| [3526] | 1 | ! |
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| 2 | ! $Id: coagulate.f90 5285 2024-10-28 13:33:29Z fhourdin $ |
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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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| [5285] | 25 | USE yomcst_mod_h |
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| [2690] | 26 | USE dimphy, ONLY : klon,klev |
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| 27 | USE aerophys |
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| [3677] | 28 | USE infotrac_phy |
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| [4950] | 29 | USE phys_local_var_mod, ONLY: DENSO4, DENSO4B, f_r_wet, f_r_wetB |
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| 30 | USE strataer_local_var_mod, ONLY: flag_new_strat_compo |
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| [5274] | 31 | |
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| [2690] | 32 | IMPLICIT NONE |
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| 33 | |
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| 34 | !-------------------------------------------------------- |
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| 35 | |
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| 36 | ! transfer variables when calling this routine |
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| 37 | REAL,INTENT(IN) :: pdtcoag ! Time step in coagulation routine [s] |
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| 38 | REAL,DIMENSION(nbtr_bin),INTENT(IN) :: mdw ! aerosol particle diameter in each bin [m] |
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| 39 | REAL,DIMENSION(klon,klev,nbtr),INTENT(INOUT) :: tr_seri ! Concentration Traceur [U/KgA] |
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| 40 | REAL,DIMENSION(klon,klev),INTENT(IN) :: t_seri ! Temperature |
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| 41 | REAL,DIMENSION(klon,klev),INTENT(IN) :: pplay ! pression pour le mileu de chaque couche (en Pa) |
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| 42 | REAL,DIMENSION(klon,klev) :: dens_aer! density of aerosol [kg/m3 aerosol] with default H2SO4 mass |
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| 43 | LOGICAL,DIMENSION(klon,klev),INTENT(IN) :: is_strato |
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| 44 | |
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| 45 | ! local variables in coagulation routine |
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| 46 | INTEGER :: i,j,k,nb,ilon,ilev |
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| [4950] | 47 | REAL, DIMENSION(nbtr_bin) :: radiusdry ! dry aerosol particle radius in each bin [m] |
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| 48 | REAL, DIMENSION(nbtr_bin) :: radiuswet ! wet aerosol particle radius in each bin [m] |
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| [2690] | 49 | REAL, DIMENSION(klon,klev,nbtr_bin) :: tr_t ! Concentration Traceur at time t [U/KgA] |
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| 50 | REAL, DIMENSION(klon,klev,nbtr_bin) :: tr_tp1 ! Concentration Traceur at time t+1 [U/KgA] |
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| 51 | REAL, DIMENSION(nbtr_bin,nbtr_bin,nbtr_bin) :: ff ! Volume fraction of intermediate particles |
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| [4950] | 52 | REAL, DIMENSION(nbtr_bin) :: Vdry ! Volume dry of bins |
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| 53 | REAL, DIMENSION(nbtr_bin) :: Vwet ! Volume wet of bins |
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| [2690] | 54 | REAL, DIMENSION(nbtr_bin,nbtr_bin) :: Vij ! Volume sum of i and j |
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| 55 | REAL :: eta ! Dynamic viscosity of air |
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| 56 | REAL, PARAMETER :: mair=4.8097E-26 ! Average mass of an air molecule [kg] |
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| 57 | REAL :: zrho ! Density of air |
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| 58 | REAL :: mnfrpth ! Mean free path of air |
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| 59 | REAL, DIMENSION(nbtr_bin) :: Kn ! Knudsen number of particle i |
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| 60 | REAL, DIMENSION(nbtr_bin) :: Di ! Particle diffusion coefficient |
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| 61 | REAL, DIMENSION(nbtr_bin) :: m_par ! Mass of particle i |
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| 62 | REAL, DIMENSION(nbtr_bin) :: thvelpar! Thermal velocity of particle i |
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| 63 | REAL, DIMENSION(nbtr_bin) :: mfppar ! Mean free path of particle i |
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| 64 | REAL, DIMENSION(nbtr_bin) :: delta! delta of particle i (from equation 21) |
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| 65 | REAL, DIMENSION(nbtr_bin,nbtr_bin) :: beta ! Coagulation kernel from Brownian diffusion |
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| 66 | REAL :: beta_const ! Constant coagulation kernel (for comparison) |
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| 67 | REAL :: num |
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| 68 | REAL :: numi |
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| 69 | REAL :: denom |
