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 calcpv(n,uuh,vvh,pvh) |
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24 | ! i i i o |
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25 | !******************************************************************************* |
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26 | ! * |
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27 | ! Note: This is the FLEXPART_WRF version of subroutine calcpv. * |
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28 | ! The computational grid is the WRF x-y grid rather than lat-lon. * |
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29 | ! * |
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30 | ! Calculation of potential vorticity on 3-d grid. * |
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31 | ! * |
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32 | ! Author: P. James * |
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33 | ! 3 February 2000 * |
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34 | ! * |
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35 | ! Adaptation to FLEXPART, A. Stohl, 1 May 2000 * |
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36 | ! * |
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37 | ! 26 Oct 2005, R. Easter - changes associated with WRF horizontal grid. * |
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38 | ! For pressure use pph instead of (akz + bkz*ps) * |
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39 | ! *** Note -- see ??? comments below regarding the pvh calculation. * |
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40 | ! 11 Nov 2005, R. Easter - fixed error involving xy to latlon * |
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41 | ! * |
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42 | !******************************************************************************* |
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43 | ! * |
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44 | ! Variables: * |
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45 | ! n temporal index for meteorological fields (1 to 2) * |
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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 | ! include 'includepar' |
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52 | ! include 'includecom' |
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53 | ! |
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54 | ! integer n,ix,jy,i,j,k,kl,ii,jj,klvrp,klvrm,klpt,kup,kdn,kch |
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55 | ! integer jyvp,jyvm,ixvp,ixvm,jumpx,jumpy,jux,juy,ivrm,ivrp,ivr |
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56 | ! integer nlck |
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57 | ! real vx(2),uy(2),phi,tanphi,cosphi,dvdx,dudy,f |
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58 | ! real theta,thetap,thetam,dthetadp,dt1,dt2,dt,ppmk |
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59 | ! real thup,thdn,eps,p0 |
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60 | ! parameter(eps=1.e-5,p0=101325) |
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61 | ! real uuh(0:nxmax-1,0:nymax-1,nuvzmax) |
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62 | ! real vvh(0:nxmax-1,0:nymax-1,nuvzmax) |
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63 | ! real pvh(0:nxmax-1,0:nymax-1,nuvzmax) |
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64 | use par_mod |
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65 | use com_mod |
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66 | |
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67 | implicit none |
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68 | |
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69 | integer :: n,ix,jy,i,j,k,kl,ii,jj,klvrp,klvrm,klpt,kup,kdn,kch |
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70 | integer :: jyvp,jyvm,ixvp,ixvm,jumpx,jumpy,jux,juy,ivrm,ivrp,ivr |
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71 | integer :: nlck |
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72 | real :: vx(2),uy(2),phi,tanphi,cosphi,dvdx,dudy,f |
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73 | real :: theta,thetap,thetam,dthetadp,dt1,dt2,dt,ppmk |
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74 | real :: pvavr,ppml(nuvzmax) |
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75 | real :: thup,thdn |
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76 | real,parameter :: eps=1.e-5, p0=101325 |
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77 | real(kind=4) :: uuh(0:nxmax-1,0:nymax-1,nuvzmax) |
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78 | real(kind=4) :: vvh(0:nxmax-1,0:nymax-1,nuvzmax) |
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79 | real :: pvh(0:nxmax-1,0:nymax-1,nuvzmax) |
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80 | |
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81 | |
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82 | |
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83 | real :: dumlon,dumlat |
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84 | real :: thh(0:nxmax-1,0:nymax-1,nuvzmax) |
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85 | real :: altit(nuvzmax) |
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86 | |
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87 | ! Set number of levels to check for adjacent theta |
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88 | nlck=nuvz/3 |
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89 | ! FLEXPART_WRF -- altit is never used, so don't calculate it |
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90 | ! do 5 k=1,nuvz |
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91 | ! altit(k)=akz(k)/p0+bkz(k) |
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92 | !5 continue |
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93 | ! *** Precalculate all theta levels for efficiency |
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94 | do jy=0,nymin1 |
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95 | do kl=1,nuvz |
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96 | do ix=0,nxmin1 |
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97 | ! FLEXPART_WRF -- use pph here |
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98 | ! ppmk=akz(kl)+bkz(kl)*ps(ix,jy,1,n) |
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99 | ppmk=pph(ix,jy,kl,n) |
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100 | thh(ix,jy,kl)=tth(ix,jy,kl,n)*(100000./ppmk)**kappa |
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101 | enddo |
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102 | enddo |
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103 | enddo |
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104 | ! |
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105 | ! Loop over entire grid |
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106 | !********************** |
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107 | do jy=0,nymin1 |
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108 | if (sglobal.and.jy.eq.0) goto 10 |
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109 | if (nglobal.and.jy.eq.nymin1) goto 10 |
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110 | |
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111 | ! for FLEXPART_WRF, x & y coords are in meters |
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112 | ! and true latitude varies with both i and j |
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113 | ! phi = (ylat0 + jy * dy) * pi / 180. |
