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本研究采用基于最优控制理论的伴随法，把观测资料同化到陆架海域潮汐 数值模型中去，优化开边界条件，提高数值预报的精度．潮汐模型的控制方程为考虑 平流项、非线性底摩擦和侧向涡动粘性项的非线性浅水方程组；采用Ｌａｇｒａｎｇｅ乘子 法建立了伴随模型．研究分两部分：第一部分即本文，建立非线性浅水方程模型的伴 随方程、给出目标函数的梯度，并实现“孪生”数值试验；第二部分另文给出．
In this study, the concomitant method based on the optimal control theory was used to assimilate the observed data into the tidal numerical model of the continental shelf and optimize the open boundary conditions to improve the accuracy of numerical prediction. The governing equations of the tidal model are nonlinear shallow water equations considering the advection term, nonlinear bottom friction and lateral eddy viscosity term. The adjoint model is established by Lagrange multiplier method. The research is divided into two parts: The first part is the article, which establishes the adjoint equation of the nonlinear shallow water equation model, gives the gradient of the objective function, and realizes the “twin” numerical experiment;