source: trunk/LMDZ.MARS/libf/phymars/nonoro_gwd_ran_mod.F90 @ 3325

MODULE nonoro_gwd_ran_mod

IMPLICIT NONE

REAL,allocatable,save :: du_nonoro_gwd(:,:) ! Zonal wind tendency due to GWD 
REAL,allocatable,save :: dv_nonoro_gwd(:,:) ! Meridional wind tendency due to GWD
REAL,ALLOCATABLE,SAVE :: east_gwstress(:,:) ! Profile of eastward stress
REAL,ALLOCATABLE,SAVE :: west_gwstress(:,:) ! Profile of westward stress

!$OMP THREADPRIVATE(du_nonoro_gwd,dv_nonoro_gwd,east_gwstress,west_gwstress)

CONTAINS

      SUBROUTINE NONORO_GWD_RAN(ngrid,nlayer,DTIME, cpnew, rnew, pp,  &
                  zmax_therm, pt, pu, pv, pdt, pdu, pdv, &
                  zustr,zvstr,d_t, d_u, d_v)

    !--------------------------------------------------------------------------------
    ! Parametrization of the momentum flux deposition due to a discrete
    ! number of gravity waves. 
    ! F. Lott
    ! Version 14, Gaussian distribution of the source
    ! LMDz model online version      
    ! ADAPTED FOR VENUS /  F. LOTT + S. LEBONNOIS
    ! Version adapted on 03/04/2013:
    !      - input flux compensated in the deepest layers
    !                           
    ! ADAPTED FOR MARS     G.GILLI     02/2016
    !        Revision with F.Forget    06/2016  Variable EP-flux according to
    !                                           PBL variation (max velocity thermals)
    ! UPDATED              D.BARDET    01/2020  - reproductibility of the
    !                                           launching altitude calculation 
    !                                           - wave characteristic
    !                                           calculation using MOD
    !                                           - adding east_gwstress and
    !                                           west_gwstress variables 
    ! UPDATED              J.LIU       12/2021  The rho (density) at the specific 
    !                                           locations is introduced. The equation
    !                                           of EP-flux is corrected by adding the
    !                                           term of density at launch (source) 
    !                                           altitude.
    !  
    !---------------------------------------------------------------------------------

      use comcstfi_h, only: g, pi, r
      USE ioipsl_getin_p_mod, ONLY : getin_p
      use vertical_layers_mod, only : presnivs
      use geometry_mod, only: cell_area
      use write_output_mod, only: write_output
#ifdef CPP_XIOS
     use xios_output_mod, only: send_xios_field
#endif      
      
      implicit none
      include "callkeys.h"

      CHARACTER (LEN=20) :: modname='nonoro_gwd_ran'
      CHARACTER (LEN=80) :: abort_message


    ! 0. DECLARATIONS:

    ! 0.1 INPUTS
    INTEGER, intent(in):: ngrid          ! number of atmospheric columns
    INTEGER, intent(in):: nlayer         ! number of atmospheric layers
    REAL, intent(in):: DTIME             ! Time step of the Physics(s)
    REAL, intent(in):: zmax_therm(ngrid) ! Altitude of max velocity thermals (m) 
    REAL,INTENT(IN) :: cpnew(ngrid,nlayer)! Cp of the atmosphere
    REAL,INTENT(IN) :: rnew(ngrid,nlayer) ! R of the atmosphere
    REAL, intent(in):: pp(ngrid,nlayer)  ! Pressure at full levels(Pa)
    REAL, intent(in):: pt(ngrid,nlayer)  ! Temp at full levels(K) 
    REAL, intent(in):: pu(ngrid,nlayer)  ! Zonal wind at full levels(m/s)
    REAL, intent(in):: pv(ngrid,nlayer)  ! Meridional winds at full levels(m/s)
    REAL,INTENT(in) :: pdt(ngrid,nlayer) ! Tendency on temperature (K/s)
    REAL,INTENT(in) :: pdu(ngrid,nlayer) ! Tendency on zonal wind (m/s/s)
    REAL,INTENT(in) :: pdv(ngrid,nlayer) ! Tendency on meridional wind (m/s/s)

