Physics

GEN1 [cf10] [cf20] [cf30] [cf40] [edmlpm] [cdrag] [umin] [cfpm]

With this command the user indicates that SWAN should run in first-generation mode (see Scientific/Technical documentation).

[cf10]	controls the linear wave growth.
	Default: [cf10] = 188.
[cf20]	controls the exponential wave growth.
	Default: [cf20] = 0.59
[cf30]	controls the exponential wave growth.
	Default: [cf30] = 0.12
[cf40]	controls the dissipation rate, i.e., the time decay scale.
	Default: [cf40] = 250.
[edmlpm]	maximum non-dimensionless energy density of the wind sea part of the spectrum
	according to Pierson Moskowitz.
	Default: [edmlpm] = 0.0036
[cdrag]	drag coefficient.
	Default: [cdrag] = 0.0012
[umin]	minimum wind velocity (relative to current; all wind speeds are taken at 10 m
	above sea level).
	Default: [umin] = 1.
[cfpm]	coefficient which determines the Pierson Moskowitz frequency:
	$\sigma_{PM} = 2\pi\, g\,$ [cfpm] $/U_{10}$
	Default: [cfpm] = 0.13

GEN2 [cf10] [cf20] [cf30] [cf40] [cf50] [cf60] [edmlpm] [cdrag] [umin] [cfpm]

With this command the user indicates that SWAN should run in second-generation mode (see Scientific/Technical documentation). The variables are identical to those in the GEN1 command except that [cf50] and [cf60] are added.

[cf50]	controls the spectral energy scale of the limit spectrum.
	Default: [cf50] = 0.0023
[cf60]	controls the spectral energy scale of the limit spectrum.
	Default: [cf60] = $-$0.223

         |    JANSsen [cds1] [delta]  |                            |
         |                            |        | -> WU  |          |
         |    KOMen   [cds2] [stpm]    > DRAG <          >         |
         |                            |        |    FIT |          |
         | -> WESTHuysen              |                            |
         |                                                         |
         |    ST6     [a1sds] [a2sds] [p1sds] [p2sds]           &  |
GEN3    <                                                           > (AGROW [a])
         |        | -> UP |    | -> HWANG |                        |
         |       <         >  <     FAN    >  VECTAU|SCATAU     &  |
         |        |  DOWN |    |    ECMWF |                        |
         |                                                         |
         |        |    TRUE10                 |                    |
         |       <                             > DEBias [cdfac]    |
         |        | -> U10Proxy [windscaling] |                    |

With this command the user indicates that SWAN should run in third-generation mode for wind input, quadruplet interactions and whitecapping. Triads, bottom friction and depth-induced breaking are not activated by this command. See also the Scientific/Technical documentation for more information. The option GEN3 WESTH is the default. Note that SWAN converts $U _{10}$ to $U _{*}$ using a wind drag formula to be specified below.


The choices with respect to option GEN3 ST6 are elaborated on here. Some background information on these choices can be found in Rogers et al. (2012) (henceforth denoted as RBW12).

• [a1sds], [a2sds], [p1sds], and [p2sds]. These correspond to $a_1$, $a_2$, $L$, and $M$, respectively, in RBW12. The examples given below are calibrated (same method as in RBW12). The calibration is affected by the VECTAU and U10PROXY settings. We recommend that this calibration be kept to the examples given. However, it is possible to recalibrate using the same method as RBW12.
• UP vs. DOWN. The command UP is the default and strongly recommended. Corresponds to selection of normalization by $E_T(f)$ or $E(f)$ as in RBW12 (right column, page 1333).
• HWANG, FAN, or ECMWF. This corresponds to the selection of the wind drag formula. HWANG is the default and is unchanged from RBW12. FAN is from Fan et al. (2012). ECMWF follows the WAM Cycle 4 (Janssen) methodology. FAN and ECMWF use iterative procedures. The user is warned that selection of non-default FAN or ECMWF will significantly change outcome, e.g. a Hs decrease from 2.48 to 2.28 m. All calibrations were performed using the default HWANG. Also note that the usual drag formula, either Wu (1982) or Zijlema et al. (2012), will not be applied.
• VECTAU vs. SCATAU. The command VECTAU is the default and strongly recommended. It permits vector calculation for the stress calculation, rather than the simplified scalar calculation of Eq. (12) in RBW12.
• TRUE10 vs. U10PROXY. Default is U10PROXY with [windscaling] = 32, a change from [windscaling] = 28 as used by RBW12. Non-default TRUE10 directly uses the U10-based formula of Donelan et al. (2006), and is not recommended. U10PROXY directs SWAN to replace the Donelan et al. (2006) $U _{10}$ with [windscaling] $\times\,\, U_*$. As noted by RBW12, Komen et al. (1984) (and so the default form of SWAN's Sds) use this approach also (with [windscaling] = 28). Increasing [windscaling] from 28 to 32 or 35 will improve prediction of mean square slope.
• DEBIAS. This option is effective only if HWANG is also used. This allows the user to counter bias in the input wind fields by providing a multiplier on the drag coefficient. Acommodation of bias in wind fields follows the idea of ST4 in WW3 (Ardhuin et al., 2010) via the Betamax parameter and ST6 in WW3 (Zieger et al., 2015) via the [cdfac] parameter. This parameter differs from Betamax insofar as former has the advantage that it is designed to be determined by evaluating by the winds, prior to the running of the wave model. By contrast the Betamax parameter is set by trial-and-error repeat runs of the wave model to reduce bias. Of course, the downside of the DEBIAS method is that it does not guarantee small bias in the wave model when it is run, though in our experience, it has resulted in small bias. [cdfac] can be simply calculated as $\mbox{mean}(\tau_{obs})/\mbox{mean}(\tau_{model})$, where $\tau$ is the wind stress, and both (observation and model, respectively, with careful attention to anemometer height when applicable) are calculated via the same formula (e.g. Hwang, 2011) from $U _{10}$. This method of selecting the wind adjustment using $U_*^2$ (at least partially) accounts for the higher importance of high wind speeds in a wave model, making it better than an adjustment based on simple $U _{10}$ bias. If the user has not evaluated the winds, it is recommended to omit this command, or use DEB 1., which has the same effect as omitting it. The effect of $\sqrt {\mbox{\tt [cdfac]}}$ is similar to changing the [fac] option (see command READINP) when reading in winds, though there are differences due to the nonlinear features of the drag formula: typically small, but larger with very strong winds. Also note that using the [fac] option will modify wind field outputs from SWAN.

Below are the ST6 calibration examples.

  GEN3 ST6 4.7E-7 6.6E-6 4.0 4.0 UP HWANG VECTAU U10PROXY 28.0 AGROW
  GEN3 ST6 4.7E-7 6.6E-6 4.0 4.0 UP FAN VECTAU U10PROXY 28.0 AGROW

  GEN3 ST6 2.8E-6 3.5E-5 4.0 4.0 UP HWANG VECTAU U10PROXY 32.0 AGROW
  GEN3 ST6 2.8E-6 3.5E-5 4.0 4.0 UP HWANG VECTAU U10PROXY 32.0 DEBIAS 0.89 AGROW

  GEN3 ST6 6.5E-6 8.5E-5 4.0 4.0 UP HWANG VECTAU U10PROXY 35.0 AGROW

Note the different values of coefficients [a1sds] and [a2sds] in case of different U10PROXY settings! Usually one of the following two lines is recommended in regular SWAN simulations. Here, the command SSWELL for swell dissipation must be indicated using a separate line (see below).

