! $Id: wake.F90 2922 2017-06-29 15:45:27Z aclsce $ SUBROUTINE wake(znatsurf, p, ph, pi, dtime, & te0, qe0, omgb, & dtdwn, dqdwn, amdwn, amup, dta, dqa, & sigd_con, & deltatw, deltaqw, sigmaw, wdens, & ! state variables dth, hw, wape, fip, gfl, & dtls, dqls, ktopw, omgbdth, dp_omgb, tu, qu, & dtke, dqke, omg, dp_deltomg, spread, cstar, & d_deltat_gw, & d_deltatw2, d_deltaqw2, d_sigmaw2, d_wdens2) ! tendencies ! ************************************************************** ! * ! WAKE * ! retour a un Pupper fixe * ! * ! written by : GRANDPEIX Jean-Yves 09/03/2000 * ! modified by : ROEHRIG Romain 01/29/2007 * ! ************************************************************** USE ioipsl_getin_p_mod, ONLY : getin_p USE dimphy use mod_phys_lmdz_para USE print_control_mod, ONLY: prt_level IMPLICIT NONE ! ============================================================================ ! But : Decrire le comportement des poches froides apparaissant dans les ! grands systemes convectifs, et fournir l'energie disponible pour ! le declenchement de nouvelles colonnes convectives. ! State variables : ! deltatw : temperature difference between wake and off-wake regions ! deltaqw : specific humidity difference between wake and off-wake regions ! sigmaw : fractional area covered by wakes. ! wdens : number of wakes per unit area ! Variable de sortie : ! wape : WAke Potential Energy ! fip : Front Incident Power (W/m2) - ALP ! gfl : Gust Front Length per unit area (m-1) ! dtls : large scale temperature tendency due to wake ! dqls : large scale humidity tendency due to wake ! hw : hauteur de la poche ! dp_omgb : vertical gradient of large scale omega ! wdens : densite de poches ! omgbdth: flux of Delta_Theta transported by LS omega ! dtKE : differential heating (wake - unpertubed) ! dqKE : differential moistening (wake - unpertubed) ! omg : Delta_omg =vertical velocity diff. wake-undist. (Pa/s) ! dp_deltomg : vertical gradient of omg (s-1) ! spread : spreading term in d_t_wake and d_q_wake ! deltatw : updated temperature difference (T_w-T_u). ! deltaqw : updated humidity difference (q_w-q_u). ! sigmaw : updated wake fractional area. ! d_deltat_gw : delta T tendency due to GW ! Variables d'entree : ! aire : aire de la maille ! te0 : temperature dans l'environnement (K) ! qe0 : humidite dans l'environnement (kg/kg) ! omgb : vitesse verticale moyenne sur la maille (Pa/s) ! dtdwn: source de chaleur due aux descentes (K/s) ! dqdwn: source d'humidite due aux descentes (kg/kg/s) ! dta : source de chaleur due courants satures et detrain (K/s) ! dqa : source d'humidite due aux courants satures et detra (kg/kg/s) ! amdwn: flux de masse total des descentes, par unite de ! surface de la maille (kg/m2/s) ! amup : flux de masse total des ascendances, par unite de ! surface de la maille (kg/m2/s) ! p : pressions aux milieux des couches (Pa) ! ph : pressions aux interfaces (Pa) ! pi : (p/p_0)**kapa (adim) ! dtime: increment temporel (s) ! Variables internes : ! rhow : masse volumique de la poche froide ! rho : environment density at P levels ! rhoh : environment density at Ph levels ! te : environment temperature | may change within ! qe : environment humidity | sub-time-stepping ! the : environment potential temperature ! thu : potential temperature in undisturbed area ! tu : temperature in undisturbed area ! qu : humidity in undisturbed area ! dp_omgb: vertical gradient og LS omega ! omgbw : wake average vertical omega ! dp_omgbw: vertical gradient of omgbw ! omgbdq : flux of Delta_q transported by LS omega ! dth : potential temperature diff. wake-undist. ! th1 : first pot. temp. for vertical advection (=thu) ! th2 : second pot. temp. for vertical advection (=thw) ! q1 : first humidity for vertical advection ! q2 : second humidity for vertical advection ! d_deltatw : terme de redistribution pour deltatw ! d_deltaqw : terme de redistribution pour deltaqw ! deltatw0 : deltatw initial ! deltaqw0 : deltaqw initial ! hw0 : hw initial ! sigmaw0: sigmaw initial ! amflux : horizontal mass flux through wake boundary ! wdens_ref: initial number of wakes per unit area (3D) or per ! unit length (2D), at the beginning of each time step ! Tgw : 1 sur la période de onde de gravité ! Cgw : vitesse de propagation de onde de gravité ! LL : distance entre 2 poches ! ------------------------------------------------------------------------- ! Déclaration de variables ! ------------------------------------------------------------------------- include "YOMCST.h" include "cvthermo.h" ! Arguments en entree ! -------------------- INTEGER, DIMENSION (klon), INTENT(IN) :: znatsurf REAL, DIMENSION (klon, klev), INTENT(IN) :: p, pi REAL, DIMENSION (klon, klev+1), INTENT(IN) :: ph REAL, DIMENSION (klon, klev), INTENT(IN) :: omgb REAL, INTENT(IN) :: dtime REAL, DIMENSION (klon, klev), INTENT(IN) :: te0, qe0 REAL, DIMENSION (klon, klev), INTENT(IN) :: dtdwn, dqdwn REAL, DIMENSION (klon, klev), INTENT(IN) :: amdwn, amup REAL, DIMENSION (klon, klev), INTENT(IN) :: dta, dqa REAL, DIMENSION (klon), INTENT(IN) :: sigd_con ! ! Input/Output ! State variables REAL, DIMENSION (klon, klev), INTENT(INOUT) :: deltatw, deltaqw REAL, DIMENSION (klon), INTENT(INOUT) :: sigmaw REAL, DIMENSION (klon), INTENT(INOUT) :: wdens ! Sorties ! -------- REAL, DIMENSION (klon, klev), INTENT(OUT) :: dth REAL, DIMENSION (klon, klev), INTENT(OUT) :: tu, qu REAL, DIMENSION (klon, klev), INTENT(OUT) :: dtls, dqls REAL, DIMENSION (klon, klev), INTENT(OUT) :: dtke, dqke REAL, DIMENSION (klon, klev), INTENT(OUT) :: spread REAL, DIMENSION (klon, klev), INTENT(OUT) :: omgbdth, omg REAL, DIMENSION (klon, klev), INTENT(OUT) :: dp_omgb, dp_deltomg REAL, DIMENSION (klon, klev), INTENT(OUT) :: d_deltat_gw REAL, DIMENSION (klon), INTENT(OUT) :: hw, wape, fip, gfl, cstar INTEGER, DIMENSION (klon), INTENT(OUT) :: ktopw ! Tendencies of state variables REAL, DIMENSION (klon, klev), INTENT(OUT) :: d_deltatw2, d_deltaqw2 REAL, DIMENSION (klon), INTENT(OUT) :: d_sigmaw2, d_wdens2 ! Variables internes ! ------------------- ! Variables à fixer INTEGER, SAVE :: igout !$OMP THREADPRIVATE(igout) REAL :: alon LOGICAL, SAVE :: first = .TRUE. !