    ! 0.2 OUTPUTS
    REAL, intent(out):: zustr(ngrid)       ! Zonal surface stress
    REAL, intent(out):: zvstr(ngrid)       ! Meridional surface stress
    REAL, intent(out):: d_t(ngrid, nlayer) ! Tendency on temperature (K/s) due to gravity waves (not used set to zero)
    REAL, intent(out):: d_u(ngrid, nlayer) ! Tendency on zonal wind (m/s/s) due to gravity waves
    REAL, intent(out):: d_v(ngrid, nlayer) ! Tendency on meridional wind (m/s/s) due to gravity waves

    ! 0.3 INTERNAL ARRAYS
    REAL :: TT(ngrid, nlayer)   ! Temperature at full levels
    REAL :: RHO(ngrid, nlayer)  ! Mass density at full levels 
    REAL :: UU(ngrid, nlayer)   ! Zonal wind at full levels
    REAL :: VV(ngrid, nlayer)   ! Meridional winds at full levels
    REAL :: BVLOW(ngrid)        ! initial N at each grid (not used)

    INTEGER II, JJ, LL

    ! 0.3.0 TIME SCALE OF THE LIFE CYCLE OF THE WAVES PARAMETERIZED
    REAL, parameter:: DELTAT = 24. * 3600.
    
    ! 0.3.1 GRAVITY-WAVES SPECIFICATIONS
    INTEGER, PARAMETER:: NK = 2 ! number of horizontal wavenumbers
    INTEGER, PARAMETER:: NP = 2 ! directions (eastward and westward) phase speed
    INTEGER, PARAMETER:: NO = 2 ! absolute values of phase speed
    INTEGER, PARAMETER:: NA = 5 ! number of realizations to get the phase speed
    INTEGER, PARAMETER:: NW = NK * NP * NO ! Total numbers of gravity waves
    INTEGER JK, JP, JO, JW      ! Loop index for NK,NP,NO, and NW

    REAL, save :: kmax             ! Max horizontal wavenumber (lambda min,lambda=2*pi/kmax),kmax=N/u, u(=30~50) zonal wind velocity at launch altitude
!$OMP THREADPRIVATE(kmax)
    REAL, save :: kmin             ! Min horizontal wavenumber (lambda max = 314 km,lambda=2*pi/kmin)
!$OMP THREADPRIVATE(kmin)
    REAL kstar                     ! Min horizontal wavenumber constrained by horizontal resolution

    REAL :: max_k(ngrid)           ! max_k=max(kstar,kmin)
    REAL, parameter:: cmin = 1.    ! Min horizontal absolute phase velocity (not used)    
    REAL CPHA(ngrid)                      ! absolute PHASE VELOCITY frequency
    REAL ZK(NW, ngrid)             ! Horizontal wavenumber amplitude
    REAL ZP(NW, ngrid)             ! Horizontal wavenumber angle        
    REAL ZO(NW, ngrid)             ! Absolute frequency

    REAL intr_freq_m(nw, ngrid)          ! Waves Intr. freq. at the 1/2 lev below the full level (previous name: ZOM)
    REAL intr_freq_p(nw, ngrid)          ! Waves Intr. freq. at the 1/2 lev above the full level (previous name: ZOP)
    REAL wwm(nw, ngrid)                  ! Wave EP-fluxes at the 1/2 level below the full level
    REAL wwp(nw, ngrid)                  ! Wave EP-fluxes at the 1/2 level above the full level
    REAL u_epflux_p(nw, ngrid)           ! Partial zonal flux (=for each wave) at the 1/2 level above the full level (previous name: RUWP)
    REAL v_epflux_p(nw, ngrid)           ! Partial meridional flux (=for each wave) at the 1/2 level above the full level (previous name: RVWP)
    REAL u_epflux_tot(ngrid, nlayer + 1) ! Total zonal flux (=for all waves (nw)) at the 1/2 level above the full level (3D) (previous name: RUW)  
    REAL v_epflux_tot(ngrid, nlayer + 1) ! Total meridional flux (=for all waves (nw)) at the 1/2 level above the full level (3D) (previous name: RVW) 
    REAL epflux_0(nw, ngrid)             ! Fluxes at launching level (previous name: RUW0)
    REAL, save :: epflux_max             ! Max EP flux value at launching altitude (previous name: RUWMAX, tunable)
!$OMP THREADPRIVATE(epflux_max)
    INTEGER LAUNCH                       ! Launching altitude
    REAL, save :: xlaunch                ! Control the launching altitude by pressure
!$OMP THREADPRIVATE(xlaunch)
    REAL, parameter:: zmaxth_top = 8000. ! Top of convective layer (approx. not used)
    REAL cmax(ngrid,nlayer)             ! Max horizontal absolute phase velocity (at the maginitide of zonal wind u at the launch altitude)

    ! 0.3.2 PARAMETERS OF WAVES DISSIPATIONS
    REAL, save :: sat                 ! saturation parameter(tunable)
!$OMP THREADPRIVATE(sat)
    REAL, save :: rdiss               ! dissipation coefficient (tunable)
!$OMP THREADPRIVATE(rdiss)
    REAL, parameter:: zoisec = 1.e-10 ! security for intrinsic frequency

    ! 0.3.3 Background flow at 1/2 levels and vertical coordinate
    REAL H0bis(ngrid, nlayer)          ! Characteristic Height of the atmosphere (specific locations)
    REAL, save:: H0                    ! Characteristic Height of the atmosphere (constant)
!$OMP THREADPRIVATE(H0)
    REAL, parameter:: pr = 250         ! Reference pressure [Pa]
    REAL, parameter:: tr = 220.        ! Reference temperature [K]
    REAL ZH(ngrid, nlayer + 1)         ! Log-pressure altitude (constant H0)
    REAL ZHbis(ngrid, nlayer + 1)      ! Log-pressure altitude (varying H0bis)
    REAL UH(ngrid, nlayer + 1)         ! zonal wind at 1/2 levels
    REAL VH(ngrid, nlayer + 1)         ! meridional wind at 1/2 levels
    REAL PH(ngrid, nlayer + 1)         ! Pressure at 1/2 levels
    REAL, parameter:: psec = 1.e-20    ! Security to avoid division by 0 pressure(!!IMPORTANT: should be lower than the topmost layer's pressure)
    REAL BV(ngrid, nlayer + 1)         ! Brunt Vaisala freq. (N^2) at 1/2 levels
    REAL, parameter:: bvsec = 1.e-5    ! Security to avoid negative BV  
    REAL HREF(nlayer + 1)              ! Reference pressure for launching altitude


    REAL RAN_NUM_1,RAN_NUM_2,RAN_NUM_3


    LOGICAL,SAVE :: firstcall = .true.
!$OMP THREADPRIVATE(firstcall)

