source: trunk/LMDZ.GENERIC/libf/phystd/gfluxv.F @ 1988

      SUBROUTINE GFLUXV(DTDEL,TDEL,TAUCUMIN,WDEL,CDEL,UBAR0,F0PI,RSF,
     *                  BTOP,BSURF,FMIDP,FMIDM,DIFFV,FLUXUP,FLUXDN)


C  THIS SUBROUTINE TAKES THE OPTICAL CONSTANTS AND BOUNDARY CONDITIONS
C  FOR THE VISIBLE  FLUX AT ONE WAVELENGTH AND SOLVES FOR THE FLUXES AT
C  THE LEVELS. THIS VERSION IS SET UP TO WORK WITH LAYER OPTICAL DEPTHS
C  MEASURED FROM THE TOP OF EACH LAYER.  (DTAU) TOP OF EACH LAYER HAS  
C  OPTICAL DEPTH TAU(N).IN THIS SUB LEVEL N IS ABOVE LAYER N. THAT IS LAYER N
C  HAS LEVEL N ON TOP AND LEVEL N+1 ON BOTTOM. OPTICAL DEPTH INCREASES
C  FROM TOP TO BOTTOM. SEE C.P. MCKAY, TGM NOTES.
C THIS SUBROUTINE DIFFERS FROM ITS IR COUNTERPART IN THAT HERE WE SOLVE FOR 
C THE FLUXES DIRECTLY USING THE GENERALIZED NOTATION OF MEADOR AND WEAVOR
C J.A.S., 37, 630-642, 1980.
C THE TRI-DIAGONAL MATRIX SOLVER IS DSOLVER AND IS DOUBLE PRECISION SO MANY 
C VARIABLES ARE PASSED AS SINGLE THEN BECOME DOUBLE IN DSOLVER
C
C NLL           = NUMBER OF LEVELS (NAYER + 1) THAT WILL BE SOLVED
C NAYER         = NUMBER OF LAYERS (NOTE DIFFERENT SPELLING HERE)
C WAVEN         = WAVELENGTH FOR THE COMPUTATION
C DTDEL(NLAYER) = ARRAY OPTICAL DEPTH OF THE LAYERS
C TDEL(NLL)     = ARRAY COLUMN OPTICAL DEPTH AT THE LEVELS
C WDEL(NLEVEL)  = SINGLE SCATTERING ALBEDO
C CDEL(NLL)     = ASYMMETRY FACTORS, 0=ISOTROPIC
C UBARV         = AVERAGE ANGLE, 
C UBAR0         = SOLAR ZENITH ANGLE
C F0PI          = INCIDENT SOLAR DIRECT BEAM FLUX
C RSF           = SURFACE REFLECTANCE
C BTOP          = UPPER BOUNDARY CONDITION ON DIFFUSE FLUX
C BSURF         = REFLECTED DIRECT BEAM = (1-RSFI)*F0PI*EDP-TAU/U
C FP(NLEVEL)    = UPWARD FLUX AT LEVELS
C FM(NLEVEL)    = DOWNWARD FLUX AT LEVELS
C FMIDP(NLAYER) = UPWARD FLUX AT LAYER MIDPOINTS
C FMIDM(NLAYER) = DOWNWARD FLUX AT LAYER MIDPOINTS
C added Dec 2002
C DIFFV         = downward diffuse solar flux at the surface
C 
!======================================================================!

      use radinc_h

      implicit none

!!      INTEGER NLP
!!      PARAMETER (NLP=101) ! MUST BE LARGER THAN NLEVEL

      REAL*8 EM, EP
      REAL*8 W0(L_NLAYRAD), COSBAR(L_NLAYRAD), DTAU(L_NLAYRAD)
      REAL*8 TAU(L_NLEVRAD), WDEL(L_NLAYRAD), CDEL(L_NLAYRAD)
      REAL*8 DTDEL(L_NLAYRAD), TDEL(L_NLEVRAD)
      REAL*8 FMIDP(L_NLAYRAD), FMIDM(L_NLAYRAD)
      REAL*8 LAMDA(L_NLAYRAD), ALPHA(L_NLAYRAD), XK1(L_NLAYRAD)
      REAL*8 XK2(L_NLAYRAD),G1(L_NLAYRAD), G2(L_NLAYRAD)
      REAL*8 G3(L_NLAYRAD), GAMA(L_NLAYRAD),CP(L_NLAYRAD),CM(L_NLAYRAD)
      REAL*8 CPM1(L_NLAYRAD),CMM1(L_NLAYRAD), E1(L_NLAYRAD)
      REAL*8 E2(L_NLAYRAD),E3(L_NLAYRAD),E4(L_NLAYRAD),EXPTRM(L_NLAYRAD)
      REAL*8 FLUXUP, FLUXDN
      REAL*8 FACTOR, TAUCUMIN(L_LEVELS), TAUCUM(L_LEVELS)

      integer NAYER, L, K
      real*8  ubar0, f0pi, rsf, btop, bsurf, g4, denom, am, ap
      real*8  taumax, taumid, cpmid, cmmid
      real*8  diffv

