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w3src4md.F90
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!> @file
!> @brief The 'SHOM/Ifremer' source terms based on P.A.E.M.
!>
!> @author F. Ardhuin
!> @date 13-Nov-2013
!>
#include "w3macros.h"
!/ ------------------------------------------------------------------- /
!>
!> @brief The 'SHOM/Ifremer' source terms based on P.A.E.M.
!>
!> @details 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
!>
!> @author F. Ardhuin
!> @date 13-Nov-2013
!>
!> @copyright Copyright 2009-2022 National Weather Service (NWS),
!> National Oceanic and Atmospheric Administration. All rights
!> reserved. WAVEWATCH III is a trademark of the NWS.
!> No unauthorized use without permission.
!>
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 )
!/ 13-Nov-2013 : Reduced frequency range with IG ( version 4.13 )
!/ 01-Mar-2023 : Clean up of SDS4 ( version 7.14 )
!/
! 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 :
!/
!/ ------------------------------------------------------------------- /
!/
PUBLIC
!/
!/ Public variables
!/
!air kinematic viscosity (used in WAM)
INTEGER, PARAMETER :: ITAUMAX=200,JUMAX=200
INTEGER, PARAMETER :: IUSTAR=100,IALPHA=200, ILEVTAIL=50
! Tables for total stress and H.F. stress as a function of 2 or 3 variables
REAL, ALLOCATABLE :: TAUT(:,:),TAUHFT(:,:),TAUHFT2(:,:,:)
REAL :: DELUST, DELALP,DELTAUW, DELU
! Table for swell damping
REAL :: DELTAIL
REAL, PARAMETER :: UMAX = 50.
REAL, PARAMETER :: TAUWMAX = 2.2361 !SQRT(5.)
INTEGER :: DIKCUMUL
! Size of wave height table for integrating the PDF of wave heights
INTEGER, PARAMETER :: NKHI=100, FAC_KD2=1000
REAL, PARAMETER :: FAC_KD1=1.01, KHSMAX=2., KHMAX=2.
REAL, PARAMETER ::KDMAX=200000.
!/
CONTAINS
!/ ------------------------------------------------------------------- /
!>
!> @brief Calculate mean wave parameters for the use in the source term
!> routines.
!>
!> @param[in] A Action density spectrum.
!> @param[in] CG Group velocities.
!> @param[in] WN Wavenumbers.
!> @param[out] EMEAN Energy.
!> @param[out] FMEAN Mean frequency for determination of tail.
!> @param[out] FMEAN1 Mean frequency (fm0,-1) used for reflection.
!> @param[out] WNMEAN Mean wavenumber.
!> @param[out] AMAX Maximum of action spectrum.
!> @param[in] U Wind speed.
!> @param[in] UDIR Wind direction.
!> @param[in] TAUA Atm total stress.
!> @param[in] TAUADIR Atm total stress direction.
!> @param[in] DAIR Air density.
!> @param[inout] USTAR Friction velocity.
!> @param[inout] USDIR Wind stress direction.
!> @param[in] TAUWX Component of wave-supported stress.
!> @param[in] TAUWY Component of wave-supported stress.
!> @param[out] CD Drag coefficient at wind level ZWND.
!> @param[out] Z0 Corresponding z0.
!> @param[out] CHARN Corresponding Charnock coefficient.
!> @param[in] LLWS Wind sea true/false array for each component.
!> @param[out] FMEANWS Mean frequency of wind sea, used for tail.
!> @param[out] DLWMEAN Mean Long wave direction (L. Romero 2019).
!>
!> @author F. Ardhuin
!> @author H. L. Tolman
!> @date 22-Feb-2020
!>
SUBROUTINE W3SPR4 (A, CG, WN, EMEAN, FMEAN, FMEAN1, WNMEAN, &
AMAX, U, UDIR, &
#ifdef W3_FLX5
TAUA, TAUADIR, DAIR, &
#endif
USTAR, USDIR, &
TAUWX, TAUWY, CD, Z0, CHARN, LLWS, FMEANWS, DLWMEAN)
!/
!/ +-----------------------------------+
!/ | WAVEWATCH III SHOM |
!/ ! F. Ardhuin !
