Topography

This set of experiments was suggested to simulate the radiative transfer regime in the red and near infra-red spectral bands for spatially heterogeneous scenes containing some degree of topography. The canopy architecture and spectral properties were chosen to reflect those of typical coniferous forests. A large number of non-overlapping tree-like entities (composed of a conically shaped crown located above a cylindrical trunk) were randomly located across (and only partially covering) a Gaussian shaped surface that represented the underlying soil topography.

The finite sized foliage was randomly distributed within the conical volumes that represented the tree crowns, and was characterized by its specific radiative properties (reflectance, transmittance), and the orientation of its scatterer-normals (uniform distribution). The radiative properties of the underlying soil were specified (in this case a simple Lambertian scattering law) to reflect ideal winter conditions, ie. snowcover.

The following figures exhibit a graphical representation of this scene:

looking from across its eastern edge in an westward direction towards the centre of the scene:

looking vertically down towards the centre of the scene:

and looking from its south-east border in a north-western direction (diagonally) towards its centre:

The architecture of this scene contains tree-like entities that are composed of a conical crown on top of a cylindrical trunk. Note that these geometrical primitives do not overlap and that they remain the same for all trees that are populating the scene.

The zero azimuth line was defined along the northern direction and coincides with the positive X-axis as indicated below:

Within the scene the X,Y location of these tree-like entities is generated in a random manner (Poisson distribution). For a given X,Y position the elevation of the soil just underneath the lower part of the tree-trunk (Z) is then computed using the elevation formula given in the table below. This formula provides a Gaussian shaped heightfield that has its maximum elevation value at the (X,Y) origin of the scene (i.e., at the scene center) and elevation values very close to zero at the edges of the scene. The underlying substrate (which is represented by this Gaussian shaped heightfield) is thus occupying the entire lower X,Y dimensions of the scene.The precise characterisation of the scene architecture is as follows: