Impacts of uncertainties in climate data analyses (IUCliD): Approaches to working with measurements as a series of probability distributions

时间序列分析对于基于观测的理解现实世界的复杂系统起着至关重要的作用。然而，大多数现有的分析测量数据的方法无法处理由时空变化或测量本身的不精确引起的不确定性。在这个项目中，将开发一个新的框架，将观测结果建模为概率分布，固有地考虑到数据集的不确定性。重点是在概率分布方面重新制定时间序列分析的两个具体分支。第一个重点是量化数据的动态特性及其相互关系，使用相关、互信息和功率谱等概念作为概率似然。第二步是扩展状态空间嵌入的框架，以确定给定数据集不确定性的嵌入的后验似然。这些理论扩展将用于从时间序列数据估计概率定义的复杂网络，并确定系统返回到早期动态状态的后验可能性。开发的技术将被应用于了解气候过程的动力学以及数据集不确定性对这些过程的影响。气候网络将根据过去50年的空间网格化气候数据进行估计，这些数据编码了两个空间分离点之间气候联系的可能性。这样的网络将有助于在分析的时间段内确定气候联系的自我和重组。对可追溯到15000年的空间分布古气候数据集的递归分析也将用于确定过去气候突变的时期。这些方法将扩展早期时间序列方法的范围，这些方法已经被证明在气候和神经科学、金融、天体物理学、生态学和医学等广泛的科学学科中使用，特别是当它们涉及到需要考虑的测量不精确性和时空变异性时。这个项目将为一种新的数据分析铺平道路，这种分析明确地基于概率分布，而不是分析点状对象。一个软件包以及一系列研讨会将支持这一目标。

Time series analysis plays a crucial role for observation-based understanding of real-world complex systems. However, most existing methods for analysing measured data are not equipped to deal with uncertainties arising from spatiotemporal variations or imprecision in the measurements themselves. In this project, a new framework that models observations as probability distributions will be developed, inherently taking into account dataset uncertainties. The focus is on reformulating two specific branches of time series analysis in terms of probability distributions. First focus is to quantify dynamical characteristics of the data and their interrelations as probabilistic likelihoods using concepts such as correlation, mutual information and power spectrum. The second step is to extend the framework of state space embedding to determine the posterior likelihood of a chosen embedding given the dataset uncertainties. These theoretical extensions will be used to estimate probabilistically defined complex networks from time series data, and to determine posterior likelihoods that a system recurs to earlier dynamical states. The developed techniques will then be applied to understand the dynamics of climatic processes as well as the impact of dataset uncertainties on such processes. Climate networks will be estimated from spatially gridded climatological data for the last 50 years which encode the likelihood of a climatic link between two spatially separated points. Such networks will help to determine self- and re-organisation of climatic links in the time periods of analysis. Recurrence analysis on spatially distributed palaeoclimatic datasets going back to 15,000 years will also be used to identify periods of abrupt climate change in the past. These methods will extend the reach of earlier time series methods which have already proven to be of use in a wide range of scientific disciplines such as climate and neuroscience, finance, astrophysics, ecology, and medicine, particularly when they involve measurement imprecision and spatiotemporal variabilities that need to be taken into account. This project will pave the way for a new kind of data analysis that is explicitly based on probability distributions instead of analysing point-like objects. A software package as well as a workshop series will support this goal.