RAMI website

# brfpp

BRF in the principal plane (total)

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

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

Principal plane of reflection is defined as the plane containing both the surface normal and the illumination direction. Specifically, brfpp measure requires to compute the BRF for multiple view zenith angles (from $1^\circ$ to $75^\circ$ in step of $2^\circ$) in the forward ($\Delta\phi=180^\circ$) and the backward ($\Delta\phi=0^\circ$) scattering directions. Notice that the $\Delta\phi$ is defined in RAMI-V as $\phi_i-\phi_r$.

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.

In RAMI-V brfpp applies to all canopy scenes.

### 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_

Scene Site Jan Apr Jul
All 60N _z82a155_ _z53a154_ _z42a149_
All 45N _z70a152_ _z42a141_ _z33a129_
All 30N _z59a146_ _z33a122_ _z28a102_
All 15N _z48a137_ _z30a096_ _z31a074_
All 00N _z40a123_ _z34a071_ _z39a055_
All 15S _z36a105_ _z43a056_ _z51a046_
All 30S _z38a086_ _z55a050_ _z64a042_

# 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	0.000000	0.453537	-1.000000
0.349066	1.274090	0.000000	0.453537	-1.000000
0.349066	1.239184	0.000000	0.453537	-1.000000
0.349066	1.204277	0.000000	0.453537	-1.000000
0.349066	1.169371	0.000000	0.453537	-1.000000
0.349066	1.134464	0.000000	0.453537	-1.000000
0.349066	1.099558	0.000000	0.453537	-1.000000
0.349066	1.064651	0.000000	0.453537	-1.000000
0.349066	1.029744	0.000000	0.453630	-1.000000
0.349066	0.994838	0.000000	0.453152	-1.000000
0.349066	0.959931	0.000000	0.451966	-1.000000
0.349066	0.925025	0.000000	0.450110	-1.000000
0.349066	0.890118	0.000000	0.448032	-1.000000
0.349066	0.855211	0.000000	0.445602	-1.000000
0.349066	0.820305	0.000000	0.442729	-1.000000
0.349066	0.785398	0.000000	0.439687	-1.000000
0.349066	0.750492	0.000000	0.436648	-1.000000
0.349066	0.715585	0.000000	0.433502	-1.000000
0.349066	0.680678	0.000000	0.430154	-1.000000
0.349066	0.645772	0.000000	0.426748	-1.000000
0.349066	0.610865	0.000000	0.423572	-1.000000
0.349066	0.575959	0.000000	0.420491	-1.000000
0.349066	0.541052	0.000000	0.417395	-1.000000
0.349066	0.506146	0.000000	0.414321	-1.000000
0.349066	0.471239	0.000000	0.411463	-1.000000
0.349066	0.436332	0.000000	0.408975	-1.000000
0.349066	0.401426	0.000000	0.406705	-1.000000
0.349066	0.366519	0.000000	0.404673	-1.000000
0.349066	0.331613	0.000000	0.403119	-1.000000
0.349066	0.296706	0.000000	0.402328	-1.000000
0.349066	0.261799	0.000000	0.402554	-1.000000
0.349066	0.226893	0.000000	0.404458	-1.000000
0.349066	0.191986	0.000000	0.409735	-1.000000
0.349066	0.157080	0.000000	0.422962	-1.000000
0.349066	0.122173	0.000000	0.458958	-1.000000
0.349066	0.087266	0.000000	0.454245	-1.000000
0.349066	0.052360	0.000000	0.411799	-1.000000
0.349066	0.017453	0.000000	0.392586	-1.000000
0.349066	0.017453	3.141593	0.381432	-1.000000
0.349066	0.052360	3.141593	0.373689	-1.000000
0.349066	0.087266	3.141593	0.367787	-1.000000
0.349066	0.122173	3.141593	0.362929	-1.000000
0.349066	0.157080	3.141593	0.358852	-1.000000
0.349066	0.191986	3.141593	0.355270	-1.000000
0.349066	0.226893	3.141593	0.352172	-1.000000
0.349066	0.261799	3.141593	0.349437	-1.000000
0.349066	0.296706	3.141593	0.347027	-1.000000
0.349066	0.331613	3.141593	0.344972	-1.000000
0.349066	0.366519	3.141593	0.343172	-1.000000
0.349066	0.401426	3.141593	0.341618	-1.000000
0.349066	0.436332	3.141593	0.340329	-1.000000
0.349066	0.471239	3.141593	0.339416	-1.000000
0.349066	0.506146	3.141593	0.338694	-1.000000
0.349066	0.541052	3.141593	0.338019	-1.000000
0.349066	0.575959	3.141593	0.337938	-1.000000
0.349066	0.610865	3.141593	0.338211	-1.000000
0.349066	0.645772	3.141593	0.338525	-1.000000
0.349066	0.680678	3.141593	0.338775	-1.000000
0.349066	0.715585	3.141593	0.339902	-1.000000
0.349066	0.750492	3.141593	0.341263	-1.000000
0.349066	0.785398	3.141593	0.342651	-1.000000
0.349066	0.820305	3.141593	0.344062	-1.000000
0.349066	0.855211	3.141593	0.345975	-1.000000
0.349066	0.890118	3.141593	0.348399	-1.000000
0.349066	0.925025	3.141593	0.351031	-1.000000
0.349066	0.959931	3.141593	0.353536	-1.000000
0.349066	0.994838	3.141593	0.356448	-1.000000
0.349066	1.029744	3.141593	0.359642	-1.000000
0.349066	1.064651	3.141593	0.363309	-1.000000
0.349066	1.099558	3.141593	0.366889	-1.000000
0.349066	1.134464	3.141593	0.370519	-1.000000
0.349066	1.169371	3.141593	0.374471	-1.000000
0.349066	1.204277	3.141593	0.378646	-1.000000
0.349066	1.239184	3.141593	0.382880	-1.000000
0.349066	1.274090	3.141593	0.386933	-1.000000
0.349066	1.308997	3.141593	0.391112	-1.000000