C======================================================================C




      NAYER  = L_NLAYRAD
      TAUMAX = L_TAUMAX    !Default is 35.0
      
!  Delta-Eddington Scaling


      FACTOR    = 1.0D0 - WDEL(1)*CDEL(1)**2

      TAU(1)    = TDEL(1)*FACTOR
      TAUCUM(1) = 0.0D0
      TAUCUM(2) = TAUCUMIN(2)*FACTOR
      TAUCUM(3) = TAUCUM(2) +(TAUCUMIN(3)-TAUCUMIN(2))*FACTOR


      DO L=1,L_NLAYRAD-1
        FACTOR      = 1.0D0 - WDEL(L)*CDEL(L)**2
        W0(L)       = WDEL(L)*(1.0D0-CDEL(L)**2)/FACTOR
        COSBAR(L)   = CDEL(L)/(1.0D0+CDEL(L))

        DTAU(L)     = DTDEL(L)*FACTOR
        TAU(L+1)    = TAU(L)+DTAU(L)
        K           = 2*(L+1)
        TAUCUM(K)   = TAU(L+1)
        TAUCUM(K+1) = TAUCUM(K) + (TAUCUMIN(K+1)-TAUCUMIN(K))*FACTOR
      END DO

!  Bottom layer

      L             = L_NLAYRAD
      FACTOR        = 1.0D0 - WDEL(L)*CDEL(L)**2
      W0(L)         = WDEL(L)*(1.0D0-CDEL(L)**2)/FACTOR
      COSBAR(L)     = CDEL(L)/(1.0D0+CDEL(L))
      DTAU(L)       = DTDEL(L)*FACTOR
      TAU(L+1)      = TAU(L)+DTAU(L)
      TAUCUM(2*L+1) = TAU(L+1)

      BSURF = RSF*UBAR0*F0PI*EXP(-MIN(TAU(L+1),TAUMAX)/UBAR0)
      ! new definition of BSURF
      ! the old one was false because it used tau, not tau'
      ! tau' includes the contribution to the downward flux
      ! of the radiation scattered in the forward direction

C     WE GO WITH THE QUADRATURE APPROACH HERE.  THE "SQRT(3)" factors
C     ARE THE UBARV TERM.

      DO L=1,L_NLAYRAD

        ALPHA(L)=SQRT( (1.0-W0(L))/(1.0-W0(L)*COSBAR(L) ) )

C       SET OF CONSTANTS DETERMINED BY DOM 

!     Quadrature method
        G1(L)    = (SQRT(3.0)*0.5)*(2.0- W0(L)*(1.0+COSBAR(L)))
        G2(L)    = (SQRT(3.0)*W0(L)*0.5)*(1.0-COSBAR(L))
        G3(L)    = 0.5*(1.0-SQRT(3.0)*COSBAR(L)*UBAR0)

!     ----- some other methods... (RDW) ------

!     Eddington method
!        G1(L)    =  0.25*(7.0 - W0(L)*(4.0 - 3.0*COSBAR(L)))
!        G2(L)    = -0.25*(1.0 - W0(L)*(4.0 - 3.0*COSBAR(L)))
!        G3(L)    =  0.25*(2.0 - 3.0*COSBAR(L)*UBAR0)

!     delta-Eddington method
!        G1(L)    =  (7.0 - 3.0*g^2 - W0(L)*(4.0 + 3.0*g) + W0(L)*g^2*(4*beta0 + 3*g)) / &
!                             (4* (1 - g^2*()   ))  0.25*(7.0 - W0(L)*(4.0 - 3.0*COSBAR(L)))

!     Hybrid modified Eddington-delta function method

!     ----------------------------------------

c     So they use Quadrature
c     but the scaling is Eddington?

