LEft

Definitions

This page contains valuable information regarding the generation of the various scene representations, as well as on the way the user simulated results are evaluated:

 Information on the various terms and definitions used by the RT modeling community. Terminology Information on the (view and illumination, zenith and azimuth) angular sign conventions used within ROMC. Sign convention for the zenith and azimuth angles Information on recommended leaf normal distributions within ROMC. Leaf angle distribution functions Information regarding the definition of reflectance measurements within RT models. RT model technicalities

#### Terminology:

All remote sensing measurements acquired from space or airborne imaging sensors in the solar domain turn out to be strongly dependent on the particular geometry of illumination and observation at the time these measurements were made. A similar situation occurs in the spectral domain: different measurement values are obtained when a target is observed in different spectral bands. The reflectance of a geophysical medium (at a particular wavelength) is thus dependent on both the orientation of the Sun and the orientation of the observer with respect to the target. Such a medium is called anisotropic, and the reflectance is characterized as bi-directional. By contrast, a perfectly reflecting, isotropic surface, i.e., a system that would reflect all incoming light equally in all directions, is called Lambertian.

The fundamental mathematical concept describing this anisotropic reflectance is the so-called Bidirectional Reflectance Distribution Function (BRDF). For practical reasons, the measured reflectance of a target is often normalized by the reflectance of a reference panel that is (ideally) a Lambertian surface, illuminated and observed under identical geometric conditions. The result of this normalisation is then called the Bi-directional Reflectance factor (BRF). For a polar plot of BRF values observed over a particular target click .

Observations that lie in the same plane as the local vertical and the incoming direct solar radiation are referred to as BRFs in the principal plane. Observations along a plane whose azimuth differs by ±90 degrees to that of the principal plane are referred to as BRFs in the . If the direction of observation coincides with that of the direct solar illumination, no shadows are observed within the target and a BRF maximum known as the effect is observed.

Since the field of radiation transfer is rather technical, a precise terminology is used to designate the various reflectance concepts. The following papers provide detailed definitions on the terms employed here.

• Nicodemus, F. E., J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, (1977) Geometrical Considerations and Nomenclature for Reflectance, US Department of Commerce, National Bureau of Standards, NBS Monograph No. 160, Washington, DC.
• Martonchik, J. V., C. J. Bruegge, and A. Strahler (2000)  'A Review of Reflectance Nomenclature Used in Remote Sensing', Remote Sensing Reviews, 19, 9-20.
• Verstraete, Michel M. and Bernard Pinty (2000) 'Environmental Information Extraction from Satellite Remote Sensing Data', in Geophysical Monograph No. 114, Edited by P. Kasibhatla, M. Heiman, P. Rayner, N. Mahowald, R. Prinn, Ronald and D. Hartley, American Geophysical Union, Washington, D.C., p. 125-137.

#### Sign convention for the zenith and azimuth angles:

• For the purpose of describing the illumination conditions of the various ROMC test cases, illumination zenith angles are counted from the local vertical and are always reported as a positive value. Illumination azimuth angles are arbitrarily counted from the positive x-axis direction toward the positive y-axis direction (of the scene at hand) and are also given as positive values. For heterogeneous scenes graphical depictions will be provided to clarify these nomenclatures.

• For the purpose of RT model computations and results submission,
• the relative azimuth angle (between the sun and the viewing directions both counted arbitrarily from the positive x-axis direction toward the positive y-axis direction - of the scene at hand) is defined as follows:
• In the principal plane, results corresponding to forward scattering (when the observer is on the other side of the local vertical with respect to the Sun) are reported with a relative azimuth angle (RAA) of ±180 deg. Conversely, results corresponding to backward scattering conditions (when the observer is on the same side of the local vertical as the Sun) are reported with a RAA of 0 deg.
• In the cross plane, the relative azimuth angle can be ±90 or 270 degrees.
• the observation zenith angle (OZA) is always reported as a positive value (counted from the local vertical).

The definition of every measurement type presented in DEBUG or VALIDATE mode contains a correctly formatted example (alternatively click on the various links in the first table on the ROMC formats page).

#### Leaf angle distribution functions:

The spatial orientation of a leaf is described by the direction of its normal ΩLL, ϕL) to the upper surface, where θL is the inclination angle of the leaf normal, and ϕL is the azimuthal angle of the outward normal. Consider a horizontally homogeneous leaf layer of unit thickness at height z, and let the sum of areas of all leaves (or parts thereof) whose normals fall within an incremental solid angle around the direction ΩL be ĝL (z, ΩL). Here all leaves are assumed to face upward, so that all leaf normals are confined to the upper hemisphere (+), and s*L(z) is the total one sided area of all leaves in this horizontal layer. The leaf-normal distribution (LND) function gL(z, ΩL) = ĝL(z, ΩL) ⁄ s*L(z), denotes the fraction of total leaf area in the horizontal layer of unit thickness at height z whose normals fall within unit solid angle around the direction ΩL, and must satisfy the following normalization criterion:

A variety of leaf angle distribution functions have been published in the literature. within ROMC, however, azimuthal invariance of the leaf normal distribution is assumed:

For the purpose of standardization and comparison the following formulae for g* are recommended:

##### Distributions from Bunnik (1978):

where:

• ag = 1.0, bg = 1.0, cg = 1.0, and dg = 0.0 for planophile distributions
• ag = 1.0, bg = −1.0, cg = 1.0, and dg = 0.0 for erectophile distributions
• ag = 0.0, bg = 0.0, cg = 0.0, and dg = 1.0 for uniform distributions
##### Distributions from Goel and Strebel (1984):

where Γ is the Γ function and 0 < θL < π ⁄ 2 is the leaf inclination angle. Furthermore, normalization, requires that:

• μ = 2.531 and ν = 1.096 for planophile distributions
• μ = 1.096 and ν = 2.531 for erectophile distributions
• μ = 1.066 and ν = 1.853 for uniform distributions

The correlation between the distribution functions of Bunnik and those of Goel and Strebel are given by the latter to be 0.9992 in the uniform case, and 0.9989 for both the planophile and erectophile cases.

##### References:
• Bunnik , N. J. J. (1978) 'The Multispectral Reflectance of Shortwave Radiation of Agricultural Crops in Relation With Their Morphological and Optical Properties', in Mededelingen Landbouwhogeschool, Wageningen, The Netherlands, 175 pages.
• Goel, Narendra S. and Strebel, D. E. (1984) 'Simple Beta Distribution Representation of Leaf Orientation in Vegetation Canopies', Agronomy Journal, 76, 800-803.

#### RT model technicalities:

If applicable to the participating RT model, cyclic boundary conditions must be applied to all test cases unless specified otherwise on the individual measurement description pages. In the case of scenes with topography, this implies a repetition of the topographic features at scales equal to the scene dimension.

By default RT simulations are carried out with respect to a reference plane. Only those portions of the incoming and exiting radiation that pass through this reference plane are to be considered in the various ROMC measurements. Unless specified otherwise, the default reference plane within ROMC covers the entire test case area (known as the "scene") and is located at the top-of-the-canopy height, that is, just above the highest structural element in the scene. The spatial extend of the reference plane can be envisaged as the (idealised) boundaries of the IFOV of a perfect sensor looking at a 'flat' surface located at the height level of the reference plane.