On the Leonardo's rule for the assessment of root profile

Leonardo's rule (Lrule) applied to below-ground systems defines a simple topological scheme that describes how the branches of root architectures develop within the soil. The approach does not consider the soil-climate-root interactions. From another hand, eco-hydrological approaches exploit physically-based formulations to derive the dynamic evolution of root profile based on soil and climate characteristics. In homogenous soil and simplified hydrological conditions, analytical solutions can be derived, as demonstrated by Laio's model, who proposed a simple exponential formulation to derive the Root Area (AR) profile. Apart from Laio's model, more generalized functions, i.e. derived by two and three parameters gamma distribution or others, can be efficiently used to derive the AR profile. This communication proposes a combination of the Lrule and eco-hydrological approaches to derive the AR profile, at given soil and climate conditions, allowing to identify a physical and theoretical meaning of the Lrule's parameters. A comprehensive root dataset from field measurements carried out in the region of Tuscany (Italy) is used. Results demonstrate that values of Lrule's parameters derived throughout the proposed mathematical relationships tend to constant values in case of exponential function, which is valid for homogenous soils. Moreover, in a realistic vegetated soil, where top-soil is different than deep-soil, functions derived from a two and three parameters gamma distribution may reproduce better root data observations.