Abstract. In previous work, it was shown that preservation of physical properties in the data assimilation framework can significantly reduce forecasting errors. Proposed data assimilation methods, such as the quadratic programming ensemble (QPEns) that can impose such constraints on the calculation of the analysis, are computationally more expensive, severely limiting their application to high dimensional prediction systems as found in earth sciences. In order to produce from a less computationally expensive, unconstrained analysis, a solution that is closer to the constrained analysis, we propose to use a convolutional neural network (CNN) trained on analyses produced by the QPEns. In this paper, we focus on conservation of mass and show in an idealized setup that the hybrid of a CNN and the ensemble Kalman filter is capable of reducing analysis and background errors to the same level as the QPEns. To obtain these positive results, it was in one case necessary to add a penalty term to the loss function of the CNN training process.

中文翻译：

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训练卷积神经网络以节省数据同化质量

摘要。在以前的工作中，表明在数据同化框架中保留物理属性可以显着减少预测误差。提议的数据同化方法（例如可以对分析的计算施加此类约束的二次编程集成（QPEns））在计算上更加昂贵，严重地限制了它们在地球科学中发现的高维预测系统中的应用。为了从计算量较少，不受约束的分析中产生更接近约束分析的解决方案，我们建议使用在QPEns产生的分析中训练的卷积神经网络（CNN）。在本文中，我们专注于质量守恒，并在理想的设置中证明了CNN和集成卡尔曼滤波器的混合能够将分析和背景误差降低到与QPEns相同的水平。为了获得这些积极的结果，在一种情况下，有必要在CNN训练过程的损失函数中增加一个惩罚项。