The polar regions of our planet (and, generally, the whole cryosphere) are unique platforms for data collection. One reason why the cryosphere is a big data reservoir is that physicists prefer to study solid matter. An experiment on matter in the solid state is more easily controlled than an experiment involving a gas or a plasma. Furthermore, cryosphere ice is not much different from laboratory ice. Therefore, all the power of experimental physics can be applied to mining cryosphere data.

Indeed, this is not a novel idea. Karl Weyprecht, an Austro-Hungarian naval officer, was the father of polar data mining. He proposed to organize the First International Polar Year (1882–1883) to collect data, mainly near the Arctic. (There was little knowledge about the Antarctic and other cold regions, and the Arctic was closer and more important for the European empires and North American countries who sponsored this giant project.)

During the four international polar years and over a period of more than 140 years of continuous Arctic observations, the experimentalists have formed a huge Arctic data pool. Now is the time for the theorists (mathematicians and theoretical physicists) to come to the pool deck.

The volume and complexity of data on ice melting is growing rapidly. Many new tools (such as remote sensing, high-performance computing) are now available for ice observation and modeling, and many data-driven physical models of ice melting have been developed using modern analytical techniques (such as data assimilation, geometrical and topological data analysis, neural networks data analysis). The complex structure of Arctic data has led to the discovery of unexplored phenomena, which require novel mathematical techniques.

The mini-symposium “The Mathematics of Arctic Data” at the 2020 SIAM Conference on Mathematics of Data Science (MDS20) brought speakers from mathematics and the geosciences together to discuss how mathematics can help Arctic data analysis and modeling, and how the analysis of complex Arctic data may inspire new mathematics.

Christian Sampson (Math, UNC-Chapel Hill) introduced a new warping metric for sea ice models. This metric outperforms the Euclidean metric in many cases and provides a measure of exactly how misaligned a geometry is through the phase distance. He intends to use this idea to improve real ice data analysis. Ivan Sudakov (Physics, University of Dayton) gave a talk on the geometry of tundra lakes. He proposed to use the fractal dimension of tundra lakes as a parameter in models of tundra lake patterns. This fractal dimension can be obtained from satellite images; however, the tundra lakes image segmentation is a tricky process, which needs the help of machine learning in terms of the lake shape uncertainty. Umesh Haritashya (Geology, University of Dayton) reviewed various approaches to cryosphere data management. He emphasized that we are suffering from an abundance, rather than a shortage of datasets, and that these data need to be assimilated in a coherent manner to produce meaningful and repeatable results. He expressed the hope that mathematics will provide new and robust tools for data management.

Ivan Sudakov, University of Dayton