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wwm_ardhuin_new.F90
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wwm_ardhuin_new.F90
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#include "wwm_functions.h"
!/ ------------------------------------------------------------------- /
MODULE W3SRC4MD
!/
!/ +-----------------------------------+
!/ | WAVEWATCH III SHOM |
!/ ! F. Ardhuin !
!/ | FORTRAN 90 |
!/ | Last update : 13-Nov-2013 |
!/ +-----------------------------------+
!/
!/ 30-Aug-2010 : Origination. ( version 3.14-Ifremer )
!/ 02-Nov-2010 : Addding fudge factor for low freq. ( version 4.03 )
!/ 02-Sep-2011 : Clean up and time optimization ( version 4.04 )
!/ 04-Sep-2011 : Estimation of whitecap stats. ( version 4.04 )
!/
! 1. Purpose :
!
! The 'SHOM/Ifremer' source terms based on P.A.E.M. Janssen's wind input
! and dissipation functions by Ardhuin et al. (2009,2010)
! and Filipot & Ardhuin (2010)
! The wind input is converted from the original
! WAM codes, courtesy of P.A.E.M. Janssen and J. Bidlot
!
!
! 2. Variables and types :
!
! Name Type Scope Description
! ----------------------------------------------------------------
! ----------------------------------------------------------------
!
! 3. Subroutines and functions :
!
! Name Type Scope Description
! ----------------------------------------------------------------
! W3SPR4 Subr. Public Mean parameters from spectrum.
! W3SIN4 Subr. Public WAM4+ input source term.
! INSIN4 Subr. Public Corresponding initialization routine.
! TABU_STRESS, TABU_TAUHF, TABU_TAUHF2
! Subr. Public Populate various tables.
! CALC_USTAR
! Subr. Public Compute stresses.
! W3SDS4 Subr. Public Dissipation (Ardhuin & al. / Filipot & Ardhuin)
! ----------------------------------------------------------------
!
! 4. Subroutines and functions used :
!
! Name Type Module Description
! ----------------------------------------------------------------
! ----------------------------------------------------------------
!
! 5. Remarks :
!
! 6. Switches :
!
! 7. Source code :
!/
!/ ------------------------------------------------------------------- /
!/
USE DATAPOOL, ONLY : rkind
SAVE
PUBLIC
!/
!/ Public variables
!/
INTEGER, PARAMETER :: NHMAX = 25
INTEGER(KIND=4) :: NH(3), THO(2,3,NHMAX)
REAL(rkind) :: HA(NHMAX,3), HD(NHMAX,3), HA2(NHMAX,3)
REAL(rkind), PARAMETER :: kappa = 0.40 !Von Karman's constant
!air kinematic viscosity (used in WAM)
REAL(rkind), PARAMETER :: nu_air = 1.4E-5
INTEGER, PARAMETER :: ITAUMAX=200,JUMAX=200
INTEGER, PARAMETER :: IUSTAR=100,IALPHA=200, ILEVTAIL=50
INTEGER, PARAMETER :: SIZEFWTABLE=300
INTEGER, PARAMETER :: IAB=200
REAL(rkind) :: TAUT(0:ITAUMAX,0:JUMAX), DELTAUW, DELU
! Table for H.F. stress as a function of 2 variables
REAL(rkind) :: TAUHFT(0:IUSTAR,0:IALPHA), DELUST, DELALP
! Table for H.F. stress as a function of 3 variables
REAL(rkind) :: TAUHFT2(0:IUSTAR,0:IALPHA,0:ILEVTAIL)
! Table for swell damping
REAL(rkind) :: SWELLFT(0:IAB)
REAL(rkind) :: DELTAIL
REAL(rkind) :: DELAB
REAL(rkind), PARAMETER :: UMAX = 50._rkind
REAL(rkind), PARAMETER :: TAUWMAX = 2.2361 !SQRT(5.)
REAL(rkind), PARAMETER :: ABMIN = 0.3_rkind
REAL(rkind), PARAMETER :: ABMAX = 8._rkind
REAL(rkind) :: FWTABLE(0:SIZEFWTABLE)
REAL(rkind), ALLOCATABLE :: XSTRESS(:),YSTRESS(:)
REAL(rkind), ALLOCATABLE :: DCKI(:,:), SATWEIGHTS(:,:)
REAL(rkind), ALLOCATABLE :: CUMULW(:,:),QBI(:,:)
INTEGER :: DIKCUMUL
! table and variable for wave breaking dissipation term
INTEGER, PARAMETER :: NDTAB=2000 ! Max depth: convolution calculation in W3SDS4
INTEGER, PARAMETER :: NKHS=2000, NKD=1300, NKHI=100
REAL(rkind), PARAMETER :: PI=3.14157, G=9.81
REAL(rkind), PARAMETER :: FAC_KD1=1.01, FAC_KD2=1000._rkind
REAL(rkind), PARAMETER :: KHSMAX=2., KHMAX=2.
REAL(rkind), PARAMETER ::KDMAX=200000._rkind
! variables for negative wind input (beta from ST2)
!
INTEGER, PARAMETER, PRIVATE :: NRSIGA = 400
INTEGER, PARAMETER, PRIVATE :: NRDRAG = 20
REAL(rkind), PARAMETER, PRIVATE :: SIGAMX = 40._rkind
REAL(rkind), PARAMETER, PRIVATE :: DRAGMX = 1.E-2
!
REAL(rkind), PRIVATE :: DSIGA, DDRAG, &
& BETATB(-NRSIGA:NRSIGA+1,NRDRAG+1)
!/
LOGICAL, PRIVATE :: FIRST = .TRUE.
!
! WWM FIELD INSERT ...
!
LOGICAL :: FLICES = .FALSE.
REAL(rkind) :: TTAUWSHELTER = 1.
