Assimilating coastal wave observations in regional swell predictions. Part I: Inverse methods

Abstract

Inverse methods are used to assimilate wave observations into numerical predictions of ocean swell (0.04-0.12 Hz surface waves) propagating over complex continental shelf bathymetry. Model predictions of swell on the shelf can be degraded by the limited accuracy and resolution of the initializing offshore (unsheltered deep water) frequency-directional spectra So, usually derived from buoy measurements or meteorological hindcasts. The authors use a spectral refraction wave propagation model to find improved estimates of So that are consistent with both unsheltered and sheltered (altered by coastal bathymetry) observations, and vary smoothly in direction and time. In Part I, linear and nonlinear inverse assimilation methods are developed. Their potential and limitations are illustrated qualitatively using a scenario where no a priori knowledge of So is used in the inverse estimates. Inverse estimates of So based solely on sheltered wave data routinely collected in the Southern California Bight are compared to meteorological hindcasts of peak offshore swell directions for two time periods dominated by swell arrivals from a distant storm. Robust model-hindcast agreement for the peak direction of an energetic, unimodal North Pacific swell event demonstrates that offshore directional information can be inferred solely from sheltered measurements. The poor model-hindcast agreement for a south swell event is markedly improved by the a priori assumption that So is unimodal with a prescribed parametric form, but assumptions about the shape of So severely reduce the generality of the approach. The authors conclude that conventional (low directional resolution) measurements from a few sheltered sites cannot be used to routinely resolve So, and offshore measurements or hindcasts of So are needed as additional constraints in practical applications. In Part II, the inverse methods are generalized to include hindcasts or unsheltered directional buoy data as primary constraints and sheltered observations are used to enhance the directional resolution and stability of So. Initialized with these So, the wave model yields improved predictions of regional swell conditions. The value of assimilating coastal observations into regional wave predictions is demonstrated with a comprehensive field study.