Abstract The formulation of boundary conditions at liquid (open) boundaries is a topical problem in mathematically modeling the hydrothermodynamics of open water areas. Variational data assimilation is one method allowing one to take into account liquid boundaries in models. According to the approach considered in this paper, observational data at a certain time are given and the problem is treated as an inverse one with open boundary flows as additional unknowns. This paper presents a formulation of the general problem of the variational assimilation of observational data for a model of the hydrothermodynamics of open water areas based on the splitting method. Algorithms for the variational assimilation of temperature and sea-level data at the liquid boundary are formulated and the results of numerical experiments on the use of the algorithms in the Baltic Sea circulation model are presented.

中文翻译：

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开放水域水物理场建模问题中的变分数据同化

摘要 液体（开放）边界处边界条件的制定是开放水域水热力学数学建模中的一个热门问题。变分数据同化是一种允许在模型中考虑液体边界的方法。根据本文所考虑的方法，给出某一时间的观测数据，并将问题作为逆问题处理，开放边界流作为额外的未知数。本文提出了基于分裂方法的开放水域水热力学模型观测数据变分同化的一般问题的表述。