## 3 Sources of Uncertainty
### Uncertainty Budget Associated with the Spectrum Measurement  
The uncertainty budget of the spectrum measurement is composed of the following items:  
* Standard lamp calibration uncertainty and drift
* Internal calibration transfer uncertainty
* Temperature control of the detectors in outdoor conditions  
As already explained, the SMR depends only on the shape of the measured curves, so systematic effects affecting uniformly all the wavelengths do not impact the SMR uncertainty; for example, since all the devices are placed on the same solar tracker, possible tracking errors have not to be taken into account in the uncertainty budget.  
The spectroradiometer used in the present study has been internally calibrated against a standard lamp, calibrated at NPL (National Physical Laboratory UK). Uncertainty arises mainly from calibration, including uncertainty of calibration laboratory and expected lamp calibration drift. Average NIST irradiance scale standard uncertainty is \(\pm\)0.70%, with calibration laboratory transfer accounting for another \(\pm\)0.55%. During 50 h of operation, the lamp drift is estimated to be \(\pm\)1.00%; if this is considered the limit of a rectangular distribution, the associated standard uncertainty is \(\pm\)0.59%. The uncertainty of the standard lamp is then transferred to the spectroradiometer via periodic internal recalibrations. During the process the main uncertainty components are stray light, lamp to spectroradiometer entrance slit distance, lamp current and lamp orientation. Stray light contribution is estimated to be \(\pm\)0.29%, even with blackened walls and surfaces, and no object in the room being at a distance less than 1.5 m from the optical table. The distance lamp-spectroradiometer is set by a 500 mm calibrated gauge block; a residual uncertainty in the lamp distance is estimated to be within \(\pm\)0.5 mm, leading to a standard uncertainty in the irradiance spectral intensity of \(\pm\)0.10%. The spectral distribution of the lamp is affected by the current injected into the lamp during calibration of the spectroradiometer. Uncertainty of the power supply is due to the instrument resolution and long-term drift; however these terms combined account for a standard uncertainty contribution of only \(\pm\)0.03%.  
During outdoor operation the two detectors (c-Si for the range 300-1150 nm and InGaAs until 1700 nm) are temperature controlled by separate Peltier elements inside the instrument case. However, a temperature gradient between the temperature read by the feedback sensor and the true junction temperature might be possible, depending upon the position of the temperature sensors inside the instruments. If the real temperature differs from the temperature at which the instrument was calibrated, the current produced by the detectors changes, due to the change of spectral responsivity of crystalline silicon and InGaAs materials with temperature. This contribution is modeled in the Monte Carlo method, by shifting the portion of spectral irradiance in the following wavelength intervals [10]:  
\[\left\{\begin{array}{cc}0.20\ \%/^{\circ}\mathrm{C}&850\ \leq\lambda\leq 1150\ \mathrm{nm}\\ \\ -0.24\ \%/^{\circ}\mathrm{C}&1500\ \leq\lambda\leq 1700\ \mathrm{nm}\end{array}\right. \tag{7}\]  
Finally, as an empirical check of the input uncertainties estimation, the expanded uncertainty (k = 2) of the spectral irradiance measurement have been compared with the deviations with respect to the average spectrum of 14 consecutive acquisitions of a steady-state solar simulator Xenon lamp. Approximately 95.45% of the points were within the uncertainty limits as expected providing a verification of the uncertainties.