!/ | H. L. Tolman |
!/ | FORTRAN 90 |
!/ | Last update : 22-Feb-2020 |
!/ +-----------------------------------+
!/
!/ 03-Oct-2007 : Origination. ( version 3.13 )
!/ 13-Jun-2011 : Adds f_m0,-1 as FMEAN in the outout ( version 4.04 )
!/ 08-Jun-2018 : use STRACE and FLUSH ( version 6.04 )
!/ 22-Feb-2020 : Merge Romero (2019) and cleanup ( version 7.06 )
!/ 22-Jun-2021 : Add FLX5 to use stresses with the ST( version 7.14 )
!/
! 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.
! TAUA Real I Atm. total stress. ( /!FLX5 )
! TAUADIR Real I Atm. total stress direction. ( /!FLX5 )
! DAIR Real I Air density. ( /!FLX5 )
! 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
! DLWMEAN Real O Mean Long wave direction (L. Romero 2019)
! ----------------------------------------------------------------
!
! 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.
! !/FLX5 Direct use of stress from atmoshperic model.
!
! 10. Source code :
!
!/ ------------------------------------------------------------------- /
USE W3ODATMD, ONLY: IAPROC
USE CONSTANTS, ONLY: TPIINV, GRAV, nu_air
USE W3GDATMD, ONLY: NK, NTH, NSPEC, SIG, DTH, DDEN, WWNMEANP, &
WWNMEANPTAIL, FTE, FTF, SSTXFTF, SSTXFTWN,&
SSTXFTFTAIL, SSWELLF, ESIN, ECOS, AAIRCMIN, &
AAIRGB, AALPHA, ZZWND, SSDSC
#ifdef W3_S
USE W3SERVMD, ONLY: STRACE
#endif
#ifdef W3_T
USE W3ODATMD, ONLY: NDST
USE W3ODATMD, ONLY: NDST
#endif
!
#ifdef W3_FLX5
USE W3FLX5MD
#endif
IMPLICIT NONE
!/
!/ ------------------------------------------------------------------- /
!/ Parameter list
!/
REAL, INTENT(IN) :: A(NTH,NK), CG(NK), WN(NK), U, UDIR
#ifdef W3_FLX5
REAL, INTENT(IN) :: TAUA, TAUADIR, DAIR
#endif
REAL, INTENT(IN) :: TAUWX, TAUWY
LOGICAL, INTENT(IN) :: LLWS(NSPEC)
REAL, INTENT(INOUT) :: USTAR ,USDIR
REAL, INTENT(OUT) :: EMEAN, FMEAN, FMEAN1, WNMEAN, AMAX, &
CD, Z0, CHARN, FMEANWS, DLWMEAN
!/
!/ ------------------------------------------------------------------- /
!/ Local parameters
!/
INTEGER :: IS, IK, ITH
#ifdef W3_S
INTEGER, SAVE :: IENT = 0
#endif
REAL :: TAUW, EBAND, EMEANWS,UNZ, &
EB(NK),EB2(NK),ELCS, ELSN, SIGFAC
!/
!/ ------------------------------------------------------------------- /
!/
#ifdef W3_S
CALL STRACE (IENT, 'W3SPR4')
#endif
!
UNZ = MAX ( 0.01 , U )
USTAR = MAX ( 0.0001 , USTAR )
!
EMEAN = 0.
EMEANWS= 0.
FMEANWS= 0.
FMEAN = 0.
FMEAN1 = 0.
WNMEAN = 0.
AMAX = 0.
DLWMEAN =0.
ELCS =0.
ELSN =0.
!
! 1. Integral over directions and maximum --------------------------- *
!
DO IK=1, NK
EB(IK) = 0.
EB2(IK) = 0.
