CAREER: Data Assimilation for Massive Spatio-Temporal Systems Using Multi-Resolution Filters

该奖项支持的研究将为具有不同程度非线性的大型时空系统的数据同化提供强大和可扩展的开放源码软件。它将在包括天气预报、气候研究、可再生能源和污染监测在内的许多科学领域利用数据同化改进推理、预测、诊断、缩小尺度和校准，对社会产生直接影响。尽管数据同化具有很高的重要性和高度的统计性质，但在这一研究领域缺乏统计学家。因此，这个项目的教育部分围绕着弥合统计学和数据同化社区之间的差距，并让更多的统计学家参与到后者中来。主要研究人员将开发对高维状态进行过滤推理的方法，这些方法在线性和非线性环境中的表现可以超过现有方法。新的方法是基于多分辨率近似的，这是一种最先进的空间协方差近似方法，在多分辨率下使用许多自适应的、紧支撑的基函数。这些方法的算法实现是高度可扩展的，并且可以充分利用大规模并行高性能计算系统的优势。这些方法的验证、测试和比较将使用从不同复杂程度的模型中模拟的真实观测进行。

The research supported by this award will produce powerful and scalable open-source software for data assimilation in large spatio-temporal systems with varying degrees of nonlinearity. It will lead to improved inference, forecasts, diagnostics, downscaling, and calibration using data assimilation in many fields of science with direct impact on society, including weather forecasting, climate studies, renewable energy, and pollution monitoring. Despite the great importance and highly statistical nature of data assimilation, there is a lack of statisticians involved in this research area. Thus, the educational component of this project revolves around bridging the gap between the statistics and data-assimilation communities, and getting more statisticians involved in the latter.The principal investigator will develop approaches for filtering inference on high-dimensional states that can outperform existing methods in linear and nonlinear settings. The novel approaches are based on the multi-resolution approximation, a state-of-the-art method for spatial covariance approximations that employs many adaptive, compactly supported basis functions at multiple resolutions. Algorithmic implementations of the methods are highly scalable and can take full advantage of massively parallel high-performance computing systems. Validation, testing, and comparison of the methods will be carried out using realistic observations simulated from models of varying complexity.