# The Outdoor Field Test and Energy Yield Model of the Four-Terminal on Si Tandem PV Module
## 2 Methods
### Spectrum Model  
The performance model we used was identical to the one we used to analyze the PV module using the 2T configuration [97]. We called it the MS2E model (Miyazaki Spectrum-to-Energy method). Let us describe a rough flow of the analysis and the model. First, we need to define the solar spectrum. The spectrum we assumed was a linear combination of the spectrum of the clear sky condition and that of the overcasting state [97]. For the spectrum of the overcasting state it was assumed that the solar power was lost just by absorption, corrected by the solid angle of the sky influenced by the slope angle of the module. Then, the global solar spectrum is approximated as Equations (1) and (2). \[I_{\lambda}=fI_{1\lambda}+(1-f)I_{2\lambda} \tag{1}\]  
\[f=\frac{DNI}{\int_{300~{}nm}^{4000~{}nm}I_{d\lambda}d\lambda} \tag{2}\]  
where, \(I_{\lambda}\) is the global spectral irradiance calculated by our spectrum model covering all weather at a wavelength. The unit of \(I_{\lambda}\) is W/m\({}^{2}\)nm. \(f\) is the weather correction factor defined by Equation (2), \(I_{1\lambda}\) is the global spectral irradiance calculated using [PERSON]'s spectrum model [96] at a wavelength. The unit of \(f\) is W/m\({}^{2}\)nm. \(I_{2\lambda}\) is the global spectral irradiance calculated by a spectrum model assuming full cloud covering the sky at a wavelength. The unit of \(I_{2\lambda}\) is W/m\({}^{2}\)nm. \(DNI\) is the direct normal irradiance, and \(I_{d\lambda}\) is the direct normal solar spectral at a wavelength. The unit of \(I_{d\lambda}\) is W/m\({}^{2}\)nm. The spectrum calculated by this model, in contrast to [PERSON]'s model, is shown in Figure 3[97]. Note that the [PERSON]'s spectrum model was improved by considering atmospheric parameter variability. The Y-axis corresponds to the normalized global spectrum irradiance by integrated spectral irradiance. The black  
Figure 2: Measured 4T III-V/Si module and its solar cell structure: (**a**) Description of measured 4T III-V/Si module, 2 + 1 junctions (right) with comparison to the 2-terminal III-V 3-junction module. Note that the number of junctions is the same; (**b**) Spectro-radiometers [97]. trend line is the measured and normalized global solar spectral irradiance. The gray trend line is the reference spectrum in AM 1.5G. The red trend line and the blue trend line are the calculated global solar spectral irradiance by the MS2E method. Note that [PERSON]'s model only considers air mass, namely, the atmospheric parameters are constant. In the wintertime, atmospheric parameters are close to those under the standard conditions, so that the estimated solar spectrum approaches to the reference AM1.5G spectrum. In the summertime, the aerosol density often drops lower than that of the standard value, and the precipitable water grows larger. The short-wavelength region of the solar spectrum becomes thick, and the long-wavelength part becomes thin. During cloudy days, the influence of cloud appears in the short-wavelength part of the solar spectrum so that the long-wavelength region drops. Figure 4 indicates the measured aerosol density and precipitable water by the curve fitting to the measured solar spectrum. The aerosol optical depth was much lower than the standard value used to the calculation of the reference spectrum in summer (Figure 4a). This is why the measured and estimated irradiances in the summertime are higher than those of global irradiances (AM 1.5G) at the wavelength range of 450-550 nm. The precipitable water was much higher than the standard value used for the calculation of the reference spectrum in summer (Figure 4b). This is why the measured and estimated irradiance dips are broader than those of global irradiances (AM 1.5G) at the wavelength range of 1350-1450 nm and around 1150 nm.