!-----------------------------------------------------------------------------------------------------------------------
!  1. INITIALISATIONS
!-----------------------------------------------------------------------------------------------------------------------
     IF (firstcall) THEN
        write(*,*) "nonoro_gwd_ran: FLott non-oro GW scheme is active!"
        epflux_max = 5.E-4 ! Mars' value !!
        call getin_p("nonoro_gwd_epflux_max", epflux_max)
        write(*,*) "nonoro_gwd_ran: epflux_max=", epflux_max
        sat = 1.5 ! default gravity waves saturation value !!
        call getin_p("nonoro_gwd_sat", sat)
        write(*,*) "nonoro_gwd_ran: sat=", sat     
!        cmax = 50. ! default gravity waves phase velocity value !!
!        call getin_p("nonoro_gwd_cmax", cmax)
!        write(*,*) "nonoro_gwd_ran: cmax=", cmax
        rdiss=0.07 ! default coefficient of dissipation !!
        call getin_p("nonoro_gwd_rdiss", rdiss)
        write(*,*) "nonoro_gwd_ran: rdiss=", rdiss
        kmax=1.E-4 ! default Max horizontal wavenumber !!
        call getin_p("nonoro_gwd_kmax", kmax)
        write(*,*) "nonoro_gwd_ran: kmax=", kmax
        kmin=7.E-6 ! default Max horizontal wavenumber !!
        call getin_p("nonoro_gwd_kmin", kmin)
        write(*,*) "nonoro_gwd_ran: kmin=", kmin
        xlaunch=0.6 ! default GW luanch altitude controller !!
        call getin_p("nonoro_gwd_xlaunch", xlaunch)
        write(*,*) "nonoro_gwd_ran: xlaunch=", xlaunch
        ! Characteristic vertical scale height
        H0 = r * tr / g
        ! Control
        if (deltat .LT. dtime) THEN
             call abort_physic("nonoro_gwd_ran","gwd random: deltat lower than dtime!",1)
        endif
        if (nlayer .LT. nw) THEN
             call abort_physic("nonoro_gwd_ran","gwd random: nlayer lower than nw!",1)
        endif
        firstcall = .false.
     ENDIF

! Compute current values of temperature and winds
    tt(:,:)=pt(:,:)+dtime*pdt(:,:)
    uu(:,:)=pu(:,:)+dtime*pdu(:,:)
    vv(:,:)=pv(:,:)+dtime*pdv(:,:)
! Compute the real mass density by rho=p/R(T)T
     DO ll=1,nlayer
       DO ii=1,ngrid
            rho(ii,ll) = pp(ii,ll)/(rnew(ii,ll)*tt(ii,ll))
       ENDDO
     ENDDO
!    print*,'epflux_max just after firstcall:', epflux_max

!-----------------------------------------------------------------------------------------------------------------------
!  2. EVALUATION OF THE BACKGROUND FLOW AT SEMI-LEVELS
!-----------------------------------------------------------------------------------------------------------------------
    ! Pressure and inverse of pressure at 1/2 level
    DO LL = 2, nlayer
       PH(:, LL) = EXP((LOG(PP(:, LL)) + LOG(PP(:, LL - 1))) / 2.)
    end DO
    PH(:, nlayer + 1) = 0. 
    PH(:, 1) = 2. * PP(:, 1) - PH(:, 2)

!    call write_output('nonoro_pp','nonoro_pp', 'm',PP(:,:))
!    call write_output('nonoro_ph','nonoro_ph', 'm',PH(:,:))

    ! Launching level for reproductible case
    !Pour revenir a la version non reproductible en changeant le nombre de
    !process
    ! Reprend la formule qui calcule PH en fonction de PP=play
    DO LL = 2, nlayer
       HREF(LL) = EXP((LOG(presnivs(LL))+ LOG(presnivs(LL - 1))) / 2.)
    end DO
    HREF(nlayer + 1) = 0.
    HREF(1) = 2. * presnivs(1) - HREF(2)

    LAUNCH=0
    DO LL = 1, nlayer
       IF (HREF(LL) / HREF(1) > XLAUNCH) LAUNCH = LL
    ENDDO 
        
    ! Log pressure vert. coordinate
       ZH(:,1) = 0. 
    DO LL = 2, nlayer + 1 
       !ZH(:, LL) = H0 * LOG(PR / (PH(:, LL) + PSEC))
        H0bis(:, LL-1) = r * TT(:, LL-1) / g 
          ZH(:, LL) = ZH(:, LL-1) &
           + H0bis(:, LL-1)*(PH(:, LL-1)-PH(:,LL))/PP(:, LL-1)
    end DO
        ZH(:, 1) = H0 * LOG(PR / (PH(:, 1) + PSEC))

!    call write_output('nonoro_zh','nonoro_zh', 'm',ZH(:,2:nlayer+1))

