Variational Data Assimilation for Near-Shore Waves Using the Extended Boussinesq Equations

摘要

This report describes a variational approach for assimilation of single-point, in-situ observations of surface elevation and velocity into the extended Boussinesq model of Wei et al. (1996). The mathematical framework for assimilation is presented, along with applications of the procedure for two cases: monochromatic waves and broad-spectrum irregular waves. Overall the performance of the approach for monochromatic waves is quite good; while for irregular waves, some of the short-wave detail, especially for waves propagating in the along-shore direction, is missed. As part of the development work, an existing parallel Boussinesq model code was improved through addition of run-up, wave-breaking and bottom-friction models, and a directional wavemaker was implemented.