  GEN3 ST6 4.7E-7 6.6E-6 U10P 28. AGROW
  GEN3 ST6 2.8E-6 3.5E-5 U10P 32. AGROW

Finally, the following two lines represent the original model described by RBW12 (see their Table 1, page 1336). Also SSWELL must be indicated using a separate line (see below).

  GEN3 ST6 5.7E-7 8.0E-6 4.0 4.0 UP HWANG U10PROXY 28.0 AGROW
  GEN3 ST6 5.7E-7 8.0E-6 4.0 4.0 UP AGROW

JANSSEN	linear growth	: Cavaleri and Malanotte-Rizzoli (1981), activated only
	if the keyword AGROW is present (see below)
exponential growth	: Janssen (1989, 1991).
[cds1]	coefficient for determining the rate of whitecapping dissipation (= $C_{\rm ds}/\tilde{s}^4_{\rm PM}$).
	Default: [cds1] = 4.5.
[delta]	coefficient which determines the dependency of the whitecapping on wave number
	(mix with Komen et al. formulation).
	Default: [delta] = 0.5.
KOMEN	linear growth	: Cavaleri and Malanotte-Rizzoli (1981), activated only
	if the keyword AGROW is present (see below)
exponential growth	: Komen et al. (1984).
[cds2]	coefficient for determining the rate of whitecapping dissipation (=$C_{\rm ds}$).
	Default: [cds2] = 2.36e-5.
[stpm]	value of the wave steepness for a Pierson-Moskowitz spectrum (= $\tilde{s}^2_{\rm PM}$).
	Default: [stpm] = 3.02e-3.
WESTH	nonlinear saturation-based whitecapping combined with wind input of Yan (1987).
	This option is the default.
DRAG	indicates the wind drag formulation.
WU	wind drag formula according to Wu (1982).
	This option is the default.
FIT	drag coefficient is based on second order polynomial fit (see Zijlema et al., 2012).
ST6	wind input and whitecapping from Rogers et al. (2012).
[a1sds]	coefficient related to local dissipation term $T_1$.
[a2sds]	coefficient related to cumulative dissipation term $T_2$.
[p1sds]	power coefficient controlling strength of dissipation term $T_1$.
	Default: [p1sds] = 4.
[p2sds]	power coefficient controlling strength of dissipation term $T_2$.
	Default: [p2sds] = 4.
UP	select $E_T(f)$ for normalization of exceedance level.
	This option is the default.
DOWN	select $E(f)$ for normalization of exceedance level.
HWANG	wind drag formula according to Hwang (2011).
	This option is the default.
	Note: the drag formula of Zijlema et al (2012) will not be applied!
FAN	wind drag formula according to Fan et al. (2012).
ECMWF	wind drag formula based on WAM Cycle 4 (Janssen).
VECTAU	use vector integral for computing wind stress.
	This option is the default.
SCATAU	use scalar integral for computing wind stress.
TRUE10	wind velocity based on $U _{10}$.
U10PROXY	$U _{10}$ = [windscaling] $\times \,\, U_{*}$.
	This option is the default.
[windscalin]	factor to scale $U _{10}$ with $U _{*}$.
	Default: [windscaling] = 28.
DEBIAS	allows user to counter bias in the input wind field.
[cdfac]	multiplier on drag coefficient.
	Default: [cdfac] = 1.
AGROW	if this keyword is used, the wave growth term of Cavaleri and Malanotte (1981) is
	activated.
	if this keyword is NOT used, the wave growth term of Cavaleri and Malanotte (1981)
	is NOT activated.
	Note that in nonstationary runs SWAN start with INIT ZERO (see command INIT),
	wave energy remains zero unless wave energy penetrates over the boundary or AGROW
	is activated. In case of stationary runs, however, SWAN will start with a first guess.
[a]	if the wave growth term of Cavaleri and Malanotte (1981) is activated, [a] is
	the proportionality coefficient in that term.
	Default: [a] = 0.0015.

        | -> ARDhuin [cdsv]
SSWELL <
        |    ZIEger  [b1]

With this command the user can influence the type of swell dissipation included in the computations. The Zieger option is intended for use with negative wind input via the NEGATINP command. Zieger non-breaking dissipation follows the method used in WAVEWATCH III version 4 and does not include the steepness-dependent swell coefficient introduced in WAVEWATCH III version 5. As noted already, if GEN3 ST6... command is used, this SSWELL command should be provided.


Examples:

  SSWELL ARDHUIN 1.2

  SSWELL ZIEGER 0.00025
  NEGATINP 0.04

ARDHUIN	non-breaking dissipation of Ardhuin et al. (2010).
[cdsv]	coefficient related to laminar atmospheric boundary layer.
	Default: [cdsv] = 1.2
ZIEGER	non-breaking dissipation of Young et al. (2013), updated by Zieger et al. (2015).
[b1]	non-dimensional proportionality coefficient.

NEGatinp  [rdcoef]

With this optional command the user activates negative wind input. This is intended only for use with non-breaking swell dissipation SSWELL ZIEGER. Parameter [rdcoef] is a fraction between 0 and 1, representing the strength of negative wind input. As an example, with [rdcoef]=0.04, for a spectral bin that is opposed to the wind direction, the wind input factor $W(k,\theta)$ is negative, and its magnitude is 4% of the corresponding value of the spectral bin that is in the opposite direction (i.e. in the wind direction). See Zieger et al. (2015) eq. 11, where $a_0$ is their notation for [rdcoef]. Default [rdcoef]=0.0 and [rdcoef]=0.04 is recommended, though as implied by Zieger et al. (2015), this value is not well-established, so the user is encouraged to experiment with other values.

          |    KOMen [cds2] [stpm] [powst] [delta] [powk]
WCAPping <
          | -> AB    [cds2] [br]  CURrent [cds3]

With this command the user can influence whitecapping which is usually included in the computations. Can be de-activated with command OFF WCAP.

KOMEN	whitecapping according to Komen et al. (1984) is applied.
[cds2]	coefficient for determining the rate of whitecapping dissipation (=$C_{\rm ds}$).
	Default: [cds2] = 2.36e-5.
[stpm]	value of the wave steepness for a Pierson-Moskowitz spectrum (= $\tilde{s}^2_{\rm PM}$).
	Default: [stpm] = 3.02e-3.
[powst]	power of steepness normalized with the wave steepness of a Pierson-Moskowitz
	spectrum.
	Default: [powst] = 2.
[delta]	coefficient which determines the dependency of the whitecapping on wave number.
	Default: [delta] = 1.
	Note that this default has been changed since version 40.91A. The setting
	[delta] = 1 will improve the prediction of the wave energy at low frequencies,
	and hence the mean wave period. The original default was [delta] = 0, which
	corresponds to WAM Cycle 3. See the Scientific/Technical documentation for
	further details.
[powk]	power of wave number normalized with the mean wave number.
	Default: [powk] = 1.
AB	whitecapping according to Alves and Banner (2003) is applied.
	See also the paper of Van der Westhuysen et al. (2007).
	This is the default.
[cds2]	proportionality coefficient due to Alves and Banner (2003).
	Default: [cds2] = 5.0e-5.
[br]	threshold saturation level.
	Default: [br] = 1.75e-3.
CURRENT	indicates that enhanced current-induced dissipation as proposed by
	Van der Westhuysen (2012) is to be added.
[cds3]	proportionality coefficient.
	Default: [cds3] = 0.8.