REAL(rkind) :: ZZ0RAT = 0.04_rkind
REAL(rkind) :: SSINTHP = 2.
INTEGER :: NK, MK, NTH, MTH, MSPEC
INTEGER, ALLOCATABLE :: IKTAB(:,:)
INTEGER, ALLOCATABLE :: SATINDICES(:,:)
LOGICAL, ALLOCATABLE :: LLWS(:)
REAL(rkind) :: SSDSC(1:9)
REAL(rkind), ALLOCATABLE :: SIG(:), SIG2(:), DDEN(:)
REAL(rkind), ALLOCATABLE :: DDEN2(:), DSII(:)
REAL(rkind), ALLOCATABLE :: DSIP(:), TH(:), ESIN(:)
REAL(rkind), ALLOCATABLE :: ECOS(:), EC2(:), ES2(:), ESC(:)
REAL(rkind) :: ZZWND, AALPHA, BBETA, ZZALP
REAL(rkind) :: DTH, FACHF, SXFR, XFR, FACHFE
REAL(rkind) :: WNMEANP, WNMEANPTAIL
REAL(rkind) :: FTE, FTF
REAL(rkind) :: STXFTF, STXFTWN, STXFTFTAIL
REAL(rkind) :: SSTXFTF, SSTXFTWN, SSTXFTFTAIL
REAL(rkind) :: SSWELLF(7) ,SSWELLFPAR
REAL(rkind) :: SWELLFPAR, SSDSTH
REAL(rkind) :: SSDSDTH, SSDSCOS, SSDSHCK
INTEGER :: SDSNTH ! This is wrongly globally defined ...
REAL(rkind) :: SSDSBCK, SSDSBINT, SSDSPBK, SSDSABK
REAL(rkind) :: SSDSC1, SSDSC2, SSDSC3, SSDSC4
REAL(rkind) :: SSDSC5, SSDSC6, SSDSCUM
REAL(rkind) :: SSDSBR, SSDSBRF1, SSDSBRF2
REAL(rkind) :: SSDSBR2, WHITECAPWIDTH
REAL(rkind) :: SSDSP
INTEGER :: SSDSISO, SSDSBRFDF
REAL(rkind) :: SSDSBM(0:4)
REAL(rkind) :: ZZ0MAX
LOGICAL :: LFIRSTSOURCE = .TRUE.
!/
CONTAINS
!/ ------------------------------------------------------------------- /
SUBROUTINE PREPARE_ARDHUIN
USE DATAPOOL
IMPLICIT NONE
INTEGER :: IK, ISP, ITH, ITH0
REAL(rkind) :: SIGMA, FR1, RTH0
NK = MSC
MK = NK ! ?
NTH = MDC
MTH = NTH ! ?
MSPEC = NSPEC
ALLOCATE(SIG(0:MSC+1), SIG2(NSPEC), DSIP(0:MSC+1), TH(MDC), stat=istat)
IF (istat/=0) CALL WWM_ABORT('wwm_ardhuin_new, allocate error 1')
SIG = ZERO
SIG2 = ZERO
DSIP = ZERO
TH = ZERO
ALLOCATE(ESIN(MSPEC+MTH), ECOS(MSPEC+MTH), EC2(MSPEC+MTH), stat=istat)
IF (istat/=0) CALL WWM_ABORT('wwm_ardhuin_new, allocate error 2')
ESIN = ZERO
ECOS = ZERO
EC2 = ZERO
ALLOCATE(ES2(MSPEC+MTH),ESC(MSPEC+MTH), stat=istat)
IF (istat/=0) CALL WWM_ABORT('wwm_ardhuin_new, allocate error 3')
ES2 = ZERO
ESC = ZERO
ALLOCATE(DSII(MSC), DDEN(MSC), DDEN2(NSPEC), stat=istat)
IF (istat/=0) CALL WWM_ABORT('wwm_ardhuin_new, allocate error 4')
DSII = ZERO
DDEN = ZERO
DDEN2 = ZERO
DTH = DDIR
FR1 = SPSIG(1)/PI2
TH = SPDIR
RTH0 = ZERO
DO ITH=1, NTH
TH (ITH) = DTH * ( RTH0 + MyREAL(ITH-1) )
ESIN(ITH) = SIN ( TH(ITH) )
ECOS(ITH) = COS ( TH(ITH) )
IF ( ABS(ESIN(ITH)) .LT. 1.E-5 ) THEN
ESIN(ITH) = ZERO
IF ( ECOS(ITH) .GT. 0.5_rkind ) THEN
ECOS(ITH) = 1._rkind
ELSE
ECOS(ITH) = -1._rkind
END IF
END IF
IF ( ABS(ECOS(ITH)) .LT. 1.E-5 ) THEN
ECOS(ITH) = ZERO
IF ( ESIN(ITH) .GT. 0.5_rkind ) THEN
ESIN(ITH) = 1.
ELSE
ESIN(ITH) = -1.
END IF
END IF
ES2 (ITH) = ESIN(ITH)**2
EC2 (ITH) = ECOS(ITH)**2
ESC (ITH) = ESIN(ITH)*ECOS(ITH)
END DO
!
