1 |
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2 | !
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3 |
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4 | ! calculate the bending angle on impact params.
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5 |
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6 | SUBROUTINE alpha_optl(nlev, & ! no. of model levs (=38)
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7 | nobs, & ! no. of bending angles in profile
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8 | roc, & ! radius of curv.
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9 | undul, & ! undulation (set to 0.0)
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10 | lat, & ! latitude of ob. location (degrees)
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11 | pres, & ! pressure on mod levels (hPa)
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12 | pres_prime, &
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13 | temp, & ! temp on model levels
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14 | temp_prime, &
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15 | q, & ! specific humidity (g/kg)
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16 | q_prime, &
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17 | zg, & ! geopotential height of model levels (m)
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18 | a, & ! impact parameters
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19 | alpha, &
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20 | alpha_prime) ! bending angles
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21 |
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22 |
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23 |
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24 |
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25 |
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26 |
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27 | IMPLICIT NONE
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28 |
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29 | !
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30 | ! subroutine args.
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31 | !
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32 |
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33 | INTEGER, INTENT(IN) :: nlev ! no. of p levels in state vec.
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34 | INTEGER, INTENT(IN) :: nobs
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35 | REAL, INTENT(IN) :: roc
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36 | REAL, INTENT(IN) :: undul
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37 | REAL, INTENT(IN) :: lat
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38 | REAL, INTENT(IN) :: pres(nlev),temp(nlev),q(nlev)
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39 | REAL, INTENT(IN) :: pres_prime(nlev),temp_prime(nlev),q_prime(nlev)
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40 | REAL, INTENT(IN) :: zg(nlev)
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41 | REAL, INTENT(IN) :: a(nobs)
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42 | REAL, INTENT(OUT) :: alpha(nobs),alpha_prime(nobs)
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43 |
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44 | !
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45 | ! local variables
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46 | !
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47 | INTEGER :: i
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48 | REAL :: refrac(nlev)
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49 | REAL :: nr(nlev),zg_prime(nlev)
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50 | REAL :: refrac_prime(nlev),nr_prime(nlev)
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51 | REAL :: roc2
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52 |
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53 | !
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54 | ! using fixed geopotential heights
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55 | !
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56 |
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57 | zg_prime = 0.0
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58 |
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59 | !
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60 | ! calculate refractivity on model levels
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61 | !
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62 |
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63 | CALL refrac_levstl(nlev, &
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64 | pres, &
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65 | pres_prime, &
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66 | temp, &
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67 | temp_prime, &
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68 | q, &
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69 | q_prime, &
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70 | refrac, &
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71 | refrac_prime)
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72 |
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73 |
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74 | !
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75 | ! calculate the refractive index * radius on model levels
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76 | !
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77 |
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78 | roc2 = roc + undul
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79 |
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80 | CALL calc_nrtl(nlev, &
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81 | roc2, &
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82 | lat, &
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83 | zg, &
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84 | zg_prime, &
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85 | refrac, &
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86 | refrac_prime, &
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87 | nr, &
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88 | nr_prime)
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89 |
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90 |
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91 |
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92 |
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93 | !
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94 | ! calculate the bending angle for the derived profile from profile
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95 | !
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96 |
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97 |
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98 | CALL calc_alphatl(nobs, &
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99 | nlev, &
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100 | a, &
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101 | refrac, &
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102 | refrac_prime, &
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103 | nr, &
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104 | nr_prime, &
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105 | alpha, &
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106 | alpha_prime)
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107 |
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108 |
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109 | RETURN
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110 |
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111 | END SUBROUTINE alpha_optl
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112 |
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113 | ! calculate the refractivity on observation heights from state vector x
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114 |
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115 |
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116 | SUBROUTINE refrac_levsTL(nlev, &
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117 | pres, &
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118 | pres_prime, &
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119 | temp, &
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120 | temp_prime,&
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121 | q, &
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122 | q_prime, &
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123 | refrac, &
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124 | refrac_prime)
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125 |
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126 |
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127 |
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128 | USE refrac_info, ONLY: &
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129 | epsilon,&
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130 | aval, &
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131 | bval, &
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132 | RMDI
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133 |
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134 |
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135 | IMPLICIT NONE
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136 |
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137 | !
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138 | ! subroutine args.
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139 | !
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140 |
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141 | INTEGER, INTENT(IN) :: nlev ! no. of p levels in state vec.
