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DISORT.f
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c ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
c RCS version control information:
c $Header: DISORT.f,v 2.1 2000/04/04 18:21:55 laszlo Exp $
c ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
SUBROUTINE DISORT( NLYR, DTAUC, SSALB, NMOM, PMOM, TEMPER, WVNMLO,
& WVNMHI, USRTAU, NTAU, UTAU, NSTR, USRANG, NUMU,
& UMU, NPHI, PHI, IBCND, FBEAM, UMU0, PHI0,
& FISOT, LAMBER, ALBEDO, BTEMP, TTEMP, TEMIS,
& PLANK, ONLYFL, ACCUR, PRNT, HEADER, MAXCLY,
& MAXULV, MAXUMU, MAXPHI, MAXMOM, RFLDIR, RFLDN,
& FLUP, DFDT, UAVG, UU, ALBMED, TRNMED )
c *******************************************************************
c Plane-parallel discrete ordinates radiative transfer program
c ( see DISORT.doc for complete documentation )
c *******************************************************************
c
c +------------------------------------------------------------------+
c Calling Tree (omitting calls to ERRMSG):
c (routines in parentheses are not in this file)
c
c DISORT-+-(R1MACH)
c +-SLFTST-+-(TSTBAD)
c +-ZEROIT
c +-CHEKIN-+-(WRTBAD)
c | +-(WRTDIM)
c | +-DREF
c +-ZEROAL
c +-SETDIS-+-QGAUSN-+-(D1MACH)
c +-PRTINP
c +-ALBTRN-+-LEPOLY
c | +-ZEROIT
c | +-SOLEIG-+-ASYMTX-+-(D1MACH)
c | +-TERPEV
c | +-SETMTX-+-ZEROIT
c | +-(SGBCO)
c | +-SOLVE1-+-ZEROIT
c | | +-(SGBSL)
c | +-ALTRIN
c | +-SPALTR
c | +-PRALTR
c +-PLKAVG-+-(R1MACH)
c +-LEPOLY
c +-SURFAC-+-QGAUSN-+-(D1MACH)
c | +-BDREF
c | +-ZEROIT
c +-SOLEIG-+-ASYMTX-+-(D1MACH)
c +-UPBEAM-+-(SGECO)
c | +-(SGESL)
c +-UPISOT-+-(SGECO)
c | +-(SGESL)
c +-TERPEV
c +-TERPSO
c +-SETMTX-+-ZEROIT
c +-SOLVE0-+-ZEROIT
c | +-(SGBCO)
c | +-(SGBSL)
c +-FLUXES--ZEROIT
c +-ZEROIT
c +-USRINT
c +-CMPINT
c +-PRAVIN
c +-ZEROIT
c +-RATIO--(R1MACH)
c +-INTCOR-+-SINSCA
c | +-SECSCA-+-XIFUNC
c +-PRTINT
c
c *** Intrinsic Functions used in DISORT package which take
c non-negligible amount of time:
c
c EXP : Called by- ALBTRN, ALTRIN, CMPINT, FLUXES, SETDIS,
c SETMTX, SPALTR, USRINT, PLKAVG
c
c SQRT : Called by- ASYMTX, SOLEIG
c
c +-------------------------------------------------------------------+
c
c Index conventions (for all DO-loops and all variable descriptions):
c
c IU : for user polar angles
c
c IQ,JQ,KQ : for computational polar angles ('quadrature angles')
c
c IQ/2 : for half the computational polar angles (just the ones
c in either 0-90 degrees, or 90-180 degrees)
c
c J : for user azimuthal angles
c
c K,L : for Legendre expansion coefficients or, alternatively,
c subscripts of associated Legendre polynomials
c
c LU : for user levels
c
c LC : for computational layers (each having a different
c single-scatter albedo and/or phase function)
c
c LEV : for computational levels
c
c MAZIM : for azimuthal components in Fourier cosine expansion
c of intensity and phase function
c
c +------------------------------------------------------------------+
c
c I N T E R N A L V A R I A B L E S
c
c AMB(IQ/2,IQ/2) First matrix factor in reduced eigenvalue problem
c of Eqs. SS(12), STWJ(8E), STWL(23f)
c (used only in SOLEIG)
c
c APB(IQ/2,IQ/2) Second matrix factor in reduced eigenvalue problem
c of Eqs. SS(12), STWJ(8E), STWL(23f)
c (used only in SOLEIG)
c
c ARRAY(IQ,IQ) Scratch matrix for SOLEIG, UPBEAM and UPISOT
c (see each subroutine for definition)
c
c B() Right-hand side vector of Eq. SC(5) going into
c SOLVE0,1; returns as solution vector
c vector L, the constants of integration
c
c BDR(IQ/2,0:IQ/2) Bottom-boundary bidirectional reflectivity for a
c given azimuthal component. First index always
c refers to a computational angle. Second index:
c if zero, refers to incident beam angle UMU0;
c if non-zero, refers to a computational angle.
c
c BEM(IQ/2) Bottom-boundary directional emissivity at compu-
c tational angles.
