| [4202] | 1 | MODULE turbulence |
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| [4194] | 2 | |
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| 3 | #include "use_logging.h" |
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| 4 | |
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| [4186] | 5 | IMPLICIT NONE |
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| 6 | SAVE |
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| [4187] | 7 | PRIVATE |
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| [4194] | 8 | |
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| [4187] | 9 | REAL, PARAMETER :: karman=0.4 |
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| [4189] | 10 | REAL :: lmixmin=100., emin_turb=1e-8 |
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| 11 | |
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| 12 | PUBLIC :: vdif, lmixmin, emin_turb |
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| [4187] | 13 | |
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| [4186] | 14 | CONTAINS |
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| [4188] | 15 | |
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| [4189] | 16 | PURE SUBROUTINE vdif_cd( ngrid,pz0,pg,pz,pu,pv,pts,ph,pcdv,pcdh) |
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| [4186] | 17 | !======================================================================= |
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| 18 | ! |
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| 19 | ! Subject: computation of the surface drag coefficient using the |
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| 20 | ! ------- approch developed by Loui for ECMWF. |
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| 21 | ! |
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| 22 | ! Author: Frederic Hourdin 15 /10 /93 |
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| 23 | ! ------- |
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| 24 | ! |
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| 25 | ! Arguments: |
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| 26 | ! ---------- |
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| 27 | ! |
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| 28 | ! inputs: |
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| 29 | ! ------ |
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| 30 | ! ngrid size of the horizontal grid |
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| [4189] | 31 | ! pz0(ngrid) roughness length ? |
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| [4186] | 32 | ! pg gravity (m s -2) |
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| 33 | ! pz(ngrid) height of the first atmospheric layer |
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| 34 | ! pu(ngrid) u component of the wind in that layer |
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| 35 | ! pv(ngrid) v component of the wind in that layer |
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| 36 | ! pts(ngrid) surfacte temperature |
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| 37 | ! ph(ngrid) potential temperature T*(p/ps)^kappa |
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| 38 | ! |
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| 39 | ! outputs: |
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| 40 | ! -------- |
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| 41 | ! pcdv(ngrid) Cd for the wind |
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| 42 | ! pcdh(ngrid) Cd for potential temperature |
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| 43 | ! |
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| 44 | !======================================================================= |
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| 45 | ! |
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| 46 | !----------------------------------------------------------------------- |
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| 47 | ! Declarations: |
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| 48 | ! ------------- |
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| 49 | |
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| 50 | ! Arguments: |
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| 51 | ! ---------- |
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| 52 | |
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| [4189] | 53 | INTEGER, INTENT(IN) :: ngrid |
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| 54 | REAL, INTENT(IN) :: pg, pz0(ngrid), pz(ngrid), & |
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| 55 | pu(ngrid),pv(ngrid), pts(ngrid),ph(ngrid) |
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| 56 | REAL, INTENT(OUT) :: pcdv(ngrid),pcdh(ngrid) |
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| [4186] | 57 | |
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| 58 | ! Local: |
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| 59 | ! ------ |
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| 60 | |
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| [4187] | 61 | REAL, PARAMETER :: b=5., c=5., d=5., umin2=1e-12, & |
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| 62 | c2b=2.*b, c3bc=3.*b*c, c3b=3.*b |
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| [4186] | 63 | INTEGER ig |
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| [4189] | 64 | REAL zu2,z1,zri,zcd0,zz |
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| [4186] | 65 | |
