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 cbl(wp,zp,ust,wst,h,rhoa,rhograd,sigmaw,dsigmawdz,tlw,ptot,Q,phi,ath,bth,ol,flagrein) |
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5 | ! i i i i i i i i i i o o o o o i o |
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6 | |
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7 | use par_mod, only:pi |
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8 | use com_mod, only:ldirect |
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9 | |
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10 | implicit none |
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11 | !======================================================================================================================================================= |
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12 | !=============== CBL skewed vertical profiles and formulation of LHH 1996 with profile of w3 from LHB 2000 ======== |
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13 | !=============== LHH formulation has been modified to account for variable density profiles and backward in time or forward in time simulations ======== |
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14 | !=============== see Cassiani et al. BLM 2014 doi for explanations and references ======== |
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15 | !======================================================================================================================================================= |
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16 | |
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17 | real :: usurad2,usurad2p,C0,costluar4,eps |
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18 | parameter (usurad2=0.7071067812,usurad2p=0.3989422804,C0=3,costluar4=0.66667,eps=0.000001) |
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19 | |
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20 | |
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21 | integer :: flagrein |
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22 | real :: wp,zp,ust,wst,h,dens,ddens,sigmaw,dsigmawdz,tlw,rhoa,rhograd |
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23 | real ::fluarw,fluarw2 |
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24 | real ::w3,w2 |
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25 | real ::dw3,dw2 |
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26 | real ::wb,wa |
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27 | real ::deltawa,deltawb |
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28 | real ::wold,wold2,wold_z |
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29 | real ::pa,pb,alfa |
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30 | real ::Phi,Q,ptot |
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31 | real :: timedir |
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32 | real ::cuberoot |
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33 | real ::z0,ol,transition |
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34 | |
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35 | |
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36 | real :: & |
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37 | erf, & |
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38 | aperfa, & |
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39 | aperfb, & |
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40 | ath, & |
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41 | bth |
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42 | |
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43 | real :: & |
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44 | pow, & |
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45 | z, & |
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46 | skew, & |
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47 | skew2, & |
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48 | radw2, & |
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49 | rluarw, & |
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50 | xluarw, & |
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51 | aluarw, & |
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52 | bluarw, & |
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53 | sigmawa, & |
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54 | sigmawb, & |
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55 | dskew, & |
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56 | dradw2, & |
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57 | dfluarw, & |
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58 | drluarw, & |
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59 | dxluarw, & |
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60 | daluarw, & |
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61 | dbluarw, & |
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62 | dsigmawa, & |
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63 | dsigmawb, & |
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64 | dwa, & |
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65 | dwb, & |
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66 | sigmawa2, & |
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67 | sigmawb2 |
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68 | |
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69 | |
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70 | dens=rhoa !put to 1 for test constant density simulation |
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71 | ddens=rhograd !put to 0 for test constant density simulation |
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72 | |
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73 | |
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74 | timedir=ldirect !ldirect contains direction of time forward (1) or backward(-1) |
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75 | !========================= assegnazione z =========================================================== |
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76 | z=(zp/h) |
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77 | |
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78 | !================== stability transition function see Cassiani et al(2015) BLM ====================== |
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79 | transition=1. |
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80 | !if (ol.lt.-50) transition=((sin(((ol+100.)/100.)*pi))-1.)/2. |
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81 | if (-h/ol.lt.15) transition=((sin((((-h/ol)+10.)/10.)*pi)))/2.+0.5 |
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82 | |
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83 | !========================= momento secondo ========================================================== |
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84 | |
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85 | w2=(sigmaw*sigmaw) |