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| 70 | |
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| [2949] | 71 | ! Additional variables for coagulation enhancement factor due to van der Waals forces |
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| [5274] | 72 | ! Taken from Chan and Mozurkewich, Measurement of the coagulation rate constant for sulfuric acid |
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| [2949] | 73 | ! particles as a function of particle size using TDMA, Aerosol Science, 32, 321-339, 2001. |
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| 74 | !--ok_vdw is 0 for no vdW forces, 1 for E(0), 2 for E(infinity) |
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| 75 | INTEGER, PARAMETER :: ok_vdw = 0 |
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| 76 | REAL, PARAMETER :: avdW1 = 0.0757 |
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| 77 | REAL, PARAMETER :: avdW3 = 0.0015 |
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| 78 | REAL, PARAMETER :: bvdW0 = 0.0151 |
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| 79 | REAL, PARAMETER :: bvdW1 = -0.186 |
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| 80 | REAL, PARAMETER :: bvdW3 = -0.0163 |
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| 81 | REAL, PARAMETER :: AvdW = 6.4e-20 !Hamaker constant in J = 1e7 erg |
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| 82 | REAL :: AvdWi |
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| 83 | REAL :: xvdW |
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| 84 | REAL :: EvdW |
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| 85 | |
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| [4762] | 86 | |
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| [4950] | 87 | ! ff(i,j,k): Volume fraction of Vi,j that is partitioned to each model bin k |
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| 88 | ! just need to be calculated in model initialization because mdw(:) size is fixed |
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| 89 | ! no need to recalculate radius, Vdry, Vij, and ff every timestep because it is for |
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| 90 | ! dry aerosols |
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| [2690] | 91 | DO i=1, nbtr_bin |
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| [4950] | 92 | radiusdry(i)=mdw(i)/2. |
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| 93 | Vdry(i)=radiusdry(i)**3. !neglecting factor 4*RPI/3 |
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| 94 | Vwet(i)=0.0 |
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| [2690] | 95 | ENDDO |
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| 96 | |
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| 97 | DO j=1, nbtr_bin |
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| [4950] | 98 | DO i=1, nbtr_bin |
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| 99 | Vij(i,j)= Vdry(i)+Vdry(j) |
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| 100 | ENDDO |
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| [2690] | 101 | ENDDO |
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| [4950] | 102 | |
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| [2690] | 103 | !--pre-compute the f(i,j,k) from Jacobson equation 13 |
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| 104 | ff=0.0 |
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| 105 | DO k=1, nbtr_bin |
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| 106 | DO j=1, nbtr_bin |
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| 107 | DO i=1, nbtr_bin |
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| 108 | IF (k.EQ.1) THEN |
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| 109 | ff(i,j,k)= 0.0 |
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| [4950] | 110 | ELSEIF (k.GT.1.AND.Vdry(k-1).LT.Vij(i,j).AND.Vij(i,j).LT.Vdry(k)) THEN |
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| [2690] | 111 | ff(i,j,k)= 1.-ff(i,j,k-1) |
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| 112 | ELSEIF (k.EQ.nbtr_bin) THEN |
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| [4950] | 113 | IF (Vij(i,j).GE.Vdry(k)) THEN |
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| [2690] | 114 | ff(i,j,k)= 1. |
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| 115 | ELSE |
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| 116 | ff(i,j,k)= 0.0 |
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| 117 | ENDIF |
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| [4950] | 118 | ELSEIF (k.LE.(nbtr_bin-1).AND.Vdry(k).LE.Vij(i,j).AND.Vij(i,j).LT.Vdry(k+1)) THEN |
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| 119 | ff(i,j,k)= Vdry(k)/Vij(i,j)*(Vdry(k+1)-Vij(i,j))/(Vdry(k+1)-Vdry(k)) |
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| [2690] | 120 | ENDIF |
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| 121 | ENDDO |
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| 122 | ENDDO |
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| 123 | ENDDO |
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| [4950] | 124 | ! End of just need to be calculated at initialization because mdw(:) size is fixed |
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| 125 | |
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| [2690] | 126 | DO ilon=1, klon |
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| 127 | DO ilev=1, klev |
