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 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. CPMID = AP CMMID = AM 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) 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