1 | !*********************************************************************** |
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2 | !* Copyright 2012,2013 * |
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3 | !* Jerome Brioude, Delia Arnold, Andreas Stohl, Wayne Angevine, * |
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4 | !* John Burkhart, Massimo Cassiani, Adam Dingwell, Richard C Easter, Sabine Eckhardt,* |
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5 | !* Stephanie Evan, Jerome D Fast, Don Morton, Ignacio Pisso, * |
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6 | !* Petra Seibert, Gerard Wotawa, Caroline Forster, Harald Sodemann, * |
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7 | !* * |
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8 | !* This file is part of FLEXPART WRF * |
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9 | !* * |
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10 | !* FLEXPART is free software: you can redistribute it and/or modify * |
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11 | !* it under the terms of the GNU General Public License as published by* |
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12 | !* the Free Software Foundation, either version 3 of the License, or * |
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13 | !* (at your option) any later version. * |
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14 | !* * |
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15 | !* FLEXPART is distributed in the hope that it will be useful, * |
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16 | !* but WITHOUT ANY WARRANTY; without even the implied warranty of * |
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17 | !* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * |
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18 | !* GNU General Public License for more details. * |
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19 | !* * |
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20 | !* You should have received a copy of the GNU General Public License * |
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21 | !* along with FLEXPART. If not, see <http://www.gnu.org/licenses/>. * |
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22 | !*********************************************************************** |
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23 | subroutine outgrid_init_irreg |
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24 | !******************************************************************************* |
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25 | ! * |
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26 | ! Note: This is the FLEXPART_WRF version of subroutine outgrid_init. * |
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27 | ! The computational grid is the WRF x-y grid rather than lat-lon. * |
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28 | ! * |
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29 | ! This routine calculates, for each grid cell of the output grid, the * |
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30 | ! volume, the surface area, and the areas of the northward and eastward * |
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31 | ! facing surfaces. * |
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32 | ! * |
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33 | ! Author: A. Stohl * |
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34 | ! * |
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35 | ! 7 August 2002 * |
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36 | ! * |
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37 | ! 26 Oct 2005, R. Easter - changes in gridarea, areaeast, areanorth * |
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38 | ! associated with WRF horizontal grid. * |
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39 | ! Dec 2005, R. Easter - changed names of "*lon0*" & "*lat0*" variables * |
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40 | ! * |
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41 | !******************************************************************************* |
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42 | ! * |
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43 | ! Variables: * |
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44 | ! * |
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45 | ! area surface area of all output grid cells * |
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46 | ! areaeast eastward facing wall area of all output grid cells * |
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47 | ! areanorth northward facing wall area of all output grid cells * |
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48 | ! volume volumes of all output grid cells * |
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49 | ! * |
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50 | !******************************************************************************* |
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51 | |
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52 | use flux_mod |
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53 | use oh_mod |
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54 | use unc_mod |
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55 | use outg_mod |
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56 | use par_mod |
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57 | use com_mod |
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58 | |
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59 | ! include 'includepar' |
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60 | ! include 'includecom' |
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61 | implicit none |
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62 | integer :: ix,jy,kz,k,i,nage,l,iix,jjy,ixp,jyp,i1,j1,j,ngrid |
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63 | ! real ylat,gridarea,ylatp,ylatm,hzone,cosfact,cosfactm,cosfactp |
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64 | real :: ymet,gridarea,xl1,xl2,yl1,yl2,m1,m2,tmpx,tmpy |
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65 | real :: xmet,xl,yl,ddx,ddy,rddx,rddy,p1,p2,p3,p4,xtn,ytn,oroh |
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66 | integer :: ks,kp,stat,ix2,jy2 |
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67 | real,parameter :: eps=nxmax/3.e5 |
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68 | real :: lon2(4),lat2(4) |
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69 | real ( kind = 8 ) :: sphere01_polygon_area,haversine,area1 |
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70 | |
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71 | |
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72 | |
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73 | ! Compute surface area and volume of each grid cell: area, volume; |
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74 | ! and the areas of the northward and eastward facing walls: areaeast, areanorth |
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75 | !*********************************************************************** |
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76 | ! do jy=0,10 |
