| 1 | ! |
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| 2 | ! $Id: cond_evap_tstep_mod.f90 5268 2024-10-23 17:02:39Z fhourdin $ |
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| 3 | ! |
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| 4 | MODULE cond_evap_tstep_mod |
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| 5 | |
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| 6 | ! based on UPMC aerosol model by Slimane Bekki |
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| 7 | ! adapted for stratospheric sulfate aerosol in LMDZ by Christoph Kleinschmitt |
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| 8 | |
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| 9 | CONTAINS |
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| 10 | |
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| 11 | SUBROUTINE condens_evapor_rate_kelvin(R2SO4G,t_seri,pplay,R2SO4, & |
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| 12 | & DENSO4,f_r_wet,R2SO4ik,DENSO4ik,f_r_wetik,FL,ASO4,DNDR) |
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| 13 | ! |
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| 14 | ! INPUT: |
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| 15 | ! R2SO4G: number density of gaseous H2SO4 [molecules/cm3] |
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| 16 | ! t_seri: temperature (K) |
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| 17 | ! pplay: pressure (Pa) |
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| 18 | ! R2SO4: aerosol H2SO4 weight fraction (percent) - flat surface (does not depend on aerosol size) |
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| 19 | ! DENSO4: aerosol density (gr/cm3) |
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| 20 | ! f_r_wet: factor for converting dry to wet radius |
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| 21 | ! assuming 'flat surface' composition (does not depend on aerosol size) |
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| 22 | ! variables that depends on aerosol size because of Kelvin effect |
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| 23 | ! R2SO4Gik: number density of gaseous H2SO4 [molecules/cm3] - depends on aerosol size |
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| 24 | ! DENSO4ik: aerosol density (gr/cm3) - depends on aerosol size |
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| 25 | ! f_r_wetik: factor for converting dry to wet radius - depends on aerosol size |
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| 26 | ! RRSI: radius [cm] |
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| 27 | |
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| 28 | USE aerophys |
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| 29 | USE infotrac_phy |
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| 30 | USE yomcst_mod_h, ONLY : RPI |
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| 31 | USE sulfate_aer_mod, ONLY : wph2so4, surftension, solh2so4, rpmvh2so4 |
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| 32 | USE strataer_local_var_mod, ONLY : ALPH2SO4, RRSI |
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| 33 | |
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| 34 | IMPLICIT NONE |
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| 35 | |
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| 36 | REAL, PARAMETER :: third=1./3. |
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| 37 | |
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| 38 | ! input variables |
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| 39 | REAL :: R2SO4G !H2SO4 number density [molecules/cm3] |
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| 40 | REAL :: t_seri |
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| 41 | REAL :: pplay |
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| 42 | REAL :: R2SO4 |
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| 43 | REAL :: DENSO4 |
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| 44 | REAL :: f_r_wet |
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| 45 | REAL :: R2SO4ik(nbtr_bin), DENSO4ik(nbtr_bin), f_r_wetik(nbtr_bin) |
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| 46 | |
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| 47 | ! output variables |
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| 48 | REAL :: FL(nbtr_bin) |
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| 49 | REAL :: ASO4(nbtr_bin) |
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| 50 | REAL :: DNDR(nbtr_bin) |
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| 51 | |
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| 52 | ! local variables |
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| 53 | INTEGER :: IK |
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| 54 | REAL :: ALPHA,CST |
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| 55 | REAL :: WH2(nbtr_bin) |
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| 56 | REAL :: RP,VTK,AA,FL1,RKNUD |
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| 57 | REAL :: DND |
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| 58 | REAL :: ATOT,AH2O |
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| 59 | REAL :: RRSI_wet(nbtr_bin) |
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| 60 | REAL :: FPATH, WPP, XA, FKELVIN |
