Units and coordinate systems

SWAN expects all quantities that are given by the user to be expressed in S.I. units: m, kg, s and composites of these with accepted compounds, such as Newton (N) and Watt (W). Consequently, the wave height and water depth are in m, wave period in s, etc. For wind and wave direction both the Cartesian and a nautical convention can be used (see below). Directions and spherical coordinates are in degrees ($^{{\rm0}}$) and not in radians.


For the output of wave energy the user can choose between variance (m$^{{\rm 2}}$) or energy (spatial) density (Joule/m$^{{\rm 2}}$, i.e. energy per unit sea surface) and the equivalents in case of energy transport (m$^{{\rm 3}}$/s or W/m, i.e. energy transport per unit length) and spectral energy density (m$^{{\rm 2}}$/Hz/Degr or Js/m$^{{\rm 2}}$/rad, i.e. energy per unit frequency and direction per unit sea surface area). The wave$-$induced stress components (obtained as spatial derivatives of wave-induced radiation stress) are always expressed in N/m$^2$ even if the wave energy is in terms of variance. Note that the energy density is also in Joule/m$^{{\rm 2}}$ in the case of spherical coordinates.


SWAN operates either in a Cartesian coordinate system or in a spherical coordinate system, i.e. in a flat plane or on a spherical Earth. In the Cartesian system, all geographic locations and orientations in SWAN, e.g. for the bottom grid or for output points, are defined in one common Cartesian coordinate system with origin (0,0) by definition. This geographic origin may be chosen totally arbitrarily by the user. However, be careful, the numbers for the origin should not be chosen too large; the user is advised to translate the coordinates with an offset. In the spherical system, all geographic locations and orientations in SWAN, e.g. for the bottom grid or for output points, are defined in geographic longitude and latitude. Both coordinate systems are designated in this manual as the problem coordinate system.


In the input and output of SWAN the direction of wind and waves are defined according to either

• the Cartesian convention, i.e. the direction to where the vector points, measured counterclockwise from the positive $x-$axis of this system (in degrees) or
• a nautical convention (there are more such conventions), i.e. the direction where the wind or the waves come from, measured clockwise from geographic North.

All other directions, such as orientation of grids, are according to the Cartesian convention!


For regular grids, i.e. uniform and rectangular, Figure 4.1 (in Section 4.5) shows how the locations of the various grids are determined with respect to the problem coordinates. All grid points of curvilinear and unstructured grids are relative to the problem coordinate system.