MODULE improvedclouds_mod IMPLICIT NONE CONTAINS subroutine improvedclouds(ngrid,nlay,microtimestep, & pplay,pteff,sum_subpdt, & pqeff,sum_subpdq,subpdqcloud,subpdtcloud, & nq,tauscaling) USE updaterad, ONLY: updaterice_micro, updaterccn USE watersat_mod, ONLY: watersat use tracer_mod, only: rho_ice, nuice_sed, igcm_h2o_vap, & igcm_h2o_ice, igcm_dust_mass, & igcm_dust_number, igcm_ccn_mass, & igcm_ccn_number, & igcm_hdo_vap,igcm_hdo_ice, & qperemin use conc_mod, only: mmean use comcstfi_h, only: pi, cpp implicit none c------------------------------------------------------------------ c This routine is used to form clouds when a parcel of the GCM is c saturated. It includes the ability to have supersaturation, a c computation of the nucleation rates, growthrates and the c scavenging of dust particles by clouds. c It is worth noting that the amount of dust is computed using the c dust optical depth computed in aeropacity.F. That's why c the variable called "tauscaling" is used to convert c pq(dust_mass) and pq(dust_number), which are relative c quantities, to absolute and realistic quantities stored in zq. c This has to be done to convert the inputs into absolute c values, but also to convert the outputs back into relative c values which are then used by the sedimentation and advection c schemes. c Authors: J.-B. Madeleine, based on the work by Franck Montmessin c (October 2011) c T. Navarro, debug,correction, new scheme (October-April 2011) c A. Spiga, optimization (February 2012) c------------------------------------------------------------------ #include "callkeys.h" #include "microphys.h" c------------------------------------------------------------------ c Inputs/outputs: INTEGER, INTENT(IN) :: ngrid,nlay INTEGER, INTENT(IN) :: nq ! nombre de traceurs REAL, INTENT(IN) :: microtimestep ! pas de temps physique (s) REAL, INTENT(IN) :: pplay(ngrid,nlay) ! pression au milieu des couches (Pa) REAL, INTENT(IN) :: pteff(ngrid,nlay) ! temperature at the middle of the ! layers (K) REAL, INTENT(IN) :: sum_subpdt(ngrid,nlay)! tendance temperature des autres ! param. REAL, INTENT(IN) :: pqeff(ngrid,nlay,nq) ! traceur (kg/kg) REAL, INTENT(IN) :: sum_subpdq(ngrid,nlay,nq) ! tendance avant condensation ! (kg/kg.s-1) REAL, INTENT(IN) :: tauscaling(ngrid) ! Convertion factor for qdust and Ndust REAL, INTENT(OUT) :: subpdqcloud(ngrid,nlay,nq) ! tendance de la condensation ! H2O(kg/kg.s-1) REAL, INTENT(OUT) :: subpdtcloud(ngrid,nlay) ! tendance temperature due ! a la chaleur latente c------------------------------------------------------------------ c Local variables: LOGICAL firstcall DATA firstcall/.true./ SAVE firstcall !