    ! Winds and Brunt Vaisala frequency
    DO LL = 2, nlayer
       UH(:, LL) = 0.5 * (UU(:, LL) + UU(:, LL - 1))                          ! Zonal wind
       VH(:, LL) = 0.5 * (VV(:, LL) + VV(:, LL - 1))                          ! Meridional wind
       ! Brunt Vaisala frequency (=g/T*[dT/dz + g/cp] )
       BV(:, LL)= G/(0.5 * (TT(:, LL) + TT(:, LL - 1)))                     &
        *((TT(:, LL) - TT(:, LL - 1)) / (ZH(:, LL) - ZH(:, LL - 1))+ &
        G / cpnew(:,LL))

       BV(:,LL) =MAX(1.E-12,BV(:,LL)) ! to ensure that BV is positive
       BV(:,LL) = MAX(BVSEC,SQRT(BV(:,LL))) ! make sure it is not too small
    end DO
    BV(:, 1) = BV(:, 2)
    UH(:, 1) = 0.
    VH(:, 1) = 0.
    BV(:, nlayer + 1) = BV(:, nlayer)
    UH(:, nlayer + 1) = UU(:, nlayer)
    VH(:, nlayer + 1) = VV(:, nlayer)
    cmax(:,launch)=UU(:, launch)
    DO ii=1,ngrid
       KSTAR = PI/SQRT(cell_area(II))
       MAX_K(II)=MAX(kmin,kstar)
    ENDDO
    call write_output('nonoro_bv','Brunt Vaisala frequency in nonoro', 'Hz',BV(:,2:nlayer+1))

!-----------------------------------------------------------------------------------------------------------------------
! 3. WAVES CHARACTERISTICS CHOSEN RANDOMLY
!-----------------------------------------------------------------------------------------------------------------------
! The mod function of here a weird arguments are used to produce the waves characteristics in a stochastic way
    DO JW = 1, NW
             !  Angle
             DO II = 1, ngrid
                ! Angle (0 or PI so far)
                RAN_NUM_1=MOD(TT(II, JW) * 10., 1.)
                RAN_NUM_2= MOD(TT(II, JW) * 100., 1.)
                ZP(JW, II) = (SIGN(1., 0.5 - RAN_NUM_1) + 1.)* PI / 2.
                
                ! Horizontal wavenumber amplitude
                ! From Venus model: TN+GG April/June 2020 (rev2381)
                ! "Individual waves are not supposed to occupy the entire domain, but only a fraction of it" (Lott+2012)
                ! ZK(JW, II) = KMIN + (KMAX - KMIN) *RAN_NUM_2
                KSTAR = PI/SQRT(cell_area(II))          
                ZK(JW, II) = MAX_K(II) + (KMAX - MAX_K(II)) *RAN_NUM_2
               
               ! Horizontal phase speed
! this computation allows to get a gaussian distribution centered on 0 (right ?)
! then cmin is not useful, and it favors small values.
                CPHA(:) = 0.
                DO JJ = 1, NA
                    RAN_NUM_3=MOD(TT(II, JW+3*JJ)**2, 1.)
                    CPHA(ii) = CPHA(ii) + 2.*CMAX(ii,launch)*      &
                           (RAN_NUM_3 -0.5)*                       &
                           SQRT(3.)/SQRT(NA*1.)
                END DO
                IF (CPHA(ii).LT.0.)  THEN
                   CPHA(ii) = -1.*CPHA(ii)
                   ZP(JW,II) = ZP(JW,II) + PI
                ENDIF
! otherwise, with the computation below, we get a uniform distribution between cmin and cmax.
!           ran_num_3 = mod(tt(ii, jw)**2, 1.)
!           cpha = cmin + (cmax - cmin) * ran_num_3

                ! Intrinsic frequency
                ZO(JW, II) = CPHA(II) * ZK(JW, II)
                ! Intrinsic frequency  is imposed
                ZO(JW, II) = ZO(JW, II)                                            &
                            + ZK(JW, II) * COS(ZP(JW, II)) * UH(II, LAUNCH)        &
                            + ZK(JW, II) * SIN(ZP(JW, II)) * VH(II, LAUNCH)
               
