For any modelmthat simulates a BRF in a given band (λ), viewing (Ω_v) and illumination (Ω₀) geometry over a surface target with structure (ζ) one can compute a corresponding z prime statistics:

where x is the model simulated BRF, X is the reference BRF under identical conditions, and u is the standard uncertainty of the reference (X) and sigma is the tolerable uncertainty (also known as proficiency standard deviation). While the standard uncertainty of the reference could be determined from a robust analysis (as described in ISO-13528) The proficiency standard deviation was set equal to 3% of the reference X.

Computing the z' statistics for each one of the simulated BRF quantities allows to group them into different categories, where z' < 2 indicates compliance with the tolerance uncertainty (green colour in bar plots below), 2 < z' < 3 indicates a warning sign according to ISO-13528 (gold colour in bar charts below), and z' > 3 indicates an 'action sign' according to ISO-13528 (red colour in bar chart below).

The bar charts below indicate the relative fractions of z' statistics obtained by different models when simulating total BRFs for the heterogeneous abstract canopy cases (white colour indicates that some results are missing).

The bar charts below indicate the relative fractions of z' statistics obtained by different models when simulating single-collided BRFs for the heterogeneous abstract canopy cases (white colour indicates that some results are missing).

The bar charts below indicate the relative fractions of z' statistics obtained by different models when simulating multiple-collided BRFs for the heterogeneous abstract canopy cases (white colour indicates that some results are missing).