c
c BPLANK Intensity emitted from bottom boundary
c
c CBAND() Matrix of left-hand side of the linear system
c Eq. SC(5), scaled by Eq. SC(12); in banded
c form required by LINPACK solution routines
c
c CC(IQ,IQ) C-sub-IJ in Eq. SS(5)
c
c CMU(IQ) Computational polar angles (Gaussian)
c
c CWT(IQ) Quadrature weights corresponding to CMU
c
c CORINT When set TRUE, correct intensities for
c delta-scaling effects (see Nakajima and Tanaka,
c 1988). When FALSE, intensities are not corrected.
c In general, CORINT should be set true when beam
c source is present (FBEAM is not zero) and DELTAM
c is TRUE in a problem including scattering.
c However, execution is faster when CORINT is FALSE,
c and intensities outside the aureole may still be
c accurate enough. When CORINT is TRUE, it is
c important to have a sufficiently high order of
c Legendre approximation of the phase function. This
c is because the intensities are corrected by
c calculating the single-scattered radiation, for
c which an adequate representation of the phase
c function is crucial. In case of a low order
c Legendre approximation of an otherwise highly
c anisotropic phase function, the intensities might
c actually be more accurate when CORINT is FALSE.
c When only fluxes are calculated (ONLYFL is TRUE),
c or there is no beam source (FBEAM=0.0), or there
c is no scattering (SSALB=0.0 for all layers) CORINT
c is set FALSE by the code.
c
c DELM0 Kronecker delta, delta-sub-M0, where M = MAZIM
c is the number of the Fourier component in the
c azimuth cosine expansion
c
c DELTAM TRUE, use delta-M method ( see Wiscombe, 1977 );
c FALSE, do not use delta-M method. In general, for
c a given number of streams, intensities and
c fluxes will be more accurate for phase functions
c with a large forward peak if DELTAM is set true.
c Intensities close to the forward scattering
c direction are often less accurate, however, when
c the delta-M method is applied. The intensity
c correction of Nakajima and Tanaka is used to
c improve the accuracy of the intensities.
c
c DITHER Small quantity subtracted from single-scattering
c albedos of unity, in order to avoid using special
c case formulas; prevents an eigenvalue of exactly
c zero from occurring, which would cause an
c immediate overflow
c
c DTAUCP(LC) Computational-layer optical depths (delta-M-scaled
c if DELTAM = TRUE, otherwise equal to DTAUC)
c
c EMU(IU) Bottom-boundary directional emissivity at user
c angles.
c
c EVAL(IQ) Temporary storage for eigenvalues of Eq. SS(12)
c
c EVECC(IQ,IQ) Complete eigenvectors of SS(7) on return from
c SOLEIG; stored permanently in GC
c
c EXPBEA(LC) Transmission of direct beam in delta-M optical
c depth coordinates
c
c FLYR(LC) Separated fraction in delta-M method
c
c GL(K,LC) Phase function Legendre polynomial expansion
c coefficients, calculated from PMOM by
c including single-scattering albedo, factor
c 2K+1, and (if DELTAM=TRUE) the delta-M
c scaling
c
c GC(IQ,IQ,LC) Eigenvectors at polar quadrature angles,
c g in Eq. SC(1)
c
c GU(IU,IQ,LC) Eigenvectors interpolated to user polar angles
c ( g in Eqs. SC(3) and S1(8-9), i.e.
c G without the L factor )
c
c IPVT(LC*IQ) Integer vector of pivot indices for LINPACK
c routines
c
c KK(IQ,LC) Eigenvalues of coeff. matrix in Eq. SS(7)
c
c KCONV Counter in azimuth convergence test
c
c LAYRU(LU) Computational layer in which user output level
c UTAU(LU) is located
c
c LL(IQ,LC) Constants of integration L in Eq. SC(1),
c obtained by solving scaled version of Eq. SC(5)
c
c LYRCUT TRUE, radiation is assumed zero below layer
c NCUT because of almost complete absorption
c
c NAZ Number of azimuthal components considered
c
c NCUT Computational layer number in which absorption
c optical depth first exceeds ABSCUT
c
c OPRIM(LC) Single scattering albedo after delta-M scaling
c
c PASS1 TRUE on first entry, FALSE thereafter
c
c PKAG(0:LC) Integrated Planck function for internal emission
c
c PRNTU0(L) logical flag to trigger printing of azimuthally-
c averaged intensities:
c L quantities printed
c -- ------------------
c 1 azimuthally-averaged intensities at user
c levels and computational polar angles
c 2 azimuthally-averaged intensities at user
c levels and user polar angles
c
c PSI0(IQ) Sum just after square bracket in Eq. SD(9)
c
c PSI1(IQ) Sum in Eq. STWL(31d)
c
c RMU(IU,0:IQ) Bottom-boundary bidirectional reflectivity for a
c given azimuthal component. First index always
c refers to a user angle. Second index:
c if zero, refers to incident beam angle UMU0;
c if non-zero, refers to a computational angle.
c
c SQT(k) Square root of k (used only in LEPOLY for
c computing associated Legendre polynomials)
c
c TAUC(0:LC) Cumulative optical depth (un-delta-M-scaled)
c
c TAUCPR(0:LC) Cumulative optical depth (delta-M-scaled if
c DELTAM = TRUE, otherwise equal to TAUC)
c
c TPLANK Intensity emitted from top boundary
c
c UUM(IU,LU) Expansion coefficients when the intensity
c (u-super-M) is expanded in Fourier cosine series
c in azimuth angle
c
c U0C(IQ,LU) Azimuthally-averaged intensity at quadrature
c angle
c
c U0U(IU,LU) If ONLYFL = FALSE, azimuthally-averaged intensity
c at user angles and user levels
c
c If ONLYFL = TRUE and MAXUMU.GE.NSTR,
c azimuthally-averaged intensity at computational
c (Gaussian quadrature) angles and user levels;
c the corresponding quadrature angle cosines are
c returned in UMU. If MAXUMU.LT.NSTR, U0U will be
c zeroed, and UMU, NUMU will not be set.
