| Line |
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! $Header$ |
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! ====================================================================== |
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✗ |
SUBROUTINE nonlocal(knon, paprs, pplay, tsol, beta, u, v, t, q, cd_h, cd_m, & |
| 6 |
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✗ |
pcfh, pcfm, cgh, cgq) |
| 7 |
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USE dimphy |
| 8 |
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IMPLICIT NONE |
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! ====================================================================== |
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! Laurent Li (LMD/CNRS), le 30 septembre 1998 |
| 11 |
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! Couche limite non-locale. Adaptation du code du CCM3. |
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! Code non teste, donc a ne pas utiliser. |
| 13 |
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! ====================================================================== |
| 14 |
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! Nonlocal scheme that determines eddy diffusivities based on a |
| 15 |
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! diagnosed boundary layer height and a turbulent velocity scale. |
| 16 |
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! Also countergradient effects for heat and moisture are included. |
| 17 |
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| 18 |
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! For more information, see Holtslag, A.A.M., and B.A. Boville, 1993: |
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! Local versus nonlocal boundary-layer diffusion in a global climate |
| 20 |
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! model. J. of Climate, vol. 6, 1825-1842. |
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! ====================================================================== |
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include "YOMCST.h" |
| 23 |
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| 24 |
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! Arguments: |
| 25 |
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| 26 |
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INTEGER knon ! nombre de points a calculer |
| 27 |
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REAL tsol(klon) ! temperature du sol (K) |
| 28 |
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REAL beta(klon) ! efficacite d'evaporation (entre 0 et 1) |
| 29 |
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REAL paprs(klon, klev+1) ! pression a inter-couche (Pa) |
| 30 |
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REAL pplay(klon, klev) ! pression au milieu de couche (Pa) |
| 31 |
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REAL u(klon, klev) ! vitesse U (m/s) |
| 32 |
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REAL v(klon, klev) ! vitesse V (m/s) |
| 33 |
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REAL t(klon, klev) ! temperature (K) |
| 34 |
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REAL q(klon, klev) ! vapeur d'eau (kg/kg) |
| 35 |
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REAL cd_h(klon) ! coefficient de friction au sol pour chaleur |
| 36 |
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REAL cd_m(klon) ! coefficient de friction au sol pour vitesse |
| 37 |
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| 38 |
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INTEGER isommet |
| 39 |
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REAL vk |
| 40 |
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PARAMETER (vk=0.40) |
| 41 |
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REAL ricr |
| 42 |
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PARAMETER (ricr=0.4) |
| 43 |
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REAL fak |
| 44 |
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PARAMETER (fak=8.5) |
| 45 |
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REAL fakn |
| 46 |
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PARAMETER (fakn=7.2) |
| 47 |
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REAL onet |
| 48 |
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PARAMETER (onet=1.0/3.0) |
| 49 |
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REAL t_coup |
| 50 |
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PARAMETER (t_coup=273.15) |
| 51 |
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REAL zkmin |
| 52 |
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PARAMETER (zkmin=0.01) |
| 53 |
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REAL betam |
| 54 |
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PARAMETER (betam=15.0) |
| 55 |
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REAL betah |
| 56 |
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PARAMETER (betah=15.0) |
| 57 |
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REAL betas |