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| 128 | !only in the stratosphere |
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| 129 | IF (is_strato(ilon,ilev)) THEN |
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| 130 | !compute actual wet particle radius & volume for every grid box |
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| [4950] | 131 | IF(flag_new_strat_compo) THEN |
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| 132 | DO i=1, nbtr_bin |
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| 133 | radiuswet(i)=f_r_wetB(ilon,ilev,i)*mdw(i)/2. |
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| 134 | Vwet(i)= radiuswet(i)**3. !neglecting factor 4*RPI/3 |
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| 135 | !! Vwet(i)= Vdry(i)*(f_r_wetB(ilon,ilev,i)**3) |
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| 136 | ENDDO |
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| 137 | ELSE |
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| 138 | DO i=1, nbtr_bin |
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| 139 | radiuswet(i)=f_r_wet(ilon,ilev)*mdw(i)/2. |
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| 140 | Vwet(i)= radiuswet(i)**3. !neglecting factor 4*RPI/3 |
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| 141 | !! Vwet(i)= Vdry(i)*(f_r_wet(ilon,ilev)**3) |
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| 142 | ENDDO |
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| 143 | ENDIF |
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| 144 | |
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| [2690] | 145 | !--Calculations for the coagulation kernel--------------------------------------------------------- |
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| 146 | |
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| 147 | zrho=pplay(ilon,ilev)/t_seri(ilon,ilev)/RD |
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| 148 | |
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| 149 | !--initialize the tracer at time t and convert from [number/KgA] to [number/m3] |
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| 150 | DO i=1, nbtr_bin |
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| 151 | tr_t(ilon,ilev,i) = tr_seri(ilon,ilev,i+nbtr_sulgas) * zrho |
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| 152 | ENDDO |
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| 153 | |
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| 154 | ! mean free path of air (Pruppacher and Klett, 2010, p.417) [m] |
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| 155 | mnfrpth=6.6E-8*(1.01325E+5/pplay(ilon,ilev))*(t_seri(ilon,ilev)/293.15) |
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| 156 | ! mnfrpth=2.*eta/(zrho*thvelair) |
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| 157 | ! mean free path of air (Prupp. Klett) in [10^-6 m] |
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| 158 | ! ZLAIR = 0.066 *(1.01325E+5/PPLAY)*(T_SERI/293.15)*1.E-06 |
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| 159 | |
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| 160 | ! dynamic viscosity of air (Pruppacher and Klett, 2010, p.417) [kg/(m*s)] |
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| 161 | IF (t_seri(ilon,ilev).GE.273.15) THEN |
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| 162 | eta=(1.718+0.0049*(t_seri(ilon,ilev)-273.15))*1.E-5 |
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| 163 | ELSE |
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| 164 | 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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| 165 | ENDIF |
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| 166 | |
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| 167 | !--pre-compute the particle diffusion coefficient Di(i) from equation 18 |
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| 168 | Di=0.0 |
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| 169 | DO i=1, nbtr_bin |
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| [4950] | 170 | Kn(i)=mnfrpth/radiuswet(i) |
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| 171 | Di(i)=RKBOL*t_seri(ilon,ilev)/(6.*RPI*radiuswet(i)*eta)*(1.+Kn(i)*(1.249+0.42*exp(-0.87/Kn(i)))) |
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| [2690] | 172 | ENDDO |
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| 173 | |
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| 174 | !--pre-compute the thermal velocity of a particle thvelpar(i) from equation 20 |
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| 175 | thvelpar=0.0 |
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| [4950] | 176 | IF(flag_new_strat_compo) THEN |
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| 177 | DO i=1, nbtr_bin |
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| 178 | m_par(i)=4./3.*RPI*radiuswet(i)**3.*DENSO4B(ilon,ilev,i)*1000. |
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| 179 | thvelpar(i)=sqrt(8.*RKBOL*t_seri(ilon,ilev)/(RPI*m_par(i))) |
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| 180 | ENDDO |
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| 181 | ELSE |
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| 182 | DO i=1, nbtr_bin |
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| 183 | m_par(i)=4./3.*RPI*radiuswet(i)**3.*DENSO4(ilon,ilev)*1000. |
