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

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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.