| 1 | SUBROUTINE surflayer_interpol(ngrid,nlay,pz0, |
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| 2 | & pg,pz,pu,pv,wmax,pts,ph,z_out,Teta_out,u_out,ustar,tstar,L_mo) |
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| 3 | IMPLICIT NONE |
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| 4 | !======================================================================= |
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| 5 | ! |
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| 6 | ! Subject: interpolation of temperature and velocity norm in the surface layer |
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| 7 | ! by recomputation of surface layer quantities (Richardson, Prandtl, Reynolds, u*, teta*) |
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| 8 | ! ------- |
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| 9 | ! |
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| 10 | ! Author: Arnaud Colaitis 05/08/11 |
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| 11 | ! ------- |
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| 12 | ! |
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| 13 | ! Arguments: |
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| 14 | ! ---------- |
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| 15 | ! |
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| 16 | ! inputs: |
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| 17 | ! ------ |
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| 18 | ! ngrid size of the horizontal grid |
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| 19 | ! pg gravity (m s -2) |
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| 20 | ! pz(ngrid,nlay) height of layers |
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| 21 | ! pu(ngrid,nlay) u component of the wind |
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| 22 | ! pv(ngrid,nlay) v component of the wind |
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| 23 | ! pts(ngrid) surface temperature |
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| 24 | ! ph(ngrid) potential temperature T*(p/ps)^kappa |
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| 25 | ! |
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| 26 | ! |
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| 27 | !======================================================================= |
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| 28 | ! |
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| 29 | !----------------------------------------------------------------------- |
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| 30 | ! Declarations: |
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| 31 | ! ------------- |
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| 32 | |
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| 33 | #include "comcstfi.h" |
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| 34 | |
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| 35 | ! Arguments: |
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| 36 | ! ---------- |
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| 37 | |
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| 38 | INTEGER, INTENT(IN) :: ngrid,nlay |
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| 39 | REAL, INTENT(IN) :: pz0(ngrid) |
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| 40 | REAL, INTENT(IN) :: pg,pz(ngrid,nlay) |
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| 41 | REAL, INTENT(IN) :: pu(ngrid,nlay),pv(ngrid,nlay) |
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| 42 | REAL, INTENT(IN) :: wmax(ngrid) |
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| 43 | REAL, INTENT(IN) :: pts(ngrid),ph(ngrid,nlay) |
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| 44 | REAL, INTENT(IN) :: z_out ! output height (in m above surface) |
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| 45 | REAL, INTENT(OUT) :: Teta_out(ngrid),u_out(ngrid)! interpolated fields at z_out : potential temperature and norm(uv) |
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| 46 | REAL, INTENT(OUT) :: ustar(ngrid), tstar(ngrid) ! u* and teta* |
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| 47 | REAL, INTENT(OUT) :: L_mo(ngrid) ! Monin-Obukhov length |
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| 48 | |
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| 49 | ! Local: |
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| 50 | ! ------ |
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| 51 | |
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| 52 | INTEGER ig |
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| 53 | |
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| 54 | REAL karman,nu |
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| 55 | DATA karman,nu/.41,0.001/ |
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| 56 | SAVE karman,nu |
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| 57 | |
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| 58 | ! Local(2): |
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| 59 | ! --------- |
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| 60 | REAL zout |
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| 61 | |
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| 62 | REAL rib(ngrid) ! Bulk Richardson number |
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| 63 | REAL fm(ngrid) ! stability function for momentum |
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| 64 | REAL fh(ngrid) ! stability function for heat |
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| 65 | REAL z1z0,z1z0t ! ratios z1/z0 and z1/z0T |
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| 66 | |
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| 67 | ! phim = 1+betam*zeta or (1-bm*zeta)**am |
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| 68 | ! phih = alphah + betah*zeta or alphah(1.-bh*zeta)**ah |
