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wwm_breaking.F90
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#include "wwm_functions.h"
!**********************************************************************
! Sept. 2020 : MP updates *
! - Restructuration of the code to account for various dissipation *
! models and associated breaking criterion *
! - New adaptive breaking coefficient *
!**********************************************************************
SUBROUTINE SDS_SWB(IP, SME, KME, ETOT, HS, ACLOC, SSBR, DSSBR)
USE DATAPOOL
IMPLICIT NONE
INTEGER, INTENT(IN) :: IP
REAL(rkind), INTENT(IN) :: ACLOC(NUMSIG,NUMDIR), SME, KME, ETOT, HS
REAL(rkind), INTENT(OUT) :: SSBR(NUMSIG,NUMDIR), DSSBR(NUMSIG,NUMDIR)
REAL(rkind) :: FPP,TPP,CPP,WNPP,CGPP,KPP,LPP,PEAKDSPR,PEAKDM,DPEAK,TPPD,KPPD,CGPD,CPPD
REAL(rkind) :: BR_COEF
REAL(rkind) :: HMAX_LOC
REAL(rkind) :: BETA, QQ, QB, BETA2, ARG
REAL(rkind) :: BIPH,Ur,S0
REAL(rkind) :: SBRD, WS, SURFA0, SURFA1
REAL(rkind) :: ERF_BETA
REAL(rkind) :: WAVEDIR, DPDW
INTEGER :: ie,inne,icount
INTEGER :: IS, ID
#ifdef SCHISM
SBR(:,IP) = ZERO
#endif
!---------------------------------------
! 1. Defining the breaking criterion
!---------------------------------------
SELECT CASE(ICRIT)
CASE(1)
! Constant breaking index (gamma) or gamma_TG
BRCRIT(IP) = BRCR
CASE(2)
! AR
! gamma based on local steepness adapted from Battjes and Stive (1985)
! MP : introduce min_BRCR, max_BRCR instead of switching to BRCR ?
IF (KME .GT. VERYSMALL) THEN
S0 = HS / (PI2/KME)
BRCRIT(IP) = 0.5_rkind + 0.4_rkind * MyTANH(33._rkind * S0)
ELSE
BRCRIT(IP) = BRCR
END IF
CASE(3)
! Breaking criterion based on the biphase (van der Westhuysen, 2010)
! Check that the user chose the correct formulation for breaking
IF (IBREAK .NE. 4) CALL WWM_ABORT('THE BIPHASE CRITERION CAN ONLY BE USED WITH IBREAK = 4')
CALL URSELL_NUMBER( HS, SME, DEP(IP), Ur)
! Default a_BIPH = 0.2D0
BIPH = 0.5D0*PI * ( -1.D0 + TANH(a_BIPH/max(0D-6,Ur)) )
IF (BRCR .GT. 0D0) THEN
CALL WWM_ABORT('THE BIPHASE REF IS IN [-PI/2,0]')
ELSE
BRCRIT(IP) = BIPH / BRCR
END IF
CASE(4)
CALL WWM_ABORT('THIS IS NOT SUPPORTED IN WWMV')
! Adaptative gamma_TG with bottom slope : BRCRIT = a_BRCR*slope + b_BRCR
! (e.g. Sallenger and Holman, 1985)
! lower and upper limit values prescribed in wwminput.nml
! CALL PEAK_PARAMETER(IP,ACLOC,NUMSIG,FPP,TPP,CPP,WNPP,CGPP,KPP,LPP,PEAKDSPR,PEAKDM,DPEAK,TPPD,KPPD,CGPD,CPPD)
!WAVEDIR = PEAKDM * PI / 180.d0 + PI / 2.d0 !conversion naut. to math. and in rad.
#ifdef SCHISM
!DPDW = tanbeta_x(IP)*COS(WAVEDIR) + tanbeta_y(IP)*SIN(WAVEDIR)
#endif
!BRCRIT(IP) = a_BRCR*dpdw + b_BRCR
!IF (BRCRIT(IP) < min_BRCR) BRCRIT(IP) = min_BRCR
!IF (BRCRIT(IP) > max_BRCR) BRCRIT(IP) = max_BRCR
CASE(5)
! Adaptive gamma with non dimensional depth : BRCRIT = a_BRCR*kph + b_BRCR
! (e.g. Ruessink et al., 2003)
! lower and upper limit values prescribed in wwminput.nml
CALL PEAK_PARAMETER(IP,ACLOC,NUMSIG,FPP,TPP,CPP,WNPP,CGPP,KPP,LPP,PEAKDSPR,PEAKDM,DPEAK,TPPD,KPPD,CGPD,CPPD)
BRCRIT(IP) = a_BRCR*KPP*DEP(IP)+b_BRCR
IF (BRCRIT(IP) < min_BRCR) BRCRIT(IP) = min_BRCR
IF (BRCRIT(IP) > max_BRCR) BRCRIT(IP) = max_BRCR
CASE(6)
! AR
! Same as ICRIT = 2 but based on peak steepness
! MP : introduce min_BRCR, max_BRCR instead of switching to BRCR ?