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77 | ! print*,areamet(1,jy),areamet(2,jy),areamet2(2,jy) |
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78 | ! enddo |
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79 | do jy=0,numygrid-1 |
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80 | |
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81 | ! ylat=outlat0+(real(jy)+0.5)*dyout |
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82 | ! ylatp=ylat+0.5*dyout |
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83 | ! ylatm=ylat-0.5*dyout |
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84 | ! if ((ylatm.lt.0).and.(ylatp.gt.0.)) then |
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85 | ! hzone=dyout*r_earth*pi180 |
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86 | ! else |
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87 | ! |
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88 | !C Calculate area of grid cell with formula M=2*pi*R*h*dx/360, |
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89 | !C see Netz, Formeln der Mathematik, 5. Auflage (1983), p.90 |
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90 | !************************************************************* |
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91 | ! |
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92 | ! cosfact=cos(ylat*pi180)*r_earth |
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93 | ! cosfactp=cos(ylatp*pi180)*r_earth |
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94 | ! cosfactm=cos(ylatm*pi180)*r_earth |
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95 | ! if (cosfactp.lt.cosfactm) then |
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96 | ! hzone=sqrt(r_earth**2-cosfactp**2)- |
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97 | ! + sqrt(r_earth**2-cosfactm**2) |
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98 | ! else |
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99 | ! hzone=sqrt(r_earth**2-cosfactm**2)- |
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100 | ! + sqrt(r_earth**2-cosfactp**2) |
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101 | ! endif |
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102 | ! endif |
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103 | ! |
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104 | !C Surface are of a grid cell at a latitude ylat |
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105 | !*********************************************** |
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106 | ! |
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107 | ! gridarea=2.*pi*r_earth*hzone*dxout/360. |
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108 | |
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109 | ! for FLEXPART_WRF, dx & dy are in meters, and no cos(lat) is needed |
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110 | ! ??? maybe should incorporate map factor here, |
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111 | ! and also for areaeast & areanorth ??? |
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112 | |
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113 | do ix=0,numxgrid-1 |
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114 | ! gridarea=dxout*dyout ! what is needed is the true area based on map factors |
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115 | !JB: find a way to get the area between 2 output grid cell using areamet |
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116 | ! xl1=(real(ix)*dxout+out_xm0)/dx |
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117 | ! yl1=(real(jy)*dyout+out_ym0)/dy |
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118 | ! xl2=(real(ix+1)*dxout+out_xm0)/dx |
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119 | ! yl2=(real(jy+1)*dyout+out_ym0)/dy |
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120 | !! xr=out_xm0+real(numxgrid)*dxout |
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121 | ! m1=0.5*(m_x(int(xl1),int(yl1),1)+m_x(int(xl2),int(yl1),1)) |
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122 | ! m2=0.5*(m_y(int(xl1),int(yl1),1)+m_x(int(xl1),int(yl2),1)) |
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123 | ! area(ix,jy)=dxout*m1*dyout*m2 |
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124 | |
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125 | ! A more precise method |
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126 | tmpx=out_xm0+(float(ix))*dxout |
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127 | tmpy=out_ym0+(float(jy))*dyout |
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128 | call xymeter_to_ll_wrf_out(tmpx,tmpy,lon2(1),lat2(1)) |
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129 | tmpx=out_xm0+(float(ix+1))*dxout |
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130 | tmpy=out_ym0+(float(jy))*dyout |
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131 | call xymeter_to_ll_wrf_out(tmpx,tmpy,lon2(2),lat2(2)) |
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132 | tmpx=out_xm0+(float(ix+1))*dxout |
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133 | tmpy=out_ym0+(float(jy+1))*dyout |
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134 | call xymeter_to_ll_wrf_out(tmpx,tmpy,lon2(3),lat2(3)) |
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135 | tmpx=out_xm0+(float(ix))*dxout |
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136 | tmpy=out_ym0+(float(jy+1))*dyout |
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137 | call xymeter_to_ll_wrf_out(tmpx,tmpy,lon2(4),lat2(4)) |
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138 | area1=sphere01_polygon_area ( 4, real(lat2,kind=8), real(lon2,kind=8) ) |
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139 | area(ix,jy)=real(area1)*6370000.*6370000./coefdx/coefdx |
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140 | ! |
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141 | ! Volume = area x box height |
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142 | !*************************** |
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143 | |
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144 | volume(ix,jy,1)=area(ix,jy)*outheight(1) |
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145 | |
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146 | ! for FLEXPART_WRF, dx & dy are in meters, and no cos(lat) is needed |
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147 | ! areaeast(ix,jy,1)=dyout*r_earth*pi180*outheight(1) |
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148 | ! areanorth(ix,jy,1)=cos(ylat*pi180)*dxout*r_earth*pi180* |
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149 | ! + outheight(1) |
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150 | areaeast(ix,jy,1)=dyout*outheight(1) |
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151 | areanorth(ix,jy,1)=dxout*outheight(1) |
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152 | |
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153 | do kz=2,numzgrid |
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154 | |
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155 | ! areaeast(ix,jy,kz)=dyout*r_earth*pi180* |
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156 | ! + (outheight(kz)-outheight(kz-1)) |
