1 | !********************************************************************** |
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2 | ! Copyright 1998,1999,2000,2001,2002,2005,2007,2008,2009,2010 * |
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3 | ! Andreas Stohl, Petra Seibert, A. Frank, Gerhard Wotawa, * |
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4 | ! Caroline Forster, Sabine Eckhardt, John Burkhart, Harald Sodemann * |
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5 | ! * |
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6 | ! This file is part of FLEXPART. * |
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7 | ! * |
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8 | ! FLEXPART is free software: you can redistribute it and/or modify * |
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9 | ! it under the terms of the GNU General Public License as published by* |
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10 | ! the Free Software Foundation, either version 3 of the License, or * |
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11 | ! (at your option) any later version. * |
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12 | ! * |
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13 | ! FLEXPART is distributed in the hope that it will be useful, * |
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14 | ! but WITHOUT ANY WARRANTY; without even the implied warranty of * |
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15 | ! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * |
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16 | ! GNU General Public License for more details. * |
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17 | ! * |
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18 | ! You should have received a copy of the GNU General Public License * |
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19 | ! along with FLEXPART. If not, see <http://www.gnu.org/licenses/>. * |
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20 | !********************************************************************** |
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21 | |
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22 | subroutine part0(dquer,dsigma,density,fract,schmi,cun,vsh) |
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23 | ! i i i o o o o |
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24 | !***************************************************************************** |
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25 | ! * |
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26 | ! Calculation of time independent factors of the dry deposition of * |
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27 | ! particles: * |
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28 | ! Log-Normal-distribution of mass [dM/dlog(dp)], unimodal * |
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29 | ! * |
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30 | ! AUTHOR: Matthias Langer, adapted by Andreas Stohl, 13 November 1993 * |
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31 | ! * |
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32 | ! Literature: * |
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33 | ! [1] Scire/Yamartino/Carmichael/Chang (1989), * |
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34 | ! CALGRID: A Mesoscale Photochemical Grid Model. * |
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35 | ! Vol II: User's Guide. (Report No.A049-1, June, 1989) * |
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36 | ! * |
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37 | !***************************************************************************** |
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38 | ! * |
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39 | ! Variables: * |
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40 | ! alpha help variable * |
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41 | ! cun 'slip-flow' correction after Cunningham * |
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42 | ! d01 [um] upper diameter * |
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43 | ! d02 [um] lower diameter * |
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44 | ! dc [m2/s] coefficient of Brownian diffusion * |
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45 | ! delta distance given in standard deviation units * |
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46 | ! density [kg/m3] density of the particle * |
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47 | ! dmean geometric mean diameter of interval * |
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48 | ! dquer [um] geometric mass mean particle diameter * |
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49 | ! dsigma e.g. dsigma=10 or dsigma=0.1 means that 68% of the mass * |
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50 | ! are between 0.1*dquer and 10*dquer * |
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51 | ! fract(ni) mass fraction of each diameter interval * |
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52 | ! kn Knudsen number * |
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53 | ! ni number of diameter intervals, for which deposition * |
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54 | ! is calculated * |
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55 | ! schmidt Schmidt number * |
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56 | ! schmi schmidt**2/3 * |
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57 | ! vsh [m/s] gravitational settling velocity of the particle * |
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58 | ! x01 normalized upper diameter * |
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59 | ! x02 normalized lower diameter * |
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60 | ! * |
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61 | ! Constants: * |
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62 | ! g [m/s2] Acceleration of gravity * |
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63 | ! kb [J/K] Stefan-Boltzmann constant * |
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64 | ! lam [m] mean free path of air molecules * |
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65 | ! myl [kg/m/s] dynamical viscosity of air * |
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66 | ! nyl [m2/s] kinematic viscosity of air * |
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67 | ! tr reference temperature * |
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68 | ! * |
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69 | ! Function: * |
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70 | ! erf calculates the integral of the Gauss function * |
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71 | ! * |
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72 | !***************************************************************************** |
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73 | |
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74 | use par_mod |
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75 | |
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76 | implicit none |
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77 | |
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78 | real,parameter :: tr=293.15 |
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79 | |
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80 | integer :: i |
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81 | real :: dquer,dsigma,density,xdummy,d01,d02,delta,x01,x02,fract(ni) |
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82 | real :: dmean,alpha,cun,dc,schmidt,schmi(ni),vsh(ni),kn,erf |
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83 | real,parameter :: myl=1.81e-5,nyl=0.15e-4 |
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84 | real,parameter :: lam=6.53e-8,kb=1.38e-23,eps=1.2e-38 |
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85 | |
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86 | |
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87 | ! xdummy constant for all intervals |
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88 | !********************************** |
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89 | |
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90 | xdummy=sqrt(2.)*alog(dsigma) |
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91 | |
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92 | |
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93 | ! particles diameters are split up to ni intervals between |
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94 | ! dquer-3*dsigma and dquer+3*dsigma |
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95 | !********************************************************* |
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96 | |
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97 | delta=6./real(ni) |
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98 | |
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99 | d01=dquer*dsigma**(-3) |
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100 | do i=1,ni |
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101 | d02=d01 |
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102 | d01=dquer*dsigma**(-3.+delta*real(i)) |
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103 | x01=alog(d01/dquer)/xdummy |
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104 | x02=alog(d02/dquer)/xdummy |
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105 | |
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106 | |
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107 | ! Area under Gauss-function is calculated and gives mass fraction of interval |
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108 | !**************************************************************************** |
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109 | |
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110 | fract(i)=0.5*(erf(x01)-erf(x02)) |
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111 | |
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112 | |
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113 | ! Geometric mean diameter of interval in [m] |
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114 | !******************************************* |
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115 | |
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116 | dmean=1.E-6*exp(0.5*alog(d01*d02)) |
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117 | |
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118 | |
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119 | ! Calculation of time independent parameters of each interval |
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120 | !************************************************************ |
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121 | |
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122 | kn=2.*lam/dmean |
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123 | if ((-1.1/kn).le.log10(eps)*log(10.)) then |
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124 | alpha=1.257 |
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125 | else |
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126 | alpha=1.257+0.4*exp(-1.1/kn) |
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127 | endif |
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128 | cun=1.+alpha*kn |
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129 | dc=kb*tr*cun/(3.*pi*myl*dmean) |
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130 | schmidt=nyl/dc |
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131 | schmi(i)=schmidt**(-2./3.) |
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132 | vsh(i)=ga*density*dmean*dmean*cun/(18.*myl) |
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133 | |
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134 | end do |
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135 | |
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136 | end subroutine part0 |
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