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module yamada4_m |
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|
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IMPLICIT NONE |
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|
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private |
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public yamada4 |
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real, parameter:: kap = 0.4 |
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|
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contains |
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|
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SUBROUTINE yamada4(ngrid, dt, g, zlev, zlay, u, v, teta, cd, q2, km, kn, kq, & |
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ustar, iflag_pbl) |
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|
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! From LMDZ4/libf/phylmd/yamada4.F, version 1.1 2004/06/22 11:45:36 |
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|
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use nr_util, only: assert |
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USE dimphy, ONLY: klev |
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|
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integer, intent(in):: ngrid |
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REAL, intent(in):: dt ! pas de temps |
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real, intent(in):: g |
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|
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REAL zlev(ngrid, klev+1) |
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! altitude \`a chaque niveau (interface inf\'erieure de la couche de |
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! m\^eme indice) |
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|
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REAL zlay(ngrid, klev) ! altitude au centre de chaque couche |
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|
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REAL u(ngrid, klev), v(ngrid, klev) |
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! vitesse au centre de chaque couche (en entr\'ee : la valeur au |
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! d\'ebut du pas de temps) |
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|
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REAL, intent(in):: teta(ngrid, klev) |
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! temp\'erature potentielle au centre de chaque couche (en entr\'ee : |
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! la valeur au d\'ebut du pas de temps) |
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|
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REAL, intent(in):: cd(:) ! (ngrid) cdrag, valeur au d\'ebut du pas de temps |
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|
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REAL, intent(inout):: q2(ngrid, klev+1) |
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! $q^2$ au bas de chaque couche |
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! En entr\'ee : la valeur au d\'ebut du pas de temps ; en sortie : la |
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! valeur \`a la fin du pas de temps. |
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|
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REAL km(ngrid, klev+1) |
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! diffusivit\'e turbulente de quantit\'e de mouvement (au bas de |
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! chaque couche) (en sortie : la valeur \`a la fin du pas de temps) |
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|
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REAL kn(ngrid, klev+1) |
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! diffusivit\'e turbulente des scalaires (au bas de chaque couche) |
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! (en sortie : la valeur \`a la fin du pas de temps) |
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|
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REAL kq(ngrid, klev+1) |
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real ustar(ngrid) |
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|
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integer, intent(in):: iflag_pbl |
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! iflag_pbl doit valoir entre 6 et 9 |
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! l = 6, on prend syst\'ematiquement une longueur d'\'equilibre |
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! iflag_pbl = 6 : MY 2.0 |
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! iflag_pbl = 7 : MY 2.0.Fournier |
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! iflag_pbl = 8 : MY 2.5 |
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! iflag_pbl = 9 : un test ? |
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|
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! Local: |
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|
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real kmin, qmin, pblhmin(ngrid), coriol(ngrid) |
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real qpre |
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REAL unsdz(ngrid, klev) |
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REAL unsdzdec(ngrid, klev+1) |
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REAL kmpre(ngrid, klev+1), tmp2 |
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REAL mpre(ngrid, klev+1) |
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real delta(ngrid, klev+1) |
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real aa(ngrid, klev+1), aa1 |
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integer, PARAMETER:: nlev = klev+1 |
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logical:: first = .true. |
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integer:: ipas = 0 |
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integer ig, k |
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real ri |
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real rif(ngrid, klev+1), sm(ngrid, klev+1), alpha(ngrid, klev) |
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real m2(ngrid, klev+1), dz(ngrid, klev+1), zq, n2(ngrid, klev+1) |
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real dtetadz(ngrid, klev+1) |
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real m2cstat, mcstat, kmcstat |
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real l(ngrid, klev+1) |
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real l0(ngrid) |
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real sq(ngrid), sqz(ngrid), zz(ngrid, klev+1) |
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integer iter |
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real:: ric = 0.195, rifc = 0.191, b1 = 16.6, kap = 0.4 |
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|
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!----------------------------------------------------------------------- |
