An entropy-based heterogeneity index for mass–size distributions in Earth science

A quantitative classification of soil texture is proposed based on an entropic index that can be easily computed from knowledge of the fractional contents of soil textural classes. It is first shown that the index formula supplies a number that agrees with the entropy dimension when the corresponding soil particle-size distribution (PSD) displays self-similar fractal features. In the absence of self-similarity, the index is further shown to retain information-theoretic content so that it becomes a meaningful diversity index in the general case. The index is defined by balancing Shannon’s entropy in an appropriate way to deal with the high variability of the interval lengths used to report soil particle size classes. The performance of the proposed formula is illustrated for standard textural data reported as clay–silt–sand soil mass fractions. The index induces a classification of a continuum of textural classes that may distinguish soils within the same standard textural class, thus establishing a continuous characterisation of textures that is complementary to the usual classification, but requires no additional information. Finally, it is shown how the balanced-entropy index might also be used as a measure of body size diversity for living organisms.