| 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 | !* 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 cbl(wp,zp,ust,wst,h,rhoa,rhograd,sigmaw,dsigmawdz,tlw,ptot,Q,phi,ath,bth,ol,flagrein) |
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| 23 | ! i i i i i i i i i i o o o o o o i i/o |
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| 24 | !=============== well mixed formulation of CBL skewed vertical profiles following LHH 1996 with profile of w3 from lHB 2000 ======== |
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| 25 | !=============== LHH formulation has been modified to account for variable density profiles and backward in time or forward in time simulations ======== |
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| 26 | !=============== by Massimo Cassiani ( mc ), NILU, 2012-2013, reference to Cassiani et al. 2013 (to be submitted...) ======== |
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| 27 | !======================================================================================================================================================= |
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| 28 | !====================================================================================================== |
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| 29 | ! wp: particle velocity |
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| 30 | ! zp: particle position |
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| 31 | ! ust: velcotiy scale |
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| 32 | ! wst: convective velcotiy scale |
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| 33 | ! h: boundary layer top |
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| 34 | ! rhoa: air density |
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| 35 | ! rhograd: air densiy vertical gradient |
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| 36 | ! sigmaw: turbulent flutuation of vertical velocity standard deviation |
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| 37 | ! dsigmawdz: derivative of above |
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| 38 | ! tlw: local lagrangina time scale |
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| 39 | ! ptot: pdf value for the particle velocity in drift coefficient, see Cassiani et al. 2013, not used |
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| 40 | ! Q: part of drift coefficient, not used |
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| 41 | ! phi: part of drift coeffcient, not used |
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| 42 | ! ath: drift coefficient, used |
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| 43 | ! bth: diffusion coeffcient, sued |
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| 44 | ! ol: Obukhov lenght |
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| 45 | ! flagrein: set accordingly to conditon below if 1 then re-initialize particle velocity |
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| 46 | !====================================================================================================== |
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| 47 | use par_mod, only:pi |
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| 48 | use com_mod, only:ldirect |
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| 49 | ! use ieee_arithmetic |
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| 50 | implicit none |
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| 51 | |
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| 52 | |
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| 53 | real :: usurad2,usurad2p,C0,costluar4,eps |
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| 54 | parameter (usurad2=0.7071067812,usurad2p=0.3989422804,C0=2,costluar4=0.66667,eps=0.000001) |
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| 55 | |
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| 56 | integer flagrein !re-initlization flag for the particle velocity |
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| 57 | |
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| 58 | real :: wp,zp,ust,wst,h,dens,ddens,sigmaw,dsigmawdz,tlw,rhoa,rhograd |
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| 59 | real ::fluarw,fluarw2 |
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| 60 | real ::w3,w2 |
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| 61 | real ::dw3,dw2 |
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| 62 | real ::wb,wa |
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| 63 | real ::deltawa,deltawb |
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| 64 | real ::wold,wold2,wold_z |
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| 65 | real ::pa,pb,alfa |
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| 66 | real ::Phi,Q,ptot |
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| 67 | real :: timedir |
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| 68 | real ::cuberoot |
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| 69 | real ::z0,ol,transition !added ol & transition with respect to cbl.f90 without transition |
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| 70 | |
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| 71 | |
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| 72 | real :: & |
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| 73 | erf, & |
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| 74 | aperfa, & |
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| 75 | aperfb, & |
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| 76 | ath, & |
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| 77 | bth |
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| 78 | |
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| 79 | real :: & |
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| 80 | pow, & |
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| 81 | z, & |
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| 82 | skew, & |
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| 83 | skew2, & |
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| 84 | radw2, & |
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| 85 | rluarw, & |
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| 86 | xluarw, & |
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| 87 | aluarw, & |
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| 88 | bluarw, & |
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| 89 | sigmawa, & |
