| 1 | SUBROUTINE pbl_parameters(ngrid,nlay,ps,pplay,pz0, |
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| 2 | & pg,zzlay,zzlev,pu,pv,wstar_in,hfmax,zmax,pts,ph,z_out,n_out, |
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| 3 | & T_out,u_out,ustar,tstar,L_mo,vhf,vvv) |
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| 4 | IMPLICIT NONE |
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| 5 | !======================================================================= |
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| 6 | ! |
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| 7 | ! Anlysis of the PBL from input temperature, wind field and thermals outputs. |
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| 8 | ! |
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| 9 | ! ------- |
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| 10 | ! |
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| 11 | ! Author: Arnaud Colaitis 09/01/12 |
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| 12 | ! ------- |
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| 13 | ! |
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| 14 | ! Arguments: |
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| 15 | ! ---------- |
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| 16 | ! |
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| 17 | ! inputs: |
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| 18 | ! ------ |
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| 19 | ! ngrid size of the horizontal grid |
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| 20 | ! nlay size of the vertical grid |
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| 21 | ! pz0(ngrid) surface roughness length |
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| 22 | ! pg gravity (m s -2) |
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| 23 | ! zzlay(ngrid,nlay) height of mid-layers |
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| 24 | ! zzlev(ngrid,nlay+1) height of layers interfaces |
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| 25 | ! pu(ngrid,nlay) u component of the wind |
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| 26 | ! pv(ngrid,nlay) v component of the wind |
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| 27 | ! wstar_in(ngrid) free convection velocity in thermals |
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| 28 | ! hfmax(ngrid) maximum vertical turbulent heat flux in thermals |
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| 29 | ! zmax(ngrid) height reached by the thermals (pbl height) |
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| 30 | ! pts(ngrid) surface temperature |
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| 31 | ! ph(ngrid,nlay) potential temperature T*(p/ps)^kappa |
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| 32 | ! z_out(n_out) heights of interpolation |
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| 33 | ! n_out number of points for interpolation |
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| 34 | ! |
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| 35 | ! outputs: |
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| 36 | ! ------ |
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| 37 | ! |
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| 38 | ! Teta_out(ngrid,n_out) interpolated teta |
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| 39 | ! u_out(ngrid,n_out) interpolated u |
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| 40 | ! ustar(ngrid) friction velocity |
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| 41 | ! tstar(ngrid) friction temperature |
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| 42 | ! wstar(ngrid) free convection velocity |
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| 43 | ! L_mo(ngrid) monin_obukhov length |
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| 44 | ! |
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| 45 | ! |
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| 46 | !======================================================================= |
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| 47 | ! |
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| 48 | !----------------------------------------------------------------------- |
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| 49 | ! Declarations: |
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| 50 | ! ------------- |
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| 51 | |
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| 52 | #include "comcstfi.h" |
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| 53 | #include "callkeys.h" |
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| 54 | |
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| 55 | ! Arguments: |
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| 56 | ! ---------- |
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| 57 | |
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| 58 | INTEGER, INTENT(IN) :: ngrid,nlay,n_out |
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| 59 | REAL, INTENT(IN) :: pz0(ngrid),ps(ngrid),pplay(ngrid,nlay) |
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| 60 | REAL, INTENT(IN) :: pg,zzlay(ngrid,nlay),zzlev(ngrid,nlay) |
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| 61 | REAL, INTENT(IN) :: pu(ngrid,nlay),pv(ngrid,nlay) |
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| 62 | REAL, INTENT(IN) :: wstar_in(ngrid),hfmax(ngrid),zmax(ngrid) |
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| 63 | REAL, INTENT(IN) :: pts(ngrid),ph(ngrid,nlay) |
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| 64 | REAL, INTENT(IN) :: z_out(n_out) |
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| 65 | |
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| 66 | ! Outputs: |
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| 67 | ! -------- |
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| 68 | |
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| 69 | REAL, INTENT(OUT) :: T_out(ngrid,n_out),u_out(ngrid,n_out) |
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| 70 | REAL Teta_out(ngrid,n_out) |
