[3526] | 1 | ! |
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| 2 | ! $Id: coagulate.F90 3677 2020-05-06 15:18:32Z jyg $ |
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| 3 | ! |
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[2690] | 4 | SUBROUTINE COAGULATE(pdtcoag,mdw,tr_seri,t_seri,pplay,dens_aer,is_strato) |
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| 5 | ! ----------------------------------------------------------------------- |
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| 6 | ! |
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| 7 | ! Author : Christoph Kleinschmitt (with Olivier Boucher) |
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| 8 | ! ------ |
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| 9 | ! |
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| 10 | ! purpose |
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| 11 | ! ------- |
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| 12 | ! |
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| 13 | ! interface |
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| 14 | ! --------- |
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| 15 | ! input |
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| 16 | ! pdtphys time step duration [sec] |
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| 17 | ! tr_seri tracer mixing ratios [kg/kg] |
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| 18 | ! mdw # or mass median diameter [m] |
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| 19 | ! |
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| 20 | ! method |
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| 21 | ! ------ |
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| 22 | ! |
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| 23 | ! ----------------------------------------------------------------------- |
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| 24 | |
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| 25 | USE dimphy, ONLY : klon,klev |
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| 26 | USE aerophys |
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[3677] | 27 | USE infotrac_phy |
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[2690] | 28 | USE phys_local_var_mod, ONLY: DENSO4, f_r_wet |
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| 29 | USE YOMCST |
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| 30 | |
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| 31 | IMPLICIT NONE |
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| 32 | |
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| 33 | !-------------------------------------------------------- |
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| 34 | |
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| 35 | ! transfer variables when calling this routine |
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| 36 | REAL,INTENT(IN) :: pdtcoag ! Time step in coagulation routine [s] |
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| 37 | REAL,DIMENSION(nbtr_bin),INTENT(IN) :: mdw ! aerosol particle diameter in each bin [m] |
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| 38 | REAL,DIMENSION(klon,klev,nbtr),INTENT(INOUT) :: tr_seri ! Concentration Traceur [U/KgA] |
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| 39 | REAL,DIMENSION(klon,klev),INTENT(IN) :: t_seri ! Temperature |
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| 40 | REAL,DIMENSION(klon,klev),INTENT(IN) :: pplay ! pression pour le mileu de chaque couche (en Pa) |
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| 41 | REAL,DIMENSION(klon,klev) :: dens_aer! density of aerosol [kg/m3 aerosol] with default H2SO4 mass |
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| 42 | LOGICAL,DIMENSION(klon,klev),INTENT(IN) :: is_strato |
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| 43 | |
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| 44 | ! local variables in coagulation routine |
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| 45 | INTEGER :: i,j,k,nb,ilon,ilev |
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| 46 | REAL, DIMENSION(nbtr_bin) :: radius ! aerosol particle radius in each bin [m] |
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| 47 | REAL, DIMENSION(klon,klev,nbtr_bin) :: tr_t ! Concentration Traceur at time t [U/KgA] |
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| 48 | REAL, DIMENSION(klon,klev,nbtr_bin) :: tr_tp1 ! Concentration Traceur at time t+1 [U/KgA] |
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| 49 | REAL, DIMENSION(nbtr_bin,nbtr_bin,nbtr_bin) :: ff ! Volume fraction of intermediate particles |
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| 50 | REAL, DIMENSION(nbtr_bin) :: V ! Volume of bins |
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| 51 | REAL, DIMENSION(nbtr_bin,nbtr_bin) :: Vij ! Volume sum of i and j |
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| 52 | REAL :: eta ! Dynamic viscosity of air |
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| 53 | REAL, PARAMETER :: mair=4.8097E-26 ! Average mass of an air molecule [kg] |
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| 54 | REAL :: zrho ! Density of air |
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| 55 | REAL :: mnfrpth ! Mean free path of air |
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| 56 | REAL, DIMENSION(nbtr_bin) :: Kn ! Knudsen number of particle i |
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| 57 | REAL, DIMENSION(nbtr_bin) :: Di ! Particle diffusion coefficient |
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| 58 | REAL, DIMENSION(nbtr_bin) :: m_par ! Mass of particle i |