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| 66 | !----------------------------------------------------------------------- |
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| 67 | ! couche de surface: |
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| 68 | ! ------------------ |
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| 69 | |
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| 70 | ! DO ig=1,ngrid |
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| 71 | ! zu2=pu(ig)*pu(ig)+pv(ig)*pv(ig)+umin2 |
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| 72 | ! pcdv(ig)=pz0(ig)*(1.+sqrt(zu2)) |
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| 73 | ! pcdh(ig)=pcdv(ig) |
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| 74 | ! ENDDO |
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| 75 | ! RETURN |
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| 76 | |
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| 77 | |
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| 78 | !!!! WARNING, verifier la formule originale de Louis! |
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| 79 | DO ig=1,ngrid |
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| 80 | zu2=pu(ig)*pu(ig)+pv(ig)*pv(ig)+umin2 |
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| 81 | zri=pg*pz(ig)*(ph(ig)-pts(ig))/(ph(ig)*zu2) |
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| 82 | z1=1.+pz(ig)/pz0(ig) |
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| 83 | zcd0=karman/log(z1) |
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| 84 | zcd0=zcd0*zcd0*sqrt(zu2) |
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| 85 | IF(zri.LT.0.) THEN |
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| 86 | z1=b*zri/(1.+c3bc*zcd0*sqrt(-z1*zri)) |
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| 87 | pcdv(ig)=zcd0*(1.-2.*z1) |
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| 88 | pcdh(ig)=zcd0*(1.-3.*z1) |
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| 89 | ELSE |
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| 90 | zz=sqrt(1.+d*zri) |
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| 91 | pcdv(ig)=zcd0/(1.+c2b*zri/zz) |
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| 92 | pcdh(ig)=zcd0/(1.+c3b*zri*zz) |
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| 93 | ENDIF |
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| 94 | ENDDO |
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| 95 | |
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| 96 | !----------------------------------------------------------------------- |
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| 97 | |
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| 98 | END SUBROUTINE vdif_cd |
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| 99 | |
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| [4189] | 100 | PURE SUBROUTINE vdif_k(ngrid,nlay, & |
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| 101 | ptimestep,pg,pzlev,pzlay,pz0,pu,pv,ph,pkv,pkh) |
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| [4187] | 102 | ! FIXME : pkh := pkv |
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| [4186] | 103 | USE planet |
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| [4189] | 104 | INTEGER, INTENT(IN) :: ngrid,nlay |
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| 105 | REAL, INTENT(IN) :: ptimestep, pg, & |
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| 106 | pzlay(ngrid,nlay),pzlev(ngrid,nlay+1), pz0(ngrid), & |
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| 107 | pu(ngrid,nlay),pv(ngrid,nlay),ph(ngrid,nlay) |
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| 108 | REAL, INTENT(OUT) :: pkv(ngrid,nlay+1),pkh(ngrid,nlay+1) |
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| [4186] | 109 | |
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| 110 | INTEGER ig,il |
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| 111 | REAL zdu,zdv,zri,zdvodz2,zdz,z1,lmix |
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| 112 | |
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| 113 | DO ig=1,ngrid |
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| 114 | pkv(ig,1)=0. |
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| 115 | pkh(ig,1)=0. |
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| 116 | pkv(ig,nlay+1)=0. |
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| 117 | pkh(ig,nlay+1)=0. |
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| 118 | ENDDO |
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| 119 | |
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| 120 | DO il=2,nlay |
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| 121 | DO ig=1,ngrid |
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| 122 | z1=pzlev(ig,il)+pz0(ig) |
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| 123 | lmix=karman*z1/(1.+karman*z1/lmixmin) |
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| 124 | ! lmix=lmixmin |
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| 125 | ! WARNING test lmix=lmixmin |
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| 126 | zdu=pu(ig,il)-pu(ig,il-1) |
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| 127 | zdv=pv(ig,il)-pv(ig,il-1) |
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| 128 | zdz=pzlay(ig,il)-pzlay(ig,il-1) |
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| 129 | zdvodz2=(zdu*zdu+zdv*zdv)/(zdz*zdz) |
