[6] | 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 richardson(psurf,ust,ttlev,qvlev,ulev,vlev,nuvz, & |
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| 23 | akz,bkz,hf,tt2,td2,h,wst,hmixplus) |
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| 24 | ! i i i i i i i |
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| 25 | ! i i i i i o o o |
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| 26 | !**************************************************************************** |
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| 27 | ! * |
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| 28 | ! Calculation of mixing height based on the critical Richardson number. * |
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| 29 | ! Calculation of convective time scale. * |
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| 30 | ! For unstable conditions, one iteration is performed. An excess * |
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| 31 | ! temperature (dependent on hf and wst) is calculated, added to the * |
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| 32 | ! temperature at the lowest model level. Then the procedure is repeated.* |
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| 33 | ! * |
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| 34 | ! Author: A. Stohl * |
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| 35 | ! * |
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| 36 | ! 22 August 1996 * |
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| 37 | ! * |
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| 38 | ! Literature: * |
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| 39 | ! Vogelezang DHP and Holtslag AAM (1996): Evaluation and model impacts * |
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| 40 | ! of alternative boundary-layer height formulations. Boundary-Layer * |
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| 41 | ! Meteor. 81, 245-269. * |
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| 42 | ! * |
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| 43 | ! Update: 1999-02-01 by G. Wotawa * |
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| 44 | ! CHANGE: 17/11/2005 Caroline Forster NCEP GFS version * |
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| 45 | ! * |
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| 46 | ! Two meter level (temperature, humidity) is taken as reference level * |
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| 47 | ! instead of first model level. * |
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| 48 | ! New input variables tt2, td2 introduced. * |
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| 49 | ! * |
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| 50 | !**************************************************************************** |
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| 51 | ! * |
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| 52 | ! Variables: * |
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| 53 | ! h mixing height [m] * |
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| 54 | ! hf sensible heat flux * |
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| 55 | ! psurf surface pressure at point (xt,yt) [Pa] * |
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| 56 | ! tv virtual temperature * |
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| 57 | ! wst convective velocity scale * |
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| 58 | ! * |
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| 59 | ! Constants: * |
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| 60 | ! ric critical Richardson number * |
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| 61 | ! * |
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| 62 | !**************************************************************************** |
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| 63 | |
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| 64 | use par_mod |
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| 65 | |
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| 66 | implicit none |
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| 67 | |
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| 68 | integer :: i,k,nuvz,iter,llev |
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| 69 | real :: tv,tvold,zref,z,zold,pint,pold,theta,thetaref,ri |
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| 70 | real :: akz(nuvz),bkz(nuvz),ulev(nuvz),vlev(nuvz),hf,wst,tt2,td2,ew |
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| 71 | real :: psurf,ust,ttlev(nuvz),qvlev(nuvz),h,excess |
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| 72 | real :: thetaold,zl,ul,vl,thetal,ril,hmixplus,wspeed,bvfsq,bvf |
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| 73 | real :: f_qvsat,rh,rhold,rhl,theta1,theta2,zl1,zl2,thetam |
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| 74 | real,parameter :: const=r_air/ga, ric=0.25, b=100., bs=8.5 |
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| 75 | integer,parameter :: itmax=3 |
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| 76 | |
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| 77 | excess=0.0 |
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| 78 | iter=0 |
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| 79 | |
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| 80 | ! NCEP version: find first model level above ground |
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| 81 | !************************************************** |
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| 82 | |
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| 83 | llev = 0 |
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| 84 | do i=1,nuvz |
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| 85 | if (psurf.lt.akz(i)) llev=i |
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| 86 | end do |
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| 87 | llev = llev+1 |
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| 88 | ! sec llev should not be 1! |
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| 89 | if (llev.eq.1) llev = 2 |
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| 90 | if (llev.gt.nuvz) llev = nuvz-1 |
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| 91 | ! NCEP version |
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| 92 | |
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| 93 | |
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| 94 | ! Compute virtual temperature and virtual potential temperature at |
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| 95 | ! reference level (2 m) |
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| 96 | !***************************************************************** |
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| 97 | |
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| 98 | 30 iter=iter+1 |
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| 99 | |
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| 100 | pold=psurf |
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| 101 | tvold=tt2*(1.+0.378*ew(td2)/psurf) |
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| 102 | zold=2.0 |
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| 103 | zref=zold |
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| 104 | rhold=ew(td2)/ew(tt2) |
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| 105 | |
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| 106 | thetaref=tvold*(100000./pold)**(r_air/cpa)+excess |