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| 59 | REAL, DIMENSION(nbtr_bin) :: thvelpar! Thermal velocity of particle i |
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| 60 | REAL, DIMENSION(nbtr_bin) :: mfppar ! Mean free path of particle i |
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| 61 | REAL, DIMENSION(nbtr_bin) :: delta! delta of particle i (from equation 21) |
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| 62 | REAL, DIMENSION(nbtr_bin,nbtr_bin) :: beta ! Coagulation kernel from Brownian diffusion |
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| 63 | REAL :: beta_const ! Constant coagulation kernel (for comparison) |
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| 64 | REAL :: num |
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| 65 | REAL :: numi |
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| 66 | REAL :: denom |
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| 67 | |
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[2949] | 68 | ! Additional variables for coagulation enhancement factor due to van der Waals forces |
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| 69 | ! Taken from Chan and Mozurkewich, Measurement of the coagulation rate constant for sulfuric acid |
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| 70 | ! particles as a function of particle size using TDMA, Aerosol Science, 32, 321-339, 2001. |
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| 71 | !--ok_vdw is 0 for no vdW forces, 1 for E(0), 2 for E(infinity) |
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| 72 | INTEGER, PARAMETER :: ok_vdw = 0 |
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| 73 | REAL, PARAMETER :: avdW1 = 0.0757 |
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| 74 | REAL, PARAMETER :: avdW3 = 0.0015 |
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| 75 | REAL, PARAMETER :: bvdW0 = 0.0151 |
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| 76 | REAL, PARAMETER :: bvdW1 = -0.186 |
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| 77 | REAL, PARAMETER :: bvdW3 = -0.0163 |
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| 78 | REAL, PARAMETER :: AvdW = 6.4e-20 !Hamaker constant in J = 1e7 erg |
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| 79 | REAL :: AvdWi |
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| 80 | REAL :: xvdW |
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| 81 | REAL :: EvdW |
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| 82 | |
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[2690] | 83 | DO i=1, nbtr_bin |
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| 84 | radius(i)=mdw(i)/2. |
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| 85 | V(i)= radius(i)**3. !neglecting factor 4*RPI/3 |
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| 86 | ENDDO |
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| 87 | |
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| 88 | DO j=1, nbtr_bin |
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| 89 | DO i=1, nbtr_bin |
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| 90 | Vij(i,j)= V(i)+V(j) |
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| 91 | ENDDO |
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| 92 | ENDDO |
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| 93 | |
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| 94 | !--pre-compute the f(i,j,k) from Jacobson equation 13 |
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| 95 | ff=0.0 |
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| 96 | DO k=1, nbtr_bin |
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| 97 | DO j=1, nbtr_bin |
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| 98 | DO i=1, nbtr_bin |
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| 99 | IF (k.EQ.1) THEN |
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| 100 | ff(i,j,k)= 0.0 |
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| 101 | ELSEIF (k.GT.1.AND.V(k-1).LT.Vij(i,j).AND.Vij(i,j).LT.V(k)) THEN |
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| 102 | ff(i,j,k)= 1.-ff(i,j,k-1) |
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| 103 | ELSEIF (k.EQ.nbtr_bin) THEN |
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| 104 | IF (Vij(i,j).GE.v(k)) THEN |
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| 105 | ff(i,j,k)= 1. |
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| 106 | ELSE |
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| 107 | ff(i,j,k)= 0.0 |
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| 108 | ENDIF |
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| 109 | ELSEIF (k.LE.(nbtr_bin-1).AND.V(k).LE.Vij(i,j).AND.Vij(i,j).LT.V(k+1)) THEN |
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| 110 | ff(i,j,k)= V(k)/Vij(i,j)*(V(k+1)-Vij(i,j))/(V(k+1)-V(k)) |
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| 111 | ENDIF |
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| 112 | ENDDO |
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| 113 | ENDDO |
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| 114 | ENDDO |
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| 115 | |
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| 116 | DO ilon=1, klon |
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| 117 | DO ilev=1, klev |
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| 118 | !only in the stratosphere |
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| 119 | IF (is_strato(ilon,ilev)) THEN |
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| 120 | !compute actual wet particle radius & volume for every grid box |