DO IK=2, NK+1
ITH0 = (IK-1)*NTH
DO ITH=1, NTH
ESIN(ITH0+ITH) = ESIN(ITH)
ECOS(ITH0+ITH) = ECOS(ITH)
ES2 (ITH0+ITH) = ES2 (ITH)
EC2 (ITH0+ITH) = EC2 (ITH)
ESC (ITH0+ITH) = ESC (ITH)
END DO
END DO
! WRITE(5001,*) 'DTH'
! WRITE(5001,*) DTH
! WRITE(5001,*) 'FR1'
! WRITE(5001,*) FR1
! WRITE(5001,*) 'TH'
! WRITE(5001,*) TH
! WRITE(5001,*) 'ESIN, ECOS, EC2'
! WRITE(5001,*) ESIN, ECOS, EC2
WNMEANP = 0.5_rkind
WNMEANPTAIL = -0.5_rkind
! WRITE(5001,*) 'WNMEANP, WNMEANPTAIL'
! WRITE(5001,*) WNMEANP, WNMEANPTAIL
XFR = EXP(FRINTF) ! Check with Fabrice ... should be 1.1
SIGMA = FR1 * TPI / XFR**2 ! What is going on here ?
SXFR = 0.5_rkind * (XFR-1./XFR)
! WRITE(5001,*) 'XFR, SIGMA, SXFR'
! WRITE(5001,*) XFR, SIGMA, SXFR
DO IK=0, NK+1
SIGMA = SIGMA * XFR ! What is going on here ...
SIG (IK) = SIGMA
DSIP(IK) = SIGMA * SXFR
END DO
! WRITE(5001,*) 'SIGMA'
! WRITE(5001,*) SIGMA
! WRITE(5001,*) 'SIG'
! WRITE(5001,*) SIG
! WRITE(5001,*) 'DSIP'
! WRITE(5001,*) DSIP
DSII(1) = 0.5_rkind * SIG( 1) * (XFR-1.)
DO IK = 2, NK - 1
DSII(IK) = DSIP(IK)
END DO
DSII(NK) = 0.5_rkind * SIG(NK) * (XFR-1.) / XFR
DO IK=1, NK
DDEN(IK) = DTH * DSII(IK) * SIG(IK)
END DO
DO ISP=1, NSPEC
IK = 1 + (ISP-1)/NTH
SIG2 (ISP) = SIG (IK)
DDEN2(ISP) = DDEN(IK)
END DO
! WRITE(5001,*) 'SIG2'
! WRITE(5001,*) SIG2
! WRITE(5001,*) 'DSII'
! WRITE(5001,*) DSII
! WRITE(5001,*) 'DDEN'
! WRITE(5001,*) DDEN
! WRITE(5001,*) 'DDEN2'
! WRITE(5001,*) DDEN2
FTE = 0.25_rkind * SIG(NK) * DTH * SIG(NK)
FTF = 0.20_rkind * DTH * SIG(NK)
FACHF = 5.
FACHFE = XFR**(-FACHF)
STXFTFTAIL = 1./(FACHF-1.-WNMEANPTAIL*2)
STXFTF = 1./(FACHF-1.-WNMEANP*2)
STXFTWN = 1./(FACHF-1.-WNMEANP*2) * SIG(NK)**(2)
! WRITE(5001,*) 'FTE, FTF, FACHF, FACHFE'
! WRITE(5001,*) FTE, FTF, FACHF, FACHFE
SSWELLF(1) = 0.8_rkind
SSWELLF(2) = -0.018_rkind
SSWELLF(3) = 0.015_rkind
SSWELLF(4) = 1.E5
SSWELLF(5) = 1.2
SSWELLF(6) = 0._rkind
SSWELLF(7) = 0._rkind
! WRITE(5001,*) 'SSWELLF'
! WRITE(5001,*) SSWELLF
AALPHA = 0.0095_rkind
BBETA = 1.54_rkind ! 1.54 for ECMWF
ZZALP = 0.006_rkind
ZZWND = 10._rkind
SWELLFPAR = 1
SSDSBRF1 = 0.5_rkind
SSDSHCK = 1._rkind
SSDSBCK = 0._rkind
SSDSBINT = 0.3_rkind
SSDSPBK = 4._rkind
SSDSABK = 1.5_rkind
SSDSBR = 9.E-4_rkind
SSDSBRFDF = 0
SSDSBRF1 = 0.5_rkind
SSDSBRF2 = 0._rkind
SSDSBR2 = 0.8_rkind
SSDSP = 2.
SSDSPBK = 4.
SSDSISO = 2
SSDSBM(0) = 1.
SSDSBM(1) = 02428._rkind
SSDSBM(2) = 1.995_rkind
SSDSBM(3) = -2.5709_rkind
SSDSBM(4) = 1.3286_rkind
ZZ0MAX = 0.002_rkind
SSINTHP = 2.0_rkind
SSWELLFPAR = 3
TTAUWSHELTER = 1.0_rkind
ZZ0RAT = 0.04_rkind
SSDSC1 = 0._rkind
SSDSC2 = -2.2E-5_rkind ! AR: was originally 2.2
!SSDSC3 = -0.80_rkind ! overwritten by SSDSCUM
SSDSC4 = 1._rkind
SSDSC5 = 0._rkind
SSDSC6 = 0.30_rkind
WHITECAPWIDTH = 0.8_rkind
SSDSCUM = -0.40344_rkind
SSDSDTH = 80._rkind ! not used ...
SSDSCOS = 2._rkind
SSDSISO = 2 !AR: changes to isotropic breaking ...
