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!
! SWAN/COMPU file 2 of 5
!
! PROGRAM SWANCOM2.FOR
!
! This file SWANCOM2 of the main program SWAN
! include the next subroutines (mainly subroutines for
! the source terms for dissipation and some general stuff):
!
! DISSIPATION SOURCE TERMS :
!
! SBOT (Bottom friction)
! SVEG (Dissipation due to vegetation) 40.55
! STURBV (dissipation due to turbulent viscosity) 40.35
! SMUD (Fluid mud-induced wave dissipation) 40.59
! SICE (dissipation by sea ice) 41.75
! FRABRE (Fraction of breaking waves) 30.77
! SSURF (Wave breaking: five formulations)
! SWCAP (White capping: seven formulations) 40.53
! SWCAP8 (Whitecapping according to Rogers et al. (JTECH 2012)) 40.88
! BRKPAR (compute variable gamma for Battjes-Janssen breaking formula)
! CNTAIL (contributions to the spectrum of the high frequency tail)
! PLTSRC (store the values for plot of the source terms and spec.)
!
!****************************************************************
!
SUBROUTINE SBOT (ABRBOT ,DEP2 ,ECOS ,ESIN ,AC2 , 41.04
& IMATDA ,KWAVE ,SPCSIG ,UBOT ,UX2 , 30.72
& UY2 ,IDCMIN ,IDCMAX ,IT ,ITER , 41.51
& SWPDIR ,PLBTFR ,ISSTOP ,DISSC1 ,VARFR , 41.51 40.67
& FRCOEF )
!
!****************************************************************
!
USE SWCOMM3 40.41
USE SWCOMM4 40.41
USE OCPCOMM4 40.41
!
IMPLICIT NONE
!
!
! --|-----------------------------------------------------------|--
! | Delft University of Technology |
! | Faculty of Civil Engineering and Geosciences |
! | Environmental Fluid Mechanics Section |
! | P.O. Box 5048, 2600 GA Delft, The Netherlands |
! | |
! | Programmers: The SWAN team |
! --|-----------------------------------------------------------|--
!
!
! SWAN (Simulating WAves Nearshore); a third generation wave model
! Copyright (C) 1993-2024 Delft University of Technology
!
! This program is free software: you can redistribute it and/or modify
! it under the terms of the GNU General Public License as published by
! the Free Software Foundation, either version 3 of the License, or
! (at your option) any later version.
!
! This program is distributed in the hope that it will be useful,
! but WITHOUT ANY WARRANTY; without even the implied warranty of
! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
! GNU General Public License for more details.
!
! You should have received a copy of the GNU General Public License
! along with this program. If not, see <http://www.gnu.org/licenses/>.
!
!
! 0. Authors
!
! 20.68: Nico Booij
! 30.72: IJsbrand Haagsma
! 40.41: Marcel Zijlema
! 40.61: Marcel Zijlema
! 40.67: Nico Booij
! 41.04: Marcel Zijlema
! 41.51: Grant Smith
!
! 1. Updates
!
! 20.68, Jan. 96: subroutine restructured variable friction coefficient
! introduced Putnam model replaced by Collins
! 30.72, Feb. 98: Introduced generic names XCGRID, YCGRID and SPCSIG for SWAN
! 40.41, Oct. 04: common blocks replaced by modules, include files removed
! 40.61, Sep. 06: introduce DISBOT variable for output purposes
! 40.67, Jun. 07: more accurate computation fo dissipation terms
! 41.04, Mar. 09: frequency-dependent JONSWAP formulation
! 41.51, Apr. 14: introduce ripples model
!
! 2. Purpose
!
! Computation of the source terms due to bottom friction
!
! 3. Method
!
! In SWAN several bottom friction dissipation models are computed, i.e.:
!
! IBOT = 1 Jonswap bottom friction model
! IBOT = 2 Collins bottom friction model
! IBOT = 3 Madsen bottom friction model (see Tolman)
! IBOT = 5 ripples model (see Smith et al, 2011)
!
! Both methods are implemented in SWAN and the user has to make
! a choice in the input file.
!
! 1. Jonswap model:
! -----------------
!
! The bottom interaction term SEbf(s,d) is supposed to take the
! Jonswap form (Hasselman et al. 1973):
! 2
! sigma E(s,d)
! SEbf = -GAMMA ----------------
! 2 2
! g sinh (kD)
! 2 -3
! where GAMMA is the decay parameter, (default GAMMA = 0.038 m s ).