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| 130 | IF(zdvodz2.LT.1.e-5) THEN |
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| 131 | pkv(ig,il)=lmix*sqrt(emin_turb) |
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| 132 | ELSE |
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| 133 | zri=2.*pg*(ph(ig,il)-ph(ig,il-1)) & |
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| 134 | / (zdz* (ph(ig,il)+ph(ig,il-1)) *zdvodz2 ) |
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| 135 | pkv(ig,il)= & |
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| 136 | lmix*sqrt(MAX(lmix*lmix*zdvodz2*(1-zri/.4),emin_turb)) |
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| 137 | ENDIF |
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| 138 | pkh(ig,il)=pkv(ig,il) |
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| 139 | ENDDO |
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| 140 | ENDDO |
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| 141 | |
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| 142 | END SUBROUTINE vdif_k |
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| [4188] | 143 | |
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| [4186] | 144 | |
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| [4188] | 145 | SUBROUTINE multipl(n,x1,x2,y) |
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| 146 | !======================================================================= |
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| 147 | ! multiplication de deux vecteurs |
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| 148 | !======================================================================= |
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| 149 | INTEGER n,i |
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| 150 | REAL x1(n),x2(n),y(n) |
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| 151 | |
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| 152 | DO i=1,n |
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| 153 | y(i)=x1(i)*x2(i) |
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| 154 | END DO |
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| 155 | END SUBROUTINE multipl |
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| 156 | |
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| 157 | SUBROUTINE vdif(ngrid,nlay,ptime, & |
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| 158 | ptimestep,pcapcal,pz0, & |
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| 159 | pplay,pplev,pzlay,pzlev, & |
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| 160 | pu,pv,ph,ptsrf,pemis, & |
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| 161 | pdufi,pdvfi,pdhfi,pfluxsrf, & |
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| 162 | pdudif,pdvdif,pdhdif,pdtsrf,pq2,pq2l, & |
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| 163 | lwrite) |
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| 164 | USE phys_const |
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| 165 | |
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| 166 | !======================================================================= |
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| 167 | ! |
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| 168 | ! Diffusion verticale |
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| 169 | ! Shema implicite |
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| 170 | ! On commence par rajouter au variables x la tendance physique |
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| 171 | ! et on resoult en fait: |
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| 172 | ! x(t+1) = x(t) + dt * (dx/dt)phys(t) + dt * (dx/dt)difv(t+1) |
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| 173 | ! |
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| 174 | ! arguments: |
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| 175 | ! ---------- |
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| 176 | ! |
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| 177 | ! entree: |
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| 178 | ! ------- |
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| 179 | ! |
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| 180 | ! |
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| 181 | !======================================================================= |
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| 182 | |
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| 183 | ! |
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| 184 | ! arguments: |
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| 185 | ! ---------- |
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| 186 | |
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| 187 | INTEGER ngrid,nlay |
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| 188 | REAL ptime,ptimestep |
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| 189 | REAL pplay(ngrid,nlay),pplev(ngrid,nlay+1) |
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| 190 | REAL pzlay(ngrid,nlay),pzlev(ngrid,nlay+1) |
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| 191 | REAL pu(ngrid,nlay),pv(ngrid,nlay),ph(ngrid,nlay) |
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| 192 | REAL ptsrf(ngrid),pemis(ngrid) |
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| 193 | REAL pdufi(ngrid,nlay),pdvfi(ngrid,nlay),pdhfi(ngrid,nlay) |
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| 194 | REAL pfluxsrf(ngrid) |