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142 | REAL, INTENT(IN) :: pres(nlev) ! in hPa
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143 | REAL, INTENT(IN) :: pres_prime(nlev) ! in hPa
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144 |
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145 | REAL, INTENT(IN) :: temp(nlev)
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146 | REAL, INTENT(IN) :: temp_prime(nlev)
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147 | REAL, INTENT(IN) :: q(nlev)
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148 | REAL, INTENT(IN) :: q_prime(nlev)
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149 | REAL, INTENT(OUT) :: refrac(nlev)
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150 | REAL, INTENT(OUT) :: refrac_prime(nlev)
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151 |
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152 | !
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153 | ! local variables
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154 | !
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155 |
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156 | INTEGER :: i
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157 |
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158 | REAL :: Ndry,Nhum
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159 | REAL :: Ndry_prime,Nhum_prime
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160 |
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161 |
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162 | !
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163 | ! now calculate the refractivity on pressure levels
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164 | !
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165 |
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166 |
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167 | refrac(:) = RMDI
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168 |
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169 | refrac_prime(:) = 0.0
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170 |
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171 | DO i = 1, nlev
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172 |
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173 | Ndry = aval * pres(i)/ temp(i)
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174 |
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175 | Ndry_prime = Ndry/pres(i)*pres_prime(i) - Ndry/temp(i) * temp_prime(i)
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176 |
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177 | Nhum = 0.0
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178 | Nhum_prime = 0.0
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179 |
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180 |
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181 | Nhum = &
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182 | 1.0E-3*bval* pres(i) * q(i)/(Epsilon*temp(i)**2)
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183 |
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184 | Nhum_prime = &
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185 | Nhum/pres(i)*pres_prime(i)-2.0*Nhum/temp(i)*temp_prime(i) + Nhum/q(i)*q_prime(i)
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186 |
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187 |
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188 | !
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189 | ! refractivity on ith pressure level
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190 | !
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191 |
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192 | refrac(i) = Ndry + Nhum
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193 |
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194 | refrac_prime(i) = Ndry_prime + Nhum_prime
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195 |
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196 |
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197 | ENDDO
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198 |
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199 | RETURN
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200 |
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201 | END SUBROUTINE refrac_levsTL
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202 |
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203 | ! calculate the nr product
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204 |
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205 | SUBROUTINE calc_nrTL(nlev, &
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206 | roc, &
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207 | lat, &
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208 | zg, &
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209 | zg_prime, &
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210 | refrac, &
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211 | refrac_prime, &
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212 | nr, &
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213 | nr_prime)
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214 |
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215 |
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216 |
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217 |
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218 | USE refrac_info, ONLY: &
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219 | g, &
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220 | RMDI
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221 |
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222 |
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223 | IMPLICIT NONE
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224 |
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225 | !
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226 | ! subroutine args.
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227 | !
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228 |
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229 | INTEGER, INTENT(IN) :: nlev ! no. of p levels in state vec.
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230 | REAL, INTENT(IN) :: roc
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231 | REAL, INTENT(IN) :: lat
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232 | REAL, INTENT(IN) :: zg(nlev)
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233 | REAL, INTENT(IN) :: zg_prime(nlev)
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234 | REAL, INTENT(IN) :: refrac(nlev)
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235 | REAL, INTENT(IN) :: refrac_prime(nlev)
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236 | REAL, INTENT(OUT) :: nr(nlev)
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237 | REAL, INTENT(OUT) :: nr_prime(nlev)
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238 |
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239 | !
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240 | ! local variables
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241 | !
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242 |
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243 | INTEGER :: i
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244 | REAL :: zed(nlev)
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245 | REAL :: rad(nlev)
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246 | REAL :: zed_prime(nlev)
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247 | REAL :: rad_prime(nlev)
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248 | REAL :: grat
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249 | REAL :: radius
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250 | REAL :: E_rad
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251 | REAL :: g_lat
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252 |
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253 | !
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254 | ! calculate the radius and g values used in the geopotential/geometric height
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255 | ! conversion.
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256 | !
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257 |
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258 | grat = g_lat(lat)/g
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259 | radius = E_rad(lat)
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260 |
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261 | !
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262 | ! calculate the geometric heights
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263 | !
