!> @file
!> @brief Contains MODULE W3SWLMD, for swell dissipation source term.
!>
!> @author H. L. Tolman @date 21-Nov-2011
!>
#include "w3macros.h"
!/ ------------------------------------------------------------------- /
!>
!> @brief Source term module for swell dissipation.
!>
!> @details Source term for swell dissipation based on different
!> physics that can be independently selected from the input
!> and whitecapping dissipation terms in the model setup.
!>
!> @author H. L. Tolman @date 21-Nov-2011
!>
MODULE W3SWLDMD
!/
!/ +-----------------------------------+
!/ | WAVEWATCH III NOAA/NCEP |
!/ | H. L. Tolman |
!/ | FORTRAN 90 |
!/ +-----------------------------------+
!/
!/ 21-Nov-2011 : Origination. ( version 4.07 )
!/
!/ Copyright 2009 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.
!/
! 1. Purpose :
!
! Source term module for swell dissipation based on different
! physics that can be independently selected form the input
! and whitecapping dissipation terms in the model setup.
!
! 2. Variables and types :
!
! Name Type Scope Description
! ----------------------------------------------------------------
! ----------------------------------------------------------------
!
! 3. Subroutines and functions :
!
! Name Type Scope Description
! ----------------------------------------------------------------
! W3SWL4 Subr. Public Ardhuin et al (2010+) swell dissipation
! W3SWL6 Subr. Public Babanin (2011) swell dissipation
!
! IRANGE Func. Private Generate a sequence of integer values
! ----------------------------------------------------------------
!
! 4. Subroutines and functions used :
!
! Name Type Module Description
! ----------------------------------------------------------------
! STRACE Subr. W3SERVMD Subroutine tracing.
! ----------------------------------------------------------------
!
! 5. Remarks :
!
!
! 6. Switches :
!
! !/S Enable subroutine tracing.
!
! 7. Source code :
!/
!/ ------------------------------------------------------------------- /
!/
PUBLIC :: W3SWL4, W3SWL6
PRIVATE :: IRANGE
!/
CONTAINS
!/ ------------------------------------------------------------------- /
!>
!> @brief FIXME
!>
!> @details A, S, D all stored as 1-D arrays with dimension NTH*NK
!> (column by column).
!>
!> @param[in] A Action density spectrum.
!> @param[in] CG Group velocities.
!> @param[in] WN Wavenumbers.
!> @param[in] DAIR Air density.
!> @param[out] S Source term.
!> @param[out] D Diagonal term of the derivative.
!>
!> @author H. L. Tolman @date 13-Aug-2021
!>
SUBROUTINE W3SWL4 (A, CG, WN, DAIR, S, D)
!/
!/ +-----------------------------------+
!/ | WAVEWATCH III NOAA/NCEP |
!/ | H. L. Tolman |
!/ | FORTRAN 90 |
!/ | Last update : 13-Aug-2021 |
!/ +-----------------------------------+
!/
!/ 29-May-2009 : Origination (w3srcxmd.ftn) ( version 3.14 )
!/ 06-Jan-2012 : Implementation (S. Zieger)
!/ 13-Aug-2021 : Consider DAIR a variable ( version x.xx )
!/
! 1. Purpose :
!
! FIXME
!
! 2. Method :
!
! 3. Parameters :
!
! Parameter list
! ----------------------------------------------------------------
! A¹ R.A. I Action density spectrum
! CG R.A. I Group velocities
! WN R.A. I Wavenumbers
! DAIR R.A. I Air density
! S¹ R.A. O Source term
! D¹ R.A. O Diagonal term of derivative
! ¹ Stored as 1-D array with dimension NTH*NK (column by column).
! ----------------------------------------------------------------
!
! 4. Subroutines used :
!
! Name Type Module Description
! ----------------------------------------------------------------
! IRANGE Func. W3SWLDMD
! STRACE Subr. W3SERVMD Subroutine tracing.
! ----------------------------------------------------------------
!
! 5. Called by :
!