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| 107 | thetaold=thetaref |
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| 108 | |
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| 109 | ! Integrate z up to one level above zt |
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| 110 | !************************************* |
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| 111 | |
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| 112 | do k=llev,nuvz |
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| 113 | pint=akz(k)+bkz(k)*psurf ! pressure on model layers |
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| 114 | tv=ttlev(k)*(1.+0.608*qvlev(k)) |
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| 115 | |
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| 116 | if (abs(tv-tvold).gt.0.2) then |
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| 117 | z=zold+const*log(pold/pint)*(tv-tvold)/log(tv/tvold) |
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| 118 | else |
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| 119 | z=zold+const*log(pold/pint)*tv |
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| 120 | endif |
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| 121 | |
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| 122 | theta=tv*(100000./pint)**(r_air/cpa) |
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| 123 | ! Petra |
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| 124 | rh = qvlev(k) / f_qvsat( pint, ttlev(k) ) |
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| 125 | |
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| 126 | |
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| 127 | !alculate Richardson number at each level |
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| 128 | !**************************************** |
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| 129 | |
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| 130 | ri=ga/thetaref*(theta-thetaref)*(z-zref)/ & |
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| 131 | max(((ulev(k)-ulev(2))**2+(vlev(k)-vlev(2))**2+b*ust**2),0.1) |
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| 132 | |
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| 133 | ! addition of second condition: MH should not be placed in an |
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| 134 | ! unstable layer (PS / Feb 2000) |
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| 135 | if (ri.gt.ric .and. thetaold.lt.theta) goto 20 |
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| 136 | |
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| 137 | tvold=tv |
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| 138 | pold=pint |
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| 139 | rhold=rh |
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| 140 | thetaold=theta |
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| 141 | zold=z |
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| 142 | end do |
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| 143 | |
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| 144 | 20 continue |
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| 145 | |
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| 146 | ! Determine Richardson number between the critical levels |
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| 147 | !******************************************************** |
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| 148 | |
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| 149 | zl1=zold |
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| 150 | theta1=thetaold |
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| 151 | do i=1,20 |
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| 152 | zl=zold+real(i)/20.*(z-zold) |
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| 153 | ul=ulev(k-1)+real(i)/20.*(ulev(k)-ulev(k-1)) |
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| 154 | vl=vlev(k-1)+real(i)/20.*(vlev(k)-vlev(k-1)) |
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| 155 | thetal=thetaold+real(i)/20.*(theta-thetaold) |
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| 156 | rhl=rhold+real(i)/20.*(rh-rhold) |
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| 157 | ril=ga/thetaref*(thetal-thetaref)*(zl-zref)/ & |
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| 158 | max(((ul-ulev(2))**2+(vl-vlev(2))**2+b*ust**2),0.1) |
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| 159 | zl2=zl |
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| 160 | theta2=thetal |
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| 161 | if (ril.gt.ric) goto 25 |
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| 162 | zl1=zl |
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| 163 | theta1=thetal |
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| 164 | end do |
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| 165 | |
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| 166 | 25 continue |
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| 167 | h=zl |
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| 168 | thetam=0.5*(theta1+theta2) |
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| 169 | wspeed=sqrt(ul**2+vl**2) ! Wind speed at z=hmix |
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| 170 | bvfsq=(ga/thetam)*(theta2-theta1)/(zl2-zl1) ! Brunt-Vaisala frequency |
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| 171 | ! at z=hmix |
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| 172 | |
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| 173 | ! Under stable conditions, limit the maximum effect of the subgrid-scale topography |
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| 174 | ! by the maximum lifting possible from the available kinetic energy |
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| 175 | !***************************************************************************** |
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| 176 | |
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| 177 | if(bvfsq.le.0.) then |
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| 178 | hmixplus=9999. |
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| 179 | else |
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| 180 | bvf=sqrt(bvfsq) |
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| 181 | hmixplus=wspeed/bvf*convke |
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| 182 | endif |
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| 183 | |
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| 184 | |
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| 185 | ! Calculate convective velocity scale |
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| 186 | !************************************ |
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| 187 | |
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| 188 | if (hf.lt.0.) then |
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| 189 | wst=(-h*ga/thetaref*hf/cpa)**0.333 |
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| 190 | excess=-bs*hf/cpa/wst |
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| 191 | if (iter.lt.itmax) goto 30 |
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| 192 | else |
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| 193 | wst=0. |
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| 194 | endif |
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| 195 | |
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| 196 | end subroutine richardson |
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