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module HBTM_m |
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IMPLICIT none |
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contains |
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SUBROUTINE HBTM(paprs, pplay, t2m, q2m, ustar, flux_t, flux_q, u, v, t, q, & |
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pblh, cape, EauLiq, ctei, pblT, therm, plcl) |
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! D'apr\'es Holstag et Boville et Troen et Mahrt |
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! JAS 47 BLM |
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! Algorithme th\'ese Anne Mathieu. Crit\'ere d'entra\^inement |
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! Peter Duynkerke (JAS 50). Written by: Anne MATHIEU and Alain |
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! LAHELLEC, 22nd November 1999. |
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! Modifications : d\'ecembre 99 passage th \`a niveau plus bas. Voir fixer |
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! la prise du th \`a z/Lambda = -.2 (max Ray) |
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! Autre algorithme : entra\^inement ~ Theta + v =constante |
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! mais comment ? The ? |
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! On peut fixer q \`a 0.7 qsat (cf. non adiabatique) d'où T2 et The2. |
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! Voir aussi KE pblh = niveau The_e ou l = env. |
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! Adaptation \`a LMDZ version coupl\'ee. Pour le moment on fait |
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! passer en argument les grandeurs de surface : flux, t, q2m. On |
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! va utiliser syst\'ematiquement les grandeurs \`a 2 m mais on |
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! garde la possibilit\'e de changer si besoin (jusqu'\`a pr\'esent |
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! la forme de HB avec le premier niveau mod\`ele \'etait |
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! conserv\'ee). |
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USE dimphy, ONLY: klev, klon |
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USE suphec_m, ONLY: rcpd, rd, retv, rg, rkappa, rtt |
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USE yoethf_m, ONLY: r2es, rvtmp2 |
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USE fcttre, ONLY: foeew |
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! Arguments: |
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! pression a inter-couche (Pa) |
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REAL, intent(in):: paprs(klon, klev+1) |
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! pression au milieu de couche (Pa) |
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REAL, intent(in):: pplay(klon, klev) |
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REAL, intent(in):: t2m(klon) ! temperature a 2 m |
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! q a 2 et 10m |
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REAL, intent(in):: q2m(klon) |
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REAL, intent(in):: ustar(:) ! (knon) |
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REAL, intent(in):: flux_t(:), flux_q(:) ! (knon) flux à la surface |
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REAL, intent(in):: u(:, :) ! (knon, klev) vitesse U (m/s) |
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REAL, intent(in):: v(:, :) ! (knon, klev) vitesse V (m/s) |
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REAL, intent(in):: t(:, :) ! (knon, klev) temperature (K) |
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REAL, intent(in):: q(:, :) ! (knon, klev) vapeur d'eau (kg/kg) |
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REAL, intent(out):: pblh(:) ! (knon) |
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! Cape du thermique |
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REAL Cape(klon) |
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! Eau liqu integr du thermique |
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REAL EauLiq(klon) |
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! Critere d'instab d'entrainmt des nuages de |
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REAL ctei(klon) |
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REAL pblT(klon) |
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! thermal virtual temperature excess |
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REAL therm(klon) |
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REAL plcl(klon) |
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! Local: |
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INTEGER knon ! nombre de points a calculer |
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INTEGER isommet |
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! limite max sommet pbl |
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PARAMETER (isommet=klev) |
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REAL vk |
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! Von Karman => passer a .41 ! cf U.Olgstrom |
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PARAMETER (vk=0.35) |
