Establishing Links between Atmospheric Dynamics and Non-Gaussian Distributions and Quantifying Their Effects on Numerical Weather Prediction

数据同化是一种用于将观测数据合并到数值模式中以改进对系统当前状态的表示的方法。数据同化在大气科学中被广泛用于辅助天气预报模型，利用来自卫星、气象站、气象气球和许多其他系统的数据。本课题研究的重点是观测值与模型状态之间产生的误差。误差假设为高斯分布，或均匀分布，但对于某些变量来说，情况可能并非如此。该奖项的研究将提高我们对非高斯误差的理解。对社会的潜在影响将是天气预报的改善。数据同化在科学的其他领域也在增长，因此这项研究具有跨领域的潜在应用。一名早期职业科学家也将在这一不断增长的研究领域接受培训。研究团队将从几个不同的方面讨论非高斯分布误差如何影响数据同化和反演系统，以及如何检测何时高斯假设不是最优的。研究将向前推进五个主题：1)从预报差场中为不同的大气动力学建立条件概率密度函数(PDF)，作为背景误差场的代理，然后开发数学和随机模型以将条件概率密度函数链接到特定的大气动力学；2)在玩具问题中推导、测试，然后将其实施到混合PDF混合变分-集合系统WRF-GSI中；3)在检索和混合数据同化系统中研究对于不同尺度的动力学的不同PDF假设的影响；4)将对数正态检测算法扩展到用于教育诊断的近实时能力，5)创建网页，说明系统产生的不同值，并结合检测算法输出，作为研究人员查看分布对检索性能影响的教育工具。

Data assimilation is a method that is used to incorporate observations into a numerical model to improve the representation of the current state of the system. Data assimilation is widely used in atmospheric sciences to assist weather forecasting models, making use of data from satellites, weather stations, weather balloons and many other systems. The focus of the research in this project are the errors that arise between the observations and model state. The errors are assumed to be Gaussian, or evenly distributed, but for some variables that may not be the case. The research in this award will improve our understanding of non-Gaussian errors. The potential impact on society would be improved weather forecasting. Data assimilation is also growing in other areas of science, so the research potentially has cross-cutting applications. An early career scientist will also be trained in this growing area of research.The research team will address several different aspects about how non-Gaussian distributed errors affect data assimilation and retrieval systems, but also how to detect when the Gaussian assumption is not optimal. Research will move forward on five topics: 1) Build conditional probability density functions (PDF) for different atmospheric dynamics from forecast difference fields, as a proxy for the background error fields, and then develop mathematical and stochastical models to link the conditional PDFs to specific atmospheric dynamics, 2) Derive, test in a toy problem, and then implement into the WRF-GSI, a mixed PDF hybrid variational-ensemble system, 3) Investigate the impact of different PDF assumptions for different scales of dynamics in both retrieval and hybrid data assimilation systems, 4) Extend the lognormal detection algorithm to a near real-time capability for educational diagnostics, 5) Create web pages to illustrate the different values that the systems produce combined with the detection algorithm output as an educational tool for researchers to see the effects of the distributions on the performance of the retrievals.