Analyzing the Impacts of Non-Gaussian Errors in Gaussian Data Assimilation Systems

分析高斯数据同化系统中非高斯误差的影响

• 批准号: 1038790
• 负责人: Steven Fletcher
• 金额: $ 59.61万
• 依托单位: Colorado State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-09-15 至 2016-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1038790&HistoricalAwards=false
• 关键词: Analyzing; Impacts; Non; Gaussian; Errors

The basis for most of the world's operational and research variational data assimilation (DA) is that all errors are Gaussian distributed. For synoptic-scale weather systems this assumption is a good approximation, however even at these large scales there some variables (e.g., positive-definite quantities such as relative humidity) cannot be properly characterized by assumed Gaussian error distributions. The impact of an imposed negative value for a positive-definite variable such as moisture is that an operational system DA system could fail to converge or otherwise yield an unstable numerical forecast or an unphysical model state. This Gaussian assumption is also present in retrieval systems that are based upon a maximum likelihood estimation (MLE) Bayesian-type approach. In some other Bayesian systems the moisture variable is assumed to be lognormally distributed and so the retrieved variable is the natural logarithm of the moisture variable. Both approaches introduce a bias into the analysis by finding the incorrect statistic to describe the probabilistic behavior of the random variable. In this project an alternative approach for non-Gaussian variables that combines a lognormal distribution with a Gaussian distribution, referred to as a mixed distribution, will be applied and evaluated. This mixed distribution allows for the retrieval and assimilation of Gaussian- and lognormally-distributed variables simultaneously. The mixed approach is different to the other two approaches in that it is finding the analysis mode with the correct covariances between the random variables, and not the mode of the best Gaussian approximation or the median of the lognormal distribution.In the first stage of this effort, methods for determining where one can and cannot impose a Gaussian assumption for humidity within DA schemes, as well to quantify the impacts of such assumptions on retrieved quantities, will be developed. The second stage will investigate the impacts of assimilating retrieved data from the Gaussian assumption approach against the mixed distribution approach into a larger 3D- or 4D-VAR (variationally-based) approach as appropriate to the particular model system being evaluated [e.g., the NSF/NCAR-supported Weather Forecasting and Research (WRF) DA system]. The intellectual merit of this work will trace to the ability to better observe and assimilate moisture fields and develop an improved understanding of their interactions with other model-prognostic fields for a variety of dimensions of atmospheric prediction: synoptic, mesoscale and cloud resolving. Anticipated Broader Impacts of this effort will come through the ability to exert carefully motivated changes in DA schemes employed in larger numerical weather prediction systems, which would in-turn be expected to foster improved predictions of severe and/or extreme weather events. Broader impacts through education will occur through the mentorship and early-career development of a supported postdoctoral research associate, who will be trained in non-Gaussian DA methods as well as gain experience with retrievals and near-operational large DA systems.

世界上大多数的业务和研究变分资料同化（DA）的基础是，所有的误差是高斯分布。 对于天气尺度的天气系统，这个假设是一个很好的近似，然而，即使在这些大尺度上，也有一些变量（例如，正定量（例如相对湿度）不能通过假定的高斯误差分布来适当地表征。 对于正定变量（如湿度）施加负值的影响是，运行系统DA系统可能无法收敛或产生不稳定的数值预报或非物理模型状态。 这种高斯假设也存在于基于最大似然估计（MLE）贝叶斯型方法的检索系统中。 在其他一些贝叶斯系统中，水分变量被假设为对数正态分布，因此检索的变量是水分变量的自然对数。 这两种方法都通过寻找不正确的统计量来描述随机变量的概率行为，从而在分析中引入偏倚。 在本项目中，将应用和评估一种将对数正态分布与高斯分布相结合的非高斯变量的替代方法，称为混合分布。 这种混合分布允许同时检索和同化高斯和对数正态分布的变量。 混合方法与其他两种方法的不同之处在于，它是找到具有随机变量之间的正确协方差的分析模式，而不是最佳高斯近似或对数正态分布的中值的模式。在这项工作的第一阶段，确定在DA方案中可以和不可以对湿度施加高斯假设的方法，以及量化这些假设对检索数量的影响。 第二阶段将研究将高斯假设方法的检索数据与混合分布方法同化为适合于正在评估的特定模型系统的更大的3D或4D-VAR（基于变分）方法的影响[例如，NSF/NCAR支持的天气预报和研究（WRF）DA系统。 这项工作的智力价值将追溯到更好地观测和同化湿度场的能力，并发展更好地了解它们与其他模式预报场的相互作用，用于各种大气预测维度：天气学，中尺度和云解析。 这一努力的预期更广泛的影响将来自于对大型数值天气预报系统中采用的DA方案进行精心激励的改变的能力，这反过来有望促进对严重和/或极端天气事件的更好预测。 通过教育产生更广泛的影响将通过一个支持的博士后研究助理的导师和早期职业发展来实现，他将接受非高斯DA方法的培训，并获得检索和近操作大型DA系统的经验。