$OMP THREADPRIVATE(firstcall) REAL*8 derf ! Error function !external derf INTEGER ig,l,i REAL zq(ngrid,nlay,nq) ! local value of tracers REAL zq0(ngrid,nlay,nq) ! local initial value of tracers REAL zt(ngrid,nlay) ! local value of temperature REAL zqsat(ngrid,nlay) ! saturation REAL lw !Latent heat of sublimation (J.kg-1) REAL cste REAL dMice ! mass of condensed ice REAL dMice_hdo ! mass of condensed HDO ice REAL alpha(ngrid,nlay) ! HDO equilibrium fractionation coefficient (Saturation=1) REAL alpha_c(ngrid,nlay) ! HDO real fractionation coefficient ! REAL sumcheck REAL*8 ph2o ! Water vapor partial pressure (Pa) REAL*8 satu ! Water vapor saturation ratio over ice REAL*8 Mo,No REAL*8 Rn, Rm, dev2, n_derf, m_derf REAL*8 n_aer(nbin_cld) ! number conc. of particle/each size bin REAL*8 m_aer(nbin_cld) ! mass mixing ratio of particle/each size bin REAL*8 sig ! Water-ice/air surface tension (N.m) EXTERNAL sig REAL dN,dM REAL rate(nbin_cld) ! nucleation rate REAL seq REAL rice(ngrid,nlay) ! Ice mass mean radius (m) ! (r_c in montmessin_2004) REAL rhocloud(ngrid,nlay) ! Cloud density (kg.m-3) REAL rdust(ngrid,nlay) ! Dust geometric mean radius (m) REAL res ! Resistance growth REAL Dv,Dv_hdo ! Water/HDO vapor diffusion coefficient c Parameters of the size discretization c used by the microphysical scheme DOUBLE PRECISION, PARAMETER :: rmin_cld = 0.1e-6 ! Minimum radius (m) DOUBLE PRECISION, PARAMETER :: rmax_cld = 10.e-6 ! Maximum radius (m) DOUBLE PRECISION, PARAMETER :: rbmin_cld = 0.0001e-6 ! Minimum boundary radius (m) DOUBLE PRECISION, PARAMETER :: rbmax_cld = 1.e-2 ! Maximum boundary radius (m) DOUBLE PRECISION vrat_cld ! Volume ratio DOUBLE PRECISION rb_cld(nbin_cld+1)! boundary values of each rad_cld bin (m) SAVE rb_cld DOUBLE PRECISION dr_cld(nbin_cld) ! width of each rad_cld bin (m) DOUBLE PRECISION vol_cld(nbin_cld) ! particle volume for each bin (m3) !$OMP THREADPRIVATE(rb_cld) REAL sigma_ice ! Variance of the ice and CCN distributions SAVE sigma_ice !$OMP THREADPRIVATE(sigma_ice) c---------------------------------- c TESTS INTEGER countcells LOGICAL test_flag ! flag for test/debuging outputs SAVE test_flag !$OMP THREADPRIVATE(test_flag) REAL satubf(ngrid,nlay),satuaf(ngrid,nlay) REAL res_out(ngrid,nlay) c------------------------------------------------------------------ ! AS: firstcall OK absolute IF (firstcall) THEN !============================================================= ! 0. Definition of the size grid !