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157 | ! areanorth(ix,jy,kz)=cos(ylat*pi180)*dxout*r_earth*pi180* |
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158 | ! + (outheight(kz)-outheight(kz-1)) |
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159 | areaeast(ix,jy,kz)=dyout*(outheight(kz)-outheight(kz-1)) |
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160 | areanorth(ix,jy,kz)=dxout*(outheight(kz)-outheight(kz-1)) |
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161 | |
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162 | volume(ix,jy,kz)=area(ix,jy)*(outheight(kz)-outheight(kz-1)) |
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163 | end do |
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164 | end do |
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165 | end do |
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166 | |
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167 | |
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168 | |
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169 | |
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170 | !****************************************************************** |
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171 | ! Determine average height of model topography in output grid cells |
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172 | !****************************************************************** |
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173 | |
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174 | ! Loop over all output grid cells |
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175 | !******************************** |
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176 | |
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177 | do jjy=0,numygrid-1 |
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178 | do iix=0,numxgrid-1 |
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179 | oroh=0. |
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180 | |
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181 | ! Take 100 samples of the topography in every grid cell |
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182 | !****************************************************** |
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183 | |
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184 | do j1=1,10 |
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185 | ! for FLEXPART_WRF, x & y coords are in meters, |
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186 | ! and the lon & lat variables below are in meters. |
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187 | ymet=out_ym0+(real(jjy)+real(j1)/10.-0.05)*dyout |
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188 | yl=(ymet-ymet0)/dy |
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189 | do i1=1,10 |
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190 | xmet=out_xm0+(real(iix)+real(i1)/10.-0.05)*dxout |
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191 | xl=(xmet-xmet0)/dx |
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192 | |
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193 | ! Determine the nest we are in |
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194 | !***************************** |
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195 | |
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196 | ngrid=0 |
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197 | do j=numbnests,1,-1 |
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198 | if ((xl.gt.xln(j)).and.(xl.lt.xrn(j)).and. & |
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199 | (yl.gt.yln(j)).and.(yl.lt.yrn(j))) then |
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200 | ngrid=j |
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201 | goto 43 |
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202 | endif |
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203 | end do |
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204 | 43 continue |
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205 | |
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206 | ! Determine (nested) grid coordinates and auxiliary parameters used for interpolation |
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207 | !************************************************************************************ |
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208 | |
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209 | if (ngrid.gt.0) then |
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210 | xtn=(xl-xln(ngrid))*xresoln(ngrid) |
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211 | ytn=(yl-yln(ngrid))*yresoln(ngrid) |
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212 | ix=int(xtn) |
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213 | jy=int(ytn) |
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214 | ddy=ytn-real(jy) |
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215 | ddx=xtn-real(ix) |
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216 | else |
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217 | ix=int(xl) |
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218 | jy=int(yl) |
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219 | ddy=yl-real(jy) |
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220 | ddx=xl-real(ix) |
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221 | endif |
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222 | ixp=ix+1 |
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223 | jyp=jy+1 |
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224 | rddx=1.-ddx |
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225 | rddy=1.-ddy |
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226 | p1=rddx*rddy |
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227 | p2=ddx*rddy |
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228 | p3=rddx*ddy |
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229 | p4=ddx*ddy |
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230 | |
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231 | if (ngrid.gt.0) then |
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232 | oroh=oroh+p1*oron(ix ,jy ,ngrid) & |
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233 | + p2*oron(ixp,jy ,ngrid) & |
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234 | + p3*oron(ix ,jyp,ngrid) & |
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235 | + p4*oron(ixp,jyp,ngrid) |
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236 | else |
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237 | oroh=oroh+p1*oro(ix ,jy) & |
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238 | + p2*oro(ixp,jy) & |
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239 | + p3*oro(ix ,jyp) & |
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240 | + p4*oro(ixp,jyp) |
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241 | endif |
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242 | end do |
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243 | end do |
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244 | |
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245 | ! Divide by the number of samples taken |
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246 | !************************************** |
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247 | |