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| 71 | REAL, INTENT(OUT) :: ustar(ngrid), tstar(ngrid) |
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| 72 | REAL wstar(ngrid) |
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| 73 | REAL, INTENT(OUT) :: L_mo(ngrid) |
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| 74 | |
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| 75 | ! Local: |
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| 76 | ! ------ |
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| 77 | |
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| 78 | INTEGER ig,k,n |
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| 79 | REAL karman,nu |
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| 80 | DATA karman,nu/.41,0.001/ |
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| 81 | SAVE karman,nu |
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| 82 | |
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| 83 | ! Local(2): |
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| 84 | ! --------- |
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| 85 | |
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| 86 | REAL zout |
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| 87 | REAL rib(ngrid) ! Bulk Richardson number |
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| 88 | REAL fm(ngrid) ! stability function for momentum |
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| 89 | REAL fh(ngrid) ! stability function for heat |
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| 90 | REAL z1z0,z1z0t ! ratios z1/z0 and z1/z0T |
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| 91 | ! phim = 1+betam*zeta or (1-bm*zeta)**am |
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| 92 | ! phih = alphah + betah*zeta or alphah(1.-bh*zeta)**ah |
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| 93 | REAL betam, betah, alphah, bm, bh, lambda |
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| 94 | ! ah and am are assumed to be -0.25 and -0.5 respectively |
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| 95 | REAL cdn(ngrid),chn(ngrid) ! neutral momentum and heat drag coefficient |
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| 96 | REAL pz0t ! initial thermal roughness length. (local) |
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| 97 | REAL ric ! critical richardson number |
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| 98 | REAL reynolds(ngrid) ! reynolds number for UBL |
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| 99 | REAL prandtl(ngrid) ! prandtl number for UBL |
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| 100 | REAL pz0tcomp(ngrid) ! computed z0t |
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| 101 | REAL ite |
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| 102 | REAL residual,zcd0,z1 |
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| 103 | REAL pcdv(ngrid),pcdh(ngrid) |
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| 104 | REAL zu2(ngrid) ! Large-scale wind at first layer |
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| 105 | REAL pbl_teta(ngrid) ! mixed-layer potential temperature |
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| 106 | INTEGER pbl_height_index(ngrid) ! index of nearest vertical grid point for zmax |
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| 107 | REAL dteta(ngrid,nlay),x(ngrid) ! potential temperature gradient and z/zi |
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| 108 | REAL dvhf(ngrid),dvvv(ngrid) ! dimensionless vertical heat flux and |
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| 109 | ! dimensionless vertical velocity variance |
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| 110 | REAL vhf(ngrid),vvv(ngrid) ! vertical heat flux and vertical velocity variance |
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| 111 | INTEGER ii(1) |
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| 112 | ! temporary |
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| 113 | INTEGER dimout |
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| 114 | |
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| 115 | !------------------------------------------------------------------------ |
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| 116 | !------------------------------------------------------------------------ |
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| 117 | ! PART I : RICHARDSON/REYNOLDS/THERMAL_ROUGHNESS/STABILITY_COEFFICIENTS |
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| 118 | !------------------------------------------------------------------------ |
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| 119 | !------------------------------------------------------------------------ |
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| 120 | |
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| 121 | DO n=1,n_out |
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| 122 | |
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| 123 | c Initialisation : |
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| 124 | |
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| 125 | L_mo(:)=0. |
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| 126 | ustar(:)=0. |
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| 127 | tstar(:)=0. |
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| 128 | zout=z_out(n) |
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| 129 | reynolds(:)=0. |
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| 130 | pz0t = 0. |
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| 131 | pz0tcomp(:) = 0.1*pz0(:) |
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| 132 | rib(:)=0. |
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| 133 | pcdv(:)=0. |
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| 134 | pcdh(:)=0. |
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| 135 | |
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| 136 | ! this formulation assumes alphah=1., implying betah=betam |
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| 137 | ! We use Dyer et al. parameters, as they cover a broad range of Richardson numbers : |