QUADrupl [iquad] [lambda] [Cnl4] [Csh1] [Csh2] [Csh3]

With this option the user can influence the computation of nonlinear quadruplet wave interactions which are usually included in the computations. Can be de-activated with command OFF QUAD.


Note that the DIA approximation of the quadruplet interactions is a poor approximation for long-crested waves and frequency resolutions that are deviating much more than 10% (see command CGRID).


Note that DIA is usually updated per sweep, either semi-implicit ([iquad] = 1) or explicit ([iquad] = 2). However, when ambient current is included, the bounds of the directional sector within a sweep may be different for each frequency bin (particularly the higher frequencies are modified by the current). So there may be some overlap of frequency bins between the sweeps, implying non-conservation of wave energy. To prevent this the user is advised to choose the integration of DIA per iteration instead of per sweep, i.e. [iquad] = 3.


If you want to speed up your computation a bit more, than the choice [iquad] = 8 is a good choice.

[iquad]	the quadruplets can be integrated by four different numerical procedures:
	= 1 semi-implicit computation of the nonlinear transfer with DIA per sweep
	= 2 fully explicit computation of the nonlinear transfer with DIA per sweep
	= 3 fully explicit computation of the nonlinear transfer with DIA per iteration
	= 8 fully explicit computation of the nonlinear transfer with DIA per iteration,
	but neighbouring interactions are interpolated in piecewise constant manner.
	other techniques for the computation of quadruplets are
	= 4 Multiple DIA
	= 51 XNL (deep water transfer)
	= 52 XNL (deep water transfer with WAM depth scaling)
	= 53 XNL (finite depth transfer)
	Default: [iquad] = 2.
[lambda]	coefficient for quadruplet configuration in case of DIA.
	Default: [lambda]=0.25.
[Cnl4]	proportionality coefficient for quadruplet interactions in case of DIA.
	Default: [Cnl4]=$3 \times 10^7$.
[Csh1]	coefficient for shallow water scaling in case of DIA.
	Default: [Csh1]=5.5.
[Csh2]	coefficient for shallow water scaling in case of DIA.
	Default: [Csh2]=0.833333.
[Csh3]	coefficient for shallow water scaling in case of DIA.
	Default: [Csh3]=$-$1.25.

           | -> CONstant [alpha] [gamma]
BREaking  <
           |    BKD [alpha] [gamma0] [a1] [a2] [a3]

With this command the user can influence depth-induced wave breaking in shallow water.


If this command is not used, SWAN will account for wave breaking anyhow (with default options and values). If the user wants to specifically ignore wave breaking, he should use the command: OFF BREAKING.

CONSTANT	indicates that a constant breaker index is to be used.
[alpha]	proportionality coefficient of the rate of dissipation.
	Default: [alpha] = 1.0.
[gamma]	the breaker index, i.e. the ratio of maximum individual
	wave height over depth.
	Default: [gamma] = 0.73.
BKD	indicates that the breaker index scales with both the
	bottom slope (=$\beta$) and the dimensionless depth (=$kd$)
[alpha]	proportionality coefficient of the rate of dissipation.
	Default: [alpha] = 1.0.
[gamma0]	the reference $\gamma$ for horizontal slopes.
	Default: [gamma0] = 0.54.
[a1]	first tunable coefficient for the breaker index.
	Default: [a1] = 7.59.
[a2]	second tunable coefficient for the breaker index.
	Default: [a2] = -8.06.
[a3]	third tunable coefficient for the breaker index.
	Default: [a3] = 8.09.

           | -> JONswap CONstant [cfjon]
           |
           |    COLLins [cfw]
FRICtion  <
           |    MADsen  [kn]
           |
           |    RIPples [S] [D]

With this optional command the user can activate bottom friction. If this command is not used, SWAN will not account for bottom friction.


In SWAN four different formulations are available, i.e., that of Hasselmann et al. (1973, JONSWAP), Collins (1972), Madsen et al. (1988) and Smith et al. (2011).


The default option is: JONSWAP with a constant friction coefficient. The recommended value for typical sandy bottoms is 0.038 m$^2$s$^{-3}$. Note that this value is to be applied for both wind sea and swell conditions. (The use of the previous default value of 0.067 m$^2$s$^{-3}$ is discouraged, even for wind sea conditions!) For smoother seafloors, like the Gulf of Mexico, a lower value of 0.019 m$^2$s$^{-3}$ is advised.

JONSWAP	indicates that the semi-empirical expression derived from the JONSWAP results
	for bottom friction dissipation (Hasselmann et al., 1973, JONSWAP) should be
	activated. This option is the default.
CONSTANT	this default option indicates that the JONSWAP coefficient is constant.
[cfjon]	coefficient of the JONSWAP formulation.
	Default: [cfjon] = 0.038.
COLLINS	indicates that the expression of Collins (1972) should be activated.
[cfw]	Collins bottom friction coefficient.
	Default: [cfw] = 0.015.
	Note that [cfw] is allowed to vary over the computational region; in that
	case use the commands INPGRID FRICTION and READINP FRICTION to define
	and read the friction data. The command FRICTION is still required to define
	the type of friction expression. The value of [cfw] in this command is then
	not required (it will be ignored).
MADSEN	indicates that the expression of Madsen et al. (1988) should be activated.
[kn]	equivalent roughness length scale of the bottom (in m).
	Default: [kn] = 0.05.
	Note that [kn] is allowed to vary over the computational region; in that case
	use the commands INPGRID FRICTION and READINP FRICTION to define and read
	the friction data. This command FRICTION is still required to define the type of
	friction expression. The value of [kn] in this command is then not required
	(it will be ignored).
RIPPLES	indicates that the expression of Smith et al. (2011) should be activated.
	Here friction depends on the formation of bottom ripples and sediment size.
[S]	the specific gravity of the sediment.
	Default: [S] = 2.65.
[D]	the sediment diameter (in m).
	Default: [D] = 0.0001.

       |                       / -> COLL |
       | -> DCTA [trfac] [p]   \    NONC |
       |                                 |
       |    LTA [trfac]                  |
TRIad <                                   >   &
       |    FTIM [trfac]                 |
       |                                 |
       |    SPB [trfac] [a]              |


                | -> ELDeberky [urcrit] |             |    FG
       BIPHase <                         >  TRAnsfer <     MS
                | DEWIT [lpar]          |             |    BRedmose
                                                      | -> QUadwave

With this command the user can activate the triad wave-wave interactions. If this command is not used, SWAN will not account for triads.