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| 61 | REAL :: surtens, mvh2so4, temp |
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| 62 | |
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| 63 | ! /// MOLEC CONDENSATION GROWTH (DUE TO CHANGES IN H2SO4 AND SO H2O) |
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| 64 | ! ------------------------------------------------------------------ |
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| 65 | ! EXCEPT CN |
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| 66 | ! RK:H2SO4 WEIGHT PERCENT DOESN'T CHANGE |
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| 67 | ! BE CAREFUL,H2SO4 WEIGHT PERCENTAGE |
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| 68 | |
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| 69 | ! MOLECULAR ACCOMODATION OF H2SO4 |
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| 70 | ! H2SO4 accommodation coefficient [condensation/evaporation] |
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| 71 | ALPHA = ALPH2SO4 |
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| 72 | ! FPLAIR=(2.281238E-5)*TAIR/PAIR |
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| 73 | ! 1.E2 (m to cm), |
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| 74 | CST=1.E2*2.281238E-5 |
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| 75 | ! same expression as in coagulate |
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| 76 | ! in coagulate: mean free path of air (Pruppacher and Klett, 2010, p.417) [m] |
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| 77 | ! mnfrpth=6.6E-8*(1.01325E+5/pplay(ilon,ilev))*(t_seri(ilon,ilev)/293.15) |
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| 78 | ! mnfrpth=2.28E-5*t_seri/pplay |
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| 79 | |
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| 80 | temp = min( max(t_seri, 190.), 300.) ! 190K <= temp <= 300K |
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| 81 | |
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| 82 | RRSI_wet(:)=RRSI(:)*f_r_wetik(:) |
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| 83 | |
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| 84 | ! Pruppa and Klett |
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| 85 | FPATH=CST*t_seri/pplay |
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| 86 | |
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| 87 | ! H2SO4 mass fraction in aerosol |
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| 88 | WH2(:)=R2SO4ik(:)*1.0E-2 |
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| 89 | |
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| 90 | ! ACTIVITY COEFFICIENT(SEE GIAUQUE,1951) |
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| 91 | ! AYERS ET AL (1980) |
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| 92 | ! (MU-MU0) |
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| 93 | ! RP=-10156.0/t_seri +16.259-(ACTSO4*4.184)/(8.31441*t_seri) |
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| 94 | ! DROPLET H2SO4 PRESSURE IN DYN.CM-2 |
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| 95 | ! RP=EXP(RP)*1.01325E6/0.086 |
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| 96 | !! RP=EXP(RP)*1.01325E6 |
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| 97 | ! H2SO4 NUMBER DENSITY NEAR DROPLET |
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| 98 | |
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| 99 | ! DND=RP*6.02E23/(8.31E7*t_seri) |
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| 100 | |
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| 101 | ! KELVIN EFFECT FACTOR |
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| 102 | !CK 20160613: bug fix, removed factor 250 (from original code by S. Bekki) |
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| 103 | !! AA =2.0*MH2O*72.0/(DENSO4*BOLZ*t_seri*250.0) |
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| 104 | ! AA =2.0*MH2O*72.0/(DENSO4*BOLZ*t_seri) |
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| 105 | |
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| 106 | ! MEAN KINETIC VELOCITY |
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| 107 | ! DYN*CM*K/(K*GR)=(CM/SEC2)*CM |
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| 108 | ! IN CM/SEC |
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| 109 | VTK=SQRT(8.0*BOLZ*t_seri/(RPI*MH2SO4)) |
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| 110 | ! KELVIN EFFECT FACTOR |
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| 111 | |
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| 112 | ! Loop on bin radius (RRSI in cm) |
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| 113 | DO IK=1,nbtr_bin |
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| 114 | |
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| 115 | IF(R2SO4ik(IK) > 0.0) THEN |
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| 116 | |
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| 117 | ! h2so4 mass fraction (0<wpp<1) |
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| 118 | wpp=R2SO4ik(IK)*1.e-2 |
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| 119 | xa=18.*wpp/(18.*wpp+98.*(1.-wpp)) |
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| 120 | ! equilibrium h2so4 number density over H2SO4/H2O solution (molec/cm3) |
