CMG Research: Enhanced Empirical Orthogonal Function (EOF) Representations and Time-varying Statistical Models for Climate Patterns

该项目旨在开发统计方法，以确定和分析大范围气候变化的模式。气候动态学家传统上依赖经验正交函数(EOF)分析(相当于主成分分析)来表征和研究气候变化模式，然而EOF分析有几个已知的局限性，特别是假设模式不会随着时间的推移而改变，以及缺乏伴随该方法的误差分析。PIS将使用现代统计方法来开发气候模式的替代表示法，以解决这两个限制。该方法的核心是基于相对较少的参数，对气象场的协方差(例如，平均海平面气压的协方差，通常用于定义北大西洋涛动，或NAO)的参数化模型。与传统的EOF/主成分分析相比，低维参数化法具有许多优点。该模型的参数对应于气候模式的重要特征，例如，活动中心的位置。使用该模型的统计推断自然会产生可变性的估计，这可以用来评估气候模式随时间的明显变化。此外，该模型还可以推广到考虑关键气候模式特征随时间的变化。主要方法包括将气象变量(例如，一组网格位置上的MSLP)的协方差矩阵表示为指定的空间基函数(例如，墨西哥帽子函数)，其依赖于其值可被调整以最大化对数似然函数的一小组参数。贝叶斯方法也将被用来获得参数估计和不确定性估计，以放松正态分布方差的假设。该模型的参数将有明确的物理解释，比如作用中心的位置。新的统计分析的初步应用将是对北大西洋涛动变化的研究，最近的一些文献指出：1)上世纪80年代和90年代，当北半球活动中心向东北方向移动时，MSLP的北大西洋涛动格局是非平稳的；2)这种格局随季节变化而变化；3)北大西洋涛动的负位相比正相更持久。将探讨这些影响对北大西洋公约与其他气候系统组成部分，特别是北冰洋海冰之间相互作用的影响。对于南半球环状模式(SAM)也将探讨类似的问题，这种模式的非平稳行为通常归因于南极臭氧空洞的变化。EOF分析在气候研究中普遍存在，因此在开发替代方案方面的进展不会缺乏误差分析和平稳性假设，可能会在整个气候动力学领域广泛使用，也许更广泛地应用于地球科学界。这项工作还将支持两名研究生，一名在统计学专业，另一名在大气科学专业，他们将受益于数学地球科学的跨学科研究。

This project seeks to develop statistical methods to identify and analyze patterns of large-scale climate variability. Climate dynamicists have traditionally relied on Empirical Orthogonal Function (EOF) analysis (equivalent to principle component analysis) to characterize and study climate variability patterns, yet EOF analysis has several known limitations, particularly the assumption that the patterns do not change over time, and the lack of error analysis accompanying the method. The PIs would use modern statistical methods to develop alternative representations of the climate patterns to address both of these limitations. The core of the approach is a parameterized model for the covariance of a meteorological field (e.g., the covariance of mean sea level pressure, or MSLP, that is typically used to define the North Atlantic Oscillation, or NAO) based on a relatively small number of parameters. The low-dimensional parameterization offers a number of advantages when compared to traditional EOF/principal component analysis. The parameters of the model correspond to important features of the climate pattern, e.g., locations of centers of action. Statistical inference using the model naturally produces estimates of variability, which can be used to evaluate apparent movement in the climate pattern over time. Also, the model can be generalized to allow for variation in key climate pattern features over time. The primary method consists of expressing the covariance matrix of meteorological variables (e.g. MSLP over a set of gridded locations) in terms of specified spatial basis functions (e.g. "Mexican hat" functions) which are dependent on a small set of parameters whose values can be adjusted to maximize a log-likelihood function. Bayesian methods would also be used to obtain parameter estimates and uncertainty estimates, in order to relax the assumption of normally distributed variance. The parameters of the model would have clear physical interpretations, like the locations of centers of action. The initial application of the new statistical analysis will be to the variability of the NAO, motivated by recent papers which claim that 1) the NAO pattern in MSLP is nonstationary as the northern center of action drifted northeastward during the 1980s and 1990s, 2) the pattern varies depending on seasonality, and 3) the negative phase of the NAO is more persistent than the positive phase. The implications of these effects for the interaction between the NAO and other climate system components, particularly Arctic sea ice, will be explored. Similar issues will be explored for the Southern Hemisphere annular mode (SAM), which has nonstationary behavior generally ascribed to changes in the Antarctic ozone hole.EOF analysis is ubiquitous in climate studies, so progress in developing alternatives which do not suffer from the lack of error analysis and the stationarity assumption could have extensive use throughout the field of climate dynamics, and perhaps more generally in the geoscience community. The work will also support two graduate students, one in a statistics program and the other in an atmospheric science program, who will benefit from exposure to interdisciplinary research in mathematical geoscience.