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248 | oroout(iix,jjy)=oroh/100. |
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249 | end do |
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250 | end do |
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251 | |
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252 | |
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253 | ! if necessary allocate flux fields |
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254 | if (iflux.eq.1) then |
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255 | allocate(flux(6,0:numxgrid-1,0:numygrid-1,numzgrid, & |
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256 | 1:nspec,1:maxpointspec_act,1:nageclass),stat=stat) |
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257 | if (stat.ne.0) write(*,*)'ERROR: could not allocate flux array ' |
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258 | endif |
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259 | |
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260 | !write (*,*) 'allocating: in a sec',OHREA |
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261 | if (OHREA.eqv..TRUE.) then |
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262 | ! write (*,*) 'allocating: ',maxxOH,maxyOH,maxzOH |
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263 | allocate(OH_field(12,0:maxxOH-1,0:maxyOH-1,maxzOH) & |
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264 | ,stat=stat) |
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265 | if (stat.ne.0) write(*,*)'ERROR: could not allocate OH array ' |
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266 | allocate(OH_field_height(7) & |
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267 | ,stat=stat) |
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268 | if (stat.ne.0) write(*,*)'ERROR: could not allocate OH array ' |
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269 | endif |
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270 | ! gridunc,griduncn uncertainty of outputted concentrations |
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271 | ! print*,'gridunc allocated' |
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272 | allocate(gridunc(0:numxgrid-1,0:numygrid-1,numzgrid,maxspec, & |
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273 | maxpointspec_act,nclassunc,maxageclass),stat=stat) |
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274 | if (stat.ne.0) write(*,*)'ERROR: could not allocate gridunc' |
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275 | if (ldirect.gt.0) then |
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276 | allocate(wetgridunc(0:numxgrid-1,0:numygrid-1,maxspec, & |
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277 | maxpointspec_act,nclassunc,maxageclass),stat=stat) |
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278 | if (stat.ne.0) write(*,*)'ERROR: could not allocate gridunc' |
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279 | allocate(drygridunc(0:numxgrid-1,0:numygrid-1,maxspec, & |
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280 | maxpointspec_act,nclassunc,maxageclass),stat=stat) |
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281 | allocate(drygridunc2(0:numxgrid-1,0:numygrid-1,maxspec, & |
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282 | maxpointspec_act,nclassunc,maxageclass),stat=stat) |
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283 | if (stat.ne.0) write(*,*)'ERROR: could not allocate gridunc' |
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284 | endif |
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285 | !write (*,*) 'Dimensions for fields', numxgrid,numygrid, & |
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286 | ! maxspec,maxpointspec_act,nclassunc,maxageclass |
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287 | |
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288 | ! print*,'alloc gridunc',numxgrid-1,numygrid-1,numzgrid,maxspec, & |
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289 | ! maxpointspec_act,nclassunc,maxageclass |
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290 | |
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291 | |
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292 | write (*,*) ' Allocating fields for nested and global output (x,y): ', & |
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293 | max(numxgrid,numxgridn),max(numygrid,numygridn) |
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294 | |
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295 | ! allocate fields for concoutput with maximum dimension of outgrid |
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296 | ! and outgrid_nest |
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297 | allocate(gridsigma(0:max(numxgrid,numxgridn)-1, & |
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298 | 0:max(numygrid,numygridn)-1,numzgrid),stat=stat) |
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299 | if (stat.ne.0) write(*,*)'ERROR: could not allocate gridunc' |
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300 | allocate(grid(0:max(numxgrid,numxgridn)-1, & |
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301 | 0:max(numygrid,numygridn)-1,numzgrid),stat=stat) |
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302 | allocate(grid2(0:max(numxgrid,numxgridn)-1, & |
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303 | 0:max(numygrid,numygridn)-1,numzgrid,maxpointspec_act),stat=stat) |
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304 | allocate(grid3(0:max(numxgrid,numxgridn)-1, & |
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305 | 0:max(numygrid,numygridn)-1,numzgrid,maxpointspec_act),stat=stat) |
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306 | if (stat.ne.0) write(*,*)'ERROR: could not allocate gridunc' |
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307 | allocate(densityoutgrid(0:max(numxgrid,numxgridn)-1, & |
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308 | 0:max(numygrid,numygridn)-1,numzgrid),stat=stat) |
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309 | if (stat.ne.0) write(*,*)'ERROR: could not allocate gridunc' |
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310 | |
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311 | allocate(factor3d(0:max(numxgrid,numxgridn)-1, & |
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312 | 0:max(numygrid,numygridn)-1,numzgrid),stat=stat) |
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313 | if (stat.ne.0) write(*,*)'ERROR: could not allocate gridunc' |
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314 | allocate(sparse_dump_r(max(numxgrid,numxgridn)* & |
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315 | max(numygrid,numygridn)*numzgrid),stat=stat) |
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316 | if (stat.ne.0) write(*,*)'ERROR: could not allocate gridunc' |
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317 | allocate(sparse_dump_i(max(numxgrid,numxgridn)* & |
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318 | max(numygrid,numygridn)*numzgrid),stat=stat) |
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319 | if (stat.ne.0) write(*,*)'ERROR: could not allocate gridunc' |
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320 | |
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321 | ! deposition fields are only allocated for forward runs |