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| 121 | DND=solh2so4(t_seri,xa) |
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| 122 | ! KELVIN EFFECT: |
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| 123 | ! surface tension (mN/m=1.e-3.kg/s2) = f(T,h2so4 mole fraction) |
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| 124 | surtens=surftension(temp,xa) |
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| 125 | ! partial molar volume of h2so4 (cm3.mol-1 =1.e-6.m3.mol-1) |
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| 126 | mvh2so4= rpmvh2so4(temp,R2SO4ik(IK)) |
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| 127 | ! Kelvin factor (MKS) |
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| 128 | fkelvin=exp( 2.*1.e-3*surtens*1.e-6*mvh2so4/ (1.e-2*RRSI_wet(IK)*rgas*temp) ) |
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| 129 | ! |
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| 130 | DNDR(IK) =DND*fkelvin |
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| 131 | |
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| 132 | FL1=RPI*ALPHA*VTK*(R2SO4G-DNDR(IK)) |
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| 133 | |
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| 134 | ! TURCO(1979) FOR HNO3:ALH2SO4 CONDENSATION= ALH2SO4 EVAPORATION |
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| 135 | ! RPI*R2*VTK IS EQUIVALENT TO DIFFUSION COEFFICIENT |
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| 136 | ! EXTENSION OF THE RELATION FOR DIFFUSION KINETICS |
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| 137 | ! KNUDSEN NUMBER FPATH/RRSI |
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| 138 | ! NEW VERSION (SEE NOTES) |
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| 139 | RKNUD=FPATH/RRSI_wet(IK) |
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| 140 | ! SENFELD |
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| 141 | FL(IK)=FL1*RRSI_wet(IK)**2*( 1.0 +RKNUD ) & |
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| 142 | & /( 1.0 +ALPHA/(2.0*RKNUD) +RKNUD ) |
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| 143 | ! TURCO |
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| 144 | ! RL= (4.0/3.0 +0.71/RKNUD)/(1.0+1.0/RKNUD) |
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| 145 | ! * +4.0*(1.0-ALPHA)/(3.0*ALPHA) |
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| 146 | ! FL=FL1*RRSI(IK)*RRSI(IK) |
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| 147 | ! * /( (3.0*ALPHA/4.0)*(1.0/RKNUD+RL*ALPHA) ) |
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| 148 | |
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| 149 | ! INITIAL NUMBER OF H2SO4 MOLEC OF 1 DROPLET |
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| 150 | ATOT=4.0*RPI*DENSO4ik(IK)*(RRSI_wet(IK)**3)/3.0 !attention: g and cm |
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| 151 | ASO4(IK)=WH2(IK)*ATOT/MH2SO4 !attention: g |
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| 152 | ! ATOT=4.0*RPI*dens_aer(I,J)/1000.*(RRSI(IK)**3)/3.0 |
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| 153 | ! ASO4=mfrac_H2SO4*ATOT/MH2SO4 |
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| 154 | ! INITIAL NUMBER OF H2O MOLEC OF 1 DROPLET |
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| 155 | AH2O=(1.0-WH2(IK))*ATOT/MH2O !attention: g |
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| 156 | |
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| 157 | ! CHANGE OF THE NUMBER OF H2SO4 MOLEC OF 1 DROPLET DURING DT |
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| 158 | ! IT IS FOR KEM BUT THERE ARE OTHER WAYS |
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| 159 | |
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| 160 | ENDIF |
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| 161 | |
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| 162 | ENDDO !loop over bins |
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| 163 | |
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| 164 | END SUBROUTINE condens_evapor_rate_kelvin |
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| 165 | |
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| 166 | !******************************************************************** |
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| 167 | SUBROUTINE condens_evapor_rate(R2SO4G,t_seri,pplay,ACTSO4,R2SO4, & |
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| 168 | & DENSO4,f_r_wet,FL,ASO4,DNDR) |
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| 169 | ! |
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| 170 | ! INPUT: |
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| 171 | ! R2SO4: aerosol H2SO4 weight fraction (percent) |
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| 172 | ! ACTSO4: H2SO4 activity |
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| 173 | ! R2SO4G: number density of gaseous H2SO4 [molecules/cm3] |
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| 174 | ! t_seri: temperature (K) |
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| 175 | ! DENSO4: aerosol density (gr/cm3) |
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| 176 | |
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| 177 | USE aerophys |
