# brfop

Results for BRF in the cross plane (perpendicular to the principal plane)

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RAMI3 phase

These objects, in turn, contained a 'gas' (to be treated as a turbid medium) of dimension-less particles representing the leaves. These scattering particles were characterized by specified radiative properties (reflectance, transmittance), and the orientation of the normals to the scatterers followed exclusively a uniform distribution function. The radiative properties of the underlying soil were also specified (in this case a simple Lambertian scattering law). The particular values selected for these input variables represented classical plant canopy conditions.

The following figures exhibit a graphical representation of such a scene, from the side

The architecture of this scene (HET02) is precisely characterized as follows:

Scene dimensions:

( X × Y × Z) | 100.0 × 100.0 × 30.0 [m × m × m] |

(Xmin, Ymin, Zmin) | −50.0, −50.0, 0.0 [m, m, m] |

(Xmin, Ymax, Zmin) | −50.0, +50.0, 0.0 [m, m, m] |

(Xmax, Ymin, Zmin) | +50.0, −50.0, 0.0 [m, m, m] |

(Xmax, Ymax, Zmin) | +50.0, +50.0, 0.0 [m, m, m] |

(Xmin, Ymin, Zmax) | −50.0, −50.0, 30.0 [m, m, m] |

(Xmin, Ymax, Zmax) | −50.0, +50.0, 30.0 [m, m, m] |

(Xmax, Ymin, Zmax) | +50.0, −50.0, 30.0 [m, m, m] |

(Xmax, Ymax, Zmax) | +50.0, +50.0, 30.0 [m, m, m] |

Scatterer shape | Disc of negligible thickness |

Scatterer radius | 0 or close to 0 [m] |

LAI of individual sphere | 5.0 |

Scatterer normal distribution | Uniform |

Number of spheres | 15 |

Fractional scene area coverage of spheres | 0.471 |

Sphere radius | 10.0 [m] |

Minimum sphere center height | 11.0 [m] |

Maximum sphere center height | 19.0 [m] |

where the Leaf Area Index (LAI) is calculated as follows:

LAI = (# of leaves × one-sided area of single leaf) ⁄ (π × square of the radius of sphere)

An ASCII file with the radius (R), centre coordinates (Xc,Yc,Zc), and direction cosines (Dx,Dy,Dz) of every single leaf in a spherical volumes centered at 0,0,0 can be found here. This file (is ~ 2.2 Mbytes and) contains 49999 lines of format R Xc Yc Zc Dx Dy Dz and may serve as input to your scene creation process (provided that you are able to create multiple instances of its content, each one of which is then translated to the actual locations of the sphere centers in the scene. The coordinates (X, Y, Z) of the various sphere centers are as follows:

−24.8302; 11.6110; 15.6210 | −38.3380; −9.06342; 17.6094 | −31.3562; 32.5297; 14.3051 |

11.9126; 8.32062; 12.1220 | 39.4855; 37.1247; 16.3647 | −8.30999; −4.39422; 14.4241 |

12.2769; −25.1402; 12.4492 | 32.4756; −26.9023; 16.3684 | −7.46991; −32.2138; 12.6678 |

−27.4794; −32.0266; 15.9146 | 33.5709; −6.31039; 14.5332 | −5.24326; 39.8405; 16.8247 |

18.1699; 35.8223; 11.5683 | −5.26569; 18.9618; 17.2535 | 37.8226; 14.6769; 11.5936 |

The underlying soil is occupying the entire lower surface of the scene, i.e., the area enclosed between the following coordinates: (−50.0, −50.0, 0.0), (−50.0, +50.0, 0.0), (+50.0, −50.0, 0.0), and (+50.0, +50.0, 0.0), where all values are in meters.

The tables below provide the details required to execute each of the experiments in this category. Every table is preceeded by the corresponding experiment identifier tag

The absence of any absolute "truth" renders the evaluation of RT models more tricky but, nevertheless, the model discernability issue can be addressed through the usage of "credible solutions". As a matter of fact, it can reasonably be admitted that the latter correspond to the actual values that could be measured from an instrument with its intrinsic limited accuracy. We attempted to examine the issue of model discernability by establishing, for all scenarios concerned, what could be considered as a "credible solution" by estimating the arithmetic mean of every BRF value calculated within a subset of the participating three-dimensional Monte Carlo model results.

Overall six different 3D MC models were allowed to contribute to the establishing of the ``credible'' solution. These are: DART, drat, FLIGHT, Rayspread, raytran, and sprint3. The following rules were applied when choosing the exact name and number of 3D MC models that then contributed to the establishing of the ``credible'' solution (note that both the name and number of 3D MC models may change between exeriments and also between individual measurement types, as outline in the table here):

- For every RAMI BRF (flux) measurement, identify at least two (one) 3-D MC models that do not belone to the same RT modelling school/family,
- If two models formt he same RT modellign school/family are available, e.g. raytran/Rayspread, choose the one with the least amount of apparent MC noise,
- Remove all those 3D MC models from the reference set that are noticeably different from the main cluster of 3D MC models,
- If sufficient models are contained in the main cluster of 3D MC simulations then remove those models that would introduce noticeable levels of MC noise into the reference set,
- If there are two distinct cluster of 3D MC models, or no obvious cluster at all, then use all available 3D MC models to define a reference truth

Once a suitable set of ``credible solutions'' are available the model discernability can then be analyzed by comparing the BRF values generated from individual models with those of the credible solution using a normalised Chi-square metric:

where the uncertainty estimator in the denominator (sigma) is simply expressed as a fraction of the credible BRF (at any given view angle).

The figure below displays the Chi-square metrics obtained in the red (x-axis) against those for the near-infrared (Y axis) using a value of 0.03 for the uncertainty f (equivalent to sensors having a 3% calibration accuracy):