$OMP THREADPRIVATE(first) !jyg< !! REAL, SAVE :: stark, wdens_ref, coefgw, alpk REAL, SAVE, DIMENSION(2) :: wdens_ref REAL, SAVE :: stark, coefgw, alpk !>jyg REAL, SAVE :: crep_upper, crep_sol !$OMP THREADPRIVATE(stark, wdens_ref, coefgw, alpk, crep_upper, crep_sol) LOGICAL, SAVE :: flag_wk_check_trgl !$OMP THREADPRIVATE(flag_wk_check_trgl) INTEGER, SAVE :: iflag_wk_check_trgl !$OMP THREADPRIVATE(iflag_wk_check_trgl) REAL :: delta_t_min INTEGER :: nsub REAL :: dtimesub REAL :: sigmad, hwmin, wapecut REAL :: sigmaw_max REAL :: dens_rate REAL :: wdens0 ! IM 080208 LOGICAL, DIMENSION (klon) :: gwake ! Variables de sauvegarde REAL, DIMENSION (klon, klev) :: deltatw0 REAL, DIMENSION (klon, klev) :: deltaqw0 REAL, DIMENSION (klon, klev) :: te, qe REAL, DIMENSION (klon) :: sigmaw0 !! REAL, DIMENSION (klon) :: sigmaw1 ! Variables pour les GW REAL, DIMENSION (klon) :: ll REAL, DIMENSION (klon, klev) :: n2 REAL, DIMENSION (klon, klev) :: cgw REAL, DIMENSION (klon, klev) :: tgw ! Variables liées au calcul de hw REAL, DIMENSION (klon) :: ptop_provis, ptop, ptop_new REAL, DIMENSION (klon) :: sum_dth REAL, DIMENSION (klon) :: dthmin REAL, DIMENSION (klon) :: z, dz, hw0 INTEGER, DIMENSION (klon) :: ktop, kupper ! Variables liées au test de la forme triangulaire du profil de Delta_theta REAL, DIMENSION (klon) :: sum_half_dth REAL, DIMENSION (klon) :: dz_half ! Sub-timestep tendencies and related variables REAL, DIMENSION (klon, klev) :: d_deltatw, d_deltaqw REAL, DIMENSION (klon, klev) :: d_te, d_qe REAL, DIMENSION (klon) :: d_sigmaw, alpha REAL, DIMENSION (klon) :: q0_min, q1_min LOGICAL, DIMENSION (klon) :: wk_adv, ok_qx_qw REAL, SAVE :: epsilon !$OMP THREADPRIVATE(epsilon) DATA epsilon/1.E-15/ ! Autres variables internes INTEGER ::isubstep, k, i REAL :: sigmaw_targ REAL, DIMENSION (klon) :: sum_thu, sum_tu, sum_qu, sum_thvu REAL, DIMENSION (klon) :: sum_dq, sum_rho REAL, DIMENSION (klon) :: sum_dtdwn, sum_dqdwn REAL, DIMENSION (klon) :: av_thu, av_tu, av_qu, av_thvu REAL, DIMENSION (klon) :: av_dth, av_dq, av_rho REAL, DIMENSION (klon) :: av_dtdwn, av_dqdwn REAL, DIMENSION (klon, klev) :: rho, rhow REAL, DIMENSION (klon, klev+1) :: rhoh REAL, DIMENSION (klon, klev) :: rhow_moyen REAL, DIMENSION (klon, klev) :: zh REAL, DIMENSION (klon, klev+1) :: zhh REAL, DIMENSION (klon, klev) :: epaisseur1, epaisseur2 REAL, DIMENSION (klon, klev) :: the, thu REAL, DIMENSION (klon, klev) :: omgbw REAL, DIMENSION (klon) :: pupper REAL, DIMENSION (klon) :: omgtop REAL, DIMENSION (klon, klev) :: dp_omgbw REAL, DIMENSION (klon) :: ztop, dztop REAL, DIMENSION (klon, klev) :: alpha_up REAL, DIMENSION (klon) :: rre1, rre2 REAL :: rrd1, rrd2 REAL, DIMENSION (klon, klev) :: th1, th2, q1, q2 REAL, DIMENSION (klon, klev) :: d_th1, d_th2, d_dth REAL, DIMENSION (klon, klev) :: d_q1, d_q2, d_dq REAL, DIMENSION (klon, klev) :: omgbdq REAL, DIMENSION (klon) :: ff, gg REAL, DIMENSION (klon) :: wape2, cstar2, heff REAL, DIMENSION (klon, klev) :: crep REAL, DIMENSION (klon, klev) :: ppi ! cc nrlmd REAL, DIMENSION (klon) :: death_rate !! REAL, DIMENSION (klon) :: nat_rate REAL, DIMENSION (klon, klev) :: entr REAL, DIMENSION (klon, klev) :: detr REAL, DIMENSION(klon) :: sigmaw_in ! pour les prints ! ------------------------------------------------------------------------- ! Initialisations ! ------------------------------------------------------------------------- ! print*, 'wake initialisations' ! Essais d'initialisation avec sigmaw = 0.02 et hw = 10. ! ------------------------------------------------------------------------- DATA wapecut, sigmad, hwmin/5., .02, 10./ ! cc nrlmd DATA sigmaw_max/0.4/ DATA dens_rate/0.1/ ! cc ! Longueur de maille (en m) ! ------------------------------------------------------------------------- ! ALON = 3.e5 alon = 1.E6 ! Configuration de coefgw,stark,wdens (22/02/06 by YU Jingmei) ! coefgw : Coefficient pour les ondes de gravité ! stark : Coefficient k dans Cstar=k*sqrt(2*WAPE) ! wdens : Densité de poche froide par maille ! ------------------------------------------------------------------------- ! cc nrlmd coefgw=10 ! coefgw=1 ! wdens0 = 1.0/(alon**2) ! cc nrlmd wdens = 1.0/(alon**2) ! cc nrlmd stark = 0.50 ! CRtest ! cc nrlmd alpk=0.1 ! alpk = 1.0 ! alpk = 0.5 ! alpk = 0.05 if (first) then igout = klon/2+1/klon crep_upper = 0.9 crep_sol = 1.0 ! cc nrlmd Lecture du fichier wake_param.data stark=0.33 CALL getin_p('stark',stark) alpk=0.25 CALL getin_p('alpk',alpk) !jyg< !! wdens_ref=8.E-12 !! CALL getin_p('wdens_ref',wdens_ref) wdens_ref(1)=8.E-12 wdens_ref(2)=8.E-12 CALL getin_p('wdens_ref_o',wdens_ref(1)) !wake number per unit area ; ocean CALL getin_p('wdens_ref_l',wdens_ref(2)) !wake number per unit area ; land !>jyg coefgw=4. CALL getin_p('coefgw',coefgw) WRITE(*,*) 'stark=', stark WRITE(*,*) 'alpk=', alpk !jyg< !! WRITE(*,*) 'wdens_ref=', wdens_ref WRITE(*,*) 'wdens_ref_o=', wdens_ref(1) WRITE(*,*) 'wdens_ref_l=', wdens_ref(2) !>jyg WRITE(*,*) 'coefgw=', coefgw flag_wk_check_trgl=.false. CALL getin_p('flag_wk_check_trgl ', flag_wk_check_trgl) WRITE(*,*) 'flag_wk_check_trgl=', flag_wk_check_trgl WRITE(*,*) 'flag_wk_check_trgl OBSOLETE. Utilisr iflag_wk_check_trgl plutot' iflag_wk_check_trgl=0 ; IF (flag_wk_check_trgl) iflag_wk_check_trgl=1 CALL getin_p('iflag_wk_check_trgl ', iflag_wk_check_trgl) WRITE(*,*) 'iflag_wk_check_trgl=', iflag_wk_check_trgl first=.false. endif ! Initialisation de toutes des densites a wdens_ref. ! Les densites peuvent evoluer si les poches debordent ! (voir au tout debut de la boucle sur les substeps) !jyg< !! wdens(:) = wdens_ref DO i = 1,klon wdens(i) = wdens_ref(znatsurf(i)+1) ENDDO !>jyg ! print*,'stark',stark ! print*,'alpk',alpk ! print*,'wdens',wdens ! print*,'coefgw',coefgw ! cc ! Minimum value for |T_wake - T_undist|. Used for wake top definition ! ------------------------------------------------------------------------- delta_t_min = 0.2 ! 