ! bvtr1 = 1.+bvtr bvtr2 = 2.5+.5*bvtr bvtr3 = 3.+bvtr bvtr4 = 4.+bvtr g1pbr = rgmma(bvtr1) g3pbr = rgmma(bvtr3) g4pbr = rgmma(bvtr4) ! 17.837825 g5pbro2 = rgmma(bvtr2) ! 1.8273 pvtr = avtr*g4pbr/6. eacrr = 1.0 pacrr = pi*n0r*avtr*g3pbr*.25*eacrr precr1 = 2.*pi*n0r*.78 precr2 = 2.*pi*n0r*.31*avtr**.5*g5pbro2 xmmax = (dimax/dicon)**2 roqimax = 2.08e22*dimax**8 ! bvts1 = 1.+bvts bvts2 = 2.5+.5*bvts bvts3 = 3.+bvts bvts4 = 4.+bvts g1pbs = rgmma(bvts1) !.8875 g3pbs = rgmma(bvts3) g4pbs = rgmma(bvts4) ! 12.0786 g5pbso2 = rgmma(bvts2) pvts = avts*g4pbs/6. pacrs = pi*n0s*avts*g3pbs*.25 precs1 = 4.*n0s*.65 precs2 = 4.*n0s*.44*avts**.5*g5pbso2 pidn0r = pi*denr*n0r pidn0s = pi*dens*n0s pacrc = pi*n0s*avts*g3pbs*.25*eacrc ! rslopermax = 1./lamdarmax rslopesmax = 1./lamdasmax rsloperbmax = rslopermax ** bvtr rslopesbmax = rslopesmax ** bvts rsloper2max = rslopermax * rslopermax rslopes2max = rslopesmax * rslopesmax rsloper3max = rsloper2max * rslopermax rslopes3max = rslopes2max * rslopesmax ! END SUBROUTINE wsm5init !------------------------------------------------------------------------------ subroutine slope_wsm5(qrs,den,denfac,t,rslope,rslopeb,rslope2,rslope3, & vt,its,ite,kts,kte) IMPLICIT NONE INTEGER :: its,ite, jts,jte, kts,kte REAL, DIMENSION( its:ite , kts:kte,2) :: & qrs, & rslope, & rslopeb, & rslope2, & rslope3, & vt REAL, DIMENSION( its:ite , kts:kte) :: & den, & denfac, & t REAL, PARAMETER :: t0c = 273.15 REAL, DIMENSION( its:ite , kts:kte ) :: & n0sfac REAL :: lamdar, lamdas, x, y, z, supcol integer :: i, j, k !---------------------------------------------------------------- ! size distributions: (x=mixing ratio, y=air density): ! valid for mixing ratio > 1.e-9 kg/kg. lamdar(x,y)= sqrt(sqrt(pidn0r/(x*y))) ! (pidn0r/(x*y))**.25 lamdas(x,y,z)= sqrt(sqrt(pidn0s*z/(x*y))) ! (pidn0s*z/(x*y))**.25 ! do k = kts, kte do i = its, ite supcol = t0c-t(i,k) !--------------------------------------------------------------- ! n0s: Intercept parameter for snow [m-4] [HDC 6] !--------------------------------------------------------------- n0sfac(i,k) = max(min(exp(alpha*supcol),n0smax/n0s),1.) if(qrs(i,k,1).le.qcrmin)then rslope(i,k,1) = rslopermax rslopeb(i,k,1) = rsloperbmax rslope2(i,k,1) = rsloper2max rslope3(i,k,1) = rsloper3max else rslope(i,k,1) = 1./lamdar(qrs(i,k,1),den(i,k)) rslopeb(i,k,1) = exp(log(rslope(i,k,1))*(bvtr)) rslope2(i,k,1) = rslope(i,k,1)*rslope(i,k,1) rslope3(i,k,1) = rslope2(i,k,1)*rslope(i,k,1) endif if(qrs(i,k,2).le.qcrmin)then rslope(i,k,2) = rslopesmax rslopeb(i,k,2) = rslopesbmax rslope2(i,k,2) = rslopes2max rslope3(i,k,2) = rslopes3max else rslope(i,k,2) = 1./lamdas(qrs(i,k,2),den(i,k),n0sfac(i,k)) rslopeb(i,k,2) = exp(log(rslope(i,k,2))*(bvts)) rslope2(i,k,2) = rslope(i,k,2)*rslope(i,k,2) rslope3(i,k,2) = rslope2(i,k,2)*rslope(i,k,2) endif vt(i,k,1) = pvtr*rslopeb(i,k,1)*denfac(i,k) vt(i,k,2) = pvts*rslopeb(i,k,2)*denfac(i,k) if(qrs(i,k,1).le.0.0) vt(i,k,1) = 0.0 if(qrs(i,k,2).le.0.0) vt(i,k,2) = 0.0 enddo enddo END subroutine slope_wsm5 !