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

数据同化是一种将观测数据纳入数值模型以改善系统当前状态表征的方法。数据同化在大气科学中广泛应用，利用来自卫星、气象站、气象气球和许多其他系统的数据来辅助天气预报模型。本项目的研究重点是观测值与模型状态之间产生的误差。假设误差是高斯分布的，或均匀分布的，但对于某些变量，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改善天气预报。数据同化在其他科学领域也在不断发展，因此这项研究可能具有跨领域的应用。一名早期职业科学家也将在这一不断发展的研究领域接受培训。研究小组将解决非高斯分布误差如何影响数据同化和检索系统的几个不同方面，以及如何检测高斯假设何时不是最优的。研究将围绕以下五个主题展开：1)从预报差场中建立不同大气动力学的条件概率密度函数（PDF），作为背景误差场的代理，然后建立数学和随机模型，将条件PDF与具体的大气动力学联系起来；2)推导，在一个小问题中进行测试，然后在WRF-GSI中实现混合PDF混合变分-集合系统。3)研究不同PDF假设对检索和混合数据同化系统中不同动态尺度的影响；4)将对数正态检测算法扩展到接近实时的教育诊断能力；5)创建网页，说明系统产生的不同值与检测算法输出相结合，作为教育工具，供研究人员查看分布对检索性能的影响。

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.