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| 138 | |
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| 139 | bm=16. !UBL |
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| 140 | bh=16. !UBL |
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| 141 | alphah=1. |
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| 142 | betam=5. !SBL |
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| 143 | betah=5. !SBL |
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| 144 | lambda=(sqrt(bh/bm))/alphah |
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| 145 | ric=betah/(betam**2) |
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| 146 | |
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| 147 | DO ig=1,ngrid |
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| 148 | ite=0. |
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| 149 | residual=abs(pz0tcomp(ig)-pz0t) |
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| 150 | zu2(ig)=MAX(pu(ig,1)*pu(ig,1)+pv(ig,1)*pv(ig,1) |
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| 151 | & ,(0.3*wstar_in(ig))**2) |
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| 152 | |
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| 153 | DO WHILE((residual .gt. 0.01*pz0(ig)) .and. (ite .lt. 10.)) |
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| 154 | |
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| 155 | pz0t=pz0tcomp(ig) |
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| 156 | IF (zu2(ig) .ne. 0.) THEN |
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| 157 | ! Richardson number formulation proposed by D.E. England et al. (1995) |
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| 158 | rib(ig) = (pg/pts(ig)) |
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| 159 | & *sqrt(zzlev(ig,2)*pz0(ig)) |
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| 160 | & *(((log(zzlev(ig,2)/pz0(ig)))**2)/(log(zzlev(ig,2)/pz0t))) |
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| 161 | & *(ph(ig,1)-pts(ig))/zu2(ig) |
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| 162 | ELSE |
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| 163 | print*,'warning, infinite Richardson at surface' |
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| 164 | print*,pu(ig,1),pv(ig,1) |
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| 165 | rib(ig) = ric |
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| 166 | ENDIF |
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| 167 | |
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| 168 | z1z0=zzlev(ig,2)/pz0(ig) |
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| 169 | z1z0t=zzlev(ig,2)/pz0t |
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| 170 | |
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| 171 | cdn(ig)=karman/log(z1z0) |
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| 172 | cdn(ig)=cdn(ig)*cdn(ig) |
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| 173 | chn(ig)=cdn(ig)*log(z1z0)/log(z1z0t) |
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| 174 | |
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| 175 | ! STABLE BOUNDARY LAYER : |
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| 176 | IF (rib(ig) .gt. 0.) THEN |
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| 177 | ! From D.E. England et al. (95) |
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| 178 | prandtl(ig)=1. |
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| 179 | if(rib(ig) .lt. ric) then |
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| 180 | ! Assuming alphah=1. and bh=bm for stable conditions : |
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| 181 | fm(ig)=((ric-rib(ig))/ric)**2 |
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| 182 | fh(ig)=((ric-rib(ig))/ric)**2 |
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| 183 | else |
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| 184 | ! For Ri>Ric, we consider Ri->Infinity => no turbulent mixing at surface |
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| 185 | fm(ig)=0. |
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| 186 | fh(ig)=0. |
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| 187 | endif |
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| 188 | ! UNSTABLE BOUNDARY LAYER : |
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| 189 | ELSE |
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| 190 | ! From D.E. England et al. (95) |
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| 191 | fm(ig)=sqrt(1.-lambda*bm*rib(ig)) |
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| 192 | fh(ig)=(1./alphah)*((1.-lambda*bh*rib(ig))**0.5)* |
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| 193 | & (1.-lambda*bm*rib(ig))**0.25 |
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| 194 | prandtl(ig)=alphah*((1.-lambda*bm*rib(ig))**0.25)/ |
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| 195 | & ((1.-lambda*bh*rib(ig))**0.5) |
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| 196 | ENDIF |
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| 197 | |
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| 198 | reynolds(ig)=karman*sqrt(fm(ig)) |
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| 199 | & *sqrt(zu2(ig)) |
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| 200 | & *pz0(ig)/(log(z1z0)*nu) |
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| 201 | pz0tcomp(ig)=pz0(ig)*exp(-karman*7.3* |
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| 202 | & (reynolds(ig)**0.25)*(prandtl(ig)**0.5)) |
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| 203 | residual = abs(pz0t-pz0tcomp(ig)) |
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| 204 | ite = ite+1 |
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| 205 | |
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| 206 | ENDDO ! of while |
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| 207 | pz0t=0. |
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| 208 | |
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| 209 | ! Drag computation: |
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| 210 | |