1. - Save initial values, initialize tendencies, initialize output fields ! ------------------------------------------------------------------------ !jyg< !! DO k = 1, klev !! DO i = 1, klon !! ppi(i, k) = pi(i, k) !! deltatw0(i, k) = deltatw(i, k) !! deltaqw0(i, k) = deltaqw(i, k) !! te(i, k) = te0(i, k) !! qe(i, k) = qe0(i, k) !! dtls(i, k) = 0. !! dqls(i, k) = 0. !! d_deltat_gw(i, k) = 0. !! d_te(i, k) = 0. !! d_qe(i, k) = 0. !! d_deltatw(i, k) = 0. !! d_deltaqw(i, k) = 0. !! ! IM 060508 beg !! d_deltatw2(i, k) = 0. !! d_deltaqw2(i, k) = 0. !! ! IM 060508 end !! END DO !! END DO ppi(:,:) = pi(:,:) deltatw0(:,:) = deltatw(:,:) deltaqw0(:,:) = deltaqw(:,:) te(:,:) = te0(:,:) qe(:,:) = qe0(:,:) dtls(:,:) = 0. dqls(:,:) = 0. d_deltat_gw(:,:) = 0. d_te(:,:) = 0. d_qe(:,:) = 0. d_deltatw(:,:) = 0. d_deltaqw(:,:) = 0. d_deltatw2(:,:) = 0. d_deltaqw2(:,:) = 0. !! DO i = 1, klon !! sigmaw_in(i) = sigmaw(i) !! END DO sigmaw_in(:) = sigmaw(:) !>jyg ! sigmaw1=sigmaw ! IF (sigd_con.GT.sigmaw1) THEN ! print*, 'sigmaw,sigd_con', sigmaw, sigd_con ! ENDIF DO i = 1, klon ! c sigmaw(i) = amax1(sigmaw(i),sigd_con(i)) !jyg< !! sigmaw(i) = amax1(sigmaw(i), sigmad) !! sigmaw(i) = amin1(sigmaw(i), 0.99) sigmaw_targ = min(max(sigmaw(i), sigmad),0.99) d_sigmaw2(i) = sigmaw_targ - sigmaw(i) sigmaw(i) = sigmaw_targ !>jyg sigmaw0(i) = sigmaw(i) wape(i) = 0. wape2(i) = 0. d_sigmaw(i) = 0. d_wdens2(i) = 0. ktopw(i) = 0 END DO ! !jyg ! IF (prt_level>=10) THEN PRINT *, 'wake-1, sigmaw(igout) ', sigmaw(igout) PRINT *, 'wake-1, deltatw(igout,k) ', (k,deltatw(igout,k), k=1,klev) PRINT *, 'wake-1, deltaqw(igout,k) ', (k,deltaqw(igout,k), k=1,klev) PRINT *, 'wake-1, dowwdraughts, amdwn(igout,k) ', (k,amdwn(igout,k), k=1,klev) PRINT *, 'wake-1, dowwdraughts, dtdwn(igout,k) ', (k,dtdwn(igout,k), k=1,klev) PRINT *, 'wake-1, dowwdraughts, dqdwn(igout,k) ', (k,dqdwn(igout,k), k=1,klev) PRINT *, 'wake-1, updraughts, amup(igout,k) ', (k,amup(igout,k), k=1,klev) PRINT *, 'wake-1, updraughts, dta(igout,k) ', (k,dta(igout,k), k=1,klev) PRINT *, 'wake-1, updraughts, dqa(igout,k) ', (k,dqa(igout,k), k=1,klev) ENDIF ! 2. - Prognostic part ! -------------------- ! 2.1 - Undisturbed area and Wake integrals ! --------------------------------------------------------- DO i = 1, klon z(i) = 0. ktop(i) = 0 kupper(i) = 0 sum_thu(i) = 0. sum_tu(i) = 0. sum_qu(i) = 0. sum_thvu(i) = 0. sum_dth(i) = 0. sum_dq(i) = 0. sum_rho(i) = 0. sum_dtdwn(i) = 0. sum_dqdwn(i) = 0. av_thu(i) = 0. av_tu(i) = 0. av_qu(i) = 0. av_thvu(i) = 0. av_dth(i) = 0. av_dq(i) = 0. av_rho(i) = 0. av_dtdwn(i) = 0. av_dqdwn(i) = 0. END DO ! Distance between wakes DO i = 1, klon ll(i) = (1-sqrt(sigmaw(i)))/sqrt(wdens(i)) END DO ! Potential temperatures and humidity ! ---------------------------------------------------------- DO k = 1, klev DO i = 1, klon ! write(*,*)'wake 1',i,k,rd,te(i,k) rho(i, k) = p(i, k)/(rd*te(i,k)) ! write(*,*)'wake 2',rho(i,k) IF (k==1) THEN ! write(*,*)'wake 3',i,k,rd,te(i,k) rhoh(i, k) = ph(i, k)/(rd*te(i,k)) ! write(*,*)'wake 4',i,k,rd,te(i,k) zhh(i, k) = 0 ELSE ! write(*,*)'wake 5',rd,(te(i,k)+te(i,k-1)) rhoh(i, k) = ph(i, k)*2./(rd*(te(i,k)+te(i,k-1))) ! write(*,*)'wake 6',(-rhoh(i,k)*RG)+zhh(i,k-1) zhh(i, k) = (ph(i,k)-ph(i,k-1))/(-rhoh(i,k)*rg) + zhh(i, k-1) END IF ! write(*,*)'wake 7',ppi(i,k) the(i, k) = te(i, k)/ppi(i, k) thu(i, k) = (te(i,k)-deltatw(i,k)*sigmaw(i))/ppi(i, k) tu(i, k) = te(i, k) - deltatw(i, k)*sigmaw(i) qu(i, k) = qe(i, k) - deltaqw(i, k)*sigmaw(i) ! write(*,*)'wake 8',(rd*(te(i,k)+deltatw(i,k))) rhow(i, k) = p(i, k)/(rd*(te(i,k)+deltatw(i,k))) dth(i, k) = deltatw(i, k)/ppi(i, k) END DO END DO DO k = 1, klev - 1 DO i = 1, klon IF (k==1) THEN n2(i, k) = 0 ELSE n2(i, k) = amax1(0., -rg**2/the(i,k)*rho(i,k)*(the(i,k+1)-the(i,k-1))/ & (p(i,k+1)-p(i,k-1))) END IF zh(i, k) = (zhh(i,k)+zhh(i,k+1))/2 cgw(i, k) = sqrt(n2(i,k))*zh(i, k) tgw(i, k) = coefgw*cgw(i, k)/ll(i) END DO END DO DO i = 1, klon n2(i, klev) = 0 zh(i, klev) = 0 cgw(i, klev) = 0 tgw(i, klev) = 0 END DO ! Calcul de la masse volumique moyenne de la colonne (bdlmd) ! ----------------------------------------------------------------- DO k = 1, klev DO i = 1, klon epaisseur1(i, k) = 0. epaisseur2(i, k) = 0. END DO END DO DO i = 1, klon epaisseur1(i, 1) = -(ph(i,2)-ph(i,1))/(rho(i,1)*rg) + 1. epaisseur2(i, 1) = -(ph(i,2)-ph(i,1))/(rho(i,1)*rg) + 1. rhow_moyen(i, 1) = rhow(i, 1) END DO DO k = 2, klev DO i = 1, klon epaisseur1(i, k) = -(ph(i,k+1)-ph(i,k))/(rho(i,k)*rg) + 1. epaisseur2(i, k) = epaisseur2(i, k-1) + epaisseur1(i, k) rhow_moyen(i, k) = (rhow_moyen(i,k-1)*epaisseur2(i,k-1)+rhow(i,k)* & epaisseur1(i,k))/epaisseur2(i, k) END DO END DO ! Choose an integration bound well above wake top ! ----------------------------------------------------------------- ! Pupper = 50000. ! melting level ! Pupper = 60000. ! Pupper = 80000. ! essais pour case_e DO i = 1, klon pupper(i) = 0.6*ph(i, 1) pupper(i) = max(pupper(i), 45000.) ! cc Pupper(i) = 60000. END DO ! Determine Wake top pressure (Ptop) from buoyancy integral ! -------------------------------------------------------- ! -1/ Pressure of the level where dth becomes less than delta_t_min. DO i = 1, klon ptop_provis(i) = ph(i, 1) END DO DO k = 2, klev DO i = 1, klon ! IM v3JYG; ptop_provis(i).LT. ph(i,1) IF (dth(i,k)>-delta_t_min .AND. dth(i,k-1)<-delta_t_min .AND. & ptop_provis(i)==ph(i,1)) THEN ptop_provis(i) = ((dth(i,k)+delta_t_min)*p(i,k-1)- & (dth(i,k-1)+delta_t_min)*p(i,k))/(dth(i,k)-dth(i,k-1)) END IF END DO END DO ! -2/ dth integral DO i = 1, klon sum_dth(i) = 0. dthmin(i) = -delta_t_min z(i) = 0. END DO DO k = 1, klev DO i = 1, klon dz(i) = -(amax1(ph(i,k+1),ptop_provis(i))-ph(i,k))/(rho(i,k)*rg) IF (dz(i)>0) THEN z(i) = z(i) + dz(i) sum_dth(i) = sum_dth(i) + dth(i, k)*dz(i) dthmin(i) = amin1(dthmin(i), dth(i,k)) END IF END DO END DO ! -3/ height of triangle with area= sum_dth and base = dthmin DO i = 1, klon hw0(i) = 2.