BRF in the cross plane (perpendicular to the principal plane)
Within RAMI the spectral Bi-directional Reflectance Factor (BRF) is defined as the radiant flux exiting from a target area in a given viewing direction ($\theta_r$, $\phi_r$) and a given direct illumination direction ($\theta_i$, $\phi_i$) normalized by the equivalent quantity leaving from an infinitely large Lambertian and ideal background (e.g. 100% reflectance).
The BRF is defined as
Alternatively, the BRF of this reference surface can be represented in terms of the Bidirectional Reflectance Distribution (BRDF) function if the model provide it. Then,
where the BRDF is defined, accordingly to Nicodemus (1977) as,
where
Specifically, brfop requires to report BRF as computerd in the orthogonal plane of reflection (i.e. for $\Delta\phi=\pm90^\circ$), and $\theta_r$ from $1^\circ$ to $75^\circ$ in step of $2^\circ$ for each side. Ideally, the position of the observer is set to $z=+\infty$. In other words, the measurement is based on counting the number of photons exiting from the top boundary of the scene in several viewing directions. 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 in the experiment description page.
Within RAMI-IV this measurement applies to all canopy scenes.
This measure should be performed for all RAMI-V bands, excluding GED.
The illumination conditions are specific of the actual/abstract scene. For actual canopy scenes, we defined the following conditions by computing the average of the sun position over the periods (Jan, Apr,Jul) defined for Sentinel-3 OLCI observations in brf_olc measurement.
The position of the Sun is expressed in terms of geometry tag _zZZaAAA_ as defined in definition section (ex. _z56a153_ stands for $\theta_i=56^\circ$ and $\phi_i=153^\circ$). Illumination conditions are the same as reported in the scene descriptions.
*: if available, otherwise set to −1.000000.
where:
76 5 1.000000 0.349066 1.308997 -1.570796 0.422619 -1.000000 0.349066 1.274090 -1.570796 0.421888 -1.000000 0.349066 1.239184 -1.570796 0.420397 -1.000000 0.349066 1.204277 -1.570796 0.418608 -1.000000 0.349066 1.169371 -1.570796 0.416181 -1.000000 0.349066 1.134464 -1.570796 0.413340 -1.000000 0.349066 1.099558 -1.570796 0.410499 -1.000000 0.349066 1.064651 -1.570796 0.407356 -1.000000 0.349066 1.029744 -1.570796 0.403885 -1.000000 0.349066 0.994838 -1.570796 0.400383 -1.000000 0.349066 0.959931 -1.570796 0.397118 -1.000000 0.349066 0.925025 -1.570796 0.393745 -1.000000 0.349066 0.890118 -1.570796 0.390221 -1.000000 0.349066 0.855211 -1.570796 0.386832 -1.000000 0.349066 0.820305 -1.570796 0.383651 -1.000000 0.349066 0.785398 -1.570796 0.380617 -1.000000 0.349066 0.750492 -1.570796 0.377556 -1.000000 0.349066 0.715585 -1.570796 0.374610 -1.000000 0.349066 0.680678 -1.570796 0.371996 -1.000000 0.349066 0.645772 -1.570796 0.369534 -1.000000 0.349066 0.610865 -1.570796 0.367106 -1.000000 0.349066 0.575959 -1.570796 0.364795 -1.000000 0.349066 0.541052 -1.570796 0.362805 -1.000000 0.349066 0.506146 -1.570796 0.361052 -1.000000 0.349066 0.471239 -1.570796 0.359393 -1.000000 0.349066 0.436332 -1.570796 0.357765 -1.000000 0.349066 0.401426 -1.570796 0.356486 -1.000000 0.349066 0.366519 -1.570796 0.355300 -1.000000 0.349066 0.331613 -1.570796 0.354271 -1.000000 0.349066 0.296706 -1.570796 0.353392 -1.000000 0.349066 0.261799 -1.570796 0.352719 -1.000000 0.349066 0.226893 -1.570796 0.352157 -1.000000 0.349066 0.191986 -1.570796 0.351708 -1.000000 0.349066 0.157080 -1.570796 0.351353 -1.000000 0.349066 0.122173 -1.570796 0.351117 -1.000000 0.349066 0.087266 -1.570796 0.350951 -1.000000 0.349066 0.052360 -1.570796 0.350809 -1.000000 0.349066 0.017453 -1.570796 0.350762 -1.000000 0.349066 0.017453 1.570796 0.350762 -1.000000 0.349066 0.052360 1.570796 0.350809 -1.000000 0.349066 0.087266 1.570796 0.350951 -1.000000 0.349066 0.122173 1.570796 0.351117 -1.000000 0.349066 0.157080 1.570796 0.351353 -1.000000 0.349066 0.191986 1.570796 0.351708 -1.000000 0.349066 0.226893 1.570796 0.352157 -1.000000 0.349066 0.261799 1.570796 0.352719 -1.000000 0.349066 0.296706 1.570796 0.353392 -1.000000 0.349066 0.331613 1.570796 0.354271 -1.000000 0.349066 0.366519 1.570796 0.355300 -1.000000 0.349066 0.401426 1.570796 0.356486 -1.000000 0.349066 0.436332 1.570796 0.357765 -1.000000 0.349066 0.471239 1.570796 0.359393 -1.000000 0.349066 0.506146 1.570796 0.361052 -1.000000 0.349066 0.541052 1.570796 0.362805 -1.000000 0.349066 0.575959 1.570796 0.364795 -1.000000 0.349066 0.610865 1.570796 0.367106 -1.000000 0.349066 0.645772 1.570796 0.369534 -1.000000 0.349066 0.680678 1.570796 0.371996 -1.000000 0.349066 0.715585 1.570796 0.374610 -1.000000 0.349066 0.750492 1.570796 0.377556 -1.000000 0.349066 0.785398 1.570796 0.380617 -1.000000 0.349066 0.820305 1.570796 0.383651 -1.000000 0.349066 0.855211 1.570796 0.386832 -1.000000 0.349066 0.890118 1.570796 0.390221 -1.000000 0.349066 0.925025 1.570796 0.393745 -1.000000 0.349066 0.959931 1.570796 0.397118 -1.000000 0.349066 0.994838 1.570796 0.400383 -1.000000 0.349066 1.029744 1.570796 0.403885 -1.000000 0.349066 1.064651 1.570796 0.407356 -1.000000 0.349066 1.099558 1.570796 0.410499 -1.000000 0.349066 1.134464 1.570796 0.413340 -1.000000 0.349066 1.169371 1.570796 0.416181 -1.000000 0.349066 1.204277 1.570796 0.418608 -1.000000 0.349066 1.239184 1.570796 0.420397 -1.000000 0.349066 1.274090 1.570796 0.421888 -1.000000 0.349066 1.308997 1.570796 0.422619 -1.000000