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322 | if (ldirect.gt.0) then |
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323 | allocate(wetgridsigma(0:max(numxgrid,numxgridn)-1, & |
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324 | 0:max(numygrid,numygridn)-1),stat=stat) |
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325 | if (stat.ne.0) write(*,*)'ERROR: could not allocate gridunc' |
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326 | allocate(drygridsigma(0:max(numxgrid,numxgridn)-1, & |
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327 | 0:max(numygrid,numygridn)-1),stat=stat) |
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328 | if (stat.ne.0) write(*,*)'ERROR: could not allocate gridunc' |
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329 | allocate(wetgrid(0:max(numxgrid,numxgridn)-1, & |
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330 | 0:max(numygrid,numygridn)-1),stat=stat) |
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331 | allocate(wetgrid2(0:max(numxgrid,numxgridn)-1, & |
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332 | 0:max(numygrid,numygridn)-1,maxpointspec_act),stat=stat) |
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333 | if (stat.ne.0) write(*,*)'ERROR: could not allocate gridunc' |
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334 | allocate(drygrid(0:max(numxgrid,numxgridn)-1, & |
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335 | 0:max(numygrid,numygridn)-1),stat=stat) |
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336 | allocate(drygrid2(0:max(numxgrid,numxgridn)-1, & |
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337 | 0:max(numygrid,numygridn)-1,maxpointspec_act),stat=stat) |
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338 | if (stat.ne.0) write(*,*)'ERROR: could not allocate gridunc' |
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339 | endif |
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340 | |
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341 | ! Initial condition field |
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342 | |
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343 | if (linit_cond.gt.0) then |
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344 | allocate(init_cond(0:numxgrid-1,0:numygrid-1,numzgrid,maxspec, & |
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345 | maxpointspec_act),stat=stat) |
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346 | if (stat.ne.0) write(*,*)'ERROR: could not allocate init_cond' |
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347 | endif |
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348 | |
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349 | !************************ |
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350 | ! Initialize output grids |
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351 | !************************ |
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352 | |
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353 | do ks=1,nspec |
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354 | do kp=1,maxpointspec_act |
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355 | do i=1,numreceptor |
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356 | ! Receptor points |
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357 | creceptor(i,ks)=0. |
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358 | end do |
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359 | do nage=1,nageclass |
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360 | do jy=0,numygrid-1 |
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361 | do ix=0,numxgrid-1 |
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362 | do l=1,nclassunc |
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363 | ! Deposition fields |
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364 | if (ldirect.gt.0) then |
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365 | wetgridunc(ix,jy,ks,kp,l,nage)=0. |
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366 | drygridunc(ix,jy,ks,kp,l,nage)=0. |
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367 | ! drygridunc2(ix,jy,ks,kp,l,nage)=0. |
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368 | endif |
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369 | do kz=1,numzgrid |
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370 | if (iflux.eq.1) then |
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371 | ! Flux fields |
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372 | do i=1,5 |
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373 | flux(i,ix,jy,kz,ks,kp,nage)=0. |
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374 | end do |
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375 | endif |
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376 | ! Initial condition field |
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377 | if ((l.eq.1).and.(nage.eq.1).and.(linit_cond.gt.0)) & |
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378 | init_cond(ix,jy,kz,ks,kp)=0. |
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379 | ! Concentration fields |
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380 | gridunc(ix,jy,kz,ks,kp,l,nage)=0. |
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381 | end do |
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382 | end do |
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383 | end do |
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384 | end do |
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385 | end do |
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386 | end do |
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387 | end do |
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388 | |
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389 | |
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390 | |
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391 | end subroutine outgrid_init_irreg |
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392 | |
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393 | function sphere01_polygon_area ( n, lat, lon ) |
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394 | |
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395 | !*****************************************************************************80 |
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396 | ! |
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397 | !! SPHERE01_POLYGON_AREA returns the area of a spherical polygon. |
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398 | ! |
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399 | ! Discussion: |
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400 | ! |
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401 | ! On a unit sphere, the area of a spherical polygon with N sides |
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402 | ! is equal to the spherical excess: |
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403 | ! |
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404 | ! E = sum ( interior angles ) - ( N - 2 ) * pi. |
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405 | ! |
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406 | ! On a sphere with radius R, the area is the spherical excess multiplied |