============================================================= c rad_cld is the primary radius grid used for microphysics computation. c The grid spacing is computed assuming a constant volume ratio c between two consecutive bins; i.e. vrat_cld. c vrat_cld is determined from the boundary values of the size grid: c rmin_cld and rmax_cld. c The rb_cld array contains the boundary values of each rad_cld bin. c dr_cld is the width of each rad_cld bin. c Volume ratio between two adjacent bins ! vrat_cld = log(rmax_cld/rmin_cld) / float(nbin_cld-1) *3. ! vrat_cld = exp(vrat_cld) vrat_cld = log(rmax_cld/rmin_cld) / float(nbin_cld-1) *3. vrat_cld = exp(vrat_cld) write(*,*) "vrat_cld", vrat_cld rb_cld(1) = rbmin_cld rad_cld(1) = rmin_cld vol_cld(1) = 4./3. * dble(pi) * rmin_cld*rmin_cld*rmin_cld ! vol_cld(1) = 4./3. * pi * rmin_cld*rmin_cld*rmin_cld do i=1,nbin_cld-1 rad_cld(i+1) = rad_cld(i) * vrat_cld**(1./3.) vol_cld(i+1) = vol_cld(i) * vrat_cld enddo do i=1,nbin_cld rb_cld(i+1)= ( (2.*vrat_cld) / (vrat_cld+1.) )**(1./3.) * & rad_cld(i) dr_cld(i) = rb_cld(i+1) - rb_cld(i) enddo rb_cld(nbin_cld+1) = rbmax_cld dr_cld(nbin_cld) = rb_cld(nbin_cld+1) - rb_cld(nbin_cld) print*, ' ' print*,'Microphysics: size bin information:' print*,'i,rb_cld(i), rad_cld(i),dr_cld(i)' print*,'-----------------------------------' do i=1,nbin_cld write(*,'(i2,3x,3(e12.6,4x))') i,rb_cld(i), rad_cld(i), & dr_cld(i) enddo write(*,'(i2,3x,e12.6)') nbin_cld+1,rb_cld(nbin_cld+1) print*,'-----------------------------------' do i=1,nbin_cld+1 ! rb_cld(i) = log(rb_cld(i)) rb_cld(i) = log(rb_cld(i)) !! we save that so that it is not computed !! at each timestep and gridpoint enddo c Contact parameter of water ice on dust ( m=cos(theta) ) c ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ! mteta = 0.95 write(*,*) 'water_param contact parameter:', mteta c Volume of a water molecule (m3) vo1 = mh2o / dble(rho_ice) c Variance of the ice and CCN distributions sigma_ice = sqrt(log(1.+nuice_sed)) write(*,*) 'Variance of ice & CCN distribs :', sigma_ice write(*,*) 'nuice for sedimentation:', nuice_sed write(*,*) 'Volume of a water molecule:', vo1 test_flag = .false. firstcall=.false. END IF !============================================================= ! 1. Initialisation !============================================================= cste = 4*pi*rho_ice*microtimestep res_out(:,:) = 0 rice(:,:) = 1.e-8 c Initialize the tendencies subpdqcloud(1:ngrid,1:nlay,1:nq)=0 subpdtcloud(1:ngrid,1:nlay)=0 zt(1:ngrid,1:nlay) = & pteff(1:ngrid,1:nlay) + & sum_subpdt(1:ngrid,1:nlay) * microtimestep zq(1:ngrid,1:nlay,1:nq) = & pqeff(1:ngrid,1:nlay,1:nq) + & sum_subpdq(1:ngrid,1:nlay,1:nq) * microtimestep WHERE( zq(1:ngrid,1:nlay,1:nq) < 1.e-30 ) & zq(1:ngrid,1:nlay,1:nq) = 1.e-30 zq0(1:ngrid,1:nlay,1:nq) = zq(1:ngrid,1:nlay,1:nq) !============================================================= ! 2. Compute saturation !============================================================= dev2 = 1. / ( sqrt(2.) * sigma_ice ) call watersat(ngrid*nlay,zt,pplay,zqsat) countcells = 0 c Main loop over the GCM's grid DO l=1,nlay DO ig=1,ngrid c Get the partial pressure of water vapor and its saturation ratio ph2o = zq(ig,l,igcm_h2o_vap) * (mmean(ig,l)/18.) * pplay(ig,l) satu = zq(ig,l,igcm_h2o_vap) / zqsat(ig,l) !