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首页> 外文期刊>International Journal for Numerical Methods in Fluids >Very large inverse problems in atmosphere and ocean modelling
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Very large inverse problems in atmosphere and ocean modelling

机译：大气和海洋模拟中的非常大的逆问题

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摘要

For the very large nonlinear dynamical systems that arise in a wide range of physical, biological and environmental problems, the data needed to initialize a numerical forecasting model are seldom available. To generate accurate estimates of the expected states of the system, both current and future, the technique of 'data assimilation' is used to combine the numerical model predictions with observations of the system measured over time. Assimilation of data is an inverse problem that for very large-scale systems is generally ill-posed. In four-dimensional variational assimilation schemes, the dynamical model equations provide constraints that act to spread information into data sparse regions, enabling the state of the system to be reconstructed accurately. The mechanism for this is not well understood. Singular value decomposition techniques are applied here to the observability matrix of the system in order to analyse the critical features in this process. Simplified models are used to demonstrate how information is propagated from observed regions into unobserved areas. The impact of the size of the observational noise and the temporal position of the observations is examined. The best signal-to-noise ratio needed to extract the most information from the observations is estimated using Tikhonov regularization theory. Copyright (c) 2005 John Wiley F Sons, Ltd.
机译：对于在广泛的物理，生物学和环境问题中出现的非常大的非线性动力学系统，很少需要初始化数值预测模型所需的数据。为了生成当前和未来系统预期状态的准确估计，使用“数据同化”技术将数值模型预测与随时间推移测得的系统观察结果结合起来。数据同化是一个反问题，对于非常大规模的系统通常是不适当的。在四维变分同化方案中，动力学模型方程式提供了一些约束条件，这些约束条件可将信息传播到数据稀疏区域中，从而可以准确地重建系统状态。对此的机制还不太了解。此处，将奇异值分解技术应用于系统的可观察性矩阵，以便分析此过程中的关键特征。简化的模型用于说明信息如何从观察区域传播到未观察区域。检查了观测噪声大小和观测时间位置的影响。使用Tikhonov正则化理论估算从观测中提取最多信息所需的最佳信噪比。版权所有（c）2005 John Wiley F Sons，Ltd.

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