SSDSC(1) = SSDSC1
SSDSC(2) = SSDSC2
SSDSC(3) = SSDSCUM
SSDSC(4) = SSDSC4
SSDSC(5) = SSDSC5
SSDSC(6) = SSDSC6
SSDSC(7) = WHITECAPWIDTH
SDSNTH = MIN(NINT(SSDSDTH/(DTH*RADDEG)),NTH/2-1)
DELAB = (ABMAX-ABMIN)/MyREAL(SIZEFWTABLE)
ALLOCATE(IKTAB(MK,NDTAB), stat=istat)
IF (istat/=0) CALL WWM_ABORT('wwm_ardhuin_new, allocate error 5')
IKTAB = 0
ALLOCATE(SATINDICES(2*SDSNTH+1,MTH), stat=istat)
IF (istat/=0) CALL WWM_ABORT('wwm_ardhuin_new, allocate error 6')
SATINDICES = 0
ALLOCATE(SATWEIGHTS(2*SDSNTH+1,MTH), stat=istat)
IF (istat/=0) CALL WWM_ABORT('wwm_ardhuin_new, allocate error 7')
SATWEIGHTS = 0._rkind
ALLOCATE(CUMULW(MK*MTH,MK*MTH), stat=istat)
IF (istat/=0) CALL WWM_ABORT('wwm_ardhuin_new, allocate error 8')
CUMULW = 0._rkind
ALLOCATE(DCKI(NKHS,NKD), stat=istat)
IF (istat/=0) CALL WWM_ABORT('wwm_ardhuin_new, allocate error 9')
DCKI = 0._rkind
ALLOCATE(LLWS(NSPEC), stat=istat)
IF (istat/=0) CALL WWM_ABORT('wwm_ardhuin_new, allocate error 10')
LLWS = .FALSE.
ALLOCATE(QBI(NKHS,NKD), stat=istat)
IF (istat/=0) CALL WWM_ABORT('wwm_ardhuin_new, allocate error 11')
QBI = 0._rkind
TAUWX = ZERO; TAUWY = ZERO; CD = ZERO; Z0 = ZERO; USTDIR = ZERO
INQUIRE(FILE='fort.5002',EXIST=LPRECOMP_EXIST)
IF (.NOT. LPRECOMP_EXIST) THEN
CALL INSIN4(.TRUE.)
ELSE
CALL READ_INSIN4
END IF
END SUBROUTINE
!**********************************************************************
!* *
!**********************************************************************
SUBROUTINE READ_INSIN4
USE DATAPOOL, ONLY : LPRECOMP_EXIST, DBG, MSC, MDC
IMPLICIT NONE
INTEGER :: MSC_TEST, MDC_TEST, ISTAT
IF (LPRECOMP_EXIST) THEN
READ (5002, IOSTAT=ISTAT) &
& MSC_TEST, MDC_TEST, &
& ZZWND, AALPHA, ZZ0MAX, BBETA, SSINTHP, ZZALP, &
& TTAUWSHELTER, SSWELLFPAR, SSWELLF, &
& ZZ0RAT, SSDSC1, SSDSC2, SSDSC3, SSDSC4, SSDSC5, &
& SSDSC6, SSDSISO, SSDSBR, SSDSBR2, SSDSBM, SSDSP, &
& SSDSCOS, SSDSDTH, SSTXFTF, &
& SSTXFTFTAIL, SSTXFTWN, SSTXFTF, SSTXFTWN, &
& SSDSBRF1, SSDSBRF2, SSDSBRFDF,SSDSBCK, SSDSABK, &
& SSDSPBK, SSDSBINT, &
& SSDSHCK, DELUST, DELTAIL, DELTAUW, &
& DELU, DELALP, DELAB, TAUT, TAUHFT, TAUHFT2, &
& SWELLFT, IKTAB, DCKI, SATINDICES, SATWEIGHTS, &
& DIKCUMUL, CUMULW, QBI
IF (ISTAT /= 0) CALL WWM_ABORT('Remove fort.5002 Error while trying to read precomputed array')
IF (MSC_TEST .NE. MSC .OR. MDC_TEST .NE. MDC) THEN
WRITE(DBG%FHNDL,*) 'MSC AND MDC READ FROM FILE AND SET IN WWMINPUT.NML ARE NOT EQUAL -STOP-'
WRITE(DBG%FHNDL,*) MSC_TEST, MSC
WRITE(DBG%FHNDL,*) MDC_TEST, MDC
CALL WWM_ABORT('THE fort.5002 file does not match your specifications. Remove and rerun')
ENDIF
END IF
END SUBROUTINE
!**********************************************************************
!* *
!**********************************************************************
SUBROUTINE W3SPR4 (A, CG, WN, EMEAN, FMEAN, FMEAN1, WNMEAN, AMAX, U, UDIR, USTAR, USDIR, TAUWX, TAUWY, CD, Z0, CHARN, LLWS, FMEANWS)
!/
!/ +-----------------------------------+
!/ | WAVEWATCH III SHOM |
!/ ! F. Ardhuin !
!/ | H. L. Tolman |
!/ | FORTRAN 90 |
!/ | Last update : 13-Jun-2011 |
!/ +-----------------------------------+
!/
!/ 03-Oct-2007 : Origination. ( version 3.13 )
!/ 13-Jun-2011 : Adds f_m0,-1 as FMEAN in the outout ( version 4.xx )
!/
! 1. Purpose :
!
! Calculate mean wave parameters for the use in the source term
! routines.
!
! 2. Method :
!
! See source term routines.
!
! 3. Parameters :
!
! Parameter list
! ----------------------------------------------------------------
! A R.A. I Action density spectrum.
! CG R.A. I Group velocities.
! WN R.A. I Wavenumbers.
! EMEAN Real O Energy
! FMEAN1 Real O Mean frequency (fm0,-1) used for reflection
! FMEAN Real O Mean frequency for determination of tail
! WNMEAN Real O Mean wavenumber.
! AMAX Real O Maximum of action spectrum.
! U Real I Wind speed.
! UDIR Real I Wind direction.
! USTAR Real I/O Friction velocity.
! USDIR Real I/O wind stress direction.
! TAUWX-Y Real I Components of wave-supported stress.
! CD Real O Drag coefficient at wind level ZWND.
! Z0 Real O Corresponding z0.
! CHARN Real O Corresponding Charnock coefficient
! LLWS L.A. I Wind sea true/false array for each component
! FMEANWS Real O Mean frequency of wind sea, used for tail
! ----------------------------------------------------------------
!
