CMG: Statistical Analysis of Nonstationary and Nonlinear Paleoclimatic Time Series

在古气候学中用作温度替代数据的数量，如在海底岩心测量的氧同位素比率，揭示了大约1000至10万年的周期。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)和鲜为人知的、复杂的、非线性的、通常是非平稳的不同大气和海洋过程的相互作用共同引起的。到目前为止，分析记录最常用的统计工具是谱技术和基于统计平稳性假设的相关分析。这个项目采用了以前在古气候学中没有太多用处的现代统计技术，研究了非线性和非平稳过程对过去500万年气候记录的影响。其中包括从频率和相位调制的角度描述非平稳性的时频分析，以及识别非线性耦合的不同气候变量组合的双谱和互谱分析。该项目由大气科学司和数学科学司联合支助，其目标之一是通过向学生和研究人员提供软件和安排专门讨论这一主题的讲习班，向古气候界提供这些统计方法。

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.