============================================================= ! 3. Nucleation !============================================================= IF ( satu .ge. 1. ) THEN ! if there is condensation call updaterccn(zq(ig,l,igcm_dust_mass), & zq(ig,l,igcm_dust_number),rdust(ig,l),tauscaling(ig)) c Expand the dust moments into a binned distribution Mo = zq(ig,l,igcm_dust_mass)* tauscaling(ig) + 1.e-30 No = zq(ig,l,igcm_dust_number)* tauscaling(ig) + 1.e-30 Rn = rdust(ig,l) Rn = -log(Rn) Rm = Rn - 3. * sigma_ice*sigma_ice n_derf = derf( (rb_cld(1)+Rn) *dev2) m_derf = derf( (rb_cld(1)+Rm) *dev2) do i = 1, nbin_cld n_aer(i) = -0.5 * No * n_derf !! this ith previously computed m_aer(i) = -0.5 * Mo * m_derf !! this ith previously computed n_derf = derf( (rb_cld(i+1)+Rn) *dev2) m_derf = derf( (rb_cld(i+1)+Rm) *dev2) n_aer(i) = n_aer(i) + 0.5 * No * n_derf m_aer(i) = m_aer(i) + 0.5 * Mo * m_derf enddo ! sumcheck = 0 ! do i = 1, nbin_cld ! sumcheck = sumcheck + n_aer(i) ! enddo ! sumcheck = abs(sumcheck/No - 1) ! if ((sumcheck .gt. 1e-5).and. (1./Rn .gt. rmin_cld)) then ! print*, "WARNING, No sumcheck PROBLEM" ! print*, "sumcheck, No",sumcheck, No ! print*, "min radius, Rn, ig, l", rmin_cld, 1./Rn, ig, l ! print*, "Dust binned distribution", n_aer ! endif ! ! sumcheck = 0 ! do i = 1, nbin_cld ! sumcheck = sumcheck + m_aer(i) ! enddo ! sumcheck = abs(sumcheck/Mo - 1) ! if ((sumcheck .gt. 1e-5) .and. (1./Rn .gt. rmin_cld)) then ! print*, "WARNING, Mo sumcheck PROBLEM" ! print*, "sumcheck, Mo",sumcheck, Mo ! print*, "min radius, Rm, ig, l", rmin_cld, 1./Rm, ig, l ! print*, "Dust binned distribution", m_aer ! endif c Get the rates of nucleation call nuclea(ph2o,zt(ig,l),satu,n_aer,rate) dN = 0. dM = 0. do i = 1, nbin_cld dN = dN + n_aer(i)*(exp(-rate(i)*microtimestep)-1.) dM = dM + m_aer(i)*(exp(-rate(i)*microtimestep)-1.) enddo c Update Dust particles zq(ig,l,igcm_dust_mass) = & zq(ig,l,igcm_dust_mass) + dM/ tauscaling(ig) !max(tauscaling(ig),1.e-10) zq(ig,l,igcm_dust_number) = & zq(ig,l,igcm_dust_number) + dN/ tauscaling(ig) !max(tauscaling(ig),1.e-10) c Update CCNs zq(ig,l,igcm_ccn_mass) = & zq(ig,l,igcm_ccn_mass) - dM/ tauscaling(ig) !max(tauscaling(ig),1.e-10) zq(ig,l,igcm_ccn_number) = & zq(ig,l,igcm_ccn_number) - dN/ tauscaling(ig) !max(tauscaling(ig),1.e-10) ENDIF ! of is satu >1 !============================================================= ! 4. Ice growth: scheme for radius evolution !