| 58 |
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PARAMETER (betas=5.0) |
| 59 |
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REAL sffrac |
| 60 |
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PARAMETER (sffrac=0.1) |
| 61 |
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REAL binm |
| 62 |
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PARAMETER (binm=betam*sffrac) |
| 63 |
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REAL binh |
| 64 |
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PARAMETER (binh=betah*sffrac) |
| 65 |
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REAL ccon |
| 66 |
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PARAMETER (ccon=fak*sffrac*vk) |
| 67 |
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| 68 |
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✗ |
REAL z(klon, klev) |
| 69 |
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REAL pcfm(klon, klev), pcfh(klon, klev) |
| 70 |
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| 71 |
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INTEGER i, k |
| 72 |
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REAL zxt, zxq, zxu, zxv, zxmod, taux, tauy |
| 73 |
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REAL zx_alf1, zx_alf2 ! parametres pour extrapolation |
| 74 |
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REAL khfs(klon) ! surface kinematic heat flux [mK/s] |
| 75 |
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REAL kqfs(klon) ! sfc kinematic constituent flux [m/s] |
| 76 |
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REAL heatv(klon) ! surface virtual heat flux |
| 77 |
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REAL ustar(klon) |
| 78 |
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REAL rino(klon, klev) ! bulk Richardon no. from level to ref lev |
| 79 |
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LOGICAL unstbl(klon) ! pts w/unstbl pbl (positive virtual ht flx) |
| 80 |
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LOGICAL stblev(klon) ! stable pbl with levels within pbl |
| 81 |
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LOGICAL unslev(klon) ! unstbl pbl with levels within pbl |
| 82 |
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LOGICAL unssrf(klon) ! unstb pbl w/lvls within srf pbl lyr |
| 83 |
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LOGICAL unsout(klon) ! unstb pbl w/lvls in outer pbl lyr |
| 84 |
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LOGICAL check(klon) ! True=>chk if Richardson no.>critcal |
| 85 |
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REAL pblh(klon) |
| 86 |
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REAL cgh(klon, 2:klev) ! counter-gradient term for heat [K/m] |
| 87 |
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REAL cgq(klon, 2:klev) ! counter-gradient term for constituents |
| 88 |
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REAL cgs(klon, 2:klev) ! counter-gradient star (cg/flux) |
| 89 |
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REAL obklen(klon) |
| 90 |
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REAL ztvd, ztvu, zdu2 |
| 91 |
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REAL therm(klon) ! thermal virtual temperature excess |
| 92 |
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REAL phiminv(klon) ! inverse phi function for momentum |
| 93 |
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REAL phihinv(klon) ! inverse phi function for heat |
| 94 |
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REAL wm(klon) ! turbulent velocity scale for momentum |
| 95 |
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REAL fak1(klon) ! k*ustar*pblh |
| 96 |
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REAL fak2(klon) ! k*wm*pblh |
| 97 |
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REAL fak3(klon) ! fakn*wstr/wm |
| 98 |
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REAL pblk(klon) ! level eddy diffusivity for momentum |
| 99 |
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REAL pr(klon) ! Prandtl number for eddy diffusivities |
| 100 |
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REAL zl(klon) ! zmzp / Obukhov length |
| 101 |
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REAL zh(klon) ! zmzp / pblh |
| 102 |
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REAL zzh(klon) ! (1-(zmzp/pblh))**2 |
| 103 |
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REAL wstr(klon) ! w*, convective velocity scale |
| 104 |
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REAL zm(klon) ! current level height |
| 105 |
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REAL zp(klon) ! current level height + one level up |
| 106 |
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REAL zcor, zdelta, zcvm5, zxqs |
| 107 |
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REAL fac, pblmin, zmzp, term |
| 108 |
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| 109 |
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include "YOETHF.h" |
| 110 |
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include "FCTTRE.h" |
| 111 |
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| 112 |
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! Initialisation |
| 113 |
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| 114 |
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isommet = klev |
| 115 |
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| 116 |
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DO i = 1, klon |
| 117 |
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pcfh(i, 1) = cd_h(i) |
| 118 |
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pcfm(i, 1) = cd_m(i) |
| 119 |
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END DO |
| 120 |
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DO k = 2, klev |
| 121 |
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DO i = 1, klon |
| 122 |
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pcfh(i, k) = zkmin |
| 123 |
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pcfm(i, k) = zkmin |
| 124 |
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cgs(i, k) = 0.0 |
| 125 |
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cgh(i, k) = 0.0 |
| 126 |
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cgq(i, k) = 0.0 |
| 127 |
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END DO |
| 128 |
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END DO |
| 129 |
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| 130 |
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! Calculer les hauteurs de chaque couche |
| 131 |
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| 132 |
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✗ |
DO i = 1, knon |
| 133 |
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z(i, 1) = rd*t(i, 1)/(0.5*(paprs(i,1)+pplay(i,1)))*(paprs(i,1)-pplay(i,1) & |
| 134 |
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✗ |
)/rg |
| 135 |
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END DO |
| 136 |
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DO k = 2, klev |
| 137 |
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DO i = 1, knon |
| 138 |
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z(i, k) = z(i, k-1) + rd*0.5*(t(i,k-1)+t(i,k))/paprs(i, k)*(pplay(i,k-1 & |
| 139 |
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)-pplay(i,k))/rg |
| 140 |
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END DO |
| 141 |
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END DO |
| 142 |
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| 143 |
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DO i = 1, knon |
| 144 |
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IF (thermcep) THEN |
| 145 |
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zdelta = max(0., sign(1.,rtt-tsol(i))) |
| 146 |
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zcvm5 = r5les*rlvtt*(1.-zdelta) + r5ies*rlstt*zdelta |
| 147 |
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zcvm5 = zcvm5/rcpd/(1.0+rvtmp2*q(i,1)) |
| 148 |
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zxqs = r2es*foeew(tsol(i), zdelta)/paprs(i, 1) |
| 149 |
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zxqs = min(0.5, zxqs) |
| 150 |
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zcor = 1./(1.-retv*zxqs) |
| 151 |
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zxqs = zxqs*zcor |
| 152 |
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ELSE |
| 153 |
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IF (tsol(i)<t_coup) THEN |
| 154 |
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zxqs = qsats(tsol(i))/paprs(i, 1) |
| 155 |
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ELSE |
| 156 |
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zxqs = qsatl(tsol(i))/paprs(i, 1) |
| 157 |
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END IF |
| 158 |
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END IF |
| 159 |
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zx_alf1 = 1.0 |
| 160 |
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zx_alf2 = 1.0 - zx_alf1 |
| 161 |
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zxt = (t(i,1)+z(i,1)*rg/rcpd/(1.+rvtmp2*q(i,1)))*(1.+retv*q(i,1))*zx_alf1 & |
| 162 |
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✗ |
+ (t(i,2)+z(i,2)*rg/rcpd/(1.+rvtmp2*q(i,2)))*(1.+retv*q(i,2))*zx_alf2 |
| 163 |
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✗ |
zxu = u(i, 1)*zx_alf1 + u(i, 2)*zx_alf2 |
| 164 |
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zxv = v(i, 1)*zx_alf1 + v(i, 2)*zx_alf2 |
| 165 |
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zxq = q(i, 1)*zx_alf1 + q(i, 2)*zx_alf2 |
| 166 |
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zxmod = 1.0 + sqrt(zxu**2+zxv**2) |
| 167 |
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khfs(i) = (tsol(i)*(1.+retv*q(i,1))-zxt)*zxmod*cd_h(i) |
| 168 |
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kqfs(i) = (zxqs-zxq)*zxmod*cd_h(i)*beta(i) |
| 169 |
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heatv(i) = khfs(i) + 0.61*zxt*kqfs(i) |
| 170 |
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taux = zxu*zxmod*cd_m(i) |
| 171 |
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tauy = zxv*zxmod*cd_m(i) |
| 172 |
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ustar(i) = sqrt(taux**2+tauy**2) |
| 173 |
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ustar(i) = max(sqrt(ustar(i)), 0.01) |
| 174 |
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END DO |
| 175 |
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| 176 |
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DO i = 1, knon |
| 177 |
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rino(i, 1) = 0.0 |
| 178 |
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check(i) = .TRUE. |
| 179 |
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pblh(i) = z(i, 1) |
| 180 |
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obklen(i) = -t(i, 1)*ustar(i)**3/(rg*vk*heatv(i)) |
| 181 |
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END DO |
| 182 |
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| 183 |
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| 184 |
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! PBL height calculation: |
| 185 |
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! Search for level of pbl. Scan upward until the Richardson number between |
| 186 |
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! the first level and the current level exceeds the "critical" value. |
| 187 |
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| 188 |
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fac = 100.0 |
| 189 |
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DO k = 1, isommet |
| 190 |
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DO i = 1, knon |
| 191 |
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IF (check(i)) THEN |
| 192 |
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zdu2 = (u(i,k)-u(i,1))**2 + (v(i,k)-v(i,1))**2 + fac*ustar(i)**2 |
| 193 |
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✗ |
zdu2 = max(zdu2, 1.0E-20) |
| 194 |
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ztvd = (t(i,k)+z(i,k)*0.5*rg/rcpd/(1.+rvtmp2*q(i, & |
| 195 |
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k)))*(1.+retv*q(i,k)) |
| 196 |
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ztvu = (t(i,1)-z(i,k)*0.5*rg/rcpd/(1.+rvtmp2*q(i, & |
| 197 |
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1)))*(1.+retv*q(i,1)) |
| 198 |
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rino(i, k) = (z(i,k)-z(i,1))*rg*(ztvd-ztvu)/(zdu2*0.5*(ztvd+ztvu)) |
| 199 |
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IF (rino(i,k)>=ricr) THEN |
| 200 |
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pblh(i) = z(i, k-1) + (z(i,k-1)-z(i,k))*(ricr-rino(i,k-1))/(rino(i, & |
| 201 |
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k-1)-rino(i,k)) |
| 202 |
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check(i) = .FALSE. |
| 203 |
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END IF |
| 204 |
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END IF |
| 205 |
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END DO |
| 206 |
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END DO |
| 207 |
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| 208 |
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| 209 |
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! Set pbl height to maximum value where computation exceeds number of |
| 210 |
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! layers allowed |
| 211 |
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| 212 |
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DO i = 1, knon |
| 213 |
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IF (check(i)) pblh(i) = z(i, isommet) |
| 214 |
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END DO |
| 215 |
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| 216 |
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! Improve estimate of pbl height for the unstable points. |
| 217 |
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! Find unstable points (sensible heat flux is upward): |
| 218 |
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| 219 |
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DO i = 1, knon |
| 220 |
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IF (heatv(i)>0.) THEN |
| 221 |
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unstbl(i) = .TRUE. |
| 222 |
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check(i) = .TRUE. |
| 223 |
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ELSE |
| 224 |
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unstbl(i) = .FALSE. |
| 225 |
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check(i) = .FALSE. |
| 226 |
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END IF |
| 227 |
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END DO |
| 228 |
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| 229 |
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! For the unstable case, compute velocity scale and the |
| 230 |
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! convective temperature excess: |
| 231 |
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| 232 |
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DO i = 1, knon |
| 233 |
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IF (check(i)) THEN |
| 234 |
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phiminv(i) = (1.-binm*pblh(i)/obklen(i))**onet |
| 235 |
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wm(i) = ustar(i)*phiminv(i) |
| 236 |
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therm(i) = heatv(i)*fak/wm(i) |
| 237 |
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rino(i, 1) = 0.0 |
| 238 |
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END IF |
| 239 |
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END DO |
| 240 |
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| 241 |
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! Improve pblh estimate for unstable conditions using the |
| 242 |
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! convective temperature excess: |
| 243 |
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| 244 |
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✗ |
DO k = 1, isommet |
| 245 |
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✗ |
DO i = 1, knon |
| 246 |
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✗ |
IF (check(i)) THEN |
| 247 |
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zdu2 = (u(i,k)-u(i,1))**2 + (v(i,k)-v(i,1))**2 + fac*ustar(i)**2 |
| 248 |
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✗ |
zdu2 = max(zdu2, 1.0E-20) |
| 249 |
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ztvd = (t(i,k)+z(i,k)*0.5*rg/rcpd/(1.+rvtmp2*q(i, & |
| 250 |
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✗ |
k)))*(1.+retv*q(i,k)) |
| 251 |
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ztvu = (t(i,1)+therm(i)-z(i,k)*0.5*rg/rcpd/(1.+rvtmp2*q(i, & |
| 252 |
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✗ |
1)))*(1.+retv*q(i,1)) |
| 253 |
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✗ |
rino(i, k) = (z(i,k)-z(i,1))*rg*(ztvd-ztvu)/(zdu2*0.5*(ztvd+ztvu)) |
| 254 |
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✗ |
IF (rino(i,k)>=ricr) THEN |
| 255 |
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pblh(i) = z(i, k-1) + (z(i,k-1)-z(i,k))*(ricr-rino(i,k-1))/(rino(i, & |
| 256 |
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✗ |
k-1)-rino(i,k)) |
| 257 |
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✗ |
check(i) = .FALSE. |
| 258 |
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END IF |
| 259 |
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END IF |
| 260 |
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END DO |
| 261 |
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END DO |
| 262 |
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| 263 |
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! Set pbl height to maximum value where computation exceeds number of |
| 264 |
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! layers allowed |
| 265 |
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| 266 |
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✗ |
DO i = 1, knon |
| 267 |
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✗ |
IF (check(i)) pblh(i) = z(i, isommet) |
| 268 |
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END DO |
| 269 |
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| 270 |
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! Points for which pblh exceeds number of pbl layers allowed; |
| 271 |
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! set to maximum |
| 272 |
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| 273 |
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✗ |
DO i = 1, knon |
| 274 |
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✗ |
IF (check(i)) pblh(i) = z(i, isommet) |
| 275 |
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END DO |
| 276 |
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| 277 |
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! PBL height must be greater than some minimum mechanical mixing depth |
| 278 |
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! Several investigators have proposed minimum mechanical mixing depth |
| 279 |
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! relationships as a function of the local friction velocity, u*. We |
| 280 |
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! make use of a linear relationship of the form h = c u* where c=700. |
| 281 |
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! The scaling arguments that give rise to this relationship most often |
| 282 |
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! represent the coefficient c as some constant over the local coriolis |
| 283 |
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! parameter. Here we make use of the experimental results of Koracin |
| 284 |
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! and Berkowicz (1988) [BLM, Vol 43] for wich they recommend 0.07/f |
| 285 |
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! where f was evaluated at 39.5 N and 52 N. Thus we use a typical mid |
| 286 |
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! latitude value for f so that c = 0.07/f = 700. |
| 287 |
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| 288 |
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✗ |
DO i = 1, knon |
| 289 |
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✗ |
pblmin = 700.0*ustar(i) |
| 290 |
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✗ |
pblh(i) = max(pblh(i), pblmin) |
| 291 |
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END DO |
| 292 |
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| 293 |
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! pblh is now available; do preparation for diffusivity calculation: |
| 294 |
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| 295 |
|
✗ |
DO i = 1, knon |
| 296 |
|
✗ |
pblk(i) = 0.0 |
| 297 |
|
✗ |
fak1(i) = ustar(i)*pblh(i)*vk |
| 298 |
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| 299 |
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! Do additional preparation for unstable cases only, set temperature |
| 300 |
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! and moisture perturbations depending on stability. |
| 301 |
|
|
|
| 302 |
|
✗ |
IF (unstbl(i)) THEN |
| 303 |
|
✗ |
zxt = (t(i,1)-z(i,1)*0.5*rg/rcpd/(1.+rvtmp2*q(i,1)))*(1.+retv*q(i,1)) |
| 304 |
|
✗ |
phiminv(i) = (1.-binm*pblh(i)/obklen(i))**onet |
| 305 |
|
✗ |
phihinv(i) = sqrt(1.-binh*pblh(i)/obklen(i)) |
| 306 |
|
✗ |
wm(i) = ustar(i)*phiminv(i) |
| 307 |
|
✗ |
fak2(i) = wm(i)*pblh(i)*vk |
| 308 |
|
✗ |
wstr(i) = (heatv(i)*rg*pblh(i)/zxt)**onet |
| 309 |
|
✗ |
fak3(i) = fakn*wstr(i)/wm(i) |
| 310 |
|
|
END IF |
| 311 |
|
|
END DO |
| 312 |
|
|
|
| 313 |
|
|
! Main level loop to compute the diffusivities and |
| 314 |
|
|
! counter-gradient terms: |
| 315 |
|
|
|
| 316 |
|
✗ |
DO k = 2, isommet |
| 317 |
|
|
|
| 318 |
|
|
! Find levels within boundary layer: |
| 319 |
|
|
|
| 320 |
|
✗ |
DO i = 1, knon |
| 321 |
|
✗ |
unslev(i) = .FALSE. |
| 322 |
|
✗ |
stblev(i) = .FALSE. |
| 323 |
|
✗ |
zm(i) = z(i, k-1) |
| 324 |
|
✗ |
zp(i) = z(i, k) |
| 325 |
|
|
IF (zkmin==0.0 .AND. zp(i)>pblh(i)) zp(i) = pblh(i) |
| 326 |
|
✗ |
IF (zm(i)<pblh(i)) THEN |
| 327 |
|
✗ |
zmzp = 0.5*(zm(i)+zp(i)) |
| 328 |
|
✗ |
zh(i) = zmzp/pblh(i) |
| 329 |
|
✗ |
zl(i) = zmzp/obklen(i) |
| 330 |
|
✗ |
zzh(i) = 0. |
| 331 |
|
✗ |
IF (zh(i)<=1.0) zzh(i) = (1.-zh(i))**2 |
| 332 |
|
|
|
| 333 |
|
|
! stblev for points zm < plbh and stable and neutral |
| 334 |
|
|
! unslev for points zm < plbh and unstable |
| 335 |
|
|
|
| 336 |
|
✗ |
IF (unstbl(i)) THEN |
| 337 |
|
✗ |
unslev(i) = .TRUE. |
| 338 |
|
|
ELSE |
| 339 |
|
✗ |
stblev(i) = .TRUE. |
| 340 |
|
|
END IF |
| 341 |
|
|
END IF |
| 342 |
|
|
END DO |
| 343 |
|
|
|
| 344 |
|
|
! Stable and neutral points; set diffusivities; counter-gradient |
| 345 |
|
|
! terms zero for stable case: |
| 346 |
|
|
|
| 347 |
|
✗ |
DO i = 1, knon |
| 348 |
|
✗ |
IF (stblev(i)) THEN |
| 349 |
|
✗ |
IF (zl(i)<=1.) THEN |
| 350 |
|
✗ |
pblk(i) = fak1(i)*zh(i)*zzh(i)/(1.+betas*zl(i)) |
| 351 |
|
|
ELSE |
| 352 |
|
✗ |
pblk(i) = fak1(i)*zh(i)*zzh(i)/(betas+zl(i)) |
| 353 |
|
|
END IF |
| 354 |
|
✗ |
pcfm(i, k) = pblk(i) |
| 355 |
|
✗ |
pcfh(i, k) = pcfm(i, k) |
| 356 |
|
|
END IF |
| 357 |
|
|
END DO |
| 358 |
|
|
|
| 359 |
|
|
! unssrf, unstable within surface layer of pbl |
| 360 |
|
|
! unsout, unstable within outer layer of pbl |
| 361 |
|
|
|
| 362 |
|
✗ |
DO i = 1, knon |
| 363 |
|
✗ |
unssrf(i) = .FALSE. |
| 364 |
|
✗ |
unsout(i) = .FALSE. |
| 365 |
|
✗ |
IF (unslev(i)) THEN |
| 366 |
|
✗ |
IF (zh(i)<sffrac) THEN |
| 367 |
|
✗ |
unssrf(i) = .TRUE. |
| 368 |
|
|
ELSE |
| 369 |
|
✗ |
unsout(i) = .TRUE. |
| 370 |
|
|
END IF |
| 371 |
|
|
END IF |
| 372 |
|
|
END DO |
| 373 |
|
|
|
| 374 |
|
|
! Unstable for surface layer; counter-gradient terms zero |
| 375 |
|
|
|
| 376 |
|
✗ |
DO i = 1, knon |
| 377 |
|
✗ |
IF (unssrf(i)) THEN |
| 378 |
|
✗ |
term = (1.-betam*zl(i))**onet |
| 379 |
|
✗ |
pblk(i) = fak1(i)*zh(i)*zzh(i)*term |
| 380 |
|
✗ |
pr(i) = term/sqrt(1.-betah*zl(i)) |
| 381 |
|
|
END IF |
| 382 |
|
|
END DO |
| 383 |
|
|
|
| 384 |
|
|
! Unstable for outer layer; counter-gradient terms non-zero: |
| 385 |
|
|
|
| 386 |
|
✗ |
DO i = 1, knon |
| 387 |
|
✗ |
IF (unsout(i)) THEN |
| 388 |
|
✗ |
pblk(i) = fak2(i)*zh(i)*zzh(i) |
| 389 |
|
✗ |
cgs(i, k) = fak3(i)/(pblh(i)*wm(i)) |
| 390 |
|
✗ |
cgh(i, k) = khfs(i)*cgs(i, k) |
| 391 |
|
✗ |
pr(i) = phiminv(i)/phihinv(i) + ccon*fak3(i)/fak |
| 392 |
|
✗ |
cgq(i, k) = kqfs(i)*cgs(i, k) |
| 393 |
|
|
END IF |
| 394 |
|
|
END DO |
| 395 |
|
|
|
| 396 |
|
|
! For all unstable layers, set diffusivities |
| 397 |
|
|
|
| 398 |
|
✗ |
DO i = 1, knon |
| 399 |
|
✗ |
IF (unslev(i)) THEN |
| 400 |
|
✗ |
pcfm(i, k) = pblk(i) |
| 401 |
|
✗ |
pcfh(i, k) = pblk(i)/pr(i) |
| 402 |
|
|
END IF |
| 403 |
|
|
END DO |
| 404 |
|
|
END DO ! end of level loop |
| 405 |
|
|
|
| 406 |
|
✗ |
RETURN |
| 407 |
|
|
END SUBROUTINE nonlocal |
| 408 |
|
|
|