                ! Momentum flux at launch level 
                epflux_0(JW, II) = epflux_max                                      &
                                  * MOD(100. * (UU(II, JW)**2 + VV(II, JW)**2), 1.)
              ENDDO
   end DO
!     print*,'epflux_0 just after waves charac. ramdon:', epflux_0

!-----------------------------------------------------------------------------------------------------------------------
! 4. COMPUTE THE FLUXES
!-----------------------------------------------------------------------------------------------------------------------
    !  4.1  Vertical velocity at launching altitude to ensure the correct value to the imposed fluxes.
    !------------------------------------------------------
    DO JW = 1, NW
       ! Evaluate intrinsic frequency at launching altitude:
       intr_freq_p(JW, :) = ZO(JW, :)                                    &
                            - ZK(JW, :) * COS(ZP(JW, :)) * UH(:, LAUNCH) &
                            - ZK(JW, :) * SIN(ZP(JW, :)) * VH(:, LAUNCH) 
    end DO

! VERSION WITHOUT CONVECTIVE SOURCE
       ! Vertical velocity at launch level, value to ensure the imposed
       ! mom flux:
         DO JW = 1, NW
       ! WW is directly a flux, here, not vertical velocity anymore
            WWP(JW, :) = epflux_0(JW,:)
            u_epflux_p(JW, :) = COS(ZP(JW, :)) * SIGN(1., intr_freq_p(JW, :)) * epflux_0(JW, :)
            v_epflux_p(JW, :) = SIN(ZP(JW, :)) * SIGN(1., intr_freq_p(JW, :)) * epflux_0(JW, :)
         end DO
    
    !  4.2 Initial flux at launching altitude
    !------------------------------------------------------
    u_epflux_tot(:, LAUNCH) = 0
    v_epflux_tot(:, LAUNCH) = 0
    DO JW = 1, NW
       u_epflux_tot(:, LAUNCH) = u_epflux_tot(:, LAUNCH) + u_epflux_p(JW, :)
       v_epflux_tot(:, LAUNCH) = v_epflux_tot(:, LAUNCH) + v_epflux_p(JW, :)
    end DO

    !  4.3 Loop over altitudes, with passage from one level to the next done by:
    !----------------------------------------------------------------------------
    !    i) conserving the EP flux, 
    !    ii) dissipating a little, 
    !    iii) testing critical levels, 
    !    iv) testing the breaking.
    !----------------------------------------------------------------------------
    DO LL = LAUNCH, nlayer - 1
       !  W(KB)ARNING: ALL THE PHYSICS IS HERE (PASSAGE FROM ONE LEVEL TO THE NEXT)
       DO JW = 1, NW
          intr_freq_m(JW, :) = intr_freq_p(JW, :)
          WWM(JW, :) = WWP(JW, :)
          ! Intrinsic Frequency
          intr_freq_p(JW, :) = ZO(JW, :) - ZK(JW, :) * COS(ZP(JW,:)) * UH(:, LL + 1)     &
                               - ZK(JW, :) * SIN(ZP(JW,:)) * VH(:, LL + 1) 
          ! Vertical velocity in flux formulation
          WWP(JW, :) = MIN(                                                              & 
                     ! No breaking (Eq.6)
                     WWM(JW, :)                                                          & 
                     ! Dissipation (Eq. 8)(real rho used here rather than pressure 
                     ! parametration because the original code has a bug if the density of 
                     ! the planet at the launch altitude not approximate 1):                     ! 
                     * EXP(- RDISS*2./rho(:, LL + 1)                                     &
                     * ((BV(:, LL + 1) + BV(:, LL)) / 2.)**3                             &
                     / MAX(ABS(intr_freq_p(JW, :) + intr_freq_m(JW, :)) / 2., ZOISEC)**4 &
                     * ZK(JW, :)**3 * (ZH(:, LL + 1) - ZH(:, LL))),                      &
                     ! Critical levels (forced to zero if intrinsic frequency 
                     ! changes sign)
                     MAX(0., SIGN(1., intr_freq_p(JW, :) * intr_freq_m(JW, :)))          &
                     ! Saturation (Eq. 12) (rho at launch altitude is imposed by J.Liu. 
                     ! Same reason with Eq. 8)
                     * ABS(intr_freq_p(JW, :))**3 / (2.*BV(:, LL+1))                     & 
                     * rho(:,launch)*exp(-zh(:, ll + 1) / H0)                            &
                     * SAT**2 *KMIN**2 / ZK(JW, :)**4)  
       end DO
       ! END OF W(KB)ARNING