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| 195 | REAL pdudif(ngrid,nlay),pdvdif(ngrid,nlay),pdhdif(ngrid,nlay) |
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| 196 | REAL pdtsrf(ngrid),pcapcal(ngrid),pz0(ngrid) |
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| 197 | REAL pq2(ngrid,nlay+1),pq2l(ngrid,nlay+1) |
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| 198 | LOGICAL lwrite |
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| 199 | ! |
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| 200 | ! local: |
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| 201 | ! ------ |
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| 202 | |
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| 203 | INTEGER ilev,ig,ilay,nlev |
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| 204 | INTEGER unit,ierr,it1,it2 |
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| 205 | INTEGER cluvdb,putdat,putvdim,setname,setvdim |
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| 206 | REAL z4st,zdplanck(ngrid),zu2 |
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| 207 | REAL zkv(ngrid,nlay+1),zkh(ngrid,nlay+1) |
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| 208 | REAL zcdv(ngrid),zcdh(ngrid) |
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| 209 | REAL zu(ngrid,nlay),zv(ngrid,nlay) |
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| 210 | REAL zh(ngrid,nlay) |
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| 211 | REAL ztsrf2(ngrid) |
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| 212 | REAL z1(ngrid),z2(ngrid) |
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| 213 | REAL za(ngrid,nlay),zb(ngrid,nlay) |
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| 214 | REAL zb0(ngrid,nlay) |
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| 215 | REAL zc(ngrid,nlay),zd(ngrid,nlay) |
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| 216 | REAL zcst1 |
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| 217 | |
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| 218 | ! |
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| 219 | !----------------------------------------------------------------------- |
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| 220 | ! initialisations: |
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| 221 | ! ---------------- |
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| 222 | |
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| 223 | nlev=nlay+1 |
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| 224 | |
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| 225 | ! computation of rho*dz and dt*rho/dz=dt*rho**2 g/dp: |
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| 226 | ! with rho=p/RT=p/ (R Theta) (p/ps)**kappa |
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| 227 | ! --------------------------------- |
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| 228 | |
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| 229 | DO ilay=1,nlay |
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| 230 | DO ig=1,ngrid |
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| 231 | za(ig,ilay) = (pplev(ig,ilay)-pplev(ig,ilay+1))/g |
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| 232 | ENDDO |
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| 233 | ENDDO |
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| 234 | |
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| 235 | zcst1=4.*g*ptimestep/(r*r) |
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| 236 | DO ilev=2,nlev-1 |
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| 237 | DO ig=1,ngrid |
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| 238 | zb0(ig,ilev)=pplev(ig,ilev) & |
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| 239 | *(pplev(ig,1)/pplev(ig,ilev))**rcp & |
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| 240 | /(ph(ig,ilev-1)+ph(ig,ilev)) |
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| 241 | zb0(ig,ilev)=zcst1*zb0(ig,ilev)*zb0(ig,ilev) & |
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| 242 | / (pplay(ig,ilev-1)-pplay(ig,ilev)) |
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| 243 | ENDDO |
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| 244 | ENDDO |
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| 245 | DO ig=1,ngrid |
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| 246 | zb0(ig,1)=ptimestep*pplev(ig,1)/(r*ptsrf(ig)) |
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| 247 | ENDDO |
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| 248 | IF(lwrite) THEN |
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| 249 | ig=ngrid/2+1 |
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| [4194] | 250 | WRITELOG(*,*) 'Pression (mbar) ,altitude (km),u,v,theta, rho dz' |
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| [4188] | 251 | DO ilay=1,nlay |
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| [4194] | 252 | WRITELOG(*,*) .01*pplay(ig,ilay),.001*pzlay(ig,ilay), & |
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| [4188] | 253 | pu(ig,ilay),pv(ig,ilay),ph(ig,ilay),za(ig,ilay) |
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| 254 | ENDDO |
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| [4194] | 255 | WRITELOG(*,*) 'Pression (mbar) ,altitude (km),zb' |
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| [4188] | 256 | DO ilev=1,nlay |
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| [4194] | 257 | WRITELOG(*,*) .01*pplev(ig,ilev),.001*pzlev(ig,ilev), & |
