CMG: Statistical Analysis of Nonstationary and Nonlinear Paleoclimatic Time Series

在古气候学中作为温度替代数据的同位素，如在海底岩芯中测量的氧同位素比率，揭示了大约1000至10万年的周期性。 这些周期是由地球轨道参数已知变化的外部强迫（所谓的米兰科维奇强迫）和不同大气和海洋过程的复杂、非线性和非平稳相互作用引起的。 到目前为止，用于分析记录的最常用的统计工具是基于统计平稳性假设的谱技术和相关分析。 该项目采用现代统计技术，研究非线性和非平稳过程对过去500万年气候记录的影响，这些技术以前在古气候学中没有太多应用。 其中包括时间-频率分析，以说明频率和相位调制方面的非平稳性，以及对气候变量的不同组合进行双谱和交叉谱分析，以识别非线性耦合。 该项目得到大气科学司和数学科学司的联合支助，其目标之一是向学生和研究人员提供软件，并安排一次专门讨论这一问题的讲习班，使古气候界能够利用这些统计方法。

Quantities that serve in paleoclimatology as proxy data for temperature, such as oxygen isotope ratios measured in seabed cores, reveal periodicities ranging from about 1000 to 100,000 years. These cycles are caused by a combination of external forcing by known changes in the Earth's orbital parameters (so-called Milankovitch forcing) and by little-understood, complex, nonlinear, and usually nonstationary interactions of different atmospheric and oceanic processes. To now, the statistical tools most commonly employed for analyzing the records have been spectral techniques and correlation analysis based on the assumption of statistical stationarity. This project examines the effects of nonlinear and nonstationary processes on the climate record of the last 5 million years by employing modern statistical techniques that have not previously seen much use in paleoclimatology. These include time-frequency analysis to characterize the non-stationarity in terms of frequency and phase modulation, and bispectral and cross-spectral analysis to different combinations of climate variables to recognize nonlinear couplings. One of the objectives of the project, which is supported jointly by the Division of Atmospheric Sciences and the Division of Mathematical Sciences, is to make these statistical methods available to the paleoclimate community by offering software to students and researchers and arranging a workshop devoted to the subject.