DCTA	indicates that the DCTA method of Booij et al. (2009) should be activated.
	This option is the default.
[trfac]	scaling factor that controls the intensity of the triad interaction due to DCTA.
	Default: [trfac] = 4.4.
[p]	shape coefficient to force the high-frequency tail.
	Default: [p] = 4/3.
COLL	indicates that the triad interactions due to DCTA are restricted to collinear ones
	only. This is the default.
NONC	indicates to include noncollinear interactions within the DCTA framework.
LTA	indicates that the extended LTA method should be activated.
[trfac]	scaling factor that controls the intensity of the triad interaction due to LTA.
	Default: [trfac] = 1.0.
FTIM	indicates that the full triad interaction model (FTIM) should be activated.
[trfac]	scaling factor that controls the intensity of the triad interaction due to FTIM.
	Default: [trfac] = 1.0.
SPB	indicates that the SPB method of Becq-Girard et al. (1999) should be activated.
[trfac]	scaling factor that controls the intensity of the triad interaction due to SPB.
	Default: [trfac] = 0.9.
[a]	calibration parameter for tuning $K$ in Eq. (5.1) of Becq-Girard et al. (1999).
	This parameter is associated with relaxation of the resonance condition and
	is a function of the local wave number: $K = a \cdot k_{\rm loc}$.
	Note that with the current tuning the nonlinear interaction coefficient of
	Madsen and Sørensen (1993) will be employed, unless specified otherwise
	(see the keyword TRANSFER below).
	Default: [a] = 0.95.
BIPHASE	defines the parametrization of biphase.
	Note: this option does not applied to the SPB method.
ELDEBERKY	the biphase parametrization as function of Ursell number as given by
	Eldeberky (1996) will be used. This is the default.
[urcrit]	the critical Ursell number appearing in the parametrization.
	Note: the value of [urcrit] is setted by Eldeberky (1996) at 0.2 based on a
	laboratory experiment, whereas Doering and Bowen (1995) employed the value
	of 0.63 based on the field experiment data.
	Default: [urcrit] = 0.63.
DEWIT	De Wit (2022) proposed a parametrization of the biphase evolution based on
	the local bed slope and peak wave period.
[lpar]	scales spatial averaging of the De Wit's biphase in terms of a multiple of peak
	wave length of the incident wave field.
	Note: [lpar] = 0 means no averaging.
	Default: [lpar] = 0.
TRANSFER	defines the interaction coefficient to describe the nonlinear energy transfers
	in triads of shoaling waves.
	Note: this option does not applied to the DCTA method.
FG	Freilich and Guza (1984) suggested the use of the Boussinesq-wave model
	of Peregrine (1967) to compute the interaction coefficient.
MS	the nonlinear transfer coefficient derived from the Boussinesq-wave theory
	of Madsen and Sørensen (1993) is employed.
BREDMOSE	The exact transfer coefficient (second order Stokes solution) of
	Bredmose et al (2005) is applied.
QUADWAVE	Akrish et al (2024) proposed the parametrized transfer coefficient that
	optimizes the nonlinearity of the fully dispersive quadratic wave model
	of Bredmose et al (2005).
	This is the default.

VEGEtation  [iveg]  < [height] [diamtr] [nstems] [drag] >

With this command the user can activate wave damping due to vegetation based on the Dalrymple's formula (1984) as implemented by Suzuki et al. (2011). This damping is uniform over the wave frequencies. An alternative is the frequency-dependent (canopy) dissipation model of Jacobsen et al. (2019). If this command is not used, SWAN will not account for vegetation effects.


The vegetation (rigid plants) can be divided over a number of vertical segments and so, the possibility to vary the vegetation vertically is included. Each vertical layer represents some characteristics of the plants. These variables as indicated below can be repeated as many vertical layers to be chosen.


Note that with respect to the Jacobsen et al. (2019) method, vertical layering of the vegetation is not yet implemented.

[iveg]	indicates the method for the vegetation computation:
	= 1 Suzuki et al. (2011)
	= 2 Jacobsen et al. (2019)
	Default: [iveg] = 1.
[height]	the plant height per layer (in m).
[diamtr]	the diameter of each plant stand per layer (in m).
[nstems]	the number of plant stands per square meter for each layer.
	Note that [nstems] is allowed to vary over the computational region to
	account for the zonation of vegetation. In that case use the commands
	INPGRID NPLANTS and READINP NPLANTS to define and read the vegetation
	density. The (vertically varying) value of [nstems] in this command will
	be multiplied by this horizontally varying plant density.
	Default: [nstems] = 1.
[drag]	the drag coefficient per layer.

MUD  [layer]  [rhom]  [viscm]

With this command the user can activate wave damping due to mud based on Ng (2000). If this command or the commands INPGRID MUDLAY and READINP MUDLAY are not used, SWAN will not account for muddy bottom effects.

[layer]	the thickness of the mud layer (in m).
	Note that [layer] is allowed to vary over the computational region to
	account for the zonation of muddy bottom. In that case use the commands
	INPGRID MUDLAY and READINP MUDLAY to define and read the layer
	thickness of mud. The value of [layer] in this command is then not
	required (it will be ignored).
[rhom]	the density of the mud layer (in kg/m$^3$).
	Default: [rhom] = 1300.
[viscm]	the kinematic viscosity of the mud layer (in m$^2$/s).
	Default: [viscm] = 0.0076.

       | -> R19   [c0] [c1] [c2] [c3] [c4] [c5] [c6]
SICE  <     D15   [Chf]
       |    M18   [Chf]
       |    R21B  [Chf npf]

Using this command, the user activates a sink term to represent the dissipation of wave energy by sea ice. The R19 method is empirical/parametric: a polynomial based on wave frequency (Rogers, 2019). This polynomial (in 1/m) has seven dimensional coefficients; see Scientific/Technical documentation for details. If this command is not used, SWAN will not account for sea ice effects.


Note that it is also necessary to describe the ice, using the ICE command (for uniform and stationary ice) or INPgrid/READinp commands (for variable ice).


The default R19 setting is the case of c2= $1.06\times 10^{-3}$ and c4= $2.3\times 10^{-2}$. Thus, the following commands are equivalent

• SICE
• SICE R19
• SICE R19 0.0 0.0 1.06E-3 0.0 2.3E-2 0.0 0.0

This recovers the polynomial of Meylan et al. (2014), calibrated for a case of ice floes, mostly 10 to 25 m in diameter, in the marginal ice zone near Antarctica. Examples for other calibrations can be found in the Scientific/Technical documentation.


The three non-default methods all include dependence on ice thickness. These are

1. D15: The method of Doble et al. (2015), with default value of [Chf]=0.1.
2. M18: A method taken from Meylan et al. (2018), with default value of [Chf]=0.059.
3. R21B: A method proposed by Rogers et al. (2021b), with default values of [Chf]=2.9 and [npf]=4.5.

Additional details about these three methods, and information about other calibrations can be found in the Scientific/Technical documentation.

