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Ｈｅｓｓｅ矩阵－目标函数关于控制变量的二阶偏导数形成的矩阵，在变分数据同化过程中以及敏感性分析等方面起着重要的作用；它可以通过建立数学模型的一阶和二阶伴随模型求得．以浅水方程模型为例，利用泛函的Ｇａｔｅａｕｘ微分和Ｈｉｌｂｅｒｔ空间上伴随算子的概念，导出了一阶和二阶伴随模型并由此得到Ｈｅｓｓｅ矩阵．改进了 Ｚｈｉ Ｗａｎｇ等（ １９９２）建立的二阶伴随模型理论．
The Hesse matrix - objective function The matrix formed by the second-order partial derivatives of the control variables plays an important role in variational data assimilation and sensitivity analysis. It can be achieved by establishing first and second order adjoint models of mathematical models Obtained. Taking the shallow water equation model as an example, the first order and the second order adjoint models are derived by using the Gateaux differential of functions and the concomitant operator in Hilbert space, and the Hesse matrix is obtained. The second-order concomitant model theory established by Zhi Wang et al. (1992) is improved.