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Scientific Reports volume 16, Article number: 5339 (2026) Cite this article
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In the operation stage of a photovoltaic (PV) power plant, the output power often differs from the expected value. This deviation is sometimes caused by the so-called spectral mismatch, i.e. the difference between the actual solar radiation spectrum and the standard AM1.5G spectrum, under which the efficiency of a PV module is measured. Spectral mismatch appears as a hidden source of uncertainty in PV production, since for the same measured value of solar irradiance, the output power fluctuates depending on the atmospheric parameters. In this study, the magnitude of the uncertainty induced by the spectral mismatch is assessed. The study was conducted following an innovative methodology based on rigorous simulations of solar spectrum in real geometric-frames and various atmospheric conditions (with a focus on aerosols). The analysis is performed in terms of the familiar spectral factor. Furthermore, the influence of spectral mismatch on PV efficiency is evaluated. Overall findings indicate that under certain conditions spectral mismatch causes a gain or loss in PV efficiency within a rough margin of 10%. Marginal loss can be recorded even under mild conditions: small tilt angle, the Sun close to the horizon and an atmosphere moderately loaded with fine absorbing aerosol.
In recent years, there has been a worrying increase in the number and frequency of extreme weather events, such as powerful storms, massive floods, temperature extremes and prolonged droughts. The general perception is that all these phenomena are signs of ongoing climate change (e.g.¹). There is a near-universal consensus, both among the public and the scientific community, that replacing fossil fuels with renewable energy sources can help reduce the carbon footprint² and slow down climate change³. Within this broad framework, this study deals with the photovoltaic (PV) conversion of solar energy.
Large-scale integration of PV plants requires accurate knowledge of PV power production. Inaccuracy in estimating the PV power production can impact the feasibility studies of PV plants causing financial losses. The main source of uncertainty in estimating PV power production comes from solar resource assessment. For example, a study on the assessment of the return of capital invested in residential PV systems installed in different Brazilian locations⁴ shows that the variation in payback years may reach 30% when different solar resource data are used to evaluate residential projects.
Tremendous effort is dedicated to increasing the performance and accessibility of solar irradiance estimation models. Based on radiative transfer through the Earth’s atmosphere and using ground or satellite measurements as inputs, the diversity of solar resource estimation models is very large (see e.g. the comprehensive review in⁵). Embedding the properties of aerosols in the atmospheric transmittance models⁶ and including cloud shadows (with all their erratic evolution)⁷ in solar irradiance models represent the main sources of uncertainty in estimating the solar resource. Recent studies have highlighted the significant role of atmospheric aerosols in modulating surface solar radiation through scattering and absorption processes. Che et al.⁸ provide a comprehensive review of aerosol optical and radiative properties using observations from China. Variations in aerosol optical properties and composition have been shown to alter both direct and diffuse irradiance, with impacts that depend on aerosol type, load, and regional atmospheric conditions^8,9. Observational analyses based on global ground-based networks further indicate that aerosol optical depth is closely linked to changes in the diffuse radiation fraction and surface solar potential, particularly in regions affected by high aerosol concentrations⁹. Complementary evidence from site-specific and long-term observations shows that temporal variability in aerosol optical properties may lead to non-negligible biases in radiative transfer estimates, particularly when time-integrated sampling approaches are used¹⁰. At regional scales, the combined effects of aerosols and clouds have been shown to significantly reduce surface solar potential, especially in areas characterized by high aerosol loading¹¹. Together, Refs.^8,9,10,11 emphasize the importance of explicitly accounting for aerosol effects when assessing and modeling surface solar radiation.
The modeling of PV converter operation represents a minor source of error in PV power production estimates compared to uncertainties in solar resource assessment. The level of solar irradiance, the degree of soiling of the PV module, and the electronic components are continuously monitored in the operation of a PV plant. Based on the collected data, deviations of energy production from the prescribed values can largely be explained. Sometimes there may be deviations that cannot be explained by routine measurements. An unseen cause of such deviation is the change in the spectral distribution of the solar radiation incident on the PV module surface. This study aims to shed light on this deviation. The physical phenomenon, known as spectral mismatch, is briefly introduced further.