[aice]	ice concentration as a fraction from 0 to 1.
	Note that [aice] is allowed to vary over the computational region to account
	for the zonation of ice concentration. In that case use the commands
	INPGRID AICE and READINP AICE to define and read the sea concentration.
	The value of [aice] in this command is then not required (it will be
	ignored).
[c0]	polynomial coefficient (in 1/m) for determining the rate of sea ice dissipation.
[c1]	polynomial coefficient (in s/m) for determining the rate of sea ice dissipation.
[c2]	polynomial coefficient (in s$^2$/m) for determining the rate of sea ice dissipation.
[c3]	polynomial coefficient (in s$^3$/m) for determining the rate of sea ice dissipation.
[c4]	polynomial coefficient (in s$^4$/m) for determining the rate of sea ice dissipation.
[c5]	polynomial coefficient (in s$^5$/m) for determining the rate of sea ice dissipation.
[c6]	polynomial coefficient (in s$^6$/m) for determining the rate of sea ice dissipation.
[Chf]	a simple coefficient of proportionality.
[npf]	controls the degree of dependence on frequency and ice thickness.

TURBulence  [ctb]  (CURrent [tbcur])

With this optional command the user can activate turbulent viscosity. This physical effect is also activated by reading values of the turbulent viscosity using the READGRID TURB command, but then with the default value of [ctb]. The command READGRID TURB is necessary if this command TURB is used since the value of the viscosity is assumed to vary over space.

[ctb]	the value of the proportionality coefficient appearing in the energy
	dissipation term.
	Default: [ctb] = 0.01.
CURRENT	if this keyword is present the turbulent viscosity will be derived from the
	product of the depth and the absolute value of the current velocity. If the
	command READGRID TURB is used, this option is ignored; the values read
	from file will prevail.
[tbcur]	the factor by which depth $\times$ current velocity is multiplied in order to
	get the turbulent viscosity.
	Default: [tbcur] = 0.004.

BRAGg [ibrag] [nreg] [cutoff]                            &

      | -> FT
     <
      |    FILE 'fname' [idla] [mkx] [mky] [dkx] [dky]

Using this optional command, the user activates a source term to represent the scattering of waves due to changes in the small-scale bathymetry based on the theory of Ardhuin and Herbers (2002). If this command is not used, SWAN will not account for Bragg scattering.


The underlying process is related to the bed elevation spectrum that describes the random variability of the bathymetry at the scale of the wave length on top of a slowly varying depth. To input this spectrum in the model, two options are available. One option is to read a spectrum from a file. This single bottom spectrum will subsequently be applied in all active grid points. The assumption being made here is that the inputted bottom is gently sloping. Note that the bottom spectrum must be given as a function of the wave number $\vec{k}$.


Another option is to compute the spectrum by a Fourier transform from $\vec{x}$ to $\vec{k}$ of the bed modulations around a computational grid point. First, one must define a square region with a fixed size around the grid point in order to perform the Fourier transform. The size should correspond to a multiple of the wave length at which refraction is resolved (i.e. consistent with the mild slope assumption). Next, the amplitude modulation of the small-scale bathymetry is obtained by substracting a slowly varying bed level from the inputted high-resolution bathymetric data within this square region. Here, the smooth bed level is achieved using a bilinear fit. During the computation, however, SWAN employs the gently sloping bed as the mean of the original bathymetry within the given square around each computational grid point. Finally, the corresponding bottom spectrum is computed with an FFT.


An important note to be made here is the fact that adding the Bragg scattering source term to the action balance equation gives rise to a fairly stiff equation. The best remedy is to run SWAN in the nonstationary mode with a relatively small time step or in the stationary mode with some under relaxation (see command NUM STAT [alfa]).

[ibrag]	indicates the computation of Bragg scattering term:
	= 1 source term is calculated per sweep and bottom spectrum is
	interpolated at the difference wave number a priori (thus
	requiring storage)
	= 2 source term is calculated per sweep and bottom spectrum is
	interpolated at the difference wave number per sweep (no storage)
	= 3 source term is calculated per iteration and bottom spectrum is
	interpolated at the difference wave number per iteration (no storage)
	Default: [ibrag] = 1.
[nreg]	size of square region around computational grid point (centered) for computing
	the mean depth and, if desired, the bed elevation spectrum. It is expressed in
	terms of the number of grid points (per direction) of the inputted bottom grid.
[cutoff]	cutoff to the ratio between surface and bottom wave numbers.
	Note: see the Scientific/Technical documentation for details.
	Default: [cutoff] = 5.
FT	if this keyword is present the bottom spectrum will be computed in each active
	grid point using an FFT.
	Note: the depth in each computational grid point is computed as the average of
	the inputted (high-resolution) bed levels within the square region.
FILE	means that the bed elevation spectrum $F^{\tiny B}(k_x,k_y)$ is read from a file.
	Note: this spectrum is taken to be uniform over the entire computational domain.
'fname'	name of the file containing the bottom spectrum.
[idla]	prescribes the order in which the spectra values should be given in the file;
	see command READINP.
[mkx]	number of cells in $x-$direction of the wave number grid related to bottom spectrum
	(this number is one less than the number of points in this direction!)
[mky]	number of cells in $y-$direction of the wave number grid related to bottom spectrum
	(this number is one less than the number of points in this direction!)
	Default: [mky] = [mkx].
[dkx]	mesh size in $x-$direction of the wave number grid related to bottom spectrum (1/m).
[dky]	mesh size in $y-$direction of the wave number grid related to bottom spectrum (1/m).
	Default: [dky] = [dkx].

LIMiter [ursell] [qb]

With this command the user can de-activate permanently the quadruplets when the actual Ursell number exceeds [ursell]. Moreover, as soon as the actual fraction of breaking waves exceeds [qb] then the action limiter will not be used in case of decreasing action density.

[ursell]	the upper threshold for Ursell number.
	Default: [ursell] = 10.0.
[qb]	the threshold for fraction of breaking waves.
	Default: [qb] = 1.0.

          | -> TRANSm [trcoef]                        |
          |                                           |
          |    TRANS1D < [trcoef] >                   |
          |                                           |
OBSTacle <     TRANS2D < [trcoef] >                    >                  &
          |                                           |
          |       | -> GODA [hgt] [alpha] [beta]      |
          |  DAM <                                    |
                  |    DANGremond [hgt] [slope] [Bk]  |

                          | -> RSPEC        |
          ( REFL [reflc] <                   > )                          &
                          |    RDIFF [pown] |

          ( FREEboard [hgt] [gammat] [gammar] Quay ) LINe <[xp] [yp]>

CANNOT BE USED IN 1D-MODE.


With this optional command the user provides the characteristics of a (line of) sub-grid obstacle(s) through which waves are transmitted or against which waves are reflected (possibly both at the same time). The obstacle is sub-grid in the sense that it is narrow compared to the spatial meshes; its length should be at least one mesh length.


The location of the obstacle is defined by a sequence of corner points of a line. The obstacles interrupt the propagation of the waves from one grid point to the next wherever this obstacle line is located between two neighbouring grid points (of the computational grid; the resolution of the obstacle is therefore equal to the computational grid spacing). This implies that an obstacle to be effective must be located such that it crosses at least one grid line. This is always the case when an obstacle is larger than one mesh length.

