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BRF in the cross plane for multiple-scattered radiation: brfop_mlt

Within RAMI the Bi-directional Reflectance Factor (BRF) at a specific wavelength is defined as the radiant flux exiting from a target area in a particular direction - passing through a (virtual) planar reference surface of specified lateral dimension and elevation above the target, and oriented perpendicular to the underlying surface normal - normalized by the equivalent quantity leaving from an infinitely large Lambertian background via the same reference surface and for the same directions of illumination and reflectance. Alternatively, the BRF of this reference surface can be said to be:

where the BRDF can be expressed in terms of the incident (i) and reflected (r) radiance L [W ⋅ m−2 ⋅ sr−1]:

The cross plane is perpendicular to the principal plane. The latter is defined by both the surface normal and the illumination directions. Simulating BRFs in the cross or principal plane thus implies to compute the BRFs for multiple view zenith angles but identical azimuth angles (±180 degree) along that plane.

For this particular measurement the component of the surface leaving radiation that has interacted twice or more with the scatterers in the scene is utilized to compute the BRFs. brfop_mlt requires measurements at 2 degree intervals of the view zenith angle covering the range −75 degree to 75 degree. Although singular directions are preferred, it is left to the RAMI participants to choose the solid angle over which to integrate the exiting radiation, as long as they are centered at the above view zenith angles and duely indicated in the report file. The height of the reference surface is that of the top of the simulated scene and covers the entire extend of that scene - unless specified otherwise.

Within RAMI-IV this measurement applies to all canopy scenes.

Formatting of measurement-file content:

Header line content # rows # columns in file Ratio of filtered rays **
Header line format integer integer real
Body lines content SZA [rad] VZA [rad] SAA - VAA [rad] BRF Std. Dev. BRF **
Body lines format real real real real real
**: if available, otherwise set to −1.000000.

where

Example output:

          76           5      1.000000
     0.349066      1.309000     -1.570800     0.260220     -1.000000
     0.349066      1.274090     -1.570800     0.262513     -1.000000
     0.349066      1.239180     -1.570800     0.263880     -1.000000
     0.349066      1.204280     -1.570800     0.264449     -1.000000
     0.349066      1.169370     -1.570800     0.264333     -1.000000
     0.349066      1.134460     -1.570800     0.263631     -1.000000
     0.349066      1.099560     -1.570800     0.262442     -1.000000
     0.349066      1.064650     -1.570800     0.260851     -1.000000
     0.349066      1.029740     -1.570800     0.258930     -1.000000
     0.349066      0.994838     -1.570800     0.256750     -1.000000
     0.349066      0.959931     -1.570800     0.254365     -1.000000
     0.349066      0.925025     -1.570800     0.251820     -1.000000
     0.349066      0.890118     -1.570800     0.249159     -1.000000
     0.349066      0.855211     -1.570800     0.246432     -1.000000
     0.349066      0.820305     -1.570800     0.243674     -1.000000
     0.349066      0.785398     -1.570800     0.240885     -1.000000
     0.349066      0.750492     -1.570800     0.238093     -1.000000
     0.349066      0.715585     -1.570800     0.235338     -1.000000
     0.349066      0.680678     -1.570800     0.232676     -1.000000
     0.349066      0.645772     -1.570800     0.230048     -1.000000
     0.349066      0.610865     -1.570800     0.227474     -1.000000
     0.349066      0.575959     -1.570800     0.224989     -1.000000
     0.349066      0.541052     -1.570800     0.222676     -1.000000
     0.349066      0.506145     -1.570800     0.220443     -1.000000
     0.349066      0.471239     -1.570800     0.218287     -1.000000
     0.349066      0.436332     -1.570800     0.216252     -1.000000
     0.349066      0.401426     -1.570800     0.214442     -1.000000
     0.349066      0.366519     -1.570800     0.212722     -1.000000
     0.349066      0.331613     -1.570800     0.211096     -1.000000
     0.349066      0.296706     -1.570800     0.209651     -1.000000
     0.349066      0.261799     -1.570800     0.208416     -1.000000
     0.349066      0.226893     -1.570800     0.207257     -1.000000
     0.349066      0.191986     -1.570800     0.206252     -1.000000
     0.349066      0.157080     -1.570800     0.205488     -1.000000
     0.349066      0.122173     -1.570800     0.204797     -1.000000
     0.349066      0.087266     -1.570800     0.204330     -1.000000
     0.349066      0.052360     -1.570800     0.203980     -1.000000
     0.349066      0.017453     -1.570800     0.203828     -1.000000
     0.349066      0.017453      1.570800     0.203828     -1.000000
     0.349066      0.052360      1.570800     0.203980     -1.000000
     0.349066      0.087266      1.570800     0.204330     -1.000000
     0.349066      0.122173      1.570800     0.204797     -1.000000
     0.349066      0.157080      1.570800     0.205488     -1.000000
     0.349066      0.191986      1.570800     0.206252     -1.000000
     0.349066      0.226893      1.570800     0.207257     -1.000000
     0.349066      0.261799      1.570800     0.208416     -1.000000
     0.349066      0.296706      1.570800     0.209651     -1.000000
     0.349066      0.331613      1.570800     0.211096     -1.000000
     0.349066      0.366519      1.570800     0.212722     -1.000000
     0.349066      0.401426      1.570800     0.214442     -1.000000
     0.349066      0.436332      1.570800     0.216252     -1.000000
     0.349066      0.471239      1.570800     0.218287     -1.000000
     0.349066      0.506145      1.570800     0.220443     -1.000000
     0.349066      0.541052      1.570800     0.222676     -1.000000
     0.349066      0.575959      1.570800     0.224989     -1.000000
     0.349066      0.610865      1.570800     0.227474     -1.000000
     0.349066      0.645772      1.570800     0.230048     -1.000000
     0.349066      0.680678      1.570800     0.232676     -1.000000
     0.349066      0.715585      1.570800     0.235338     -1.000000
     0.349066      0.750492      1.570800     0.238093     -1.000000
     0.349066      0.785398      1.570800     0.240885     -1.000000
     0.349066      0.820305      1.570800     0.243674     -1.000000
     0.349066      0.855211      1.570800     0.246432     -1.000000
     0.349066      0.890118      1.570800     0.249159     -1.000000
     0.349066      0.925025      1.570800     0.251820     -1.000000
     0.349066      0.959931      1.570800     0.254365     -1.000000
     0.349066      0.994838      1.570800     0.256750     -1.000000
     0.349066      1.029740      1.570800     0.258930     -1.000000
     0.349066      1.064650      1.570800     0.260851     -1.000000
     0.349066      1.099560      1.570800     0.262442     -1.000000
     0.349066      1.134460      1.570800     0.263631     -1.000000
     0.349066      1.169370      1.570800     0.264333     -1.000000
     0.349066      1.204280      1.570800     0.264449     -1.000000
     0.349066      1.239180      1.570800     0.263880     -1.000000
     0.349066      1.274090      1.570800     0.262513     -1.000000
     0.349066      1.309000      1.570800     0.260220     -1.000000