c
c UTAUPR(LU) Optical depths of user output levels in delta-M
c coordinates; equal to UTAU(LU) if no delta-M
c
c WK() scratch array
c
c XR0(LC) X-sub-zero in expansion of thermal source func-
c tion preceding Eq. SS(14)(has no mu-dependence);
c b-sub-zero in Eq. STWL(24d)
c
c XR1(LC) X-sub-one in expansion of thermal source func-
c tion; see Eqs. SS(14-16); b-sub-one in STWL(24d)
c
c YLM0(L) Normalized associated Legendre polynomial
c of subscript L at the beam angle (not saved
c as function of superscipt M)
c
c YLMC(L,IQ) Normalized associated Legendre polynomial
c of subscript L at the computational angles
c (not saved as function of superscipt M)
c
c YLMU(L,IU) Normalized associated Legendre polynomial
c of subscript L at the user angles
c (not saved as function of superscipt M)
c
c Z() scratch array used in SOLVE0, ALBTRN to solve
c a linear system for the constants of integration
c
c Z0(IQ) Solution vectors Z-sub-zero of Eq. SS(16)
c
c Z0U(IU,LC) Z-sub-zero in Eq. SS(16) interpolated to user
c angles from an equation derived from SS(16)
c
c Z1(IQ) Solution vectors Z-sub-one of Eq. SS(16)
c
c Z1U(IU,LC) Z-sub-one in Eq. SS(16) interpolated to user
c angles from an equation derived from SS(16)
c
c ZBEAM(IU,LC) Particular solution for beam source
c
c ZJ(IQ) Right-hand side vector X-sub-zero in
c Eq. SS(19), also the solution vector
c Z-sub-zero after solving that system
c
c ZZ(IQ,LC) Permanent storage for the beam source vectors ZJ
c
c ZPLK0(IQ,LC) Permanent storage for the thermal source
c vectors Z0 obtained by solving Eq. SS(16)
c
c ZPLK1(IQ,LC) Permanent storage for the thermal source
c vectors Z1 obtained by solving Eq. SS(16)
c
c +-------------------------------------------------------------------+
c
c LOCAL SYMBOLIC DIMENSIONS (have big effect on storage requirements):
c
c MXCLY = Max no. of computational layers
c MXULV = Max no. of output levels
c MXCMU = Max no. of computation polar angles
c MXUMU = Max no. of output polar angles
c MXPHI = Max no. of output azimuthal angles
c MXSQT = Max no. of square roots of integers (for LEPOLY)
c +-------------------------------------------------------------------+
c .. Parameters ..
INTEGER MXCLY, MXULV, MXCMU, MXUMU, MXPHI, MI, MI9M2, NNLYRI,
& MXSQT
PARAMETER ( MXCLY = 131, MXULV = 1, MXCMU = 48, MXUMU = 16,
& MXPHI = 3, MI = MXCMU / 2, MI9M2 = 9*MI - 2,
& NNLYRI = MXCMU*MXCLY, MXSQT = 1000 )
c ..
c .. Scalar Arguments ..
CHARACTER HEADER*0
LOGICAL LAMBER, ONLYFL, PLANK, USRANG, USRTAU
INTEGER IBCND, MAXCLY, MAXMOM, MAXPHI, MAXULV, MAXUMU, NLYR,
& NMOM, NPHI, NSTR, NTAU, NUMU
REAL ACCUR, ALBEDO, BTEMP, FBEAM, FISOT, PHI0, TEMIS, TTEMP,
& UMU0, WVNMHI, WVNMLO
c ..
c .. Array Arguments ..
LOGICAL PRNT( 5 )
REAL ALBMED( MAXUMU ), DFDT( MAXULV ), DTAUC( MAXCLY ),
& FLUP( MAXULV ), PHI( MAXPHI ), PMOM( 0:MAXMOM, MAXCLY ),
& RFLDIR( MAXULV ), RFLDN( MAXULV ), SSALB( MAXCLY ),
& TEMPER( 0:MAXCLY ), TRNMED( MAXUMU ), UAVG( MAXULV ),
& UMU( MAXUMU ), UTAU( MAXULV ),
& UU( MAXUMU, MAXULV, MAXPHI )
c ..
c .. Local Scalars ..
LOGICAL COMPAR, CORINT, DELTAM, LYRCUT, PASS1
INTEGER IQ, IU, J, KCONV, L, LC, LEV, LU, MAZIM, NAZ, NCOL,
& NCOS, NCUT, NN, NS
REAL ANGCOS, AZERR, AZTERM, BPLANK, COSPHI, DELM0, DITHER,
& DUM, PI, RPD, SGN, TPLANK
c ..
c .. Local Arrays ..