! In the Jonswap form the current velocities are not taken into
! account.
! Note that the value of 0.038 must be combined with second order 41.49
! polynomial wind drag 41.49
!
! 2. COLLINS model:
! -----------------
!
! The energy dissipation due to bottom friction is modelled
! according the quadratic friction law:
! 2
! SE = Tau * |U|
!
! which for a spectrum can be written as:
! 2
! sigma
! SE(s,d)= - ---------------- * (Cfw.Ub + Cfc.Uc) * E(s,d)
! 2
! g sinh (K(s) * D)
!
! Ub is the velocity due to the wave at the bottom
!
! The current velocity is Uc
!
! 3. MADSEN formulation:
! ----------------------
!
! The bottom friction dissipation applying Madsen formulation is as
! follows:
!
! fw [n - 1/2] UBR E(s,d)
! [1] Sdsb(s,d) = - ------------------------
! D
!
! in which :
! 2
! s * D
! [1a] (n - 1/2) = -------------
! 2
! 2 g sinh (kD)
!
! UBOT(IX,IY) is computed in the subroutine SINTGRL. The friction
! factor fw is estimated using the formulation of Jonsson (1963,
! 1966a):
!
! 1 1 Ab,r
! [2] -------- + log { ---------- } = mf + log { ----- }
! 4 sqrt(fw) 10 4 sqrt(fw) 10 Kn
!
! with:
!
! 2 // 1
! [3] Ab,r = 2 * // -------------- E(s,d) ds dd
! // 2
! sinh (kD)
!
! with: Ab,r is the representative near bottom excursion
! amplitude
! Kn equivalent roughness
! mf constant ( mf = -0.08) (determined by Jonsson
! and Carlssen 1976 )
!
! [2] is only valid for Ab,r/Kn larger than approximately 1.
! For smaller values a constant value of fw is used (fw = 0.3
! for Ab,r/Kn < 1.57 )
!
! 4. RIPPLES model:
! -----------------
!
! Friction depends on the formation process of bottom ripples and on
! the grain size of the sediment.
!
! Details can be found in
!
! Smith, Babanin, Riedel and Young (2011)
! Introduction of a new friction routine into the SWAN model that
! evaluates roughness due to bedform and sediment size changes
! Coastal Engineering, 58, 317-326
!
! 4. Argument variables
!
! SPCSIG: Relative frequencies in computational domain in sigma-space 30.72
!
REAL SPCSIG(MSC) 30.72
!
! INTEGERS :
! --------
!
! IX Counter of gridpoints in x-direction
! IY Counter of gridpoints in y-direction
! IS Counter of relative frequency band
! ID Counter of the spectral direction
! IBOT Indicator if bottom friction is on
! ICUR Indicator if a current is present
! IT current time step
! MBOT Maximum array size for the array PBOT
! MXC Maximum counter of gridppoints in x-direction
! MYC Maximum counter of gridppoints in y-direction
! MSC Maximum counter of relative frequency
! MDC Maximum counter of directional distribution
! ISSTOP Maximum counter of wave component in frequency
! space that is propagated
!
! REALS:
! ---------
!
! ABRBOT Near bottom excursion amplitude
! FACB an auxiliary factor contributing to bottom friction
! FW Friction factor
! GRAV Gravitational acceleration
! KD Wavenumber * Depth
! SBOTEO Sourceterm for the bottom friction to be stored
! in the array IMATDA
! CURR Main current velocity
! UC Absolute value of the current
! AKN Nikuradse bottom roughness
! S specific gravity of sediment
! D grain size of sediment
! PHI mobility number for determination of ripple geometry
! THETA Shields entrainment parameter
! DAST dimensionless sediment parameter
! THETAC critical Shields parameter where sediment becomes mobile
! RIPH ripple height
! RIPW ripple wavelength
!
! one and more dimensional arrays:
! ---------------------------------
!
! AC2 2D Action density
! DEP2 2D Depth
! ESIN 1D Sin per spectral direction (id)
! ECOS 1D Cos per spectral direction (id)
! IMATDA 2D Coefficients of diagonal of matrix
! KWAVE 2D Wavenumber function of frequency and IC
! PBOT 1D Coefficient for bottom friction models
! UBOT 2D Near bottom velocity as function of X,Y
! UX2 2D Current velocity in y direction as function of X,Y
! UY2 2D Current velocity in y direction as function of X,Y
! DISSC1 2D Dissipation coefficient, function of sigma and theta
! FRCOEF 2D Spatially variable friction coefficient 20.68
!