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REAL ricr |
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PARAMETER (ricr=0.4) |
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! a |
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REAL onet |
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PARAMETER (onet=1.0/3.0) |
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REAL zkmin |
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PARAMETER (zkmin=0.01) |
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REAL betam |
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! pour Phim / h dans la S.L stable |
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PARAMETER (betam=15.0) |
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! z/OBL<>1 |
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REAL sffrac |
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! S.L. = z/h < .1 |
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PARAMETER (sffrac=0.1) |
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REAL binm |
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PARAMETER (binm=betam*sffrac) |
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REAL q_star, t_star |
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! Lambert correlations T' q' avec T* q* |
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REAL b1, b2, b212, b2sr |
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PARAMETER (b1=70., b2=20.) |
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REAL z(klon, klev) |
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REAL zref |
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! Niveau de ref a 2m peut eventuellement |
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PARAMETER (zref=2.) |
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! etre choisi a 10m |
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INTEGER i, k |
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REAL zxt |
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! surface kinematic heat flux [mK/s] |
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REAL khfs(klon) |
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! sfc kinematic constituent flux [m/s] |
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REAL kqfs(klon) |
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! surface virtual heat flux |
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REAL heatv(klon) |
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! bulk Richardon no. mais en Theta_v |
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REAL rhino(klon, klev) |
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! pts w/unstbl pbl (positive virtual ht flx) |
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LOGICAL unstbl(klon) |
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LOGICAL check(klon) ! Richardson number > critical |
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! flag de prolongerment cape pour pt Omega |
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LOGICAL omegafl(klon) |
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! Monin-Obukhov lengh |
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REAL obklen(klon) |
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REAL zdu2 |
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! Algorithme thermique |
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REAL s(klon, klev) ! [P/Po]^Kappa milieux couches |
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! total water of thermal |
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REAL qT_th(klon) |
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! T thermique niveau precedent |
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REAL qsatbef(klon) |
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! le thermique est sature |
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LOGICAL Zsat(klon) |
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REAL zthvd, zthvu, qqsat |
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REAL t2 |
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! inverse phi function for momentum |
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REAL phiminv(klon) |
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! turbulent velocity scale for momentum |
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REAL wm(klon) |
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! current level height + one level up |
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REAL zp(klon) |
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REAL zcor |
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REAL pblmin |
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!----------------------------------------------------------------- |
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knon = size(pblh) |
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! initialisations |
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q_star = 0 |
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t_star = 0 |
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b212=sqrt(b1*b2) |
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b2sr=sqrt(b2) |
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! Calculer les hauteurs de chaque couche |
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! (geopotentielle Int_dp/ro = Int_[Rd.T.dp/p] z = geop/g) |