LOGICAL PRNTU0( 2 )
INTEGER IPVT( NNLYRI ), LAYRU( MXULV )
REAL AMB( MI, MI ), APB( MI, MI ), ARRAY( MXCMU, MXCMU ),
& B( NNLYRI ), BDR( MI, 0:MI ), BEM( MI ),
& CBAND( MI9M2, NNLYRI ), CC( MXCMU, MXCMU ),
& CMU( MXCMU ), CWT( MXCMU ), DTAUCP( MXCLY ),
& EMU( MXUMU ), EVAL( MI ), EVECC( MXCMU, MXCMU ),
& EXPBEA( 0:MXCLY ), FLDIR( MXULV ), FLDN( MXULV ),
& FLYR( MXCLY ), GC( MXCMU, MXCMU, MXCLY ),
& GL( 0:MXCMU, MXCLY ), GU( MXUMU, MXCMU, MXCLY ),
& KK( MXCMU, MXCLY ), LL( MXCMU, MXCLY ), OPRIM( MXCLY ),
& PHASA( MXCLY ), PHAST( MXCLY ), PHASM( MXCLY ),
& PHIRAD( MXPHI ), PKAG( 0:MXCLY ), PSI0( MXCMU ),
& PSI1( MXCMU ), RMU( MXUMU, 0:MI ), SQT( MXSQT ),
& TAUC( 0:MXCLY ), TAUCPR( 0:MXCLY ), U0C( MXCMU, MXULV ),
& U0U( MXUMU, MXULV ), UTAUPR( MXULV ),
& UUM( MXUMU, MXULV ), WK( MXCMU ), XR0( MXCLY ),
& XR1( MXCLY ), YLM0( 0:MXCMU ), YLMC( 0:MXCMU, MXCMU ),
& YLMU( 0:MXCMU, MXUMU ), Z( NNLYRI ), Z0( MXCMU ),
& Z0U( MXUMU, MXCLY ), Z1( MXCMU ), Z1U( MXUMU, MXCLY ),
& ZBEAM( MXUMU, MXCLY )
REAL ZJ( MXCMU ), ZPLK0( MXCMU, MXCLY ),
& ZPLK1( MXCMU, MXCLY ), ZZ( MXCMU, MXCLY )
DOUBLE PRECISION AAD( MI, MI ), EVALD( MI ), EVECCD( MI, MI ),
& WKD( MXCMU )
c ..
c .. External Functions ..
REAL PLKAVG, D1MACH, RATIO
EXTERNAL PLKAVG, D1MACH, RATIO
c ..
c .. External Subroutines ..
EXTERNAL ALBTRN, CHEKIN, CMPINT, FLUXES, INTCOR, LEPOLY, PRAVIN,
& PRTINP, PRTINT, SETDIS, SETMTX, SLFTST, SOLEIG, SOLVE0,
& SURFAC, TERPEV, TERPSO, UPBEAM, UPISOT, USRINT, ZEROAL,
& ZEROIT
c ..
c .. Intrinsic Functions ..
INTRINSIC ABS, ASIN, COS, FLOAT, LEN, MAX, SQRT
c ..
SAVE DITHER, PASS1, PI, RPD, SQT
DATA PASS1 / .TRUE. /, PRNTU0 / 2*.FALSE. /
DELTAM = .TRUE.
CORINT = .FALSE.
IF( PASS1 ) THEN
PI = 2.*ASIN( 1.0 )
DITHER = 10.*D1MACH( 4 )
c ** Must dither more on high (14-digit)
c ** precision machine
IF( DITHER.LT.1.E-10 ) DITHER = 10.*DITHER
RPD = PI / 180.0
DO 10 NS = 1, MXSQT
SQT( NS ) = SQRT( FLOAT( NS ) )
10 CONTINUE
c ** Set input values for self-test.
c ** Be sure SLFTST sets all print flags off.
COMPAR = .FALSE.
