1 | ! SPDX-FileCopyrightText: FLEXPART 1998-2019, see flexpart_license.txt |
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2 | ! SPDX-License-Identifier: GPL-3.0-or-later |
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3 | |
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4 | subroutine interpol_wind(itime,xt,yt,zt) |
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5 | ! i i i i |
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6 | !***************************************************************************** |
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7 | ! * |
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8 | ! This subroutine interpolates the wind data to current trajectory position.* |
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9 | ! * |
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10 | ! Author: A. Stohl * |
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11 | ! * |
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12 | ! 16 December 1997 * |
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13 | ! * |
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14 | ! Revision March 2005 by AST : all output variables in common block cal- * |
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15 | ! culation of standard deviation done in this * |
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16 | ! routine rather than subroutine call in order * |
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17 | ! to save computation time * |
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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 | ! u,v,w wind components * |
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23 | ! itime [s] current temporal position * |
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24 | ! memtime(3) [s] times of the wind fields in memory * |
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25 | ! xt,yt,zt coordinates position for which wind data shall be * |
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26 | ! calculated * |
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27 | ! * |
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28 | ! Constants: * |
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29 | ! * |
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30 | !***************************************************************************** |
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31 | |
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32 | use par_mod |
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33 | use com_mod |
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34 | use interpol_mod |
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35 | |
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36 | implicit none |
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37 | |
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38 | integer :: itime |
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39 | real :: xt,yt,zt |
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40 | |
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41 | ! Auxiliary variables needed for interpolation |
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42 | real :: dz1,dz2,dz |
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43 | real :: u1(2),v1(2),w1(2),uh(2),vh(2),wh(2) |
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44 | real :: usl,vsl,wsl,usq,vsq,wsq,xaux |
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45 | integer :: i,m,n,indexh,indzh |
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46 | real,parameter :: eps=1.0e-30 |
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47 | |
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48 | |
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49 | !******************************************** |
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50 | ! Multilinear interpolation in time and space |
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51 | !******************************************** |
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52 | |
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53 | ! Determine the lower left corner and its distance to the current position |
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54 | !************************************************************************* |
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55 | |
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56 | ddx=xt-real(ix) |
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57 | ddy=yt-real(jy) |
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58 | rddx=1.-ddx |
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59 | rddy=1.-ddy |
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60 | p1=rddx*rddy |
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61 | p2=ddx*rddy |
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62 | p3=rddx*ddy |
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63 | p4=ddx*ddy |
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64 | |
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65 | ! Calculate variables for time interpolation |
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66 | !******************************************* |
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67 | |
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68 | dt1=real(itime-memtime(1)) |
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69 | dt2=real(memtime(2)-itime) |
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70 | dtt=1./(dt1+dt2) |
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71 | |
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72 | ! Determine the level below the current position for u,v |
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73 | !******************************************************* |
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74 | |
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75 | do i=2,nz |
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76 | if (height(i).gt.zt) then |
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77 | indz=i-1 |
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78 | goto 6 |
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79 | endif |
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80 | end do |
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81 | 6 continue |
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82 | |
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83 | |
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84 | ! Vertical distance to the level below and above current position |
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85 | !**************************************************************** |
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86 | |
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87 | dz=1./(height(indz+1)-height(indz)) |
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88 | dz1=(zt-height(indz))*dz |
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89 | dz2=(height(indz+1)-zt)*dz |
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90 | |
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91 | !********************************************************************** |
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92 | ! 1.) Bilinear horizontal interpolation |
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93 | ! This has to be done separately for 6 fields (Temporal(2)*Vertical(3)) |
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94 | !********************************************************************** |
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95 | |
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96 | ! Loop over 2 time steps and 2 levels |
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97 | !************************************ |
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98 | |
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99 | usl=0. |
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100 | vsl=0. |
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101 | wsl=0. |
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102 | usq=0. |
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103 | vsq=0. |
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104 | wsq=0. |
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105 | do m=1,2 |
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106 | indexh=memind(m) |
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107 | do n=1,2 |
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108 | indzh=indz+n-1 |
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109 | |
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110 | if (ngrid.lt.0) then |
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111 | u1(n)=p1*uupol(ix ,jy ,indzh,indexh) & |
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112 | +p2*uupol(ixp,jy ,indzh,indexh) & |
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113 | +p3*uupol(ix ,jyp,indzh,indexh) & |
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114 | +p4*uupol(ixp,jyp,indzh,indexh) |