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| [4188] | 258 | zb0(ig,ilev) |
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| 259 | ENDDO |
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| [4199] | 260 | LOG_DBG('vdif') |
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| [4188] | 261 | ENDIF |
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| 262 | |
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| 263 | !----------------------------------------------------------------------- |
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| 264 | ! 2. ajout des tendances physiques: |
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| 265 | ! ------------------------------ |
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| 266 | |
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| 267 | DO ilev=1,nlay |
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| 268 | DO ig=1,ngrid |
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| 269 | zu(ig,ilev)=pu(ig,ilev)+pdufi(ig,ilev)*ptimestep |
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| 270 | zv(ig,ilev)=pv(ig,ilev)+pdvfi(ig,ilev)*ptimestep |
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| 271 | zh(ig,ilev)=ph(ig,ilev)+pdhfi(ig,ilev)*ptimestep |
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| 272 | ENDDO |
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| 273 | ENDDO |
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| 274 | |
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| 275 | !----------------------------------------------------------------------- |
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| 276 | ! 3. calcul de cd : |
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| 277 | ! ---------------- |
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| 278 | ! |
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| 279 | CALL vdif_cd( ngrid,pz0,g,pzlay,pu,pv,ptsrf,ph,zcdv,zcdh) |
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| [4189] | 280 | CALL vdif_k(ngrid,nlay,ptimestep,g,pzlev,pzlay,pz0,pu,pv,ph,zkv,zkh) |
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| [4188] | 281 | |
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| 282 | DO ig=1,ngrid |
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| 283 | zu2=pu(ig,1)*pu(ig,1)+pv(ig,1)*pv(ig,1) |
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| 284 | zcdv(ig)=zcdv(ig)*sqrt(zu2) |
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| 285 | zcdh(ig)=zcdh(ig)*sqrt(zu2) |
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| 286 | ENDDO |
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| 287 | |
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| [4210] | 288 | IF(lwrite) THEN |
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| [4194] | 289 | WRITELOG(*,*) 'Diagnostique diffusion verticale' |
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| 290 | WRITELOG(*,*) 'LMIXMIN',lmixmin |
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| [4210] | 291 | WRITELOG(*,*) 'coefficients Cd pour v et h' |
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| 292 | WRITELOG(*,*) zcdv(ngrid/2+1),zcdh(ngrid/2+1) |
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| 293 | WRITELOG(*,*) ,'coefficients K pour v et h' |
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| [4188] | 294 | DO ilev=1,nlay |
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| [4210] | 295 | WRITELOG(*,*) zkv(ngrid/2+1,ilev),zkh(ngrid/2+1,ilev) |
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| [4188] | 296 | ENDDO |
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| [4199] | 297 | LOG_DBG('vdif') |
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| [4188] | 298 | ENDIF |
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| 299 | |
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| 300 | !----------------------------------------------------------------------- |
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| 301 | ! integration verticale pour u: |
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| 302 | ! ----------------------------- |
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| 303 | |
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| 304 | CALL multipl((nlay-1)*ngrid,zkv(1,2),zb0(1,2),zb(1,2)) |
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| 305 | CALL multipl(ngrid,zcdv,zb0,zb) |
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| 306 | DO ig=1,ngrid |
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| 307 | z1(ig)=1./(za(ig,nlay)+zb(ig,nlay)) |
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| 308 | zc(ig,nlay)=za(ig,nlay)*zu(ig,nlay)*z1(ig) |
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| 309 | zd(ig,nlay)=zb(ig,nlay)*z1(ig) |
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| 310 | ENDDO |
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| 311 | |
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| 312 | DO ilay=nlay-1,1,-1 |
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| 313 | DO ig=1,ngrid |
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| 314 | z1(ig) = 1./(za(ig,ilay)+zb(ig,ilay) & |
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| 315 | + zb(ig,ilay+1)*(1.-zd(ig,ilay+1))) |
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| 316 | zc(ig,ilay) = (za(ig,ilay)*zu(ig,ilay) & |
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| 317 | + zb(ig,ilay+1)*zc(ig,ilay+1))*z1(ig) |