c CALL SLFTST( CORINT, ACCUR, ALBEDO, BTEMP, DELTAM, DTAUC( 1 ),
c & FBEAM, FISOT, IBCND, LAMBER, NLYR, PLANK, NPHI,
c & NUMU, NSTR, NTAU, ONLYFL, PHI( 1 ), PHI0, NMOM,
c & PMOM( 0,1 ), PRNT, PRNTU0, SSALB( 1 ), TEMIS,
c & TEMPER( 0 ), TTEMP, UMU( 1 ), USRANG, USRTAU,
c & UTAU( 1 ), UMU0, WVNMHI, WVNMLO, COMPAR, DUM,
c & DUM, DUM, DUM )
END IF
20 CONTINUE
IF( .NOT.PASS1 .AND. LEN( HEADER ).NE.0 )
& WRITE( *,'(//,1X,100(''*''),/,A,/,1X,100(''*''))' )
& ' DISORT: '//HEADER
c ** Calculate cumulative optical depth
c ** and dither single-scatter albedo
c ** to improve numerical behavior of
c ** eigenvalue/vector computation
CALL ZEROIT( TAUC, MXCLY + 1 )
DO 30 LC = 1, NLYR
IF( SSALB( LC ).EQ.1.0 ) SSALB( LC ) = 1.0 - DITHER
TAUC( LC ) = TAUC( LC - 1 ) + DTAUC( LC )
30 CONTINUE
c ** Check input dimensions and variables
c CALL CHEKIN( NLYR, DTAUC, SSALB, NMOM, PMOM, TEMPER, WVNMLO,
c & WVNMHI, USRTAU, NTAU, UTAU, NSTR, USRANG,
c & NUMU, UMU, NPHI, PHI, IBCND, FBEAM, UMU0,
c & PHI0, FISOT, LAMBER, ALBEDO, BTEMP, TTEMP,
c & TEMIS, PLANK, ONLYFL, DELTAM, CORINT, ACCUR,
c & TAUC, MAXCLY, MAXULV, MAXUMU, MAXPHI, MAXMOM,
c & MXCLY, MXULV, MXUMU, MXCMU, MXPHI, MXSQT )
c ** Zero internal and output arrays
CALL ZEROAL( MXCLY, EXPBEA(1), FLYR, OPRIM, PHASA, PHAST, PHASM,
& TAUCPR(1), XR0, XR1,
& MXCMU, CMU, CWT, PSI0, PSI1, WK, Z0, Z1, ZJ,
& MXCMU+1, YLM0,
& MXCMU**2, ARRAY, CC, EVECC,
& (MXCMU+1)*MXCLY, GL,
& (MXCMU+1)*MXCMU, YLMC,
& (MXCMU+1)*MXUMU, YLMU,
& MXCMU*MXCLY, KK, LL, ZZ, ZPLK0, ZPLK1,
& MXCMU**2*MXCLY, GC,
& MXULV, LAYRU, UTAUPR,
& MXUMU*MXCMU*MXCLY, GU,
& MXUMU*MXCLY, Z0U, Z1U, ZBEAM,
& MI, EVAL,
& MI**2, AMB, APB,
& NNLYRI, IPVT, Z,
& MAXULV, RFLDIR, RFLDN, FLUP, UAVG, DFDT,
& MAXUMU, ALBMED, TRNMED,
& MXUMU*MXULV, U0U,
& MAXUMU*MAXULV*MAXPHI, UU )
c ** Perform various setup operations
CALL SETDIS( CMU, CWT, DELTAM, DTAUC, DTAUCP, EXPBEA, FBEAM, FLYR,
& GL, IBCND, LAYRU, LYRCUT, MAXMOM, MAXUMU, MXCMU,
& NCUT, NLYR, NTAU, NN, NSTR, PLANK, NUMU, ONLYFL,
& CORINT, OPRIM, PMOM, SSALB, TAUC, TAUCPR, UTAU,
& UTAUPR, UMU, UMU0, USRTAU, USRANG )
c ** Print input information
IF( PRNT( 1 ) )
& CALL PRTINP( NLYR, DTAUC, DTAUCP, SSALB, NMOM, PMOM, TEMPER,
& WVNMLO, WVNMHI, NTAU, UTAU, NSTR, NUMU, UMU,
& NPHI, PHI, IBCND, FBEAM, UMU0, PHI0, FISOT,
& LAMBER, ALBEDO, BTEMP, TTEMP, TEMIS, DELTAM,
& PLANK, ONLYFL, CORINT, ACCUR, FLYR, LYRCUT,
& OPRIM, TAUC, TAUCPR, MAXMOM, PRNT( 5 ) )
c ** Handle special case for getting albedo
c ** and transmissivity of medium for many
c ** beam angles at once
IF( IBCND.EQ.1 ) THEN
CALL ALBTRN( ALBEDO, AMB, APB, ARRAY, B, BDR, CBAND, CC, CMU,
& CWT, DTAUCP, EVAL, EVECC, GL, GC, GU, IPVT, KK,
& LL, NLYR, NN, NSTR, NUMU, PRNT, TAUCPR, UMU, U0U,
& WK, YLMC, YLMU, Z, AAD, EVALD, EVECCD, WKD, MI,
& MI9M2, MAXUMU, MXCMU, MXUMU, NNLYRI, SQT, ALBMED,
& TRNMED )
RETURN
END IF
c ** Calculate Planck functions
IF( .NOT.PLANK ) THEN
BPLANK = 0.0
TPLANK = 0.0
CALL ZEROIT( PKAG, MXCLY + 1 )
ELSE
TPLANK = TEMIS*PLKAVG( WVNMLO, WVNMHI, TTEMP )
BPLANK = PLKAVG( WVNMLO, WVNMHI, BTEMP )
DO 40 LEV = 0, NLYR
PKAG( LEV ) = PLKAVG( WVNMLO, WVNMHI, TEMPER( LEV ) )
40 CONTINUE
END IF
c ======== BEGIN LOOP TO SUM AZIMUTHAL COMPONENTS OF INTENSITY =======
c (EQ STWJ 5, STWL 6)
KCONV = 0
NAZ = NSTR - 1
c ** Azimuth-independent case
IF( FBEAM.EQ.0.0 .OR. ABS(1.-UMU0).LT.1.E-5 .OR. ONLYFL .OR.
& ( NUMU.EQ.1 .AND. ABS(1.-UMU(1)).LT.1.E-5 ) .OR.
& ( NUMU.EQ.1 .AND. ABS(1.+UMU(1)).LT.1.E-5 ) .OR.
& ( NUMU.EQ.2 .AND. ABS(1.+UMU(1)).LT.1.E-5 .AND.
