Motivation: Climate is fluctuating on decadal to millennial time scales. We evaluate the mechanisms of abrupt climate change, the long-term evolution of climate variability and their link to extremes by time series analysis and analysis of models. This PhD topic is to develop and apply statistical tools which can be used for long climate time series as well as for spatio-temporal output of climate models. As one example, the left panel shows past extents of summer sea ice (Kinnard et al., 2011), and indicates that -although extensive uncertainties remain- both the duration and magnitude of the current decline in sea ice seem to be unprecedented for the past 1450 years. Sea ice may have passed a critical threshold. Our methods can detect tipping points and forecast non-linear changes (e.g., Kwasniok and Lohmann, 2009). The right panel shows the time series and potential for such abrupt climate changes from the past 70.000 years. Our analyses will be applied to observational, reconstructed and reanalysis data, and will be complemented by output generated by complex climate models.

Aim: The aim is to detect the underlying dynamics of climate change across time scales by dynamic factor models (DFMs). DFMs are multivariate time series models, where it is assumed that the observational process can be decomposed into the sum of (latent) common and idiosyncratic factors. The common factors are assumed to capture the significant part of the joint dynamics of the original time series, whereas the dynamics pertaining only to the individual series are contained in the idiosyncratic factors. DFMs can be utilized as a dimension reduction tool (e.g., Zuur et al. (2007) for applications in ecology) as well as to provide meaningful interpretations of the dynamics driving certain observational processes. From the statistical perspective, we have recently worked out simultaneous multiple test procedures for parameters of DFMs (Dickhaus and Pauly, 2016; Dickhaus and Sirotko-Sibirskaya, 2019). With these methods, it is possible to carry out multiple statistical hypothesis tests regarding specifications of the model. Various applications are available for climate change questions (e.g. Lohmann, 2018).

Objectives: (1) Develop algorithms for dynamic factor models, (2) Develop and apply the methods for climate change detection and tipping points, (3) Apply to time series and high-resolution model output.

Competences: The candidate should have a solid background in mathematics with programming skills and statistics or in theoretical physics with emphasis on time series analysis and pattern detection methods. Motivation for interdisciplinary work in climate sciences.

References:

Dickhaus, T., Sirotko-Sibirskaya, N., 2019: Simultaneous statistical inference in dynamic factor models: Chi-square approximation and model-based bootstrap. Computational Statistics and Data Analysis 129, 30-46.

Dickhaus, T., Pauly, M., 2016: Simultaneous statistical inference in dynamic factor models. In: Rojas, I., Pomares, H. (eds.), Time Series Analysis and Forecasting. Springer, 27-45.

Kinnard, C., et al., 2011: Reconstructed changes in Arctic sea ice over the past 1,450 years. Nature. 2011. doi:10.1038/nature10581

Kwasniok, F., Lohmann, G., 2009: Deriving dynamical models from paleoclimatic records: application to glacial millennial-scale climate variability. Phys. Rev. E 80 (6), 066104, doi:10.1103/PhysRevE.80.066104

Lohmann, G., 2018: ESD Ideas: The stochastic climate model shows that underestimated Holocene trends and variability represent two sides of the same coin. Earth Syst. Dynam. 9, 1279-1281. doi:10.5194/esd-9-1279-2018

Zuur, A., et al., 2007: Analyzing Ecological Data. Statistics for Biology and Health, Springer.