----------------------------------------------------------------------------- subroutine slope_rain(qrs,den,denfac,t,rslope,rslopeb,rslope2,rslope3, & vt,its,ite,kts,kte) IMPLICIT NONE INTEGER :: its,ite, jts,jte, kts,kte REAL, DIMENSION( its:ite , kts:kte) :: & qrs, & rslope, & rslopeb, & rslope2, & rslope3, & vt, & den, & denfac, & t REAL, PARAMETER :: t0c = 273.15 REAL, DIMENSION( its:ite , kts:kte ) :: & n0sfac REAL :: lamdar, x, y, z, supcol integer :: i, j, k !---------------------------------------------------------------- ! size distributions: (x=mixing ratio, y=air density): ! valid for mixing ratio > 1.e-9 kg/kg. lamdar(x,y)= sqrt(sqrt(pidn0r/(x*y))) ! (pidn0r/(x*y))**.25 ! do k = kts, kte do i = its, ite if(qrs(i,k).le.qcrmin)then rslope(i,k) = rslopermax rslopeb(i,k) = rsloperbmax rslope2(i,k) = rsloper2max rslope3(i,k) = rsloper3max else rslope(i,k) = 1./lamdar(qrs(i,k),den(i,k)) rslopeb(i,k) = rslope(i,k)**bvtr rslope2(i,k) = rslope(i,k)*rslope(i,k) rslope3(i,k) = rslope2(i,k)*rslope(i,k) endif vt(i,k) = pvtr*rslopeb(i,k)*denfac(i,k) if(qrs(i,k).le.0.0) vt(i,k) = 0.0 enddo enddo END subroutine slope_rain !------------------------------------------------------------------------------ subroutine slope_snow(qrs,den,denfac,t,rslope,rslopeb,rslope2,rslope3, & vt,its,ite,kts,kte) IMPLICIT NONE INTEGER :: its,ite, jts,jte, kts,kte REAL, DIMENSION( its:ite , kts:kte) :: & qrs, & rslope, & rslopeb, & rslope2, & rslope3, & vt, & den, & denfac, & t REAL, PARAMETER :: t0c = 273.15 REAL, DIMENSION( its:ite , kts:kte ) :: & n0sfac REAL :: lamdas, x, y, z, supcol integer :: i, j, k !---------------------------------------------------------------- ! size distributions: (x=mixing ratio, y=air density): ! valid for mixing ratio > 1.e-9 kg/kg. lamdas(x,y,z)= sqrt(sqrt(pidn0s*z/(x*y))) ! (pidn0s*z/(x*y))**.25 ! do k = kts, kte do i = its, ite supcol = t0c-t(i,k) !--------------------------------------------------------------- ! n0s: Intercept parameter for snow [m-4] [HDC 6] !--------------------------------------------------------------- n0sfac(i,k) = max(min(exp(alpha*supcol),n0smax/n0s),1.) if(qrs(i,k).le.qcrmin)then rslope(i,k) = rslopesmax rslopeb(i,k) = rslopesbmax rslope2(i,k) = rslopes2max rslope3(i,k) = rslopes3max else rslope(i,k) = 1./lamdas(qrs(i,k),den(i,k),n0sfac(i,k)) rslopeb(i,k) = rslope(i,k)**bvts rslope2(i,k) = rslope(i,k)*rslope(i,k) rslope3(i,k) = rslope2(i,k)*rslope(i,k) endif vt(i,k) = pvts*rslopeb(i,k)*denfac(i,k) if(qrs(i,k).le.0.0) vt(i,k) = 0.0 enddo enddo END subroutine slope_snow !