SIGFAC=SIG(IK)**SSDSC(12) * DDEN(IK) / CG(IK)
DO ITH=1, NTH
IS=ITH+(IK-1)*NTH
EB(IK) = EB(IK) + A(ITH,IK)
ELCS = ELCS + A(ITH,IK)*ECOS(IS)*SIGFAC
ELSN = ELSN + A(ITH,IK)*ESIN(IS)*SIGFAC
IF (LLWS(IS)) EB2(IK) = EB2(IK) + A(ITH,IK)
AMAX = MAX ( AMAX , A(ITH,IK) )
END DO
END DO
!
DLWMEAN=ATAN2(ELSN,ELCS)
!
! 2. Integrate over directions -------------------------------------- *
!
DO IK=1, NK
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.*WWNMEANPTAIL))
WNMEAN = WNMEAN + EB(IK) *(WN(IK)**WWNMEANP)
EMEANWS = EMEANWS+ EB2(IK)
FMEANWS = FMEANWS+ EB2(IK)*(SIG(IK)**(2.*WWNMEANPTAIL))
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 = TPIINV * EMEAN / MAX ( 1.E-7 , FMEAN )
IF (FMEAN1.LT.1.E-7) THEN
FMEAN1=TPIINV * SIG(NK)
ELSE
FMEAN1 = TPIINV *( MAX ( 1.E-7 , FMEAN1 ) &
/ MAX ( 1.E-7 , EMEAN ))**(1/(2.*WWNMEANPTAIL))
ENDIF
WNMEAN = ( MAX ( 1.E-7 , WNMEAN ) &
/ MAX ( 1.E-7 , EMEAN ) )**(1/WWNMEANP)
IF (FMEANWS.LT.1.E-7.OR.EMEANWS.LT.1.E-7) THEN
FMEANWS=TPIINV * SIG(NK)
ELSE
FMEANWS = TPIINV *( MAX ( 1.E-7 , FMEANWS ) &
/ MAX ( 1.E-7 , EMEANWS ))**(1/(2.*WWNMEANPTAIL))
END IF
!
! 5. Cd and z0 ----------------------------------------------- *
!
TAUW = SQRT(TAUWX**2+TAUWY**2)
!
#ifdef W3_FLX5
CALL W3FLX5 ( ZZWND, U, UDIR, TAUA, TAUADIR, DAIR, &
USTAR, USDIR, Z0, CD, CHARN )
#else
CALL CALC_USTAR(U,TAUW,USTAR,Z0,CHARN)
UNZ = MAX ( 0.01 , U )
CD = (USTAR/UNZ)**2
USDIR = UDIR
#endif
!
! 6. Final test output ---------------------------------------------- *
!
#ifdef W3_T
WRITE (NDST,9060) EMEAN, WNMEAN, TPIINV, USTAR, CD, Z0
#endif
!
RETURN
!
! Formats
!
#ifdef W3_T
9060 FORMAT (' TEST W3SPR4 : E,WN MN :',F8.3,F8.4/ &
' TPIINV, USTAR, CD, Z0 :',F8.3,F7.2,1X,2F9.5)
#endif
!/
!/ End of W3SPR4 ----------------------------------------------------- /
!/
END SUBROUTINE W3SPR4
!/ ------------------------------------------------------------------- /
!>
!> @brief Calculate diagonal and input source term for WAM4+ approach.
!>
!> @verbatim
!> 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)
!> @endverbatim
!>
!> @param[in] A Action density spectrum (1-D).
!> @param[in] CG Group speed.
!> @param[in] K Wavenumber for entire spectrum.
!> @param[in] U Wind speed.
!> @param[in] USTAR Friction velocity.
!> @param[in] DRAT Air/water density ratio.
!> @param[in] AS Air-sea temperature difference.
!> @param[in] USDIR Wind stress direction.
!> @param[in] Z0 Air-sea roughness length.
!> @param[in] CD Wind drag coefficient.
!> @param[out] TAUWX Component of the wave-supported stress.
!> @param[out] TAUWY Component of the wave-supported stress.
!> @param[out] TAUWNX Component of the negative wave-supported stress.
!> @param[out] TAUWNY Component of the negative wave-supported stress.