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| 318 | zd(ig,ilay) = zb(ig,ilay)*z1(ig) |
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| 319 | ENDDO |
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| 320 | ENDDO |
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| 321 | |
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| 322 | DO ig=1,ngrid |
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| 323 | zu(ig,1)=zc(ig,1) |
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| 324 | ENDDO |
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| 325 | DO ilay=2,nlay |
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| 326 | DO ig=1,ngrid |
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| 327 | zu(ig,ilay)=zc(ig,ilay)+zd(ig,ilay)*zu(ig,ilay-1) |
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| 328 | ENDDO |
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| 329 | ENDDO |
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| 330 | |
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| 331 | !----------------------------------------------------------------------- |
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| 332 | ! integration verticale pour v: |
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| 333 | ! ----------------------------- |
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| 334 | ! |
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| 335 | DO ig=1,ngrid |
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| 336 | z1(ig)=1./(za(ig,nlay)+zb(ig,nlay)) |
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| 337 | zc(ig,nlay)=za(ig,nlay)*zv(ig,nlay)*z1(ig) |
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| 338 | zd(ig,nlay)=zb(ig,nlay)*z1(ig) |
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| 339 | ENDDO |
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| 340 | |
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| 341 | DO ilay=nlay-1,1,-1 |
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| 342 | DO ig=1,ngrid |
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| 343 | z1(ig)=1./(za(ig,ilay)+zb(ig,ilay) & |
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| 344 | + zb(ig,ilay+1)*(1.-zd(ig,ilay+1))) |
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| 345 | zc(ig,ilay)=(za(ig,ilay)*zv(ig,ilay) & |
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| 346 | + zb(ig,ilay+1)*zc(ig,ilay+1))*z1(ig) |
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| 347 | zd(ig,ilay)=zb(ig,ilay)*z1(ig) |
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| 348 | ENDDO |
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| 349 | ENDDO |
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| 350 | |
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| 351 | DO ig=1,ngrid |
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| 352 | zv(ig,1)=zc(ig,1) |
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| 353 | ENDDO |
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| 354 | DO ilay=2,nlay |
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| 355 | DO ig=1,ngrid |
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| 356 | zv(ig,ilay)=zc(ig,ilay)+zd(ig,ilay)*zv(ig,ilay-1) |
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| 357 | ENDDO |
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| 358 | ENDDO |
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| 359 | |
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| 360 | !----------------------------------------------------------------------- |
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| 361 | ! integration verticale pour h: |
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| 362 | ! ----------------------------- |
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| 363 | ! |
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| 364 | CALL multipl((nlay-1)*ngrid,zkh(1,2),zb0(1,2),zb(1,2)) |
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| 365 | CALL multipl(ngrid,zcdh,zb0,zb) |
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| 366 | DO ig=1,ngrid |
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| 367 | z1(ig)=1./(za(ig,nlay)+zb(ig,nlay)) |
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| 368 | zc(ig,nlay)=za(ig,nlay)*zh(ig,nlay)*z1(ig) |
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| 369 | zd(ig,nlay)=zb(ig,nlay)*z1(ig) |
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| 370 | ENDDO |
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| 371 | |
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| 372 | DO ilay=nlay-1,1,-1 |
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| 373 | DO ig=1,ngrid |
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| 374 | z1(ig)=1./(za(ig,ilay)+zb(ig,ilay) & |
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| 375 | + zb(ig,ilay+1)*(1.-zd(ig,ilay+1))) |
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| 376 | zc(ig,ilay)=(za(ig,ilay)*zh(ig,ilay) & |
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| 377 | + zb(ig,ilay+1)*zc(ig,ilay+1))*z1(ig) |
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| 378 | zd(ig,ilay)=zb(ig,ilay)*z1(ig) |
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| 379 | ENDDO |
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| 380 | ENDDO |
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| 381 | |
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| 382 | !----------------------------------------------------------------------- |
