1 | subroutine get_settling(itime,xt,yt,zt,nsp,settling) |
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2 | ! i i i i i o |
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3 | !***************************************************************************** |
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4 | ! * |
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5 | ! This subroutine calculates particle settling velocity. * |
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6 | ! * |
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7 | ! Author: A. Stohl * |
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8 | ! * |
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9 | ! May 2010 * |
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10 | ! * |
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11 | ! Improvement over traditional settling calculation in FLEXPART: * |
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12 | ! generalize to higher Reynolds numbers and also take into account the * |
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13 | ! temperature dependence of dynamic viscosity. * |
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14 | ! * |
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15 | ! Based on: * |
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16 | ! Naeslund E., and Thaning, L. (1991): On the settling velocity in a * |
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17 | ! nonstationary atmosphere, Aerosol Science and Technology 14, 247-256. * |
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18 | ! * |
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19 | !***************************************************************************** |
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20 | ! * |
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21 | ! Variables: * |
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22 | ! itime [s] current temporal position * |
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23 | ! xt,yt,zt coordinates position for which wind data shall be cal- * |
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24 | ! culated * |
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25 | ! * |
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26 | ! Constants: * |
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27 | ! * |
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28 | !***************************************************************************** |
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29 | |
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30 | use par_mod |
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31 | use com_mod |
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32 | |
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33 | implicit none |
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34 | |
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35 | integer :: itime,indz |
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36 | real :: xt,yt,zt |
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37 | |
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38 | ! Auxiliary variables needed for interpolation |
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39 | real :: dz1,dz2,dz |
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40 | real :: rho1(2),tt1(2),temperature,airdens,vis_dyn,vis_kin,viscosity |
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41 | real :: settling,settling_old,reynolds,c_d |
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42 | integer :: i,n,nix,njy,indzh,nsp |
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43 | |
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44 | |
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45 | !***************************************************************************** |
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46 | ! 1. Interpolate temperature and density: nearest neighbor interpolation sufficient |
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47 | !***************************************************************************** |
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48 | |
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49 | nix=int(xt) |
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50 | njy=int(yt) |
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51 | |
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52 | ! Determine the level below the current position for u,v |
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53 | !******************************************************* |
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54 | |
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55 | do i=2,nz |
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56 | if (height(i).gt.zt) then |
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57 | indz=i-1 |
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58 | goto 6 |
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59 | endif |
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60 | end do |
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61 | 6 continue |
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62 | |
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63 | |
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64 | ! Vertical distance to the level below and above current position |
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65 | !**************************************************************** |
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66 | |
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67 | dz=1./(height(indz+1)-height(indz)) |
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68 | dz1=(zt-height(indz))*dz |
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69 | dz2=(height(indz+1)-zt)*dz |
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70 | |
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71 | |
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72 | ! Bilinear horizontal interpolation |
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73 | !********************************** |
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74 | |
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75 | ! Loop over 2 levels |
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76 | !******************* |
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77 | |
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78 | do n=1,2 |
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79 | indzh=indz+n-1 |
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80 | rho1(n)=rho(nix,njy,indzh,1) |
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81 | tt1(n)=tt(nix,njy,indzh,1) |
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82 | end do |
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83 | |
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84 | |
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85 | ! Linear vertical interpolation |
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86 | !****************************** |
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87 | |
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88 | temperature=dz2*tt1(1)+dz1*tt1(2) |
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89 | airdens=dz2*rho1(1)+dz1*rho1(2) |
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90 | |
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91 | |
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92 | vis_dyn=viscosity(temperature) |
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93 | vis_kin=vis_dyn/airdens |
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94 | |
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95 | reynolds=dquer(nsp)/1.e6*abs(vsetaver(nsp))/vis_kin |
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96 | |
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97 | |
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98 | |
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99 | ! Iteration to determine both Reynolds number and settling velocity |
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100 | !****************************************************************** |
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101 | |
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102 | settling_old=vsetaver(nsp) ! initialize iteration with Stokes' law, constant viscosity estimate |
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103 | |
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104 | do i=1,20 ! do a few iterations |
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105 | |
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106 | if (reynolds.lt.1.917) then |
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107 | c_d=24./reynolds |
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108 | else if (reynolds.lt.500.) then |
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109 | c_d=18.5/(reynolds**0.6) |
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110 | else |
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111 | c_d=0.44 |
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112 | endif |
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113 | |
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114 | settling=-1.* & |
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115 | sqrt(4*ga*dquer(nsp)/1.e6*density(nsp)*cunningham(nsp)/ & |
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116 | (3.*c_d*airdens)) |
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117 | |
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118 | if (abs((settling-settling_old)/settling).lt.0.01) goto 11 ! stop iteration |
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119 | |
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120 | reynolds=dquer(nsp)/1.e6*abs(settling)/vis_kin |
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121 | settling_old=settling |
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122 | end do |
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123 | |
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124 | 11 continue |
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125 | |
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126 | end subroutine get_settling |
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