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| 211 | pcdv(ig)=cdn(ig)*fm(ig) |
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| 212 | pcdh(ig)=chn(ig)*fh(ig) |
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| 213 | |
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| 214 | ENDDO ! of ngrid |
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| 215 | |
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| 216 | !------------------------------------------------------------------------ |
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| 217 | !------------------------------------------------------------------------ |
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| 218 | ! PART II : USTAR/TSTAR/U_OUT/TETA_OUT COMPUTATIONS |
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| 219 | !------------------------------------------------------------------------ |
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| 220 | !------------------------------------------------------------------------ |
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| 221 | |
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| 222 | |
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| 223 | ! Large-scale wind at first layer (without gustiness) and |
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| 224 | ! u* theta* computation |
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| 225 | |
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| 226 | DO ig=1,ngrid |
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| 227 | IF (rib(ig) .ge. ric) THEN |
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| 228 | ustar(ig)=0. |
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| 229 | tstar(ig)=0. |
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| 230 | ELSE |
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| 231 | ustar(ig)=sqrt(pcdv(ig)) |
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| 232 | & *sqrt(pu(ig,1)*pu(ig,1)+pv(ig,1)*pv(ig,1)) |
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| 233 | tstar(ig)=-pcdh(ig)*(pts(ig)-ph(ig,1)) |
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| 234 | & /sqrt(pcdv(ig)) |
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| 235 | ENDIF |
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| 236 | ENDDO |
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| 237 | |
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| 238 | ! Monin Obukhov length: |
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| 239 | |
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| 240 | DO ig=1,ngrid |
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| 241 | IF (rib(ig) .gt. ric) THEN |
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| 242 | L_mo(ig)=0. |
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| 243 | ELSE |
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| 244 | L_mo(ig)=pts(ig)*(ustar(ig)**2)/(pg*karman*tstar(ig)) !as defined here, L is positive for SBL, negative for UBL |
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| 245 | ENDIF |
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| 246 | ENDDO |
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| 247 | |
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| 248 | ! Interpolation: |
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| 249 | |
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| 250 | DO ig=1,ngrid |
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| 251 | IF(zout .lt. pz0tcomp(ig)) THEN |
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| 252 | u_out(ig,n)=0. |
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| 253 | Teta_out(ig,n)=pts(ig) |
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| 254 | ELSEIF (L_mo(ig) .gt. 0.) THEN |
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| 255 | u_out(ig,n)=(ustar(ig)/karman)*log(zout/pz0(ig)) + |
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| 256 | & 5.*(ustar(ig)/(karman*L_mo(ig)))*(zout-pz0(ig)) |
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| 257 | Teta_out(ig,n)=pts(ig)+(tstar(ig)/(prandtl(ig)*karman)) |
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| 258 | & *log(zout/pz0tcomp(ig)) + |
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| 259 | & 5.*(tstar(ig)/(prandtl(ig)*karman*L_mo(ig))) |
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| 260 | & *(zout-pz0tcomp(ig)) |
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| 261 | ELSEIF (L_mo(ig) .lt. 0.) THEN |
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| 262 | |
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| 263 | IF(L_mo(ig) .gt. -1000.) THEN |
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| 264 | |
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| 265 | u_out(ig,n)=(ustar(ig)/karman)*( |
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| 266 | & 2.*atan((1.-16.*zout/L_mo(ig))**0.25) |
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| 267 | & -2.*atan((1.-16.*pz0(ig)/L_mo(ig))**0.25) |
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| 268 | & -2.*log(1.+(1.-16.*zout/L_mo(ig))**0.25) |
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| 269 | & +2.*log(1.+(1.-16.*pz0(ig)/L_mo(ig))**0.25) |
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| 270 | & - log(1.+sqrt(1.-16.*zout/L_mo(ig))) |
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| 271 | & + log(1.+sqrt(1.-16.*pz0(ig)/L_mo(ig))) |
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| 272 | & + log(zout/pz0(ig)) |
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| 273 | & ) |
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| 274 | |
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| 275 | Teta_out(ig,n)=MAX(pts(ig)+(tstar(ig)/(prandtl(ig)*karman))*( |
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| 276 | & 2.*log(1.+sqrt(1.-16.*pz0tcomp(ig)/L_mo(ig))) |
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| 277 | & -2.*log(1.+sqrt(1.-16.*zout/L_mo(ig))) |
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| 278 | & + log(zout/pz0tcomp(ig)) |
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| 279 | & ),ph(ig,1)) |
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| 280 | |
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| 281 | ELSE |