*sum_dth(i)/amin1(dthmin(i), -0.5) hw0(i) = amax1(hwmin, hw0(i)) END DO ! -4/ now, get Ptop DO i = 1, klon z(i) = 0. ptop(i) = ph(i, 1) END DO DO k = 1, klev DO i = 1, klon dz(i) = amin1(-(ph(i,k+1)-ph(i,k))/(rho(i,k)*rg), hw0(i)-z(i)) IF (dz(i)>0) THEN z(i) = z(i) + dz(i) ptop(i) = ph(i, k) - rho(i, k)*rg*dz(i) END IF END DO END DO IF (prt_level>=10) THEN PRINT *, 'wake-2, ptop_provis(igout), ptop(igout) ', ptop_provis(igout), ptop(igout) ENDIF ! -5/ Determination de ktop et kupper DO k = klev, 1, -1 DO i = 1, klon IF (ph(i,k+1)-delta_t_min .AND. dth(i,k-1)<-delta_t_min) THEN ptop_new(i) = ((dth(i,k)+delta_t_min)*p(i,k-1)-(dth(i, & k-1)+delta_t_min)*p(i,k))/(dth(i,k)-dth(i,k-1)) END IF END DO END DO DO i = 1, klon ptop(i) = ptop_new(i) END DO DO k = klev, 1, -1 DO i = 1, klon IF (ph(i,k+1)=10) THEN PRINT *, 'wake-3, ktop(igout), kupper(igout) ', ktop(igout), kupper(igout) ENDIF ! -5/ Set deltatw & deltaqw to 0 above kupper DO k = 1, klev DO i = 1, klon IF (k>=kupper(i)) THEN deltatw(i, k) = 0. deltaqw(i, k) = 0. d_deltatw2(i,k) = -deltatw0(i,k) d_deltaqw2(i,k) = -deltaqw0(i,k) END IF END DO END DO ! Vertical gradient of LS omega DO k = 1, klev DO i = 1, klon IF (k<=kupper(i)) THEN dp_omgb(i, k) = (omgb(i,k+1)-omgb(i,k))/(ph(i,k+1)-ph(i,k)) END IF END DO END DO ! Integrals (and wake top level number) ! -------------------------------------- ! Initialize sum_thvu to 1st level virt. pot. temp. DO i = 1, klon z(i) = 1. dz(i) = 1. sum_thvu(i) = thu(i, 1)*(1.+epsim1*qu(i,1))*dz(i) sum_dth(i) = 0. END DO DO k = 1, klev DO i = 1, klon dz(i) = -(amax1(ph(i,k+1),ptop(i))-ph(i,k))/(rho(i,k)*rg) IF (dz(i)>0) THEN z(i) = z(i) + dz(i) sum_thu(i) = sum_thu(i) + thu(i, k)*dz(i) sum_tu(i) = sum_tu(i) + tu(i, k)*dz(i) sum_qu(i) = sum_qu(i) + qu(i, k)*dz(i) sum_thvu(i) = sum_thvu(i) + thu(i, k)*(1.+epsim1*qu(i,k))*dz(i) sum_dth(i) = sum_dth(i) + dth(i, k)*dz(i) sum_dq(i) = sum_dq(i) + deltaqw(i, k)*dz(i) sum_rho(i) = sum_rho(i) + rhow(i, k)*dz(i) sum_dtdwn(i) = sum_dtdwn(i) + dtdwn(i, k)*dz(i) sum_dqdwn(i) = sum_dqdwn(i) + dqdwn(i, k)*dz(i) END IF END DO END DO DO i = 1, klon hw0(i) = z(i) END DO ! 2.1 - WAPE and mean forcing computation ! --------------------------------------- ! --------------------------------------- ! Means DO i = 1, klon av_thu(i) = sum_thu(i)/hw0(i) av_tu(i) = sum_tu(i)/hw0(i) av_qu(i) = sum_qu(i)/hw0(i) av_thvu(i) = sum_thvu(i)/hw0(i) ! av_thve = sum_thve/hw0 av_dth(i) = sum_dth(i)/hw0(i) av_dq(i) = sum_dq(i)/hw0(i) av_rho(i) = sum_rho(i)/hw0(i) av_dtdwn(i) = sum_dtdwn(i)/hw0(i) av_dqdwn(i) = sum_dqdwn(i)/hw0(i) wape(i) = -rg*hw0(i)*(av_dth(i)+ & epsim1*(av_thu(i)*av_dq(i)+av_dth(i)*av_qu(i)+av_dth(i)*av_dq(i)))/av_thvu(i) END DO ! 2.2 Prognostic variable update ! ------------------------------ ! Filter out bad wakes DO k = 1, klev DO i = 1, klon IF (wape(i)<0.) THEN deltatw(i, k) = 0. deltaqw(i, k) = 0. dth(i, k) = 0. d_deltatw2(i,k) = -deltatw0(i,k) d_deltaqw2(i,k) = -deltaqw0(i,k) END IF END DO END DO DO i = 1, klon IF (wape(i)<0.) THEN wape(i) = 0. cstar(i) = 0. hw(i) = hwmin !jyg< !! sigmaw(i) = amax1(sigmad, sigd_con(i)) sigmaw_targ = max(sigmad, sigd_con(i)) d_sigmaw2(i) = d_sigmaw2(i) + sigmaw_targ - sigmaw(i) sigmaw(i) = sigmaw_targ !>jyg fip(i) = 0. gwake(i) = .FALSE. ELSE cstar(i) = stark*sqrt(2.*wape(i)) gwake(i) = .TRUE. END IF END DO ! Check qx and qw positivity ! -------------------------- DO i = 1, klon q0_min(i) = min((qe(i,1)-sigmaw(i)*deltaqw(i,1)), & (qe(i,1)+(1.-sigmaw(i))*deltaqw(i,1))) END DO DO k = 2, klev DO i = 1, klon q1_min(i) = min((qe(i,k)-sigmaw(i)*deltaqw(i,k)), & (qe(i,k)+(1.-sigmaw(i))*deltaqw(i,k))) IF (q1_min(i)<=q0_min(i)) THEN q0_min(i) = q1_min(i) END IF END DO END DO DO i = 1, klon ok_qx_qw(i) = q0_min(i) >= 0. alpha(i) = 1. END DO IF (prt_level>=10) THEN PRINT *, 'wake-4, sigmaw(igout), cstar(igout), wape(igout), ktop(igout) ', & sigmaw(igout), cstar(igout), wape(igout), ktop(igout) ENDIF ! C ----------------------------------------------------------------- ! Sub-time-stepping ! ----------------- nsub = 10 dtimesub = dtime/nsub ! ------------------------------------------------------------ DO isubstep = 1, nsub ! ------------------------------------------------------------ ! wk_adv is the logical flag enabling wake evolution in the time advance ! loop DO i = 1, klon wk_adv(i) = ok_qx_qw(i) .AND. alpha(i) >= 1. END DO IF (prt_level>=10) THEN PRINT *, 'wake-4.1, isubstep,wk_adv(igout),cstar(igout),wape(igout), ptop(igout) ', & isubstep,wk_adv(igout),cstar(igout),wape(igout), ptop(igout) ENDIF ! cc nrlmd Ajout d'un recalcul de wdens dans le cas d'un entrainement ! négatif de ktop à kupper -------- ! cc On calcule pour cela une densité wdens0 pour laquelle on ! aurait un entrainement nul --- DO i = 1, klon ! c print *,' isubstep,wk_adv(i),cstar(i),wape(i) ', ! c $ isubstep,wk_adv(i),cstar(i),wape(i) IF (wk_adv(i) .AND. cstar(i)>0.01) THEN omg(i, kupper(i)+1) = -rg*amdwn(i, kupper(i)+1)/sigmaw(i) + & rg*amup(i, kupper(i)+1)/(1.-sigmaw(i)) wdens0 = (sigmaw(i)/(4.*3.14))* & ((1.-sigmaw(i))*omg(i,kupper(i)+1)/((ph(i,1)-pupper(i))*cstar(i)))**(2) IF (wdens(i)<=wdens0*1.1) THEN wdens(i) = wdens0 END IF ! c print*,'omg(i,kupper(i)+1),wdens0,wdens(i),cstar(i) ! c $ ,ph(i,1)-pupper(i)', ! c $ omg(i,kupper(i)+1),wdens0,wdens(i),cstar(i) ! c $ ,ph(i,1)-pupper(i) END IF END DO ! cc nrlmd DO i = 1, klon IF (wk_adv(i)) THEN gfl(i) = 2.*sqrt(3.14*wdens(i)*sigmaw(i)) !jyg< !! sigmaw(i) = amin1(sigmaw(i), sigmaw_max) sigmaw_targ = min(sigmaw(i), sigmaw_max) d_sigmaw2(i) = d_sigmaw2(i) + sigmaw_targ - sigmaw(i) sigmaw(i) = sigmaw_targ !>jyg END IF END DO DO i = 1, klon IF (wk_adv(i)) THEN ! cc nrlmd Introduction du taux de mortalité des poches et ! test sur sigmaw_max=0.4 ! cc d_sigmaw(i) = gfl(i)*Cstar(i)*dtimesub IF (sigmaw(i)>=sigmaw_max) THEN death_rate(i) = gfl(i)*cstar(i)/sigmaw(i) ELSE death_rate(i) = 0. END IF d_sigmaw(i) = gfl(i)*cstar(i)*dtimesub - death_rate(i)*sigmaw(i)* & dtimesub ! $ - nat_rate(i)*sigmaw(i)*dtimesub ! c print*, 'd_sigmaw(i),sigmaw(i),gfl(i),Cstar(i),wape(i), ! c $ death_rate(i),ktop(i),kupper(i)', ! c $ d_sigmaw(i),sigmaw(i),gfl(i),Cstar(i),wape(i), ! c $ death_rate(i),ktop(i),kupper(i) ! sigmaw(i) =sigmaw(i) + gfl(i)*Cstar(i)*dtimesub ! sigmaw(i) =min(sigmaw(i),0.99) !!!!!!!! ! wdens = wdens0/(10.