A limitation in the performance rating of solar cells and modules is that they are tested using a single value for the s olar spectrum. To map the performance expected under the varying spectra found in operating conditions, solar cell efficiencies have been evaluated using solar spectra generated by the National Solar Radiation Database , applied to confirmed record -efficiency cel l parameters . Nine solar cell types (single -junction and multijunction) are evaluated using spectra at more than forty locations , spanning 76° of latitud e and 150° of longitude , at hourly intervals over a year. Relative to the standard test efficiency, i ncreases in annual operating efficiency are seen in cadmium telluride and single -junction perovskite designs , while efficiency decreases are observed in two -terminal multijunction structures. Though s ilicon exhibits the least variation, its -3% to +2% range in relative efficiency is equivalent to ~20° C of temperature variation. This divergence in operating efficienc ies indicat es that evaluation using a single spectrum is not a sufficient basis for comparison , or prediction of energy yield in operation . Application of an additional “operating spectr um,” to comp lement the standard test spectrum, is proposed . Fig. 1. Source locations for spectra in this study. Each marker represents about 4000 hourly spectra, for wavelengths from 280 nm to 4000 nm. In six locations, hourly spectra were generated for direct normal irradiance (DNI) using inputs from the Typical Meteorological Year 3 database (NREL, 2010) to generate spectra using the SMARTS model (Gueymard, 1995) . Map courtesy of NREL’s NSRDB. 1. Introduction While remarkable change has swept across the solar photovoltaics industry in the last four decade s, there has been at least one constant : efficiency of cells and modules is determined using a single standard spectrum (ASTM G173 -03, 2013; First Solar, 2020; Green et al., 2020a; G reen and Emery, 1993; Gueymard et al., 2002; IEC 61215 -1, 2016; IEC 61853 -2, 2016; Myers et al., 2004, 2002; SunPower, 2020) . To obtain repeatable measurements, solar cells and modules are tested under indoor solar simulators that are calibrated to del iver a given irradiance and spectrum (Fraunhofer ISE, 2020; IE C 60904 -9, 2006) . Use of a single , fixed standard spectrum value has deliver ed valuable continuity over the years and consistency across academia and industry . Single -value testing cannot , of course, provide insigh t into the impact of spectrum variation on solar operations worldwide . When comparing devices with different spectral responses for their usefulness in outdoor energy generation , the results of single -spectrum testing , if not representative of operating spectra , are potentially mislead ing (Amillo et al., 2015; Faine et al., 1991; Lee et al., 2015; Nann and Emery, 1992; Schweiger, 2015) . This work maps the impact of operating spectrum variation over a range of latitudes and longitudes and offers a template for determining energy generation for various solar cell types. 2. Synthetic spectra Published version : Solar Energy v. 217, Pages 49 -57, 2021 , doi.org/10.1016/j.solener.2021.01.024 2 Synthetic spectra (Fig . 1) have been obtained from the National Renewable Energy Laboratory’s (NREL’s) National Solar Radiation Database (NSRDB) (Habte et al., 2017; Sengupta et al., 2018) . Spectra are generated via the Fast All -sky Radiation Model for Solar applications with Narrowband Irradiances on Tilted surfaces (FARMS - NIT) model (Xie et al., 2019; Xie and Sengupta, 2018) . These “global” s pectra (includ ing scattered sunlight from the hemisphere of the sky) are generated by the model at hourly intervals for fixed -tilt and single -axis tracking panel orientations (Figure 1) . For the fixed -tilt configuration , the site latitude was chosen as the tilt angle. Six hourly “direct” spectra (for sunlight coming directly from the vicinity of the solar dis c, derived separately ) are also included (Kinsey et al., 2013) . The direct spectra are relevant primarily for the III -V multijunctions, which are most often used in optical systems that effectively capture only the direct solar beam (Appendix C ). Each dataset (global or direct) represents about 4000 hourly spectra for which the model calculated a non -zero irradiance , with a wavelength range of 280 nm to 4000 nm (Supplemental Table E.1). Fig. 2. Annual summations of seventy -six hourly global operating spectra from forty -five locations