! Name Type Module Description
! ----------------------------------------------------------------
! W3SRCE Subr. W3SRCEMD Source term integration.
! W3EXPO Subr. N/A Point output post-processor.
! GXEXPO Subr. N/A GrADS point output post-processor.
! ----------------------------------------------------------------
!
! 6. Error messages :
!
! None.
!
! 7. Remarks :
!
! 8. Structure :
!
! See comments in source code.
!
! 9. Switches :
!
! !/S Enable subroutine tracing.
!
! 10. Source code :
!
!/ ------------------------------------------------------------------- /
USE CONSTANTS, ONLY: GRAV, DWAT
USE W3GDATMD, ONLY: NK, NTH, NSPEC, SIG2, DDEN, FTE, SWL6B1
#ifdef W3_S
USE W3SERVMD, ONLY: STRACE
#endif
!/
IMPLICIT NONE
!/
!/ ------------------------------------------------------------------- /
!/ Parameter list
REAL, INTENT(IN) :: A(NSPEC), CG(NK), WN(NK), DAIR
REAL, INTENT(OUT) :: S(NSPEC), D(NSPEC)
!/
!/ ------------------------------------------------------------------- /
!/ Local parameters
#ifdef W3_S
INTEGER, SAVE :: IENT = 0
#endif
INTEGER :: IKN(NK), ITH
REAL, PARAMETER :: VA = 1.4E-5 ! Air kinematic viscosity (used in WAM).
REAL :: EB(NK), WN2(NSPEC), EMEAN
REAL :: FE, AORB, RE, RECRIT, UOSIG, CDSV
!/
!/ ------------------------------------------------------------------- /
!/
#ifdef W3_S
CALL STRACE (IENT, 'W3SWL4')
#endif
!
IKN = IRANGE(1,NSPEC,NTH)
D = 0.
WN2 = 0.
!
DO ITH = 1, NTH
WN2(IKN+(ITH-1)) = WN ! Wavenumbers to all directions.
END DO
!
EB = SUM(RESHAPE(A,(/ NTH,NK /)),1) * DDEN(1:NK) / CG
EMEAN = SUM(EB) + (EB(NK) / DDEN(NK)) * FTE
!
AORB = 2.0*SQRT(EMEAN)
!
EB = SUM(RESHAPE(A*SIG2**2,(/ NTH,NK /)),1) * DDEN(1:NK) / CG
UOSIG = 2.0*SQRT(SUM(EB))
FE = SWL6B1 ! (from NAMELIST)
! FE = 0.001 ! (from NAMELIST)
!/ 0.001 - 0.019 with median value 0.007 (Ardhuin et al 2009, Babanin 2011)
CDSV = 1.2
!
RECRIT = 1.0E5
RE = 4.0 * UOSIG * AORB / VA
!
IF (RE .GT. RECRIT) THEN
D = -(16.0/GRAV) * (DAIR/DWAT) * FE * (SIG2**2) *UOSIG
ELSE
D = -2.0 * (DAIR/DWAT) * CDSV * WN2 * SQRT(2.0 * VA * SIG2)
END IF
!
S = D * A
!
! WRITE(*,*) ' FE =',FE
! WRITE(*,*) ' HS =',4.*SQRT(EMEAN)
! WRITE(*,*) ' UOSIG =',UOSIG
! WRITE(*,*) ' AORB =',AORB
! WRITE(*,*) ' RE/RECRIT=',RE/RECRIT
! WRITE(*,*) ' SWL4_tot =',SUM(SUM(RESHAPE(S,(/ NTH,NK /)),1)*DDEN/CG)
!/
!/ End of W3SWL4 ----------------------------------------------------- /
!/
END SUBROUTINE W3SWL4
!/ ------------------------------------------------------------------- /
!>
!> @brief Turbulent dissipation of narrow-banded swell.
!>
!>
!> @details A, S, D all stored as 1-D arrays with dimension NTH*NK
!> (column by column).
!>
!> Described in Babanin (2011, Section 7.5).
!> Babanin 2011: Cambridge Press, 295-321, 463pp.