*sigmaw) ! sigmaw =max(sigmaw,sigd_con) ! sigmaw =max(sigmaw,sigmad) END IF END DO ! calcul de la difference de vitesse verticale poche - zone non perturbee ! IM 060208 differences par rapport au code initial; init. a 0 dp_deltomg ! IM 060208 et omg sur les niveaux de 1 a klev+1, alors que avant l'on definit ! IM 060208 au niveau k=1..? !JYG 161013 Correction : maintenant omg est dimensionne a klev. DO k = 1, klev DO i = 1, klon IF (wk_adv(i)) THEN !!! nrlmd dp_deltomg(i, k) = 0. END IF END DO END DO DO k = 1, klev DO i = 1, klon IF (wk_adv(i)) THEN !!! nrlmd omg(i, k) = 0. END IF END DO END DO DO i = 1, klon IF (wk_adv(i)) THEN z(i) = 0. omg(i, 1) = 0. dp_deltomg(i, 1) = -(gfl(i)*cstar(i))/(sigmaw(i)*(1-sigmaw(i))) END IF END DO DO k = 2, klev DO i = 1, klon IF (wk_adv(i) .AND. k<=ktop(i)) THEN dz(i) = -(ph(i,k)-ph(i,k-1))/(rho(i,k-1)*rg) z(i) = z(i) + dz(i) dp_deltomg(i, k) = dp_deltomg(i, 1) omg(i, k) = dp_deltomg(i, 1)*z(i) END IF END DO END DO DO i = 1, klon IF (wk_adv(i)) THEN dztop(i) = -(ptop(i)-ph(i,ktop(i)))/(rho(i,ktop(i))*rg) ztop(i) = z(i) + dztop(i) omgtop(i) = dp_deltomg(i, 1)*ztop(i) END IF END DO IF (prt_level>=10) THEN PRINT *, 'wake-4.2, omg(igout,k) ', (k,omg(igout,k), k=1,klev) PRINT *, 'wake-4.2, omgtop(igout), ptop(igout), ktop(igout) ', & omgtop(igout), ptop(igout), ktop(igout) ENDIF ! ----------------- ! From m/s to Pa/s ! ----------------- DO i = 1, klon IF (wk_adv(i)) THEN omgtop(i) = -rho(i, ktop(i))*rg*omgtop(i) dp_deltomg(i, 1) = omgtop(i)/(ptop(i)-ph(i,1)) END IF END DO DO k = 1, klev DO i = 1, klon IF (wk_adv(i) .AND. k<=ktop(i)) THEN omg(i, k) = -rho(i, k)*rg*omg(i, k) dp_deltomg(i, k) = dp_deltomg(i, 1) END IF END DO END DO ! raccordement lineaire de omg de ptop a pupper DO i = 1, klon IF (wk_adv(i) .AND. kupper(i)>ktop(i)) THEN omg(i, kupper(i)+1) = -rg*amdwn(i, kupper(i)+1)/sigmaw(i) + & rg*amup(i, kupper(i)+1)/(1.-sigmaw(i)) dp_deltomg(i, kupper(i)) = (omgtop(i)-omg(i,kupper(i)+1))/ & (ptop(i)-pupper(i)) END IF END DO ! c DO i=1,klon ! c print*,'Pente entre 0 et kupper (référence)' ! c $ ,omg(i,kupper(i)+1)/(pupper(i)-ph(i,1)) ! c print*,'Pente entre ktop et kupper' ! c $ ,(omg(i,kupper(i)+1)-omgtop(i))/(pupper(i)-ptop(i)) ! c ENDDO ! c DO k = 1, klev DO i = 1, klon IF (wk_adv(i) .AND. k>ktop(i) .AND. k<=kupper(i)) THEN dp_deltomg(i, k) = dp_deltomg(i, kupper(i)) omg(i, k) = omgtop(i) + (ph(i,k)-ptop(i))*dp_deltomg(i, kupper(i)) END IF END DO END DO !! print *,'omg(igout,k) ', (k,omg(igout,k),k=1,klev) ! cc nrlmd ! c DO i=1,klon ! c print*,'deltaw_ktop,deltaw_conv',omgtop(i),omg(i,kupper(i)+1) ! c END DO ! cc ! -- Compute wake average vertical velocity omgbw DO k = 1, klev DO i = 1, klon IF (wk_adv(i)) THEN omgbw(i, k) = omgb(i, k) + (1.-sigmaw(i))*omg(i, k) END IF END DO END DO ! -- and its vertical gradient dp_omgbw DO k = 1, klev-1 DO i = 1, klon IF (wk_adv(i)) THEN dp_omgbw(i, k) = (omgbw(i,k+1)-omgbw(i,k))/(ph(i,k+1)-ph(i,k)) END IF END DO END DO DO i = 1, klon IF (wk_adv(i)) THEN dp_omgbw(i, klev) = 0. END IF END DO ! -- Upstream coefficients for omgb velocity ! -- (alpha_up(k) is the coefficient of the value at level k) ! -- (1-alpha_up(k) is the coefficient of the value at level k-1) DO k = 1, klev DO i = 1, klon IF (wk_adv(i)) THEN alpha_up(i, k) = 0. IF (omgb(i,k)>0.) alpha_up(i, k) = 1. END IF END DO END DO ! Matrix expressing [The,deltatw] from [Th1,Th2] DO i = 1, klon IF (wk_adv(i)) THEN rre1(i) = 1. - sigmaw(i) rre2(i) = sigmaw(i) END IF END DO rrd1 = -1. rrd2 = 1. ! -- Get [Th1,Th2], dth and [q1,q2] DO k = 1, klev DO i = 1, klon IF (wk_adv(i) .AND. k<=kupper(i)+1) THEN dth(i, k) = deltatw(i, k)/ppi(i, k) th1(i, k) = the(i, k) - sigmaw(i)*dth(i, k) ! undisturbed area th2(i, k) = the(i, k) + (1.-sigmaw(i))*dth(i, k) ! wake q1(i, k) = qe(i, k) - sigmaw(i)*deltaqw(i, k) ! undisturbed area q2(i, k) = qe(i, k) + (1.-sigmaw(i))*deltaqw(i, k) ! wake END IF END DO END DO DO i = 1, klon IF (wk_adv(i)) THEN !!! nrlmd d_th1(i, 1) = 0. d_th2(i, 1) = 0. d_dth(i, 1) = 0. d_q1(i, 1) = 0. d_q2(i, 1) = 0. d_dq(i, 1) = 0. END IF END DO DO k = 2, klev DO i = 1, klon IF (wk_adv(i) .AND. k<=kupper(i)+1) THEN d_th1(i, k) = th1(i, k-1) - th1(i, k) d_th2(i, k) = th2(i, k-1) - th2(i, k) d_dth(i, k) = dth(i, k-1) - dth(i, k) d_q1(i, k) = q1(i, k-1) - q1(i, k) d_q2(i, k) = q2(i, k-1) - q2(i, k) d_dq(i, k) = deltaqw(i, k-1) - deltaqw(i, k) END IF END DO END DO DO i = 1, klon IF (wk_adv(i)) THEN omgbdth(i, 1) = 0. omgbdq(i, 1) = 0. END IF END DO DO k = 2, klev DO i = 1, klon IF (wk_adv(i) .AND. k<=kupper(i)+1) THEN ! loop on interfaces omgbdth(i, k) = omgb(i, k)*(dth(i,k-1)-dth(i,k)) omgbdq(i, k) = omgb(i, k)*(deltaqw(i,k-1)-deltaqw(i,k)) END IF END DO END DO IF (prt_level>=10) THEN PRINT *, 'wake-4.3, th1(igout,k) ', (k,th1(igout,k), k=1,klev) PRINT *, 'wake-4.3, th2(igout,k) ', (k,th2(igout,k), k=1,klev) PRINT *, 'wake-4.3, dth(igout,k) ', (k,dth(igout,k), k=1,klev) PRINT *, 'wake-4.3, omgbdth(igout,k) ', (k,omgbdth(igout,k), k=1,klev) ENDIF ! ----------------------------------------------------------------- DO k = 1, klev-1 DO i = 1, klon IF (wk_adv(i) .AND. k<=kupper(i)-1) THEN ! ----------------------------------------------------------------- ! Compute redistribution (advective) term d_deltatw(i, k) = dtimesub/(ph(i,k)-ph(i,k+1))* & (rrd1*omg(i,k)*sigmaw(i)*d_th1(i,k) - & rrd2*omg(i,k+1)*(1.-sigmaw(i))*d_th2(i,k+1)- & (1.-alpha_up(i,k))*omgbdth(i,k)- & alpha_up(i,k+1)*omgbdth(i,k+1))*ppi(i, k) ! print*,'d_deltatw=', k, d_deltatw(i,k) d_deltaqw(i, k) = dtimesub/(ph(i,k)-ph(i,k+1))* & (rrd1*omg(i,k)*sigmaw(i)*d_q1(i,k)- & rrd2*omg(i,k+1)*(1.-sigmaw(i))*d_q2(i,k+1)- & (1.-alpha_up(i,k))*omgbdq(i,k)- & alpha_up(i,k+1)*omgbdq(i,k+1)) ! print*,'d_deltaqw=', k, d_deltaqw(i,k) ! and increment large scale tendencies ! C ! ----------------------------------------------------------------- d_te(i, k) = dtimesub*((rre1(i)*omg(i,k)*sigmaw(i)*d_th1(i,k)- & rre2(i)*omg(i,k+1)*(1.-sigmaw(i))*d_th2(i,k+1))/ & (ph(i,k)-ph(i,k+1)) & -sigmaw(i)*(1.-sigmaw(i))*dth(i,k)*(omg(i,k)-omg(i,k+1))/ & (ph(i,k)-ph(i,k+1)) )*ppi(i, k) d_qe(i, k) = dtimesub*((rre1(i)*omg(i,k)*sigmaw(i)*d_q1(i,k)- & rre2(i)*omg(i,k+1)*(1.-sigmaw(i))*d_q2(i,k+1))/ & (ph(i,k)-ph(i,k+1)) & -sigmaw(i)*(1.