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114 | ! f = 0.00014585 * sin(phi) |
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115 | ! tanphi = tan(phi) |
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116 | ! cosphi = cos(phi) |
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117 | |
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118 | ! Provide a virtual jy+1 and jy-1 in case we are on domain edge (Lat) |
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119 | jyvp=jy+1 |
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120 | jyvm=jy-1 |
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121 | if (jy.eq.0) jyvm=0 |
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122 | if (jy.eq.nymin1) jyvp=nymin1 |
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123 | ! Define absolute gap length |
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124 | jumpy=2 |
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125 | if (jy.eq.0.or.jy.eq.nymin1) jumpy=1 |
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126 | if (sglobal.and.jy.eq.1) then |
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127 | jyvm=1 |
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128 | jumpy=1 |
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129 | end if |
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130 | if (nglobal.and.jy.eq.ny-2) then |
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131 | jyvp=ny-2 |
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132 | jumpy=1 |
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133 | end if |
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134 | juy=jumpy |
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135 | ! |
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136 | do ix=0,nxmin1 |
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137 | |
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138 | ! for FLEXPART_WRF, x & y coords are in meters, |
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139 | ! and true latitude varies with both i and j |
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140 | call xyindex_to_ll_wrf( & |
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141 | 0, real(ix), real(jy), dumlon, dumlat ) |
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142 | phi = dumlat * pi / 180. |
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143 | f = 0.00014585 * sin(phi) |
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144 | tanphi = tan(phi) |
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145 | cosphi = cos(phi) |
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146 | |
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147 | ! Provide a virtual ix+1 and ix-1 in case we are on domain edge (Long) |
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148 | ixvp=ix+1 |
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149 | ixvm=ix-1 |
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150 | jumpx=2 |
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151 | if (xglobal) then |
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152 | ivrp=ixvp |
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153 | ivrm=ixvm |
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154 | if (ixvm.lt.0) ivrm=ixvm+nxmin1 |
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155 | if (ixvp.ge.nx) ivrp=ixvp-nx+1 |
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156 | else |
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157 | if (ix.eq.0) ixvm=0 |
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158 | if (ix.eq.nxmin1) ixvp=nxmin1 |
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159 | ivrp=ixvp |
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160 | ivrm=ixvm |
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161 | ! Define absolute gap length |
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162 | if (ix.eq.0.or.ix.eq.nxmin1) jumpx=1 |
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163 | end if |
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164 | jux=jumpx |
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165 | ! Precalculate pressure values for efficiency |
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166 | do kl=1,nuvz |
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167 | ! FLEXPART_WRF -- use pph here |
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168 | ! ppml(kl)=akz(kl)+bkz(kl)*ps(ix,jy,1,n) |
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169 | ppml(kl)=pph(ix,jy,kl,n) |
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170 | enddo |
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171 | ! |
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172 | ! Loop over the vertical |
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173 | !*********************** |
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174 | |
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175 | do kl=1,nuvz |
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176 | theta=thh(ix,jy,kl) |
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177 | klvrp=kl+1 |
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178 | klvrm=kl-1 |
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179 | klpt=kl |
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180 | ! If top or bottom level, dthetadp is evaluated between the current |
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181 | ! level and the level inside, otherwise between level+1 and level-1 |
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182 | ! |
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183 | if (klvrp.gt.nuvz) klvrp=nuvz |
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184 | if (klvrm.lt.1) klvrm=1 |
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185 | thetap=thh(ix,jy,klvrp) |
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186 | thetam=thh(ix,jy,klvrm) |
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187 | dthetadp=(thetap-thetam)/(ppml(klvrp)-ppml(klvrm)) |
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188 | |
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189 | ! Compute vertical position at pot. temperature surface on subgrid |
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190 | ! and the wind at that position |
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191 | !***************************************************************** |
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192 | ! a) in x direction |
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193 | ii=0 |
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194 | do i=ixvm,ixvp,jumpx |
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195 | ivr=i |
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196 | if (xglobal) then |
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197 | if (i.lt.0) ivr=ivr+nxmin1 |
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198 | if (i.ge.nx) ivr=ivr-nx+1 |
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199 | end if |
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200 | ii=ii+1 |
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201 | ! Search adjacent levels for current theta value |
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202 | ! Spiral out from current level for efficiency |
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203 | kup=klpt-1 |
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204 | kdn=klpt |
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205 | kch=0 |
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206 | 40 continue |
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207 | ! Upward branch |
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208 | kup=kup+1 |