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| 121 | DO i=1, nbtr_bin |
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| 122 | radius(i)=f_r_wet(ilon,ilev)*mdw(i)/2. |
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| 123 | V(i)= radius(i)**3. !neglecting factor 4*RPI/3 |
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| 124 | ENDDO |
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| 125 | |
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| 126 | !--Calculations for the coagulation kernel--------------------------------------------------------- |
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| 127 | |
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| 128 | zrho=pplay(ilon,ilev)/t_seri(ilon,ilev)/RD |
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| 129 | |
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| 130 | !--initialize the tracer at time t and convert from [number/KgA] to [number/m3] |
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| 131 | DO i=1, nbtr_bin |
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| 132 | tr_t(ilon,ilev,i) = tr_seri(ilon,ilev,i+nbtr_sulgas) * zrho |
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| 133 | ENDDO |
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| 134 | |
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| 135 | ! mean free path of air (Pruppacher and Klett, 2010, p.417) [m] |
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| 136 | mnfrpth=6.6E-8*(1.01325E+5/pplay(ilon,ilev))*(t_seri(ilon,ilev)/293.15) |
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| 137 | ! mnfrpth=2.*eta/(zrho*thvelair) |
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| 138 | ! mean free path of air (Prupp. Klett) in [10^-6 m] |
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| 139 | ! ZLAIR = 0.066 *(1.01325E+5/PPLAY)*(T_SERI/293.15)*1.E-06 |
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| 140 | |
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| 141 | ! dynamic viscosity of air (Pruppacher and Klett, 2010, p.417) [kg/(m*s)] |
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| 142 | IF (t_seri(ilon,ilev).GE.273.15) THEN |
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| 143 | eta=(1.718+0.0049*(t_seri(ilon,ilev)-273.15))*1.E-5 |
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| 144 | ELSE |
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| 145 | eta=(1.718+0.0049*(t_seri(ilon,ilev)-273.15)-1.2E-5*(t_seri(ilon,ilev)-273.15)**2)*1.E-5 |
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| 146 | ENDIF |
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| 147 | |
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| 148 | !--pre-compute the particle diffusion coefficient Di(i) from equation 18 |
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| 149 | Di=0.0 |
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| 150 | DO i=1, nbtr_bin |
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| 151 | Kn(i)=mnfrpth/radius(i) |
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| 152 | Di(i)=RKBOL*t_seri(ilon,ilev)/(6.*RPI*radius(i)*eta)*(1.+Kn(i)*(1.249+0.42*exp(-0.87/Kn(i)))) |
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| 153 | ENDDO |
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| 154 | |
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| 155 | !--pre-compute the thermal velocity of a particle thvelpar(i) from equation 20 |
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| 156 | thvelpar=0.0 |
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| 157 | DO i=1, nbtr_bin |
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| 158 | m_par(i)=4./3.*RPI*radius(i)**3.*DENSO4(ilon,ilev)*1000. |
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| 159 | thvelpar(i)=sqrt(8.*RKBOL*t_seri(ilon,ilev)/(RPI*m_par(i))) |
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| 160 | ENDDO |
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| 161 | |
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| 162 | !--pre-compute the particle mean free path mfppar(i) from equation 22 |
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| 163 | mfppar=0.0 |
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| 164 | DO i=1, nbtr_bin |
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| 165 | mfppar(i)=8.*Di(i)/(RPI*thvelpar(i)) |
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| 166 | ENDDO |
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| 167 | |
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| 168 | !--pre-compute the mean distance delta(i) from the center of a sphere reached by particles |
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| 169 | !--leaving the surface of the sphere and traveling a distance of particle mfppar(i) from equation 21 |
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| 170 | delta=0.0 |
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| 171 | DO i=1, nbtr_bin |
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| 172 | delta(i)=((2.*radius(i)+mfppar(i))**3.-(4.*radius(i)**2.+mfppar(i)**2.)**1.5)/ & |
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| 173 | & (6.*radius(i)*mfppar(i))-2.*radius(i) |
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| 174 | ENDDO |
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| 175 | |
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[2949] | 176 | !--pre-compute the beta(i,j) from equation 17 in Jacobson |
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[2690] | 177 | num=0.0 |
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| 178 | DO j=1, nbtr_bin |
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| 179 | DO i=1, nbtr_bin |
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[2949] | 180 | ! |