-sigmaw(i))*deltaqw(i,k)*(omg(i,k)-omg(i,k+1))/ & (ph(i,k)-ph(i,k+1)) ) ELSE IF (wk_adv(i) .AND. k==kupper(i)) THEN d_te(i, k) = dtimesub*(rre1(i)*omg(i,k)*sigmaw(i)*d_th1(i,k)/(ph(i,k)-ph(i,k+1)))*ppi(i, k) d_qe(i, k) = dtimesub*(rre1(i)*omg(i,k)*sigmaw(i)*d_q1(i,k)/(ph(i,k)-ph(i,k+1))) END IF ! cc END DO END DO ! ------------------------------------------------------------------ IF (prt_level>=10) THEN PRINT *, 'wake-4.3, d_deltatw(igout,k) ', (k,d_deltatw(igout,k), k=1,klev) PRINT *, 'wake-4.3, d_deltaqw(igout,k) ', (k,d_deltaqw(igout,k), k=1,klev) ENDIF ! Increment state variables DO k = 1, klev DO i = 1, klon ! cc nrlmd IF( wk_adv(i) .AND. k .LE. kupper(i)-1) THEN IF (wk_adv(i) .AND. k<=kupper(i)) THEN ! cc ! Coefficient de répartition crep(i, k) = crep_sol*(ph(i,kupper(i))-ph(i,k))/ & (ph(i,kupper(i))-ph(i,1)) crep(i, k) = crep(i, k) + crep_upper*(ph(i,1)-ph(i,k))/ & (p(i,1)-ph(i,kupper(i))) ! Reintroduce compensating subsidence term. ! dtKE(k)=(dtdwn(k)*Crep(k))/sigmaw ! dtKE(k)=dtKE(k)-(dtdwn(k)*(1-Crep(k))+dta(k)) ! . /(1-sigmaw) ! dqKE(k)=(dqdwn(k)*Crep(k))/sigmaw ! dqKE(k)=dqKE(k)-(dqdwn(k)*(1-Crep(k))+dqa(k)) ! . /(1-sigmaw) ! dtKE(k)=(dtdwn(k)*Crep(k)+(1-Crep(k))*dta(k))/sigmaw ! dtKE(k)=dtKE(k)-(dtdwn(k)*(1-Crep(k))+dta(k)*Crep(k)) ! . /(1-sigmaw) ! dqKE(k)=(dqdwn(k)*Crep(k)+(1-Crep(k))*dqa(k))/sigmaw ! dqKE(k)=dqKE(k)-(dqdwn(k)*(1-Crep(k))+dqa(k)*Crep(k)) ! . /(1-sigmaw) dtke(i, k) = (dtdwn(i,k)/sigmaw(i)-dta(i,k)/(1.-sigmaw(i))) dqke(i, k) = (dqdwn(i,k)/sigmaw(i)-dqa(i,k)/(1.-sigmaw(i))) ! print*,'dtKE= ',dtKE(i,k),' dqKE= ',dqKE(i,k) ! ! cc nrlmd Prise en compte du taux de mortalité ! cc Définitions de entr, detr detr(i, k) = 0. entr(i, k) = detr(i, k) + gfl(i)*cstar(i) + & sigmaw(i)*(1.-sigmaw(i))*dp_deltomg(i, k) spread(i, k) = (entr(i,k)-detr(i,k))/sigmaw(i) ! cc spread(i,k) = ! (1.-sigmaw(i))*dp_deltomg(i,k)+gfl(i)*Cstar(i)/ ! cc $ sigmaw(i) ! ajout d'un effet onde de gravité -Tgw(k)*deltatw(k) 03/02/06 YU ! Jingmei ! write(lunout,*)'wake.F ',i,k, dtimesub,d_deltat_gw(i,k), ! & Tgw(i,k),deltatw(i,k) d_deltat_gw(i, k) = d_deltat_gw(i, k) - tgw(i, k)*deltatw(i, k)* & dtimesub ! write(lunout,*)'wake.F ',i,k, dtimesub,d_deltatw(i,k) ff(i) = d_deltatw(i, k)/dtimesub ! Sans GW ! deltatw(k)=deltatw(k)+dtimesub*(ff+dtKE(k)-spread(k)*deltatw(k)) ! GW formule 1 ! deltatw(k) = deltatw(k)+dtimesub* ! $ (ff+dtKE(k) - spread(k)*deltatw(k)-Tgw(k)*deltatw(k)) ! GW formule 2 IF (dtimesub*tgw(i,k)<1.E-10) THEN d_deltatw(i, k) = dtimesub*(ff(i)+dtke(i,k) - & entr(i,k)*deltatw(i,k)/sigmaw(i) - & (death_rate(i)*sigmaw(i)+detr(i,k))*deltatw(i,k)/(1.-sigmaw(i)) - & ! cc tgw(i,k)*deltatw(i,k) ) ELSE d_deltatw(i, k) = 1/tgw(i, k)*(1-exp(-dtimesub*tgw(i,k)))* & (ff(i)+dtke(i,k) - & entr(i,k)*deltatw(i,k)/sigmaw(i) - & (death_rate(i)*sigmaw(i)+detr(i,k))*deltatw(i,k)/(1.-sigmaw(i)) - & tgw(i,k)*deltatw(i,k) ) END IF dth(i, k) = deltatw(i, k)/ppi(i, k) gg(i) = d_deltaqw(i, k)/dtimesub d_deltaqw(i, k) = dtimesub*(gg(i)+dqke(i,k) - & entr(i,k)*deltaqw(i,k)/sigmaw(i) - & (death_rate(i)*sigmaw(i)+detr(i,k))*deltaqw(i,k)/(1.-sigmaw(i))) ! cc ! cc nrlmd ! cc d_deltatw2(i,k)=d_deltatw2(i,k)+d_deltatw(i,k) ! cc d_deltaqw2(i,k)=d_deltaqw2(i,k)+d_deltaqw(i,k) ! cc END IF END DO END DO ! Scale tendencies so that water vapour remains positive in w and x. CALL wake_vec_modulation(klon, klev, wk_adv, epsilon, qe, d_qe, deltaqw, & d_deltaqw, sigmaw, d_sigmaw, alpha) ! cc nrlmd ! c print*,'alpha' ! c do i=1,klon ! c print*,alpha(i) ! c end do ! cc DO k = 1, klev DO i = 1, klon IF (wk_adv(i) .AND. k<=kupper(i)) THEN d_te(i, k) = alpha(i)*d_te(i, k) d_qe(i, k) = alpha(i)*d_qe(i, k) d_deltatw(i, k) = alpha(i)*d_deltatw(i, k) d_deltaqw(i, k) = alpha(i)*d_deltaqw(i, k) d_deltat_gw(i, k) = alpha(i)*d_deltat_gw(i, k) END IF END DO END DO DO i = 1, klon IF (wk_adv(i)) THEN d_sigmaw(i) = alpha(i)*d_sigmaw(i) END IF END DO ! Update large scale variables and wake variables ! IM 060208 manque DO i + remplace DO k=1,kupper(i) ! IM 060208 DO k = 1,kupper(i) DO k = 1, klev DO i = 1, klon IF (wk_adv(i) .AND. k<=kupper(i)) THEN dtls(i, k) = dtls(i, k) + d_te(i, k) dqls(i, k) = dqls(i, k) + d_qe(i, k) ! cc nrlmd d_deltatw2(i, k) = d_deltatw2(i, k) + d_deltatw(i, k) d_deltaqw2(i, k) = d_deltaqw2(i, k) + d_deltaqw(i, k) ! cc END IF END DO END DO DO k = 1, klev DO i = 1, klon IF (wk_adv(i) .AND. k<=kupper(i)) THEN te(i, k) = te0(i, k) + dtls(i, k) qe(i, k) = qe0(i, k) + dqls(i, k) the(i, k) = te(i, k)/ppi(i, k) deltatw(i, k) = deltatw(i, k) + d_deltatw(i, k) deltaqw(i, k) = deltaqw(i, k) + d_deltaqw(i, k) dth(i, k) = deltatw(i, k)/ppi(i, k) ! c print*,'k,qx,qw',k,qe(i,k)-sigmaw(i)*deltaqw(i,k) ! c $ ,qe(i,k)+(1-sigmaw(i))*deltaqw(i,k) END IF END DO END DO DO i = 1, klon IF (wk_adv(i)) THEN sigmaw(i) = sigmaw(i) + d_sigmaw(i) !jyg< d_sigmaw2(i) = d_sigmaw2(i) + d_sigmaw(i) !>jyg END IF END DO ! Determine Ptop from buoyancy integral ! --------------------------------------- ! - 1/ Pressure of the level where dth changes sign. DO i = 1, klon IF (wk_adv(i)) THEN ptop_provis(i) = ph(i, 1) END IF END DO DO k = 2, klev DO i = 1, klon IF (wk_adv(i) .AND. ptop_provis(i)==ph(i,1) .AND. & dth(i,k)>-delta_t_min .AND. dth(i,k-1)<-delta_t_min) THEN ptop_provis(i) = ((dth(i,k)+delta_t_min)*p(i,k-1) - & (dth(i,k-1)+delta_t_min)*p(i,k))/(dth(i,k)-dth(i,k-1)) END IF END DO END DO ! - 2/ dth integral DO i = 1, klon IF (wk_adv(i)) THEN !!! nrlmd sum_dth(i) = 0. dthmin(i) = -delta_t_min z(i) = 0. END IF END DO DO k = 1, klev DO i = 1, klon IF (wk_adv(i)) THEN dz(i) = -(amax1(ph(i,k+1),ptop_provis(i))-ph(i,k))/(rho(i,k)*rg) IF (dz(i)>0) THEN z(i) = z(i) + dz(i) sum_dth(i) = sum_dth(i) + dth(i, k)*dz(i) dthmin(i) = amin1(dthmin(i), dth(i,k)) END IF END IF END DO END DO ! - 3/ height of triangle with area= sum_dth and base = dthmin DO i = 1, klon IF (wk_adv(i)) THEN hw(i) = 2.*sum_dth(i)/amin1(dthmin(i), -0.5) hw(i) = amax1(hwmin, hw(i)) END IF END DO ! - 4/ now, get Ptop DO i = 1, klon IF (wk_adv(i)) THEN !!! nrlmd ktop(i) = 0 z(i) = 0. END IF END DO DO k = 1, klev DO i = 1, klon IF (wk_adv(i)) THEN dz(i) = amin1(-(ph(i,k+1)-ph(i,k))/(rho(i,k)*rg), hw(i)-z(i)) IF (dz(i)>0) THEN z(i) = z(i) + dz(i) ptop(i) = ph(i, k) - rho(i, k)*rg*dz(i) ktop(i) = k END IF END IF END DO END DO ! 