for NSRDB spectrum year 2018 . For comparison with the standard global terrestrial spectrum ( AM1.5G , gray) and the standard e xtraterrestrial spectrum (AM0, black), the global operating spectra amplitudes have been normalized to that of AM0 at 1050 nm. 3. Analysis Analysis focuses on the global spectra provided by the NSRDB (Fig. 2). Relative to AM1.5G, the annual global spectra exhibit more power density in the visible wavelengths (400 -700 nm). Since single -axis trackers follow the sun from/to the horizons, the resulting aggregate d spectral content appears less “blue” than for the latitude -tilt (fixed ) orientation s (Figs. E.1 & E.2 ). (a) (b) Fig. 3. Quantum efficiencies for seven of the nine cell types in this study, digitized at 5-nm intervals from figures in the Solar Cell Efficiency Tables : (a) silicon (Si), cadmium telluride (CdTe), and CIGS ; (b) perovskite (PVSK), perovskite -CIGS tandem (PVSK -CIGS), perovski te-silicon tandem (PVSK -Si) and a III -V three -junction cell. The quantum efficiencies for the III -V four - junction and III -V six -junction cells are shown in Supplemental Fig. E.4. Performance data for nine confirmed current -best solar cells, chronicled in the Solar Cell Efficiency Tables (Green et al., 2020a) and displayed on NREL’s Best Research -Cell Efficiency Chart (NREL, 2020 ), are compared . Four single -junction cells (silicon (Green et al., 2017) , cadmium telluride (Green et al., 2015) , CIGS (Green et al., Published version : Solar Energy v. 217, Pages 49 -57, 2021 , doi.org/10.1016/j.solener.2021.01.024 3 2019) , and perovskite (Green et al., 2020b) ) are included, as well as five two -terminal multijunctions (perovskite -CIGS (Green et al., 2020a) , perovskite -silicon (Green et al., 2020a) , and three -, four - and six -junction III-Vs (Green et al., 2019, 2015, 2013) . Multijunctions use two or more semiconductor junctions to convert solar energy. Stacking the junctions increases the cell voltage, but the two -terminal configuration implies a series connect ion, so the device current is limited by whichever junction is prod ucing the least current. Two -terminal multijunctions are therefore more sensitive to spectrum variation. Fig. 4. Current densities for the silicon cell derived from its quantum efficiency combined with spectral irradiances for the standard global spec trum (AM1.5G) and the annual global operating spectrum for single -axis tracking in Montreal. The purple line indicates the relative increase in integrated current density for Montreal with respect to AM1.5G. Spectral irradiances in the background a re not shown to scale. In calculation of the operating efficiencies at 25° C, the open -circuit voltage (VOC) and fill factor (FF) are those confirmed under Standard Test Conditions (IEC 61853 -2, 2016 , Appendix A ). Second -order ef fects, such as changes to voltage or fill factor with changing irradiance (Kinsey et al., 2008) or increases in fill factor in multijunctions due to current mismatch (Reynolds and Smirnov, 2015) are neglected . Spectrum variations (and their integral, the irradiance) are assumed to affect only the cell shor t-circuit current. The short -circuit current is derived from a cell’s quantum efficiency, which is a measure of the percentage of incoming photons at each wavelength that are converted by a solar cell into current. Quantum efficiencies provided in the Solar Cell Efficiency Tables are digitized at 5 -nm wavelength intervals (Fig. 3) . Since the amplitude of the published quantum efficiencies is often normalized, the amplitudes are re-normalized to deliver the short -circuit current confirmed under the stand ard spectrum, AM1.5G (AM1.5D , for the III -V multijunctions , Appendix B ). Fig. 5. Annual operating efficiencies under variable operating spectra at 25° C, compared against the values under Standard Test Conditions ( “STC”, largest icons: 25° C, 1000 W/m2, and AM1.5G or AM1.5D spectrum , Appendix A ). Symbols for operating spectra are arranged in order of increasing annual site irradiance ; lateral positions are adjusted to improve visibility. The rightmost data (smalle st symbols, separated by a gap) are for the six direct normal irradiance datasets. Best Research -Cell Efficiency chart courtesy of NREL (NREL, 2020) . Published version : Solar Energy v. 217, Pages 49 -57, 2021 , doi.org/10.1016/j.solener.2021.01.024 4 To determine the short -circuit current under a given spectrum, the hourly spectra are converted to 5 -nm intervals , to pair with