------------------------------------------------------------------- SUBROUTINE nislfv_rain_plm(im,km,denl,denfacl,tkl,dzl,wwl,rql,precip,dt,id,iter) !------------------------------------------------------------------- ! ! for non-iteration semi-Lagrangain forward advection for cloud ! with mass conservation and positive definite advection ! 2nd order interpolation with monotonic piecewise linear method ! this routine is under assumption of decfl < 1 for semi_Lagrangian ! ! dzl depth of model layer in meter ! wwl terminal velocity at model layer m/s ! rql cloud density*mixing ration ! precip precipitation ! dt time step ! id kind of precip: 0 test case; 1 raindrop 2: snow ! iter how many time to guess mean terminal velocity: 0 pure forward. ! 0 : use departure wind for advection ! 1 : use mean wind for advection ! > 1 : use mean wind after iter-1 iterations ! ! author: hann-ming henry juang ! implemented by song-you hong ! implicit none integer im,km,id real dt real dzl(im,km),wwl(im,km),rql(im,km),precip(im) real denl(im,km),denfacl(im,km),tkl(im,km) ! integer i,k,n,m,kk,kb,kt,iter real tl,tl2,qql,dql,qqd real th,th2,qqh,dqh real zsum,qsum,dim,dip,c1,con1,fa1,fa2 real allold, allnew, zz, dzamin, cflmax, decfl real dz(km), ww(km), qq(km), wd(km), wa(km), was(km) real den(km), denfac(km), tk(km) real wi(km+1), zi(km+1), za(km+1) real qn(km), qr(km),tmp(km),tmp1(km),tmp2(km),tmp3(km) real dza(km+1), qa(km+1), qmi(km+1), qpi(km+1) ! precip(:) = 0.0 ! i_loop : do i=1,im ! ----------------------------------- dz(:) = dzl(i,:) qq(:) = rql(i,:) ww(:) = wwl(i,:) den(:) = denl(i,:) denfac(:) = denfacl(i,:) tk(:) = tkl(i,:) ! skip for no precipitation for all layers allold = 0.0 do k=1,km allold = allold + qq(k) enddo if(allold.le.0.0) then cycle i_loop endif ! ! compute interface values zi(1)=0.0 do k=1,km zi(k+1) = zi(k)+dz(k) enddo ! ! save departure wind wd(:) = ww(:) n=1 100 continue ! plm is 2nd order, we can use 2nd order wi or 3rd order wi ! 2nd order interpolation to get wi wi(1) = ww(1) wi(km+1) = ww(km) do k=2,km wi(k) = (ww(k)*dz(k-1)+ww(k-1)*dz(k))/(dz(k-1)+dz(k)) enddo ! 3rd order interpolation to get wi fa1 = 9./16. fa2 = 1./16. wi(1) = ww(1) wi(2) = 0.5*(ww(2)+ww(1)) do k=3,km-1 wi(k) = fa1*(ww(k)+ww(k-1))-fa2*(ww(k+1)+ww(k-2)) enddo wi(km) = 0.5*(ww(km)+ww(km-1)) wi(km+1) = ww(km) ! ! terminate of top of raingroup do k=2,km if( ww(k).eq.0.0 ) wi(k)=ww(k-1) enddo ! ! diffusivity of wi con1 = 0.05 do k=km,1,-1 decfl = (wi(k+1)-wi(k))*dt/dz(k) if( decfl .gt. con1 ) then wi(k) = wi(k+1) - con1*dz(k)/dt endif enddo ! compute arrival point do k=1,km+1 za(k) = zi(k) - wi(k)*dt enddo ! do k=1,km dza(k) = za(k+1)-za(k) enddo