! 7. Common blocks used
!
!
! 8. Subroutines used
!
! ---
!
! 9. Subroutines calling
!
! SOURCE
!
! 10. Error Messages
!
! ---
!
! 11. Remarks
!
! According to Gleb Pantalev., Mar 3 2017, in the calculation of DDUM:
! ADUM should be replaced with "ADUM*log(10)"
! DDUM = ( ADUM + LOG10(ADUM) - XDUM ) /
! & ( 1.+ ( 1. / ADUM) )
! ^^^^
!
! 12. Structure
!
! ------------------------------------------------------------
! Compute CFBOT according to friction model
! For every spectral frequency do
! compute SBOTEO = CFBOT * (sigma/sinh(kd))**2
! For every spectral direction do
! add SBOTEO to matrix (IMATDA)
! -------------------------------------------------------------
!
! 13. Source text
!
INTEGER IENT, ID ,IDDUM, IS ,ISSTOP, IT, ITER, J, SWPDIR
!
REAL AKN ,XDUM ,KD ,SBOTEO,FACB ,
& CFW ,FW ,CURR ,UC ,ABRBOT,
& ADUM ,CDUM ,DDUM
REAL CFBOT(MSC)
REAL DSP ,ETOT ,EEX ,EEY ,EAD
REAL S ,D ,PHI ,THETA , 41.51
& DAST ,THETAC ,RIPH ,RIPW 41.51
!
LOGICAL VARFR
!
REAL AC2(MDC,MSC,MCGRD) , 41.04
& DEP2(MCGRD) ,
& ECOS(MDC) ,
& ESIN(MDC) ,
& IMATDA(MDC,MSC) ,
& KWAVE(MSC,MICMAX) ,
& PLBTFR(MDC,MSC,NPTST) , 40.00
& UBOT(MCGRD) ,
& UX2(MCGRD) ,
& UY2(MCGRD) ,
& DISSC1(MDC,MSC,1:MDISP) , 40.67
& FRCOEF(MCGRD) 20.68
!
INTEGER IDCMIN(MSC) ,
& IDCMAX(MSC)
!
SAVE IENT
DATA IENT/0/
IF (LTRACE) CALL STRACE (IENT,'SBOT')
!
IF ( IBOT .GE. 1 .AND. DEP2(KCGRD(1)) .GT. 0.) THEN
IF (IBOT.EQ.1) THEN
!
! *** Jonswap model ***
!
! PBOT(3) = GAMMA (a) in the Jonswap formulation
!
CFBOT = PBOT(3) / GRAV**2
ELSEIF (IBOT.EQ.2) THEN
!
! *** Collins model ***
!
! PBOT(2) = [cfw]
!
IF (VARFR) THEN 20.68
CFW = FRCOEF(KCGRD(1))
ELSE
CFW = PBOT(2)
ENDIF
CFBOT = CFW * UBOT(KCGRD(1)) / GRAV
ELSEIF (IBOT.EQ.3) THEN
!
! *** Madsen model ***
!
IF (VARFR) THEN 20.68
AKN = FRCOEF(KCGRD(1))
ELSE
AKN = PBOT(5)
ENDIF
IF (.NOT. AKN.NE.0.) AKN = 0.001
!
! *** PBOT(4) = Mf ***
! *** AKN = PBOT(5) = [kn] (roughness) ***
!
IF ( (ABRBOT / AKN ) .GT. 1.57 ) THEN
XDUM = PBOT(4) + LOG10 ( ABRBOT / AKN )
!
! *** solving the implicit equation using a Newton ***
! *** Rapshon iteration proces : a + log a = b ***
! *** the start value for ADUM = 0.3 because 0.3626 ***
! *** is the minimum value of ADUM with b=-0.08. ***
!