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| 282 | |
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| 283 | ! We have to treat the case where L is very large and negative, |
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| 284 | ! corresponding to a very nearly stable atmosphere (but not quite !) |
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| 285 | ! i.e. teta* <0 and almost zero. We choose the cutoff |
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| 286 | ! corresponding to L_mo < -1000 and use a 3rd order taylor expansion. The difference |
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| 287 | ! between the two expression for z/L = -1/1000 is -1.54324*10^-9 |
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| 288 | ! (we do that to avoid using r*4 precision, otherwise, we get -inf values) |
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| 289 | |
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| 290 | u_out(ig,n)=(ustar(ig)/karman)*( |
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| 291 | & (4./L_mo(ig))*(zout-pz0(ig)) |
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| 292 | & + (20./(L_mo(ig))**2)*(zout**2-pz0(ig)**2) |
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| 293 | & + (160./(L_mo(ig))**3)*(zout**3-pz0(ig)**3) |
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| 294 | & + log(zout/pz0(ig)) |
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| 295 | & ) |
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| 296 | |
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| 297 | Teta_out(ig,n)=MAX(pts(ig)+(tstar(ig)/(prandtl(ig)*karman))*( |
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| 298 | & (8./L_mo(ig))*(zout-pz0tcomp(ig)) |
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| 299 | & + (48./(L_mo(ig))**2)*(zout**2-pz0tcomp(ig)**2) |
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| 300 | & + (1280./(3.*(L_mo(ig))**3))*(zout**3-pz0tcomp(ig)**3) |
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| 301 | & + log(zout/pz0tcomp(ig)) |
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| 302 | & ),ph(ig,1)) |
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| 303 | |
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| 304 | ENDIF |
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| 305 | ELSE |
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| 306 | u_out(ig,n)=0. |
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| 307 | Teta_out(ig,n)=pts(ig) |
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| 308 | ENDIF |
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| 309 | IF(zout .lt. pz0(ig)) THEN |
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| 310 | u_out(ig,n)=0. |
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| 311 | ENDIF |
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| 312 | ENDDO |
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| 313 | |
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| 314 | ! when using convective adjustment without thermals, a vertical potential temperature |
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| 315 | ! profile is assumed up to the thermal roughness length. Hence, theoretically, theta |
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| 316 | ! interpolated at any height in the surface layer is theta at the first level. |
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| 317 | |
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| 318 | IF ((.not.calltherm).and.(calladj)) THEN |
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| 319 | Teta_out(:,n)=ph(:,1) |
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| 320 | u_out(:,n)=(sqrt(cdn(:))*sqrt(pu(:,1)*pu(:,1)+pv(:,1)*pv(:,1)) |
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| 321 | & /karman)*log(zout/pz0(:)) |
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| 322 | ENDIF |
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| 323 | T_out(:,n) = Teta_out(:,n)*(exp( |
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| 324 | & (zout/zzlay(:,1))*(log(pplay(:,1)/ps)) |
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| 325 | & ) |
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| 326 | & )**rcp |
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| 327 | |
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| 328 | ENDDO !of n=1,n_out |
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| 329 | |
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| 330 | !------------------------------------------------------------------------ |
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| 331 | !------------------------------------------------------------------------ |
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| 332 | ! PART III : WSTAR COMPUTATION |
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| 333 | !------------------------------------------------------------------------ |
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| 334 | !------------------------------------------------------------------------ |
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| 335 | |
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| 336 | ! Detection of the mixed-layer potential temperature |
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| 337 | ! ------------ |
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| 338 | |
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| 339 | ! Nearest index for the pbl height |
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| 340 | |
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| 341 | IF (calltherm) THEN |
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| 342 | |
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| 343 | pbl_height_index(:)=1 |
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| 344 | |
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| 345 | DO k=1,nlay-1 |
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| 346 | DO ig=1, ngrid |
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| 347 | IF (abs(zmax(ig)-zzlay(ig,k)) .lt. |
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| 348 | & abs(zmax(ig)-zzlay(ig,pbl_height_index(ig)))) THEN |
