1 | !********************************************************************** |
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2 | ! Copyright 1998,1999,2000,2001,2002,2005,2007,2008,2009,2010 * |
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3 | ! Andreas Stohl, Petra Seibert, A. Frank, Gerhard Wotawa, * |
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4 | ! Caroline Forster, Sabine Eckhardt, John Burkhart, Harald Sodemann * |
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5 | ! * |
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6 | ! This file is part of FLEXPART. * |
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7 | ! * |
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8 | ! FLEXPART is free software: you can redistribute it and/or modify * |
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9 | ! it under the terms of the GNU General Public License as published by* |
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10 | ! the Free Software Foundation, either version 3 of the License, or * |
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11 | ! (at your option) any later version. * |
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12 | ! * |
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13 | ! FLEXPART is distributed in the hope that it will be useful, * |
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14 | ! but WITHOUT ANY WARRANTY; without even the implied warranty of * |
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15 | ! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * |
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16 | ! GNU General Public License for more details. * |
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17 | ! * |
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18 | ! You should have received a copy of the GNU General Public License * |
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19 | ! along with FLEXPART. If not, see <http://www.gnu.org/licenses/>. * |
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20 | !********************************************************************** |
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21 | |
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22 | subroutine pbl_profile(ps,td2m,zml1,t2m,tml1,u10m,uml1,stress,hf) |
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23 | |
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24 | !******************************************************************** |
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25 | ! * |
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26 | ! G. WOTAWA, 1995-07-07 * |
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27 | ! * |
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28 | !******************************************************************** |
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29 | ! * |
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30 | ! DESCRIPTION: CALCULATION OF FRICTION VELOCITY AND SURFACE SENS- * |
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31 | ! IBLE HEAT FLUX USING THE PROFILE METHOD (BERKOVICZ * |
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32 | ! AND PRAHM, 1982) * |
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33 | ! * |
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34 | ! Output now is surface stress instead of ustar * |
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35 | ! * |
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36 | ! * |
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37 | !******************************************************************** |
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38 | ! * |
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39 | ! INPUT: * |
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40 | ! * |
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41 | ! * |
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42 | ! ps surface pressure(Pa) * |
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43 | ! td2m two metre dew point(K) * |
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44 | ! zml1 heigth of first model level (m) * |
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45 | ! t2m two metre temperature (K) * |
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46 | ! tml1 temperature first model level (K) * |
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47 | ! u10m ten metre wind speed (ms-1) * |
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48 | ! uml1 wind speed first model level (ms-1) * |
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49 | ! * |
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50 | !******************************************************************** |
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51 | ! * |
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52 | ! OUTPUT: * |
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53 | ! * |
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54 | ! stress surface stress (i.e., friction velocity (ms-1) squared * |
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55 | ! multiplied with air density) * |
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56 | ! hf surface sensible heat flux (Wm-2) * |
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57 | ! * |
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58 | !******************************************************************** |
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59 | ! ustar friction velocity (ms-1) * |
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60 | ! maxiter maximum number of iterations * |
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61 | !******************************************************************** |
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62 | |
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63 | use par_mod |
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64 | |
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65 | implicit none |
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66 | |
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67 | integer :: iter |
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68 | real :: ps,td2m,rhoa,zml1,t2m,tml1,u10m,uml1,ustar,hf |
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69 | real :: al,alold,aldiff,tmean,crit |
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70 | real :: deltau,deltat,thetastar,psim,psih,e,ew,tv,stress |
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71 | integer,parameter :: maxiter=10 |
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72 | real,parameter :: r1=0.74 |
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73 | |
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74 | e=ew(td2m) ! vapor pressure |
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75 | tv=t2m*(1.+0.378*e/ps) ! virtual temperature |
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76 | rhoa=ps/(r_air*tv) ! air density |
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77 | |
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78 | deltau=uml1-u10m !! Wind Speed difference between |
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79 | !! Model level 1 and 10 m |
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80 | |
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81 | if(deltau.le.0.001) then !! Monin-Obukhov Theory not |
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82 | al=9999. !! applicable --> Set dummy values |
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83 | ustar=0.01 |
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84 | stress=ustar*ustar*rhoa |
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85 | hf=0.0 |
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86 | return |
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87 | endif |
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88 | deltat=tml1-t2m+0.0098*(zml1-2.) !! Potential temperature difference |
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89 | !! between model level 1 and 10 m |
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90 | |
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91 | if(abs(deltat).le.0.03) then !! Neutral conditions |
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92 | hf=0.0 |
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93 | al=9999. |
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94 | ustar=(vonkarman*deltau)/ & |
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95 | (log(zml1/10.)-psim(zml1,al)+psim(10.,al)) |
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96 | stress=ustar*ustar*rhoa |
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97 | return |
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98 | endif |
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99 | |
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100 | tmean=0.5*(t2m+tml1) |
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101 | crit=(0.0219*tmean*(zml1-2.0)*deltau**2)/ & |
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102 | (deltat*(zml1-10.0)**2) |
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103 | if((deltat.gt.0).and.(crit.le.1.)) then |
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104 | !! Successive approximation will |
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105 | al=50. !! not converge |
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106 | ustar=(vonkarman*deltau)/ & |
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107 | (log(zml1/10.)-psim(zml1,al)+psim(10.,al)) |
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108 | thetastar=(vonkarman*deltat/r1)/ & |
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109 | (log(zml1/2.)-psih(zml1,al)+psih(2.,al)) |
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110 | hf=rhoa*cpa*ustar*thetastar |
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111 | stress=ustar*ustar*rhoa |
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112 | return |
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113 | endif |
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114 | |
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115 | al=9999. ! Start iteration assuming neutral conditions |
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116 | do iter=1,maxiter |
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117 | alold=al |
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118 | ustar=(vonkarman*deltau)/ & |
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119 | (log(zml1/10.)-psim(zml1,al)+psim(10.,al)) |
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120 | thetastar=(vonkarman*deltat/r1)/ & |
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121 | (log(zml1/2.)-psih(zml1,al)+psih(2.,al)) |
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122 | al=(tmean*ustar**2)/(ga*vonkarman*thetastar) |
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123 | aldiff=abs((al-alold)/alold) |
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124 | if(aldiff.lt.0.01) goto 30 !! Successive approximation successful |
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125 | end do |
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126 | 30 hf=rhoa*cpa*ustar*thetastar |
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127 | if(al.gt.9999.) al=9999. |
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128 | if(al.lt.-9999.) al=-9999. |
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129 | |
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130 | stress=ustar*ustar*rhoa |
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131 | |
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132 | end subroutine pbl_profile |
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