[e200b7a] | 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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