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| 178 | USE infotrac_phy |
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| 179 | USE yomcst_mod_h, ONLY : RPI |
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| 180 | USE strataer_local_var_mod, ONLY : ALPH2SO4, RRSI |
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| 181 | |
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| 182 | IMPLICIT NONE |
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| 183 | |
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| 184 | ! input variables |
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| 185 | REAL R2SO4G !H2SO4 number density [molecules/cm3] |
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| 186 | REAL t_seri |
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| 187 | REAL pplay |
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| 188 | REAL ACTSO4 |
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| 189 | REAL R2SO4 |
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| 190 | REAL DENSO4 |
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| 191 | REAL f_r_wet |
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| 192 | |
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| 193 | ! output variables |
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| 194 | REAL FL(nbtr_bin) |
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| 195 | REAL ASO4(nbtr_bin) |
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| 196 | REAL DNDR(nbtr_bin) |
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| 197 | |
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| 198 | ! local variables |
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| 199 | INTEGER IK |
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| 200 | REAL ALPHA,CST |
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| 201 | REAL WH2,RP,VTK,AA,FL1,RKNUD |
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| 202 | REAL DND |
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| 203 | REAL ATOT,AH2O |
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| 204 | REAL RRSI_wet(nbtr_bin) |
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| 205 | REAL FPATH |
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| 206 | |
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| 207 | ! /// MOLEC CONDENSATION GROWTH (DUE TO CHANGES IN H2SO4 AND SO H2O) |
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| 208 | ! ------------------------------------------------------------------ |
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| 209 | ! EXCEPT CN |
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| 210 | ! RK:H2SO4 WEIGHT PERCENT DOESN'T CHANGE |
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| 211 | ! BE CAREFUL,H2SO4 WEIGHT PERCENTAGE |
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| 212 | |
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| 213 | ! MOLECULAR ACCOMODATION OF H2SO4 |
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| 214 | ! H2SO4 accommodation coefficient [condensation/evaporation] |
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| 215 | ALPHA = ALPH2SO4 |
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| 216 | ! FPLAIR=(2.281238E-5)*TAIR/PAIR |
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| 217 | ! 1.E2 (m to cm), |
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| 218 | CST=1.E2*2.281238E-5 |
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| 219 | |
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| 220 | ! compute local wet particle radius [cm] |
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| 221 | RRSI_wet(:)=RRSI(:)*f_r_wet |
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| 222 | |
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| 223 | ! Pruppa and Klett |
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| 224 | FPATH=CST*t_seri/pplay |
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| 225 | |
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| 226 | |
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| 227 | ! H2SO4 mass fraction in aerosol |
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| 228 | WH2=R2SO4*1.0E-2 |
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| 229 | IF(WH2.EQ.0.0) RETURN |
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| 230 | ! ACTIVITY COEFFICIENT(SEE GIAUQUE,1951) |
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| 231 | ! AYERS ET AL (1980) |
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| 232 | ! (MU-MU0) |
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| 233 | RP=-10156.0/t_seri +16.259-(ACTSO4*4.184)/(8.31441*t_seri) |
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| 234 | ! DROPLET H2SO4 PRESSURE IN DYN.CM-2 |
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| 235 | RP=EXP(RP)*1.01325E6/0.086 |
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| 236 | ! RP=EXP(RP)*1.01325E6 |
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| 237 | ! H2SO4 NUMBER DENSITY NEAR DROPLET |
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| 238 | ! R=8.31E7 DYN.CM.MOL-1*K-1 |
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| 239 | ! R/AVOGADRO NUMBER=DYN.CM.MOLEC-1*K-1 |
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| 240 | DND=RP*6.02E23/(8.31E7*t_seri) |