ADUM = 0.3
DO 28 J = 1, 50
CDUM = ADUM
DDUM = ( ADUM + LOG10(ADUM) - XDUM ) /
& ( 1.+ ( 1. / ADUM) )
ADUM = ADUM - DDUM
IF ( ABS(CDUM - ADUM) .LT. 1.E-4 ) GOTO 29
28 CONTINUE
WRITE(*,*) ' error in iteration fw: Madsen formulation'
29 CONTINUE
! 1 1
! *** computation of FW --> A = ----- --> FW = -----
! 4 uFW 16 A**2
FW = 1. / (16. * ADUM**2)
ELSE
FW = 0.3
ENDIF
CFBOT = UBOT(KCGRD(1)) * FW / (SQRT(2.) * GRAV)
ELSEIF ( IBOT.EQ.4 ) THEN
!
! *** Jonswap model with variable friction coefficient ***
! *** as function of frequency-dependent directional ***
! spreading (varies linearly between 0.038 - 0.067) ***
!
DO IS = 1, MSC
ETOT = 0.
EEX = 0.
EEY = 0.
DO ID = 1, MDC
EAD = SPCSIG(IS)*AC2(ID,IS,KCGRD(1))
ETOT = ETOT + EAD
EEX = EEX + EAD * ECOS(ID)
EEY = EEY + EAD * ESIN(ID)
ENDDO
IF ( ETOT.GT.0. ) THEN
XDUM = 1.-MIN(1.,SQRT(EEX*EEX+EEY*EEY)/ETOT)
DSP = SQRT(2.*XDUM) *180./PI
ELSE
DSP = 0.
ENDIF
IF ( DSP.LT.PBOT(8) ) THEN
CFBOT(IS) = PBOT(6)
ELSEIF ( DSP.GT.PBOT(9) ) THEN
CFBOT(IS) = PBOT(7)
ELSE
CFBOT(IS) = PBOT(6) + (PBOT(7)-PBOT(6))*(DSP-PBOT(8))/
& (PBOT(9)-PBOT(8))
ENDIF
CFBOT(IS) = CFBOT(IS) / GRAV**2
ENDDO
ELSEIF ( IBOT.EQ.5 ) THEN
!
! *** ripples model ***
!
! set some constants
S = PBOT(6)
D = PBOT(7)
IF ( NSTATC.EQ.1 .AND. IT.EQ.1 ) THEN
! if nonstationary and first time step, roughness is based on grain size (assumes no ripples)
AKN = 2.5*D
IF ( (AKN/ABRBOT).LT.0.63 ) THEN
! friction factor based on Swart formula
FW = EXP(5.213*((AKN/ABRBOT)**0.194)-5.977)
ELSE
FW = 0.3
ENDIF
ELSEIF ( NSTATC.EQ.0 .AND. ITER.EQ.1 ) THEN
! if stationary and first iteration, roughness is based on grain size (assumes no ripples)
AKN = 2.5*D
IF ( (AKN/ABRBOT).LT.0.63 ) THEN
! friction factor based on Swart formula
FW = EXP(5.213*((AKN/ABRBOT)**0.194)-5.977)
ELSE
FW = 0.3
ENDIF
ELSE
! set friction factor obtained from previous time step or iteration
FW = FRCOEF(KCGRD(1))
ENDIF
! mobility number
PHI = ((UBOT(KCGRD(1)))**2)/((S-1.)*GRAV*D)
! Shields entrainment parameter
THETA = 0.5 * FW * PHI
! dimensionless sediment size parameter
DAST = (((GRAV*(S-1.))/((1.36E-6)**2))**(1./3.))*D
! critical Shields parameter where sediment begins to move
THETAC = 0.3/(1.+(1.2*DAST))+0.055*(1-(2.718**(-0.02*DAST)))
IF ( THETA.LE.1. .AND. THETA.GE.THETAC ) THEN
! case for mobile seabed where ripples are likely to occur
! calculation of ripple height
IF ( PHI.GT.10 ) THEN
RIPH = ABRBOT*(21.*PHI**(-1.85))
ELSE
RIPH = ABRBOT*(0.275-0.022*(PHI**0.5))
ENDIF
! calculation of ripple wavelength
RIPW = RIPH/(0.342-0.34*THETA**0.25)
! roughness coefficient calculation incorporating ripple height and wavelength
AKN = ((8.*RIPH**2)/RIPW)+(170.*D*(THETA-0.05)**0.5)
ELSEIF ( THETA.GT.1. ) THEN
! case of sheet flow, ripples are flattened
AKN = 170.*D*((THETA-0.05)**0.5)
ELSE
! immobile seabed case: zero concentration and friction based on grain size
AKN = 2.5*D
ENDIF
! final friction factor calculation from Swart formula
IF ( (AKN/ABRBOT).LT.0.63 ) THEN
FW = EXP(5.213*((AKN/ABRBOT)**0.194)-5.977)
ELSE
FW = 0.3
ENDIF
! bottom friction coefficient based on friction factor
CFBOT = UBOT(KCGRD(1)) * FW / (SQRT(2.) * GRAV)
! save friction factor to FRCOEF for next time step or iteration
IF (( SWPDIR .EQ. 1) .OR.
