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brfop

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

$BRF(\theta_i, \phi_i,\theta_r,\phi_r) = \frac{L_r(\theta_i, \phi_i,\theta_r,\phi_r)}{L_r^{lamb}(\theta_i, \phi_i,\theta_r,\phi_r)}$

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,

$BRF (\theta_i, \phi_i,\theta_r,\phi_r) = \pi BRDF (\theta_i, \phi_i,\theta_r,\phi_r) $

where the BRDF is defined, accordingly to Nicodemus (1977) as,

$BRDF(\theta_i, \phi_i,\theta_r,\phi_r) = \frac {dL_r(\theta_i,\phi_i,\theta_r,\phi_r)} {L_i(\theta_i, \phi_i) d\Omega_i}$

where

$d\Omega_i = cos\theta_i sin\theta_id\theta_i d\phi_i$.

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.

The reference plane
The reference plane.

Spectral characteristics

This measure should be performed for all RAMI-V bands, excluding GED.

Illumination

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.


Scene Site Jan Apr Jul
HET07_JPS_SUM Järvselja _z56a153_ _z41a147_
HET08_OPS_WIN Järvselja _z76a155_ _z56a153_
HET09_JBS_SUM Järvselja _z56a153_ _z41a147_
HET15_JBS_WIN Järvselja _z76a155_ _z56a153_
HET14_WCO_UND Wellington _z42a076_ _z60a045_ _z67a041_
HET16_SRF_UND Zerbolo _z71a153_ _z36a137_ _z34a130_
HET50_SAV_PRE Skukuza _z37a089_ _z50a051_ _z60a041_
HET50_SAV_PST Skukuza _z37a089_ _z50a051_ _z60a041_
HET51_WWO_TLS Wytham Wood _z75a154_ _z46a147_ _z35a138_

Header

Header line content Header line format
# rows %4d
# columns in file %4d
Ratio of filtered rays * %.6f

Columns content

Body lines content Body lines format
$\theta_i$ [rad] %.6f
$\theta_r$ [rad] %.6f
$\phi_i$ - $\phi_r$ [rad] %.6f
BRF %.6f
Std. Dev. BRF * %.6f

*: if available, otherwise set to −1.000000.

where:

  • $\theta_i$: Solar Zenith Angle;
  • $\phi_i$: Solar Azimuth Angle;
  • $\theta_r$: Viewing Zenith Angle
  • $\phi_r$: Viewing Azimuth Angle
  • Ratio of filtered rays: The number of rays that perform the measurement divided by the total number of incident rays (for ray-tracing RT models only).
  • Std. Dev. BRF: Indication of the uncertainty in the BRF estimate as estimated from the radiative transfer model itself 
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