S2 L1 radiometric model
The radiometric uncertainty analysis starts by identifying the different steps in the Sentinel-2 MSI instrument and L1 processing chain. The figure below displays graphically these steps. The complete Sentinel-2 L1 radiometric model can be found in 
S2 L1 uncertainty contributions
From the previous radiometric model, it is possible to identify the sources of uncertainty at each step of the processing chain. The table shows the uncertainty contributions for the L1C product with the associated parameter in the model. The contributions in dark orange are included in RUTv1. The contributions with negligible impact are shown in light orange and, in white, the contributions to be included in next versions.
S2 L1 uncertainty combination
The model follows the GUM  to combine the L1 radiometric uncertainty. The equation for the expanded uncertainty (i.e. the uncertainty at a defined coverage probability) is:
Two uncorrected systematic effects enlarge ONLY the expanded uncertainty.
No significant correlation between contributors has been identified due to the independent nature of the L1 parameters. This simplifies the combination of the standard uncertainty as shown.
The same concept can be applied to the different terms in the standard uncertainty combination model:
S2 L1 uncertainty combination validation
Validation of the central limit theorem and normal distribution
The GUM model relies on the assumption that a generalised central limit theorem applies to the combination model. In those circumstances, the standard uncertainty can be associated to the normal distribution and a specific coverage probability can be determined. An initial comparison to the Monte-Carlo method in  determined the validity of the normal distribution except at very low radiance levels (i.e. close to Lmin) levels). A more extensive validation has been performed. The figure below shows the difference between the uncertainty k=1 by using the GUM combination and by determining an area of the Monte-Carlo distribution symmetric from the mean. The range of radiance goes from approximately Lmin to Lref.
The results clearly indicate the validity of the GUM approach for the radiance range under study with the exception of those values at very low radiance levels. In that case, the instability of the quantisation noise invalidates the GUM combination.
Impact of the sensitivity coefficient
The terms u'DS and u'ADC are further calculated as follows:
The sensitivity coefficient cy requires the use of a per-pixel relative gains coefficients. A study of its value showed that the coefficient ranges around 1 ± 10%. Thus, the impact at the expanded uncertainty can be considered negligible and the sensitivity coefficient in the RUTv1 is set to 1. Here below we show the distribution of sensitivity coefficients for B5:
 ESA. (2015). "Sentinel-2 MSI Technical Guide." from https://sentinel.esa.int/web/sentinel/technical-guides/sentinel-2-msi
 BIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP and OIML (2008). Guide to the Expression of Uncertainty in Measurement, JCGM 100:2008.
 Javier Gorroño; Ferran Gascon; Nigel P. Fox; Radiometric uncertainty per pixel for the Sentinel-2 L1C products. Proc. SPIE 9639, Sensors, Systems, and Next-Generation Satellites XIX, 96391G (October 12, 2015)