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86 | dw2=(2.*sigmaw*dsigmawdz) |
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87 | |
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88 | |
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89 | !=================== dissipazione ======================================= |
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90 | |
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91 | alfa=2.*w2/(C0*tlw) |
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92 | |
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93 | !======================================================================== |
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94 | |
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95 | wold=timedir*wp |
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96 | |
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97 | !========================================================================= |
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98 | !------------------------------ momento terzo ============================ |
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99 | |
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100 | w3=((1.2*z*((1.-z)**(3./2.)))+eps)*(wst**3)*transition |
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101 | dw3=(1.2*(((1.-z)**(3./2.))+z*1.5*((1.-z)**(1./2.))*(-1.)))*(wst**3)*(1./h)*transition |
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102 | |
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103 | !===========================================================================0 |
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104 | |
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105 | skew=w3/(w2**1.5) |
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106 | skew2=skew*skew |
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107 | dskew=(dw3*w2**(1.5)-w3*1.5*w2**0.5*dw2)/w2**3 |
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108 | radw2=w2**0.5 |
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109 | dradw2=0.5*w2**(-0.5)*dw2 |
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110 | !costluar4=0.66667 ! costante da LHH |
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111 | fluarw=costluar4*(cuberoot(skew)) !skew**(1./3.) |
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112 | fluarw2=fluarw*fluarw |
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113 | |
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114 | if (skew.ne.0) then |
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115 | |
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116 | dfluarw=costluar4*(1./3.)*cuberoot(skew**(-2.))*dskew |
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117 | |
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118 | rluarw=(1.+fluarw2)**3.*skew2/((3.+fluarw2)**2.*fluarw2) !-> r |
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119 | xluarw=(1.+fluarw2)**1.5*skew/((3.+fluarw2)*fluarw) !----> r^1/2 |
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120 | |
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121 | drluarw=( ((3.*(1.+fluarw2)**2*(2.*fluarw*dfluarw)*skew2)+ & |
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122 | (1.+fluarw2)**3*2.*skew*dskew) *(3.+fluarw2)**2.*fluarw2 - & |
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123 | (1.+fluarw2)**3*skew2* & |
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124 | ( (2.*(3.+fluarw2)*(2.*fluarw*dfluarw)*fluarw2) + & |
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125 | (3.+fluarw2)**2*2.*fluarw*dfluarw) )/ & |
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126 | (((3.+fluarw2)**2.*fluarw2)**2) |
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127 | |
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128 | dxluarw=( ((1.5*(1.+fluarw2)**0.5*(2.*fluarw*dfluarw)*skew)+ & |
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129 | (1.+fluarw2)**1.5*dskew) *(3.+fluarw2)*fluarw - & |
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130 | (1.+fluarw2)**1.5*skew* & |
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131 | (3.*dfluarw+3*fluarw2*dfluarw) )/ & |
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132 | (((3.+fluarw2)*fluarw)**2) |
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133 | |
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134 | else |
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135 | dfluarw=0. |
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136 | rluarw=0. |
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137 | drluarw=0. |
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138 | xluarw=0. |
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139 | dxluarw=0. |
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140 | end if |
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141 | |
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142 | |
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143 | |
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144 | aluarw=0.5*(1.-xluarw/(4.+rluarw)**0.5) |
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145 | bluarw=1.-aluarw |
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146 | |
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147 | daluarw=-0.5*( (dxluarw*(4.+rluarw)**0.5) - & |
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148 | (0.5*xluarw*(4.+rluarw)**(-0.5)*drluarw) ) & |
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149 | /(4.+rluarw) |
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150 | dbluarw=-daluarw |
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151 | |
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152 | sigmawa=radw2*(bluarw/(aluarw*(1.+fluarw2)))**0.5 |
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153 | sigmawb=radw2*(aluarw/(bluarw*(1.+fluarw2)))**0.5 |
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154 | |
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155 | dsigmawa=dradw2*(bluarw/(aluarw*(1.+fluarw2)))**0.5+ & |
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156 | radw2*( & |
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157 | (0.5*(bluarw/(aluarw*(1.+fluarw2)))**(-0.5)) * & |
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158 | ( & |
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159 | (dbluarw*(aluarw*(1.+fluarw2))- & |
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160 | bluarw*(daluarw*(1.+fluarw2)+aluarw*2.*fluarw*dfluarw)) & |
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161 | /((aluarw*(1.+fluarw2))**2) & |
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162 | ) & |
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163 | ) |
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164 | dsigmawb=dradw2*(aluarw/(bluarw*(1.+fluarw2)))**0.5+ & |
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165 | radw2*( & |
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166 | (0.5*(aluarw/(bluarw*(1.+fluarw2)))**(-0.5)) * & |