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264 |
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265 | rad(:) = RMDI
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266 | nr(:) = RMDI
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267 |
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268 | rad_prime(:) = 0.0
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269 | nr_prime(:) = 0.0
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270 |
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271 |
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272 | DO i=1,nlev
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273 |
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274 | IF (zg(i) > 0.0 .AND. refrac(i) > 0.0 ) THEN
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275 |
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276 | zed(i)=zg(i)/(grat - zg(i)/radius)
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277 |
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278 | zed_prime(i) = grat/(grat-zg(i)/radius)**2 * zg_prime(i)
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279 |
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280 | !
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281 | ! calculate radius value
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282 | !
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283 |
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284 | rad(i) = roc + zed(i)
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285 |
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286 | rad_prime(i) = zed_prime(i)
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287 |
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288 | !
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289 | ! calculate the radius times refractive index product.
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290 | !
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291 |
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292 | nr(i) = rad(i) * (1.0+1.0E-6*refrac(i))
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293 |
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294 | nr_prime(i) = rad_prime(i) * (1.0+1.0E-6*refrac(i)) &
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295 | + 1.0E-6* rad(i)* refrac_prime(i)
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296 |
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297 |
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298 |
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299 | ENDIF
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300 |
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301 |
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302 | ENDDO
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303 |
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304 |
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305 | END SUBROUTINE calc_nrTL
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306 |
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307 | ! calculate the bending angle "alpha" for impact parameters a
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308 |
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309 | SUBROUTINE calc_alphaTL(nobs, &
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310 | nlev, &
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311 | a, &
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312 | refrac, &
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313 | refrac_prime, &
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314 | nr, &
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315 | nr_prime, &
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316 | alpha, &
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317 | alpha_prime)
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318 |
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319 |
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320 | USE refrac_info, ONLY: &
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321 | RMDI, &
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322 | pi
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323 |
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324 |
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325 |
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326 | IMPLICIT NONE
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327 |
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328 | !
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329 | ! subroutine args.
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330 | !
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331 |
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332 | INTEGER, INTENT(IN) :: nobs ! size of ob. vector
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333 | INTEGER, INTENT(IN) :: nlev ! no. of refractivity levels
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334 | REAL, INTENT(IN) :: a(nobs) ! impact parameter
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335 | REAL, INTENT(IN) :: refrac(nlev) ! refractivity values on levels
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336 | REAL, INTENT(IN) :: refrac_prime(nlev)
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337 | REAL, INTENT(IN) :: nr(nlev) ! index * radius product
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338 | REAL, INTENT(IN) :: nr_prime(nlev)
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339 | REAL, INTENT(OUT) :: alpha(nobs)
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340 | REAL, INTENT(OUT) :: alpha_prime(nobs) ! bending angle
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341 |
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342 | !
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343 | ! local variables
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344 | !
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345 |
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346 | INTEGER :: i,n,ibot,jbot
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347 | REAL :: kval(nlev-1)
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348 | REAL :: kval_prime(nlev-1)
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349 | REAL :: root_2pia
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350 | REAL :: ref_low
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351 | REAL :: ref_low_prime
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352 | REAL :: nr_low
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353 | REAL :: nr_low_prime
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354 | REAL :: tup,tlow
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355 | REAL :: tup_prime,tlow_prime
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356 | REAL :: dalpha
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357 | REAL :: dalpha_prime
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358 | REAL :: erf
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359 | REAL :: diff_erf
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360 | REAL :: diff_erf_prime
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361 |
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362 |
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363 | alpha(:) = RMDI
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364 |
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365 | alpha_prime(:) = 0.0
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366 |
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367 | jbot = 1
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368 |
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369 | DO
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370 |
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371 | IF (refrac(jbot) > 0.0 .AND. nr(jbot) > 0.0) EXIT
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372 |
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373 | jbot = jbot + 1
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374 |
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375 | ENDDO
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376 |
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377 |
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378 | !
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379 | ! calculate the exponential decay rate between levels
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380 | !
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381 |
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382 |
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383 | DO i=jbot,nlev-1
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384 |
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385 | kval(i) = LOG(refrac(i)/refrac(i+1)) / &
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386 | MAX(1.0,(nr(i+1)-nr(i)))
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387 |
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388 | Kval(i) = MAX(1.0E-6,kval(i))
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389 | kval_prime(i) = 0.0
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390 |
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391 |
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392 | IF (kval(i) > 1.0E-6) &
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393 | kval_prime(i) = ((kval(i)*(nr_prime(i)-nr_prime(i+1))) + &
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394 | (refrac_prime(i)/refrac(i)- &
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395 | refrac_prime(i+1)/refrac(i+1)))/ &
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396 | MAX(1.0,(nr(i+1)-nr(i)))
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397 |
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398 | ENDDO
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399 |
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400 | !