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| 69 | REAL betam, betah, alphah, bm, bh, lambda |
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| 70 | ! ah and am are assumed to be -0.25 and -0.5 respectively |
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| 71 | |
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| 72 | REAL cdn(ngrid),chn(ngrid) ! neutral momentum and heat drag coefficient |
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| 73 | REAL pz0t ! initial thermal roughness length. (local) |
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| 74 | REAL ric ! critical richardson number |
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| 75 | REAL reynolds(ngrid) ! reynolds number for UBL |
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| 76 | REAL prandtl(ngrid) ! prandtl number for UBL |
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| 77 | REAL pz0tcomp(ngrid) ! computed z0t |
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| 78 | REAL ite |
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| 79 | REAL residual |
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| 80 | REAL pcdv(ngrid),pcdh(ngrid) |
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| 81 | ! For output : |
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| 82 | |
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| 83 | REAL zu2(ngrid) ! Large-scale wind at first layer |
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| 84 | !----------------------------------------------------------------------- |
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| 85 | ! couche de surface: |
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| 86 | ! ------------------ |
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| 87 | zout=z_out |
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| 88 | tstar(:)=0. |
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| 89 | ustar(:)=0. |
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| 90 | reynolds(:)=0. |
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| 91 | |
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| 92 | ! New formulation (AC) : |
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| 93 | |
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| 94 | ! phim = 1+betam*zeta or (1-bm*zeta)**am |
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| 95 | ! phih = alphah + betah*zeta or alphah(1.-bh*zeta)**ah |
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| 96 | ! am=-0.25, ah=-0.5 |
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| 97 | |
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| 98 | pz0t = 0. ! for the sake of simplicity |
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| 99 | pz0tcomp(:) = 0.1*pz0(:) |
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| 100 | rib(:)=0. |
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| 101 | pcdv(:)=0. |
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| 102 | pcdh(:)=0. |
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| 103 | |
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| 104 | ! this formulation assumes alphah=1., implying betah=betam |
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| 105 | ! We use Dyer et al. parameters, as they cover a broad range of Richardson numbers : |
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| 106 | bm=16. !UBL |
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| 107 | bh=16. !UBL |
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| 108 | alphah=1. |
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| 109 | betam=5. !SBL |
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| 110 | betah=5. !SBL |
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| 111 | lambda=(sqrt(bh/bm))/alphah |
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| 112 | ric=betah/(betam**2) |
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| 113 | |
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| 114 | DO ig=1,ngrid |
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| 115 | |
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| 116 | ite=0. |
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| 117 | residual=abs(pz0tcomp(ig)-pz0t) |
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| 118 | |
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| 119 | do while((residual .gt. 0.01*pz0(ig)) .and. (ite .lt. 10.)) |
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| 120 | |
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| 121 | pz0t=pz0tcomp(ig) |
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| 122 | |
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| 123 | if ((pu(ig,1) .ne. 0.) .or. (pv(ig,1) .ne. 0.)) then |
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| 124 | |
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| 125 | ! Classical Richardson number formulation |
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| 126 | |
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| 127 | ! rib(ig) = (pg/ph(ig,1))*pz(ig,1)*(ph(ig,1)-pts(ig)) |
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| 128 | ! & /(pu(ig,1)*pu(ig,1) + pv(ig,1)*pv(ig,1)) |
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| 129 | |
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| 130 | ! Richardson number formulation proposed by D.E. England et al. (1995) |
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| 131 | |
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| 132 | ! IF((pu(ig,1)*pu(ig,1) + pv(ig,1)*pv(ig,1) .lt. 1.) |
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| 133 | ! & .and. (wmax(ig) .gt. 0.)) THEN |
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| 134 | zu2(ig)= |
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| 135 | ! & (MAX(pu(ig,1)*pu(ig,1) + pv(ig,1)*pv(ig,1),wmax(ig)**2)) |
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| 136 | & ( pu(ig,1)*pu(ig,1) + pv(ig,1)*pv(ig,1)) |