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| 241 | ! MEAN KINETIC VELOCITY |
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| 242 | ! DYN*CM*K/(K*GR)=(CM/SEC2)*CM |
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| 243 | ! IN CM/SEC |
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| 244 | VTK=SQRT(8.0*BOLZ*t_seri/(RPI*MH2SO4)) |
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| 245 | ! KELVIN EFFECT FACTOR |
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| 246 | !CK 20160613: bug fix, removed factor 250 (from original code by S. Bekki) |
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| 247 | ! AA =2.0*MH2O*72.0/(DENSO4*BOLZ*t_seri*250.0) |
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| 248 | AA =2.0*MH2O*72.0/(DENSO4*BOLZ*t_seri) |
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| 249 | |
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| 250 | ! Loop on bin radius (RRSI in cm) |
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| 251 | DO IK=1,nbtr_bin |
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| 252 | ! KELVIN EFFECT |
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| 253 | DNDR(IK) =DND*EXP(AA/RRSI_wet(IK)) |
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| 254 | |
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| 255 | FL1=RPI*ALPHA*VTK*(R2SO4G-DNDR(IK)) |
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| 256 | |
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| 257 | ! TURCO(1979) FOR HNO3:ALH2SO4 CONDENSATION= ALH2SO4 EVAPORATION |
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| 258 | ! RPI*R2*VTK IS EQUIVALENT TO DIFFUSION COEFFICIENT |
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| 259 | ! EXTENSION OF THE RELATION FOR DIFFUSION KINETICS |
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| 260 | ! KNUDSEN NUMBER FPATH/RRSI |
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| 261 | ! NEW VERSION (SEE NOTES) |
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| 262 | RKNUD=FPATH/RRSI_wet(IK) |
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| 263 | ! SENFELD |
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| 264 | FL(IK)=FL1*RRSI_wet(IK)**2*( 1.0 +RKNUD ) & |
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| 265 | & /( 1.0 +ALPHA/(2.0*RKNUD) +RKNUD ) |
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| 266 | ! TURCO |
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| 267 | ! RL= (4.0/3.0 +0.71/RKNUD)/(1.0+1.0/RKNUD) |
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| 268 | ! * +4.0*(1.0-ALPHA)/(3.0*ALPHA) |
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| 269 | ! FL=FL1*RRSI(IK)*RRSI(IK) |
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| 270 | ! * /( (3.0*ALPHA/4.0)*(1.0/RKNUD+RL*ALPHA) ) |
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| 271 | |
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| 272 | ! INITIAL NUMBER OF H2SO4 MOLEC OF 1 DROPLET |
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| 273 | ATOT=4.0*RPI*DENSO4*(RRSI_wet(IK)**3)/3.0 !attention: g and cm |
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| 274 | ASO4(IK)=WH2*ATOT/MH2SO4 !attention: g |
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| 275 | ! ATOT=4.0*RPI*dens_aer(I,J)/1000.*(RRSI(IK)**3)/3.0 |
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| 276 | ! ASO4=mfrac_H2SO4*ATOT/MH2SO4 |
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| 277 | ! INITIAL NUMBER OF H2O MOLEC OF 1 DROPLET |
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| 278 | AH2O=(1.0-WH2)*ATOT/MH2O !attention: g |
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| 279 | |
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| 280 | ! CHANGE OF THE NUMBER OF H2SO4 MOLEC OF 1 DROPLET DURING DT |
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| 281 | ! IT IS FOR KEM BUT THERE ARE OTHER WAYS |
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| 282 | |
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| 283 | ENDDO !loop over bins |
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| 284 | |
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| 285 | END SUBROUTINE condens_evapor_rate |
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| 286 | |
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| 287 | !******************************************************************** |
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| 288 | SUBROUTINE condens_evapor_part(dt,FL,ASO4,f_r_wet,tr_seri) |
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| 289 | |
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| 290 | USE aerophys |
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| 291 | USE infotrac_phy |
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| 292 | USE yomcst_mod_h, ONLY : RPI |
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| 293 | USE strataer_local_var_mod, ONLY : RRSI,Vbin |
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| 294 | |
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| 295 | IMPLICIT NONE |
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| 296 | |
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| 297 | ! input variables |
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| 298 | REAL dt |
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| 299 | REAL FL(nbtr_bin) |
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| 300 | REAL ASO4(nbtr_bin) |
