# Gaussianizing the Earth: Multidimensional Information Measures for Earth Data Analysis

arXiv: https://arxiv.org/abs/2010.06476 · HTML: https://mlsanity.com/paper/2010.06476/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Oct 2020.

## Built on by (most cited first, 4 of 4)

- [OceanBench: The Sea Surface Height Edition](https://mlsanity.com/paper/2309.15599/) (2023)
- [AI for Extreme Event Modeling and Understanding: Methodologies and Challenges](https://mlsanity.com/paper/2406.20080/) (2024)
- [Unsupervised Anomaly and Change Detection with Multivariate Gaussianization](https://mlsanity.com/paper/2204.05699/) (2022)
- [Orthonormal Convolutions for the Rotation Based Iterative Gaussianization](https://mlsanity.com/paper/2206.03860/) (2022)

## Abstract (arXiv)

Information theory is an excellent framework for analyzing Earth system data because it allows us to characterize uncertainty and redundancy, and is universally interpretable. However, accurately estimating information content is challenging because spatio-temporal data is high-dimensional, heterogeneous and has non-linear characteristics. In this paper, 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 allows us to estimate information-theoretic measures to characterize multivariate densities: information, entropy, total correlation, and mutual information. We demonstrate how information theory measures can be applied in various Earth system data analysis problems. First we show how the method can be used to jointly Gaussianize radar backscattering intensities, synthesize hyperspectral data, and quantify of information content in aerial optical images. We also quantify the information content of several variables describing the soil-vegetation status in agro-ecosystems, and investigate the temporal scales that maximize their shared information under extreme events such as droughts. Finally, we measure the relative information content of space and time dimensions in remote sensing products and model simulations involving long records of key variables such as precipitation, sensible heat and evaporation. Results confirm the validity of the method, for which we anticipate a wide use and adoption. Code and demos of the implemented algorithms and information-theory measures are provided.