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407 | ! by R * R. |
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408 | ! |
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409 | ! The code was revised in accordance with suggestions in Carvalho and |
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410 | ! Cavalcanti. |
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411 | ! |
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412 | ! Licensing: |
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413 | ! |
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414 | ! This code is distributed under the GNU LGPL license. |
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415 | ! |
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416 | ! Modified: |
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417 | ! |
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418 | ! 12 August 2005 |
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419 | ! |
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420 | ! Author: |
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421 | ! |
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422 | ! Original C version by Robert Miller. |
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423 | ! FORTRAN90 version by John Burkardt. |
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424 | ! |
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425 | ! Reference: |
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426 | ! |
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427 | ! Paulo Cezar Pinto Carvalho, Paulo Roma Cavalcanti, |
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428 | ! Point in Polyhedron Testing Using Spherical Polygons, |
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429 | ! in Graphics Gems V, |
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430 | ! edited by Alan Paeth, |
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431 | ! Academic Press, 1995, |
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432 | ! ISBN: 0125434553, |
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433 | ! LC: T385.G6975. |
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434 | ! |
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435 | ! Robert Miller, |
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436 | ! Computing the Area of a Spherical Polygon, |
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437 | ! Graphics Gems, Volume IV, pages 132-138, |
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438 | ! Edited by Paul Heckbert, |
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439 | ! Academic Press, 1994, T385.G6974. |
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440 | ! |
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441 | ! Eric Weisstein, |
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442 | ! "Spherical Polygon", |
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443 | ! CRC Concise Encyclopedia of Mathematics, |
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444 | ! CRC Press, 1999. |
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445 | ! |
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446 | ! Parameters: |
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447 | ! |
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448 | ! Input, integer ( kind = 4 ) N, the number of vertices. |
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449 | ! |
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450 | ! Input, real ( kind = 8 ) LAT[N], LON[N], the latitudes and longitudes |
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451 | ! of the vertices of the spherical polygon. |
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452 | ! |
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453 | ! Output, real ( kind = 8 ) SPHERE01_POLYGON_AREA, the area of the |
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454 | ! spherical polygon, measured in spherical radians. |
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455 | ! |
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456 | implicit none |
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457 | |
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458 | integer ( kind = 4 ) n |
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459 | |
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460 | real ( kind = 8 ) a |
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461 | real ( kind = 8 ) area |
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462 | real ( kind = 8 ) b |
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463 | real ( kind = 8 ) beta1 |
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464 | real ( kind = 8 ) beta2 |
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465 | real ( kind = 8 ) c |
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466 | real ( kind = 8 ) cos_b1 |
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467 | real ( kind = 8 ) cos_b2 |
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468 | real ( kind = 8 ) excess |
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469 | real ( kind = 8 ) hav_a |
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470 | real ( kind = 8 ) haversine |
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471 | integer ( kind = 4 ) j |
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472 | integer ( kind = 4 ) k |
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473 | real ( kind = 8 ) lam |
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474 | real ( kind = 8 ) lam1 |
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475 | real ( kind = 8 ) lam2 |
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476 | real ( kind = 8 ) lat(n) |
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477 | real ( kind = 8 ) lon(n) |
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478 | real ( kind = 8 ), parameter :: pi_half = 1.5707963267948966192313D+00 |
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479 | real ( kind = 8 ) s |
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480 | real ( kind = 8 ) sphere01_polygon_area |
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481 | real ( kind = 8 ) t |
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482 | real ( kind = 8 ),parameter :: degrees_to_radians=3.141592653589793D+00 / 180.0D+00 |
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483 | |
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484 | area = 0.0D+00 |
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485 | |
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486 | do j=1,n |
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487 | lon(j)=lon(j)*degrees_to_radians |
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488 | lat(j)=lat(j)*degrees_to_radians |
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489 | enddo |
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490 | do j = 1, n + 1 |
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491 | ! do j = 1, n |
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492 | |
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493 | if ( j == 1 ) then |
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494 | lam1 = lon(j) |
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495 | beta1 = lat(j) |
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496 | lam2 = lon(j+1) |
