Effect of Wave Data Assimilation on the Numerical Simulation of Wave Energy Advection

摘要

Simulated observations are assimilated into a simple wave model, in which only propagation is considered. The approach used to assimilate them is called 'model fitting.' It looks for the solution of the model equations which best fits the observations to the space-time domain one is considering. It is also required that the deviation from 'a priori' knowledge (in this case the model initial state) remains as small as possible, in some well specified sense. The method is based on the minimization of a so called 'cost function,' which is a quadratic function of the differences between modeled data and observations on the one hand, and between modeled and 'a priori' data on the other hand. The minimization of the cost function is done by means of an iterative gradient-based descent method. After assimilation, new model results, which fit better to the observations and prior knowledge considered, are produced. Therefore, one concludes that the data assimilation process improves the wave field, but its effect is more clearly noticed around the observations than elsewhere, and it does not remain long after stopping assimilating.