! 4. Subroutines used :
!
! STRACE Service routine.
!
! 5. Called by :
!
! W3SRCE Source term integration routine.
! W3OUTP Point output program.
! GXEXPO GrADS point output program.
!
! 6. Error messages :
!
! 7. Remarks :
!
! 8. Structure :
!
! See source code.
!
! 9. Switches :
!
! !/S Enable subroutine tracing.
! !/T Enable test output.
!
! 10. Source code :
!
!/ ------------------------------------------------------------------- /
USE DATAPOOL, ONLY: SPSIG, INVPI2, PI2, RKIND, NSPEC
USE DATAPOOL, ONLY: ZERO, ONE
!/T USE W3ODATMD, ONLY: NDST
!
IMPLICIT NONE
!/
!/ ------------------------------------------------------------------- /
!/ Parameter list
!/
REAL(rkind), INTENT(IN) :: A(NTH,NK), CG(NK), WN(NK)
REAL(rkind), INTENT(IN) :: TAUWX, TAUWY, U, UDIR
LOGICAL, INTENT(IN) :: LLWS(NSPEC)
REAL(rkind), INTENT(INOUT) :: USTAR ,USDIR
REAL(rkind), INTENT(OUT) :: EMEAN, FMEAN, FMEAN1, WNMEAN, &
& AMAX, CD, Z0, CHARN, FMEANWS
!/
!/ ------------------------------------------------------------------- /
!/ Local parameters
!/
INTEGER :: IS, IK, ITH
!/S INTEGER, SAVE :: IENT = 0
REAL(rkind) :: TAUW, EBAND, EMEANWS, RDCH, FXPMC, &
WNP, UNZ, FP, &
R1, CP, EB(NK),EB2(NK),ALFA(NK)
!/
!/ ------------------------------------------------------------------- /
!/
!/S CALL STRACE (IENT, 'W3SPR3')
!
UNZ = MAX ( 0.01_rkind , U )
USTAR = MAX ( 0.0001_rkind , USTAR )
!
EMEAN = ZERO
EMEANWS= ZERO
FMEANWS= ZERO
FMEAN = ZERO
FMEAN1 = ZERO
WNMEAN = ZERO
AMAX = ZERO
!
! 1. Integral over directions and maximum --------------------------- *
!
DO IK=1, NK
EB(IK) = ZERO
EB2(IK) = ZERO
DO ITH=1, NTH
IS=ITH+(IK-1)*NTH
EB(IK) = EB(IK) + A(ITH,IK)
IF (LLWS(IS)) EB2(IK) = EB2(IK) + A(ITH,IK)
AMAX = MAX ( AMAX , A(ITH,IK) )
END DO
! WRITE(DBG%FHNDL,*) IK, EB(IK), IK, ITH, A(ITH,IK)
END DO
!
! 2. Integrate over directions -------------------------------------- *
!
DO IK=1, NK
ALFA(IK) = 2. * DTH * SIG(IK) * EB(IK) * WN(IK)**3
EB(IK) = EB(IK) * DDEN(IK) / CG(IK)
EB2(IK) = EB2(IK) * DDEN(IK) / CG(IK)
EMEAN = EMEAN + EB(IK)
FMEAN = FMEAN + EB(IK) /SIG(IK)
FMEAN1 = FMEAN1 + EB(IK) *(SIG(IK)**(2.*WNMEANPTAIL))
WNMEAN = WNMEAN + EB(IK) *(WN(IK)**WNMEANP)
EMEANWS = EMEANWS+ EB2(IK)
FMEANWS = FMEANWS+ EB2(IK)*(SIG(IK)**(2.*WNMEANPTAIL))
END DO
!
! 3. Add tail beyond discrete spectrum and get mean pars ------------ *
! ( DTH * SIG absorbed in FTxx )
!
EBAND = EB(NK) / DDEN(NK)
EMEAN = EMEAN + EBAND * FTE
FMEAN = FMEAN + EBAND * FTF
FMEAN1 = FMEAN1 + EBAND * SSTXFTFTAIL
WNMEAN = WNMEAN + EBAND * SSTXFTWN
EBAND = EB2(NK) / DDEN(NK)
EMEANWS = EMEANWS + EBAND * FTE
FMEANWS = FMEANWS + EBAND * SSTXFTFTAIL
!
! 4. Final processing
!
FMEAN = INVPI2 * EMEAN / MAX ( 1.E-7_rkind , FMEAN )
IF (FMEAN1.LT.1.E-7) THEN
FMEAN1=INVPI2 * SIG(NK)
ELSE
FMEAN1 = INVPI2 *( MAX ( 1.E-7_rkind , FMEAN1 ) &
& / MAX ( 1.E-7_rkind , EMEAN ))**(1.d0/(2.*WNMEANPTAIL))
ENDIF
WNMEAN = ( MAX ( 1.E-7_rkind , WNMEAN ) &
& / MAX ( 1.E-7_rkind , EMEAN ) )**(1.d0/WNMEANP)
IF (FMEANWS.LT.1.E-7.OR.EMEANWS.LT.1.E-7) THEN
FMEANWS=INVPI2 * SIG(NK)
ELSE
FMEANWS = INVPI2 *( MAX ( 1.E-7_rkind , FMEANWS ) &
& / MAX ( 1.E-7_rkind , EMEANWS ))**(1/(2.*WNMEANPTAIL))
END IF
!
! 5. Cd and z0 ----------------------------------------------- *
!
TAUW = SQRT(TAUWX**2+TAUWY**2)
Z0=ZERO
CALL CALC_USTAR(U,TAUW,USTAR,Z0,CHARN)
UNZ = MAX ( 0.01_rkind , U )
CD = (USTAR/UNZ)**2
USDIR = UDIR
!