!> @param[out] S Source term (1-D version).
!> @param[out] D Diagonal term of derivative.
!> @param[out] LLWS
!> @param[in] IX
!> @param[in] IY
!> @param[in] BRLAMBDA
!>
!> @author F. Ardhuin
!> @author H. L. Tolman
!> @date 05-Dec-2013
!>
SUBROUTINE W3SIN4 (A, CG, K, U, USTAR, DRAT, AS, USDIR, Z0, CD, &
TAUWX, TAUWY, TAUWNX, TAUWNY, S, D, LLWS, &
IX, IY, BRLAMBDA)
!/
!/ +-----------------------------------+
!/ | WAVEWATCH III SHOM |
!/ ! F. Ardhuin !
!/ | H. L. Tolman |
!/ | FORTRAN 90 |
!/ | Last update : 05-Dec-2013 |
!/ +-----------------------------------+
!/
!/ 09-Oct-2007 : Origination. ( version 3.13 )
!/ 24-Jan-2013 : Adding breaking-related input ( version 4.16 )
!/ 05-Dec-2013 : Cleaning up the ICE input ( version 4.16 )
!/
! 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.
! 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 CONSTANTS, ONLY: GRAV,nu_air,KAPPA,TPI,FWTABLE,SIZEFWTABLE, &
#ifdef W3_T
RADE, &
#endif
DELAB,ABMIN
USE W3GDATMD, ONLY: NK, NTH, NSPEC, DDEN, SIG, SIG2, TH, &
ESIN, ECOS, EC2, ZZWND, AALPHA, BBETA, ZZALP,&
TTAUWSHELTER, SSWELLF, DDEN2, DTH, SSINTHP, &
ZZ0RAT, SSINBR, SINTAILPAR
#ifdef W3_S
USE W3SERVMD, ONLY: STRACE
#endif
#ifdef W3_T
USE W3ODATMD, ONLY: NDST
#endif
#ifdef W3_T0
USE W3ODATMD, ONLY: NDST
#endif
USE W3ODATMD, ONLY: IAPROC
#ifdef W3_T0
USE W3ARRYMD, ONLY: PRT2DS
#endif
#ifdef W3_T1
USE W3ARRYMD, ONLY: OUTMAT
#endif
!
IMPLICIT NONE
!/
!/ ------------------------------------------------------------------- /
!/ Parameter list
!/
REAL, INTENT(IN) :: A(NSPEC), BRLAMBDA(NSPEC)
REAL, INTENT(IN) :: CG(NK), K(NSPEC),Z0,U, CD
REAL, INTENT(IN) :: USTAR, USDIR, AS, DRAT
REAL, INTENT(OUT) :: S(NSPEC), D(NSPEC), TAUWX, TAUWY, TAUWNX, TAUWNY
LOGICAL, INTENT(OUT) :: LLWS(NSPEC)
INTEGER, INTENT(IN) :: IX, IY
!/
!/ ------------------------------------------------------------------- /
!/ Local parameters
!/
INTEGER :: IS,IK,ITH
#ifdef W3_S
INTEGER, SAVE :: IENT = 0
#endif
REAL :: FACLN1, FACLN2, LAMBDA
REAL :: COSU, SINU, TAUX, TAUY, USDIRP, USTP
REAL :: TAUPX, TAUPY, UST2, TAUW, TAUWB
REAL , PARAMETER :: EPS1 = 0.00001, EPS2 = 0.000001
REAL :: Usigma !standard deviation of U due to gustiness
REAL :: USTARsigma !standard deviation of USTAR due to gustiness
REAL :: CM,UCN,ZCN, &
Z0VISC, Z0NOZ, EB, &
EBX, EBY, AORB, AORB1, FW, UORB, TH2, &
RE, FU, FUD, SWELLCOEFV, SWELLCOEFT
REAL :: PTURB, PVISC, SMOOTH
REAL XI,DELI1,DELI2
REAL XJ,DELJ1,DELJ2
REAL XK,DELK1,DELK2
REAL :: CONST, CONST0, CONST2, TAU1, TAU1NT, ZINF, TENSK
REAL X,ZARG,ZLOG,UST
REAL :: COSWIND, XSTRESS, YSTRESS, TAUHF
REAL TEMP, TEMP2
INTEGER IND,J,I,ISTAB
REAL DSTAB(3,NSPEC), DVISC, DTURB
REAL STRESSSTAB(3,2),STRESSSTABN(3,2)
!