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401 | ! now calculate the bending angle values
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402 | !
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403 |
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404 |
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405 |
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406 | DO n=1,nobs
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407 |
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408 |
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409 | IF (a(n) < nr(jbot) .OR. a(n) > nr(nlev)) CYCLE
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410 |
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411 | Root_2PIa = SQRT(2.0*pi*a(n))
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412 |
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413 | ibot = jbot
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414 |
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415 | DO
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416 |
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417 | IF (a(n) < nr(ibot+1)) EXIT
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418 |
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419 | ibot=ibot+1
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420 |
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421 | ENDDO
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422 |
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423 | !
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424 | ! set bending angle value
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425 | !
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426 |
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427 | alpha(n) = 0.0
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428 |
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429 | alpha_prime(n) = 0.0
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430 |
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431 | DO i = ibot, nlev-1
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432 |
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433 | IF ( i == ibot) THEN
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434 |
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435 | ref_low = refrac(i)*EXP(-kval(i)*(a(n)-nr(i)))
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436 |
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437 |
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438 | ref_low_prime = ref_low* &
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439 | (refrac_prime(i)/refrac(i) - &
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440 | kval_prime(i)*(a(n)-nr(i)) + &
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441 | kval(i)*nr_prime(i))
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442 |
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443 |
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444 | nr_low = a(n)
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445 |
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446 | nr_low_prime = 0.0
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447 |
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448 |
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449 |
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450 | ELSE
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451 |
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452 | ref_low = refrac(i)
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453 |
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454 | ref_low_prime = refrac_prime(i)
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455 |
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456 | nr_low = nr(i)
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457 |
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458 | nr_low_prime = nr_prime(i)
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459 |
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460 | ENDIF
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461 | tup = SQRT(kval(i)*(nr(i+1)-a(n)))
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462 |
|
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463 | tup_prime = 0.5*(kval_prime(i)*(nr(i+1)-a(n)) + &
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464 | kval(i)*nr_prime(i+1))/tup
|
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465 |
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466 | tlow = 0.0
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467 |
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468 | tlow_prime = 0.0
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469 |
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470 | IF (i > ibot) THEN
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471 |
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472 | tlow = SQRT(kval(i)*(nr(i) -a(n)))
|
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473 |
|
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474 | tlow_prime = 0.5*(kval_prime(i)*(nr(i)-a(n)) + &
|
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475 | kval(i)*nr_prime(i))/tlow
|
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476 |
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477 | ENDIF
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478 |
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479 |
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480 | IF (i < nlev-1) THEN
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481 |
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482 |
|
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483 | diff_erf = erf(tup) - erf(tlow)
|
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484 |
|
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485 | diff_erf_prime = 2.0/SQRT(pi)*(EXP(-tup**2)*tup_prime - &
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486 | EXP(-tlow**2)*tlow_prime )
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487 |
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488 | ELSE
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489 |
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490 |
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491 | diff_erf = 1.0 - erf(tlow)
|
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492 |
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493 | diff_erf_prime = -2.0/SQRT(pi)*EXP(-tlow**2)*tlow_prime
|
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494 |
|
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495 | ENDIF
|
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496 |
|
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497 |
|
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498 | dalpha = &
|
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499 | + 1.0E-6 * Root_2PIa * SQRT(kval(i)) &
|
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500 | * ref_low*EXP(kval(i)*(nr_low-a(n)))*diff_erf
|
---|
501 |
|
---|
502 |
|
---|
503 | dalpha_prime = dalpha * ( &
|
---|
504 | ref_low_prime/MAX(1.0E-10,ref_low) + &
|
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505 | diff_erf_prime/MAX(1.0E-10,diff_erf) + &
|
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506 | kval(i)*nr_low_prime + &
|
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507 | (nr_low-a(n) + 0.5/kval(i))* kval_prime(i))
|
---|
508 |
|
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509 |
|
---|
510 | alpha(n) = alpha(n) + dalpha
|
---|
511 |
|
---|
512 |
|
---|
513 |
|
---|
514 | alpha_prime(n) = alpha_prime(n) + dalpha_prime
|
---|
515 |
|
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516 |
|
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517 | ENDDO
|
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518 |
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519 |
|
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520 | ENDDO
|
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521 |
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522 |
|
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523 | END SUBROUTINE calc_alphaTL
|
---|
524 |
|
---|