! 6. Final test output ---------------------------------------------- *
!
!/T WRITE (NDST,9060) EMEAN, WNMEAN, TPIINV, CP, CD, Z0
!
!/T 9060 FORMAT (' TEST W3SPR3 : E,WN MN :',F8.3,F8.4/ &
!/T ' FP, CP, CD, Z0 :',F8.3,F7.2,1X,2F9.5)
!/
!/ End of W3SPR3 ----------------------------------------------------- /
!/
END SUBROUTINE
!/ ------------------------------------------------------------------- /
SUBROUTINE W3SIN4 (IP, A, CG, K, U, USTAR, DRAT, AS, USDIR, Z0, CD, TAUWX, TAUWY, TAUWNX, TAUWNY, S, D, LLWS, BRLAMBDA)
!/
!/ +-----------------------------------+
!/ | WAVEWATCH III SHOM |
!/ ! F. Ardhuin !
!/ | H. L. Tolman |
!/ | FORTRAN 90 |
!/ | Last update : 16-May-2010 |
!/ +-----------------------------------+
!/
!/ 09-Oct-2007 : Origination. ( version 3.13 )
!/ 16-May-2010 : Adding sea ice ( version 3.14_Ifremer )
!/
! 1. Purpose :
!
! Calculate diagonal and input source term for WAM4+ approach.
!
! 2. Method :
!
! WAM-4 : Janssen et al.
! WAM-"4.5" : gustiness effect (Cavaleri et al. )
! SAT : high-frequency input reduction for balance with
! saturation dissipation (Ardhuin et al., 2008)
! SWELL : negative wind input (Ardhuin et al. 2008)
!
! 3. Parameters :
!
! Parameter list
! ----------------------------------------------------------------
! A R.A. I Action density spectrum (1-D).
! CG R.A. I Group speed *)
! K R.A. I Wavenumber for entire spectrum. *)
! U Real I WIND SPEED
! USTAR Real I Friction velocity.
! DRAT Real I Air/water density ratio.
! AS Real I Air-sea temperature difference
! USDIR Real I wind stress direction
! Z0 Real I Air-side roughness lengh.
! CD Real I Wind drag coefficient.
! USDIR Real I Direction of friction velocity
! TAUWX-Y Real I Components of the wave-supported stress.
! TAUWNX Real I Component of the negative wave-supported stress.
! TAUWNY Real I Component of the negative wave-supported stress.
! ICE Real I Sea ice fraction.
! S R.A. O Source term (1-D version).
! D R.A. O Diagonal term of derivative. *)
! ----------------------------------------------------------------
! *) Stored as 1-D array with dimension NTH*NK
!
! 4. Subroutines used :
!
! STRACE Subroutine tracing. ( !/S switch )
! PRT2DS Print plot of spectrum. ( !/T0 switch )
! OUTMAT Print out matrix. ( !/T1 switch )
!
! 5. Called by :
!
! W3SRCE Source term integration.
! W3EXPO Point output program.
! GXEXPO GrADS point output program.
!
! 6. Error messages :
!
! 7. Remarks :
!
! 8. Structure :
!
! See source code.
!
! 9. Switches :
!
! !/S Enable subroutine tracing.
! !/T Enable general test output.
! !/T0 2-D print plot of source term.
! !/T1 Print arrays.
!
! 10. Source code :
!
!/ ------------------------------------------------------------------- /
USE DATAPOOL, ONLY : ICOMP, G9, PI2, RADDEG, MSC, MDC, &
& MSC, MDC, TAUTOT, RKIND, NSPEC, ZERO, ONE, DBG, THR8, SINBR
!/S USE W3SERVMD, ONLY: STRACE
!/T USE W3ODATMD, ONLY: NDST
!/T0 USE W3ARRYMD, ONLY: PRT2DS
!/T1 USE W3ARRYMD, ONLY: OUTMAT
!
IMPLICIT NONE
!/
!/ ------------------------------------------------------------------- /
!/ Parameter list
!/
INTEGER, INTENT(IN) :: IP
REAL(rkind), INTENT(IN) :: A(NSPEC), BRLAMBDA(NSPEC)
REAL(rkind), INTENT(IN) :: CG(NK), K(NSPEC),Z0,U, CD
REAL(rkind), INTENT(IN) :: USTAR, USDIR, AS, DRAT
REAL(rkind), INTENT(OUT) :: S(NSPEC), D(NSPEC), TAUWX, TAUWY, TAUWNX, TAUWNY
LOGICAL, INTENT(OUT) :: LLWS(NSPEC)
!/
!/ ------------------------------------------------------------------- /
!/ Local parameters
!/
INTEGER :: IS,IK,ITH, IOMA, ICL
!/S INTEGER, SAVE :: IENT = 0
REAL(rkind) :: FACLN1, FACLN2, ULAM, CLAM, OMA, &
RD1, RD2, LAMBDA, COSFAC
REAL(rkind) :: COSU, SINU, TAUX, TAUY, USDIRP, USTP
REAL(rkind) :: TAUPX, TAUPY, UST2, TAUW, TAUWB
REAL(rkind) , PARAMETER :: EPS1 = 0.00001, EPS2 = 0.000001
REAL(rkind) :: Usigma !standard deviation of U due to gustiness
REAL(rkind) :: USTARsigma !standard deviation of USTAR due to gustiness
REAL(rkind) :: BETA, mu_janssen, omega_janssen, &
CM,ZCO,UCO,UCN,ZCN, &
Z0VISC, Z0NOZ, EB, &
EBX, EBY, AORB, AORB1, FW, UORB, M2, TH2, &
RE, FU, FUD, SWELLCOEFV, SWELLCOEFT
REAL(rkind) :: HSBLOW, ABJSEA, FACTOR
REAL(rkind) :: PTURB, PVISC, SMOOTH
REAL(rkind) :: XI,DELI1,DELI2
REAL(rkind) :: XJ,DELJ1,DELJ2
REAL(rkind) :: XK,DELK1,DELK2
REAL(rkind) :: CONST, CONST0, CONST2, TAU1
REAL(rkind) :: X,ZARG,ZLOG,UST
REAL(rkind) :: COSWIND, XSTRESS, YSTRESS, TAUHF
REAL(rkind) :: TEMP, TEMP2
INTEGER IND,J,I,ISTAB
REAL(rkind) :: DSTAB(3,NSPEC), DVISC, DTURB
REAL(rkind) :: STRESSSTAB(3,2),STRESSSTABN(3,2)
!/T0 REAL :: DOUT(NK,NTH)
!/
!/ ------------------------------------------------------------------- /
!/
!/S CALL STRACE (IENT, 'W3SIN3')
!