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! pourquoi ne pas utiliser Phi/RG ? |
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DO i = 1, knon |
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z(i, 1) = RD * t(i, 1) / (0.5*(paprs(i, 1)+pplay(i, 1))) & |
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* (paprs(i, 1)-pplay(i, 1)) / RG |
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s(i, 1) = (pplay(i, 1)/paprs(i, 1))**RKappa |
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ENDDO |
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! s(k) = [pplay(k)/ps]^kappa |
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! + + + + + + + + + pplay <-> s(k) t dp=pplay(k-1)-pplay(k) |
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! ----------------- paprs <-> sig(k) |
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! + + + + + + + + + pplay <-> s(k-1) |
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! + + + + + + + + + pplay <-> s(1) t dp=paprs-pplay z(1) |
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! ----------------- paprs <-> sig(1) |
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DO k = 2, klev |
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DO i = 1, knon |
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z(i, k) = z(i, k-1) & |
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+ RD * 0.5*(t(i, k-1)+t(i, k)) / paprs(i, k) & |
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* (pplay(i, k-1)-pplay(i, k)) / RG |
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s(i, k) = (pplay(i, k) / paprs(i, 1))**RKappa |
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ENDDO |
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ENDDO |
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! Determination des grandeurs de surface |
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DO i = 1, knon |
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! Niveau de ref choisi a 2m |
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zxt = t2m(i) |
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! convention >0 vers le bas ds lmdz |
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khfs(i) = - flux_t(i)*zxt*Rd / (RCPD*paprs(i, 1)) |
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kqfs(i) = - flux_q(i)*zxt*Rd / paprs(i, 1) |
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! verifier que khfs et kqfs sont bien de la forme w'l' |
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heatv(i) = khfs(i) + 0.608*zxt*kqfs(i) |
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! a comparer aussi aux sorties de clqh : flux_T/RoCp et flux_q/RoLv |
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! Theta et qT du thermique sans exces (interpolin vers surf) |
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! chgt de niveau du thermique (jeudi 30/12/1999) |
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! (interpolation lineaire avant integration phi_h) |
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qT_th(i) = q2m(i) |
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ENDDO |
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DO i = 1, knon |
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! Global Richardson |
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rhino(i, 1) = 0.0 |
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check(i) = .TRUE. |
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! on initialise pblh a l'altitude du 1er niv |
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pblh(i) = z(i, 1) |
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plcl(i) = 6000. |
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! Lambda = -u*^3 / (alpha.g.kvon.<w'Theta'v> |
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obklen(i) = -t(i, 1)*ustar(i)**3/(RG*vk*heatv(i)) |
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ENDDO |
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! PBL height calculation: Search for level of pbl. Scan upward |
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! until the Richardson number between the first level and the |
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! current level exceeds the "critical" value. (bonne idee Nu de |
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! separer le Ric et l'exces de temp du thermique) |
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DO k = 2, isommet |
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DO i = 1, knon |
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IF (check(i)) THEN |
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! pourquoi / niveau 1 (au lieu du sol) et le terme en u*^2 ? |
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zdu2 = u(i, k)**2+v(i, k)**2 |
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zdu2 = max(zdu2, 1.0e-20) |
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! Theta_v environnement |
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zthvd=t(i, k)/s(i, k)*(1.+RETV*q(i, k)) |
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! therm Theta_v sans exces (avec hypothese fausse de H&B, sinon, |
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! passer par Theta_e et virpot) |
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zthvu = T2m(i)*(1.+RETV*qT_th(i)) |