INTEGER, PARAMETER :: JTOT=50
REAL , PARAMETER :: KM=363.,CMM=0.2325 ! K and C at phase speed minimum in rad/m
REAL :: OMEGACC, OMEGA, ZZ0, ZX, ZBETA, USTR, TAUR, &
CONST1, LEVTAIL0, X0, Y, DELY, YC, ZMU, &
LEVTAIL, CGTAIL, ALPHAM, FM, ALPHAT, FMEAN
REAL, ALLOCATABLE :: W(:)
#ifdef W3_T0
REAL :: DOUT(NK,NTH)
#endif
!/
!/ ------------------------------------------------------------------- /
!/
#ifdef W3_S
CALL STRACE (IENT, 'W3SIN4')
#endif
!
#ifdef W3_T
WRITE (NDST,9000) BBETA, USTAR, USDIR*RADE
#endif
!
! 1. Preparations
!
!JDM: Initializing values to zero, they shouldn't be used unless
!set in another place, but seems to solve some bugs with certain
!compilers.
DSTAB =0.
STRESSSTAB =0.
STRESSSTABN =0.
!
! Coupling coefficient times density ratio DRAT
!
CONST1=BBETA/KAPPA**2 ! needed for the tail
CONST0=CONST1*DRAT ! needed for the resolved spectrum
!
! 1.a estimation of surface roughness parameters
!
Z0VISC = 0.1*nu_air/MAX(USTAR,0.0001)
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) !correct for deep water only
END DO
! FMEAN = SQRT((UORB+1E-6)/(AORB+1E-6))
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 = 0.
PVISC = 1.
ELSE
PTURB = 1.
PVISC = 0.
END IF
END IF
ELSE
PTURB=1.
PVISC=1.
END IF
!
IF (SSWELLF(2).EQ.0) THEN
FW=MAX(ABS(SSWELLF(3)),0.)
FU=0.
FUD=0.
ELSE
FU=ABS(SSWELLF(3))
FUD=SSWELLF(2)
AORB=2*SQRT(AORB)
XI=(ALOG10(MAX(AORB/Z0NOZ,3.))-ABMIN)/DELAB
IND = MIN (SIZEFWTABLE-1, INT(XI))
DELI1= MIN (1. ,XI-FLOAT(IND))
DELI2= 1. - DELI1
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 W3_STAB3
IF ( ISNAN(AS) ) THEN
! AS is typically NaN on land and can propagate into the domain by interpolation
Usigma = 0.
ELSE
Usigma = MAX(0.,-0.025*AS)
END IF
USTARsigma=(1.0+U/(10.+U))*Usigma
#endif
#ifdef W3_T
WRITE (NDST,9003) AS, Usigma, USTARsigma, U
#endif
UST=USTAR
ISTAB=3
#ifdef W3_STAB3
DO ISTAB=1,2
IF (ISTAB.EQ.1) UST=USTAR*(1.-USTARsigma)
IF (ISTAB.EQ.2) UST=USTAR*(1.+USTARsigma)
#endif
TAUX = UST**2* COS(USDIR)
TAUY = UST**2* SIN(USDIR)
#ifdef W3_T
WRITE (NDST,9001) ISTAB, TAUX, TAUY, UST
#endif
!
! Loop over the resolved part of the spectrum
!
STRESSSTAB(ISTAB,:)=0.
STRESSSTABN(ISTAB,:)=0.
!
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?