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|
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call assert(iflag_pbl >= 6 .and. iflag_pbl <= 9, "yamada4") |
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|
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ipas = ipas+1 |
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|
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! les increments verticaux |
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DO ig = 1, ngrid |
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! alerte: zlev n'est pas declare a nlev |
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zlev(ig, nlev) = zlay(ig, klev) +(zlay(ig, klev) - zlev(ig, nlev-1)) |
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ENDDO |
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|
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DO k = 1, klev |
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DO ig = 1, ngrid |
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unsdz(ig, k) = 1.E+0/(zlev(ig, k+1)-zlev(ig, k)) |
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ENDDO |
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ENDDO |
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|
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DO ig = 1, ngrid |
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unsdzdec(ig, 1) = 1.E+0/(zlay(ig, 1)-zlev(ig, 1)) |
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ENDDO |
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|
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DO k = 2, klev |
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DO ig = 1, ngrid |
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unsdzdec(ig, k) = 1.E+0/(zlay(ig, k)-zlay(ig, k-1)) |
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ENDDO |
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ENDDO |
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|
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DO ig = 1, ngrid |
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unsdzdec(ig, klev+1) = 1.E+0/(zlev(ig, klev+1)-zlay(ig, klev)) |
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ENDDO |
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|
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do k = 2, klev |
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do ig = 1, ngrid |
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dz(ig, k) = zlay(ig, k)-zlay(ig, k-1) |
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m2(ig, k) = ((u(ig, k)-u(ig, k-1))**2+(v(ig, k)-v(ig, k-1))**2) & |
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/(dz(ig, k)*dz(ig, k)) |
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dtetadz(ig, k) = (teta(ig, k)-teta(ig, k-1))/dz(ig, k) |
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n2(ig, k) = g*2.*dtetadz(ig, k)/(teta(ig, k-1)+teta(ig, k)) |
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ri = n2(ig, k)/max(m2(ig, k), 1.e-10) |
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if (ri.lt.ric) then |
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rif(ig, k) = frif(ri) |
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else |
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rif(ig, k) = rifc |
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endif |
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if (rif(ig, k).lt.0.16) then |
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alpha(ig, k) = falpha(rif(ig, k)) |
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sm(ig, k) = fsm(rif(ig, k)) |
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else |
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alpha(ig, k) = 1.12 |
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sm(ig, k) = 0.085 |
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endif |
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zz(ig, k) = b1*m2(ig, k)*(1.-rif(ig, k))*sm(ig, k) |
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enddo |
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enddo |
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|
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! Au premier appel, on d\'etermine l et q2 de façon it\'erative. |
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! It\'eration pour d\'eterminer la longueur de m\'elange |
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|
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if (first .or. iflag_pbl == 6) then |
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do ig = 1, ngrid |
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l0(ig) = 10. |
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enddo |
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do k = 2, klev-1 |
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do ig = 1, ngrid |
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l(ig, k) = l0(ig) * kap * zlev(ig, k) & |
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/ (kap * zlev(ig, k) + l0(ig)) |
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enddo |
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enddo |
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|
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do iter = 1, 10 |
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do ig = 1, ngrid |
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sq(ig) = 1e-10 |
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sqz(ig) = 1e-10 |
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enddo |
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do k = 2, klev-1 |
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do ig = 1, ngrid |
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q2(ig, k) = l(ig, k)**2 * zz(ig, k) |
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l(ig, k) = fl(zlev(ig, k), l0(ig), q2(ig, k), n2(ig, k)) |
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zq = sqrt(q2(ig, k)) |
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sqz(ig) = sqz(ig) + zq * zlev(ig, k) & |
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* (zlay(ig, k) - zlay(ig, k-1)) |
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sq(ig) = sq(ig) + zq * (zlay(ig, k) - zlay(ig, k-1)) |
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enddo |
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enddo |
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do ig = 1, ngrid |
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l0(ig) = 0.2 * sqz(ig) / sq(ig) |
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enddo |
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enddo |
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endif |
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|
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! Calcul de la longueur de melange. |
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|
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! Mise a jour de l0 |
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do ig = 1, ngrid |
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sq(ig) = 1.e-10 |
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sqz(ig) = 1.e-10 |