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| 301 | REAL f_r_wet |
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| 302 | |
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| 303 | ! output variables |
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| 304 | REAL tr_seri(nbtr) |
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| 305 | |
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| 306 | ! local variables |
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| 307 | REAL tr_seri_new(nbtr) |
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| 308 | INTEGER IK,JK,k |
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| 309 | REAL Vnew |
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| 310 | REAL RRSI_wet(nbtr_bin) |
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| 311 | REAL Vbin_wet(nbtr_bin) |
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| 312 | REAL sum_IK(nbtr_bin) |
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| 313 | REAL ff(nbtr_bin,nbtr_bin) |
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| 314 | |
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| 315 | tr_seri_new(:)=tr_seri(:) |
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| 316 | |
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| 317 | ! compute local wet particle radius and volume |
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| 318 | RRSI_wet(:)=RRSI(:)*f_r_wet |
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| 319 | Vbin_wet(:)=Vbin(:)*f_r_wet**3 *1.e6 !Vbin_wet in cm3 (as Vnew) |
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| 320 | |
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| 321 | ! compute distribution factor for particles of intermediate size (from Jacobson 1994, equation 13) |
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| 322 | DO IK=1,nbtr_bin |
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| 323 | Vnew=4.0*RPI*(RRSI_wet(IK)**3)/3.0*(1.+FL(IK)*dt/ASO4(IK)) |
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| 324 | ff(IK,:)=0.0 |
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| 325 | DO k=1, nbtr_bin |
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| 326 | IF (k.LE.(nbtr_bin-1)) THEN |
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| 327 | IF (Vbin_wet(k).LE.Vnew.AND.Vnew.LT.Vbin_wet(k+1)) THEN |
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| 328 | ff(IK,k)= Vbin_wet(k)/Vnew*(Vbin_wet(k+1)-Vnew)/(Vbin_wet(k+1)-Vbin_wet(k)) |
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| 329 | ENDIF |
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| 330 | ENDIF |
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| 331 | IF (k.EQ.1.AND.Vnew.LE.Vbin_wet(k)) THEN |
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| 332 | ff(IK,k)= 1. |
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| 333 | ENDIF |
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| 334 | IF (k.GT.1) THEN |
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| 335 | IF (Vbin_wet(k-1).LT.Vnew.AND.Vnew.LT.Vbin_wet(k)) THEN |
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| 336 | ff(IK,k)= 1.-ff(IK,k-1) |
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| 337 | ENDIF |
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| 338 | ENDIF |
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| 339 | IF (k.EQ.nbtr_bin.AND.Vnew.GE.Vbin_wet(k)) THEN |
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| 340 | ff(IK,k)= 1. |
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| 341 | ENDIF |
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| 342 | ENDDO |
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| 343 | ! correction of ff for volume conservation |
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| 344 | DO k=1, nbtr_bin |
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| 345 | ff(IK,k)=ff(IK,k)*Vnew/Vbin_wet(k) |
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| 346 | ENDDO |
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| 347 | ENDDO !loop over bins |
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| 348 | |
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| 349 | DO IK=1, nbtr_bin |
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| 350 | sum_IK(IK)=0.0 |
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| 351 | DO JK=1, nbtr_bin |
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| 352 | sum_IK(IK)=sum_IK(IK)+tr_seri(JK+nbtr_sulgas)*ff(JK,IK) |
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| 353 | ENDDO |
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| 354 | ! compute new particle concentrations |
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| 355 | tr_seri_new(IK+nbtr_sulgas)=sum_IK(IK) |
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| 356 | ENDDO |
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| 357 | |
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| 358 | tr_seri(:)=tr_seri_new(:) |
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| 359 | |
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| 360 | END SUBROUTINE condens_evapor_part |
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| 361 | |
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| 362 | END MODULE cond_evap_tstep_mod |
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