Wave boundary and initial conditions

To obtain the numerical solution of the action balance equation (2.16), the wave boundary and initial conditions should be provided. The incoming wave components at the up-wave boundaries in the SWAN model are specified by a two-dimensional spectrum. Several options are available:

• A parametric one-dimensional spectrum with a certain imposed directional distribution. An example is a Jonswap spectrum.
• A discrete one-dimensional spectrum with a certain imposed directional distribution. This is often obtained from measurements.
• A discret two-dimensional spectrum. This may be obtained from other SWAN runs or other models, e.g. WAM and WAVEWATCH III.

For the parametric one-dimensional spectrum, the following optional forms have been recommended: a Pierson-Moskowitz spectrum (Pierson and Moskowitz, 1964), a Jonswap spectrum (Hasselmann et al., 1973) and a Gaussian-shaped spectrum.


The boundaries in frequency space are fully absorbing at the lowest and the highest discrete frequency. So, energy can freely propagate across these boundaries and thus total energy might not be conserved in some cases. However, a diagnostic tail $f^{-m}$ ($m=4$ or $m=5$) is added above the high frequency cut-off, which is used to compute nonlinear wave-wave interactions at the high frequencies and to compute integral wave parameters. When the directional space is a closed circular, no directional boundary conditions are needed. However, for reasons of economy, SWAN has an option to compute only wave components in a pre-defined directional sector. In this case, the boundaries of this sector are fully absorbing (action density might be removed from the model by refraction).


To facilitate the integration process of the action balance equation, wave boundary conditions in geographical space need to be provided. The boundaries of the computational grid in SWAN are either land or water. In case of land there is no problem. The land does not generate waves and in SWAN it absorbs all incoming wave energy. But in the case of a water boundary there is a problem. If observations are available, they can be used as inputs at the boundary. In case no wave conditions are given along the boundary, SWAN assumes that no waves enter the model and waves can leave the model freely along that boundary. This assumption results in errors. Therefore, to get reliable results, especially for such case, the model boundaries must be placed far away from the area of interest.


In case of nonstationary computation, the default initial spectra are computed from the local wind velocities using the deep-water growth curve of Kahma and Calkoen (1992), cut off at values of significant wave height and peak frequency from Pierson and Moskowitz (1964). The average (over the model area) spatial step size is used as fetch with local wind. The shape of the spectrum is default Jonswap with a $\cos^2 (\theta)$ directional distribution centred around the local wind direction.


The first guess conditions of a stationary run of SWAN are default determined with the second generation mode of SWAN.


It is possible to obtain an initial state by carrying out a previous stationary or nonstationary computation.