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167 | ( & |
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168 | (daluarw*(bluarw*(1.+fluarw2))- & |
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169 | aluarw*(dbluarw*(1.+fluarw2)+bluarw*2.*fluarw*dfluarw)) & |
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170 | /((bluarw*(1.+fluarw2))**2) & |
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171 | ) & |
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172 | ) |
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173 | |
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174 | wa=(fluarw*sigmawa) |
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175 | wb=(fluarw*sigmawb) |
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176 | dwa=dfluarw*sigmawa+fluarw*dsigmawa |
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177 | dwb=dfluarw*sigmawb+fluarw*dsigmawb |
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178 | |
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179 | deltawa=wold-wa |
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180 | deltawb=wold+wb |
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181 | wold2=wold*wold |
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182 | sigmawa2=sigmawa*sigmawa |
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183 | sigmawb2=sigmawb*sigmawb |
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184 | |
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185 | if (abs(deltawa).gt.6.*sigmawa.and.abs(deltawb).gt.6.*sigmawb) flagrein=1 |
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186 | |
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187 | pa=(usurad2p*(1./sigmawa))*(exp(-(0.5*((deltawa/sigmawa)**2.)))) |
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188 | pb=(usurad2p*(1./sigmawb))*(exp(-(0.5*((deltawb/sigmawb)**2.)))) |
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189 | |
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190 | ptot=dens*aluarw*pa+dens*bluarw*pb |
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191 | |
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192 | aperfa=deltawa*usurad2/sigmawa |
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193 | aperfb=deltawb*usurad2/sigmawb |
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194 | |
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195 | Phi=-0.5* & |
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196 | (aluarw*dens*dwa+dens*wa*daluarw+aluarw*wa*ddens)*erf(aperfa) & |
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197 | +sigmawa*(aluarw*dens*dsigmawa*(wold2/sigmawa2+1.)+ & |
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198 | sigmawa*dens*daluarw+sigmawa*ddens*aluarw+ & |
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199 | aluarw*wold*dens/sigmawa2*(sigmawa*dwa-wa*dsigmawa))*pa & |
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200 | +0.5* & |
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201 | (bluarw*dens*dwb+wb*dens*dbluarw+wb*bluarw*ddens)*erf(aperfb) & |
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202 | +sigmawb*(bluarw*dens*dsigmawb*(wold2/sigmawb2+1.)+ & |
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203 | sigmawb*dens*dbluarw+sigmawb*ddens*bluarw+ & |
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204 | bluarw*wold*dens/sigmawb2*(-sigmawb*dwb+wb*dsigmawb))*pb |
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205 | |
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206 | Q=timedir*((aluarw*dens*deltawa/sigmawa2)*pa+ & |
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207 | (bluarw*dens*deltawb/sigmawb2)*pb) |
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208 | |
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209 | ath=(1./ptot)*(-(C0/2.)*alfa*Q+phi) |
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210 | bth=sqrt(C0*alfa) |
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211 | !bth=sngl(sigmaw*sqrt(2.*tlw)) |
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212 | |
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213 | return |
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214 | end |
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215 | |
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216 | |
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217 | |
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218 | |
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219 | |
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220 | FUNCTION CUBEROOT (X) RESULT (Y) |
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221 | |
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222 | IMPLICIT NONE |
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223 | |
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224 | real, INTENT(IN) :: X |
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225 | real:: Y |
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226 | |
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227 | real, PARAMETER :: THIRD = 0.333333333 |
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228 | |
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229 | |
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230 | Y = SIGN((ABS(X))**THIRD, X) |
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231 | |
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232 | RETURN |
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233 | |
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234 | END FUNCTION CUBEROOT |
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235 | |
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236 | |
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237 | |
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238 | |
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239 | FUNCTION CUBEROOTD (X) RESULT (Y) |
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240 | |
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241 | IMPLICIT NONE |
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242 | |
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243 | DOUBLE PRECISION, INTENT(IN) :: X |
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244 | DOUBLE PRECISION :: Y |
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245 | |
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246 | DOUBLE PRECISION, PARAMETER :: THIRD = 0.33333333333333333333333333333333333333333333333333333333333333333333333333333333333D0 |
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247 | |
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248 | |
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249 | Y = SIGN((ABS(X))**THIRD, X) |
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250 | |
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251 | RETURN |
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252 | |
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253 | END FUNCTION CUBEROOTD |
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