       ! Evaluate EP-flux from Eq. 7 and give the right orientation to the stress
       DO JW = 1, NW
          u_epflux_p(JW, :) = SIGN(1.,intr_freq_p(JW, :)) * COS(ZP(JW, :)) *  WWP(JW, :)
          v_epflux_p(JW, :) = SIGN(1.,intr_freq_p(JW, :)) * SIN(ZP(JW, :)) *  WWP(JW, :)
       end DO
 
       u_epflux_tot(:, LL + 1) = 0.
       v_epflux_tot(:, LL + 1) = 0.
       DO JW = 1, NW
          u_epflux_tot(:, LL + 1) = u_epflux_tot(:, LL + 1) + u_epflux_p(JW, :) 
          v_epflux_tot(:, LL + 1) = v_epflux_tot(:, LL + 1) + v_epflux_p(JW, :) 
          EAST_GWSTRESS(:, LL)=EAST_GWSTRESS(:, LL)+MAX(0.,u_epflux_p(JW,:))/FLOAT(NW)
          WEST_GWSTRESS(:, LL)=WEST_GWSTRESS(:, LL)+MIN(0.,u_epflux_p(JW,:))/FLOAT(NW)
       end DO       
    end DO ! DO LL = LAUNCH, nlayer - 1

!-----------------------------------------------------------------------------------------------------------------------
! 5. TENDENCY CALCULATIONS 
!-----------------------------------------------------------------------------------------------------------------------

    ! 5.1 Flow rectification at the top and in the low layers
    ! --------------------------------------------------------
    ! Warning, this is the total on all GW
    u_epflux_tot(:, nlayer + 1) = 0.
    v_epflux_tot(:, nlayer + 1) = 0.

    ! Here, big change compared to FLott version:
    ! We compensate (u_epflux_tot(:, LAUNCH), ie total emitted upward flux
    !  over the layers max(1,LAUNCH-3) to LAUNCH-1
    DO LL = 1, max(1,LAUNCH-3)
      u_epflux_tot(:, LL) = 0.
      v_epflux_tot(:, LL) = 0.
    end DO
    DO LL = max(2,LAUNCH-2), LAUNCH-1
       u_epflux_tot(:, LL) = u_epflux_tot(:, LL - 1) + u_epflux_tot(:, LAUNCH) *          &
                             (PH(:,LL)-PH(:,LL-1)) / (PH(:,LAUNCH)-PH(:,max(1,LAUNCH-3)))
       v_epflux_tot(:, LL) = v_epflux_tot(:, LL - 1) + v_epflux_tot(:, LAUNCH) *          &
                             (PH(:,LL)-PH(:,LL-1)) / (PH(:,LAUNCH)-PH(:,max(1,LAUNCH-3)))
       EAST_GWSTRESS(:,LL) = EAST_GWSTRESS(:, LL - 1) +                                   &
                             EAST_GWSTRESS(:, LAUNCH) * (PH(:,LL)-PH(:,LL-1))/            &
                             (PH(:,LAUNCH)-PH(:,max(1,LAUNCH-3)))
       WEST_GWSTRESS(:,LL) = WEST_GWSTRESS(:, LL - 1) +                                   &
                             WEST_GWSTRESS(:, LAUNCH) * (PH(:,LL)-PH(:,LL-1))/            &
                             (PH(:,LAUNCH)-PH(:,max(1,LAUNCH-3)))
    end DO
    ! This way, the total flux from GW is zero, but there is a net transport
    ! (upward) that should be compensated by circulation 
    ! and induce additional friction at the surface 
    call write_output('nonoro_u_epflux_tot','Total EP Flux along U in nonoro', '',u_epflux_tot(:,2:nlayer+1))
    call write_output('nonoro_v_epflux_tot','Total EP Flux along V in nonoro', '',v_epflux_tot(:,2:nlayer+1))

