特征线计算格式下共轭方程两种导出途径的比较

共轭方程的导出是建立资料同化模型的关键，其导出方式有两种途径：AFD形式与FDA形式。在特征线计算格式基础上针对一类较广泛海洋动力控制方程分析了其两种共轭方程（AFD形式与FDA形式）之间的关系，并将理论结果应用于波谱共轭方程的讨论。

DIFFERENCE OF ADJOINT EQUATIONS BETWEEN TWO APPROACHES BASED ON THE CHARACTERISTIC INLAID METHOD

The characteristic inlaid method is widely used to integrate a general first-order partial differential equation, such as the wave energy propagation equations in large scale ocean phenomena. For data assimilation, there are two approaches which are commonly used to formulate the adjoint to the given control model as stated above. The first involves writing the adjoint equations of the linearing continuous model equations and then designing an appropriate finite-difference formulation. The second derives the adjoint equations directly from the finite-difference equations of the forward model. Here these two adjoint equations are obtained respectively for the general first-order partial differential equation based on the characteristic inlaid computational method. And the difference between these two eguations is also analyzed. Then the theoretical results are applied to discussing the adjoint ocean wave energy spectrum equation, which indicates that the two approaches are almost the same for practical situations if the numerical model is calculated by using the characteristic inlaid method.