& ( SWPDIR .EQ. 2 .AND. IXCGRD(1) .EQ. 1) .OR.
& ( SWPDIR .EQ. 3 .AND. IYCGRD(1) .EQ. 1) .OR.
& ( SWPDIR .EQ. 4 .AND.
& (IXCGRD(1).EQ.MXC .AND. IYCGRD(1).EQ.1) )) THEN
! save only for first encounter in a sweep
FRCOEF(KCGRD(1)) = FW
ENDIF
ENDIF
!
! *** test output ***
!
IF (TESTFL .AND. ITEST.GE.60) THEN
WRITE (PRTEST, 910) IBOT, KCGRD(1), DEP2(KCGRD(1)), CFBOT(1)
910 FORMAT (' SBOT :IBOT INDX DEP CFBOT:', 2I5, 2E12.4)
ENDIF
!
DO 700 IS = 1, ISSTOP
KD = KWAVE(IS,1) * DEP2(KCGRD(1))
IF ( KD .LT. 10. ) THEN
FACB = CFBOT(IS) * (SPCSIG(IS) / SINH(KD)) **2 41.04 40.57 30.72
!
DO 690 IDDUM = IDCMIN(IS) , IDCMAX(IS)
ID = MOD ( IDDUM - 1 + MDC , MDC ) + 1
!
SBOTEO = FACB 40.57
IF (IBOT.EQ.2 .AND. ICUR.EQ.1 .AND. PBOT(1).GT.0.) THEN
! additional dissipation due to current, seldom used
CURR = UX2(KCGRD(1))*ECOS(ID) + UY2(KCGRD(1))*ESIN(ID)
UC = ABS(CURR)
! PBOT(1) = [cfc]
SBOTEO = FACB + PBOT(1) * UC * 40.57
& (SPCSIG(IS) / SINH(KD)) **2 30.72
ENDIF
!
! *** store the results in the array IMATDA ***
! *** if testfl store results in array for isoline plot ***
!
IMATDA(ID,IS) = IMATDA(ID,IS) + SBOTEO
IF (TESTFL) PLBTFR(ID,IS,IPTST) = -1.* SBOTEO 40.00
DISSC1(ID,IS,3) = DISSC1(ID,IS,3) + SBOTEO 40.67
690 CONTINUE
ENDIF
700 CONTINUE
!
ENDIF
!
! End of subroutine SBOT
RETURN
END
!
!****************************************************************
!
SUBROUTINE SVEG ( DEP2 ,IMATDA ,ETOT ,SMEBRK ,
& KWAVE ,KMESPC ,PLVEGT ,
& IDCMIN ,IDCMAX ,ISSTOP ,DISSC1 ,
& NPLA2 )
!
!****************************************************************
!
USE SWCOMM2
USE SWCOMM3
USE SWCOMM4
USE OCPCOMM4
USE M_GENARR
!
IMPLICIT NONE
!
!
! --|-----------------------------------------------------------|--
! | Delft University of Technology |
! | Faculty of Civil Engineering and Geosciences |
! | Environmental Fluid Mechanics Section |
! | P.O. Box 5048, 2600 GA Delft, The Netherlands |
! | |
! | Programmers: The SWAN team |
! --|-----------------------------------------------------------|--
!
!
! SWAN (Simulating WAves Nearshore); a third generation wave model
! Copyright (C) 1993-2024 Delft University of Technology
!
! This program is free software: you can redistribute it and/or modify
! it under the terms of the GNU General Public License as published by
! the Free Software Foundation, either version 3 of the License, or
! (at your option) any later version.
!
! This program is distributed in the hope that it will be useful,
! but WITHOUT ANY WARRANTY; without even the implied warranty of
! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
! GNU General Public License for more details.
!
! You should have received a copy of the GNU General Public License
! along with this program. If not, see <http://www.gnu.org/licenses/>.
!
!
! 0. Authors
!