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! Le Ri par Theta_v |
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! On a nveau de ref a 2m ??? |
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rhino(i, k) = (z(i, k)-zref)*RG*(zthvd-zthvu) & |
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/(zdu2*0.5*(zthvd+zthvu)) |
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IF (rhino(i, k).GE.ricr) THEN |
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pblh(i) = z(i, k-1) + (z(i, k-1)-z(i, k)) * & |
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(ricr-rhino(i, k-1))/(rhino(i, k-1)-rhino(i, k)) |
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! test04 |
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pblh(i) = pblh(i) + 100. |
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pblT(i) = t(i, k-1) + (t(i, k)-t(i, k-1)) * & |
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(pblh(i)-z(i, k-1))/(z(i, k)-z(i, k-1)) |
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check(i) = .FALSE. |
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ENDIF |
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ENDIF |
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ENDDO |
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ENDDO |
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! Set pbl height to maximum value where computation exceeds number of |
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! layers allowed |
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DO i = 1, knon |
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if (check(i)) pblh(i) = z(i, isommet) |
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ENDDO |
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! Improve estimate of pbl height for the unstable points. |
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! Find unstable points (sensible heat flux is upward): |
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DO i = 1, knon |
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IF (heatv(i) > 0.) THEN |
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unstbl(i) = .TRUE. |
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check(i) = .TRUE. |
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ELSE |
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unstbl(i) = .FALSE. |
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check(i) = .FALSE. |
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ENDIF |
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ENDDO |
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! For the unstable case, compute velocity scale and the |
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! convective temperature excess: |
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DO i = 1, knon |
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IF (check(i)) THEN |
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phiminv(i) = (1.-binm*pblh(i)/obklen(i))**onet |
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! CALCUL DE wm |
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! Ici on considerera que l'on est dans la couche de surf jusqu'a 100 |
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! On prend svt couche de surface=0.1*h mais on ne connait pas h |
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! Dans la couche de surface |
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wm(i)= ustar(i)*phiminv(i) |
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! forme Mathieu : |
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q_star = kqfs(i)/wm(i) |
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t_star = khfs(i)/wm(i) |
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therm(i) = sqrt( b1*(1.+2.*RETV*qT_th(i))*t_star**2 & |
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+ (RETV*T2m(i))**2*b2*q_star**2 & |
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+ max(0., 2.*RETV*T2m(i)*b212*q_star*t_star)) |
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! Theta et qT du thermique (forme H&B) avec exces |
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! (attention, on ajoute therm(i) qui est virtuelle ...) |
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! pourquoi pas sqrt(b1)*t_star ? |
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qT_th(i) = qT_th(i) + b2sr*q_star |
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! new on differre le calcul de Theta_e |
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rhino(i, 1) = 0. |
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ENDIF |
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ENDDO |
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! Improve pblh estimate for unstable conditions using the |
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! convective temperature excess : |
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DO k = 2, isommet |
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DO i = 1, knon |
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IF (check(i)) THEN |
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zdu2 = u(i, k)**2 + v(i, k)**2 |
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zdu2 = max(zdu2, 1e-20) |
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! Theta_v environnement |
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zthvd=t(i, k)/s(i, k)*(1.+RETV*q(i, k)) |
