A Topology-Based Approach To Characterization and Detection of Weather Patterns in Climate Model Output: Application to Atmospheric Blocking Events

Understanding and predicting how extreme weather events will change under different global warming scenarios, in particular, how the intensity, frequency and location statistics of such events may change due to global warming is one of the most pressing problems in climate science today. Given the sheer volume, velocity, variability and veracity of climate data (the big data problem), a fundamental requirement for such analyses is fast, efficient and accurate methods that can automatically detect and characterize weather patterns in climate data.

Machine Learning is rapidly becoming a powerful tool for various tasks of relevance to the climate community. In particular, deep learning is already making significant progress in various pattern recognition problems in climate science. However, a great challenge is to combine various dimensionality reduction and feature extraction approaches with ML to design fast, efficient, accurate and powerful methods for detection and characterization of weather patterns associated with extreme events.

We propose a new approach based on recent advances in topology and dynamical systems, combined with ML, to detecting Atmospheric Blocking events (ABs) in large multi-variate climate model output. ABs are stationary high-pressure systems in the troposphere and lower stratosphere. This type of weather system can change the climatological eastward flow at mid-latitudes in the Northern and Southern hemispheres and remain over certain region for several days or even weeks. These strong anomalies are responsible for many of the severe heat waves and cold snaps in many mid-latitude regions of the world, including the United States and Europe [1].

In this new approach we combine ideas from Dynamical Systems Theory (DST), Manifold-Learning (M-L) and Topological Data Analysis (TDA) along with ML for detecting and characterizing ABs. Using an extension of Takens’ sliding window coordinate embedding from DST [2] to raw 2-dimensional patches of climate model output we provide a high-dimensional representation of the multivariate spatio-temporal climate data. We then use a low-dimensional embedding computed by the Diffusion Maps algorithm from M-L [3] to reduce the dimensionality of the problem while preserving nonlinear relationships. We then apply a persistent homology algorithm from TDA [4, 5] to the low-dimensional space that quantifies the “lifetime” of each topological feature descriptor in the data, i.e. connected components, loops, voids and higher-dimensional structures. Finally, we use the generated numerical feature descriptors with ML classifiers (e.g., Support Vector Machines) to detect (classify & localize) ABs. Preliminary results from fluid dynamical simulation data and climate data (reanalysis) indicate that the proposed approach that combines methods from these diverse disciplines can be successful in detecting and characterizing ABs. Furthermore, this methodology may be generalizable to a broader class of weather patterns, and extreme events in particular, with the potential to provide meaningful insights across different climate datasets.

[1] Barnes, Elizabeth A., et al. "Exploring recent trends in Northern Hemisphere blocking." Geophysical Research Letters 41.2 (2014): 638-644.

[2] Takens, Floris. "Detecting strange attractors in turbulence." Dynamical systems and turbulence, Warwick (1980). Springer, Berlin, Heidelberg, 1981. 366-381.

[3] Coifman, Ronald R., and Stéphane Lafon. "Diffusion maps." Applied and computational harmonic analysis 21.1 (2006): 5-30.

[4] Carlsson, Gunnar. "Topology and data." Bulletin of the American Mathematical Society 46.2 (2009): 255-308.

[5] Ghrist, Robert. "Barcodes: the persistent topology of data." Bulletin of the American Mathematical Society 45.1 (2008): 61-75.