Collaborative Research: CMG--Ensemble Data Assimilation for Nonlinear and Nondifferentiable Problems in Geosciences

数据同化是观测和预测大气状态的重要组成部分，大气状态被定义为特定位置的温度、压力、湿度、风速和其他变量的值。数据同化系统通常有两个组成部分：1）一组不完善的观测，在空间和时间上分布不均匀，并以复杂的方式与状态相关（例如，卫星感知辐射与温度和湿度间接相关，雷达回波与降水间接相关）; 2）复杂且不完善的预报模型，提供大气状态的“初步猜测”。数据同化的目标是最佳地联合收割机组合模式的第一次猜测和观测，以产生最好的状态表示，伴随着由观测和预测模型的限制引起的状态不确定性的估计。EnsDA是一种数据同化方法，其中在每个同化周期中使用预报集合，因此预报集合成员之间的差异提供了一种表达模式生成的第一猜测的概率性质的方法。例如，一个单一的预报将预测在给定的位置下雨或不下雨，而预报的集合可以估计降雨的概率。由于大气变率的复杂性和观测与状态的间接关系，EnsDA方法通常需要简化假设，以便实际使用。常见的简化假设包括：1）观测值可以通过简单的线性函数与状态相关; 2）大气层平滑地演变，因此大气状态可以被视为在空间和时间上以平滑、可微的方式变化。虽然方便，但这些假设在物理上是不合理的，本提案中的研究试图找到不依赖于这些假设的新EnsDA方法。这项工作首先量化的误差估计的大气状态使用的“成本函数”，这是最小化产生的同化状态。在大气状态的演变和状态观测关系的非线性和不可微性导致成本函数的非线性和不可微性。本研究解决了缺乏平滑的成本函数，1）评估不可微的成本函数最小化方法适合EnsDA; 2）检查混合集合数据同化方法的非线性和不可微的应用程序的价值;和3）开发和评估一个非线性和不可微EnsDA方法，旨在量化现实的高维地球科学应用中的不确定性。该研究旨在找到更好的方法来利用现有的数据和模型来理解和预测大气的行为。这些努力最终将导致更好的恶劣天气预报，这将有利于社会。此外，为大气开发的EnsDA技术将适用于海洋和用于预测气候变化的大气-海洋耦合模型。这笔赠款还将通过资助一名研究生的教育和培训，为培训下一代科学家做出贡献。

Data assimilation is an essential component of attempts to observe and predict the state of the atmosphere, defined as the values of temperature, pressure, humidity, wind speed, and other variables at specific locations. A data assimilation system typically has two components:1) a set of observations which are imperfect, unevenly distributed in space and time, and related to the state in complex ways (e.g. satellites sense radiation which is indirectly related to temperature and moisture, radar returns are indirectly related to precipitation); and 2) a complex and imperfect forecast model, which provides a "first guess" of the atmospheric state. The goal of data assimilation is to optimally combine the model first guess and the observations to produce the best possible representation of the state, accompanied by an estimate of the state uncertainty caused by the limitations of the observations and the forecast model. Ensemble data assimilation (EnsDA) is a data assimilation method in which an ensemble of forecasts is used in each assimilation cycle, so that differences among the forecast ensemble members provide a means of expressing the probabilistic nature of the model-generated first guess. For example, a single forecast will predict either rain or no rain at a given location, whereas an ensemble of forecasts can estimate the probability of rainfall. Due to the complexity of atmospheric variability and the indirect ways in which observations are related to the state, EnsDA methods usually require simplifying assumptions in order to be practically useful. Among the common simplifying assumptions are 1) that the observations can be related to the state through simple linear functions; and 2) that the atmosphere evolves smoothly, so that the atmospheric state can be treated as varying in space and time in a smooth, differentiable way. While convenient, these assumptions are not physically justifiable, and the research in this proposal is an attempt to find new EnsDA methods which do not rely on these assumptions. The work begins by quantifying the error in the estimated atmospheric state using a "cost function", which is minimized to produce the assimilated state. Nonlinearity and nondifferentiability in the evolution of the atmospheric state and in state-observation relationships leads to nonlinearity and nondifferentiability in the cost function. This research addresses the lack of smoothness in the cost function by 1) evaluating nondifferentiable cost function minimization methods suitable for EnsDA; 2) examining the value of hybrid ensemble data assimilation methods for nonlinear and nondifferentiable applications; and 3) developing and evaluating a nonlinear and nondifferentiable EnsDA method designed to quantify uncertainty in realistic high-dimensional geosciences applications. The research is intended to find better ways to use existing data and models to understand and predict the behavior of the atmosphere. These efforts will ultimately lead to better forecasts of severe weather which will benefit society. In addition, EnsDA techniques developed for the atmosphere will be applicable to the ocean and to coupled atmosphere-ocean models used to anticipate climate change. The grant will also contribute to the training of the next generation of scientists, by funding the education and training of a graduate student.