Wave Spectrum Stability Of The Energy Equation, The Sensitivity Analysis And Wave Variational Assimilation Study

The following are the major work in this thesis which has been studied and still needs to be studied further in the future: 1) An improved adjoint variational method is developed, thus it can be applied to the LAGFD-WAM Wave Numerical Model for data assimilation; 2) A linear evolution equation of spectral perturbation is derived in order to analyze its increasing or decreasing mechanism. The duration of spectral perturbation is calculated under the swell situation after the linear evolution equation of spectral perturbation is simplified. The evolution of perturbation under the wind sea situation is also analyzed primarily; 3) The sensitivity of distance function in the wave assimilation model is studied with the use of adjoint spectrum balance equation. Disregard its primary, the spacial value distribution of sensitivity is important for oceanic convention observation, etc. 4) The improved adjoint variational method is applied to the wave energy spectrum balance equation, and then the continuous wave data assimilation model is developed. Especially the adjoint source functions of wind input function, wave breaking dissipation function, bottom friction function, wave-wave nonlinear interaction and wave-current interaction are derived rigorously; 5) The assimilation experiments based on the level of spectrum and significant wave height are implemented and analyzed respectively. The new ideas in this thesis are stated below: The adjoint variational method is improved with the use of semigroups of linear operators for wide application; The linear evolution equation of spectral perturbation is derived, which is then used to analyze the instability of wave energy spectrum balance equation; The nonlinear interaction operator constructed by the superposition of a small number of discrete-interaction configurations is formularized in order to derive its adjoint operator. The adjoint operator is then derived and formularized as well; The continuous wave data assimilation model is developed to optimize the initial spectrum; Two different assimilation processes are developed under the level that the observation is spectrum by SAR or significant wave height by ALT.