USTP=MIN((TAUPX**2+TAUPY**2)**0.25,MAX(UST,0.3))
USDIRP=ATAN2(TAUPY,TAUPX)
COSU = COS(USDIRP)
SINU = SIN(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
*GRAV/(SIG(IK)/K(IS)*DRAT) ! coefficient to get momentum
CONST=SIG2(IS)*CONST0
! CM parameter is 1 / C_phi
! Z0 corresponds to Z0+Z1 of the Janssen eq. 14
ZCN=ALOG(K(IS)*Z0)
!
! precomputes swell factors
!
SWELLCOEFV=-SSWELLF(5)*DRAT*2*K(IS)*SQRT(2*NU_AIR*SIG2(IS))
SWELLCOEFT=-DRAT*SSWELLF(1)*16*SIG2(IS)**2/GRAV
!
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
IF (ZLOG.LT.0.) THEN
! The source term Sp is beta * omega * X**2
! as given by Janssen 1991 eq. 19
! Note that this is slightly diffent from ECWAM code CY45R2 where ZLOG is replaced by ??
DSTAB(ISTAB,IS) = CONST*EXP(ZLOG)*ZLOG**4*UCN*UCN*COSWIND**SSINTHP
! Below is an example with breaking probability feeding back to the input...
!DSTAB(ISTAB,IS) = CONST*EXP(ZLOG)*ZLOG**4 &
! *UCN*UCN*COSWIND**SSINTHP *(1+BRLAMBDA(IS)*20*SSINBR)
LLWS(IS)=.TRUE.
ELSE
DSTAB(ISTAB,IS) = 0.
LLWS(IS)=.FALSE.
END IF
!
! Added for consistency with ECWAM implsch.F
!
IF (28.*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
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)
#ifdef W3_STAB3
END DO
D(:)=0.5*(DSTAB(1,:)+DSTAB(2,:))
XSTRESS=0.5*(STRESSSTAB(1,1)+STRESSSTAB(2,1))
YSTRESS=0.5*(STRESSSTAB(1,2)+STRESSSTAB(2,2))
TAUWNX=0.5*(STRESSSTABN(1,1)+STRESSSTABN(2,1))
TAUWNY=0.5*(STRESSSTABN(1,2)+STRESSSTABN(2,2))
#endif
#ifdef W3_T
WRITE (NDST,9002) SUM(D), SUM(A), XSTRESS, YSTRESS, TAUWNX, TAUWNY
#endif
S = D * A
!
! ... Test output of arrays
!
#ifdef W3_T0
DO IK=1, NK
DO ITH=1, NTH
DOUT(IK,ITH) = D(ITH+(IK-1)*NTH)
END DO
END DO
CALL PRT2DS (NDST, NK, NK, NTH, DOUT, SIG(1), ' ', 1., &
0.0, 0.001, 'Diag Sin', ' ', 'NONAME')
#endif
!
#ifdef W3_T1
CALL OUTMAT (NDST, D, NTH, NTH, NK, 'diag Sin')
#endif
!
TAUPX=TAUX-ABS(TTAUWSHELTER)*XSTRESS
TAUPY=TAUY-ABS(TTAUWSHELTER)*YSTRESS
USTP=(TAUPX**2+TAUPY**2)**0.25
USDIRP=ATAN2(TAUPY,TAUPX)
UST=USTP
!
! Computes HF tail
!
! Computes the high-frequency contribution
! the difference in spectal density (kx,ky) to (f,theta)
! is integrated in this modified CONST0
CONST0=DTH*SIG(NK)**5/((GRAV**2)*tpi) &
*TPI*SIG(NK) / CG(NK) !conversion WAM (E(f,theta) to WW3 A(k,theta)
TEMP=0.
DO ITH=1,NTH
IS=ITH+(NK-1)*NTH
COSWIND=(ECOS(IS)*COSU+ESIN(IS)*SINU)
TEMP=TEMP+A(IS)*(MAX(COSWIND,0.))**3
END DO
!
