European Commission - RAMI website

Description

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_

Table 1: Sun positions to be considered for each actual scene. They are computed by averaging $\theta_s$ and $\phi_s$ over Jan, Apr, and Jul given for the corresponding OLCI geometries in the brf_sat measurement.

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_

Table 2: The 21 Sun positions to be considered for all abstract canopies. They are computed by averaging $\theta_s$ and $\phi_s$ over Jan, Apr, and Jul given for OLCI geometries in the brf_sat measurement.

Output file format

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

Example output

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