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| 383 | ! rajout eventuel de planck dans le shema implicite: |
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| 384 | ! -------------------------------------------------- |
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| 385 | |
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| 386 | z4st=4.*5.67e-8*ptimestep |
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| 387 | DO ig=1,ngrid |
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| 388 | zdplanck(ig)=z4st*pemis(ig)*ptsrf(ig)*ptsrf(ig)*ptsrf(ig) |
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| 389 | ENDDO |
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| 390 | |
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| 391 | !----------------------------------------------------------------------- |
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| 392 | ! calcul le l'evolution de la temperature du sol: |
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| 393 | ! ----------------------------------------------- |
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| 394 | |
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| 395 | DO ig=1,ngrid |
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| 396 | z1(ig) = pcapcal(ig)*ptsrf(ig)+cpp*zb(ig,1)*zc(ig,1) & |
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| 397 | + zdplanck(ig)*ptsrf(ig)+ pfluxsrf(ig)*ptimestep |
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| 398 | z2(ig) = pcapcal(ig)+cpp*zb(ig,1)*(1.-zd(ig,1))+zdplanck(ig) |
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| 399 | ztsrf2(ig) = z1(ig)/z2(ig) |
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| 400 | zh(ig,1) = zc(ig,1)+zd(ig,1)*ztsrf2(ig) |
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| 401 | pdtsrf(ig) = (ztsrf2(ig)-ptsrf(ig))/ptimestep |
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| 402 | ENDDO |
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| 403 | |
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| 404 | !----------------------------------------------------------------------- |
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| 405 | ! integration verticale finale: |
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| 406 | ! ----------------------------- |
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| 407 | |
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| 408 | DO ilay=2,nlay |
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| 409 | DO ig=1,ngrid |
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| 410 | zh(ig,ilay)=zc(ig,ilay)+zd(ig,ilay)*zh(ig,ilay-1) |
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| 411 | ENDDO |
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| 412 | ENDDO |
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| 413 | |
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| 414 | !----------------------------------------------------------------------- |
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| 415 | ! calcul final des tendances de la diffusion verticale: |
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| 416 | ! ----------------------------------------------------- |
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| 417 | |
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| 418 | DO ilev = 1, nlay |
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| 419 | DO ig=1,ngrid |
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| 420 | pdudif(ig,ilev) = ( zu(ig,ilev) & |
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| 421 | - (pu(ig,ilev)+pdufi(ig,ilev)*ptimestep) )/ptimestep |
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| 422 | pdvdif(ig,ilev) = ( zv(ig,ilev) & |
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| 423 | - (pv(ig,ilev)+pdvfi(ig,ilev)*ptimestep) )/ptimestep |
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| 424 | pdhdif(ig,ilev) = ( zh(ig,ilev) & |
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| 425 | - (ph(ig,ilev)+pdhfi(ig,ilev)*ptimestep) )/ptimestep |
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| 426 | ENDDO |
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| 427 | ENDDO |
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| 428 | |
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| 429 | IF(lwrite) THEN |
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| [4210] | 430 | WRITELOG(*,*) |
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| 431 | WRITELOG(*,*) ,'Diagnostique de la diffusion verticale' |
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| 432 | WRITELOG(*,*) ,'h avant et apres diffusion verticale' |
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| 433 | WRITELOG(*,*) ,ptsrf(ngrid/2+1),ztsrf2(ngrid/2+1) |
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| [4188] | 434 | DO ilev=1,nlay |
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| [4210] | 435 | WRITELOG(*,*) ph(ngrid/2+1,ilev),zh(ngrid/2+1,ilev) |
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| [4188] | 436 | ENDDO |
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| [4210] | 437 | LOG_DBG('vdif') |
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| [4188] | 438 | END IF |
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| 439 | |
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| 440 | END SUBROUTINE vdif |
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| 441 | |
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| [4202] | 442 | END MODULE turbulence |
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