LEVTAIL0= CONST0*TEMP ! LEVTAIL is sum over theta of A(k,theta)*cos^3(theta-wind)*DTH*SIG^5/(g^2*2pi)*2*pi*SIG/CG
! which is the same as sum of E(f,theta)*cos^3(theta-wind)*DTH*SIG^5/(g^2*2pi)
! reminder: sum of E(f,theta)*DTH*SIG^5/(g^2*2pi) is 2*k^3*E(k)
!
! Computation of stress supported by tail: uses table if SINTAILPAR(1)=1 , correspoding to SINTABLE = 1
!
IF (SINTAILPAR(1).LT.0.5) THEN
ALLOCATE(W(JTOT))
W(2:JTOT-1)=1.
W(1)=0.5
W(JTOT)=0.5
X0 = 0.05
!
USTR= UST
ZZ0=Z0
OMEGACC = MAX(SIG(NK),X0*GRAV/UST)
YC = OMEGACC*SQRT(ZZ0/GRAV)
! DELY = MAX((1.-YC)/REAL(JTOT),0.)
! Changed integration variable from Y to LOG(Y) and to log(K)
!ZINF = LOG(YC)
!DELY = MAX((1.-ZINF)/REAL(JTOT),0.)
ZINF = LOG(SIG(NK)**2/GRAV)
DELY = (LOG(TPI/0.005)-ZINF)/REAL(JTOT)
TAUR=UST**2
TAU1=0.
! Integration loop over the tail wavenumbers or frequencies ...
DO J=1,JTOT
!Y = YC+REAL(J-1)*DELY
!OMEGA = Y*SQRT(GRAV/ZZ0)
!OMEGA = SQRT(GRAV*Y)
! This is the deep water phase speed... No surface tension !!
!CM = GRAV/OMEGA
! With this form, Y is the wavenumber in the tail;
Y= EXP(ZINF+REAL(J-1)*DELY)
TENSK =1+(Y/KM)**2
OMEGA = SQRT(GRAV*Y*TENSK)
CM = SQRT(GRAV*TENSK/Y)
CGTAIL = 0.5*(3*(Y/KM)**2+1)*SQRT(GRAV/(Y*TENSK))
!this is the inverse wave age, shifted by ZZALP (tuning)
ZX = USTR/CM +ZZALP
ZARG = MIN(KAPPA/ZX,20.)
! ZMU corresponds to EXP(ZCN)
ZMU = MIN(GRAV*ZZ0/CM**2*EXP(ZARG),1.)
ZLOG = MIN(ALOG(ZMU),0.)
ZBETA = CONST1*ZMU*ZLOG**4
!
! Optional addition of capillary wave peak if SINTAIL2=1
!
IF (SINTAILPAR(3).GT.0) THEN
IF (USTR.LT.CM) THEN
ALPHAM=MAX(0.,0.01*(1.+ALOG(USTR/CM)))
ELSE
ALPHAM=0.01*(1+3.*ALOG(USTR/CM))
END IF
FM=EXP(-0.25*(Y/KM-1)**2)
ALPHAT=ALPHAM*(CMM/CM)*FM ! equivalent to 2*Bh in Elfouhaily et al.
LEVTAIL=LEVTAIL0*0.5*(1-tanh((Y-20)/5))+SINTAILPAR(3)*0.5*(1+TANH((Y-20)/5))*ALPHAT
ELSE
LEVTAIL=LEVTAIL0
END IF
! WRITE(991,*) 'TAIL??',SINTAILPAR(3),LEVTAIL0,LEVTAIL,ALPHAT,Y,Y/KM,OMEGA/(TPI)
!TAU1=TAU1+W(J)*ZBETA*(USTR/UST)**2/Y*DELY ! integration over LOG(Y)
TAU1=TAU1+W(J)*ZBETA*USTR**2*LEVTAIL*DELY*CGTAIL/CM ! integration over LOG(K)
! NB: the factor ABS(TTAUWSHELTER) was forgotten in the TAUHFT2 table
!TAUR=TAUR-W(J)*ABS(TTAUWSHELTER)*USTR**2*ZBETA*LEVTAIL/Y*DELY
!TAUR=TAUR-W(J)*USTR**2*ZBETA*LEVTAIL*DELY ! integration over LOG(Y)
TAUR=TAUR-W(J)*SINTAILPAR(2)*USTR**2*ZBETA*LEVTAIL*DELY*CGTAIL/CM ! DK/K*CG/C = D OMEGA / OMEGA
USTR=SQRT(MAX(TAUR,0.))
