Analytical determination and numerical computation of extinction coefficients for vegetation with given leaf distribution

A study has been carried out, with both analytical and numerical methods, on the effective extinction coefficient of a medium featuring a given vegetation. The studied domain contains a heterogeneous medium involving in successive cases: leaves under planophile, erectophile, plagiophile, extremophile orientations, and a mixing of these conditions, all situations assuming a uniform distribution in space. A ray tracing method has been used in order to identify an effective extinction coefficient after computation of the mean free path. For these academical situations, comparisons with some analytical formulations have been carried out in order to achieve the validation of the numerical method. Then, the role of a heterogeneous distribution in space has been studied, introducing morphological properties (orientation and spatial heterogeneities) which produce a set of leaves featuring a sort of virtual vegetation, numerically built in a box. In particular, conditions of leaves mainly located at the periphery of a crown have been considered. Numerical results show that analytical relations for the extinction coefficient may be used for the different leaf orientations, when the spatial distribution is assumed homogeneous. However, some discrepancies from these solutions appear when heterogeneous distributions in space are used, suggesting that such relationships will become less accurate when applied on a true vegetation. The numerical tool is now ready and will be used on a vegetation built with true morphological characteristics.