The standard efficiency of a commercial PV module is rated under specific test conditions STC (IEC 60904-3 standard). STC specifies an in-plane solar irradiance of 1000 W/m² with a spectral distribution AM1.5G¹² and a cell temperature of 25 °C. A PV module normally operates in an open-air environment, where the solar radiation spectrum rarely meets the AM1.5G characteristics. Since the composition of the atmosphere is constantly changing, the efficiency of PV modules operating open-air is also constantly changing, becoming a hidden source of uncertainty in the evaluation of PV plants’ performance. Sometimes, the spectral mismatch can be so large that the open-air efficiency of a PV module moves away from the standard efficiency measured at STC. Inadequate treatment of the spectral influence on PV performance may induce errors up to 14% for silicon-based technology^13,14. Aerosols are the most volatile atmospheric constituents. It is well documented that an insufficient representation of aerosols in solar irradiance estimation models can lead to significant errors¹⁵. Due to the large diversity of aerosols in nature, the spectral effect of aerosols on solar radiation flux is highly complex. Therefore, aerosols may induce fluctuations in PV performance caused by the spectral mismatch¹⁶.
The spectral characteristics of materials and light have been documented for centuries (e.g.¹⁷). The mismatch between the absorption spectrum of solar cells and the solar radiation spectrum is also well-known. However, the impact of the changes in solar radiation spectrum on PV power production has only recently become a topic of interest. The lack of systematic measurements of spectral solar radiation represents a barrier to research in the field. In recent years, many studies were conducted based on spectra measured in campaigns with field spectroradiometers. But even such observational spectral information is seldom available^16,18. In practice, accurate estimation of spectral effects on PV performance is hampered by the cost of monitoring spectral solar irradiance. Empirical solutions have been developed to reduce the costs and computational effort¹⁹.
The power gain or loss that a PV module may experience under the actual solar radiation spectrum compared to the standard AM1.5G spectrum is typically quantified by the spectral factor (SF). SF is introduced in the next section. SF and other spectral quantifiers have been reviewed in¹³, showing that accurate modelling of spectral effects in the absence of spectral measurements require direct atmospheric parameters. In the absence of atmospheric parameter measurements, satellite and reanalysis products show a promising accuracy in spectral solar irradiance modelling²⁰. Global analysis of SF for various PV technologies, based on simulated¹⁶ and measured spectra¹⁴, points out relatively low variation of SF for crystalline silicon cells. However, since PV modules made of crystalline silicon largely dominate the PV market, our study specifically targets this technology. In the field of building integrated photovoltaics (BIPV) capturing spectral effects through SF plays an important role, especially when dealing with facades. A recent study has revealed the impact on SF of the receiving surface’s tilt angles and their orientation²¹. Additionally, colored coatings on BIPV modules show a significant trade-off between aesthetics and efficiency losses caused by the spectral characteristics of the coating²².
The aim of this study is to evaluate the magnitude of the uncertainty induced by the spectral mismatch in PV efficiency. A methodology based on rigorous simulations of solar spectra in real geometric-frames (given the relative position between the Sun and the PV module surface) and various atmospheric conditions (with a focus on atmospheric aerosol loading and the nature of the aerosol) is applied. In the first part, the influence of the atmosphere on the solar radiation spectra is originally evaluated in analogy to the perception of color by the human eye. At the upper limit of the atmosphere, sunlight has a nearly constant spectral distribution. When crossing the atmosphere, through scattering and absorption, aerosols contribute to changes in the spectral distribution of sunlight and thus to the color of the Sun’s disc and the sky as perceived by the human eye. The human eye perceives light from the visible spectrum. A PV module “sees” sunlight in the same way as the human eye, but in a wider spectral range. Next, the analysis of spectral mismatch is rigorously performed in terms of SF. It includes a study of how the amount and nature of aerosols changes SF at different times of the day (indicated by the atmospheric optical mass) and at different inclinations of the PV module. This analysis goes beyond the traditional spectral factor calculation, as it also discusses the influence of spectral mismatch on the PV efficiency. In the second part, considering spectral mismatch, the efficiency of a silicon PV module is estimated in almost 900,000 instances. To achieve this, the model systematically varies parameters, such as geographical latitude, PV module tilt angle, atmospheric optical mass, water vapor column content, Ångström turbidity coefficient, Ångström exponent, single scattering albedo, to emulate most open-air operating conditions. Thus, the study innovatively brings to light the scale of the gain/loss in PV performance due to spectral mismatch in most places of Earth.
In this section, the spectral factor is defined. Its functionality as a proxy in the evaluation of a PV module efficiency deviation from STC, due to the spectral mismatch, is highlighted. In the second part of the section, the spectral solar irradiance model SMARTS2²³ is briefly introduced, and its application to the generation of synthetic solar radiation spectra under clear skies and arbitrary atmospheric conditions is described.
According to IEC 60904-7:2019²⁴, SF is defined as follows:
where (Gleft( lambda right)) denotes the solar irradiance in the spectral band ([lambda_{min } ,lambda_{max } ]) and the subscript STC indicates the standard test conditions.(SRleft( lambda right)) represents the relative spectral response of a solar cell at wavelength λ, being specific to a PV technology. (SRleft( lambda right)) is related to the short-circuit current (I_{SC} left( lambda right)) generated by a solar cell exposed to a solar radiation flux (Gleft( lambda right)) incident on its surface of area A.