the digitized quantum efficiencies . Fig. 4 illustrates the relationship between spectral irradiance and a cell’s spectral current density. Spectral current density is integrated across all wavelengths to give the short -circuit current density , JSC [A/cm2]. The product V OC·FF·JSC is then the cell power density [W/ cm2]. Dividing by the irradiance [W/ cm2] gives the effi ciency. Resulting annual operating efficiencies (at 25° C) are shown in Fig. 5, against a backdrop of the confirmed values under AM1.5 G (AM1.5D, for the III -V multijunctions) . The corresponding relative efficiencies are given in Fig. 6. While the efficiencies for silicon and CIGS are clustered around their value s under the standard spectrum , those of the other cell types diverge . Cadmium telluride and the single -junction perovs kite deliver higher efficiencies at most locations , while the multijunctions deliver lower. As might be expected, sensitivity to spectrum variation increases with the number of junctions, leading to decreased efficiency and greater variation between locati ons. Researchers recognize this limitation of two -terminal (series -connected) multijunctions ; the search for practical three - or four -terminal alternatives is underway (Futscher and Ehrler, 2017) . (a) (b) Fig. 6. Efficiencies under annual global spectra at 25° C, relative to that confirmed under a standard spectrum . Data grouped by cell type in (a) is shown as a function of site daily irradiation in (b). Linear regressions to the data are included in (b) solely as guides to the eye. Abbreviations: silicon (Si); cadmium telluride (CdTe); perovskite (PVSK). Two locations, Montreal, Canada and Alamosa, USA , are highlighted in Fig. 6 to illustrate the varyin g impact of given spectr al conditions on different cell designs: as cell spectral sensitivity increase s from left to right in Fig. 6(a), the higher efficiencies found in Montreal (for single -junctions) shift to Alamosa (for multijunctions) . Efficiencies as a function of site latitude are given in Fig. E.7. Relative to silicon, t he higher efficiency of cadmium telluride and single -junction perovskite is notable in sites like Montreal . It can be understood with reference to the integrated current density in Fig. 4, obtained by summing the spectral current density in th e direction of increasing wavelength . Examination of Fig. 3 shows that q uantum efficiency goes to zero above 840 nm for single -junction perovskite and 915 nm for cadmium tellurid e, while for silicon it extends to 1200 nm. The increase in integrated current density for silicon in Montreal (with respect to AM1.5G) is 4.1 % at 840 nm, 3.9% at 915 nm, but drops to 3.4% at 1200 nm . The peak benefit s are therefore with the perovskite and cadmium telluride cells, while silicon receives a lower proportional benefit . The 3.4% gain in current density for silicon is partly offset by a corresponding rise in irradiance (2. 4%, not shown) for a net efficiency gain of 1.0%, relative . Divergence in cell response under spectrum variation is further evident when plotted as a function of irradiance in Fig. 6(b). The atmospheric conditions that determine spectrum at the surface are complex, so a simple linear relations hip between cell efficiency and site irradia tion is not expected. However, site conditions are frequently covariant; a dry, high -altitude site such as Alamosa, USA will often have fewer clouds, fewer aerosols , and less water in the atmosphere . Across the highland plateaus of South America , spectra can approach the shape of the extraterrestrial spectrum ( Fig. E.9). In contrast , lower daily irradiance levels in sites such as Montreal often imply a wider range of atmospheric conditions that lead s to larger divergence s in the spectra and the cell efficiencies in both seasonal and hourly timescales (Figs. E.1, E.2, E.3 ). Published version : Solar Energy v. 217, Pages 49 -57, 2021 , doi.org/10.1016/j.solener.2021.01.024 5 The output files from the NSRDB include hourly ambient temperature, so temperature corrections to open - circuit voltage, fill factor, and the short -circuit current densities are applied ( using temperature coefficients in Table E.2). Table 1 includes annual summaries of the spectrum - and tempera ture -corrected data . For single junctions, the effects of operating spectral variation are comparable in magnitude to the effects of temperature. Silicon shows the least sensitivity to spectral variation, yet its ~5% variation range at 25° C (-3% to +2%) is equivalent to 20° C of temperature excursion. For cadmium telluride, which exhibits larger spectral variation and has a smaller temperature coefficient, the ~8% variation range is equivalent to over 3 0° C of temperature excursion. Table 1. Efficiency under standard test conditions ( 𝜂𝑆𝑇𝐶), operating spectra at 25° C ( 𝜂25℃), and operating spectra and temperature ( 𝜂𝑇). Cell (junctions) 𝜂𝑆𝑇𝐶 [%] 𝜂25℃ [%] median 𝜂25℃ 𝜂25℃ −𝜂𝑆𝑇𝐶 𝜂𝑆𝑇𝐶 𝜂𝑇 𝜂𝑇−𝜂𝑆𝑇𝐶 𝜂𝑆𝑇𝐶 1-axis lat.