dza(km+1) = zi(km+1) - za(km+1) ! ! computer deformation at arrival point do k=1,km qa(k) = qq(k)*dz(k)/dza(k) qr(k) = qa(k)/den(k) enddo qa(km+1) = 0.0 ! call maxmin(km,1,qa,' arrival points ') ! ! compute arrival terminal velocity, and estimate mean terminal velocity ! then back to use mean terminal velocity if( n.le.iter ) then if (id.eq.1) then call slope_rain(qr,den,denfac,tk,tmp,tmp1,tmp2,tmp3,wa,1,1,1,km) else call slope_snow(qr,den,denfac,tk,tmp,tmp1,tmp2,tmp3,wa,1,1,1,km) endif if( n.ge.2 ) wa(1:km)=0.5*(wa(1:km)+was(1:km)) do k=1,km !#ifdef DEBUG ! print*,' slope_wsm3 ',qr(k)*1000.,den(k),denfac(k),tk(k),tmp(k),tmp1(k),tmp2(k),ww(k),wa(k) !#endif ! mean wind is average of departure and new arrival winds ww(k) = 0.5* ( wd(k)+wa(k) ) enddo was(:) = wa(:) n=n+1 go to 100 endif ! ! estimate values at arrival cell interface with monotone do k=2,km dip=(qa(k+1)-qa(k))/(dza(k+1)+dza(k)) dim=(qa(k)-qa(k-1))/(dza(k-1)+dza(k)) if( dip*dim.le.0.0 ) then qmi(k)=qa(k) qpi(k)=qa(k) else qpi(k)=qa(k)+0.5*(dip+dim)*dza(k) qmi(k)=2.0*qa(k)-qpi(k) if( qpi(k).lt.0.0 .or. qmi(k).lt.0.0 ) then qpi(k) = qa(k) qmi(k) = qa(k) endif endif enddo qpi(1)=qa(1) qmi(1)=qa(1) qmi(km+1)=qa(km+1) qpi(km+1)=qa(km+1) ! ! interpolation to regular point qn = 0.0 kb=1 kt=1 intp : do k=1,km kb=max(kb-1,1) kt=max(kt-1,1) ! find kb and kt if( zi(k).ge.za(km+1) ) then exit intp else find_kb : do kk=kb,km if( zi(k).le.za(kk+1) ) then kb = kk exit find_kb else cycle find_kb endif enddo find_kb find_kt : do kk=kt,km if( zi(k+1).le.za(kk) ) then kt = kk exit find_kt else cycle find_kt endif enddo find_kt kt = kt - 1 ! compute q with piecewise constant method if( kt.eq.kb ) then tl=(zi(k)-za(kb))/dza(kb) th=(zi(k+1)-za(kb))/dza(kb) tl2=tl*tl th2=th*th qqd=0.5*(qpi(kb)-qmi(kb)) qqh=qqd*th2+qmi(kb)*th qql=qqd*tl2+qmi(kb)*tl qn(k) = (qqh-qql)/(th-tl) else if( kt.gt.kb ) then tl=(zi(k)-za(kb))/dza(kb) tl2=tl*tl qqd=0.5*(qpi(kb)-qmi(kb)) qql=qqd*tl2+qmi(kb)*tl dql = qa(kb)-qql zsum = (1.-tl)*dza(kb) qsum = dql*dza(kb) if( kt-kb.gt.1 ) then do m=kb+1,kt-1 zsum = zsum + dza(m) qsum = qsum + qa(m) * dza(m) enddo endif th=(zi(k+1)-za(kt))/dza(kt) th2=th*th qqd=0.5*(qpi(kt)-qmi(kt)) dqh=qqd*th2+qmi(kt)*th zsum = zsum + th*dza(kt) qsum = qsum + dqh*dza(kt) qn(k) = qsum/zsum endif cycle intp endif ! enddo intp ! ! rain out sum_precip: do k=1,km if( za(k).lt.0.0 .and. za(k+1).lt.0.0 ) then precip(i) = precip(i) + qa(k)*dza(k) cycle sum_precip else if ( za(k).lt.0.0 .and. za(k+1).ge.0.0 ) then precip(i) = precip(i) + qa(k)*(0.0-za(k)) exit sum_precip endif exit sum_precip enddo sum_precip ! ! replace the new values rql(i,:) = qn(:) ! ! ---------------------------------- enddo i_loop ! END SUBROUTINE nislfv_rain_plm END MODULE module_mp_wsm5 #endif