From zero to infinity: minimum to maximum diversity of the planet by spatio-parametric Rao’s quadratic entropy

The majority of work done to gather information on the Earth's biodiversity has been carried out using in‐situ data, with known issues related to epistemology (e.g., species determination and taxonomy), spatial uncertainty, logistics (time and costs), among others. An alternative way to gather information about spatial ecosystem variability is the use of satellite remote sensing. It works as a powerful tool for attaining rapid and standardized information. Several metrics used to calculate remotely sensed diversity of ecosystems are based on Shannon’s information theory, namely on the differences in relative abundance of pixel reflectances in a certain area. Additional metrics like the Rao’s quadratic entropy allow the use of spectral distance beside abundance, but they are point descriptors of diversity, that is they can account only for a part of the whole diversity continuum. The aim of this paper is thus to generalize the Rao’s quadratic entropy by proposing its parameterization for the first time.