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enddo |
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do k = 2, klev-1 |
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do ig = 1, ngrid |
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zq = sqrt(q2(ig, k)) |
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sqz(ig) = sqz(ig)+zq*zlev(ig, k)*(zlay(ig, k)-zlay(ig, k-1)) |
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sq(ig) = sq(ig)+zq*(zlay(ig, k)-zlay(ig, k-1)) |
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enddo |
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enddo |
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do ig = 1, ngrid |
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l0(ig) = 0.2*sqz(ig)/sq(ig) |
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enddo |
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! calcul de l(z) |
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do k = 2, klev |
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do ig = 1, ngrid |
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l(ig, k) = fl(zlev(ig, k), l0(ig), q2(ig, k), n2(ig, k)) |
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if (first) then |
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q2(ig, k) = l(ig, k)**2 * zz(ig, k) |
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endif |
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enddo |
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enddo |
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|
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! Yamada 2.0 |
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if (iflag_pbl == 6) then |
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do k = 2, klev |
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do ig = 1, ngrid |
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q2(ig, k) = l(ig, k)**2 * zz(ig, k) |
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enddo |
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enddo |
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else if (iflag_pbl == 7) then |
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! Yamada 2.Fournier |
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|
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! Calcul de l, km, au pas precedent |
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do k = 2, klev |
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do ig = 1, ngrid |
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delta(ig, k) = q2(ig, k) / (l(ig, k)**2 * sm(ig, k)) |
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kmpre(ig, k) = l(ig, k) * sqrt(q2(ig, k)) * sm(ig, k) |
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mpre(ig, k) = sqrt(m2(ig, k)) |
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enddo |
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enddo |
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|
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do k = 2, klev-1 |
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do ig = 1, ngrid |
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m2cstat = max(alpha(ig, k)*n2(ig, k)+delta(ig, k)/b1, 1.e-12) |
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mcstat = sqrt(m2cstat) |
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|
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! puis on ecrit la valeur de q qui annule l'equation de m |
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! supposee en q3 |
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|
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IF (k == 2) THEN |
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kmcstat = 1.E+0 / mcstat & |
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*(unsdz(ig, k)*kmpre(ig, k+1) & |
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*mpre(ig, k+1) & |
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+unsdz(ig, k-1) & |
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*cd(ig) & |
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*(sqrt(u(ig, 3)**2+v(ig, 3)**2) & |
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-mcstat/unsdzdec(ig, k) & |
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-mpre(ig, k+1)/unsdzdec(ig, k+1))**2) & |
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/(unsdz(ig, k)+unsdz(ig, k-1)) |
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ELSE |
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kmcstat = 1.E+0 / mcstat & |
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*(unsdz(ig, k)*kmpre(ig, k+1) & |
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*mpre(ig, k+1) & |
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+unsdz(ig, k-1)*kmpre(ig, k-1) & |
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*mpre(ig, k-1)) & |
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/(unsdz(ig, k)+unsdz(ig, k-1)) |
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ENDIF |
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tmp2 = kmcstat / (sm(ig, k) / q2(ig, k)) /l(ig, k) |
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q2(ig, k) = max(tmp2, 1.e-12)**(2./3.) |
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enddo |
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enddo |
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else if (iflag_pbl >= 8) then |
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! Yamada 2.5 a la Didi |
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|
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! Calcul de l, km, au pas precedent |
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do k = 2, klev |
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do ig = 1, ngrid |
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delta(ig, k) = q2(ig, k)/(l(ig, k)**2*sm(ig, k)) |
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if (delta(ig, k).lt.1.e-20) then |
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delta(ig, k) = 1.e-20 |
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endif |
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km(ig, k) = l(ig, k)*sqrt(q2(ig, k))*sm(ig, k) |
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aa1 = (m2(ig, k)*(1.-rif(ig, k))-delta(ig, k)/b1) |
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aa(ig, k) = aa1*dt/(delta(ig, k)*l(ig, k)) |
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qpre = sqrt(q2(ig, k)) |
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if (iflag_pbl == 8) then |
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if (aa(ig, k).gt.0.) then |
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q2(ig, k) = (qpre+aa(ig, k)*qpre*qpre)**2 |
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else |
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q2(ig, k) = (qpre/(1.-aa(ig, k)*qpre))**2 |
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endif |
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else |
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! iflag_pbl = 9 |
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if (aa(ig, k)*qpre.gt.0.9) then |
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q2(ig, k) = (qpre*10.)**2 |