-tilt Silicon (1) 26.7 25.8 -27.1 26.7 26.7 -3% to +2% 24.5 -26.5 -8% to -1% CdTe (1) 22.1 21.3 -23.1 22.5 22.5 -4% to +4% 20.8 -22.5 -6% to +2% CIGS (1) 23.4 22.3 -23.6 23.2 23.1 -5% to +1% 20.9 -23.0 -11% to -2% PVSK (1) 25.2 24.5 -26.7 25.8 25.9 -3% to +6% 23.8 -25.9 -5% to +3% PVSK -CIGS (2) 24.2 23.0 -23.9 23.5 23.5 -5% to -1% 21.2 -23.4 -12% to -3% PVSK -Si: (2) 29.2 26.7 -28.1 27.6 27.4 -9% to -4% 24.8 -27.5 -15% to -6% III-V (3) 44.4 39.5 -42.3 41.7 41.2 -11% to -5% 39.0 -41.9 -12% to -6% III-V (4) 46.0 36.6 -41.8 40.3 39.6 -20% to -9% 35.7 -41.1 -22% to -11% III-V (6) 47.1 35.5 -42.4 40.1 39.2 -25% to -10% 34.6 -41.4 -27% to -12% If not accounted for, such variation leads to m iscalculations of solar power generati on capability that impact project economics and climate change mitigation. For a notional 100 -MW solar project commissioned at €1/W, generating 1500 kWh/kW/year and selling into the electrical grid at €0.05/kWh, a 2% difference between predicted an d actual output translates to a project cost difference of €2 million and an annual revenue difference of €150,000. If th is solar plant displaces fossil fuel generating carbon dioxide at 0.5 kg/kWh (Foster and Bedrosyan, 2014) , the annual difference in greenhouse gases would be 1,500 tons in the first year , the equivalent of around 9 flights from New York to Paris (Air Transport Action Group, 2020 , Appendix D ). (a) (b) Fig. 7. Daily relative efficiencies at 25° C for Alamosa, USA (latitude -tilt) and Montreal, Canada (one -axis tracking) . Results for other sites are in Table E.4. The value of solar to the grid depends on the season and time of day that it is generated. The hourly granularity of NSRDB spectral irradiance outputs enables investigation of these variations (Fig. 7 , Table E.4, Fig. E.3). Along with the greater daily fluctuations seen in t he Montreal climate , there are also differences in the curvature s of cell efficiency due to seasonality . The seasonal curvature s of silicon, cadmium telluride, and CIGS cells are more pronounced in Montreal; the May -August peak seen in the performance of the perovskite single junction in Alamosa is more of a trough in Montreal. Seasonal variation of silicon and cadmium telluride across multiple sites is shown in Fig. E.8. Published version : Solar Energy v. 217, Pages 49 -57, 2021 , doi.org/10.1016/j.solener.2021.01.024 6 4. Discussion In 1992, Keith Emery of NREL, ever a c hampion of rigorous testing standards, co -authored a paper addressing the many discrepancies between then -standard testing and outdoor performance. Regarding spectrum, t he authors observed: …There are changes in the relative spectral distribution which lea d to higher or lower efficiencies compared to the efficiency under the AM1.5 reference spectrum… With a few exceptions, all PV -modules have been overrated because the single -value specification of efficiency under standard reporting conditions is a more fa vorable specification than that measured outdoors under real conditions. This discrepancy, however, should occur between measurements and rating, but not between rating and customer. (Nann and Emery, 1992) In the decades since , multiple values for other factors that affect performance (temperature, irradiance, wind speed , e.g.) ha ve been standardized and incorporated into test protocols, product data sheets (First Solar, 2020; Solar Frontier, 2020; SunPower, 2020) , and warranty coverage terms (Jinko Solar, 2020) , so that the link between standard testing and outdoor operation is understood . Use of a single spectrum has become the outlier. Today’s international standard for energy rating of photovoltaic modules (IEC 61853 -2, 2016) define s four temperatures, four irradiances … And one spectrum. An impediment to d efining additional “operating spectra ,” consistent with what is now required for temperature and irradiance, has been the uncertainty around what those operating spectra should be. Results presented here and in the literature (Alonso -Abella et al., 2014; Amillo