An understanding of the Earth's climate system benefits all sectors of the economy and environment. Several challenges faced when modeling the Earth's climate system include: estimating geographical features of global datasets, making inferences from multiple data-products, and providing diagnostic tools for complex Earth models. Existing geostatistical approaches address these challenges by modeling points on a high-dimensional space. However, we know that many of the climate datasets additionally have inherent high-dimensional geometric structures.
In this talk, I will provide new insights into problems in climate data science by exploring high-dimensional geometric structures on a manifold. First, I will discuss an approach to improve future projections of a climate variable (e.g., sea-level changes, precipitation changes) by learning the scale of correlation, an essential regional feature of climate datasets. Second, I will provide a new framework for data-fusion from multiple sources of information for a given climate variable. Third, I will describe diagnostic tools we created to compare and emulate various Earth system models from numerous international teams and for differing future climate scenarios. With these contributions, I will demonstrate that we can improve the inferences made from geostatistical models by including information about the high-dimensional structures of climate datasets. The proposed novel framework will benefit not only the climate community but also decision makers when identifying plans to mitigate the impact of climate change.