1. If a straight line is defined with more than two points, then the sum of the reflection of the parts may differ from the situation when you define it with just two points. This is due to the way obstacles are handled numerically in SWAN. It defines from computational grid point to its neighbor whether there is a crossing with an obstacle. In defining which directions of the wave spectrum should be reflected, i.e which directions are pointed towards the obstacle, it uses the obstacle coordinates as defined by the user to define the angle of inclusion. This angle will be smaller if more points are defined, and so the reflected energy will be less for the computational grid point. This problem becomes smaller if the computational grid points are closer to the obstacle.
   
   So the advise is to define obstacles with the least amount of points possible.
2. In case of sharp angles in the obstacles, it is very likely that there are more than one crossing between two computational grid points. In this case SWAN does not give correct reflection results.
   • Avoid sharp angles in the obstacle definition.
   • If necessary, put corner point of the sharp edge exactly on a line between two computational grid points, but not exactly on the grid point.
3. At the boundaries of the computational area, the reflected spectrum is not taken into account. This can only be resolved by a different treatment of the boundaries in the program. Until this time, it is recommended to place obstacles at the inner area of the computational grid, not at or through the boundaries.
4. Obstacle lines are only effective when the obstacle line is bordered by wet points on both sides. In practice, this may give problems when a reflection line is also used to specify a boundary between wet and land points. This can be avoided by shifting the position of the reflection line or by creating wet points on the land side of the obstacle line.

The computation of transmission and reflection is problematic if an obstacle runs exactly through one or more grid points of the computational structured grid; SWAN will move the obstacle over a small distance (1% of the mesh size) if this occurs. Note that this will not be done in case of unstructured grids.


The reflection results are incorrect if more than one obstacle crosses the same grid line between two neighbouring grid points. SWAN is not able to detect this, so the user must check if his model fulfills this condition.

TRANSM	with this option the user indicates that the transmission coefficient is a constant.
[trcoef]	constant transmission coefficient, formulated in terms of wave height, i.e. ratio
	of transmitted significant wave height over incoming significant wave height.
	Default: [trcoef]=0.0 (no transmission = complete blockage).
TRANS1D	with this option the user indicates that the transmission coefficient is frequency
	dependent. For each frequency the user can specify a transmission coefficient as
	indicated below. The number of these transmission values must be equal to the
	number of frequencies, i.e. [msc] + 1.
[trcoef]	transmission coefficient per frequency, formulated in terms of wave height, i.e.
	ratio of transmitted significant wave height over incoming significant wave height.
TRANS2D	with this option the user indicates that the transmission coefficient is frequency
	and direction dependent. For each direction the user can assign different trans-
	mission coefficients to frequencies. The number of these transmission values must
	be equal to the number of frequencies multiplied by the number of directions.
[trcoef]	transmission coefficient per frequency for each direction, formulated in terms of
	wave height, i.e. ratio of transmitted significant wave height over incoming
	significant wave height. It is advised to put the values assigned to all frequencies
	on a single line for each direction. So the number of lines equals the number of
	directions. Each line may be terminated with a continuation mark &.
DAM	with this option the user indicates that the transmission coefficient depends on
	the incident wave conditions at the obstacle and on the obstacle height (which
	may be submerged).
GODA	with this option the user indicates to use the Goda/Seelig formula (1979) for
	computing transmission coefficient.
[hgt]	the elevation of the top of the obstacle above reference level (same reference
	level as for bottom etc.); use a negative value if the top is below that reference
	level. If this command is used, this value is required.
[alpha]	coefficient determining the transmission coefficient for Goda's transmission formula.
	Default: [alpha]=2.6.
[beta]	another coefficient determining the transmission coefficient for Goda's transmission
	formula.
	Default: [beta]=0.15.
DANGREMOND	with this option the user indicates to use the d'Angremond/Van der Meer formula
	(1996) for computing the transmission coefficient.
[hgt]	the elevation of the top of the obstacle above reference level (same reference
	level as for bottom etc.); use a negative value if the top is below that reference
	level. If this command is used, this value is required.
[slope]	the slope of the obstacle (in degrees). If this command is used, this value is required.
[Bk]	the crest width of the obstacle. If this command is used, this value is required.
REFL	if this keyword is present the obstacle will reflect wave energy (possibly in
	combination with transmission). Reflections will be computed only if the spectral
	directions cover the full 360$^{\rm o}$, i.e. if in the command CGRID the option CIRCLE
	is activated.
[reflc]	constant reflection coefficient, formulated in terms of wave height, i.e. ratio
	of reflected significant wave height over incoming significant wave height.
	Restriction: $0 \leq$ [reflc] $\leq 1$.
	Default: [reflc]=1, if the keyword REFL is present, otherwise [reflc]=0.
	Note: the program checks if the criterion [reflc]$^2 +$[trcoef]$^2 \leq 1$ is
	fulfilled.
RSPEC	indicates specular reflection which is the default. The angle of reflection
	equals the angle of incidence.
RDIFF	indicates diffuse reflection, i.e. specular reflection where incident waves
	are scattered over reflected direction.
[pown]	each incoming direction $\theta$ is scattered over reflected direction $\theta_{\rm refl}$
	according to $\cos^{{\tt [pown]}} (\theta - \theta_{\rm refl})$. The parameter [pown] indicates the width
	of the redistribution function.
	Default: [pown] = 1.
FREEBOARD	with this option the user indicates that the fixed transmission [trcoef]
	and reflection [reflc] coefficients are freeboard dependent. The freeboard
	dependency has no effect on the transmission coefficient as computed using
	the DAM option.
[hgt]	the elevation of the top of the obstacle or height of the quay above the reference
	level (same reference level as for the bottom). Use a negative value if the top is
	below that reference level. Specifying this parameter is required when option
	FREE is used. In case [hgt] is also specified in the DAM option, both values of
	[hgt] should be equal for consistency.
[gammat]	shape parameter of relative freeboard dependency of transmission coefficient.
	This parameter should be higher than zero. See Scientific/Technical documentation
	for background information.
	Default: [gammat] = 1.
[gammar]	shape parameter of relative freeboard dependency of reflection coefficient.
	This parameter should be higher than zero. See Scientific/Technical documentation
	for background information.
	Default: [gammar] = 1.
QUAY	with this option the user indicates that the freeboard dependency of the transmission
	and reflection coefficients also depends on the relative position of an obstacle-linked
	grid point with respect to the position of the obstacle line representing the edge of a
	quay. In case the active grid point is on the deeper side of the obstacle, then the
	correction factors are applied using the parameters [hgt], [gammat] and [gammar].
	In case the active grid point is on the shallower side of the obstacle, the reflection
	coefficient is set to 0 and the transmission coefficient to 1. This option only works
	in combination with the keyword FREE. See Scientific/Technical documentation
	for background information.
LINE	with this required keyword the user defines the location of the obstacle(s).
[xp], [yp]	coordinates of a corner point of the line that defines the location of the
	obstacle(s) (in problem coordinates):
	if Cartesian coordinates are used in m or
	if spherical coordinates are used in degrees (see command COORD).
	At least two corner points must be provided.

OBSTacle  FIG [alpha1] [hss] [tss] [dss] [dd]  REFL [reflc]   LINe <[xp] [yp]>

CANNOT BE USED IN 1D-MODE.