!>
!> S = D * A
!>
!> @param[in] A Action density spectrum.
!> @param[in] CG Group velocities.
!> @param[in] WN Wavenumbers.
!> @param[out] S Source term.
!> @param[out] D Diagonal term of the derivative.
!>
!> @author H. L. Tolman @date 16-Feb-2012
!>
SUBROUTINE W3SWL6 (A, CG, WN, S, D)
!/
!/ +-----------------------------------+
!/ | WAVEWATCH III NOAA/NCEP |
!/ | H. L. Tolman |
!/ | FORTRAN 90 |
!/ | Last update : 16-Feb-2012 |
!/ +-----------------------------------+
!/
!/ 29-May-2009 : Origination (w3srcxmd.ftn) ( version 3.14 )
!/ 16-Feb-2012 : Implementation ( version 4.07 )
!/ (S. Zieger)
!/
! 1. Purpose :
!
! Turbulent dissipation of narrow-banded swell as described in
! Babanin (2011, Section 7.5).
!
! Babanin 2011: Cambridge Press, 295-321, 463pp.
!
! 2. Method :
!
! S = D * A
!
! 3. Parameters :
!
! Parameter list
! ----------------------------------------------------------------
! A¹ R.A. I Action density spectrum
! CG R.A. I Group velocities
! WN R.A. I Wavenumbers
! S¹ R.A. O Source term
! D¹ R.A. O Diagonal term of derivative
! ¹ Stored as 1-D array with dimension NTH*NK (column by column).
! ----------------------------------------------------------------
!
! 4. Subroutines used :
!
! Name Type Module Description
! ----------------------------------------------------------------
! IRANGE Func. W3SWLDMD
! STRACE Subr. W3SERVMD Subroutine tracing.
! ----------------------------------------------------------------
!
! 5. Called by :
!
! Name Type Module Description
! ----------------------------------------------------------------
! W3SRCE Subr. W3SRCEMD Source term integration.
! W3EXPO Subr. N/A Point output post-processor.
! GXEXPO Subr. N/A GrADS point output post-processor.
! ----------------------------------------------------------------
!
! 6. Error messages :
!
! None.
!
! 7. Remarks :
!
! 8. Structure :
!
! See comments in source code.
!
! 9. Switches :
!
! !/S Enable subroutine tracing.
!
! 10. Source code :
!
!/ ------------------------------------------------------------------- /
USE CONSTANTS, ONLY: GRAV
USE W3GDATMD, ONLY: NK, NTH, NSPEC, SIG, DDEN, DTH
USE W3GDATMD, ONLY: SWL6CSTB1, SWL6B1, FTE, FTWN
#ifdef W3_T6
USE W3ODATMD, ONLY: NDST
#endif
#ifdef W3_S
USE W3SERVMD, ONLY: STRACE
#endif
!/
IMPLICIT NONE
!/
!/ ------------------------------------------------------------------- /
!/ Parameter list
REAL, INTENT(IN) :: A(NSPEC), CG(NK), WN(NK)
REAL, INTENT(OUT) :: S(NSPEC), D(NSPEC)
!/
!/ ------------------------------------------------------------------- /
!/ Local parameters
#ifdef W3_S
INTEGER, SAVE :: IENT = 0
#endif
INTEGER :: IK, ITH, IKN(NK)
REAL, DIMENSION(NK) :: ABAND, KMAX, ANAR, BN, AORB, DDIS
REAL :: K(NTH,NK), B1
!/
!/ ------------------------------------------------------------------- /
!/
#ifdef W3_S
CALL STRACE (IENT, 'W3SWL6')
#endif
!
!/ 0) --- Initialize parameters -------------------------------------- /
IKN = IRANGE(1,NSPEC,NTH) ! Index vector for array access, e.g.
! ! in form of WN(1:NK) == WN2(IKN).
ABAND = SUM(RESHAPE(A,(/ NTH,NK /)),1) ! action density as function of wavenumber
DDIS = 0.
D = 0.
B1 = SWL6B1 ! empirical constant from NAMELIST
!
