Visualization of topological structures in uncertain fields

• Applicant: Professor Dr. Gerik Scheuermann
• Subject Area: Image and Language Processing, Computer Graphics and Visualisation, Human Computer Interaction, Ubiquitous and Wearable Computing
• Term: from 2014 to 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 266686043

• Final Report Year: 2025

Final Report Abstract

Topological features and structure enable a compact and distilled description of fields – representations of spatio-temporally varying quantities – which occur frequently in science and technology. For example, when analyzing data from climate simulations, one is often interested in regions of high or low values, their relation and relative position. While there exist methods for the topological analysis of deterministic fields, within this project new methods in the area of topological analysis of uncertain scalar fields were developed. These are applicable to the study of ensemble data from climate simulations, which are characterized by multiple simulation runs with slightly different initial conditions, and are now examined with respect to commonalities, differences, and the probability of the occurrence of certain events. Within the project methods were developed that serve, among other things, to directly show the variation in the evolution of ensemble members, with application to study the change in world-wide precipitation in different climate change scenarios. Furthermore, methods were developed to extract critical points in uncertain scalar fields and to identify them across ensemble members in order to determine the probability of occurrence, the position, and the strength of features. This was applied to climate simulations of the Northern Atlantic to study a possible shift of the so-called Icelandic Low and Azores High. The position and strength of these two pressure systems the the main drivers of the so-called Northern Atlantic Oscillation, which transports war humid air to Europe in winter time and thus causes mild winters there. With the methods developed in the project we obtained a robust finding that the Icelandic Low shifts and that the strength of this shift coincides with the strength of climate change.

Publications

• Critical Points of Gaussian‐Distributed Scalar Fields on Simplicial Grids. Computer Graphics Forum, 35(3), 361-370.
  Liebmann, T. & Scheuermann, G.
  
• Hierarchical Correlation Clustering in Multiple 2D Scalar Fields. Computer Graphics Forum, 37(3), 1-12.
  Liebmann, Tom; Weber, Gunther H. & Scheuermann, Gerik
  
• An Extension of Empirical Orthogonal Functions for the Analysis of Time-Dependent 2D Scalar Field Ensembles. 2021 IEEE 14th Pacific Visualization Symposium (PacificVis), 46-50. IEEE.
  Vietinghoff, Dominik; Heine, Christian; Bottinger, Michael & Scheuermann, Gerik
  
• Visual Analysis of Spatio-Temporal Trends in Time-Dependent Ensemble Data Sets on the Example of the North Atlantic Oscillation. 2021 IEEE 14th Pacific Visualization Symposium (PacificVis), 71-80. IEEE.
  Vietinghoff, Dominik; Heine, Christian; Bottinger, Michael; Maher, Nicola; Jungclaus, Johann & Scheuermann, Gerik
  
• Detecting Critical Points in 2D Scalar Field Ensembles Using Bayesian Inference. 2022 IEEE 15th Pacific Visualization Symposium (PacificVis), 1-10. IEEE.
  Vietinghoff, Dominik; Bottinger, Michael; Scheuermann, Gerik & Heine, Christian
  
• Visualizing Confidence Intervals for Critical Point Probabilities in 2D Scalar Field Ensembles. 2022 IEEE Visualization and Visual Analytics (VIS), 145-149. IEEE.
  Vietinghoff, Dominik; Bottinger, Michael; Scheuermann, Gerik & Heine, Christian
  
• A Mathematical Foundation for the Spatial Uncertainty of Critical Points in Probabilistic Scalar Fields. 2023 Topological Data Analysis and Visualization (TopoInVis), 30-40. IEEE.
  Vietinghoff, Dominik; Böttinger, Michael; Scheuermann, Gerik & Heine, Christian
  
• Visualization of 2D Scalar Field Ensembles Using Volume Visualization of the Empirical Distribution Function. 2024 IEEE Visualization and Visual Analytics (VIS), 191-195. IEEE.
  Daetz, Tomas; Böttinger, Michael; Scheuermann, Gerik & Heine, Christian