    ! 5.2 AR-1 RECURSIVE FORMULA (13) IN VERSION 4
    !---------------------------------------------
    DO LL = 1, nlayer
       !Notice here the d_u and d_v are tendency (For Mars) but not increment(Venus).
       d_u(:, LL) = G * (u_epflux_tot(:, LL + 1) - u_epflux_tot(:, LL)) &
                    / (PH(:, LL + 1) - PH(:, LL)) 
       d_v(:, LL) = G * (v_epflux_tot(:, LL + 1) - v_epflux_tot(:, LL)) &
                    / (PH(:, LL + 1) - PH(:, LL)) 
    ENDDO
    d_t(:,:) = 0.
!    call write_output('nonoro_d_u','nonoro_d_u', '',d_u(:,:))
!    call write_output('nonoro_d_v','nonoro_d_v', '',d_v(:,:))

    ! 5.3 Update tendency of wind with the previous (and saved) values
    !-----------------------------------------------------------------
    d_u(:,:) = DTIME/DELTAT/REAL(NW) * d_u(:,:)                       &
               + (1.-DTIME/DELTAT) * du_nonoro_gwd(:,:)
    d_v(:,:) = DTIME/DELTAT/REAL(NW) * d_v(:,:)                       &
               + (1.-DTIME/DELTAT) * dv_nonoro_gwd(:,:)
    du_nonoro_gwd(:,:) = d_u(:,:)
    dv_nonoro_gwd(:,:) = d_v(:,:)

    call write_output('du_nonoro_gwd','Tendency on U due to nonoro GW', 'm.s-2',du_nonoro_gwd(:,:))
    call write_output('dv_nonoro_gwd','Tendency on V due to nonoro GW', 'm.s-2',dv_nonoro_gwd(:,:))
    
    ! Cosmetic: evaluation of the cumulated stress
    ZUSTR(:) = 0.
    ZVSTR(:) = 0.
    DO LL = 1, nlayer
       ZUSTR(:) = ZUSTR(:) + D_U(:, LL) *rho(:, LL) * (ZH(:, LL + 1) - ZH(:, LL))*DTIME
       ZVSTR(:) = ZVSTR(:) + D_V(:, LL) *rho(:, LL) * (ZH(:, LL + 1) - ZH(:, LL))*DTIME
    ENDDO

  END SUBROUTINE NONORO_GWD_RAN



! ========================================================
! Subroutines used to allocate/deallocate module variables       
! ========================================================
  SUBROUTINE ini_nonoro_gwd_ran(ngrid,nlayer)

  IMPLICIT NONE

      INTEGER, INTENT (in) :: ngrid  ! number of atmospheric columns
      INTEGER, INTENT (in) :: nlayer ! number of atmospheric layers

         allocate(du_nonoro_gwd(ngrid,nlayer))
         allocate(dv_nonoro_gwd(ngrid,nlayer))
         allocate(east_gwstress(ngrid,nlayer))
         east_gwstress(:,:)=0
         allocate(west_gwstress(ngrid,nlayer))
         west_gwstress(:,:)=0

  END SUBROUTINE ini_nonoro_gwd_ran
! ----------------------------------
  SUBROUTINE end_nonoro_gwd_ran

  IMPLICIT NONE

         if (allocated(du_nonoro_gwd)) deallocate(du_nonoro_gwd)
         if (allocated(dv_nonoro_gwd)) deallocate(dv_nonoro_gwd)
         if (allocated(east_gwstress)) deallocate(east_gwstress)
         if (allocated(west_gwstress)) deallocate(west_gwstress)

  END SUBROUTINE end_nonoro_gwd_ran

END MODULE nonoro_gwd_ran_mod