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209 | if (kch.ge.nlck) goto 21 ! No more levels to check, |
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210 | ! ! and no values found |
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211 | if (kup.ge.nuvz) goto 41 |
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212 | kch=kch+1 |
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213 | k=kup |
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214 | thdn=thh(ivr,jy,k) |
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215 | thup=thh(ivr,jy,k+1) |
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216 | if (((thdn.ge.theta).and.(thup.le.theta)).or. & |
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217 | ((thdn.le.theta).and.(thup.ge.theta))) then |
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218 | dt1=abs(theta-thdn) |
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219 | dt2=abs(theta-thup) |
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220 | dt=dt1+dt2 |
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221 | if (dt.lt.eps) then ! Avoid division by zero error |
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222 | dt1=0.5 ! G.W., 10.4.1996 |
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223 | dt2=0.5 |
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224 | dt=1.0 |
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225 | endif |
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226 | vx(ii)=(vvh(ivr,jy,k)*dt2+vvh(ivr,jy,k+1)*dt1)/dt |
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227 | goto 20 |
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228 | endif |
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229 | 41 continue |
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230 | ! Downward branch |
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231 | kdn=kdn-1 |
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232 | if (kdn.lt.1) goto 40 |
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233 | kch=kch+1 |
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234 | k=kdn |
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235 | thdn=thh(ivr,jy,k) |
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236 | thup=thh(ivr,jy,k+1) |
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237 | if (((thdn.ge.theta).and.(thup.le.theta)).or. & |
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238 | ((thdn.le.theta).and.(thup.ge.theta))) then |
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239 | dt1=abs(theta-thdn) |
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240 | dt2=abs(theta-thup) |
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241 | dt=dt1+dt2 |
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242 | if (dt.lt.eps) then ! Avoid division by zero error |
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243 | dt1=0.5 ! G.W., 10.4.1996 |
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244 | dt2=0.5 |
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245 | dt=1.0 |
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246 | endif |
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247 | vx(ii)=(vvh(ivr,jy,k)*dt2+vvh(ivr,jy,k+1)*dt1)/dt |
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248 | goto 20 |
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249 | endif |
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250 | goto 40 |
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251 | ! This section used when no values were found |
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252 | 21 continue |
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253 | ! Must use vv at current level and long. jux becomes smaller by 1 |
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254 | vx(ii)=vvh(ix,jy,kl) |
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255 | jux=jux-1 |
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256 | ! Otherwise OK |
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257 | 20 continue |
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258 | end do |
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259 | |
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260 | if (jux.gt.0) then |
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261 | ! for FLEXPART_WRF, dx & dy are in meters. |
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262 | ! dvdx=(vx(2)-vx(1))/real(jux)/(dx*pi/180.) |
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263 | dvdx=(vx(2)-vx(1))/real(jux)/dx |
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264 | else |
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265 | dvdx=vvh(ivrp,jy,kl)-vvh(ivrm,jy,kl) |
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266 | ! dvdx=dvdx/real(jumpx)/(dx*pi/180.) |
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267 | dvdx=dvdx/real(jumpx)/dx |
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268 | ! Only happens if no equivalent theta value |
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269 | ! can be found on either side, hence must use values |
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270 | ! from either side, same pressure level. |
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271 | end if |
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272 | |
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273 | ! b) in y direction |
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274 | |
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275 | jj=0 |
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276 | do j=jyvm,jyvp,jumpy |
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277 | jj=jj+1 |
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278 | ! Search adjacent levels for current theta value |
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279 | ! Spiral out from current level for efficiency |
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280 | kup=klpt-1 |
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281 | kdn=klpt |
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282 | kch=0 |
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283 | 70 continue |
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284 | ! Upward branch |
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285 | kup=kup+1 |
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286 | if (kch.ge.nlck) goto 51 ! No more levels to check, |
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287 | ! ! and no values found |
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288 | if (kup.ge.nuvz) goto 71 |
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289 | kch=kch+1 |
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290 | k=kup |
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291 | thdn=thh(ix,j,k) |
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292 | thup=thh(ix,j,k+1) |
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293 | if (((thdn.ge.theta).and.(thup.le.theta)).or. & |
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294 | ((thdn.le.theta).and.(thup.ge.theta))) then |
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295 | dt1=abs(theta-thdn) |
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296 | dt2=abs(theta-thup) |
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297 | dt=dt1+dt2 |
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298 | if (dt.lt.eps) then ! Avoid division by zero error |
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299 | dt1=0.5 ! G.W., 10.4.1996 |
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300 | dt2=0.5 |
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301 | dt=1.0 |
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302 | endif |
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303 | uy(jj)=(uuh(ix,j,k)*dt2+uuh(ix,j,k+1)*dt1)/dt |