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! et therm Theta_v (avec hypothese de constance de H&B, |
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zthvu = T2m(i)*(1.+RETV*qT_th(i)) + therm(i) |
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! Le Ri par Theta_v |
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! Niveau de ref 2m |
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rhino(i, k) = (z(i, k)-zref)*RG*(zthvd-zthvu) & |
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/(zdu2*0.5*(zthvd+zthvu)) |
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IF (rhino(i, k).GE.ricr) THEN |
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pblh(i) = z(i, k-1) + (z(i, k-1)-z(i, k)) * & |
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(ricr-rhino(i, k-1))/(rhino(i, k-1)-rhino(i, k)) |
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! test04 |
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pblh(i) = pblh(i) + 100. |
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pblT(i) = t(i, k-1) + (t(i, k)-t(i, k-1)) * & |
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(pblh(i)-z(i, k-1))/(z(i, k)-z(i, k-1)) |
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check(i) = .FALSE. |
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ENDIF |
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ENDIF |
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ENDDO |
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ENDDO |
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! Set pbl height to maximum value where computation exceeds number of |
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! layers allowed |
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DO i = 1, knon |
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if (check(i)) pblh(i) = z(i, isommet) |
| 322 |
|
|
ENDDO |
| 323 |
|
|
|
| 324 |
|
|
! PBL height must be greater than some minimum mechanical mixing depth |
| 325 |
|
|
! Several investigators have proposed minimum mechanical mixing depth |
| 326 |
|
|
! relationships as a function of the local friction velocity, u*. We |
| 327 |
|
|
! make use of a linear relationship of the form h = c u* where c=700. |
| 328 |
|
|
! The scaling arguments that give rise to this relationship most often |
| 329 |
|
|
! represent the coefficient c as some constant over the local coriolis |
| 330 |
|
|
! parameter. Here we make use of the experimental results of Koracin |
| 331 |
|
|
! and Berkowicz (1988) [BLM, Vol 43] for wich they recommend 0.07/f |
| 332 |
|
|
! where f was evaluated at 39.5 N and 52 N. Thus we use a typical mid |
| 333 |
|
|
! latitude value for f so that c = 0.07/f = 700. |
| 334 |
|
|
DO i = 1, knon |
| 335 |
|
|
pblmin = 700. * ustar(i) |
| 336 |
|
|
pblh(i) = MAX(pblh(i), pblmin) |
| 337 |
|
|
! par exemple : |
| 338 |
|
|
pblT(i) = t(i, 2) + (t(i, 3)-t(i, 2)) * & |
| 339 |
|
|
(pblh(i)-z(i, 2))/(z(i, 3)-z(i, 2)) |
| 340 |
|
|
ENDDO |
| 341 |
|
|
|
| 342 |
|
|
! pblh is now available; do preparation for diffusivity calculation: |
| 343 |
|
|
DO i = 1, knon |
| 344 |
|
|
check(i) = .TRUE. |
| 345 |
|
|
Zsat(i) = .FALSE. |
| 346 |
|
|
! omegafl utilise pour prolongement CAPE |
| 347 |
|
|
omegafl(i) = .FALSE. |
| 348 |
|
|
Cape(i) = 0. |
| 349 |
|
|
EauLiq(i) = 0. |
| 350 |
|
|
CTEI(i) = 0. |
| 351 |
|
|
|
| 352 |
|
|
! Do additional preparation for unstable cases only, set temperature |
| 353 |
|
|
! and moisture perturbations depending on stability. |
| 354 |
|
|
! Remarque : les formule sont prises dans leur forme CS |
| 355 |
|
|
IF (unstbl(i)) THEN |
| 356 |
|
|
! Niveau de ref du thermique |
| 357 |
|
|
zxt=(T2m(i)-zref*0.5*RG/RCPD/(1.+RVTMP2*qT_th(i))) & |
| 358 |
|
|
*(1.+RETV*qT_th(i)) |
| 359 |
guez |
3 |
phiminv(i) = (1. - binm*pblh(i)/obklen(i))**onet |
| 360 |
guez |
37 |
wm(i) = ustar(i)*phiminv(i) |
| 361 |
|
|
ENDIF |
| 362 |
|
|
ENDDO |
| 363 |
guez |
3 |
|
| 364 |
guez |
37 |
! Main level loop to compute the diffusivities and |
| 365 |
|
|
! counter-gradient terms: |
| 366 |
guez |
49 |
loop_level: DO k = 2, isommet |
| 367 |
guez |
37 |
! Find levels within boundary layer: |
| 368 |
|
|
DO i = 1, knon |
| 369 |
|
|
zp(i) = z(i, k) |
| 370 |
|
|
IF (zkmin == 0. .AND. zp(i) > pblh(i)) zp(i) = pblh(i) |
| 371 |
|
|
ENDDO |
| 372 |
|
|
|
| 373 |
|
|
! For all layers, compute integral info and CTEI |
| 374 |
|
|
DO i = 1, knon |
| 375 |
guez |
49 |
if (check(i) .or. omegafl(i)) then |
| 376 |
|
|
if (.not. Zsat(i)) then |
| 377 |
guez |
37 |
T2 = T2m(i) * s(i, k) |
| 378 |
|
|
! thermodyn functions |
| 379 |
guez |
103 |
qqsat= r2es * FOEEW(T2, RTT >= T2) / pplay(i, k) |
| 380 |
guez |
37 |
qqsat=MIN(0.5, qqsat) |
| 381 |
|
|
zcor=1./(1.-retv*qqsat) |
| 382 |
|
|
qqsat=qqsat*zcor |
| 383 |
|
|
|
| 384 |
|
|
if (qqsat < qT_th(i)) then |
| 385 |
|
|
! on calcule lcl |
| 386 |
|
|
if (k == 2) then |
| 387 |
|
|
plcl(i) = z(i, k) |
| 388 |
|
|
else |
| 389 |
|
|
plcl(i) = z(i, k-1) + (z(i, k-1)-z(i, k)) & |
| 390 |
|
|
* (qT_th(i)-qsatbef(i)) / (qsatbef(i)-qqsat) |
| 391 |
|
|
endif |
| 392 |
|
|
Zsat(i) = .true. |
| 393 |
|
|
endif |
| 394 |
|
|
endif |
| 395 |
|
|
qsatbef(i) = qqsat |
| 396 |
|
|
! cette ligne a deja ete faite normalement ? |
| 397 |
guez |
3 |
endif |
| 398 |
guez |
37 |
ENDDO |
| 399 |
guez |
49 |
end DO loop_level |
| 400 |
guez |
37 |
|
| 401 |
|
|
END SUBROUTINE HBTM |
| 402 |
|
|
|
| 403 |
|
|
end module HBTM_m |
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