!/T WRITE (NDST,9000) BBETA, USTAR, USDIR*RADE
!
! 1. Preparations
!
!
! 1.a estimation of surface roughness parameters
!
Z0VISC = 0.1_rkind*nu_air/MAX(USTAR,0.0001_rkind)
Z0NOZ = MAX(Z0VISC,ZZ0RAT*Z0)
FACLN1 = U / LOG(ZZWND/Z0NOZ)
FACLN2 = LOG(Z0NOZ)
!
! 1.b estimation of surface orbital velocity and displacement
!
UORB=0.
AORB=0.
DO IK=1, NK
EB = 0.
EBX = 0.
EBY = 0.
DO ITH=1, NTH
IS=ITH+(IK-1)*NTH
EB = EB + A(IS)
END DO
!
! At this point UORB and AORB are the variances of the orbital velocity and surface elevation
!
UORB = UORB + EB *SIG(IK)**2 * DDEN(IK) / CG(IK)
AORB = AORB + EB * DDEN(IK) / CG(IK) !deep water only
END DO
UORB = 2*SQRT(UORB) ! significant orbital amplitude
AORB1 = 2*AORB**(1-0.5*SSWELLF(6)) ! half the significant wave height ... if SWELLF(6)=1
RE = 4*UORB*AORB1 / NU_AIR ! Reynolds number
!
! Defines the swell dissipation based on the "Reynolds number"
!
IF (SSWELLF(4).GT.0) THEN
IF (SSWELLF(7).GT.0.) THEN
SMOOTH = 0.5*TANH((RE-SSWELLF(4))/SSWELLF(7))
PTURB=(0.5+SMOOTH)
PVISC=(0.5-SMOOTH)
ELSE
IF (RE.LE.SSWELLF(4)) THEN
PTURB = ZERO
PVISC = ONE
ELSE
PTURB = ONE
PVISC = ZERO
END IF
END IF
ELSE
PTURB=ONE
PVISC=ONE
END IF
!
IF (SSWELLF(2).EQ.0) THEN
FW=MAX(ABS(SSWELLF(3)),ZERO)
FU=ZERO
FUD=ZERO
ELSE
FU=ABS(SSWELLF(3))
FUD=SSWELLF(2)
AORB=2*SQRT(AORB)
XI=(LOG10(MAX(AORB/Z0NOZ,3._rkind))-ABMIN)/DELAB
IND = MIN (SIZEFWTABLE-1, INT(XI))
DELI1= MIN (ONE ,XI-MyREAL(IND))
DELI2= ONE - DELI1
!WRITE(DBG%FHNDL,'(A10,I10,5F15.8)') 'TEST IND',IND, XI, AORB, Z0NOZ, ABMIN, DELAB
FW =FWTABLE(IND)*DELI2+FWTABLE(IND+1)*DELI1
END IF
!
! 2. Diagonal
!
! Here AS is the air-sea temperature difference in degrees. Expression given by
! Abdalla & Cavaleri, JGR 2002 for Usigma. For USTARsigma ... I do not see where
! I got it from, maybe just made up from drag law ...
!
# ifdef STAB3
Usigma=MAX(0.,-0.025_rkind*AS)
USTARsigma=(ONE+U/(10._rkind+U))*Usigma
# endif
UST=USTAR
ISTAB=3
# ifdef STAB3
DO ISTAB=1,2
IF (ISTAB.EQ.1) UST=USTAR*(ONE - USTARsigma)
IF (ISTAB.EQ.2) UST=USTAR*(ONE + USTARsigma)
# endif
TAUX = UST**2* MyCOS(USDIR)
TAUY = UST**2* MySIN(USDIR)
!WRITE(DBG%FHNDL,*) 'TAU USTAR', TAUX, TAUY, UST, USDIR, USTAR
!
! Loop over the resolved part of the spectrum
!
STRESSSTAB(ISTAB,:)=ZERO
STRESSSTABN(ISTAB,:)=ZERO
!
! Coupling coefficient times densit ration and fraction of free surface (1-ICE)
!
IF (FLICES) THEN
STOP 'NO ICE HERE'
!CONST0=MIN(ZERO,MAX(ONE,ONE-ICE))*BBETA*DRAT/(kappa**2)
ELSE
CONST0=BBETA*DRAT/(kappa**2)
END IF
DO IK=1, NK
TAUPX=TAUX-ABS(TTAUWSHELTER)*STRESSSTAB(ISTAB,1)
TAUPY=TAUY-ABS(TTAUWSHELTER)*STRESSSTAB(ISTAB,2)
! With MIN and MAX the bug should disappear.... but where did it come from?
! AR: This is ugly ...