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[2690] | 181 | num=4.*RPI*(radius(i)+radius(j))*(Di(i)+Di(j)) |
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| 182 | denom=(radius(i)+radius(j))/(radius(i)+radius(j)+sqrt(delta(i)**2.+delta(j)**2.))+ & |
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| 183 | & 4.*(Di(i)+Di(j))/(sqrt(thvelpar(i)**2.+thvelpar(j)**2.)*(radius(i)+radius(j))) |
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| 184 | beta(i,j)=num/denom |
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[2949] | 185 | ! |
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| 186 | !--compute enhancement factor due to van der Waals forces |
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| 187 | IF (ok_vdw .EQ. 0) THEN !--no enhancement factor |
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| 188 | Evdw=1.0 |
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| 189 | ELSEIF (ok_vdw .EQ. 1) THEN !--E(0) case |
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[2950] | 190 | AvdWi = AvdW/(RKBOL*t_seri(ilon,ilev))*(4.*radius(i)*radius(j))/(radius(i)+radius(j))**2. |
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[2949] | 191 | xvdW = LOG(1.+AvdWi) |
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| 192 | EvdW = 1. + avdW1*xvdW + avdW3*xvdW**3 |
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| 193 | ELSEIF (ok_vdw .EQ. 2) THEN !--E(infinity) case |
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[2950] | 194 | AvdWi = AvdW/(RKBOL*t_seri(ilon,ilev))*(4.*radius(i)*radius(j))/(radius(i)+radius(j))**2. |
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[2949] | 195 | xvdW = LOG(1.+AvdWi) |
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| 196 | EvdW = 1. + SQRT(AvdWi/3.)/(1.+bvdW0*SQRT(AvdWi)) + bvdW1*xvdW + bvdW3*xvdW**3. |
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| 197 | ENDIF |
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| 198 | ! |
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| 199 | beta(i,j)=beta(i,j)*EvdW |
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| 200 | |
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[2690] | 201 | ENDDO |
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| 202 | ENDDO |
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| 203 | |
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| 204 | !--external loop for equation 14 |
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| 205 | DO k=1, nbtr_bin |
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| 206 | |
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| 207 | !--calculating denominator sum |
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| 208 | denom=0.0 |
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| 209 | DO j=1, nbtr_bin |
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| 210 | denom=denom+(1.-ff(k,j,k))*beta(k,j)*tr_t(ilon,ilev,j) |
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| 211 | ENDDO |
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| 212 | |
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| 213 | IF (k.EQ.1) THEN |
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| 214 | !--calculate new concentration of smallest bin |
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| 215 | tr_tp1(ilon,ilev,k)=tr_t(ilon,ilev,k)/(1.+pdtcoag*denom) |
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| 216 | ELSE |
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| 217 | !--calculating double sum terms in numerator of eq 14 |
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| 218 | num=0.0 |
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| 219 | DO j=1, k |
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| 220 | numi=0.0 |
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| 221 | DO i=1, k-1 |
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| 222 | numi=numi+ff(i,j,k)*beta(i,j)*V(i)*tr_tp1(ilon,ilev,i)*tr_t(ilon,ilev,j) |
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| 223 | ENDDO |
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| 224 | num=num+numi |
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| 225 | ENDDO |
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| 226 | |
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| 227 | !--calculate new concentration of other bins |
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| 228 | tr_tp1(ilon,ilev,k)=(V(k)*tr_t(ilon,ilev,k)+pdtcoag*num)/(1.+pdtcoag*denom)/V(k) |
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| 229 | ENDIF |
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| 230 | |
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| 231 | ENDDO !--end of loop k |
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| 232 | |
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| 233 | !--convert tracer concentration back from [number/m3] to [number/KgA] and write into tr_seri |
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| 234 | DO i=1, nbtr_bin |
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| 235 | tr_seri(ilon,ilev,i+nbtr_sulgas) = tr_tp1(ilon,ilev,i) / zrho |
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| 236 | ENDDO |
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| 237 | |
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| 238 | ENDIF ! IF IN STRATOSPHERE |
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| 239 | ENDDO !--end of loop klev |
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| 240 | ENDDO !--end of loop klon |
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| 241 | |
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| 242 | END SUBROUTINE COAGULATE |
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