& ABS(1.-UMU(2)).LT.1.E-5 ) )
& NAZ = 0
DO 180 MAZIM = 0, NAZ
IF( MAZIM.EQ.0 ) DELM0 = 1.0
IF( MAZIM.GT.0 ) DELM0 = 0.0
c ** Get normalized associated Legendre
c ** polynomials for
c ** (a) incident beam angle cosine
c ** (b) computational and user polar angle
c ** cosines
IF( FBEAM.GT.0.0 ) THEN
NCOS = 1
ANGCOS = -UMU0
CALL LEPOLY( NCOS, MAZIM, MXCMU, NSTR-1, ANGCOS, SQT, YLM0 )
END IF
IF( .NOT.ONLYFL .AND. USRANG )
& CALL LEPOLY( NUMU, MAZIM, MXCMU, NSTR-1, UMU, SQT, YLMU )
CALL LEPOLY( NN, MAZIM, MXCMU, NSTR-1, CMU, SQT, YLMC )
c ** Get normalized associated Legendre polys.
c ** with negative arguments from those with
c ** positive arguments; Dave/Armstrong Eq. (15),
c ** STWL(59)
SGN = -1.0
DO 70 L = MAZIM, NSTR - 1
SGN = -SGN
DO 60 IQ = NN + 1, NSTR
YLMC( L, IQ ) = SGN*YLMC( L, IQ - NN )
60 CONTINUE
70 CONTINUE
c ** Specify users bottom reflectivity
c ** and emissivity properties
IF( .NOT.LYRCUT )
& CALL SURFAC( ALBEDO, DELM0, CMU, FBEAM, LAMBER, MI, MAZIM,
& MXUMU, NN, NUMU, ONLYFL, PI, UMU, UMU0,
& USRANG, WVNMLO, WVNMHI, BDR, EMU, BEM, RMU )
c =================== BEGIN LOOP ON COMPUTATIONAL LAYERS =============
DO 80 LC = 1, NCUT
c ** Solve eigenfunction problem in Eq. STWJ(8B),
c ** STWL(23f); return eigenvalues and eigenvectors
CALL SOLEIG( AMB, APB, ARRAY, CMU, CWT, GL( 0,LC ), MI,
& MAZIM, MXCMU, NN, NSTR, YLMC, CC, EVECC, EVAL,
& KK( 1,LC ), GC( 1,1,LC ), AAD, EVECCD, EVALD,
& WKD )
c ** Calculate particular solutions of
c ** Eq. SS(18), STWL(24a) for incident
c ** beam source
IF( FBEAM.GT.0.0 )
& CALL UPBEAM( ARRAY, CC, CMU, DELM0, FBEAM, GL( 0,LC ),
& IPVT, MAZIM, MXCMU, NN, NSTR, PI, UMU0, WK,
& YLM0, YLMC, ZJ, ZZ( 1,LC ) )
c ** Calculate particular solutions of Eq.
c ** SS(15), STWL(25) for thermal emission
c ** source
c
IF( PLANK .AND. MAZIM.EQ.0 ) THEN
XR1( LC ) = 0.0
IF( DTAUCP( LC ).GT.0.0 ) XR1( LC ) =
& ( PKAG( LC ) - PKAG( LC-1 ) ) / DTAUCP( LC )
XR0( LC ) = PKAG( LC-1 ) - XR1( LC )*TAUCPR( LC-1 )
CALL UPISOT( ARRAY, CC, CMU, IPVT, MXCMU, NN, NSTR,
& OPRIM( LC ), WK, XR0( LC ), XR1( LC ),
& Z0, Z1, ZPLK0( 1,LC ), ZPLK1( 1,LC ) )
END IF
IF( .NOT.ONLYFL .AND. USRANG ) THEN
c ** Interpolate eigenvectors
c ** to user angles
CALL TERPEV( CWT, EVECC, GL( 0,LC ), GU( 1,1,LC ), MAZIM,
& MXCMU, MXUMU, NN, NSTR, NUMU, WK, YLMC,
& YLMU )
c ** Interpolate source terms
c ** to user angles
CALL TERPSO( CWT, DELM0, FBEAM, GL( 0,LC ), MAZIM, MXCMU,
& PLANK, NUMU, NSTR, OPRIM( LC ), PI, YLM0,
& YLMC, YLMU, PSI0, PSI1, XR0( LC ),
& XR1( LC ), Z0, Z1, ZJ, ZBEAM( 1,LC ),
& Z0U( 1,LC ), Z1U( 1,LC ) )
END IF
80 CONTINUE
c =================== END LOOP ON COMPUTATIONAL LAYERS ===============
c ** Set coefficient matrix of equations combining
c ** boundary and layer interface conditions
CALL SETMTX( BDR, CBAND, CMU, CWT, DELM0, DTAUCP, GC, KK,
& LAMBER, LYRCUT, MI, MI9M2, MXCMU, NCOL, NCUT,
& NNLYRI, NN, NSTR, TAUCPR, WK )
c ** Solve for constants of integration in homo-
c ** geneous solution (general boundary conditions)
CALL SOLVE0( B, BDR, BEM, BPLANK, CBAND, CMU, CWT, EXPBEA,
& FBEAM, FISOT, IPVT, LAMBER, LL, LYRCUT, MAZIM, MI,
& MI9M2, MXCMU, NCOL, NCUT, NN, NSTR, NNLYRI, PI,
