Topological Data Analysis and Machine Learning methods for pattern detection in spatiotemporal climate data

Understanding and predicting how extreme weather events may change under different global warming scenarios, in particular, how the intensity, frequency, and location statistics of such events may vary due to global warming is one of the most pressing problems in climate science. Furthermore, advances in high-performance computing technology have enabled producing climate model outputs at ever more prodigious rates---the big data problem. A fundamental requirement for analysis of such a problem is fast, efficient, and accurate methods that can automatically detect, classify, and characterize patterns in climate simulation products.Statistical and Machine Learning (ML) is rapidly becoming a powerful tool for various tasks of relevance to the climate community. Deep Learning (DL) is already achieving successes in pattern recognition problems in climate science [4], but a great challenge that remains is to combine feature representation approaches with ML/DL to develop interpretable, fast, and accurate learning methods for detection and characterization of weather patterns usually associated with extreme events.Following a successful application of Topological Data Analysis (TDA) and ML to classify Atmospheric Rivers in climate data [3], we propose a new approach based on recent advances in TDA, combined with DL, to detecting Atmospheric Blocking (AB) events, which are often associated with Rossby Wave Breaking [5], in large multivariate 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 both in the Northern and Southern hemispheres. Resilient blocking events can remain over certain region for several days or even weeks and are responsible for many of the severe heat waves and cold snaps in mid-latitudes, including Europe and the United States [1].In this approach we combine tools from TDA along with DL for detecting and characterizing ABs. Using Persistent Homology [2] from TDA applied to raw images of climate model output we compute a new multiscale representation of geometric features of the associated topological properties in multivariate spatio-temporal climate data. The generated numerical features together with provided labeled data [6,7] are then used as an input for Convolutional Neural Network from DL to detect AB patterns (supervised learning). The approach may be generalizable to a broader class of weather patterns, and extreme weather events with potential to provide meaningful insights across different spatial and temporal resolutions of climate model.

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

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

[3] Muszynski, Grzegorz, et al. "Topological data analysis and machine learning for recognizing atmospheric river patterns in large climate datasets." Geoscientific Model Development 12.2 (2019): 613-628.

[4] Racah, Evan, et al. "ExtremeWeather: A large-scale climate dataset for semi-supervised detection, localization, and understanding of extreme weather events." Advances in Neural Information Processing Systems (2017).

[5] Tyrlis, E., and B. J. Hoskins. "The morphology of Northern Hemisphere blocking." Journal of the Atmospheric Sciences 65.5 (2008): 1653-1665.

[6] Schwierz, C., M. Croci‐Maspoli, and H. C. Davies, Perspicacious indicators of atmospheric blocking, Geophys. Res. Lett., 31, L06125, (2004).

[7] Sprenger, M., G. Fragkoulidis, H. Binder, M. Croci-Maspoli, P. Graf, C.M. Grams, P. Knippertz, E. Madonna, S. Schemm, B. Škerlak, and H. Wernli: Global Climatologies of Eulerian and Lagrangian Flow Features based on ERA-Interim. Bull. Amer. Meteor. Soc., 98, 1739–1748, (2017).