et al., 2015; Cornaro and Andreotti, 2013; Dirnberger et al., 2015; Faine et al., 1991; Fernandez et al., 2015; Gottschalg et al., 2004; Huld and Gracia Amillo, 2015; Ishii et al., 2013; Kinsey et al., 2013; Kinsey, 2015; Lee et al., 2015; Marzo et al., 2017; Minemoto e t al., 2007; Monokroussos et al., 2011; Nann and Emery, 1992; Peters and Buonassisi, 2018; Philipps et al., 2010; Schweiger, 2015; Simon and Meyer, 2011; Ye et al., 2014) indicate that this concern is s ubordinate to the uncertainty arising from reliance on testing under a single -value standard spectrum. Any additional standard spectrum will convert the existing single -value specification into a performance range that, however limited, will enable interpolation and/or extrapolation to conditions of interest to the “customer”. One candidate for a “standard operating spectrum ” might be something like the com posite of seventy -six annual spectr a shown in Fig. 2. However, two other candidates are already qualified as standards and can therefore be implemented immediately: AM1.5D (ASTM G173 -03, 2012) and AM0 (ASTM E490 -00a, 2014) . While AM0, the standard for space (Fig. C.1), would be an extreme choice in terms of representing terrestrial spectra (Fig. E.6, Table E.3), AM0 paired with AM1.5G would bracket most operating spectral conditions worldwide and serve as a lower bound for predicting cell and module operating efficienc ies. Conclusion Nine cell types have been evaluated under operating spectra obtained from the N ational Solar Radiation Database . The resulting variation in cell operating efficiencies is comparable to that resulting from temperature variations. Efficiencies diverge for cells with different spectrum sensitivities, so testing under more than a single spectrum is indicated for comparison and energy yield prediction . Implement ation of one or more standard operating spectra , to suppleme nt the standard test spectrum , will reduce uncertainty in the costs and benefits in deploy ing solar photovoltaics. Published version : Solar Energy v. 217, Pages 49 -57, 2021 , doi.org/10.1016/j.solener.2021.01.024 7 Appendix A: m ethods Synthesized spectra Sophisticated models for solar spec tral irradiance have been developed to enable synthesis of spectral using input atmospheric conditions. Inputs include site pressure and aerosol, water vapor, ozone, and CO 2 levels. The outputs are corroborated with a growing body of measurements from both satellite (NOAA/NASA GOES -R) and ground -based spectroradiometer data. The National Solar Radiation Database at NREL hosts Spec tral On- Demand , a tool accessible online as part of the satellite -derived data in the NSRDB Data Viewer . Spectral On- Demand generat es synthetic spectra for points within the area defined by NREL’s Physic al Solar Model: longitude: -25°E to -175°W, latitude: -20°S to 60°N) . Spectr um data is generated at one -hour intervals using the Fast All -sky Radiation Model for Solar applications with Narrowband Irradiances on Tilted surfaces (FARMS -NIT. Within FARMS -NIT, clear -sky irradiance is first calculated using SMARTS (Simple Model of the Atmospheric Radiative Transfer of Sunshine) (Gueymard, 1995; Myers and Gueymard, 2004) . SMARTS has demonstrated predictive power for the operation of spectrum -sensitive solar cells (Kinsey et al., 2013) . A version of SMARTS (v. 2.9.2) is the basis for defin ing the current American Society for Testing and Materials standards for AM1.5G and AM1.5D (ASTM G173 -03), as well as the International Electrotechnical Commiss ion (IEC) standard for AM1.5 (IEC 60904 -03). The NSRDB spectrum year used here is 2018. For direct normal irradiance, the Typical Meteorological Year 3 database (NREL, 2010) , a predecessor to NREL’s Physical Solar Model , was used for inputs to the SMARTS model. Standard Test Conditions Standard Test Conditions (STC) require a 2 5° C cell temperature, 1000 W/m2 irradiance, and the AM1.5G spectrum for cells and modules . An exception is made for components under optical concentration and using the ASTM standard (III-V multijunctions, e.g.) , for which the irradiance is 900 W/m2 and the spectrum is AM1.5D. Standard operating conditions are defined for sets of temperature and irradiance. An example is IEC 61853, “Photovoltaic (PV) module performance testing and energy rating” : Table A.1. Standard test condi tions per IEC 61853. Irradiance Temperature (point of reference) Spectrum Standard Test Conditions 1000 W/m2 25° C (cell) AM1.5 Nominal