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304 | goto 50 |
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305 | endif |
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306 | 71 continue |
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307 | ! Downward branch |
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308 | kdn=kdn-1 |
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309 | if (kdn.lt.1) goto 70 |
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310 | kch=kch+1 |
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311 | k=kdn |
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312 | thdn=thh(ix,j,k) |
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313 | thup=thh(ix,j,k+1) |
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314 | if (((thdn.ge.theta).and.(thup.le.theta)).or. & |
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315 | ((thdn.le.theta).and.(thup.ge.theta))) then |
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316 | dt1=abs(theta-thdn) |
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317 | dt2=abs(theta-thup) |
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318 | dt=dt1+dt2 |
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319 | if (dt.lt.eps) then ! Avoid division by zero error |
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320 | dt1=0.5 ! G.W., 10.4.1996 |
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321 | dt2=0.5 |
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322 | dt=1.0 |
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323 | endif |
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324 | uy(jj)=(uuh(ix,j,k)*dt2+uuh(ix,j,k+1)*dt1)/dt |
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325 | goto 50 |
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326 | endif |
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327 | goto 70 |
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328 | ! This section used when no values were found |
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329 | 51 continue |
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330 | ! Must use uu at current level and lat. juy becomes smaller by 1 |
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331 | uy(jj)=uuh(ix,jy,kl) |
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332 | juy=juy-1 |
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333 | ! Otherwise OK |
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334 | 50 continue |
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335 | end do |
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336 | |
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337 | if (juy.gt.0) then |
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338 | ! for FLEXPART_WRF, dx & dy are in meters. |
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339 | ! dudy=(uy(2)-uy(1))/real(juy)/(dy*pi/180.) |
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340 | dudy=(uy(2)-uy(1))/real(juy)/dy |
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341 | else |
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342 | dudy=uuh(ix,jyvp,kl)-uuh(ix,jyvm,kl) |
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343 | ! dudy=dudy/real(jumpy)/(dy*pi/180.) |
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344 | dudy=dudy/real(jumpy)/dy |
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345 | end if |
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346 | ! |
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347 | |
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348 | ! for FLEXPART_WRF, dx & dy are in meters. |
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349 | ! don't need to divide by r_earth when doing d/dy |
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350 | ! don't need to divide by r_earth*cosphi when doing d/dx |
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351 | ! ??? I don't understand the uuh*tanphi term, but leave it in for now ??? |
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352 | ! ??? What is the "-1.e6" factor ??? |
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353 | ! |
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354 | ! pvh(ix,jy,kl)=dthetadp*(f+(dvdx/cosphi-dudy |
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355 | ! + +uuh(ix,jy,kl)*tanphi)/r_earth)*(-1.e6)*9.81 |
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356 | pvh(ix,jy,kl)=dthetadp*( f + dvdx - dudy & |
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357 | + (uuh(ix,jy,kl)*tanphi/r_earth) )*(-1.e6)*9.81 |
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358 | |
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359 | ! |
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360 | ! Resest jux and juy |
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361 | jux=jumpx |
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362 | juy=jumpy |
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363 | end do |
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364 | end do |
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365 | 10 continue |
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366 | end do |
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367 | |
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368 | ! |
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369 | ! Fill in missing PV values on poles, if present |
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370 | ! Use mean PV of surrounding latitude ring |
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371 | ! |
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372 | if (sglobal) then |
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373 | do kl=1,nuvz |
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374 | pvavr=0. |
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375 | do ix=0,nxmin1 |
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376 | pvavr=pvavr+pvh(ix,1,kl) |
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377 | end do |
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378 | pvavr=pvavr/real(nx) |
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379 | jy=0 |
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380 | do ix=0,nxmin1 |
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381 | pvh(ix,jy,kl)=pvavr |
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382 | end do |
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383 | end do |
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384 | end if |
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385 | if (nglobal) then |
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386 | do kl=1,nuvz |
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387 | pvavr=0. |
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388 | do ix=0,nxmin1 |
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389 | pvavr=pvavr+pvh(ix,ny-2,kl) |
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390 | end do |
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391 | pvavr=pvavr/real(nx) |
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392 | jy=nymin1 |
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393 | do ix=0,nxmin1 |
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394 | pvh(ix,jy,kl)=pvavr |
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395 | end do |
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396 | end do |
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397 | end if |
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398 | |
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399 | end subroutine calcpv |
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400 | |
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