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

Subject Area Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
Term from 2016 to 2022
Project identifier Deutsche Forschungsgemeinschaft (DFG) - Project number 318206658
 
Final Report Year 2022

Final Report Abstract

The project was designed to establish a framework for the analysis of time series with uncertainties. This involved the development of new methods, extension of existing ideas to incorporate data represented as probability distributions, and the application of the developed concepts to target domains of palaeoclimate and meteorology. We designed four modules for the project. Module 1 dealt with the development of new methods and estimation of joint distributions between probability distributions at two time points. Module 2 involved the extension of time series concepts such as cross-correlation and power spectra to incorporate probability density series. It also envisioned the implementation of a probabilistic time series embedding technique to implement nonlinear methods to probability density time series. Module 3 contained real-world applications to climate networks and palaeoclimate proxy records. Module 4 dealt with the dissemination of our work to domain specific audience and to the general public. In the first year of the project, we were able to demonstrate the utility of the probability density series framework by demonstrating the detection of abrupt transitions in palaeoclimatic, meteorological, and financial data. However, around the same time, we realised that the estimation of joint distributions from the marginal probability densities at two time points was not feasible. We decided to proceed with an ensemble approach which implied that the ensembles had to be estimated in a problem-specific way for each research domain. The targets in Module 1 were thus only partly achieved. The ensemble approach allowed us to fulfill part of Module 2, which involved the extension of linear time series analysis methods such as cross-correlation to probability density series. We showed that, using the established COPRA approach, ensembles created for palaeoclimate proxy records allowed the estimation of distributions of cross-correlation between records, thus conducting the entire analysis in an uncertainty-aware manner. The second part of Module 2, involving probabilistic time delay embedding, was not achievable as we realised that the typical time series embedding techniques themselves needed a re-evaluation. We developed a new method, PECUZAL, which combined the well established continuity statistic and L-statistic to embed the time series with multiple time series and multiple time delays. This, along with other related work, has led us to the stage where we are working on incorporating on using neural ordinary differential equations, or neuralODE, to embed time series in an uncertainty-aware manner. This, however, is ongoing work. We applied our concepts to climate networks and to palaeoclimate time series analysis. We developed novel statistical models to incorporate additional, spatial uncertainties that arise due to the geometry of the earth and due to the estimation procedure of climate network links. We also developed an innovative Bayesian approach to evaluate the influence of volcanic eruptions on the ENSO-Indian Monsoon coupling from palaeoclimate records. We applied our abrupt transition detection method to a last glacial monsoon record from northeast and detected transitions connected to large climate shifts recorded also in Greenland ice cores, as well as additional strong regional transitions. Besides these, we actively collaborated with other groups to detect transitions in multiproxy records, estimate correlation of proxy records, and develop methods to estimate interrelation of really short data sets. Overall, the project has led to an increased visibility of the topic of uncertainty in among palaeoclimate scientists, geoscientists, and meteorologists. Our work has led to further more interesting work packages in other projects, such as the work package on uncertainties in the TiPES project (EU Horizon 2020). Although not all of the original questions were answered, the work done has shown us the way how we can arrive at the final answers. “Uncertainty-aware” approaches need more work for sure, but they are here to stay.

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