============================================================= c We trigger crystal growth if and only if there is at least one nuclei (N>1). c Indeed, if we are supersaturated and still don't have at least one nuclei, we should better wait c to avoid unrealistic value for nuclei radius and so on for cases that remain negligible. IF ( zq(ig,l,igcm_ccn_number)*tauscaling(ig).ge. 1.) THEN ! we trigger crystal growth call updaterice_micro(zq(ig,l,igcm_h2o_ice), & zq(ig,l,igcm_ccn_mass),zq(ig,l,igcm_ccn_number), & tauscaling(ig),rice(ig,l),rhocloud(ig,l)) No = zq(ig,l,igcm_ccn_number)* tauscaling(ig) + 1.e-30 c saturation at equilibrium c rice should not be too small, otherwise seq value is not valid seq = exp(2.*sig(zt(ig,l))*mh2o / (rho_ice*rgp*zt(ig,l)* & max(rice(ig,l),1.e-7))) c get resistance growth call growthrate(zt(ig,l),pplay(ig,l), & real(ph2o/satu),rice(ig,l),res,Dv) res_out(ig,l) = res ccccccc implicit scheme of mass growth dMice = & (zq(ig,l,igcm_h2o_vap)-seq*zqsat(ig,l)) & /(res*zqsat(ig,l)/(cste*No*rice(ig,l)) + 1.) ! With the above scheme, dMice cannot be bigger than vapor, ! but can be bigger than all available ice. dMice = max(dMice,-zq(ig,l,igcm_h2o_ice)) dMice = min(dMice,zq(ig,l,igcm_h2o_vap)) ! this should be useless... zq(ig,l,igcm_h2o_ice) = zq(ig,l,igcm_h2o_ice)+dMice zq(ig,l,igcm_h2o_vap) = zq(ig,l,igcm_h2o_vap)-dMice countcells = countcells + 1 ! latent heat release lw=(2834.3-0.28*(zt(ig,l)-To)- & 0.004*(zt(ig,l)-To)*(zt(ig,l)-To))*1.e+3 subpdtcloud(ig,l)= dMice*lw/cpp/microtimestep c Special case of the isotope of water HDO if (hdo) then !! condensation if (dMice.gt.0.0) then !! do we use fractionation? if (hdofrac) then !! Calculation of the HDO vapor coefficient Dv_hdo = 1./3. * sqrt( 8*kbz*zt(ig,l)/(pi*mhdo/nav) ) & * kbz * zt(ig,l) / & ( pi * pplay(ig,l) * (molco2+molhdo)*(molco2+molhdo) & * sqrt(1.+mhdo/mco2) ) !! Calculation of the fractionnation coefficient at equilibrium alpha(ig,l) = exp(16288./zt(ig,l)**2.-9.34d-2) c alpha = exp(13525./zt(ig,l)**2.-5.59d-2) !Lamb !! Calculation of the 'real' fractionnation coefficient alpha_c(ig,l) = (alpha(ig,l)*satu)/ & ( (alpha(ig,l)*(Dv/Dv_hdo)*(satu-1.)) + 1.) c alpha_c(ig,l) = alpha(ig,l) ! to test without the effect of cinetics else alpha_c(ig,l) = 1.d0 endif if (zq0(ig,l,igcm_h2o_vap).gt.qperemin) then dMice_hdo= & dMice*alpha_c(ig,l)* & ( zq0(ig,l,igcm_hdo_vap) & /zq0(ig,l,igcm_h2o_vap) ) else dMice_hdo=0. endif !! sublimation else if (zq0(ig,l,igcm_h2o_ice).gt.qperemin) then dMice_hdo= & dMice* & ( zq0(ig,l,igcm_hdo_ice) & /zq0(ig,l,igcm_h2o_ice) ) else dMice_hdo=0. endif endif !if (dMice.gt.0.0) dMice_hdo = max(dMice_hdo,-zq(ig,l,igcm_hdo_ice)) dMice_hdo = min(dMice_hdo,zq(ig,l,igcm_hdo_vap)) zq(ig,l,igcm_hdo_ice) = zq(ig,l,igcm_hdo_ice)+dMice_hdo zq(ig,l,igcm_hdo_vap) = zq(ig,l,igcm_hdo_vap)-dMice_hdo endif ! if (hdo) !============================================================= ! 