Operating Cell Temperature 800 W/m2 20° C (ambient) AM1.5 Low Irradiance Condition 200 W/m2 25° C (cell) AM1.5 High Temperature Condition 1000 W/m2 75° C (cell) AM1.5 Low Temperature Condition 500 W/m2 15° C (cell) AM1.5 The “AM1.5” spectrum in IEC 61853 is defined in IEC 60904 -03 and is consistent with (though not quite identical to) AM1.5G, as defined by ASTM G 173-03. Quantum efficiency and calculation of current density Quantum efficiencies are measured under short -circuit conditions, where the cell is expected to produce the maximum amount of current. To obtain the current generated under a given s pectrum, the spectral irradiance is divided by the photon energy at each wavelength to give the number of photons in that interval (5-nm intervals were used in this study) . Multiplying by the quantum efficiency gives the “spectral current density” [mA/cm2/nm] that would be converted to current at that wavelength. Multiplying by the wavelength interval yields current density [mA/cm2] for each interval ; integrating over all wavelengths obtain s the short -circuit current density. Published version : Solar Energy v. 217, Pages 49 -57, 2021 , doi.org/10.1016/j.solener.2021.01.024 8 Appendix B: standard spectra Three standard spectra are in use for space and terrestrial solar applications: AM0, AM1.5D, and AM1.5G. “AM” is short for “air mass” and represents the hypothetical column of air between the sun and the incident surface. AM0 ( defined in 1974), is used for solar cells under extraterrestrial radiation, in earth orbit above the atmosphere (zero air mass) . An air mass of one ( “AM1” ) would represent the conditions when the sun is directly overhead. When a standard for the terrestrial spectrum was first established by the American Society for Testing and Materials (ASTM) in 1982, AM1.5 was selected to represent a “typical” solar module tilted at a fixed angle of 37° (mid -latitude USA) and pointed due south. The geometry of AM1.5 implies a sun zenith angle of 48.2°. For forty -four sites with one -axis tracking data, the annual, irradiance -weighted zenith angles were obtained (Table E.1); the median irradiance -weighted sun zenith angle for this group is 46.6°. AM1.5D is the ASTM “direct” spectrum for this orientation, intended to represent only the sunlight coming directly from the sun (or its near vicinity). AM1.5D finds practical application in systems using two -axis trackers and optical concentration (lenses or mirrors) to boost solar cells’ power and efficiency. These optical concentrators are effective in concentrating only the collimated rays that come directly from the solar disc. The “global” spectrum, AM1.5G, consists of these direct rays, as well as su nlight that has been scattered by the atmosphere and is arriving on the tilted surface from the hemispherical dome of the sky. Though solar panels in 2020 are at least as likely to be found on trackers as on fixed racks (and even more likely to be installe d remote from 37° northern latitudes), use of AM1.5G has remained the convention t hroughout academia and industry. Appendix C: III-V multijunctions & global vs. direct normal irradiance Direct spectra are relevant for solar systems using optical concentr ation and two -axis tracking; these systems typically employ III -V multijunction cells. The trend in III -V multijunction efficiencies notable in Fig. 5, where the efficiencies in the global spectra rise (or , in the case of the three -junction, fall) to appro ach those for the direct spectra, is consistent with their design. III-V multijunctions are tuned by their designers for operation under a direct spectrum (AM1.5D) . Fig. C.1. Three standard spectra (AM0, AM1.5D, and AM1.5G) compared against seventy -six annual global spectra (one -axis and latitude -tilt) derived from the National Solar Radiation Database (NSRDB) hourly spectra, converted to 5 -nm wavelength intervals. The NSRDB global spectra are normalized to the AM0 value at 1050 nm. Appendix D : estimates of greenhouse gas equivalents in air travel A Boeing 787 -9 carries up to 289 passengers (Boeing, 2020) and consumes approximately 2.9 litres of jet fuel per 100 km per passenger once it is at cruising altitude (Lufthansa, 2020) . The 5,800 -km trip from Paris to New York will consume approxi mately 50,000 litres. A litre of jet fuel weighs about 0.8 kg and produces 3.2 kg of CO 2 (Air Transport Action Group, 2020) . One-hundred and sixty tons is released for one trip between New York and Paris (0.5 tons per passenger , 83 kg per passenger per hour on a full flight ). Published version : Solar Energy v. 217, Pages 49 -57, 2021 , doi.org/10.1016/j.solener.2021.01.024 9 Appendix E: supplemental data Table E.1. Site detail s: annual values for NSRDB year 2018 . One-axis tracking Latitude -tilt Direct normal Location Temp. [° C] (Irradiance - weighted *) Sun zenith angle [°] (Irradiance - weighted *) Daily irradiation [kW- hr/m2/day] # of spectra Daily irradiation [kW- hr/m2/day] # of spectra Daily irradiation [kW- hr/m2/day] # of spectra Azores -Ponta Delgada 17.0 48.9 5.1 4137 Bolivia -Uyuni 14.0 44.9 10.3 4110 8.0 4110 Brazil -Mariana 5.1 4207 Brazil -Patos 32.3 41.1 9.0 4299 5.1 4137 Brazil -Sao Desiderio 30.1 42.1 8.4 4183 Cabo Verde -Praia 23.1 41.6 8.4 4156 6.9 4153 Canada -Calgary 14.8 54.6 4.9 4032 4.2 3878 Canada -Montreal 15.1 51.8 4.1 4010 5.0 4102 Chile -Putre 15.4 43.8 9.5 4109 8.0 4222 Colombia -Cali 24.7 39.0 6.3 4067 5.4 4066 Costa Rica -Punta Arenas 30.7 39.8 7.5 4208 6.3 4182 Ecuador -Galapagos 24.0 42.7 6.7 4036 5.3 4036 Ecuador -Quito 15.5 39.9 5.3 4171 6.3 4171 French Guiana -Kourou 27.9 39.5 7.3 4249 8.4 4183 Haiti 22.6 45.3 6.7 4201 Mexico -Mazatlan 28.9 43.7 8.2 4179 6.8 4159 Mexico -Mexico City 22.4 41.5 7.6 4138 6.5 4138 Mexico -Monterrey 30.7 43.4 6.6 4178 5.5 4133 Peru -Cusco 12.9 42.1 6.9 4171 4.4 3969 Peru -Puno 13.3 42.7 8.9 4123 7.3 4123 Samoa -Apia 25.4 41.7 9.4 4174 7.6 4174 USA-AK-Ketchikan 13.4 55.9 3.5 4013 2.9 3928 USA-AR-Little Rock 23.9 47.7 5.1 4058 6.2 4127 USA-AZ-Tucson 9.2 4426 USA-CA-Joshua Tree 24.4 49.0 8.9 4140 7.3 4028 USA-CA-Palmdale 26.4 48.8 8.6 4117 8.8 4457 USA-CA-Sacramento 25.2 49.6 7.4 4139 USA-CO-Alamosa 17.3 50.1 7.9 4119 6.7 4066 9.9 4259 USA-CO-Denver 20.5 50.7 6.7 4140 5.8 4076 USA-FL-Cocoa 25.9 46.1 7.0 4178 6.3 4171 USA-GA-Atlanta 22.9 47.0 5.2 4121 6.3 4182 USA-HI-Hilo 27.9 40.7 5.0 4137 USA-HI-Kona 23.6 45.7 5.1 4140 USA-MA-Boston 16.6 51.0 5.2 4105 4.4 3969 USA-MN-Rochester 15.3 52.1 5.3 4124 4.4 4015 USA-MO-Kansas City 21.9 49.7 5.9 4138 4.9 4026 USA-MT-Butte 14.5 52.9 5.7 4090 USA-ND-Fargo 17.1 52.4 5.2 4079 6.3 4157 USA-NM-Albuquerque 23.8 48.7 8.2 4112 6.8 4052 9.2 4433 USA-NM-Las Cruces 9.2 4429 USA-NV-Las Vegas 29.1 49.4 8.3 4157 6.8 4028 9.0 4307 USA-NY-New Paltz 17.4 50.5 5.0 4148 5.0 4102 USA-OH-Xenia 19.3 48.9 5.1 4123 4.2 4038 USA-OK-Yale 23.6 48.5 6.3 4157 USA-TX-Austin 28.1 45.4 6.6 4211 5.4 4109 USA-WA-Seattle 17.9 51.9 5.0 4088 4.2 3998 Venezuela -Apure 31.2 41.0 8.0 4222 *The irradiance used is the one -axis tracking irradiance. Published version : Solar Energy v. 217, Pages 49 -57, 2021 , doi.org/10.1016/j.solener.2021.01.024 10 Alamosa (latitude -tilt) & Montreal (one -axis tracking) data: Fig. E.1. Daily spectral irradiances for Alamosa (latitude -tilt) and Montreal (one -axis tracking). Amplitudes are normalized to the peak at each respective location. Hourly data on the summer solstice in Alamosa, USA and Montreal, Canada (a) Alamosa, USA (b) Montreal, Canada. Fig. E.2. Morning hourly spectra (up to the peak daily irradiance , near solar noon ) on the summer solstice ( 21 June 2018) . For the latitude -tilt orientation, the first non -zero spectrum is at 6:00 am in Alamosa and 7:00 am (local time) in Montreal. Published version : Solar Energy v. 217, Pages 49 -57, 2021 , doi.org/10.1016/j.solener.2021.01.024 11 (a) Alamosa, USA: one-axis tracking (b) Montreal, Canada: one-axis tracking (c) Alamosa, USA: latitude -tilt (d) Montreal, Canada: latitude -tilt Fig. E.3. Relative efficiencie s at 25° C on the summer solstice (21 June 2018) as a function of local time . Quantum efficiencies Fig. E.4. Quantum efficiencies of the III -V four - and six -junction cells (Green et al., 2019, 2015) . Published version : Solar Energy v. 217, Pages 49 -57, 2021 , doi.org/10.1016/j.solener.2021.01.024 12 Efficiencies under operating spectra and temperatures : Fig. E.5. Efficiencies under operating spectra and temperatures . Efficiencies under operating spectra , AM1.5G, AM1.5D, and AM0 Fig. E.6. Efficiencies under operating spectra (at 25° C), AM1.5G, AM1.5D, and AM0. Some lateral positions are adjusted to improve visibility. Table E.3. Efficiencies under three standard spectra (at 25 ° C). Cell (# junctions) AM0 AM1.5G AM1.5D Silicon (1) 24.2% 26.7% 26.7% CdTe (1) 20.9% 23.4% 23.5% CIGS (1) 19.7% 22.1% 21.8% PVSK (1) 22.8% 25.2% 24.7% PVSK -CIGS (2) 22.0% 24.2% 23.5% PVSK -Si: (2) 25.5% 29.2% 28.6% III-V (3) 36.5% 44.6% 44.4% III-V (4) 37.6% 43.8% 46.0% III-V (6) 38.0% 44.0% 47.1% Published