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else |
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q2(ig, k) = (qpre/(1.-aa(ig, k)*qpre))**2 |
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endif |
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endif |
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q2(ig, k) = min(max(q2(ig, k), 1.e-10), 1.e4) |
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enddo |
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enddo |
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endif |
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|
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! Calcul des coefficients de m\'elange |
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do k = 2, klev |
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do ig = 1, ngrid |
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zq = sqrt(q2(ig, k)) |
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km(ig, k) = l(ig, k)*zq*sm(ig, k) |
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kn(ig, k) = km(ig, k)*alpha(ig, k) |
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kq(ig, k) = l(ig, k)*zq*0.2 |
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enddo |
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enddo |
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|
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! Traitement des cas noctrunes avec l'introduction d'une longueur |
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! minilale. |
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|
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! Traitement particulier pour les cas tres stables. |
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! D'apres Holtslag Boville. |
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|
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do ig = 1, ngrid |
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coriol(ig) = 1.e-4 |
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pblhmin(ig) = 0.07*ustar(ig)/max(abs(coriol(ig)), 2.546e-5) |
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enddo |
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|
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print *, 'pblhmin ', pblhmin |
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do k = 2, klev |
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do ig = 1, ngrid |
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if (teta(ig, 2).gt.teta(ig, 1)) then |
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qmin = ustar(ig)*(max(1.-zlev(ig, k)/pblhmin(ig), 0.))**2 |
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kmin = kap*zlev(ig, k)*qmin |
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else |
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kmin = -1. ! kmin n'est utilise que pour les SL stables. |
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endif |
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if (kn(ig, k).lt.kmin.or.km(ig, k).lt.kmin) then |
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kn(ig, k) = kmin |
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km(ig, k) = kmin |
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kq(ig, k) = kmin |
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! la longueur de melange est suposee etre l = kap z |
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! K = l q Sm d'ou q2 = (K/l Sm)**2 |
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q2(ig, k) = (qmin/sm(ig, k))**2 |
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endif |
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enddo |
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enddo |
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|
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first = .false. |
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|
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end SUBROUTINE yamada4 |
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|
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!******************************************************************* |
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|
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real function frif(ri) |
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|
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real, intent(in):: ri |
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|
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frif = 0.6588*(ri+0.1776-sqrt(ri*ri-0.3221*ri+0.03156)) |
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|
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end function frif |
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|
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!******************************************************************* |
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|
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real function falpha(ri) |
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|
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real, intent(in):: ri |
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|
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falpha = 1.318*(0.2231-ri)/(0.2341-ri) |
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|
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end function falpha |
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|
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!******************************************************************* |
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|
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real function fsm(ri) |
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|
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real, intent(in):: ri |
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|
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fsm = 1.96*(0.1912-ri)*(0.2341-ri)/((1.-ri)*(0.2231-ri)) |
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|
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end function fsm |
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|
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!******************************************************************* |
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|
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real function fl(zzz, zl0, zq2, zn2) |
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|
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real, intent(in):: zzz, zl0, zq2, zn2 |
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|
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fl = max(min(zl0 * kap * zzz / (kap * zzz + zl0), & |
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0.5 * sqrt(zq2) / sqrt(max(zn2, 1e-10))), 1.) |
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|
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end function fl |
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|
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end module yamada4_m |
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