CALL PEAK_PARAMETER(IP,ACLOC,NUMSIG,FPP,TPP,CPP,WNPP,CGPP,KPP,LPP,PEAKDSPR,PEAKDM,DPEAK,TPPD,KPPD,CGPD,CPPD)
IF (LPP .GT. VERYSMALL) THEN
S0 = HS/LPP
BRCRIT(IP) = 0.5_rkind + 0.4_rkind * MyTANH(33._rkind * S0)
ELSE
BRCRIT(IP) = BRCR
END IF
CASE DEFAULT
CALL WWM_ABORT('ICRIT HAS A WRONG VALUE')
END SELECT
!! Conversion to monochromatic waves if needed
IF (LMONO_IN) HMAX(IP) = HMAX(IP) * SQRT(TWO)
!-----------------------------------------
! 2. Defining the breaking coefficient
!-----------------------------------------
! Breaking coefficient parameterization
IF (BR_COEF_METHOD == 1) THEN
! Constant
SELECT CASE(IBREAK)
CASE(1,5)
BR_COEF = ALPBJ
CASE(2,3,4,6)
BR_COEF = ALPBJ**3D0
END SELECT
ELSE IF (BR_COEF_METHOD == 2) THEN
! Adaptive with bottom slope (Pezerat et al., 2020 - under review)
BR_COEF = A_BR_COEF(IP)
ELSE
CALL WWM_ABORT('BR_COEF_METHOD HAS A WRONG VALUE')
END IF
!----------------------------------------------------
! 3. Computing momentum sink due to wave breaking
!----------------------------------------------------
SELECT CASE(IBREAK)
CASE(1)
!*************************
! Battjes and Janssen (1978)
!*************************
HMAX_LOC = BRCRIT(IP) * DEP(IP)
IF ( (HMAX_LOC .GT. VERYSMALL) .AND. (ETOT .GT. VERYSMALL) ) THEN
BETA = SQRT(8. * ETOT / HMAX_LOC**2D0)
BETA2 = BETA**2D0
ELSE
BETA = ZERO
BETA2 = ZERO
END IF
IF (BETA <= 0.5D0) THEN
QQ = ZERO
ELSE IF (BETA <= ONE) THEN
QQ = (TWO*BETA-ONE)**2
END IF
IF (BETA .LT. 0.2D0) THEN
QB = ZERO
ELSE IF (BETA .LT. ONE) THEN
ARG = EXP((QQ - ONE) / BETA2)
QB = QQ - BETA2 * (QQ - ARG)/(BETA2 - ARG)
DO IS = 1, 3
QB = EXP((QB-ONE)/BETA2)
END DO
ELSE
QB = ONE - SMALL
ENDIF
QBLOCAL(IP) = QB
! Implicit solver
! Source terms are linearized using a Newton-Raphson approach
IF (.false.) THEN!ICOMP .GE. 2) THEN
IF ( BETA2 .GT. VERYSMALL .AND. MyABS(BETA2 - QB) .GT. VERYSMALL ) THEN
IF ( BETA2 .LT. ONE) THEN
WS = (BR_COEF / PI) * QB * SME / BETA2
SbrD = WS * (ONE - QB) / (BETA2 - QB)
ELSE
WS = (BR_COEF / PI) * SME * BETA2**2
SbrD = ZERO
END IF
SURFA0 = SbrD
SURFA1 = WS + SbrD
ELSE
SURFA0 = ZERO
SURFA1 = ZERO
END IF
! Explicit solver
ELSE
IF ( BETA2 .GT. ZERO .AND. MyABS(BETA2 - QB) .GT. ZERO ) THEN
IF ( BETA2 .LT. ONE) THEN
SURFA0 = - BR_COEF / PI * QB * SME / BETA2
ELSE
SURFA0 = - BR_COEF / PI * SME * BETA2**2 ! degeneraive regime not covered by BJ78, all energy must vansh
END IF
ELSE
SURFA0 = 0D0
END IF
END IF
CASE(2)
!**********************************************
! Thornton and Guza (1983) - Saturation concept
!**********************************************
IF ( (DEP(IP) .GT. VERYSMALL) .AND. (ETOT .GT. VERYSMALL) ) THEN
BETA = SQRT(8. * ETOT / (BRCRIT(IP)*DEP(IP))**2D0)
BETA2 = BETA**2D0
ELSE
BETA = ZERO
BETA2 = ZERO
END IF
! Implicit solver
! Source terms are linearized using a Newton-Raphson approach
IF (ICOMP .GE. 2) THEN