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| 90 | sigmawb, & |
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| 91 | dskew, & |
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| 92 | dradw2, & |
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| 93 | dfluarw, & |
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| 94 | drluarw, & |
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| 95 | dxluarw, & |
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| 96 | daluarw, & |
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| 97 | dbluarw, & |
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| 98 | dsigmawa, & |
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| 99 | dsigmawb, & |
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| 100 | dwa, & |
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| 101 | dwb, & |
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| 102 | sigmawa2, & |
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| 103 | sigmawb2 |
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| 104 | |
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| 105 | |
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| 106 | dens=rhoa |
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| 107 | ddens=rhograd |
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| 108 | |
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| 109 | |
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| 110 | timedir=ldirect !direction of time forward (1) or backward(-1) |
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| 111 | !========================= assign z ============================== |
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| 112 | z=(zp/h) |
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| 113 | |
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| 114 | transition=1. |
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| 115 | !if (ol.lt.-50) transition=((sin(((ol+100.)/100.)*pi))-1.)/2. |
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| 116 | if (-h/ol.lt.15) transition=((sin((((-h/ol)+10.)/10.)*pi)))/2.+0.5 !transition fucntion to smoohtly |
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| 117 | !========================= secondo moment of vertical velocity ===================== |
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| 118 | !!! w2=1.4*(z**1.5*(1.-z))**(2./3.) |
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| 119 | !w2=(1.7*(z*(1.-0.7*z)*(1.-z))**(2./3.))*(wst**2) |
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| 120 | w2=(sigmaw*sigmaw) |
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| 121 | dw2=(2.*sigmaw*dsigmawdz) |
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| 122 | !dw2=(1.7*(2./3.)*(z*(1.-0.7*z)*(1.-z))**(-1./3.)* & |
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| 123 | !(((1.-0.7*z)*(1.-z))+z*(-0.7)*(1.-z)+z*(1.-0.7*z)*(-1.))) *(wst**2)*1/h |
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| 124 | |
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| 125 | !=================== dissipation fo turbulent tke ========================= |
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| 126 | !alfa=0.4 !(0.75-(0.5*z*z))**(3./2.) DISSIPAZIONE ADIMENSIONALE |
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| 127 | alfa=2.*w2/(C0*tlw) |
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| 128 | |
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| 129 | !======================================================================== |
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| 130 | wold=timedir*wp !time direction enter here for backward calculualtions |
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| 131 | !wold_z=wp |
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| 132 | ! ======================================================================= |
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| 133 | !------------------------------ momento terzo ============================ |
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| 134 | !! w3=0.8*(w2**(3./2.)) |
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| 135 | !! dw3=0.8*1.5*w2**0.5*dw2 |
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| 136 | |
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| 137 | ! dw3=((1.2*z*((1.-z)**(3./2.)))+eps)*(wst**3) |
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| 138 | ! dw3=(1.2*(((1.-z)**(3./2.))+z*1.5*((1.-z)**(1./2.))*(-1.)))*(wst**3) |
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| 139 | ! 3=(1.2*z*((1.-z)**(3./2.))) |
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| 140 | ! w3=(1.2*(((1.-z)**(3./2.))+z*1.5*((1.-z)**(1./2.))*(-1.))) |
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| 141 | |
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| 142 | !w3=((1.2*z*((1.-z)**(3./2.)))*1.5+eps)*(wst**3) !§1.5 to increase skeweness see also initalize_cbl_vel.f90 |
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| 143 | !dw3=(1.2*(((1.-z)**(3./2.))+z*1.5*((1.-z)**(1./2.))*(-1.)))*(wst**3)*(1./h)*1.5 |
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| 144 | |
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| 145 | w3=((1.2*z*((1.-z)**(3./2.)))+eps)*(wst**3)*transition |
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| 146 | dw3=(1.2*(((1.-z)**(3./2.))+z*1.5*((1.-z)**(1./2.))*(-1.)))*(wst**3)*(1./h)*transition |
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| 147 | !============================================================================0 |
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| 148 | |
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| 149 | |
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| 150 | skew=w3/(w2**1.5) |
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| 151 | skew2=skew*skew |
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| 152 | dskew=(dw3*w2**(1.5)-w3*1.5*w2**0.5*dw2)/w2**3 |
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| 153 | radw2=w2**0.5 |
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| 154 | dradw2=0.5*w2**(-0.5)*dw2 |
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| 155 | !costluar4=0.66667 ! costante da LHH |
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| 156 | fluarw=costluar4*(cuberoot(skew)) ! |
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| 157 | fluarw2=fluarw*fluarw |
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| 158 | |
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| 159 | |
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| 160 | if (skew.ne.0) then |