5. Dust cores released, tendancies, latent heat, etc ... !============================================================= c If all the ice particles sublimate, all the condensation c nuclei are released: if (zq(ig,l,igcm_h2o_ice).le.1.e-28) then c Water zq(ig,l,igcm_h2o_vap) = zq(ig,l,igcm_h2o_vap) & + zq(ig,l,igcm_h2o_ice) zq(ig,l,igcm_h2o_ice) = 0. if (hdo) then zq(ig,l,igcm_hdo_vap) = zq(ig,l,igcm_hdo_vap) & + zq(ig,l,igcm_hdo_ice) zq(ig,l,igcm_hdo_ice) = 0. endif c Dust particles zq(ig,l,igcm_dust_mass) = zq(ig,l,igcm_dust_mass) & + zq(ig,l,igcm_ccn_mass) zq(ig,l,igcm_dust_number) = zq(ig,l,igcm_dust_number) & + zq(ig,l,igcm_ccn_number) c CCNs zq(ig,l,igcm_ccn_mass) = 0. zq(ig,l,igcm_ccn_number) = 0. endif ENDIF !of if Nccn>1 ENDDO ! of ig loop ENDDO ! of nlayer loop ! Get cloud tendencies subpdqcloud(1:ngrid,1:nlay,igcm_h2o_vap) = & (zq(1:ngrid,1:nlay,igcm_h2o_vap) - & zq0(1:ngrid,1:nlay,igcm_h2o_vap))/microtimestep subpdqcloud(1:ngrid,1:nlay,igcm_h2o_ice) = & (zq(1:ngrid,1:nlay,igcm_h2o_ice) - & zq0(1:ngrid,1:nlay,igcm_h2o_ice))/microtimestep if (hdo) then subpdqcloud(1:ngrid,1:nlay,igcm_hdo_vap) = & (zq(1:ngrid,1:nlay,igcm_hdo_vap) - & zq0(1:ngrid,1:nlay,igcm_hdo_vap))/microtimestep subpdqcloud(1:ngrid,1:nlay,igcm_hdo_ice) = & (zq(1:ngrid,1:nlay,igcm_hdo_ice) - & zq0(1:ngrid,1:nlay,igcm_hdo_ice))/microtimestep endif subpdqcloud(1:ngrid,1:nlay,igcm_ccn_mass) = & (zq(1:ngrid,1:nlay,igcm_ccn_mass) - & zq0(1:ngrid,1:nlay,igcm_ccn_mass))/microtimestep subpdqcloud(1:ngrid,1:nlay,igcm_ccn_number) = & (zq(1:ngrid,1:nlay,igcm_ccn_number) - & zq0(1:ngrid,1:nlay,igcm_ccn_number))/microtimestep if (scavenging) then subpdqcloud(1:ngrid,1:nlay,igcm_dust_mass) = & (zq(1:ngrid,1:nlay,igcm_dust_mass) - & zq0(1:ngrid,1:nlay,igcm_dust_mass))/microtimestep subpdqcloud(1:ngrid,1:nlay,igcm_dust_number) = & (zq(1:ngrid,1:nlay,igcm_dust_number) - & zq0(1:ngrid,1:nlay,igcm_dust_number))/microtimestep endif !!!!!!!!!!!!!! TESTS OUTPUTS TESTS OUTPUTS TESTS OUTPUTS TESTS OUTPUTS !!!!!!!!!!!!!! TESTS OUTPUTS TESTS OUTPUTS TESTS OUTPUTS TESTS OUTPUTS !!!!!!!!!!!!!! TESTS OUTPUTS TESTS OUTPUTS TESTS OUTPUTS TESTS OUTPUTS IF (test_flag) then ! error2d(:) = 0. DO l=1,nlay DO ig=1,ngrid ! error2d(ig) = max(abs(error_out(ig,l)),error2d(ig)) satubf(ig,l) = zq0(ig,l,igcm_h2o_vap)/zqsat(ig,l) satuaf(ig,l) = zq(ig,l,igcm_h2o_vap)/zqsat(ig,l) ENDDO ENDDO print*, 'count is ',countcells, ' i.e. ', & countcells*100/(nlay*ngrid), '% for microphys computation' #ifndef MESOSCALE ! IF (ngrid.ne.1) THEN ! 3D ! call WRITEDIAGFI(ngrid,"satu","ratio saturation","",3, ! & satu_out) ! call WRITEDIAGFI(ngrid,"dM","ccn variation","kg/kg",3, ! & dM_out) ! call WRITEDIAGFI(ngrid,"dN","ccn variation","#",3, ! & dN_out) ! call WRITEDIAGFI(ngrid,"error","dichotomy max error","%",2, ! & error2d) ! call WRITEDIAGFI(ngrid,"zqsat","zqsat","kg",3, ! & zqsat) ! ENDIF ! IF (ngrid.eq.1) THEN ! 