A note on G-functions within the scope of radiative transfer in turbid vegetation media

This work reports on the use of leaf normal distribution functions (LNDFs) in the radiative transfer theory of turbid vegetation media to calculate the so-called G-function (GF). We revisit the normalisation condition of the LNDFs and present an extended set of fully explicit analytical expressions for GF considering commonly used standard LNDFs from purely vertical to purely horizontal model leaves. Applying them we derive GF for a generalised LNDF, which is written as a series of cosine functions with a number of free parameters. This generalisation opens up the possibility to fit leaf orientation measurements to our generalised LNDF and to determine the respective analytical GF. Thus, an extended range of leaf architectures, beyond the usual and less realistic standard LNDFs, can be considered with respect to applications of the radiative transfer theory in turbid vegetation media.