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| 137 | ! & pu(ig,1)*pu(ig,1) + pv(ig,1)*pv(ig,1) |
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| 138 | ! ELSE |
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| 139 | ! zu2(ig)=pu(ig,1)*pu(ig,1) + pv(ig,1)*pv(ig,1) |
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| 140 | ! ENDIF |
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| 141 | |
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| 142 | rib(ig) = (pg/ph(ig,1)) |
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| 143 | ! & *pz(ig,1)*pz0(ig)/sqrt(pz(ig,1)*pz0t) |
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| 144 | & *sqrt(pz(ig,1)*pz0(ig)) |
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| 145 | & *(((log(pz(ig,1)/pz0(ig)))**2)/(log(pz(ig,1)/pz0t))) |
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| 146 | & *(ph(ig,1)-pts(ig))/(zu2(ig) + (0.5*wmax(ig))**2) |
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| 147 | |
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| 148 | ! & /(MAX(pu(ig,1)*pu(ig,1) + pv(ig,1)*pv(ig,1),wmax(ig)**2)) |
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| 149 | ! & /( pu(ig,1)*pu(ig,1) + pv(ig,1)*pv(ig,1) + wmax(ig)**2) |
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| 150 | |
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| 151 | else |
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| 152 | print*,'warning, infinite Richardson at surface' |
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| 153 | print*,pu(ig,1),pv(ig,1) |
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| 154 | rib(ig) = ric ! traiter ce cas ! |
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| 155 | endif |
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| 156 | |
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| 157 | z1z0=pz(ig,1)/pz0(ig) |
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| 158 | z1z0t=pz(ig,1)/pz0t |
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| 159 | |
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| 160 | cdn(ig)=karman/log(z1z0) |
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| 161 | cdn(ig)=cdn(ig)*cdn(ig) |
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| 162 | chn(ig)=cdn(ig)*log(z1z0)/log(z1z0t) |
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| 163 | |
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| 164 | ! Stable case : |
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| 165 | if (rib(ig) .gt. 0.) then |
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| 166 | ! From D.E. England et al. (95) |
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| 167 | prandtl(ig)=1. |
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| 168 | if(rib(ig) .lt. ric) then |
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| 169 | ! Assuming alphah=1. and bh=bm for stable conditions : |
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| 170 | fm(ig)=((ric-rib(ig))/ric)**2 |
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| 171 | fh(ig)=((ric-rib(ig))/ric)**2 |
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| 172 | else |
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| 173 | ! For Ri>Ric, we consider Ri->Infinity => no turbulent mixing at surface |
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| 174 | fm(ig)=0. |
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| 175 | fh(ig)=0. |
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| 176 | endif |
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| 177 | ! Unstable case : |
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| 178 | else |
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| 179 | ! From D.E. England et al. (95) |
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| 180 | fm(ig)=sqrt(1.-lambda*bm*rib(ig)) |
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| 181 | fh(ig)=(1./alphah)*((1.-lambda*bh*rib(ig))**0.5)* |
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| 182 | & (1.-lambda*bm*rib(ig))**0.25 |
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| 183 | prandtl(ig)=alphah*((1.-lambda*bm*rib(ig))**0.25)/ |
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| 184 | & ((1.-lambda*bh*rib(ig))**0.5) |
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| 185 | endif |
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| 186 | |
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| 187 | reynolds(ig)=karman*sqrt(fm(ig)) |
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| 188 | & *sqrt(zu2(ig)+(0.5*wmax(ig))**2) |
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| 189 | ! & *sqrt(pu(ig,1)**2 + pv(ig,1)**2) |
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| 190 | & *pz0(ig)/(log(z1z0)*nu) |
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| 191 | pz0tcomp(ig)=pz0(ig)*exp(-karman*7.3* |
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| 192 | & (reynolds(ig)**0.25)*(prandtl(ig)**0.5)) |
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| 193 | |
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| 194 | |
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| 195 | residual = abs(pz0t-pz0tcomp(ig)) |
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| 196 | ite = ite+1 |
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| 197 | ! if(ite .eq. 10) then |
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| 198 | ! print*, 'iteration max reached' |
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| 199 | ! endif |
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| 200 | ! print*, "iteration nnumber, residual",ite,residual |
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| 201 | |
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| 202 | enddo ! of while |
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| 203 | |
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| 204 | pz0t=0. |
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| 205 | |
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| 206 | ! Drag computation : |
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| 207 | |
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| 208 | pcdv(ig)=cdn(ig)*fm(ig) |
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| 209 | pcdh(ig)=chn(ig)*fh(ig) |
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| 210 | |
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| 211 | ENDDO |
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| 212 | |
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| 213 | ! Large-scale wind at first layer (without gustiness) and |
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| 214 | ! u* theta* computation |
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| 215 | DO ig=1,ngrid |
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| 216 | |
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| 217 | if (rib(ig) .gt. ric) then |
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| 218 | ustar(ig)=0. |
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| 219 | tstar(ig)=0. |
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| 220 | else |
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| 221 | |
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| 222 | ! ustar(ig)=karman*sqrt(fm(ig)*zu2(ig))/(log(pz(ig,1)/pz0(ig))) |
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| 223 | ! tstar(ig)=karman*fh(ig)*(ph(ig,1)-pts(ig)) |
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| 224 | ! & /(log(pz(ig,1)/pz0tcomp(ig))*sqrt(fm(ig))) |
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| 225 | |
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| 226 | !simpler definition of u* and teta*, equivalent to the formula above : |
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| 227 | |
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| 228 | ustar(ig)=sqrt(pcdv(ig))*sqrt(zu2(ig)) |
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| 229 | tstar(ig)=-pcdh(ig)*(pts(ig)-ph(ig,1)) |
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| 230 | & /sqrt(pcdv(ig)) |
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| 231 | |
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| 232 | if (tstar(ig) .lt. -50) then |
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| 233 | print*, fh(ig),rib(ig),(ph(ig,1)-pts(ig)) |
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| 234 | & ,log(pz(ig,1)/pz0tcomp(ig)),sqrt(fm(ig)) |
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| 235 | endif |
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| 236 | endif |
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| 237 | ENDDO |
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| 238 | |
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| 239 | ! Monin Obukhov length : |
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| 240 | |
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| 241 | DO ig=1,ngrid |
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| 242 | if (rib(ig) .gt. ric) then |
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| 243 | L_mo(ig)=0. |
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| 244 | else |
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| 245 | 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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| 246 | endif |
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| 247 | ENDDO |
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| 248 | |
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| 249 | DO ig=1,ngrid |
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| 250 | IF(zout .ge. pz(ig,1)) THEN |
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| 251 | zout=1. |
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| 252 | print*, 'Warning, z_out should be less than the first |
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| 253 | & vertical grid-point' |
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| 254 | print*, 'z1 =',pz(ig,1) |
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| 255 | print*, 'z_out=',z_out |
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| 256 | print*, 'z_out has been changed to 1m |
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| 257 | & and computation is resumed' |
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| 258 | ENDIF |
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| 259 | |
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| 260 | IF(zout .lt. pz0tcomp(ig)) THEN |
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| 261 | zout=pz0tcomp(ig) |
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| 262 | print*, 'Warning, z_out should be more than the thermal |
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| 263 | & roughness length' |
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| 264 | print*, 'z0 =',pz0tcomp(ig) |
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| 265 | print*, 'z_out=',z_out |
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| 266 | print*, 'z_out has been changed to z0t |
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| 267 | & and computation is resumed' |
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| 268 | ENDIF |
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| 269 | ENDDO |
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| 270 | |
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| 271 | print*, 'interpolation of u and teta at z_out=',zout |
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| 272 | |
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| 273 | DO ig=1,ngrid |
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| 274 | IF (L_mo(ig) .gt. 0.) THEN |
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| 275 | u_out(ig)=(ustar(ig)/karman)*log(zout/pz0(ig)) + |
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| 276 | & 5.*(ustar(ig)/(karman*L_mo(ig)))*(zout-pz0(ig)) |
