A variational data assimilation system for nearshore applications of SWAN

Abstract

This paper uses the variational approach described by Walker (2006) for assimilation of data into the nearshore spectral wave model SWAN. The system uses observed two-dimensional spectra from the interior of the domain to correct the prescribed boundary conditions for the forward model. The objective function that determines the amount of correction to be applied is derived with the assumption that the differences between observations and model predictions are mainly a result of specification of incorrect spectra at the boundary. Using synthetic data, we show that the system reproduces the correct wave spectra at the boundary and converges to the solution with accuracy greater than 95% in only a few model iterations. Use of the assimilation system to estimate the wave field is demonstrated for Santa Rosa Island, FL. Results show excellent agreement with independent observations of the bulk (or integrated) wave parameters such as significant wave heights, peak wave periods and mean wave directions, and good agreement with observations of the two-dimensional wave spectra. The accuracy of the system is reduced when there is relatively little energy at the assimilation location or when the nonlinear processes due to wind (such as active wave growth, nonlinear transfer of energy between frequencies and directions, and breaking) are dominant in the region of interest.