! 40.55: Bastiaan Burger, Martijn Meijer
! 40.61: Marcel Zijlema
! 40.58: Tomo Suzuki, Marcel Zijlema
! 41.77: Jaime Ascencio
!
! 1. Updates
!
! 40.55, May. 05: implementation of vegetation dissipation formula
! 40.61, Sep. 06: introduce DISVEG variable for output purposes
! 40.58, Nov. 08: some modifications and corrections
! 41.77, Feb. 20: adding Jacobsen vegetation formulation
! 41.98, Sep. 22: speed up Jacobsen vegetation computation
!
! 2. Purpose
!
! Computation of the source term due to vegetation dissipation
!
! 3. Method
!
! The energy dissipation due to vegetation is described by a
! Morrison type equation, modelling the plants as vertical,
! noncompliant cylinders, neclecting swaying motions induced by
! waves. Vegetation characteristics that are used as input are
! drag coefficient, vegetation height, plant density and diameter.
!
! The formula used in SWAN is due to Dalrymple (1984)
! (see Mendez and Losada, 2004):
!
! d(Cg E)
! ------- = -epsv
! dx
!
! with dissipation due to vegetation:
!
! epsv = 1/2 * 1/sqrt(pi) * rho * Cd * bv * Nv *
! 3
! (gk/2sigma)^3 * ((A + B)/C) * Hrms
!
! where
!
! rho = water density
! k = wave number
! sigma = angular frequency
! Cd = drag coefficient
! bv = stem thickness
! Nv = vegetation density
! Hrms = rms wave height
!
! and the coefficients
!
! A = sinh^3 k*ah
! B = 3*sinh k*ah
! C = 3k*cosh^3 kh
!
! with ah the vegetation height
!
! The source term to be used in SWAN is based on the
! corresponding dissipation rate and reads
!
! Dtot = -epsv / rho / g
!
! In the formulation, the mean average wavenumber according
! to the WAM-formulation and the mean frequency will be employed
!
! Now, the source term is:
!
! E
! Sveg = Dtot * ------ = factor * sqrt(Etot) * E
! Etot
!
! and is linearized by means of the Picard iteration
!
! Jacobsen et al. (2019) published a frequency-dependent
! dissipation model for waves propagating over a canopy
!
! The dissipation per frequency is
!
! ----------
! | 2 mu,0
! dv_spectral = 2 F Su | -------
! | pi
! \|
!
! where
!
! F = 1/2 * rho * alpha^3 * Cd * bv * Nv
!
! The velocity spectrum Su is associated with the
! water surface spectral distribution Sn, as given by
!
! 2
! w * cosh k(h+z)
! Su = ( ----------------- ) * Sn
! sinh kh
!
! where
!
! dv_spectral = dissipation per frequency and layer [kg^2/ms]
! F = canopy factor [kg/m^4]
! Su = velocity spectrum [m^2/s]
! mu,0 = first moment velocity spectrum [m^2/s^2]
! rho = water density [kg/m^3]
! Nv = vegetation density [stems/m^2]
! bv = stem thickness [m]
! Cd = drag coefficient vegetation [-]
! alpha = 1 = velocity reduction factor by canopies [-]
! w = radian frequency (per component) [1/s]
! k = wave number (per component) [1/m]
! z = elevation of still water level [m]
! (z = 0 at water surface)
! h = water depth [m]
! Sn = variance density spectrum [m^2*s]
!
! The depth-integrated and frequency-dependent dissipation is then
!
!
! -h + ah
! |\
! |
! Sveg = - | dv_spectral dz / rho / g
! |
! \|
! -h
!
! where
!
! ah = canopy height (under water) [m]
!
! The vertical integration is approximated using the Simpson's rule.
! A minimum number of integration points would be needed to reduce
! the error of the approximation; 21 points appeared to be sufficient
!
! Note: current effects are not included in Jacobsen et al. (2019)
!
! 4. Argument variables
!
! DEP2 water depth
! DISSC1 dissipation coefficient
! ETOT total energy per spatial gridpoint
! IDCMIN frequency dependent counter in directional space
! IDCMAX frequency dependent counter in directional space
! IMATDA coefficients of diagonal of matrix
! ISSTOP maximum counter of wave component in frequency
! space that is propagated
! KMESPC mean average wavenumber according to the WAM-formulation
! KWAVE wave number
! NPLA2 number of plants per square meter (depth-averaged)
! PLVEGT array containing the vegetation source term for test-output
! SMEBRK mean frequency according to first order moment
!