IF ( BETA.GT.0D0 ) THEN
IF ( BETA.LT.1D0 ) THEN ! AR: need to put the parameters of the breaking function in the input file
WS = 75D-2*0.42d0*BR_COEF*SME*BETA2**INT(0.5*(3.d0+1.d0))/SQRTPI
SbrD = 5D-1*(3.+7.)*WS
ELSE
WS = 75D-2*0.42*BR_COEF*SME/SQRTPI
SbrD = WS
END IF
SURFA0 = SbrD - WS
SURFA1 = SbrD
ELSE
SURFA0 = 0D0
SURFA1 = 0D0
END IF
! Explicit solver
ELSE
IF ( BETA .GT. 0D0 ) THEN
IF ( BETA .LT. 1D0 ) THEN
SURFA0 = - 0.75D0 * BR_COEF * SME / SQRTPI * BRCRIT(IP) * BETA**5D0
ELSE
SURFA0 = - 0.75D0 * BR_COEF * SME / SQRTPI * BRCRIT(IP)
END IF
ELSE
SURFA0 = 0D0
END IF
END IF
CASE(3)
!*******************************************************
! Thornton and Guza (1983) - Skewed breaking probability
!*******************************************************
IF ( (DEP(IP) .GT. VERYSMALL) .AND. (ETOT .GT. VERYSMALL) ) THEN
BETA = SQRT(8. * ETOT / (BRCRIT(IP)*DEP(IP))**2D0)
BETA2 = BETA**2D0
ELSE
BETA = ZERO
BETA2 = ZERO
END IF
! Implicit solver
! TO DO
IF (ICOMP .GE. 2) THEN
CALL WWM_ABORT('IBREAK=3 not yet implemented in implicit')
! Explicit Solver
ELSE
IF ( BETA .GT. 0D0 ) THEN
IF ( BETA .LT. 1D0 ) THEN
SURFA0 = - 0.75D0 * BR_COEF * SME / SQRTPI * BRCRIT(IP) &
& * BETA**3D0 * (1D0 - (1D0 + BETA2)**(-5D0 / 2D0))
ELSE
SURFA0 = - 0.75D0 * BR_COEF * SME / SQRTPI * BRCRIT(IP) &
& * (1 - 2**(-5D0 / 2D0))
END IF
ELSE
SURFA0 = 0.D0
END IF
END IF
CASE(4)
!*******************
! Westhuysen (2010)
!*******************
IF ((DEP(IP) .GT. VERYSMALL) .AND. (ETOT .GT. VERYSMALL)) THEN
BETA = SQRT(8D0 * ETOT) / DEP(IP)
ELSE
BETA = ZERO
END IF
! Implicit solver
! TO DO
IF (ICOMP .GE. 2) THEN
CALL WWM_ABORT('IBREAK=4 not yet implemented in implicit')
! Explicit Solver
ELSE
IF ( BRCRIT(IP) .GT. 0D0 ) THEN
IF ( BRCRIT(IP) .LT. 1D0 ) THEN
SURFA0 = - 0.75D0 * BR_COEF * SME / SQRTPI * BRCRIT(IP)**2.5D0 * BETA
ELSE
SURFA0 = - 0.75D0 * BR_COEF * SME / SQRTPI * BETA
END IF
ELSE
SURFA0 = 0.D0
END IF
END IF
CASE(5)
!*************************************************************
! Baldock et al. (1998) modified by Janssen and Battjes (2007)
!*************************************************************
HMAX_LOC = BRCRIT(IP) * DEP(IP)
IF ( (HMAX_LOC .GT. VERYSMALL) .AND. (ETOT .GT. VERYSMALL) ) THEN
BETA = SQRT(HMAX_LOC**2D0 / (8. * ETOT) )
ELSE
BETA = ZERO
END IF
CALL COMPUTE_ERF(BETA,ERF_BETA)
! Implicit solver
! TO DO
IF (ICOMP .GE. 2) THEN
CALL WWM_ABORT('IBREAK=5 not yet implemented in implicit')
! Explicit Solver
ELSE
IF (BETA .GT. 0D0) THEN
SURFA0 = -0.75D0 * BR_COEF * SME / SQRTPI * BRCRIT(IP) / BETA &
& * (1D0 + 4D0 / (3D0 * SQRTPI) * (BETA**3D0 + 1.5D0 * BETA) &
& * exp(-BETA**2) - ERF_BETA)
ELSE
SURFA0 = 0D0
END IF
END IF
CASE(6)
!***************************
! Church and Thornton (1993)
!***************************
IF ( (DEP(IP) .GT. VERYSMALL) .AND. (ETOT .GT. VERYSMALL) ) THEN
