  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.