INTEGER ISSTOP, IDCMIN(MSC), IDCMAX(MSC)
REAL DEP2(MCGRD) ,
& IMATDA(MDC,MSC) ,
& KWAVE(MSC,MICMAX) ,
& DISSC1(MDC,MSC,MDISP),
& PLVEGT(MDC,MSC,NPTST),
& NPLA2 (MCGRD)
REAL ETOT, SMEBRK, KMESPC
!
! 5. Parameter variables
!
! ALFU (orbital) velocity reduction factor by canopies
! NIP total number of subintervals used by Simpson's rule
!
INTEGER, PARAMETER :: NIP = 20
REAL , PARAMETER :: ALFU = 1.
!
! 6. Local variables
!
! A : auxiliary variable
! B : auxiliary variable
! C : auxiliary variable
! D : auxiliary variable
! DCIP : frequency-dependent dissipation for each integration point
! DZ : interval for vertical integration
! EKZ : exponential of k(h+z)
! FDD : factor with orbital velocity to determine Su from Sn
! ID : counter of the spectral direction
! IDDUM : counter
! IENT : number of entries
! IK : counter
! IL : counter
! IS : counter of relative frequency band
! KC : wavenumber times canopy layer height
! KD : wavenumber times water depth
! KVEGH : wavenumber times plant height
! KZ : wavenumber times z
! LAYPRT: part of layer below water level
! MU : first order moment of velocity spectrum
! SINHK : sinh(kh)
! SLAYH : total sum of layer thicknesses
! SLAYH1: sum of layer thicknesses below water level
! SLAYH2: sum of layer thicknesses below water level
! SVEG1 : layer-independent dissipation factor
! SVEG2 : total sum of dissipation factor over layers
! SVEGET: source term containing dissipation due to vegetation
! to be stored in the array IMATDA
! ZDH : vertical point z between -depth to 0 or - value water clearance in water column
! ZH : cumulative layer thickness for velocities, bottom up
! (z+d between 0 and vegetation height or depth value in water column)
!
INTEGER ID, IDDUM, IENT, IK, IL, IS
REAL A, B, C, D, KD, KVEGH, LAYPRT, SINHK, SLAYH,
& SLAYH1, SLAYH2, SVEG1, SVEG2
REAL DZ, EKZ, KC, KZ, MU, ZDH, ZH
REAL DCIP(0:NIP,MSC), FDD(MSC), SVEGET(MSC)
!
! 9. Subroutines calling
!
! SOURCE
!
! 12. Structure
!
! Vegetation parameters are given per layer thickness, so for
! each layer the contribution to wave damping is calculated
!
! This routine checks in which layer the water level is present
!
! -----------
! ILMAX
! -----------
! _ d 2
! --|--------
! | 1
! --|--------
!
! d = waterdepth
! ILMAX = number of layers in grid point
!
! Subsequently, the vegetation parameters up to the layer where the
! water level is in, are used to calculate dissipation for each layer
!
! Thereafter, the contributions to disspation are summed up
!
! With this summation the total dissipation due to vertical varying
! vegetation is calculated
!
! Note: in Jacobsen et al. (2019) vegetation parameters are uniform
! distributed over the vertical
!
! 13. Source text
!
SAVE IENT
DATA IENT/0/
IF (LTRACE) CALL STRACE (IENT,'SVEG')
! --- compute total sum of layer thicknesses
SLAYH = 0.
DO IL = 1, ILMAX
SLAYH = SLAYH + LAYH(IL)
END DO
IF ( IVEG.EQ.1 ) THEN
! --- Suzuki et al. (2011)
! --- compute layer-independent vegetation dissipation factor
KD = KMESPC * DEP2(KCGRD(1))
IF ( KD.GT.10. ) RETURN
C = 3.*KMESPC*(COSH(KD))**3
SVEG1 = SQRT(2./PI)*GRAV**2 * (KMESPC/SMEBRK)**3 * SQRT(ETOT)/C
IF ( VARNPL ) SVEG1 = SVEG1 * NPLA2(KCGRD(1))
! --- compute dissipation factor for each layer and summed up
KVEGH = 0.
C = 0.
D = 0.
SVEG2 = 0.