The standard efficiency (eta_{STC}) of a PV module (provided by manufacturers) is defined as the ratio of the maximum output power P_m,STC to the solar irradiance measured on its surface A at STC (A cdot G_{STC}): (eta_{STC} = {{P_{m,STC} } mathord{left/ {vphantom {{P_{m,STC} } {left( {A cdot G_{STC} } right)}}} right. kern-0pt} {left( {A cdot G_{STC} } right)}}). At a certain value of irradiance G, the PV module efficiency becomes (eta = {{P_{text{m}} } mathord{left/ {vphantom {{P_{text{m}} } {left( {A cdot G} right)}}} right. kern-0pt} {left( {A cdot G} right)}}) and can be related to the efficiency at STC as follows:
Equation (3) is based on the observation that the voltage V_M at the maximum power point MPP varies insignificantly with the in-plane solar irradiance. Approximation (3) has been successfully applied in previous research (e.g.^25,26). As is defined by Eq. (1), SF > 1 indicates a spectral gain in power compared to STC while SF < 1 indicates a spectral loss. According to Eq. (3), the actual atmospheric conditions can cause a higher or lower conversion efficiency of a PV module than that measured at STC, inducing uncertainty in the assessment of the energy produced by a PV system operating outdoors. To isolate the influence of spectral distribution on PV performance, a constant temperature of the solar cells was assumed throughout the study.
The uncertainty induced by random changes in the solar radiation spectrum is not apparent, not being accessible to direct measurement. This is intuitively illustrated in Fig. 1, considering a crystalline silicon PV module with a generic spectral response (SRleft( lambda right))²⁷, provided by the Python Library PVLIB²⁸. (SRleft( lambda right)) is graphically presented in Fig. 1, being further used in all simulations performed in the study. Figure 1 shows two synthetic solar spectra, (G_{1} left( lambda right)) and (G_{2} left( lambda right)), generated at the same receiving surface tilt of 37° atmospheric optical mass m = 1.5 and aerosol type (α = 1.3, SSA = 0.93), but under different atmospheric conditions defined by different values for the turbidity (β = 0.031 for G₁ and β = 0.2935 for G₂), water vapor (w = 5 g/cm² for G₁ and w = 0.5 g/cm² for G₂), and ozone column content (l_O3 = 0.4 cm⋅atm for G₁, l_O3 = 0.17 cm⋅atm for G₂). The difference between the two spectra in Fig. 1 is visible to the naked eye. However, the solar irradiances, calculated by integrating the two spectra with respect the wavelength, have the same value: (intlimits_{{0.28,{mu m}}}^{{4,{mu m}}} {G_{1} left( lambda right)dlambda } = intlimits_{{0.28,{mu m}}}^{{4,{mu m}}} {G_{2} left( lambda right)dlambda } = 870,{text{W/m}}^{{2}}). Figure 1 also shows the effective spectral irradiances (G_{e1} left( lambda right) = G_{1} left( lambda right)SRleft( lambda right)) and (G_{e2} left( lambda right) = G_{2} left( lambda right)SRleft( lambda right)). It can be seen that G₁(λ) determines a PV effect greater than G₂(λ). More precisely, by performing the calculations, we obtain (intlimits_{{0.28,{mu m}}}^{{4,{mu m}}} {G_{1} left( lambda right)SRleft( lambda right)dlambda } = ,476.0;{text{W/m}}^{{2}}) and (intlimits_{{0.28,{mu m}}}^{{4,{mu m}}} {G_{2} left( lambda right)SRleft( lambda right)dlambda } = ,457.6;{text{W/m}}^{{2}}). Based on the definition of the spectral factor and Eq. (3), elementary calculations lead to the following conclusion: even if in these two distinct atmospheric conditions the solar irradiance is the same, the output power of the PV module roughly differs by 4%.
Standard solar irradiance (Gleft( lambda right)) under two different atmospheric conditions, the spectral response of a silicon solar cell (SRleft( lambda right))²⁷ and the effective spectral irradiance (Gleft( lambda right) cdot SRleft( lambda right)). The two atmospheric conditions share the same aerosol type (α = 1.3, SSA = 0.93), same atmospheric optical mass m = 1.5, receiving surface tilt of 37°, with different values for the turbidity (β = 0.031 for G₁ and β = 0.2935 for G₂), water vapor (w = 5 g/cm² for G₁ and w = 0.5 g/cm² for G₂), and ozone column content (l_O3 = 0.4 cm⋅atm for G₁, l_O3 = 0.17 cm⋅atm for G₂).
