## 4 Results
### Contribution of Temperature Errors on Measured Spectrum  
As already described, the direct normal spectral irradiance is measured using a calibrated grating spectroradiometer with two detectors. The measurement has to be performed maintaining both detectors at the same temperature at which the calibration of the spectroradiometer was performed. The sensors have their temperature controlled by two separate Peltier elements, but the measured temperature differs from the effective junction temperature, due to the position of the temperature sensor with respect to the detector, to the irradiance variability during the measurement, and to the exposition of the spectroradiometer body to the outdoor conditions. The effect of this uncertainty has to be estimated; in the present study it is modeled with a Gaussian distribution with \(\pm 1.5\)\({}^{\circ}\)C. The uncertainty associated with the temperature of the two sensors does not affect all the wavelengths, but only the intervals specified in Equation (7) [10]. The algorithm to adjust the measured spectra is  
\[G\left(t,\lambda;T^{(i)}_{c-Si^{\prime}}\,T^{(i)}_{InGaAs}\right)=p(\lambda;T ^{(i)}_{c-Si^{\prime}},T^{(i)}_{InGaAs})G(t,\lambda) \tag{8}\]  
where the function p acts as a weighting factor only in the regions \(850\leq\lambda\leq 1150\) nm and \(1500\leq\lambda\leq 1700\) nm, otherwise it is unity. The index (\(i\)) in Equation (8) refers to the trial number, because the function changes at each iteration following the Gaussian of all the possible values of temperature errors. The two Gaussian curves modeling crystalline silicon and InGaAs temperature errors are independently generated. An example is shown in Figure 8.  
In order to study the uncertainty component associated with each of the two temperature errors, the factors of c-Si and InGaAs have been used alternately, varying the amplitude of the Gaussian probability:  
\[\begin{array}{ll}c-\text{Si temperature}&p(\lambda;T^{(i)}_{c-Si^{\prime}},T^{(i)}_{InGaAs})\to p(\lambda;T^{(i)}_{c-Si})\\ \text{InGaAs temperature}&p(\lambda;T^{(i)}_{c-Si^{\prime}},T^{(i)}_{ InGaAs}) \to p(\lambda;T^{(i)}_{InGaAs})\end{array}\]  
Figure 7: Impact of random errors of measured spectrum on the three SMR. The linearity of the functions is notable, and the slopes indicate that the spectral random errors have the same impact on all the three SMR. (**a**) case of \(\text{SMR}_{12}\); (**b**) case of \(\text{SMR}_{13}\); (**c**) case of \(\text{SMR}_{23}\).  
The results are shown in Figure 9 for c-Si and InGaAs separately, considering the different spectra. The c-Si temperature error affects all the three SMR, because it is present in both the Top and Middle junctions; the magnitude of the variation of the three SMR depends on the values of spectral irradiance and spectral responsivities in the interval [850; 1150] nm. Regarding the variation associated with error in InGaAs, only the bottom junction responds in the wavelength range from 1500 to 1700 nm. Therefore, only SMR\({}_{13}\) and SMR\({}_{23}\) are affected, and by the same amount, because the error source is the same.  
Figure 8: Weighting factor generated in 3 different Monte Carlo runs to adjust the spectrum in the InGaAs and c-Si regions independently. The weighting factor is always equal to one except in the interested wavelengths, where the spectrum is scaled up or down depending on the random number sampled from the Gaussian distribution.  
Figure 9: _Cont._  
Considering the estimated \(\sigma\) = \(\pm\)1.5 \({}^{\circ}\)C the corresponding output standard deviations are summarized in Table 1.