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115 | v1(n)=p1*vvpol(ix ,jy ,indzh,indexh) & |
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116 | +p2*vvpol(ixp,jy ,indzh,indexh) & |
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117 | +p3*vvpol(ix ,jyp,indzh,indexh) & |
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118 | +p4*vvpol(ixp,jyp,indzh,indexh) |
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119 | usl=usl+uupol(ix ,jy ,indzh,indexh)+ & |
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120 | uupol(ixp,jy ,indzh,indexh) & |
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121 | +uupol(ix ,jyp,indzh,indexh)+uupol(ixp,jyp,indzh,indexh) |
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122 | vsl=vsl+vvpol(ix ,jy ,indzh,indexh)+ & |
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123 | vvpol(ixp,jy ,indzh,indexh) & |
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124 | +vvpol(ix ,jyp,indzh,indexh)+vvpol(ixp,jyp,indzh,indexh) |
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125 | |
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126 | usq=usq+uupol(ix ,jy ,indzh,indexh)* & |
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127 | uupol(ix ,jy ,indzh,indexh)+ & |
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128 | uupol(ixp,jy ,indzh,indexh)*uupol(ixp,jy ,indzh,indexh)+ & |
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129 | uupol(ix ,jyp,indzh,indexh)*uupol(ix ,jyp,indzh,indexh)+ & |
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130 | uupol(ixp,jyp,indzh,indexh)*uupol(ixp,jyp,indzh,indexh) |
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131 | vsq=vsq+vvpol(ix ,jy ,indzh,indexh)* & |
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132 | vvpol(ix ,jy ,indzh,indexh)+ & |
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133 | vvpol(ixp,jy ,indzh,indexh)*vvpol(ixp,jy ,indzh,indexh)+ & |
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134 | vvpol(ix ,jyp,indzh,indexh)*vvpol(ix ,jyp,indzh,indexh)+ & |
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135 | vvpol(ixp,jyp,indzh,indexh)*vvpol(ixp,jyp,indzh,indexh) |
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136 | else |
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137 | u1(n)=p1*uu(ix ,jy ,indzh,indexh) & |
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138 | +p2*uu(ixp,jy ,indzh,indexh) & |
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139 | +p3*uu(ix ,jyp,indzh,indexh) & |
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140 | +p4*uu(ixp,jyp,indzh,indexh) |
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141 | v1(n)=p1*vv(ix ,jy ,indzh,indexh) & |
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142 | +p2*vv(ixp,jy ,indzh,indexh) & |
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143 | +p3*vv(ix ,jyp,indzh,indexh) & |
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144 | +p4*vv(ixp,jyp,indzh,indexh) |
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145 | usl=usl+uu(ix ,jy ,indzh,indexh)+uu(ixp,jy ,indzh,indexh) & |
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146 | +uu(ix ,jyp,indzh,indexh)+uu(ixp,jyp,indzh,indexh) |
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147 | vsl=vsl+vv(ix ,jy ,indzh,indexh)+vv(ixp,jy ,indzh,indexh) & |
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148 | +vv(ix ,jyp,indzh,indexh)+vv(ixp,jyp,indzh,indexh) |
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149 | |
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150 | usq=usq+uu(ix ,jy ,indzh,indexh)*uu(ix ,jy ,indzh,indexh)+ & |
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151 | uu(ixp,jy ,indzh,indexh)*uu(ixp,jy ,indzh,indexh)+ & |
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152 | uu(ix ,jyp,indzh,indexh)*uu(ix ,jyp,indzh,indexh)+ & |
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153 | uu(ixp,jyp,indzh,indexh)*uu(ixp,jyp,indzh,indexh) |
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154 | vsq=vsq+vv(ix ,jy ,indzh,indexh)*vv(ix ,jy ,indzh,indexh)+ & |
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155 | vv(ixp,jy ,indzh,indexh)*vv(ixp,jy ,indzh,indexh)+ & |
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156 | vv(ix ,jyp,indzh,indexh)*vv(ix ,jyp,indzh,indexh)+ & |
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157 | vv(ixp,jyp,indzh,indexh)*vv(ixp,jyp,indzh,indexh) |
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158 | endif |
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159 | w1(n)=p1*ww(ix ,jy ,indzh,indexh) & |
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160 | +p2*ww(ixp,jy ,indzh,indexh) & |
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161 | +p3*ww(ix ,jyp,indzh,indexh) & |
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162 | +p4*ww(ixp,jyp,indzh,indexh) |
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163 | wsl=wsl+ww(ix ,jy ,indzh,indexh)+ww(ixp,jy ,indzh,indexh) & |
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164 | +ww(ix ,jyp,indzh,indexh)+ww(ixp,jyp,indzh,indexh) |
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165 | wsq=wsq+ww(ix ,jy ,indzh,indexh)*ww(ix ,jy ,indzh,indexh)+ & |
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166 | ww(ixp,jy ,indzh,indexh)*ww(ixp,jy ,indzh,indexh)+ & |
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167 | ww(ix ,jyp,indzh,indexh)*ww(ix ,jyp,indzh,indexh)+ & |
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168 | ww(ixp,jyp,indzh,indexh)*ww(ixp,jyp,indzh,indexh) |
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169 | end do |
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170 | |
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171 | |
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172 | !********************************** |
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173 | ! 2.) Linear vertical interpolation |
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174 | !********************************** |
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175 | |
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176 | uh(m)=dz2*u1(1)+dz1*u1(2) |
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177 | vh(m)=dz2*v1(1)+dz1*v1(2) |
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178 | wh(m)=dz2*w1(1)+dz1*w1(2) |
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179 | end do |
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180 | |
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181 | |
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182 | !************************************ |
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183 | ! 3.) Temporal interpolation (linear) |
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184 | !************************************ |
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185 | |
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186 | u=(uh(1)*dt2+uh(2)*dt1)*dtt |
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187 | v=(vh(1)*dt2+vh(2)*dt1)*dtt |
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188 | w=(wh(1)*dt2+wh(2)*dt1)*dtt |
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189 | |
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190 | |
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191 | ! Compute standard deviations |
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192 | !**************************** |
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193 | |
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194 | xaux=usq-usl*usl/16. |
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195 | if (xaux.lt.eps) then |
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196 | usig=0. |
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197 | else |
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198 | usig=sqrt(xaux/15.) |
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199 | endif |
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200 | |
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201 | xaux=vsq-vsl*vsl/16. |
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202 | if (xaux.lt.eps) then |
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203 | vsig=0. |
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204 | else |
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205 | vsig=sqrt(xaux/15.) |
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206 | endif |
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207 | |
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208 | |
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209 | xaux=wsq-wsl*wsl/16. |
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210 | if (xaux.lt.eps) then |
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211 | wsig=0. |
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212 | else |
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213 | wsig=sqrt(xaux/15.) |
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214 | endif |
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215 | |
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216 | end subroutine interpol_wind |
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