!/ 1) --- Choose calculation of steepness a*k ------------------------ /
!/ Replace the measure of steepness with the spectral
! saturation after Banner et al. (2002) ---------------------- /
K = RESHAPE(A,(/ NTH,NK /))
KMAX = MAXVAL(K,1)
DO IK = 1,NK
IF (KMAX(IK).LT.1.0E-34) THEN
K(1:NTH,IK) = 1.
ELSE
K(1:NTH,IK) = K(1:NTH,IK)/KMAX(IK)
END IF
END DO
ANAR = 1.0/( SUM(K,1) * DTH )
BN = ANAR * ( ABAND * SIG(1:NK) * DTH ) * WN**3
!
IF (.NOT.SWL6CSTB1) THEN
!
!/ --- A constant value for B1 attenuates swell too strong in the
!/ western central Pacific (i.e. cross swell less than 1.0m).
!/ Workaround is to scale B1 with steepness a*kp, where kp is
!/ the peak wavenumber. SWL6B1 remains a scaling constant, but
!/ with different magnitude. --------------------------------- /
IK = MAXLOC(ABAND,1) ! Index for peak
! EMEAN = SUM(ABAND * DDEN / CG) ! Total sea surface variance
B1 = SWL6B1 * ( 2. * SQRT(SUM(ABAND*DDEN/CG)) * WN(IK) )
!
END IF
!
!/ 2) --- Calculate the derivative term only (in units of 1/s) ------- /
DO IK = 1,NK
IF (ABAND(IK) .GT. 1.E-30) THEN
DDIS(IK) = -(2./3.) * B1 * SIG(IK) * SQRT(BN(IK))
END IF
END DO
!
!/ 3) --- Apply dissipation term of derivative to all directions ----- /
DO ITH = 1, NTH
D(IKN+(ITH-1)) = DDIS
END DO
!
S = D * A
!
! WRITE(*,*) ' B1 =',B1
! WRITE(*,*) ' DDIS_tot =',SUM(DDIS*ABAND*DDEN/CG)
! WRITE(*,*) ' EDENS_tot=',sum(aband*dden/cg)
! WRITE(*,*) ' EDENS_tot=',sum(aband*sig*dth*dsii/cg)
! WRITE(*,*) ' '
! WRITE(*,*) ' SWL6_tot =',sum(SUM(RESHAPE(S,(/ NTH,NK /)),1)*DDEN/CG)
!
!/
!/ End of W3SWL6 ----------------------------------------------------- /
!/
END SUBROUTINE W3SWL6
!/ ------------------------------------------------------------------- /
!/
!>
!> @brief Generate a linear-spaced sequence of integer numbers.
!>
!> @details Used for array addressing (indexing).
!>
!> @param X0
!> @param X1
!> @param DX
!> @returns IX
!>
!> @author H. L. Tolman
!> @author S. Zieger
!> @date 15-Feb-2011
!>
FUNCTION IRANGE(X0,X1,DX) RESULT(IX)
!/
!/ +-----------------------------------+
!/ | WAVEWATCH III NOAA/NCEP |
!/ | H. L. Tolman |
!/ | S. Zieger |
!/ | FORTRAN 90 |
!/ | Last update : 15-Feb-2011 |
!/ +-----------------------------------+
!/
!/ 15-Feb-2011 : Origination from W3SRC6MD ( version 4.07 )
!/ (S. Zieger)
!/
! 1. Purpose :
! Generate a linear-spaced sequence of integer
! numbers. Used for array addressing (indexing).
!
!/
IMPLICIT NONE
INTEGER, INTENT(IN) :: X0, X1, DX
INTEGER, ALLOCATABLE :: IX(:)
INTEGER :: N
INTEGER :: I
!
N = INT(REAL(X1-X0)/REAL(DX))+1
ALLOCATE(IX(N))
DO I = 1, N
IX(I) = X0+ (I-1)*DX
END DO
!/
END FUNCTION IRANGE
!/ ------------------------------------------------------------------- /
!/
END MODULE W3SWLDMD