        LAMDA(L) = SQRT(G1(L)**2 - G2(L)**2)
        GAMA(L)  = (G1(L)-LAMDA(L))/G2(L)
      END DO


      DO L=1,L_NLAYRAD
        G4    = 1.0-G3(L)
        DENOM = LAMDA(L)**2 - 1./UBAR0**2
 
C       THERE IS A POTENTIAL PROBLEM HERE IF W0=0 AND UBARV=UBAR0
C       THEN DENOM WILL VANISH. THIS ONLY HAPPENS PHYSICALLY WHEN 
C       THE SCATTERING GOES TO ZERO
C       PREVENT THIS WITH AN IF STATEMENT

        IF ( DENOM .EQ. 0.) THEN
          DENOM=1.E-10
        END IF


        AM = F0PI*W0(L)*(G4   *(G1(L)+1./UBAR0) +G2(L)*G3(L) )/DENOM
        AP = F0PI*W0(L)*(G3(L)*(G1(L)-1./UBAR0) +G2(L)*G4    )/DENOM

C       CPM1 AND CMM1 ARE THE CPLUS AND CMINUS TERMS EVALUATED
C       AT THE TOP OF THE LAYER, THAT IS LOWER   OPTICAL DEPTH TAU(L)
 
        CPM1(L) = AP*EXP(-TAU(L)/UBAR0)
        CMM1(L) = AM*EXP(-TAU(L)/UBAR0)

C       CP AND CM ARE THE CPLUS AND CMINUS TERMS EVALUATED AT THE
C       BOTTOM OF THE LAYER.  THAT IS AT HIGHER OPTICAL DEPTH TAU(L+1)

        CP(L) = AP*EXP(-TAU(L+1)/UBAR0)
        CM(L) = AM*EXP(-TAU(L+1)/UBAR0)

      END DO


 
C     NOW CALCULATE THE EXPONENTIAL TERMS NEEDED
C     FOR THE TRIDIAGONAL ROTATED LAYERED METHOD

      DO L=1,L_NLAYRAD
        EXPTRM(L) = MIN(TAUMAX,LAMDA(L)*DTAU(L))  ! CLIPPED EXPONENTIAL
        EP = EXP(EXPTRM(L))

        EM        = 1.0/EP
        E1(L)     = EP+GAMA(L)*EM
        E2(L)     = EP-GAMA(L)*EM
        E3(L)     = GAMA(L)*EP+EM
        E4(L)     = GAMA(L)*EP-EM
      END DO

      CALL DSOLVER(NAYER,GAMA,CP,CM,CPM1,CMM1,E1,E2,E3,E4,BTOP,
     *             BSURF,RSF,XK1,XK2)

C     NOW WE CALCULATE THE FLUXES AT THE MIDPOINTS OF THE LAYERS.
 
      DO L=1,L_NLAYRAD-1
        EXPTRM(L) = MIN(TAUMAX,LAMDA(L)*(TAUCUM(2*L+1)-TAUCUM(2*L)))
 
        EP = EXP(EXPTRM(L))

        EM    = 1.0/EP
        G4    = 1.0-G3(L)
        DENOM = LAMDA(L)**2 - 1./UBAR0**2

C       THERE IS A POTENTIAL PROBLEM HERE IF W0=0 AND UBARV=UBAR0
C       THEN DENOM WILL VANISH. THIS ONLY HAPPENS PHYSICALLY WHEN 
C       THE SCATTERING GOES TO ZERO
C       PREVENT THIS WITH A IF STATEMENT


        IF ( DENOM .EQ. 0.) THEN
          DENOM=1.E-10
        END IF

        AM = F0PI*W0(L)*(G4   *(G1(L)+1./UBAR0) +G2(L)*G3(L) )/DENOM
        AP = F0PI*W0(L)*(G3(L)*(G1(L)-1./UBAR0) +G2(L)*G4    )/DENOM

C       CPMID AND CMMID  ARE THE CPLUS AND CMINUS TERMS EVALUATED
C       AT THE MIDDLE OF THE LAYER.

        TAUMID   = TAUCUM(2*L+1)

        CPMID = AP*EXP(-TAUMID/UBAR0)
        CMMID = AM*EXP(-TAUMID/UBAR0)

        FMIDP(L) = XK1(L)*EP + GAMA(L)*XK2(L)*EM + CPMID
        FMIDM(L) = XK1(L)*EP*GAMA(L) + XK2(L)*EM + CMMID
 
C       ADD THE DIRECT FLUX TO THE DOWNWELLING TERM

        FMIDM(L)= FMIDM(L)+UBAR0*F0PI*EXP(-MIN(TAUMID,TAUMAX)/UBAR0)
   