& TPLANK, TAUCPR, UMU0, Z, ZZ, ZPLK0, ZPLK1 )
c ** Compute upward and downward fluxes
IF( MAZIM.EQ.0 )
& CALL FLUXES( CMU, CWT, FBEAM, GC, KK, LAYRU, LL, LYRCUT,
& MAXULV, MXCMU, MXULV, NCUT, NN, NSTR, NTAU,
& PI, PRNT, PRNTU0( 1 ), SSALB, TAUCPR, UMU0,
& UTAU, UTAUPR, XR0, XR1, ZZ, ZPLK0, ZPLK1,
& DFDT, FLUP, FLDN, FLDIR, RFLDIR, RFLDN, UAVG,
& U0C )
IF( ONLYFL ) THEN
IF( MAXUMU.GE.NSTR ) THEN
c ** Save azimuthal-avg intensities
c ** at quadrature angles
DO 100 LU = 1, NTAU
DO 90 IQ = 1, NSTR
U0U( IQ, LU ) = U0C( IQ, LU )
90 CONTINUE
100 CONTINUE
END IF
GO TO 190
END IF
CALL ZEROIT( UUM, MXUMU*MXULV )
IF( USRANG ) THEN
c ** Compute azimuthal intensity
c ** components at user angles
CALL USRINT( BPLANK, CMU, CWT, DELM0, DTAUCP, EMU, EXPBEA,
& FBEAM, FISOT, GC, GU, KK, LAMBER, LAYRU, LL,
& LYRCUT, MAZIM, MXCMU, MXULV, MXUMU, NCUT, NLYR,
& NN, NSTR, PLANK, NUMU, NTAU, PI, RMU, TAUCPR,
& TPLANK, UMU, UMU0, UTAUPR, WK, ZBEAM, Z0U, Z1U,
& ZZ, ZPLK0, ZPLK1, UUM )
ELSE
c ** Compute azimuthal intensity
c ** components at quadrature angles
CALL CMPINT( FBEAM, GC, KK, LAYRU, LL, LYRCUT, MAZIM, MXCMU,
& MXULV, MXUMU, NCUT, NN, NSTR, PLANK, NTAU,
& TAUCPR, UMU0, UTAUPR, ZZ, ZPLK0, ZPLK1, UUM )
END IF
IF( MAZIM.EQ.0 ) THEN
c ** Save azimuthally averaged intensities
DO 130 LU = 1, NTAU
DO 120 IU = 1, NUMU
U0U( IU, LU ) = UUM( IU, LU )
DO 110 J = 1, NPHI
UU( IU, LU, J ) = UUM( IU, LU )
110 CONTINUE
120 CONTINUE
130 CONTINUE
c ** Print azimuthally averaged intensities
c ** at user angles
IF( PRNTU0( 2 ) )
& CALL PRAVIN( UMU, NUMU, MXUMU, UTAU, NTAU, U0U )
IF( NAZ.GT.0 ) THEN
CALL ZEROIT( PHIRAD, MXPHI )
DO 140 J = 1, NPHI
PHIRAD( J ) = RPD*( PHI( J ) - PHI0 )
140 CONTINUE
END IF
ELSE
c ** Increment intensity by current
c ** azimuthal component (Fourier
c ** cosine series); Eq SD(2), STWL(6)
AZERR = 0.0
DO 170 J = 1, NPHI
COSPHI = COS( MAZIM*PHIRAD( J ) )
DO 160 LU = 1, NTAU
DO 150 IU = 1, NUMU
AZTERM = UUM( IU, LU )*COSPHI
UU( IU, LU, J ) = UU( IU, LU, J ) + AZTERM
AZERR = MAX( AZERR,
& RATIO( ABS(AZTERM), ABS(UU(IU,LU,J)) ) )
150 CONTINUE
160 CONTINUE
170 CONTINUE
IF( AZERR.LE.ACCUR ) KCONV = KCONV + 1
IF( KCONV.GE.2 ) GO TO 190
END IF
180 CONTINUE
c =================== END LOOP ON AZIMUTHAL COMPONENTS ===============
190 CONTINUE
c ** Apply Nakajima/Tanaka intensity
c ** corrections
IF( CORINT )
& CALL INTCOR( DITHER, FBEAM, FLYR, LAYRU, LYRCUT, MAXMOM,
& MAXULV, MAXUMU, NMOM, NCUT, NPHI, NSTR, NTAU,
& NUMU, OPRIM, PHASA, PHAST, PHASM, PHIRAD, PI,
& RPD, PMOM, SSALB, DTAUC, TAUC, TAUCPR, UMU,
& UMU0, UTAU, UTAUPR, UU )
c ** Print intensities
IF( PRNT( 3 ) .AND. .NOT.ONLYFL )
& CALL PRTINT( UU, UTAU, NTAU, UMU, NUMU, PHI, NPHI, MAXULV,
& MAXUMU )
IF( PASS1 ) THEN
c ** Compare test case results with
c ** correct answers and abort if bad
COMPAR = .TRUE.
c CALL SLFTST( CORINT, ACCUR, ALBEDO, BTEMP, DELTAM, DTAUC( 1 ),
c & FBEAM, FISOT, IBCND, LAMBER, NLYR, PLANK, NPHI,
c & NUMU, NSTR, NTAU, ONLYFL, PHI( 1 ), PHI0, NMOM,
c & PMOM( 0,1 ), PRNT, PRNTU0, SSALB( 1 ), TEMIS,
c & TEMPER( 0 ), TTEMP, UMU( 1 ), USRANG, USRTAU,
c & UTAU( 1 ), UMU0, WVNMHI, WVNMLO, COMPAR,
c & FLUP( 1 ), RFLDIR( 1 ), RFLDN( 1 ), UU( 1,1,1 ) )
PASS1 = .FALSE.