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| 161 | |
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| 162 | dfluarw=costluar4*(1./3.)*cuberoot(skew**(-2.))*dskew |
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| 163 | |
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| 164 | rluarw=(1.+fluarw2)**3.*skew2/((3.+fluarw2)**2.*fluarw2) !-> r |
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| 165 | xluarw=(1.+fluarw2)**1.5*skew/((3.+fluarw2)*fluarw) ! |
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| 166 | |
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| 167 | drluarw=( ((3.*(1.+fluarw2)**2*(2.*fluarw*dfluarw)*skew2)+ & |
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| 168 | (1.+fluarw2)**3*2.*skew*dskew) *(3.+fluarw2)**2.*fluarw2 - & |
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| 169 | (1.+fluarw2)**3*skew2* & |
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| 170 | ( (2.*(3.+fluarw2)*(2.*fluarw*dfluarw)*fluarw2) + & |
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| 171 | (3.+fluarw2)**2*2.*fluarw*dfluarw) )/ & |
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| 172 | (((3.+fluarw2)**2.*fluarw2)**2) |
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| 173 | |
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| 174 | dxluarw=( ((1.5*(1.+fluarw2)**0.5*(2.*fluarw*dfluarw)*skew)+ & |
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| 175 | (1.+fluarw2)**1.5*dskew) *(3.+fluarw2)*fluarw - & |
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| 176 | (1.+fluarw2)**1.5*skew* & |
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| 177 | (3.*dfluarw+3*fluarw2*dfluarw) )/ & |
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| 178 | (((3.+fluarw2)*fluarw)**2) |
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| 179 | |
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| 180 | |
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| 181 | else |
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| 182 | dfluarw=0. |
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| 183 | rluarw=0. |
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| 184 | drluarw=0. |
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| 185 | xluarw=0. |
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| 186 | dxluarw=0. |
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| 187 | end if |
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| 188 | |
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| 189 | |
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| 190 | |
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| 191 | aluarw=0.5*(1.-xluarw/(4.+rluarw)**0.5) |
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| 192 | bluarw=1.-aluarw |
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| 193 | |
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| 194 | daluarw=-0.5*( (dxluarw*(4.+rluarw)**0.5) - & |
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| 195 | (0.5*xluarw*(4.+rluarw)**(-0.5)*drluarw) ) & |
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| 196 | /(4.+rluarw) |
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| 197 | dbluarw=-daluarw |
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| 198 | |
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| 199 | |
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| 200 | sigmawa=radw2*(bluarw/(aluarw*(1.+fluarw2)))**0.5 |
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| 201 | sigmawb=radw2*(aluarw/(bluarw*(1.+fluarw2)))**0.5 |
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| 202 | |
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| 203 | |
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| 204 | dsigmawa=dradw2*(bluarw/(aluarw*(1.+fluarw2)))**0.5+ & |
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| 205 | radw2*( & |
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| 206 | (0.5*(bluarw/(aluarw*(1.+fluarw2)))**(-0.5)) * & |
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| 207 | ( & |
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| 208 | (dbluarw*(aluarw*(1.+fluarw2))- & |
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| 209 | bluarw*(daluarw*(1.+fluarw2)+aluarw*2.*fluarw*dfluarw)) & |
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| 210 | /((aluarw*(1.+fluarw2))**2) & |
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| 211 | ) & |
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| 212 | ) |
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| 213 | |
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| 214 | dsigmawb=dradw2*(aluarw/(bluarw*(1.+fluarw2)))**0.5+ & |
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| 215 | radw2*( & |
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| 216 | (0.5*(aluarw/(bluarw*(1.+fluarw2)))**(-0.5)) * & |
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| 217 | ( & |
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| 218 | (daluarw*(bluarw*(1.+fluarw2))- & |
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| 219 | aluarw*(dbluarw*(1.+fluarw2)+bluarw*2.*fluarw*dfluarw)) & |
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| 220 | /((bluarw*(1.+fluarw2))**2) & |
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| 221 | ) & |
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| 222 | ) |
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| 223 | |
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| 224 | wa=(fluarw*sigmawa) |
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| 225 | wb=(fluarw*sigmawb) |
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| 226 | dwa=dfluarw*sigmawa+fluarw*dsigmawa |
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| 227 | dwb=dfluarw*sigmawb+fluarw*dsigmawb |
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| 228 | |
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| 229 | deltawa=wold-wa |
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| 230 | deltawb=wold+wb |
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| 231 | wold2=wold*wold |
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| 232 | sigmawa2=sigmawa*sigmawa |
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| 233 | sigmawb2=sigmawb*sigmawb |
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| 234 | |
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| 235 | pa=(usurad2p*(1./sigmawa))*(exp(-(0.5*((deltawa/sigmawa)**2.)))) |
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| 236 | pb=(usurad2p*(1./sigmawb))*(exp(-(0.5*((deltawb/sigmawb)**2.)))) |