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| 277 | Teta_out(ig)=pts(ig)+(tstar(ig)/(prandtl(ig)*karman)) |
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| 278 | & *log(zout/pz0tcomp(ig)) + |
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| 279 | & 5.*(tstar(ig)/(prandtl(ig)*karman*L_mo(ig))) |
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| 280 | & *(zout-pz0tcomp(ig)) |
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| 281 | ELSEIF (L_mo(ig) .lt. 0.) THEN |
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| 282 | |
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| 283 | IF(L_mo(ig) .gt. -1000.) THEN |
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| 284 | |
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| 285 | u_out(ig)=(ustar(ig)/karman)*( |
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| 286 | & 2.*atan((1.-16.*zout/L_mo(ig))**0.25) |
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| 287 | & -2.*atan((1.-16.*pz0(ig)/L_mo(ig))**0.25) |
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| 288 | & -2.*log(1.+(1.-16.*zout/L_mo(ig))**0.25) |
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| 289 | & +2.*log(1.+(1.-16.*pz0(ig)/L_mo(ig))**0.25) |
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| 290 | & - log(1.+sqrt(1.-16.*zout/L_mo(ig))) |
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| 291 | & + log(1.+sqrt(1.-16.*pz0(ig)/L_mo(ig))) |
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| 292 | & + log(zout/pz0(ig)) |
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| 293 | & ) |
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| 294 | |
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| 295 | Teta_out(ig)=pts(ig)+(tstar(ig)/(prandtl(ig)*karman))*( |
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| 296 | & 2.*log(1.+sqrt(1.-16.*pz0tcomp(ig)/L_mo(ig))) |
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| 297 | & -2.*log(1.+sqrt(1.-16.*zout/L_mo(ig))) |
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| 298 | & + log(zout/pz0tcomp(ig)) |
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| 299 | & ) |
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| 300 | |
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| 301 | ELSE |
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| 302 | |
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| 303 | ! We have to treat the case where L is very large and negative, |
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| 304 | ! corresponding to a very nearly stable atmosphere (but not quite !) |
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| 305 | ! i.e. teta* <0 and almost zero. We choose the cutoff |
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| 306 | ! corresponding to L_mo < -1000 and use a 3rd order taylor expansion. The difference |
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| 307 | ! between the two expression for z/L = -1/1000 is -1.54324*10^-9 |
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| 308 | ! (we do that to avoid using r*4 precision, otherwise, we get -inf values) |
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| 309 | |
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| 310 | u_out(ig)=(ustar(ig)/karman)*( |
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| 311 | & (4./L_mo(ig))*(zout-pz0(ig)) |
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| 312 | & + (20./(L_mo(ig))**2)*(zout**2-pz0(ig)**2) |
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| 313 | & + (160./(L_mo(ig))**3)*(zout**3-pz0(ig)**3) |
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| 314 | & + log(zout/pz0(ig)) |
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| 315 | & ) |
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| 316 | |
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| 317 | Teta_out(ig)=pts(ig)+(tstar(ig)/(prandtl(ig)*karman))*( |
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| 318 | & (8./L_mo(ig))*(zout-pz0tcomp(ig)) |
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| 319 | & + (48./(L_mo(ig))**2)*(zout**2-pz0tcomp(ig)**2) |
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| 320 | & + (1280./(3.*(L_mo(ig))**3))*(zout**3-pz0tcomp(ig)**3) |
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| 321 | & + log(zout/pz0tcomp(ig)) |
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| 322 | & ) |
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| 323 | |
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| 324 | ENDIF |
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| 325 | ELSE |
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| 326 | u_out(ig)=0. |
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| 327 | Teta_out(ig)=pts(ig) |
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| 328 | ENDIF |
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| 329 | ENDDO |
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| 330 | |
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| 331 | ! Usefull diagnostics for the interpolation routine : |
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| 332 | |
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| 333 | ! call WRITEDIAGFI(ngrid,'z0T', |
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| 334 | ! & 'thermal roughness length','m', |
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| 335 | ! & 2,pz0tcomp) |
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| 336 | ! call WRITEDIAGFI(ngrid,'z0', |
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| 337 | ! & 'roughness length','m', |
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| 338 | ! & 2,pz0) |
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| 339 | |
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| 340 | |
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| 341 | RETURN |
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| 342 | END |
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