BETA = SQRT(8. * ETOT / ((BRCRIT(IP)*DEP(IP))**2D0))
BETA2 = BETA**2D0
ELSE
BETA = ZERO
BETA2 = ZERO
END IF
IF (ICOMP .GE. 2) THEN
!MP: These lines have to be checked
!IF ( BETA .GT. 0D0 ) THEN
! IF ( BETA .LT. 1D0 ) THEN
! WS = -(0.75d0*BR_COEF*SME/MyREAL(SQRT(PI)))*SQRT(8.d0*ETOT)/DEP(IP)&
! & *(1+tanh(8*(BETA-1)))*(1-(1+BETA**2)**(-5/2))
! SbrD = 5D-1*MyREAL(7.)*WS
! ELSE
! WS = -(0.75d0*BR_COEF*SME/MyREAL(SQRT(PI)))*SQRT(8.d0*ETOT)/DEP(IP)
! SbrD = WS
! ENDIF
! SURFA0 = SbrD - WS
! SURFA1 = SbrD
!ELSE
! SURFA0 = 0D0
! SURFA1 = 0D0
!ENDIF
CALL WWM_ABORT('IBREAK=6 not yet implemented in implicit')
ELSE ! AR : Only works in explicit for now
IF ( BETA .GT. 0D0 ) THEN
IF ( BETA .LT. 1D0 ) THEN
SURFA0 = - 0.75D0 * BR_COEF * SME / SQRTPI * BRCRIT(IP) * BETA &
& * (1 + tanh(8 * (BETA - 1))) * (1 - (1 + BETA**2)**(-5/2))
ELSE
SURFA0 = - 0.75D0 * BR_COEF * SME / SQRTPI * BRCRIT(IP) &
& * (1 - 2**(-5D0 / 2D0))
END IF
ELSE
SURFA0 = 0D0
END IF
END IF
END SELECT
!----------------------------------
! 4. Filling the matrixes
!----------------------------------
DO IS = 1, NUMSIG
DO ID = 1, NUMDIR
IF (ICOMP .GE. 2) THEN
DSSBR(IS,ID) = SURFA0
SSBR(IS,ID) = SURFA0 * ACLOC(IS,ID)
ELSE IF (ICOMP .LT. 2) THEN
DSSBR(IS,ID) = SURFA0
SSBR(IS,ID) = SURFA0 * ACLOC(IS,ID)
END IF
END DO
END DO
END SUBROUTINE
!**********************************************************************
!* *
!**********************************************************************
SUBROUTINE COMPUTE_SBR(IP,SSBR)
USE DATAPOOL
IMPLICIT NONE
INTEGER :: IS, ID
INTEGER, INTENT(IN) :: IP
REAL(rkind), INTENT(IN) :: SSBR(NUMSIG,NUMDIR)
! Initialization
#ifdef SCHISM
SBR(:,IP) = ZERO
! Loop over frequencies and directions
DO IS = 1, NUMSIG
DO ID = 1, NUMDIR
SBR(1,IP) = SBR(1,IP) + G9*COSTH(ID)*WK(IS,IP)*SSBR(IS,ID)*DS_INCR(IS)*DDIR
SBR(2,IP) = SBR(2,IP) + G9*SINTH(ID)*WK(IS,IP)*SSBR(IS,ID)*DS_INCR(IS)*DDIR
END DO
END DO
#endif
END SUBROUTINE
!**********************************************************************
!* *
!**********************************************************************
SUBROUTINE COMPUTE_ERF(x,erfx)
! # MS Fortran
! Error function from Numerical Recipes.
! erf(x) = 1 - erfc(x)
USE DATAPOOL, only : rkind
IMPLICIT NONE
REAL(rkind), INTENT(IN) :: x
REAL(rkind), INTENT(OUT) :: erfx
REAL(rkind) :: dumerfc, t, z
z = abs(x)
t = 1.0 / ( 1.0 + 0.5 * z )
dumerfc = t * exp(-z * z - 1.26551223 + t * &
( 1.00002368 + t * ( 0.37409196 + t * &
( 0.09678418 + t * (-0.18628806 + t * &
( 0.27886807 + t * (-1.13520398 + t * &
( 1.48851587 + t * (-0.82215223 + t * 0.17087277 )))))))))
IF ( x.lt.0.0 ) dumerfc = 2.0 - dumerfc
erfx = 1.0 - dumerfc
END SUBROUTINE COMPUTE_ERF
!**********************************************************************
!* *
!**********************************************************************