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| 237 | |
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| 238 | if (abs(deltawa).gt.10.*sigmawa.and.abs(deltawb).gt.10.*sigmawb) flagrein=1 !added control flag for re-initialization of velocity |
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| 239 | ! if (abs(deltawa).gt.6.*sigmawa.and.abs(deltawb).gt.6.*sigmawb) flagrein=1 !added control flag for re-initialization of velocity |
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| 240 | |
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| 241 | ptot=dens*aluarw*pa+dens*bluarw*pb |
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| 242 | |
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| 243 | aperfa=deltawa*usurad2/sigmawa |
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| 244 | aperfb=deltawb*usurad2/sigmawb |
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| 245 | |
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| 246 | ! if ((ieee_is_nan(aperfa).or.ieee_is_nan(aperfb)).and.flagrein.eq.0) & |
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| 247 | ! print*,'PROBLEM',deltawa,deltawb,sigmawa,sigmawb,wp,zp,ust,wst,h,rhoa,rhograd,sigmaw,dsigmawdz,tlw,ptot,Q,phi,ath,bth,ol,flagrein |
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| 248 | Phi=-0.5* & |
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| 249 | (aluarw*dens*dwa+dens*wa*daluarw+aluarw*wa*ddens)*erf(aperfa) & |
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| 250 | +sigmawa*(aluarw*dens*dsigmawa*(wold2/sigmawa2+1.)+ & |
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| 251 | sigmawa*dens*daluarw+sigmawa*ddens*aluarw+ & |
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| 252 | aluarw*wold*dens/sigmawa2*(sigmawa*dwa-wa*dsigmawa))*pa & |
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| 253 | +0.5* & |
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| 254 | (bluarw*dens*dwb+wb*dens*dbluarw+wb*bluarw*ddens)*erf(aperfb) & |
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| 255 | +sigmawb*(bluarw*dens*dsigmawb*(wold2/sigmawb2+1.)+ & |
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| 256 | sigmawb*dens*dbluarw+sigmawb*ddens*bluarw+ & |
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| 257 | bluarw*wold*dens/sigmawb2*(-sigmawb*dwb+wb*dsigmawb))*pb |
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| 258 | |
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| 259 | |
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| 260 | Q=timedir*((aluarw*dens*deltawa/sigmawa2)*pa+ & |
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| 261 | (bluarw*dens*deltawb/sigmawb2)*pb) |
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| 262 | |
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| 263 | |
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| 264 | |
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| 265 | |
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| 266 | ath=(1./ptot)*(-(C0/2.)*alfa*Q+phi) !drift coefficient |
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| 267 | bth=sqrt(C0*alfa) !diffusion coefficient |
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| 268 | |
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| 269 | |
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| 270 | |
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| 271 | |
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| 272 | return |
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| 273 | |
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| 274 | |
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| 275 | end |
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| 276 | |
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| 277 | |
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| 278 | |
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| 279 | |
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| 280 | |
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| 281 | FUNCTION CUBEROOT (X) RESULT (Y) |
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| 282 | |
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| 283 | IMPLICIT NONE |
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| 284 | |
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| 285 | real, INTENT(IN) :: X |
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| 286 | real:: Y |
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| 287 | |
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| 288 | real, PARAMETER :: THIRD = 0.333333333 |
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| 289 | |
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| 290 | |
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| 291 | Y = SIGN((ABS(X))**THIRD, X) |
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| 292 | |
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| 293 | RETURN |
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| 294 | |
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| 295 | END FUNCTION CUBEROOT |
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| 296 | |
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| 297 | |
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| 298 | |
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| 299 | |
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| 300 | FUNCTION CUBEROOTD (X) RESULT (Y) |
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| 301 | |
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| 302 | IMPLICIT NONE |
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| 303 | |
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| 304 | DOUBLE PRECISION, INTENT(IN) :: X |
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| 305 | DOUBLE PRECISION :: Y |
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| 306 | |
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| 307 | DOUBLE PRECISION, PARAMETER :: THIRD = 0.33333333333333333333333333333333333333333333333333333333333333333333333333333333333D0 |
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| 308 | |
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| 309 | |
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| 310 | Y = SIGN((ABS(X))**THIRD, X) |
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| 311 | |
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| 312 | RETURN |
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| 313 | |
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| 314 | END FUNCTION CUBEROOTD |
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