4.5/Correct ktop and ptop DO i = 1, klon IF (wk_adv(i)) THEN ptop_new(i) = ptop(i) END IF END DO DO k = klev, 2, -1 DO i = 1, klon ! IM v3JYG; IF (k .GE. ktop(i) IF (wk_adv(i) .AND. k<=ktop(i) .AND. ptop_new(i)==ptop(i) .AND. & dth(i,k)>-delta_t_min .AND. dth(i,k-1)<-delta_t_min) THEN ptop_new(i) = ((dth(i,k)+delta_t_min)*p(i,k-1) - & (dth(i,k-1)+delta_t_min)*p(i,k))/(dth(i,k)-dth(i,k-1)) END IF END DO END DO DO i = 1, klon IF (wk_adv(i)) THEN ptop(i) = ptop_new(i) END IF END DO DO k = klev, 1, -1 DO i = 1, klon IF (wk_adv(i)) THEN !!! nrlmd IF (ph(i,k+1)=kupper(i)) THEN deltatw(i, k) = 0. deltaqw(i, k) = 0. d_deltatw2(i,k) = -deltatw0(i,k) d_deltaqw2(i,k) = -deltaqw0(i,k) END IF END DO END DO ! -------------Cstar computation--------------------------------- DO i = 1, klon IF (wk_adv(i)) THEN !!! nrlmd sum_thu(i) = 0. sum_tu(i) = 0. sum_qu(i) = 0. sum_thvu(i) = 0. sum_dth(i) = 0. sum_dq(i) = 0. sum_rho(i) = 0. sum_dtdwn(i) = 0. sum_dqdwn(i) = 0. av_thu(i) = 0. av_tu(i) = 0. av_qu(i) = 0. av_thvu(i) = 0. av_dth(i) = 0. av_dq(i) = 0. av_rho(i) = 0. av_dtdwn(i) = 0. av_dqdwn(i) = 0. END IF END DO ! Integrals (and wake top level number) ! -------------------------------------- ! Initialize sum_thvu to 1st level virt. pot. temp. DO i = 1, klon IF (wk_adv(i)) THEN !!! nrlmd z(i) = 1. dz(i) = 1. sum_thvu(i) = thu(i, 1)*(1.+epsim1*qu(i,1))*dz(i) sum_dth(i) = 0. END IF END DO DO k = 1, klev DO i = 1, klon IF (wk_adv(i)) THEN !!! nrlmd dz(i) = -(max(ph(i,k+1),ptop(i))-ph(i,k))/(rho(i,k)*rg) IF (dz(i)>0) THEN z(i) = z(i) + dz(i) sum_thu(i) = sum_thu(i) + thu(i, k)*dz(i) sum_tu(i) = sum_tu(i) + tu(i, k)*dz(i) sum_qu(i) = sum_qu(i) + qu(i, k)*dz(i) sum_thvu(i) = sum_thvu(i) + thu(i, k)*(1.+epsim1*qu(i,k))*dz(i) sum_dth(i) = sum_dth(i) + dth(i, k)*dz(i) sum_dq(i) = sum_dq(i) + deltaqw(i, k)*dz(i) sum_rho(i) = sum_rho(i) + rhow(i, k)*dz(i) sum_dtdwn(i) = sum_dtdwn(i) + dtdwn(i, k)*dz(i) sum_dqdwn(i) = sum_dqdwn(i) + dqdwn(i, k)*dz(i) END IF END IF END DO END DO DO i = 1, klon IF (wk_adv(i)) THEN !!! nrlmd hw0(i) = z(i) END IF END DO ! - WAPE and mean forcing computation ! --------------------------------------- ! --------------------------------------- ! Means DO i = 1, klon IF (wk_adv(i)) THEN !!! nrlmd av_thu(i) = sum_thu(i)/hw0(i) av_tu(i) = sum_tu(i)/hw0(i) av_qu(i) = sum_qu(i)/hw0(i) av_thvu(i) = sum_thvu(i)/hw0(i) av_dth(i) = sum_dth(i)/hw0(i) av_dq(i) = sum_dq(i)/hw0(i) av_rho(i) = sum_rho(i)/hw0(i) av_dtdwn(i) = sum_dtdwn(i)/hw0(i) av_dqdwn(i) = sum_dqdwn(i)/hw0(i) wape(i) = -rg*hw0(i)*(av_dth(i)+epsim1*(av_thu(i)*av_dq(i) + & av_dth(i)*av_qu(i)+av_dth(i)*av_dq(i)))/av_thvu(i) END IF END DO ! Filter out bad wakes DO k = 1, klev DO i = 1, klon IF (wk_adv(i)) THEN !!! nrlmd IF (wape(i)<0.) THEN deltatw(i, k) = 0. deltaqw(i, k) = 0. dth(i, k) = 0. d_deltatw2(i,k) = -deltatw0(i,k) d_deltaqw2(i,k) = -deltaqw0(i,k) END IF END IF END DO END DO DO i = 1, klon IF (wk_adv(i)) THEN !!! nrlmd IF (wape(i)<0.) THEN wape(i) = 0. cstar(i) = 0. hw(i) = hwmin !jyg< !! sigmaw(i) = max(sigmad, sigd_con(i)) sigmaw_targ = max(sigmad, sigd_con(i)) d_sigmaw2(i) = d_sigmaw2(i) + sigmaw_targ - sigmaw(i) sigmaw(i) = sigmaw_targ !>jyg fip(i) = 0. gwake(i) = .FALSE. ELSE cstar(i) = stark*sqrt(2.*wape(i)) gwake(i) = .TRUE. END IF END IF END DO END DO ! end sub-timestep loop IF (prt_level>=10) THEN PRINT *, 'wake-5, sigmaw(igout), cstar(igout), wape(igout), ptop(igout) ', & sigmaw(igout), cstar(igout), wape(igout), ptop(igout) ENDIF ! ---------------------------------------------------------- ! Determine wake final state; recompute wape, cstar, ktop; ! filter out bad wakes. ! ---------------------------------------------------------- ! 2.1 - Undisturbed area and Wake integrals ! --------------------------------------------------------- DO i = 1, klon ! cc nrlmd if (wk_adv(i)) then !!! nrlmd IF (ok_qx_qw(i)) THEN ! cc z(i) = 0. sum_thu(i) = 0. sum_tu(i) = 0. sum_qu(i) = 0. sum_thvu(i) = 0. sum_dth(i) = 0. sum_half_dth(i) = 0. sum_dq(i) = 0. sum_rho(i) = 0. sum_dtdwn(i) = 0. sum_dqdwn(i) = 0. av_thu(i) = 0. av_tu(i) = 0. av_qu(i) = 0. av_thvu(i) = 0. av_dth(i) = 0. av_dq(i) = 0. av_rho(i) = 0. av_dtdwn(i) = 0. av_dqdwn(i) = 0. dthmin(i) = -delta_t_min END IF END DO ! Potential temperatures and humidity ! ---------------------------------------------------------- DO k = 1, klev DO i = 1, klon ! cc nrlmd IF ( wk_adv(i)) THEN IF (ok_qx_qw(i)) THEN ! cc rho(i, k) = p(i, k)/(rd*te(i,k)) IF (k==1) THEN rhoh(i, k) = ph(i, k)/(rd*te(i,k)) zhh(i, k) = 0 ELSE rhoh(i, k) = ph(i, k)*2./(rd*(te(i,k)+te(i,k-1))) zhh(i, k) = (ph(i,k)-ph(i,k-1))/(-rhoh(i,k)*rg) + zhh(i, k-1) END IF the(i, k) = te(i, k)/ppi(i, k) thu(i, k) = (te(i,k)-deltatw(i,k)*sigmaw(i))/ppi(i, k) tu(i, k) = te(i, k) - deltatw(i, k)*sigmaw(i) qu(i, k) = qe(i, k) - deltaqw(i, k)*sigmaw(i) rhow(i, k) = p(i, k)/(rd*(te(i,k)+deltatw(i,k))) dth(i, k) = deltatw(i, k)/ppi(i, k) END IF END DO END DO ! Integrals (and wake top level number) ! ----------------------------------------------------------- ! Initialize sum_thvu to 1st level virt. pot. temp. DO i = 1, klon ! cc nrlmd IF ( wk_adv(i)) THEN IF (ok_qx_qw(i)) THEN ! cc z(i) = 1. dz(i) = 1. dz_half(i) = 1. sum_thvu(i) = thu(i, 1)*(1.+epsim1*qu(i,1))*dz(i) sum_dth(i) = 0. END IF END DO DO k = 1, klev DO i = 1, klon ! cc nrlmd IF ( wk_adv(i)) THEN IF (ok_qx_qw(i)) THEN ! cc dz(i) = -(amax1(ph(i,k+1),ptop(i))-ph(i,k))/(rho(i,k)*rg) dz_half(i) = -(amax1(ph(i,k+1),0.5*(ptop(i)+ph(i,1)))-ph(i,k))/(rho(i,k)*rg) IF (dz(i)>0) THEN z(i) = z(i) + dz(i) sum_thu(i) = sum_thu(i) + thu(i, k)*dz(i) sum_tu(i) = sum_tu(i) + tu(i, k)*dz(i) sum_qu(i) = sum_qu(i) + qu(i, k)*dz(i) sum_thvu(i) = sum_thvu(i) + thu(i, k)*(1.+epsim1*qu(i,k))*dz(i) sum_dth(i) = sum_dth(i) + dth(i, k)*dz(i) sum_dq(i) = sum_dq(i) + deltaqw(i, k)*dz(i) sum_rho(i) = sum_rho(i) + rhow(i, k)*dz(i) sum_dtdwn(i) = sum_dtdwn(i) + dtdwn(i, k)*dz(i) sum_dqdwn(i) = sum_dqdwn(i) + dqdwn(i, k)*dz(i) ! dthmin(i) = min(dthmin(i), dth(i,k)) END IF IF (dz_half(i)>0) THEN sum_half_dth(i) = sum_half_dth(i) + dth(i, k)*dz_half(i) END IF END IF END DO END DO DO i = 1, klon ! cc nrlmd IF ( wk_adv(i)) THEN IF (ok_qx_qw(i)) THEN ! cc hw0(i) = z(i) END IF END DO ! - WAPE and mean forcing computation ! ------------------------------------------------------------- ! Means DO i = 1, klon ! cc nrlmd IF ( wk_adv(i)) THEN IF (ok_qx_qw(i)) THEN ! cc av_thu(i) = sum_thu(i)/hw0(i) av_tu(i) = sum_tu(i)/hw0(i) av_qu(i) = sum_qu(i)/hw0(i) av_thvu(i) = sum_thvu(i)/hw0(i) av_dth(i) = sum_dth(i)/hw0(i) av_dq(i) = sum_dq(i)/hw0(i) av_rho(i) = sum_rho(i)/hw0(i) av_dtdwn(i) = sum_dtdwn(i)/hw0(i) av_dqdwn(i) = sum_dqdwn(i)/hw0(i) wape2(i) = -rg*hw0(i)*(av_dth(i)+epsim1*(av_thu(i)*av_dq(i) + & av_dth(i)*av_qu(i)+av_dth(i)*av_dq(i)))/av_thvu(i) END IF END DO ! Prognostic variable update ! ------------------------------------------------------------ ! Filter out bad wakes IF (iflag_wk_check_trgl>=1) THEN ! Check triangular shape of dth profile DO i = 1, klon IF (ok_qx_qw(i)) THEN !! print *,'wake, hw0(i), dthmin(i) ', hw0(i), dthmin(i) !! print *,'wake, 2.