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497 | beta2 = lat(j+1) |
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498 | cos_b1 = cos ( beta1 ) |
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499 | cos_b2 = cos ( beta2 ) |
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500 | else |
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501 | ! k = mod ( j + 1, n + 1 ) |
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502 | ! k = mod ( j , n ) |
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503 | k=j |
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504 | if (j.gt.n) k=1 |
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505 | lam1 = lam2 |
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506 | beta1 = beta2 |
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507 | lam2 = lon(k) |
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508 | beta2 = lat(k) |
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509 | ! print*,'sphere',n,k,lon(k),lat(k) |
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510 | cos_b1 = cos_b2 |
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511 | cos_b2 = cos ( beta2 ) |
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512 | end if |
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513 | |
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514 | if ( lam1 /= lam2 ) then |
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515 | |
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516 | hav_a = haversine ( beta2 - beta1 ) & |
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517 | + cos_b1 * cos_b2 * haversine ( lam2 - lam1 ) |
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518 | a = 2.0D+00 * asin ( sqrt ( hav_a ) ) |
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519 | |
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520 | b = pi_half - beta2 |
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521 | c = pi_half - beta1 |
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522 | s = 0.5D+00 * ( a + b + c ) |
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523 | ! |
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524 | ! Given the three sides of a spherical triangle, we can use a formula |
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525 | ! to find the spherical excess. |
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526 | ! |
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527 | t = tan ( s / 2.0D+00 ) * tan ( ( s - a ) / 2.0D+00 ) & |
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528 | * tan ( ( s - b ) / 2.0D+00 ) * tan ( ( s - c ) / 2.0D+00 ) |
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529 | |
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530 | excess = abs ( 4.0D+00 * atan ( sqrt ( abs ( t ) ) ) ) |
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531 | |
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532 | if ( lam1 < lam2 ) then |
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533 | lam = lam2 - lam1 |
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534 | else |
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535 | lam = lam2 - lam1 + 4.0D+00 * pi_half |
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536 | end if |
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537 | |
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538 | if ( 2.0D+00 * pi_half < lam ) then |
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539 | excess = -excess |
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540 | end if |
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541 | |
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542 | area = area + excess |
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543 | |
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544 | end if |
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545 | |
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546 | end do |
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547 | |
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548 | sphere01_polygon_area = abs ( area ) |
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549 | |
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550 | return |
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551 | end |
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552 | |
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553 | function haversine ( a ) |
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554 | |
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555 | !*****************************************************************************80 |
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556 | ! |
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557 | !! HAVERSINE computes the haversine of an angle. |
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558 | ! |
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559 | ! Discussion: |
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560 | ! |
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561 | ! haversine(A) = ( 1 - cos ( A ) ) / 2 |
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562 | ! |
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563 | ! The haversine is useful in spherical trigonometry. |
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564 | ! |
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565 | ! Licensing: |
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566 | ! |
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567 | ! This code is distributed under the GNU LGPL license. |
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568 | ! |
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569 | ! Modified: |
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570 | ! |
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571 | ! 02 July 2001 |
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572 | ! |
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573 | ! Author: |
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574 | ! |
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575 | ! John Burkardt |
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576 | ! |
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577 | ! Parameters: |
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578 | ! |
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579 | ! Input, real ( kind = 8 ) A, the angle. |
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580 | ! |
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581 | ! Output, real ( kind = 8 ) HAVERSINE, the haversine of the angle. |
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582 | ! |
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583 | implicit none |
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584 | |
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585 | real ( kind = 8 ) a |
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586 | real ( kind = 8 ) haversine |
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587 | |
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588 | haversine = ( 1.0D+00 - cos ( a ) ) / 2.0D+00 |
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589 | |
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590 | return |
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591 | end |
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