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| 184 | thvelpar(i)=sqrt(8.*RKBOL*t_seri(ilon,ilev)/(RPI*m_par(i))) |
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| 185 | ENDDO |
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| 186 | ENDIF |
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| [2690] | 187 | |
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| 188 | !--pre-compute the particle mean free path mfppar(i) from equation 22 |
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| 189 | mfppar=0.0 |
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| 190 | DO i=1, nbtr_bin |
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| 191 | mfppar(i)=8.*Di(i)/(RPI*thvelpar(i)) |
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| 192 | ENDDO |
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| 193 | |
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| 194 | !--pre-compute the mean distance delta(i) from the center of a sphere reached by particles |
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| 195 | !--leaving the surface of the sphere and traveling a distance of particle mfppar(i) from equation 21 |
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| 196 | delta=0.0 |
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| 197 | DO i=1, nbtr_bin |
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| [4950] | 198 | delta(i)=((2.*radiuswet(i)+mfppar(i))**3.-(4.*radiuswet(i)**2.+mfppar(i)**2.)**1.5)/ & |
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| 199 | & (6.*radiuswet(i)*mfppar(i))-2.*radiuswet(i) |
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| [2690] | 200 | ENDDO |
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| 201 | |
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| [4950] | 202 | ! beta(i,j): coagulation kernel (rate coefficient) of 2 colliding particles i,j |
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| [2949] | 203 | !--pre-compute the beta(i,j) from equation 17 in Jacobson |
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| [2690] | 204 | num=0.0 |
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| 205 | DO j=1, nbtr_bin |
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| 206 | DO i=1, nbtr_bin |
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| [2949] | 207 | ! |
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| [4950] | 208 | num=4.*RPI*(radiuswet(i)+radiuswet(j))*(Di(i)+Di(j)) |
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| 209 | denom=(radiuswet(i)+radiuswet(j))/(radiuswet(i)+radiuswet(j)+sqrt(delta(i)**2.+delta(j)**2.))+ & |
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| 210 | & 4.*(Di(i)+Di(j))/(sqrt(thvelpar(i)**2.+thvelpar(j)**2.)*(radiuswet(i)+radiuswet(j))) |
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| 211 | beta(i,j)=num/denom |
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| [2949] | 212 | ! |
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| 213 | !--compute enhancement factor due to van der Waals forces |
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| 214 | IF (ok_vdw .EQ. 0) THEN !--no enhancement factor |
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| [4950] | 215 | Evdw=1.0 |
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| [2949] | 216 | ELSEIF (ok_vdw .EQ. 1) THEN !--E(0) case |
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| [4950] | 217 | AvdWi = AvdW/(RKBOL*t_seri(ilon,ilev))*(4.*radiuswet(i)*radiuswet(j))/(radiuswet(i)+radiuswet(j))**2. |
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| 218 | xvdW = LOG(1.+AvdWi) |
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| 219 | EvdW = 1. + avdW1*xvdW + avdW3*xvdW**3 |
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| [2949] | 220 | ELSEIF (ok_vdw .EQ. 2) THEN !--E(infinity) case |
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| [4950] | 221 | AvdWi = AvdW/(RKBOL*t_seri(ilon,ilev))*(4.*radiuswet(i)*radiuswet(j))/(radiuswet(i)+radiuswet(j))**2. |
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| 222 | xvdW = LOG(1.+AvdWi) |
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| 223 | EvdW = 1. + SQRT(AvdWi/3.)/(1.+bvdW0*SQRT(AvdWi)) + bvdW1*xvdW + bvdW3*xvdW**3. |
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| [2949] | 224 | ENDIF |
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| 225 | ! |
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| 226 | beta(i,j)=beta(i,j)*EvdW |
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| 227 | |
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| [2690] | 228 | ENDDO |
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| 229 | ENDDO |
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| 230 | |
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| 231 | !--external loop for equation 14 |
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| 232 | DO k=1, nbtr_bin |
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| 233 | |
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| 234 | !--calculating denominator sum |
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| 235 | denom=0.0 |
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| 236 | DO j=1, nbtr_bin |
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| [4950] | 237 | ! fraction of coagulation of k and j that is not giving k |
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| 238 | denom=denom+(1.-ff(k,j,k))*beta(k,j)*tr_t(ilon,ilev,j) |