With this optional command the user specifies the obstacles along which the free infragravity (FIG) energy is radiated. By placing the obstacles close to the shorelines SWAN will include the FIG source term along the coastlines according to the parametrization of Ardhuin et al. (2014).


The location of the obstacle is defined by a sequence of corner points of a line. For an obstacle line to be effective its length is at least one mesh size large. It is recommended to place the obstacles at the inner area of the computational grid, not at or through the boundaries. In particular, each obstacle line must be bordered by wet points on both sides.


In addition, the orientation of the obstacle line determines from which side of the obstacle the FIG wave energy is radiated away. If the begin point of the line is below or left of the end point, that is, pointing upwards/to the right, then FIG energy is radiated from the west/north side of the line. If the begin point is above or right of the end point (pointing downwards/to the left), then FIG energy is radiated away from the east/south side of the obstacle line.

FIG	with this option the user indicates that FIG source term is included along
	the obstacle(s). It will be included only if the spectral directions cover the
	full 360$^{\rm o}$, i.e. if in the command CGRID the option CIRCLE is activated.
[alpha1]	calibration parameter (in 1/s) for determining the rate of radiating FIG
	energy from the shorelines.
[hss]	the sea-swell significant wave height (in m).
[tss]	a sea-swell mean wave period (in s).
[dss]	the sea-swell mean wave direction (in degrees).
	Default: [dss]=-999.
[dd]	power $m$ of directional spreading $cos^m(\theta)$ for radiated FIG.
	Default: [dd]=0.
REFL	if this keyword is present then any shoreward propagating (FIG) wave is
	specular reflected.
[reflc]	constant reflection coefficient, formulated in terms of wave height, i.e. ratio
	of reflected significant wave height over incoming significant wave height.
	Restriction: $0 \leq$ [reflc] $\leq 1$.
	Default: [reflc]=1, if the keyword REFL is present, otherwise [reflc]=0.
LINE	with this required keyword the user defines the location of the obstacle(s).
[xp], [yp]	coordinates of a corner point of the line that defines the location of the
	obstacle(s) (in problem coordinates):
	if Cartesian coordinates are used, in m, or
	if spherical coordinates are used, in degrees (see command COORD).
	At least two corner points must be provided.

Note that either [hss] or [tss] or [dss] or all three are allowed to vary over the computational domain. In that case use the commands INPGRID HSS and READINP HSS and/or the commands INPGRID TSS and READINP TSS and/or the commands INPGRID DSS and READINP DSS to define and read the sea-swell wave height/period/direction. It is permissible to have one or two constant sea-swell parameters, while the other(s) is (are) non-constant. The command OBST FIG is still required to define the obstacles. The values of [hss] and/or [tss] and/or [dss] in this command are then not required (they will be ignored).


Also noted that if [dss] = -999 or [dd] = 0, then no directional spreading for radiated FIG energy will be included.

SETUP [supcor]

CANNOT BE USED IN CASE OF UNSTRUCTURED GRIDS.


If this optional command is given, the wave-induced set-up is computed and accounted for in the wave computations (during the computation it is added to the depth that is obtained from the READ BOTTOM and READ WLEVEL commands). This approximation in SWAN can only be applied to open coast (unlimited supply of water from outside the domain, e.g. nearshore coasts) in contrast to closed basin, e.g. lakes and estuaries, where this option should not be used. Note that set-up is not computed correctly with spherical coordinates. Note that set-up is not supported in case of parallel runs using either MPI or OpenMP!

[supcor]	by default the wave-induced set-up is computed with a constant added such
	that the set-up is zero in the deepest point in the computational grid. The
	user can modify this constant by the value of [supcor]. The user can thus
	impose a set-up in any one point (and only one) in the computational grid
	by first running SWAN, then reading the set-up in that point and adding or
	subtracting the required value of [supcor] (in m; positive if the set-up has
	to rise).
	Default: [supcor]=0.

DIFFRACtion [idiffr] [smpar] [smnum] [cgmod]

If this optional command is given, the diffraction is included in the wave computation. But the diffraction approximation in SWAN does not properly handle diffraction in harbours or in front of reflecting obstacles (see Scientific/Technical documentation). Behind breakwaters with a down-wave beach, the SWAN results seem reasonable. The spatial resolution near (the tip of) the diffraction obstacle should be 1/5 to 1/10 of the dominant wave length.


Without extra measures, the diffraction computations with SWAN often converge poorly or not at all. Two measures can be taken:

1. (RECOMMENDED) The user can request under-relaxation. See command NUMERIC parameter [alpha] and Scientific/Technical documentation (Eq. (3.31)). Very limited experience suggests [alpha] = 0.01.
2. Alternatively, the user can request smoothing of the wave field for the computation of the diffraction parameter (the wave field remains intact for all other computations and output). This is done with a repeated convolution filtering. The mother filter is
   $$E^n_{i,j} = E^{n-1}_{i,j} - a \left[ E_{i-1,j} + E_{i,j-1} -4E_{i,j} + E_{i+1,j} + E_{i,j+1} \right]^{n-1}$$
   For $a = 0.2$ (recommended), the final width of the filter is $\varepsilon_x = \frac{1}{2} \sqrt{3n} \Delta x$ (in $x-$direction and similarly in $y-$direction) and $n$ is the number of repetitions (see Scientific/Technical documentation, Eq. (2.100)). Note that this smoothing option can not be applied in case of unstructured meshes.

[idiffr]	indicates the use of diffraction. If [idiffr]=0 then no diffraction is taken
	into account.
	Default: [idiffr]=1.
[smpar]	smoothing parameter for the calculation of $\nabla \cdot \sqrt{E_{\rm tot}}$. During every
	smoothing step all grid points exchange [smpar] times the energy with their
	neighbours. Note that [smpar] is parameter $a$ in the above text.
	Default: [smpar] = 0.
[smnum]	number of smoothing steps ($n$ in the above text). For $a = 0.2$, it should be
	approximately equal to $\lfloor \frac{4\varepsilon_x^2}{3\Delta x^2} \rfloor$.
	Default: [smnum] = 0.
[cgmod]	adaption of propagation velocities in geographic space due to diffraction.
	If [cgmod]=0 then no adaption.
	Default: [cgmod]=1.

SURFBeat  [df] [nmax] [emin]  UNIForm/LOGarithmic

CANNOT BE USED IN CASE OF CURVILINEAR or UNSTRUCTURED GRIDS AND NOT IN 1D-MODE.


Using this optional command, the user activates the Infragravity Energy Module (IEM) of Reniers and Zijlema (2022). Besides the energy balance equation for a sea-swell wave field, another energy balance is included to account for the transfer of sea-swell energy to the bound infragravity (BIG) wave. This infragravity energy balance also involves a nonlinear transfer, expressed by the biphase, through the phase coupling between the radiation stress forcing and the BIG wave. For the prediction of the biphase for obliquely incident waves, an evolution equation is provided under the assumption that the bottom slopes are mild and alongshore uniform.


The IEM framework is applied as follows. First, we assume that the conditions under which the surfbeat is modelled are stationary, and that the overall prediction of the sea-swell and infragravity wave fields (both bound and free) is carried out with two COMPUTEs.


