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The Wave Refraction Model

The wave conditions along the Canterbury coast are simulated using the SWAN wave refraction model (Booij et al. 1999; Ris et al. 1999). For given incipient deep-water wave conditions and wind-field data, the SWAN model enables the effects of wave generation by local winds and refraction over the seabed to be taken into account. The method computes an equilibrium sea state for a given wind field and offshore boundary wave conditions as if these conditions had been present for an indefinite time. This does not take into account the history of these forcings, which may, for example, result in the sea state being not fully developed in a strengthening wind, or remnant seas being left in a weakening wind. However, this is a relatively small limitation over short spatial scales. For example, at typical wave speeds of 8 m/s (for 10 s period waves in deep-water), a 120 km domain, such as that used in the model grid for the Canterbury Coast, is crossed in around 4 hours. So only variations in the forcings at shorter time scales than this will result in non-equilibrium conditions.

Application to Canterbury Coast

The model output grid covers the South Island east coast north of the Otago Peninsula to the southern end of the North Island, and is oriented at 40° from True North to align with the trend of the coastline. The model is run at 2 km resolution with 59 cells in the cross-shore direction and 316 cells in the long-shore direction. The colour-scaled plot shows the predicted significant wave height, with mean wave direction shown by arrows in every fourth grid cell. The model results at the northern and southern ends of the grid, beyond the Canterbury region, may be unreliable, and are not plotted.

The sea state along the deep-water boundary is assumed to be spatially uniform. We use the significant wave height, mean period, and mean direction at the peak of the spectrum from the most recent 30 minute wave buoy sample from the NIWA wave buoy off Banks Peninsula, and assuming these parameters are representative of the ocean swell, apply these parameters along the deep-water boundary.

Likewise a spatially uniform wind field is assumed to simulate the locally generated wind sea. Hourly average wind data at corresponding times are obtained from the Kyle Street, Christchurch, automatic weather station. This data is scaled by a factor of 2.0 to account for the higher mean wind speed (4.9 m/s) near the offshore location of the wave buoy, in comparison to that at Christchurch Airport (3.6 m/s), and a derived relationship between average wind speed at Kyle St. and at Christchurch Airport. For this comparison, wind speed near the wave buoy was estimated from the European Centre for Medium Range Weather Forecasts (ECMWF) reanalysis dataset.

The spatially uniform wind field is a first approximation. A better representation of the actual wind field could be obtained by incorporating real-time data from more than one climate station. In particular, wind conditions along the Canterbury Bight and farther south would probably be better estimated from readings taken at Timaru airport than at Christchurch. Additional climate stations may be incorporated as a future enhancement.


Booij, N.; Ris, R.C.; Holthuijsen, L.H. (1999). A third-generation wave model for coastal regions 1. Model description and validation. Journal of Geophysical Research 104(C4): 7649-7666.

Gorman, R.M.; Laing, A.K. (2001). Bringing wave hindcasts to the New Zealand coast. Journal of Coastal Research Special Issue 34 (ICS 2000 New Zealand): 30-37.

Ris, R.C.; Holthuijsen, L.H.; Booij, N.; (1999). A third-generation wave model for coastal regions 2. Verification. Journal of Geophysical Research 104(C4): 7667-7681.