Gaussianizing the Earth: Multidimensional information measures for Earth data analysis

Information theory (IT) is an excellent framework for analyzing Earth system data because it enables us to characterize uncertainty and redundancy and is universally interpretable. However, accurately estimating information content is challenging because spatiotemporal data are high-dimensional and heterogeneous and have nonlinear characteristics. In this article, we apply multivariate Gaussianization for probability density estimation, which is robust to dimensionality, comes with statistical guarantees, and is easy to apply. In addition, this methodology enables us to estimate information-theoretic measures to characterize multivariate densities: information, entropy, total correlation, and mutual information (MI). We demonstrate how IT measures can be applied in various Earth system data analysis problems.