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This paper describes a variational data assimilation algorithm based on the Simulating WAves Nearshore (SWAN) wave spectrum model. The approach allows single-point wave spectrum observations to be used to estimate the wave field for a nearshore region under stationary conditions, assuming a spatially uniform incident wave spectrum at the offshore boundary. The assimilated data are in the form of Fourier directional coefficients, the standard output from operational wave buoys, and are used directly by incorporating the relationship between directional spectrum and the Fourier coefficients into the formulation. The algorithm was tested on data from nearshore buoys deployed off the coast of North Carolina in May 2012, and the estimated wave field is compared to both the input data and independent observation data. The results compare favorably to the independent data with overall RMS errors of 10%–20% for significant wave height, about half a second for mean wave period, and as much as three to four SWAN spectral grid cells for mean direction. Overall, the results show that the algorithm can be effectively used to estimate the offshore boundary spectrum and accurately reproduce wave conditions in the domain.

Estimating Nearshore Waves by Assimilating Buoy Directional Spectrum Data in SWAN