*sum_dth(i)/(hw0(i)*dthmin(i)) ', & !! 2.*sum_dth(i)/(hw0(i)*dthmin(i)) !! print *,'wake, sum_half_dth(i), sum_dth(i) ', & !! sum_half_dth(i), sum_dth(i) IF ((hw0(i) < 1.) .or. (dthmin(i) >= -delta_t_min) ) THEN wape2(i) = -1. !! print *,'wake, rej 1' ELSE IF (iflag_wk_check_trgl==1.AND.abs(2.*sum_dth(i)/(hw0(i)*dthmin(i)) - 1.) > 0.5) THEN wape2(i) = -1. !! print *,'wake, rej 2' ELSE IF (abs(sum_half_dth(i)) < 0.5*abs(sum_dth(i)) ) THEN wape2(i) = -1. !! print *,'wake, rej 3' END IF END IF END DO END IF DO k = 1, klev DO i = 1, klon ! cc nrlmd IF ( wk_adv(i) .AND. wape2(i) .LT. 0.) THEN IF (ok_qx_qw(i) .AND. wape2(i)<0.) THEN ! cc deltatw(i, k) = 0. deltaqw(i, k) = 0. dth(i, k) = 0. d_deltatw2(i,k) = -deltatw0(i,k) d_deltaqw2(i,k) = -deltaqw0(i,k) END IF END DO END DO DO i = 1, klon ! cc nrlmd IF ( wk_adv(i)) THEN IF (ok_qx_qw(i)) THEN ! cc IF (wape2(i)<0.) THEN wape2(i) = 0. cstar2(i) = 0. hw(i) = hwmin !jyg< !! sigmaw(i) = amax1(sigmad, sigd_con(i)) sigmaw_targ = max(sigmad, sigd_con(i)) d_sigmaw2(i) = d_sigmaw2(i) + sigmaw_targ - sigmaw(i) sigmaw(i) = sigmaw_targ !>jyg fip(i) = 0. gwake(i) = .FALSE. ELSE IF (prt_level>=10) PRINT *, 'wape2>0' cstar2(i) = stark*sqrt(2.*wape2(i)) gwake(i) = .TRUE. END IF END IF END DO DO i = 1, klon ! cc nrlmd IF ( wk_adv(i)) THEN IF (ok_qx_qw(i)) THEN ! cc ktopw(i) = ktop(i) END IF END DO DO i = 1, klon ! cc nrlmd IF ( wk_adv(i)) THEN IF (ok_qx_qw(i)) THEN ! cc IF (ktopw(i)>0 .AND. gwake(i)) THEN ! jyg1 Utilisation d'un h_efficace constant ( ~ feeding layer) ! cc heff = 600. ! Utilisation de la hauteur hw ! c heff = 0.7*hw heff(i) = hw(i) fip(i) = 0.5*rho(i, ktopw(i))*cstar2(i)**3*heff(i)*2* & sqrt(sigmaw(i)*wdens(i)*3.14) fip(i) = alpk*fip(i) ! jyg2 ELSE fip(i) = 0. END IF END IF END DO ! Limitation de sigmaw ! cc nrlmd ! DO i=1,klon ! IF (OK_qx_qw(i)) THEN ! IF (sigmaw(i).GE.sigmaw_max) sigmaw(i)=sigmaw_max ! ENDIF ! ENDDO ! cc DO k = 1, klev DO i = 1, klon ! cc nrlmd On maintient désormais constant sigmaw en régime ! permanent ! cc IF ((sigmaw(i).GT.sigmaw_max).or. IF (((wape(i)>=wape2(i)) .AND. (wape2(i)<=1.0)) .OR. (ktopw(i)<=2) .OR. & .NOT. ok_qx_qw(i)) THEN ! cc dtls(i, k) = 0. dqls(i, k) = 0. deltatw(i, k) = 0. deltaqw(i, k) = 0. d_deltatw2(i,k) = -deltatw0(i,k) d_deltaqw2(i,k) = -deltaqw0(i,k) END IF END DO END DO ! cc nrlmd On maintient désormais constant sigmaw en régime permanent DO i = 1, klon IF (((wape(i)>=wape2(i)) .AND. (wape2(i)<=1.0)) .OR. (ktopw(i)<=2) .OR. & .NOT. ok_qx_qw(i)) THEN ktopw(i) = 0 wape(i) = 0. cstar(i) = 0. !!jyg Outside subroutine "Wake" hw and sigmaw are zero when there are no wakes !! hw(i) = hwmin !jyg !! sigmaw(i) = sigmad !jyg hw(i) = 0. !jyg sigmaw(i) = 0. !jyg fip(i) = 0. ELSE wape(i) = wape2(i) cstar(i) = cstar2(i) END IF ! c print*,'wape wape2 ktopw OK_qx_qw =', ! c $ wape(i),wape2(i),ktopw(i),OK_qx_qw(i) END DO IF (prt_level>=10) THEN PRINT *, 'wake-6, wape wape2 ktopw OK_qx_qw =', & wape(igout),wape2(igout),ktopw(igout),OK_qx_qw(igout) ENDIF ! ----------------------------------------------------------------- ! Get back to tendencies per second DO k = 1, klev DO i = 1, klon ! cc nrlmd IF ( wk_adv(i) .AND. k .LE. kupper(i)) THEN !jyg< !! IF (ok_qx_qw(i) .AND. k<=kupper(i)) THEN IF (ok_qx_qw(i)) THEN !>jyg ! cc dtls(i, k) = dtls(i, k)/dtime dqls(i, k) = dqls(i, k)/dtime d_deltatw2(i, k) = d_deltatw2(i, k)/dtime d_deltaqw2(i, k) = d_deltaqw2(i, k)/dtime d_deltat_gw(i, k) = d_deltat_gw(i, k)/dtime ! c print*,'k,dqls,omg,entr,detr',k,dqls(i,k),omg(i,k),entr(i,k) ! c $ ,death_rate(i)*sigmaw(i) END IF END DO END DO !jyg< DO i = 1, klon d_sigmaw2(i) = d_sigmaw2(i)/dtime d_wdens2(i) = d_wdens2(i)/dtime ENDDO !>jyg RETURN END SUBROUTINE wake SUBROUTINE wake_vec_modulation(nlon, nl, wk_adv, epsilon, qe, d_qe, deltaqw, & d_deltaqw, sigmaw, d_sigmaw, alpha) ! ------------------------------------------------------ ! Dtermination du coefficient alpha tel que les tendances ! corriges alpha*d_G, pour toutes les grandeurs G, correspondent ! a une humidite positive dans la zone (x) et dans la zone (w). ! ------------------------------------------------------ IMPLICIT NONE ! Input REAL qe(nlon, nl), d_qe(nlon, nl) REAL deltaqw(nlon, nl), d_deltaqw(nlon, nl) REAL sigmaw(nlon), d_sigmaw(nlon) LOGICAL wk_adv(nlon) INTEGER nl, nlon ! Output REAL alpha(nlon) ! Internal variables REAL zeta(nlon, nl) REAL alpha1(nlon) REAL x, a, b, c, discrim REAL epsilon ! DATA epsilon/1.e-15/ INTEGER i,k DO k = 1, nl DO i = 1, nlon IF (wk_adv(i)) THEN IF ((deltaqw(i,k)+d_deltaqw(i,k))>=0.) THEN zeta(i, k) = 0. ELSE zeta(i, k) = 1. END IF END IF END DO DO i = 1, nlon IF (wk_adv(i)) THEN x = qe(i, k) + (zeta(i,k)-sigmaw(i))*deltaqw(i, k) + d_qe(i, k) + & (zeta(i,k)-sigmaw(i))*d_deltaqw(i, k) - d_sigmaw(i) * & (deltaqw(i,k)+d_deltaqw(i,k)) a = -d_sigmaw(i)*d_deltaqw(i, k) b = d_qe(i, k) + (zeta(i,k)-sigmaw(i))*d_deltaqw(i, k) - & deltaqw(i, k)*d_sigmaw(i) c = qe(i, k) + (zeta(i,k)-sigmaw(i))*deltaqw(i, k) + epsilon discrim = b*b - 4.*a*c ! print*, 'x, a, b, c, discrim', x, a, b, c, discrim IF (a+b>=0.) THEN !! Condition suffisante pour la positivité de ovap alpha1(i) = 1. ELSE IF (x>=0.) THEN alpha1(i) = 1. ELSE IF (a>0.) THEN alpha1(i) = 0.9*min( (2.*c)/(-b+sqrt(discrim)), & (-b+sqrt(discrim))/(2.*a) ) ELSE IF (a==0.) THEN alpha1(i) = 0.9*(-c/b) ELSE ! print*,'a,b,c discrim',a,b,c discrim alpha1(i) = 0.9*max( (2.*c)/(-b+sqrt(discrim)), & (-b+sqrt(discrim))/(2.*a)) END IF END IF END IF alpha(i) = min(alpha(i), alpha1(i)) END IF END DO END DO RETURN END SUBROUTINE wake_vec_modulation