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• Bands used to calculate NDVI index: B4, B8
• Bands used by the script: B2, B3, B4, B8

This script allows you to visually interpret how the normalized density vegetation index (NDVI) [1] is affected by the uncertainties in detector reflectances of the L1C products.

Since NDVI is defined as a ratio of difference over sum of bands 8 and 4 (near infrared and red):
$NDVI:=\mathtt{Index}(B8,B4)=\frac{B8-B4}{B8+B4}.$

the uncertainty propagation [3] gives us the uncertainty of the index itself as

${\mathrm{\Delta }}_{NDVI}:=\frac{\sqrt{B{8}^2{\mathrm{\Delta }}_{B4}^2+B{4}^2{\mathrm{\Delta }}_{B8}^2-2B4B8{\mathrm{\Delta }}_{B4B8}}}{(B8+B4{)}^2}$.

where ${\mathrm{\Delta }}_{B4}$ and ${\mathrm{\Delta }}_{B8}$ are uncertainties of red and near infrared bands respectively (reported by ESA to be 0.02 and 0.03). We left out the mixed part ${\mathrm{\Delta }}_{B4B8}$ as if the two uncertainties were not correlated.

The script encodes the uncertainty with darkness, as can be seen in following figure [2]

[1] Wikipedia, Normalized Difference Vegetation Index . Accessed on October 4th 2017.
[2] Sentinel-Hub, Ad hoc testing of algorithms globally. Accessed October 10th 2017.
[3] Wikipedia, Propagation of uncertainty. Accessed October 10th 2017.