IF ( DEP2(KCGRD(1)).GT.SLAYH ) THEN
DO IL = 1, ILMAX
KVEGH = KVEGH + KMESPC * LAYH(IL)
SINHK = SINH(KVEGH)
A = C
B = D
C = SINHK**3
D = 3.*SINHK
A = C - A
B = D - B
SVEG2 = SVEG2 + VEGDRL(IL)*VEGDIL(IL)*VEGNSL(IL)*(A + B)
END DO
ELSE IF ( DEP2(KCGRD(1)).LT.LAYH(1) ) THEN
SINHK = SINH(KD)
A = SINHK**3
B = 3.*SINHK
SVEG2 = VEGDRL(1)*VEGDIL(1)*VEGNSL(1)*(A + B)
ELSE
SLAYH1 = 0.
SLAYH2 = 0.
LAYPRT = 0.
VGLOOP : DO IL = 1, ILMAX
SLAYH1 = SLAYH1 + LAYH(IL)
IF (DEP2(KCGRD(1)).LE.SLAYH1) THEN
DO IK = 1, IL-1
SLAYH2 = SLAYH2 + LAYH(IK)
END DO
LAYPRT = DEP2(KCGRD(1)) - SLAYH2
DO IK = 1, IL-1
KVEGH = KVEGH + KMESPC * LAYH(IK)
SINHK = SINH(KVEGH)
A = C
B = D
C = SINHK**3
D = 3.*SINHK
A = C - A
B = D - B
SVEG2 = SVEG2+VEGDRL(IK)*VEGDIL(IK)*VEGNSL(IK)*(A+B)
END DO
KVEGH = KVEGH + KMESPC * LAYPRT
SINHK = SINH(KVEGH)
A = C
B = D
C = SINHK**3
D = 3.*SINHK
A = C - A
B = D - B
SVEG2 = SVEG2 + VEGDRL(IL)*VEGDIL(IL)*VEGNSL(IL)*(A+B)
EXIT VGLOOP
END IF
END DO VGLOOP
END IF
! --- compute total dissipation
SVEGET(1:MSC) = SVEG1 * SVEG2
ELSE IF ( IVEG.EQ.2 ) THEN
! --- Jacobsen et al. (2019)
! --- compute layer- and frequency-independent canopy dissipation factor
SVEG1 = SQRT(2./PI)*(1/GRAV) * ALFU**3 *
& VEGDRL(1) * VEGDIL(1) * VEGNSL(1)
IF ( VARNPL ) SVEG1 = SVEG1 * NPLA2(KCGRD(1))
SVEGET = 0.
IF ( .NOT. SVEG1.NE.0. ) GOTO 90
! --- determine integration interval (submerged vegetation is assumed)
DZ = MIN( SLAYH, DEP2(KCGRD(1)) ) / REAL(NIP)
! --- integration from bottom to surface using Simpson's rule
DO IK = 0, NIP
ZH = DZ * REAL(IK)
ZDH = ZH - DEP2(KCGRD(1))
MU = 0.
DO IS = 1, ISSTOP
KD = KWAVE(IS,1) * DEP2(KCGRD(1))
KC = KWAVE(IS,1) * ZH
KZ = KWAVE(IS,1) * ZDH
IF ( KD.LT.20. ) THEN
! for all wave-water regimes
FDD(IS) = ( SPCSIG(IS) * COSH(KC)/SINH(KD) )**2 ! coshk/sinhk should be smaller than 1 but for large kd numbers, almost 1
ELSE
!option A: deep water orbital velocity
EKZ = EXP(KZ) ! argument of exp is negative
FDD(IS) = ( SPCSIG(IS) * EKZ )**2
!option B: very small energy in very high frequencies, neglect its dissipation
!FDD(IS) = 0.
END IF
! --- compute first order moment
DO ID = 1, MDC
MU = MU + FDD(IS) * SPCSIG(IS)**2 * AC2(ID,IS,KCGRD(1)) ! based on velocity spectrum Su
END DO
END DO
! --- integrate Su in frequencies and directions
MU = MU * DDIR * FRINTF
! --- determine weight coefficient for integration based on Simpson's rule
IF ( IK.EQ.0 .OR. IK.EQ.NIP ) THEN
C = 1. / 3.
ELSE IF ( MOD(IK,2).EQ.0 ) THEN
C = 2. / 3.
ELSE
C = 4. / 3.
END IF
! --- compute frequency-distributed dissipation per integration point
DO IS = 1, ISSTOP