USTP=MIN((TAUPX**2+TAUPY**2)**0.25_rkind,MAX(UST,0.3_rkind))
!WRITE(DBG%FHNDL,*) 'USTP', IK, USTP, STRESSSTAB(ISTAB,1), STRESSSTAB(ISTAB,2), TTAUWSHELTER
USDIRP=ATAN2(TAUPY,TAUPX)
COSU = MyCOS(USDIRP)
SINU = MySIN(USDIRP)
IS=1+(IK-1)*NTH
CM=K(IS)/SIG2(IS) !inverse of phase speed
UCN=USTP*CM+ZZALP !this is the inverse wave age
! the stress is the real stress (N/m^2) divided by
! rho_a, and thus comparable to USTAR**2
! it is the integral of rho_w g Sin/C /rho_a
! (air-> waves momentum flux)
CONST2=DDEN2(IS)/CG(IK) & !Jacobian to get energy in band
& *G9/(SIG(IK)/K(IS)*DRAT) ! coefficient to get momentum
CONST=SIG2(IS)*CONST0
! this CM parameter is 1 / C_phi
! this is the "correct" shallow-water expression
! here Z0 corresponds to Z0+Z1 of the Janssen eq. 14
#ifdef USE_SINGLE
ZCN=LOG(K(IS)*Z0)
#else
ZCN=DLOG(K(IS)*Z0)
#endif
! below is the original WAM version (OK for deep water) g*z0/C^2
! ZCN=LOG(G*Z0b(I)*CM(I)**2)
!
! precomputes swell factors
!
SWELLCOEFV=-SSWELLF(5)*DRAT*2*K(IS)*SQRT(2*NU_AIR*SIG2(IS))
SWELLCOEFT=-DRAT*SSWELLF(1)*16*SIG2(IS)**2/G9
!
!WRITE(DBG%FHNDL,*) 'UCN', IK, IS, USTP, CM ,K(IK), DDEN2(IS), Z0
DO ITH=1,NTH
IS=ITH+(IK-1)*NTH
COSWIND=(ECOS(IS)*COSU+ESIN(IS)*SINU)
IF (COSWIND.GT.0.01) THEN
X=COSWIND*UCN
! this ZARG term is the argument of the exponential
! in Janssen 1991 eq. 16.
ZARG=KAPPA/X
! ZLOG is ALOG(MU) where MU is defined by Janssen 1991 eq. 15
! MU=
ZLOG=ZCN+ZARG
!WRITE(DBG%FHNDL,*) 'ZLOG', IK, ITH, ZCN, ZARG, X, KAPPA, UCN
IF (ZLOG.LT.0.) THEN
! The source term Sp is beta * omega * X**2
! as given by Janssen 1991 eq. 19
! for a faster performance EXP(X)*X**4 should be tabulated
DSTAB(ISTAB,IS) = CONST*EXP(ZLOG)*ZLOG**4 &
*UCN*UCN*COSWIND**SSINTHP *(1+BRLAMBDA(IS)*20*SINBR)
LLWS(IS)=.TRUE.
ELSE
DSTAB(ISTAB,IS) = 0.
LLWS(IS)=.FALSE.
END IF
!WRITE(DBG%FHNDL,*) 'DSTAB', DSTAB(ISTAB,IS), CONST,EXP(ZLOG),ZLOG**4,UCN**2,COSWIND,SSINTHP
!
! Added for consistency with ECWAM implsch.F
!
IF (28._rkind*CM*USTAR*COSWIND.GE.1) THEN
LLWS(IS)=.TRUE.
END IF
ELSE ! (COSWIND.LE.0.01)
DSTAB(ISTAB,IS) = 0.
LLWS(IS)=.FALSE.
END IF
IF ((SSWELLF(1).NE.0.AND.DSTAB(ISTAB,IS).LT.1E-7*SIG2(IS)) &
& .OR.SSWELLF(3).GT.0) THEN
!
DVISC=SWELLCOEFV ! + SSWELLF(7)/SIG2(IS) ! fudge for low frequency
DTURB=SWELLCOEFT*(FW*UORB+(FU+FUD*COSWIND)*USTP)
DSTAB(ISTAB,IS) = DSTAB(ISTAB,IS) + PTURB*DTURB + PVISC*DVISC
END IF
!
! Sums up the wave-supported stress
!
! Wave direction is "direction to"
! therefore there is a PLUS sign for the stress
TEMP2=CONST2*DSTAB(ISTAB,IS)*A(IS)
IF (DSTAB(ISTAB,IS).LT.0) THEN
STRESSSTABN(ISTAB,1)=STRESSSTABN(ISTAB,1)+TEMP2*ECOS(IS)
STRESSSTABN(ISTAB,2)=STRESSSTABN(ISTAB,2)+TEMP2*ESIN(IS)
ELSE
STRESSSTAB(ISTAB,1)=STRESSSTAB(ISTAB,1)+TEMP2*ECOS(IS)
STRESSSTAB(ISTAB,2)=STRESSSTAB(ISTAB,2)+TEMP2*ESIN(IS)
END IF
END DO
END DO
!
D(:)=DSTAB(3,:)
XSTRESS=STRESSSTAB (3,1)
YSTRESS=STRESSSTAB (3,2)
TAUWNX =STRESSSTABN(3,1)
TAUWNY =STRESSSTABN(3,2)
!/STAB3 END DO
!/STAB3 D(:)=0.5*(DSTAB(1,:)+DSTAB(2,:))
!/STAB3 XSTRESS=0.5*(STRESSSTAB(1,1)+STRESSSTAB(2,1))
!/STAB3 YSTRESS=0.5*(STRESSSTAB(1,2)+STRESSSTAB(2,2))
!/STAB3 TAUWNX=0.5*(STRESSSTABN(1,1)+STRESSSTABN(2,1))
!/STAB3 TAUWNY=0.5*(STRESSSTABN(1,2)+STRESSSTABN(2,2))