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| [2690] | 239 | ENDDO |
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| 240 | |
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| 241 | IF (k.EQ.1) THEN |
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| 242 | !--calculate new concentration of smallest bin |
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| 243 | tr_tp1(ilon,ilev,k)=tr_t(ilon,ilev,k)/(1.+pdtcoag*denom) |
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| 244 | ELSE |
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| 245 | !--calculating double sum terms in numerator of eq 14 |
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| 246 | num=0.0 |
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| 247 | DO j=1, k |
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| [4950] | 248 | numi=0.0 |
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| 249 | DO i=1, k-1 |
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| 250 | ! |
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| 251 | ! see Jacobson: " In order to conserve volume and volume concentration (which |
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| 252 | ! coagulation physically does) while giving up some accuracy in number concentration" |
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| 253 | ! |
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| 254 | ! Coagulation of i and j giving k |
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| 255 | ! with V(i) and then V(j) because it considers i,j and j,i with the double loop |
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| 256 | ! |
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| 257 | ! BUT WHY WET VOLUME V(i) in old STRATAER? tracers are already dry aerosols and coagulation |
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| 258 | ! kernel beta(i,j) accounts for wet aerosols -> reply below |
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| 259 | ! |
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| 260 | ! 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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| 261 | numi=numi+ff(i,j,k)*beta(i,j)*Vdry(i)*tr_tp1(ilon,ilev,i)*tr_t(ilon,ilev,j) |
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| 262 | ENDDO |
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| 263 | num=num+numi |
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| [2690] | 264 | ENDDO |
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| 265 | |
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| 266 | !--calculate new concentration of other bins |
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| [4950] | 267 | ! tr_tp1(ilon,ilev,k)=(V(k)*tr_t(ilon,ilev,k)+pdtcoag*num)/( (1.+pdtcoag*denom)*V(k) ) |
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| 268 | tr_tp1(ilon,ilev,k)=(Vdry(k)*tr_t(ilon,ilev,k)+pdtcoag*num)/( (1.+pdtcoag*denom)*Vdry(k) ) |
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| 269 | ! |
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| 270 | ! In constant composition (no dependency on aerosol size because no kelvin effect) |
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| 271 | ! V(l)= (f_r_wet(ilon,ilev)**3)*((mdw(l)/2.)**3) = (f_r_wet(ilon,ilev)**3)*Vdry(i) |
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| 272 | ! so numi and num are proportional (f_r_wet(ilon,ilev)**3) |
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| 273 | ! and so |
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| 274 | ! tr_tp1(ilon,ilev,k)=(V(k)*tr_t(ilon,ilev,k)+pdtcoag*num)/( (1.+pdtcoag*denom)*V(k) ) |
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| 275 | ! =(Vdry(k)*tr_t(ilon,ilev,k)+pdtcoag*num_dry)/( (1.+pdtcoag*denom)*Vdry(k) ) |
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| 276 | ! with num_dry=...beta(i,j)*Vdry(i)*.... |
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| 277 | ! so in old STRATAER (.not.flag_new_strat_compo), it was correct |
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| [2690] | 278 | ENDIF |
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| 279 | |
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| 280 | ENDDO !--end of loop k |
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| 281 | |
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| 282 | !--convert tracer concentration back from [number/m3] to [number/KgA] and write into tr_seri |
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| 283 | DO i=1, nbtr_bin |
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| [4950] | 284 | tr_seri(ilon,ilev,i+nbtr_sulgas) = tr_tp1(ilon,ilev,i) / zrho |
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| [2690] | 285 | ENDDO |
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| 286 | |
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| 287 | ENDIF ! IF IN STRATOSPHERE |
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| 288 | ENDDO !--end of loop klev |
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| 289 | ENDDO !--end of loop klon |
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| [4950] | 290 | ! ********************************************* |
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| [2690] | 291 | |
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| 292 | END SUBROUTINE COAGULATE |
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