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| 349 | pbl_height_index(ig)=k |
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| 350 | ENDIF |
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| 351 | ENDDO |
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| 352 | ENDDO |
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| 353 | |
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| 354 | ! Potential temperature gradient |
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| 355 | |
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| 356 | dteta(:,nlay)=0. |
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| 357 | DO k=1,nlay-1 |
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| 358 | DO ig=1, ngrid |
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| 359 | dteta(ig,k) = (ph(ig,k+1)-ph(ig,k))/(zzlay(ig,k+1)-zzlay(ig,k)) |
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| 360 | ENDDO |
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| 361 | ENDDO |
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| 362 | |
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| 363 | ! Computation of the pbl mixed layer temperature |
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| 364 | |
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| 365 | DO ig=1, ngrid |
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| 366 | ii=MINLOC(abs(dteta(ig,1:pbl_height_index(ig)))) |
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| 367 | pbl_teta(ig) = ph(ig,ii(1)) |
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| 368 | ENDDO |
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| 369 | |
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| 370 | ! Recompute wstar |
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| 371 | ! We follow Spiga et. al 2010 (QJRMS) |
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| 372 | ! ------------ |
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| 373 | |
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| 374 | DO ig=1, ngrid |
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| 375 | IF (zmax(ig) .gt. 0.) THEN |
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| 376 | wstar(ig)=(pg*zmax(ig)*hfmax(ig)/pbl_teta(ig))**(1./3.) |
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| 377 | ELSE |
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| 378 | wstar(ig)=0. |
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| 379 | ENDIF |
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| 380 | ENDDO |
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| 381 | |
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| 382 | !------------------------------------------------------------------------ |
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| 383 | !------------------------------------------------------------------------ |
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| 384 | ! PART IV : VERTICAL_VELOCITY_VARIANCE/VERTICAL_TURBULENT_FLUX PROFILES |
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| 385 | !------------------------------------------------------------------------ |
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| 386 | !------------------------------------------------------------------------ |
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| 387 | |
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| 388 | ! We follow Spiga et. al 2010 (QJRMS) |
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| 389 | ! ------------ |
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| 390 | |
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| 391 | DO ig=1, ngrid |
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| 392 | IF (zmax(ig) .gt. 0.) THEN |
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| 393 | x(ig) = zout/zmax(ig) |
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| 394 | ELSE |
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| 395 | x(ig) = 999. |
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| 396 | ENDIF |
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| 397 | ENDDO |
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| 398 | |
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| 399 | DO ig=1, ngrid |
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| 400 | ! dimensionless vertical heat flux |
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| 401 | IF (x(ig) .le. 0.3) THEN |
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| 402 | dvhf(ig) = ((-3.85/log(x(ig)))+0.07*log(x(ig))) |
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| 403 | & *exp(-4.61*x(ig)) |
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| 404 | ELSEIF (x(ig) .le. 1.) THEN |
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| 405 | dvhf(ig) = -1.52*x(ig) + 1.24 |
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| 406 | ELSE |
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| 407 | dvhf(ig) = 0. |
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| 408 | ENDIF |
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| 409 | ! dimensionless vertical velocity variance |
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| 410 | IF (x(ig) .le. 1.) THEN |
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| 411 | dvvv(ig) = 2.05*(x(ig)**(2./3.))*(1.-0.64*x(ig))**2 |
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| 412 | ELSE |
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| 413 | dvvv(ig) = 0. |
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| 414 | ENDIF |
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| 415 | ENDDO |
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| 416 | |
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| 417 | vhf(:) = dvhf(:)*hfmax(:) |
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| 418 | vvv(:) = dvvv(:)*(wstar(:))**2 |
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| 419 | |
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| 420 | ENDIF ! of if calltherm |
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| 421 | |
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| 422 | RETURN |
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| 423 | END |
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