version : Solar Energy v. 217, Pages 49 -57, 2021 , doi.org/10.1016/j.solener.2021.01.024 13 (a) (b) Fig. E.7. Relative efficiency (at 25 ° C) under annual operating spectra ( global, one-axis tracking) as a function of (a) site latitude and (b) site elevation. Cell parameters Table E.2. Cell parameters used in efficiency calculations. Cell (# junctions) Si (1) CdTe (1) CIGS (1) PVSK (1) PVSK - CIGS (2) PVSK -Si (2) III-V (3) III-V (4) III-V (6) Voc (25° C) 0.738 0.8872 0.734 1.1805 1.897 1.768 3.555 4.23 6.286 FF (25° C) 0.849 0.785 0.804 0.848 0.778 0.729 0.872 0.85 0.872 dVOC/dT [%/°C] -0.00241 -0.0027 -0.00300 -0.0012 -0.00167* -0.0020* -0.00135 -0.00135 -0.00135 dISC/dT [%/°C] 0.00055 0.0004 0.0001 -0.00054 -0.00012* -0.00027* 0.0006 0.0006 0.0006 dFF/dT [%/°C] -0.00072 -0.0002 -0.000020 -0.00094 -0.00086* -0.00063* -0.00053 -0.00053 -0.00053 dP/dT [%/°C] -0.00258 -0.0025 -0.0031 -0.0027 -0.0026* -0.0029* -0.0013 -0.0013 -0.0013 *The temperature coefficients of perovskites are not yet well understood; the temperature coefficient for perovskite fill fac tor was taken as a mean from the range of values shown in the supplement to Jošt et al., 2020 . Temp erature coefficients for PVSK -CIGS and PVSK -Si are calculated as the V OC-weighted averages of the coefficients of the two materials. Values for the open -circuit voltage (V OC) and fill factor (FF) are found in Green et al., 2020a . The sources for temperature coefficients are: silicon (SunPower, 2020) ; cadmium te lluride (First Solar, 2020) ; CIGS (Solar Frontie r, 2020) ; perovskite (Jošt et al., 2020) ; III-Vs (Fernández et al., 2012) Published version : Solar Energy v. 217, Pages 49 -57, 2021 , doi.org/10.1016/j.solener.2021.01.024 14 Table E.4. Select daily efficiencies (global & direct spectr a, 25° C) . Azores -Ponta Delgada (one -axis tracking ) Bolivia -Uyuni (one -axis tracking ) Bolivia -Uyuni (latitude -tilt) Brazil -Mariana (latitude -tilt) Brazil -Patos (one -axis tracking ) Brazil -Patos (latitude -tilt) Brazil -Sao Desiderio (one -axis tracking) Canada -Montreal (one -axis tracking) Canada -Montreal (latitude -tilt) Cabo Verde -Praia (one -axis tracking ) Ecuador -Galapagos (latitude -tilt) French Guiana -Kourou (one -axis tracking) Haiti -Port -au-Prince (one -axis tracking) Mexico -Mexico City (one -axis tracking) Mexico -Mexico City (latitude -tilt) Published version : Solar Energy v. 217, Pages 49 -57, 2021 , doi.org/10.1016/j.solener.2021.01.024 15 Mexico -Monterrey (one -axis tracking) Mexico -Monterrey (latitude -tilt) Peru -Cusco (one -axis tracking) Peru -Puno (one -axis tracking) Peru -Puno (latitude -tilt) Peru -Cusco (latitude -tilt) Samoa -Apia (one -axis tracking) Samoa -Apia (latitude -tilt) USA-Alamosa (one -axis tracking) USA-Alamosa (latitude -tilt) USA-Alamosa (direct normal) USA-Albuquerque (one -axis tracking) USA-Albuquerque (latitude -tilt) USA-Albuquerque (direct normal) Published version : Solar Energy v. 217, Pages 49 -57, 2021 , doi.org/10.1016/j.solener.2021.01.024 16 USA-Atlanta (one -axis tracking) USA-Atlanta (latitude -tilt) USA-Butte, ID (one -axis tracking) USA-Cocoa, FL (one -axis tracking) USA-Cocoa, FL (latitude -tilt) USA-Fargo, ND (one -axis tracking) USA-Denver (one -axis tracking) USA-Denver (latitude -tilt) USA-Kona (one -axis tracking) USA-Joshua Tree (one -axis tracking) USA-Joshua Tree (latitude -tilt) USA-Ketchikan (one -axis tracking) USA-Kansas City (one -axis tracking) USA-Kansas City (latitude -tilt) USA-Ketchikan (latitude -tilt) Published version : Solar Energy v. 217, Pages 49 -57, 2021 , doi.org/10.1016/j.solener.2021.01.024 17 USA-Las Vegas (one -axis tracking) USA-Las Vegas (latitude -tilt) USA-Las Vegas (direct normal) USA-Little Rock (one -axis tracking) USA-Little Rock (latitude -tilt) USA-Rochester, MN (one -axis tracking) Venezuela -Apure (one -axis tracking) Daily v ariation under g lobal operating spectr a: silicon and cadmium telluride (a) (b) Fig. E.8. Daily relative efficiencies of (a) silicon and (b) cadmium telluride cells under global operating spectra ( 25° C) for the sites in Table E.4. Published version : Solar Energy v. 217, Pages 49 -57, 2021 , doi.org/10.1016/j.solener.2021.01.024 18 High i rradiance on South American highland plateaus Fig. E.9. The three highest hourly irradiances in the data catalog , obtained for Uyuni, Bolivia and Putre, Chile. Amplitudes are normalized to AM0 at 1050 nm. Published version : Solar Energy v. 217, Pages 49 -57, 2021 , doi.org/10.1016/j.solener.2021.01.024 19