GO TO 20
END IF
RETURN
END
SUBROUTINE ASYMTX( AA, EVEC, EVAL, M, IA, IEVEC, IER, WKD, AAD,
& EVECD, EVALD )
c ======= D O U B L E P R E C I S I O N V E R S I O N ======
c Solves eigenfunction problem for real asymmetric matrix
c for which it is known a priori that the eigenvalues are real.
c This is an adaptation of a subroutine EIGRF in the IMSL
c library to use real instead of complex arithmetic, accounting
c for the known fact that the eigenvalues and eigenvectors in
c the discrete ordinate solution are real. Other changes include
c putting all the called subroutines in-line, deleting the
c performance index calculation, updating many DO-loops
c to Fortran77, and in calculating the machine precision
c TOL instead of specifying it in a data statement.
c EIGRF is based primarily on EISPACK routines. The matrix is
c first balanced using the Parlett-Reinsch algorithm. Then
c the Martin-Wilkinson algorithm is applied.
c There is a statement 'J = WKD( I )' that converts a double
c precision variable to an integer variable, that seems dangerous
c to us in principle, but seems to work fine in practice.
c References:
c Dongarra, J. and C. Moler, EISPACK -- A Package for Solving
c Matrix Eigenvalue Problems, in Cowell, ed., 1984:
c Sources and Development of Mathematical Software,
c Prentice-Hall, Englewood Cliffs, NJ
c Parlett and Reinsch, 1969: Balancing a Matrix for Calculation
c of Eigenvalues and Eigenvectors, Num. Math. 13, 293-304
c Wilkinson, J., 1965: The Algebraic Eigenvalue Problem,
c Clarendon Press, Oxford
c I N P U T V A R I A B L E S:
c
c AA : input asymmetric matrix, destroyed after solved
c
c M : order of AA
c
c IA : first dimension of AA
c
c IEVEC : first dimension of EVEC
c
c
c O U T P U T V A R I A B L E S:
c
c EVEC : (unnormalized) eigenvectors of AA
c ( column J corresponds to EVAL(J) )
c
c EVAL : (unordered) eigenvalues of AA ( dimension at least M )
c
c IER : if .NE. 0, signals that EVAL(IER) failed to converge;
c in that case eigenvalues IER+1,IER+2,...,M are
c correct but eigenvalues 1,...,IER are set to zero.
c
c
c S C R A T C H V A R I A B L E S:
c
c WKD : work area ( dimension at least 2*M )
c AAD : double precision stand-in for AA
c EVECD : double precision stand-in for EVEC
c EVALD : double precision stand-in for EVAL
c
c Called by- SOLEIG
c Calls- D1MACH, ERRMSG
c +-------------------------------------------------------------------+
c .. Scalar Arguments ..
INTEGER IA, IER, IEVEC, M
c ..
c .. Array Arguments ..
REAL AA( IA, M ), EVAL( M ), EVEC( IEVEC, M )
DOUBLE PRECISION AAD( IA, M ), EVALD( M ), EVECD( IA, M ),
& WKD( * )
c ..
c .. Local Scalars ..
LOGICAL NOCONV, NOTLAS
INTEGER I, II, IN, J, K, KA, KKK, L, LB, LLL, N, N1, N2
DOUBLE PRECISION C1, C2, C3, C4, C5, C6, COL, DISCRI, F, G, H,
& ONE, P, Q, R, REPL, RNORM, ROW, S, SCALE, SGN, T,
& TOL, UU, VV, W, X, Y, Z, ZERO
c ..
c .. External Functions ..
DOUBLE PRECISION D1MACH
EXTERNAL D1MACH
c ..
c .. External Subroutines ..
EXTERNAL ERRMSG
c ..
c .. Intrinsic Functions ..
INTRINSIC ABS, MIN, SIGN, SQRT
c ..
DATA C1 / 0.4375D0 / , C2 / 0.5D0 / , C3 / 0.75D0 / ,
& C4 / 0.95D0 / , C5 / 16.D0 / , C6 / 256.D0 / ,
& ZERO / 0.D0 / , ONE / 1.D0 /
IER = 0
TOL = D1MACH( 4 )
IF( M.LT.1 .OR. IA.LT.M .OR. IEVEC.LT.M )
& CALL ERRMSG( 'ASYMTX--bad input variable(s)', .TRUE. )
c ** Handle 1x1 and 2x2 special cases
IF( M.EQ.1 ) THEN
EVAL( 1 ) = AA( 1,1 )
EVEC( 1,1 ) = 1.0
RETURN
ELSE IF( M.EQ.2 ) THEN
DISCRI = ( AA( 1,1 ) - AA( 2,2 ) )**2 + 4.*AA( 1,2 )*AA( 2,1 )
IF( DISCRI .LT. 0.0 )
& CALL ERRMSG( 'ASYMTX--complex evals in 2x2 case',.TRUE. )
SGN = ONE