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

该奖项支持的研究将产生强大的和可扩展的开源软件，用于具有不同程度非线性的大型时空系统的数据同化。它将导致改进的推理，预测，诊断，降尺度和校准使用数据同化在许多科学领域对社会有直接影响，包括天气预报，气候研究，可再生能源和污染监测。尽管数据同化非常重要，而且具有高度统计性质，但这一研究领域缺乏统计人员。因此，该项目的教育部分围绕着弥合统计和数据同化社区之间的差距，并让更多的统计学家参与后者。首席研究员将开发用于过滤高维状态的推断的方法，该方法可以在线性和非线性设置中优于现有方法。新的方法是基于多分辨率近似，一个国家的最先进的空间协方差近似的方法，采用许多自适应，companies支持的基函数在多个分辨率。该方法的计算机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。验证，测试和比较的方法将进行使用不同复杂性的模型模拟现实的观察。

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.