To what extent can multifractal measures provide an accurate model of the porosity of soils?

Over the last decades, several authors have suggested that multifractal measures, that is, self‐similar measures defined on fractal or non‐fractal objects, could be useful to describe soil properties, to model soil processes, and to deal with their extreme microscale heterogeneity. In this context, a key question relates to the extent to which multifractal measures can indeed fulfill all the expectations they have generated. To address this question, we discuss the possibility of generating a synthetic soil image exhibiting multifractal porosity. To this end, a simple geometrical multifractal model in 2D is developed, which helps us to better understand the concept of multifractality and to generate images. We show that it is possible to generate synthetic binary images over a limited range of scales, but that a pure multifractal model for the distribution of the solid or pore mass cannot be developed due to physical constraints. Moreover, in the generated images mimicking multifractal solid space, a higher degree of multifractality corresponds to a larger porosity, rendering it difficult to tune model parameters to match actual soil properties. In addition, simple statistics relying on power‐law fits appear insufficient to characterize soil architecture even if they may capture some key multiscale indicators of observed spatial heterogeneity. We argue that the same conclusions would be reached in a three‐dimensional space, as well as for grey‐scales images.