During the first COMPUTE both the short and bound long wave spectra are computed. In this respect, the user specifies a frequency range for the sea-swell spectrum that is bounded below by an infragravity frequency cut-off $f_{\rm ig}$ (see command CGRID). Basically, this spectrum is subject to propagation, shoaling, refraction, surf breaking and bottom friction (other processes should not be included). In addition, an offshore directionally spread spectrum must be imposed on the west side of the computational domain. (Currently, it is assumed that a regular grid is defined with the direction of the positive $x-$axis pointing eastward.)


Next, to add BIG components with frequencies less than or equal to $f_{\rm ig}$, the infragravity energy balance is solved. This equation is forced by bichromatic wave groups related to all pairs in the sea-swell spectrum with a frequency difference less or equal to $f_{\rm ig}$. In addition, this equation is solved in tandem with the evolution equation for the biphase.


By the finish of the first COMPUTE, the user may include some plotting commands related to both the short and long wave spectra, including the integral parameters.


Finally, the BIG waves are assumed to reflect at the shoreline (on the east side of the domain). Accordingly, the user must specify an obstacle line alongshore (parallel with $y-$axis) with a reflection coefficient (see command OBST REFL ... LINE ...; for reasons of consistency, the same obstacle line must be specified in the first COMPUTE with a transmission coefficient of 1, so that the wave field will not be affected).


The reflected ig waves are assumed to be free and their evolution can be predicted by the conventional energy balance equation during the second COMPUTE. In view of this, a frequency range $[{\tt [df]},f_{\rm ig}]$ must be specified which can be either uniform or logarithmic.

[df]	the constant size of BIG frequency bin (in Hz).
	Default: [df]=0.01.
[nmax]	the maximum number of short-wave pairs for creating bichromatic wave groups.
	Default: [nmax] = 50000.
[emin]	the energy threshold in fraction of energy spectrum peak.
	With this threshold one takes into account those short wave components to
	create bichromatic wave groups while their energy levels are larger than
	[emin] $\times E_{\rm max}$ with $E_{\rm max}$ the peak of the spectrum.
	Default: [emin] = 0.05.
UNIFORM	frequencies for reflected ig waves are uniformly distributed.
	This is the default.
LOGARITHMIC	frequencies for reflected ig waves are logarithmically distributed.

SCAT [iqcm]                    &

     ( GRId [rfac] )           &

     ( TRUnc [alpha] [qmax] )

Using this optional command, the user activates a source term that allows for the generation and propagation of cross correlations between scattered waves due to variations in the bathymetry and mean currents. Such variations are rapid compared to the distance between the crossing waves (at the scale of 100$-$1000 m) and is particularly relevant for cases involving narrowband waves (swells) in coastal regions with shallow water and ambient currents. In turn, the immediate spatial effects of coherent scattering, interference, refraction and diffraction can cause large-scale changes in the wave parameters.


The underlying modelling concept has been introduced and developed by Smit and Janssen (2013), Smit et al. (2015a,b) and Akrish et al. (2020) and is now known as the quasi-coherent (QC) model. The QC framework has been made consistent with the action balance equation through the addition of a scattering source term and is hereby adopted in the current operational version of SWAN (version 41.41). This source term involves a convolution integral which relates the spectral representation of wave action, including cross correlations, and the response of the small-scale medium variations (through the dispersion relation).


The modelling strategy by means of the QC scattering term provides the ability to readily nest a QC model into a conventional, regional-scale SWAN (or other spectral) model. However, when setting up a QC model, other existing (shallow-water) source terms (e.g., surf breaking, triad wave-wave interactions) should not be included as they do not account for the cross correlations among wave components of the scattered field and, in turn, their effects on wave interference patterns. Therefore, the user should be aware of the currently limited use of the QC model in support of the complete description of the wave field, including the dissipation and nonlinear effects. The inclusion of QC-consistent depth-induced wave breaking and nonlinear (triad) interactions will be considered in the near future (see also Smit et al., 2015b and Smit and Janssen, 2016).


In order to apply the QC approximation properly, an incident wave spectrum must be imposed at the wave maker. This provides input used in defining the coherent radius of the scattered wave field and in designating the grid spacing in wave number space. The definition of the coherent region is especially relevant for the discrete Fourier transform of the modulation of the dispersion relation (owing to the medium variations). Furthermore, the grid domain in wave number space defines a region in which the effects of cross correlations are resolved. This will be constructed by SWAN with the aid of the discrete frequency-direction sector (see command CGRID SECTOR). The associated resolution is determined by the characteristic width (or standard deviation) of the incoming spectrum, $\Delta k$ (in 1/m), and the user-defined resolution factor $r_f \geq 1$, and is expressed as $\Delta k / r_f$. The correlation (or coherent) length scale is then given by $2\pi\,r_f/\Delta k$.


The unbounded convolution integral of the scattering source term is computed as the sum over a finite range of wave numbers. The extent of this range reflects the scale to which variations in the medium (seabed and/or mean currents) affect the wave field. The convolution sum is thus limited to the range $[-q_{\rm max}\,,\,q_{\rm max}]$ with $q_{\rm max}$ the maximum scattering wave number. This maximum can either be directly set or can be taken as a multiple of the mean wave number at the wave maker.

[iqcm]	indicates the modelling and computation of QC scattering:
	= 0 no scattering
	= 1 scattering due to non-uniform bathymetry and currents
	(the latter only if applicable; see command INPGRID CURRENT)
	= 2 wave-current interaction under the assumption of a slowly varying
	bathymetry
	Default: [iqcm] = 1.
GRID	with this option the user controls the grid resolution of the wave number
	space. It is defined as a multiple of the characteristic width of the
	incoming wave spectrum.
[rfac]	the resolution factor through which the incident spectral width is
	multiplied. Note that this factor must be larger or equal 1.
	Default: [rfac] = 1.
TRUNC	with this option the user truncates the infinite convolution sum at
	either the multiple of the mean wave number at the wave maker (the
	default option), or at the maximum scattering wave number. When
	specifying both parameters, then their mimimum is considered as the
	final limit on the sum.
[alpha]	the coefficient by which the mean wave number is multiplied to set
	the limit on the convolution sum.
	Default: [alpha] = 1.
[qmax]	the maximum scattering wave number (in 1/m).

     |  WINDGrowth |
     |             |
     |  QUADrupl   |
     |             |
     |  WCAPping   |
OFF <               >
     |  BREaking   |
     |             |
     |  REFrac     |
     |             |
     |  FSHift     |
     |             |
     |  BNDCHK     |

With this optional command the user can change the default inclusion of various physical processes (e.g. for research purposes). This command is not recommended for operational use.

WINDGROWTH	switches off wind growth (in commands GEN1, GEN2 and GEN3).
QUADRUPL	switches off quadruplet wave-wave interactions (in command GEN3).
WCAPPING	switches off whitecapping (in command GEN3).
BREAKING	switches off depth-induced breaking dissipation.
	Caution: wave heights may diverge in very shallow water.
REFRAC	switches off refraction (action transport in $\theta-$direction).
FSHIFT	switches off frequency shifting in frequency space (action transport in $\sigma-$space).
BNDCHK	switches off the checking of the difference between imposed and computed
	significant wave height at the boundary of the computational grid (see also
	command SET).