Numerical investigation of radiation extinction coefficient using fractal geometry for vegetation modelling

As radiative transfer plays a key role in the forest fire propagation process, an accurate knowledge for the radiative properties of the vegetation has to be defined. Indeed, the radiative transfer is mainly depending on the extinction coefficient value. This coefficient for every kind of vegetation is usually evaluated using the well-known De Mestre correlation. This relation does not take into account the leaf orientation and position. In order to evaluate the role of the leaf orientation and position on the extinction coefficient, a realistic vegetal structure is numerically created using Leaf Area Index data from measurements on real trees, De Wit’s model to represent the leaf orientation and fractal geometry to compute the tree structure. A ray-tracing method is used to simulate the radiative transfer inside the numerical tree. Then, the extinction coefficient is computed as the inverse of the mean free path between two extinction events. A sensitivity study is conducted on the extinction coefficient according to the radiation propagation direction. The paper will present the discrepancies between the De Mestre correlation and the numerical results in order to evaluate the role of the leaf orientation and position in the extinction coefficient determination. Introduction The radiative transfer clearly drives the propagation of forest fires. A precise knowledge for the radiative properties of the flame and of the vegetation is then required for any physical modelling. This paper is devoted to the characterization of the radiative properties of a vegetation set. For the physical modelling, two strategies can occur, either a total description of the tree / leaf set has to be done, or the vegetation set is represented by an equivalent homogeneous medium. Due to computational costs, at large spatial scales, the description of the 3D vegetal structure cannot be readily taken into account, the equivalent homogeneous medium assumption provides an alternative way to account for the effects of the vegetal set. The study of the extinction coefficient for a vegetal set has to be carried on a tree. Indeed, it was demonstrated in a previous work [1], that the minimum volume of a vegetal canopy needed to assume the medium as a continuum (the Representative Elementary Volume or REV) is a tree. The determination of this coefficient is of major interest in the radiative modelling of vegetation. The knowledge of extinction coefficient is then required to represent the real medium. This coefficient can deserve several purposes. In environmental modelling, for example, the prediction of the photosynthetically active radiation absorption (PAR absorption) is needed for determining the dry matter that can be synthetised by each plant. In [2] a modelling of the PAR using Beer-Lambert law which involves the extinction coefficient has been realised. This coefficient for every kinds of vegetation is usually evaluated using the so-called De Mestre relationship [3]: