## 3 Results
### Normal Multi-function vs. Super-Multi-Junction; Practical Conditions
#### 3.2.1 Modeling the Practical Spectrum Variation  
To develop the operation model of the multi-junction solar cells affected by the probability distribution of the crucial parameters for the basic calculation flow in Figure 2, we defined the parameters by random numbers. Table 2 is the independent parent variables and Table 3 is the dependent variables calculated by the parent independent probability variables, considering local conditions. The crucial probability parameters are the first two in Table 2. The distribution of these parameters was analyzed by the comparison between measured atmospheric parameters from the seasonal trend  
\begin{table}
\begin{tabular}{c c c} \hline  & **Range and Type** & **Description** \\ \hline Variation factor in aerosol density & Normal distribution centered on 0 & Calculated by the residual errors in the measured point form \\  & & the smooth trend line. \\ \hline Variation factor in water precipitation & Normal distribution centered on 0 & Calculated by the residual errors in the measured point form \\  & & the smooth trend line. \\ \hline Variation factor in solar irradiance 1 & Ranged uniform distribution in [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38; 39;  
lines. The seasonal trend lines of the atmospheric parameters, specifically aerosol density and water precipitation, are plotted in Figure 8. These were calculated by the data-fitting of the periodically observed solar spectrum line in a horizontal plane at the University of Miyazaki, Japan (N31.83\({}^{\circ}\), E131.42\({}^{\circ}\)) [61; 92; 93; 99; 100; 106]. Generally, the aerosol density is high in winter but low in summer, and the water precipitation, on the other hand, is high in summer. This trend can be seen for the entire region of Japan. However, there may be some regional characteristics. In Miyazaki, for example, a distinct peak in aerosol density appears in April that corresponds to the pollen of cedar and cypress trees. The fluctuation of the parameters from the trend lines can be modeled by the approximation of the distribution function of the residual error. The residual errors of the measured atmospheric parameters from the trend line (relative to the values in the trend line) are plotted in Figure 9.  
To find the best representative distribution, we used a Q-Q plot, i.e., a quantile-quantile plot that examines the values of two distributions (Figure 10). The best results were found in the normal distribution in both cases. In this plot, the \(x\)-axis corresponds to the values distributed to the normal distribution, and the \(y\)-axis corresponds to the measured values. If these two distributions are entirely  
Figure 8: Seasonal fluctuation of the atmospheric parameters around the University of Miyazaki, taken by the curve-fitting method to the spectral profile modeled by SpectrI2 [95]. The trend line was defined by the local least-square-error method. Figure 9: Histogram of the residual errors of the measured atmospheric parameters from the trend line (relative to the values in the trend line): (**a**) Aerosol density; (**b**) Water precipitation. matched, the plotline will be along the 45\({}^{\circ}\) (y = x) line. The parameter sets of the normal distribution of the aerosol density and water precipitation were (0, 0.30) and (0, 0.38). The first term inside the parentheses is the mean value, and that of the second value is the standard deviation. We also examined the statistical adequateness by the one-sample Kolmogorov-Smirnov test [106]. The alternative hypothesis was \"True: cumulative distribution function is not the normal distribution with given parameters, for example (0, 0.30) for aerosol density, with estimated parameters\". The p-value in both cases was zero, implying that it is next to impossible to deny that both distributions of the relative residual errors of atmospheric parameters from the reference trend lines are different from the normal distribution.