1D ! call WRITEDIAGFI(ngrid,"error","incertitude sur glace","%",1, ! & error_out) call WRITEdiagfi(ngrid,"resist","resistance","s/m2",1, & res_out) call WRITEdiagfi(ngrid,"satu_bf","satu before","kg/kg",1, & satubf) call WRITEdiagfi(ngrid,"satu_af","satu after","kg/kg",1, & satuaf) call WRITEdiagfi(ngrid,"vapbf","h2ovap before","kg/kg",1, & zq0(1,1,igcm_h2o_vap)) call WRITEdiagfi(ngrid,"vapaf","h2ovap after","kg/kg",1, & zq(1,1,igcm_h2o_vap)) call WRITEdiagfi(ngrid,"icebf","h2oice before","kg/kg",1, & zq0(1,1,igcm_h2o_ice)) call WRITEdiagfi(ngrid,"iceaf","h2oice after","kg/kg",1, & zq(1,1,igcm_h2o_ice)) call WRITEdiagfi(ngrid,"ccnbf","ccn before","/kg",1, & zq0(1,1,igcm_ccn_number)) call WRITEdiagfi(ngrid,"ccnaf","ccn after","/kg",1, & zq(1,1,igcm_ccn_number)) c call WRITEDIAGFI(ngrid,"growthrate","growth rate","m^2/s",1, c & gr_out) c call WRITEDIAGFI(ngrid,"nuclearate","nucleation rate","",1, c & rate_out) c call WRITEDIAGFI(ngrid,"dM","ccn variation","kg",1, c & dM_out) c call WRITEDIAGFI(ngrid,"dN","ccn variation","#",1, c & dN_out) call WRITEdiagfi(ngrid,"zqsat","p vap sat","kg/kg",1, & zqsat) ! call WRITEDIAGFI(ngrid,"satu","ratio saturation","",1, ! & satu_out) call WRITEdiagfi(ngrid,"rice","ice radius","m",1, & rice) ! call WRITEDIAGFI(ngrid,"rdust_sca","rdust","m",1, ! & rdust) ! call WRITEDIAGFI(ngrid,"rsedcloud","rsedcloud","m",1, ! & rsedcloud) ! call WRITEDIAGFI(ngrid,"rhocloud","rhocloud","kg.m-3",1, ! & rhocloud) ! ENDIF #endif ENDIF ! endif test_flag !!!!!!!!!!!!!! TESTS OUTPUTS TESTS OUTPUTS TESTS OUTPUTS TESTS OUTPUTS !!!!!!!!!!!!!! TESTS OUTPUTS TESTS OUTPUTS TESTS OUTPUTS TESTS OUTPUTS !!!!!!!!!!!!!! TESTS OUTPUTS TESTS OUTPUTS TESTS OUTPUTS TESTS OUTPUTS return cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc c The so -called "phi" function is such as phi(r) - phi(r0) = t - t0 c It is an analytical solution to the ice radius growth equation, c with the approximation of a constant 'reduced' cunningham correction factor c (lambda in growthrate.F) taken at radius req instead of rice cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc c subroutine phi(rice,req,coeff1,coeff2,time) c c implicit none c c ! inputs c real rice ! ice radius c real req ! ice radius at equilibirum c real coeff1 ! coeff for the log c real coeff2 ! coeff for the arctan c c ! output c real time c c !local c real var c c ! 1.73205 is sqrt(3) c c var = max( c & abs(rice-req) / sqrt(rice*rice + rice*req + req*req),1e-30) c c time = c & coeff1 * c & log( var ) c & + coeff2 * 1.73205 * c & atan( (2*rice+req) / (1.73205*req) ) c c return c end END SUBROUTINE improvedclouds END MODULE improvedclouds_mod