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 richardson(psurf,ust,ttlev,qvlev,ulev,vlev,nuvz, & |
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24 | pplev,hf,tt2,td2,h,wst,hmixplus,ierr,sfc_option) |
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25 | ! subroutine richardson(psurf,ust,ttlev,qvlev,ulev,vlev,nuvz, |
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26 | ! +akz,bkz,hf,tt2,td2,h,wst,hmixplus,ierr) |
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27 | |
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28 | ! i i i i i i i |
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29 | ! i i i i i o o o |
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30 | !**************************************************************************** |
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31 | ! * |
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32 | ! Note: This is the FLEXPART_WRF version of subroutine richardson. * |
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33 | ! * |
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34 | ! Calculation of mixing height based on the critical Richardson number. * |
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35 | ! Calculation of convective time scale. * |
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36 | ! For unstable conditions, one iteration is performed. An excess * |
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37 | ! temperature (dependent on hf and wst) is calculated, added to the * |
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38 | ! temperature at the lowest model level. Then the procedure is repeated.* |
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39 | ! * |
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40 | ! Author: A. Stohl * |
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41 | ! * |
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42 | ! 22 August 1996 * |
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43 | ! * |
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44 | ! Literature: * |
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45 | ! Vogelezang DHP and Holtslag AAM (1996): Evaluation and model impacts * |
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46 | ! of alternative boundary-layer height formulations. Boundary-Layer * |
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47 | ! Meteor. 81, 245-269. * |
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48 | ! * |
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49 | ! Update: 1999-02-01 by G. Wotawa * |
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50 | ! * |
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51 | ! Two meter level (temperature, humidity) is taken as reference level * |
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52 | ! instead of first model level. * |
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53 | ! New input variables tt2, td2 introduced. * |
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54 | ! * |
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55 | ! 17 Oct 2005 - R. Easter - added ierr status flag (0=ok, -1=fail) * |
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56 | ! 15 Nov 2005 - R. Easter - use pplev instead of akz,bkz * |
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57 | ! * |
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58 | !**************************************************************************** |
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59 | ! * |
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60 | ! Variables: * |
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61 | ! h mixing height [m] * |
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62 | ! hf sensible heat flux * |
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63 | ! psurf surface pressure at point (xt,yt) [Pa] * |
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64 | ! tv virtual temperature * |
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65 | ! wst convective velocity scale * |
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66 | ! * |
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67 | ! Constants: * |
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68 | ! ric critical Richardson number * |
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69 | ! * |
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70 | !**************************************************************************** |
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71 | |
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72 | ! include 'includepar' |
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73 | |
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74 | ! integer ierr |
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75 | ! integer i,k,nuvz,itmax,iter |
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76 | ! real tv,tvold,zref,z,zold,pint,pold,theta,thetaref,ri |
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77 | !! real akz(nuvz),bkz(nuvz),ulev(nuvz),vlev(nuvz),hf,wst,tt2,td2,ew |
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78 | ! real pplev(nuvz),ulev(nuvz),vlev(nuvz),hf,wst,tt2,td2,ew |
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79 | ! real psurf,ust,ttlev(nuvz),qvlev(nuvz),h,const,ric,b,excess,bs |
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80 | ! real thetaold,zl,ul,vl,thetal,ril,hmixplus,wspeed,bvfsq,bvf |
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81 | ! real f_qvsat,rh,rhold,rhl,theta1,theta2,zl1,zl2,thetam |
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82 | ! parameter(const=r_air/ga,ric=0.25,b=100.,bs=8.5,itmax=3) |
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83 | |
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84 | use par_mod |
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85 | |
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86 | implicit none |
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87 | |
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88 | integer :: i,k,nuvz,iter,ierr |
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89 | real :: tv,tvold,zref,z,zold,pint,pold,theta,thetaref,ri |
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90 | real :: pplev(nuvz),ulev(nuvz),vlev(nuvz),hf,wst,tt2,td2,ew |
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91 | real :: psurf,ust,ttlev(nuvz),qvlev(nuvz),h,excess |
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92 | real :: thetaold,zl,ul,vl,thetal,ril,hmixplus,wspeed,bvfsq,bvf |
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93 | real :: f_qvsat,rh,rhold,rhl,theta1,theta2,zl1,zl2,thetam |
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94 | |
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95 | real,parameter :: const=r_air/ga, ric=0.25, b=100., bs=8.5 |
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96 | integer,parameter :: itmax=3 |
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97 | |
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98 | real :: duma |
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99 | integer :: sfc_option |
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100 | |
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101 | excess=0.0 |
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102 | iter=0 |
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103 | |
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104 | ! Compute virtual temperature and virtual potential temperature at |
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105 | ! reference level (2 m) |
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106 | !***************************************************************** |
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107 | |
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108 | 30 iter=iter+1 |
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109 | |
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110 | pold=psurf |
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111 | tvold=tt2*(1.+0.378*ew(td2)/psurf) |
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112 | zold=2.0 |
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113 | zref=zold |
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114 | rhold=ew(td2)/ew(tt2) |
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115 | |
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116 | thetaref=tvold*(100000./pold)**(r_air/cpa)+excess |
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117 | thetaold=thetaref |
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118 | |
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119 | |
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120 | ! Integrate z up to one level above zt |
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121 | !************************************* |
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122 | |
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123 | do k=2,nuvz |
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124 | ! pint=akz(k)+bkz(k)*psurf ! pressure on model layers |
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125 | pint=pplev(k) ! pressure on model layers |
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126 | tv=ttlev(k)*(1.+0.608*qvlev(k)) |
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127 | |
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128 | if (abs(tv-tvold).gt.0.2) then |
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129 | z=zold+const*log(pold/pint)*(tv-tvold)/log(tv/tvold) |
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130 | else |
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131 | z=zold+const*log(pold/pint)*tv |
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132 | endif |
