[e200b7a] | 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 get_settling(itime,xt,yt,zt,nsp,settling) |
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| 23 | ! i i i i i o |
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| 24 | !***************************************************************************** |
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| 25 | ! * |
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| 26 | ! This subroutine calculates particle settling velocity. * |
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| 27 | ! * |
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| 28 | ! Author: A. Stohl * |
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| 29 | ! * |
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| 30 | ! May 2010 * |
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| 31 | ! * |
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| 32 | ! Improvement over traditional settling calculation in FLEXPART: * |
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| 33 | ! generalize to higher Reynolds numbers and also take into account the * |
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| 34 | ! temperature dependence of dynamic viscosity. * |
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| 35 | ! * |
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| 36 | ! Based on: * |
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| 37 | ! Naeslund E., and Thaning, L. (1991): On the settling velocity in a * |
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| 38 | ! nonstationary atmosphere, Aerosol Science and Technology 14, 247-256. * |
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| 39 | ! * |
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| 40 | !***************************************************************************** |
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| 41 | ! * |
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| 42 | ! Variables: * |
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| 43 | ! itime [s] current temporal position * |
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| 44 | ! xt,yt,zt coordinates position for which wind data shall be cal- * |
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| 45 | ! culated * |
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| 46 | ! * |
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| 47 | ! Constants: * |
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| 48 | ! * |
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| 49 | !***************************************************************************** |
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| 50 | |
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| 51 | use par_mod |
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| 52 | use com_mod |
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| 53 | |
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| 54 | implicit none |
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| 55 | |
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| 56 | integer :: itime,indz |
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| 57 | real :: xt,yt,zt |
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| 58 | |
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| 59 | ! Auxiliary variables needed for interpolation |
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| 60 | real :: dz1,dz2,dz |
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| 61 | real :: rho1(2),tt1(2),temperature,airdens,vis_dyn,vis_kin,viscosity |
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| 62 | real :: settling,settling_old,reynolds,c_d |
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| 63 | integer :: i,n,nix,njy,indzh,nsp |
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| 64 | |
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| 65 | |
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| 66 | !***************************************************************************** |
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| 67 | ! 1. Interpolate temperature and density: nearest neighbor interpolation sufficient |
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| 68 | !***************************************************************************** |
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| 69 | |
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| 70 | nix=int(xt) |
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| 71 | njy=int(yt) |
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| 72 | |
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| 73 | ! Determine the level below the current position for u,v |
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| 74 | !******************************************************* |
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| 75 | |
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| 76 | do i=2,nz |
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| 77 | if (height(i).gt.zt) then |
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| 78 | indz=i-1 |
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| 79 | goto 6 |
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| 80 | endif |
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| 81 | end do |
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| 82 | 6 continue |
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| 83 | |
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| 84 | |
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| 85 | ! Vertical distance to the level below and above current position |
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| 86 | !**************************************************************** |
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| 87 | |
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| 88 | dz=1./(height(indz+1)-height(indz)) |
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| 89 | dz1=(zt-height(indz))*dz |
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| 90 | dz2=(height(indz+1)-zt)*dz |
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| 91 | |
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| 92 | |
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| 93 | ! Bilinear horizontal interpolation |
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| 94 | !********************************** |
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| 95 | |
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| 96 | ! Loop over 2 levels |
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| 97 | !******************* |
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| 98 | |
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| 99 | do n=1,2 |
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| 100 | indzh=indz+n-1 |
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| 101 | rho1(n)=rho(nix,njy,indzh,1) |
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| 102 | tt1(n)=tt(nix,njy,indzh,1) |
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| 103 | end do |
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| 104 | |
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| 105 | |
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| 106 | ! Linear vertical interpolation |
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| 107 | !****************************** |
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| 108 | |
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| 109 | temperature=dz2*tt1(1)+dz1*tt1(2) |
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| 110 | airdens=dz2*rho1(1)+dz1*rho1(2) |
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| 111 | |
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| 112 | |
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| 113 | vis_dyn=viscosity(temperature) |
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| 114 | vis_kin=vis_dyn/airdens |
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| 115 | |
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| 116 | reynolds=dquer(nsp)/1.e6*abs(vsetaver(nsp))/vis_kin |
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| 117 | |
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| 118 | |
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| 119 | |
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| 120 | ! Iteration to determine both Reynolds number and settling velocity |
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| 121 | !****************************************************************** |
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| 122 | |
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| 123 | settling_old=vsetaver(nsp) ! initialize iteration with Stokes' law, constant viscosity estimate |
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| 124 | |
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| 125 | do i=1,20 ! do a few iterations |
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| 126 | |
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| 127 | if (reynolds.lt.1.917) then |
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| 128 | c_d=24./reynolds |
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| 129 | else if (reynolds.lt.500.) then |
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| 130 | c_d=18.5/(reynolds**0.6) |
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| 131 | else |
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| 132 | c_d=0.44 |
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| 133 | endif |
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| 134 | |
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| 135 | settling=-1.* & |
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| 136 | sqrt(4*ga*dquer(nsp)/1.e6*density(nsp)*cunningham(nsp)/ & |
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| 137 | (3.*c_d*airdens)) |
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| 138 | |
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| 139 | if (abs((settling-settling_old)/settling).lt.0.01) goto 11 ! stop iteration |
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| 140 | |
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| 141 | reynolds=dquer(nsp)/1.e6*abs(settling)/vis_kin |
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| 142 | settling_old=settling |
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| 143 | end do |
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| 144 | |
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| 145 | 11 continue |
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| 146 | |
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| 147 | end subroutine get_settling |
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