END DO
DEALLOCATE(W)
TAU1NT=TAU1
TAUHF = TAU1
!
! In this case, uses tables for high frequency contribution to TAUW.
!
ELSE
! finds the values in the tabulated stress TAUHFT
XI=UST/DELUST
IND = MAX(1,MIN (IUSTAR-1, INT(XI)))
DELI1= MAX(MIN (1. ,XI-FLOAT(IND)),0.)
DELI2= 1. - DELI1
XJ=MAX(0.,(GRAV*Z0/MAX(UST,0.00001)**2-AALPHA) / DELALP)
J = MAX(1 ,MIN (IALPHA-1, INT(XJ)))
DELJ1= MAX(0.,MIN (1. , XJ-FLOAT(J)))
DELJ2=1. - DELJ1
IF (TTAUWSHELTER.GT.0) THEN
XK = LEVTAIL0/ DELTAIL
I = MIN (ILEVTAIL-1, INT(XK))
DELK1= MIN (1. ,XK-FLOAT(I))
DELK2=1. - DELK1
TAU1 =((TAUHFT2(IND,J,I)*DELI2+TAUHFT2(IND+1,J,I)*DELI1 )*DELJ2 &
+(TAUHFT2(IND,J+1,I)*DELI2+TAUHFT2(IND+1,J+1,I)*DELI1)*DELJ1)*DELK2 &
+((TAUHFT2(IND,J,I+1)*DELI2+TAUHFT2(IND+1,J,I+1)*DELI1 )*DELJ2 &
+(TAUHFT2(IND,J+1,I+1)*DELI2+TAUHFT2(IND+1,J+1,I+1)*DELI1)*DELJ1)*DELK1
ELSE
TAU1 =(TAUHFT(IND,J)*DELI2+TAUHFT(IND+1,J)*DELI1 )*DELJ2 &
+(TAUHFT(IND,J+1)*DELI2+TAUHFT(IND+1,J+1)*DELI1)*DELJ1
END IF
!
TAUHF = LEVTAIL0*UST**2*TAU1
END IF ! End of test on use of table
TAUWX = XSTRESS+TAUHF*COS(USDIRP)
TAUWY = YSTRESS+TAUHF*SIN(USDIRP)
!
! Reduces tail effect to make sure that wave-supported stress
! is less than total stress, this is borrowed from ECWAM Stresso.F
!
TAUW = SQRT(TAUWX**2+TAUWY**2)
UST2 = MAX(USTAR,EPS2)**2
TAUWB = MIN(TAUW,MAX(UST2-EPS1,EPS2**2))
IF (TAUWB.LT.TAUW) THEN
TAUWX=TAUWX*TAUWB/TAUW
TAUWY=TAUWY*TAUWB/TAUW
END IF
!
RETURN
!
! Formats
!
#ifdef W3_T
9000 FORMAT (' TEST W3SIN4 : COMMON FACT.: ',3E10.3)
9001 FORMAT (' TEST W3SIN4 : ISTAB :',I2/ &
' TAUX :',E12.3/ &
' TAUY :',E12.3/ &
' UST :',E12.3)
9002 FORMAT (' TEST W3SIN4 : SUM(D) :',E12.3/ &
' SUM(A) :',E12.3/ &
' STRESSX :',E12.3/ &
' STRESSY :',E12.3/ &
' TAUWNX :',E12.3/ &
' TAUWNY :',E12.3)
9003 FORMAT (' TEST W3SIN4 : AS :',F8.4/ &
' Usigma :',E12.3/ &
' USTARsigma :',E12.3/ &
' U :',E12.3)
#endif
!/
!/ End of W3SIN4 ----------------------------------------------------- /
!/
END SUBROUTINE W3SIN4