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133 | |
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134 | theta=tv*(100000./pint)**(r_air/cpa) |
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135 | ! Petra |
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136 | rh = qvlev(k) / f_qvsat( pint, ttlev(k) ) |
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137 | |
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138 | |
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139 | !alculate Richardson number at each level |
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140 | !**************************************** |
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141 | |
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142 | ri=ga/thetaref*(theta-thetaref)*(z-zref)/ & |
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143 | max(((ulev(k)-ulev(2))**2+(vlev(k)-vlev(2))**2+b*ust**2),0.1) |
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144 | |
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145 | ! addition of second condition: MH should not be placed in an |
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146 | ! unstable layer (PS / Feb 2000) |
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147 | if (ri.gt.ric .and. thetaold.lt.theta) goto 20 |
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148 | |
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149 | tvold=tv |
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150 | pold=pint |
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151 | rhold=rh |
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152 | thetaold=theta |
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153 | zold=z |
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154 | end do |
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155 | |
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156 | if (k .ge. nuvz) then |
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157 | write(*,*) 'richardson not working -- k = nuvz' |
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158 | ierr = -10 |
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159 | goto 7000 |
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160 | end if |
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161 | |
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162 | 20 continue |
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163 | |
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164 | ! Determine Richardson number between the critical levels |
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165 | !******************************************************** |
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166 | |
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167 | zl1=zold |
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168 | theta1=thetaold |
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169 | do i=1,20 |
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170 | zl=zold+float(i)/20.*(z-zold) |
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171 | ul=ulev(k-1)+float(i)/20.*(ulev(k)-ulev(k-1)) |
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172 | vl=vlev(k-1)+float(i)/20.*(vlev(k)-vlev(k-1)) |
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173 | thetal=thetaold+float(i)/20.*(theta-thetaold) |
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174 | rhl=rhold+float(i)/20.*(rh-rhold) |
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175 | ril=ga/thetaref*(thetal-thetaref)*(zl-zref)/ & |
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176 | max(((ul-ulev(2))**2+(vl-vlev(2))**2+b*ust**2),0.1) |
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177 | zl2=zl |
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178 | theta2=thetal |
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179 | if (ril.gt.ric) goto 25 |
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180 | zl1=zl |
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181 | theta1=thetal |
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182 | enddo |
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183 | |
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184 | 25 continue |
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185 | ! if sfc_option = sfc_option_wrf, |
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186 | ! pbl heights are read from WRF met. files and put into hmix (=h) |
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187 | !JB |
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188 | ! h=zl |
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189 | if(sfc_option .eq. sfc_option_diagnosed) h=zl |
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190 | if (h .le. 0.0) then |
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191 | write(*,*) 'richardson not working -- bad h =', h |
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192 | ierr = -20 |
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193 | goto 7000 |
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194 | ! else if (h .lt. 10.0) then |
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195 | ! write(*,*) 'richardson not working -- too small h =', h |
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196 | ! ierr = +20 |
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197 | ! return |
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198 | end if |
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199 | |
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200 | thetam=0.5*(theta1+theta2) |
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201 | wspeed=sqrt(ul**2+vl**2) ! Wind speed at z=hmix |
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202 | bvfsq=(ga/thetam)*(theta2-theta1)/(zl2-zl1) ! Brunt-Vaisala frequency |
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203 | ! at z=hmix |
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204 | |
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205 | ! Under stable conditions, limit the maximum effect of the subgrid-scale topography |
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206 | ! by the maximum lifting possible from the available kinetic energy |
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207 | !********************************************************************************** |
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208 | |
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209 | if(bvfsq.le.0.) then |
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210 | hmixplus=9999. |
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211 | else |
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212 | bvf=sqrt(bvfsq) |
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213 | hmixplus=wspeed/bvf*convke ! keconv = kinetic energy |
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214 | endif ! used for lifting |
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215 | |
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216 | |
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217 | ! Calculate convective velocity scale |
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218 | !************************************ |
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219 | |
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220 | if (hf.lt.0.) then |
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221 | wst=(-h*ga/thetaref*hf/cpa)**0.333 |
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222 | excess=-bs*hf/cpa/wst |
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223 | if (iter.lt.itmax) goto 30 |
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224 | else |
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225 | wst=0. |
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226 | endif |
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227 | |
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228 | ierr = 0 |
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229 | return |
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230 | |
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231 | ! Fatal error -- print the inputs |
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232 | 7000 continue |
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233 | write(*,'(a )') 'nuvz' |
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234 | write(*,'(i5 )') nuvz |
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235 | write(*,'(a )') 'psurf,ust,hf,tt2,td2,h,wst,hmixplus' |
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236 | write(*,'(1p,4e18.10)') psurf,ust,hf,tt2,td2,h,wst,hmixplus |
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237 | write(*,'(a )') 'ttlev' |
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238 | write(*,'(1p,4e18.10)') ttlev |
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239 | write(*,'(a )') 'qvlev' |
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240 | write(*,'(1p,4e18.10)') qvlev |
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241 | write(*,'(a )') 'ulev' |
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242 | write(*,'(1p,4e18.10)') ulev |
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243 | write(*,'(a )') 'vlev' |
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244 | write(*,'(1p,4e18.10)') vlev |
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245 | write(*,'(a )') 'pplev' |
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246 | write(*,'(1p,4e18.10)') pplev |
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247 | return |
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248 | |
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249 | end subroutine richardson |
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250 | |
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