      END DO
 
C     FLUX AT THE Ptop layer

!      EP    = 1.0
!      EM    = 1.0
C JL18 correction to account for the fact that the radiative top is not at zero optical depth.
      EXPTRM(L) = MIN(TAUMAX,LAMDA(L)*(TAUCUM(2)))
      EP = EXP(EXPTRM(L))
      EM    = 1.0/EP
      G4    = 1.0-G3(1)
      DENOM = LAMDA(1)**2 - 1./UBAR0**2

C     THERE IS A POTENTIAL PROBLEM HERE IF W0=0 AND UBARV=UBAR0
C     THEN DENOM WILL VANISH. THIS ONLY HAPPENS PHYSICALLY WHEN 
C     THE SCATTERING GOES TO ZERO
C     PREVENT THIS WITH A IF STATEMENT

      IF ( DENOM .EQ. 0.) THEN
        DENOM=1.E-10
      END IF

      AM = F0PI*W0(1)*(G4   *(G1(1)+1./UBAR0) +G2(1)*G3(1) )/DENOM
      AP = F0PI*W0(1)*(G3(1)*(G1(1)-1./UBAR0) +G2(1)*G4    )/DENOM

C     CPMID AND CMMID  ARE THE CPLUS AND CMINUS TERMS EVALUATED
C     AT THE MIDDLE OF THE LAYER.

C      CPMID  = AP
C      CMMID  = AM
C JL18 correction to account for the fact that the radiative top is not at zero optical depth.
      TAUMID   = TAUCUM(2)
      CPMID = AP*EXP(-TAUMID/UBAR0)
      CMMID = AM*EXP(-TAUMID/UBAR0)

      FLUXUP = XK1(1)*EP + GAMA(1)*XK2(1)*EM + CPMID
      FLUXDN = XK1(1)*EP*GAMA(1) + XK2(1)*EM + CMMID

C     ADD THE DIRECT FLUX TO THE DOWNWELLING TERM

!      fluxdn = fluxdn+UBAR0*F0PI*EXP(-MIN(TAUCUM(1),TAUMAX)/UBAR0)
!JL18 the line above assumed that the top of the radiative model was P=0
!   it seems to be better for the IR to use the middle of the last physical layer as the radiative top. 
!   so we correct the downwelling flux below for the calculation of the heating rate
      fluxdn = fluxdn+UBAR0*F0PI*EXP(-TAUCUM(2)/UBAR0)

C     This is for the "special" bottom layer, where we take
C     DTAU instead of DTAU/2.

      L     = L_NLAYRAD 
      EXPTRM(L) = MIN(TAUMAX,LAMDA(L)*(TAUCUM(L_LEVELS)-
     *                                 TAUCUM(L_LEVELS-1)))

      EP    = EXP(EXPTRM(L))
      EM    = 1.0/EP
      G4    = 1.0-G3(L)
      DENOM = LAMDA(L)**2 - 1./UBAR0**2


C     THERE IS A POTENTIAL PROBLEM HERE IF W0=0 AND UBARV=UBAR0
C     THEN DENOM WILL VANISH. THIS ONLY HAPPENS PHYSICALLY WHEN 
C     THE SCATTERING GOES TO ZERO
C     PREVENT THIS WITH A IF STATEMENT


      IF ( DENOM .EQ. 0.) THEN
        DENOM=1.E-10
      END IF

      AM = F0PI*W0(L)*(G4   *(G1(L)+1./UBAR0) +G2(L)*G3(L) )/DENOM
      AP = F0PI*W0(L)*(G3(L)*(G1(L)-1./UBAR0) +G2(L)*G4    )/DENOM

C     CPMID AND CMMID  ARE THE CPLUS AND CMINUS TERMS EVALUATED
C     AT THE MIDDLE OF THE LAYER.

      TAUMID   = MIN(TAUCUM(L_LEVELS),TAUMAX)
      CPMID    = AP*EXP(-MIN(TAUMID,TAUMAX)/UBAR0)
      CMMID    = AM*EXP(-MIN(TAUMID,TAUMAX)/UBAR0)


      FMIDP(L) = XK1(L)*EP + GAMA(L)*XK2(L)*EM + CPMID
      FMIDM(L) = XK1(L)*EP*GAMA(L) + XK2(L)*EM + CMMID

C  Save the diffuse downward flux for TEMPGR calculations

      DIFFV = FMIDM(L)


C     ADD THE DIRECT FLUX TO THE DOWNWELLING TERM

      FMIDM(L)= FMIDM(L)+UBAR0*F0PI*EXP(-MIN(TAUMID,TAUMAX)/UBAR0)


      RETURN
      END