Synthetic spectra were generated with SMARTS2²³, a widely used and well-validated radiative transfer model²⁹. The version SMARTS 2.9.5 was used³⁰. SMARTS2 constitutes a reference model for PV spectral studies and is widely used to generate PV reference spectra¹⁶. This widespread use is motivated by validated accuracy with detailed input parameters, computational efficiency compared to more complex radiative transfer models, and the capability to compute global tilted spectral irradiance.
SMARTS2 simulates the solar radiation spectrum at ground level depending on several geometric (atmospheric optical mass) and atmospheric parameters (ozone column content, water vapor column content, atmospheric aerosol loading). Some of the parameters were kept constant throughout the study: atmospheric pressure 1013.25 mbar, loading the atmosphere with certain gases (O₃ (0.34 cm⋅atm), NO₂ (0.0002 cm⋅atm), CO₂ (370 ppm)) and aerosol asymmetry factor (0.7). SMARTS2 treats aerosols based on predefined models, such as Shettle and Fenn³¹, or by applying information about aerosol properties to the model input. In order to have better control over aerosol properties, in this study we chose the second option. Accordingly, aerosols were characterized by three varying parameters: Ångström turbidity coefficient β, Ångström exponent α and single scattering albedo SSA. Aerosol optical depth was calculated based on the well-known empirical Ångström formula³²: (tau_{a} left( lambda right) = beta lambda^{ – alpha }).
To estimate total solar irradiance on tilted surfaces, SMARTS2 utilizes isotropic transposition in the UV spectral band and anisotropic transposition in VIS and IR spectral bands²³. The model inputs for transposition are the solar zenith angle (corresponding to a certain atmospheric optical mass) and the solar azimuth angle (conditioned by the local geographical latitude). A common ground albedo ρ = 0.2 was assumed. This assumption is a simplification, in fact ground albedo is spectrally dependent. Since this study is focused on aerosol influence on SF, assuming a flat ground albedo removes a degree of freedom from the model. Always the PV module has been considered in Northen hemisphere and facing South. The computation was performed during the equinox day.
The influence of aerosols on spectral solar radiation can be studied from two basic perspectives: the aerosol nature and the aerosol loading of the atmosphere. The aerosol nature has the most complex influence. Classifying aerosols according to their physical properties is a difficult task. In this study, starting from the results in³³ we classified aerosols into five classes: marine (MA), desert dust (DD), mixed (MX), urban-industrial (UI) and biomass burning (BB). The classification was made based on two parameters: the Ångström exponent α (low α indicates a coarse mode while a high α indicates fine mode) and the single scattering albedo SSA (lower SSA means a more absorptive aerosol while higher SSA means a more reflective aerosol). The geometric loci that define these classes in the (α, SSA) plane are quite extensive, are not disjoint and the transition from one class to another is fuzzy (see the first frame in Fig. 5). An aerosol class can be defined by a representative point in the (α, SSA) plane (Table 1).
The study was conducted in two stages, with distinct targets. In the first stage, aerosol-induced changes in the solar radiation spectrum were simulated. Based on SF, the spectral mismatch was assessed for a generic crystalline silicon PV module operating in open air. The influence of aerosol quantity and characteristics on SF was evaluated in depth. In the second stage, from a more practical perspective, the impact of spectral mismatch on PV performance is analyzed with further focus on aerosols considering the location and placement of the PV module as well.
Comparative visual inspection is perhaps the simplest method for assessing the impact of different types of atmospheric aerosol on the solar radiation spectrum. Thus, Fig. 2 shows the spectra of solar radiation in the case of an atmosphere successively loaded with the five types of aerosols, defined by α and SSA from Table 1. All other atmospheric parameters were kept constant at the following values: m = 2, w = 1.42 g/cm² and β = 0.1. The wavelength was limited to the range of 300–1200 nm, corresponding to the absorption domain of crystalline silicon. Visual inspection of Fig. 2 shows that the shapes of the spectra are the same. When moving from one class of aerosols to another, the spectral irradiance changes, the change becoming more defined as the wavelength decreases. The highest values of spectral irradiance are recorded in an atmosphere loaded with aerosols of class MA, followed by increasingly lower values for loading with aerosols from classes DD, UI, MX and BB. The picture in Fig. 2 intuitively indicates a red-richer spectrum when moving from one aerosol class to another, starting with MA and ending with BB. The red-rich magnitude is evaluated in terms of weighted average wavelength (Lambda_{m} = {{hc} mathord{left/ {vphantom {{hc} {APE}}} right. kern-0pt} {APE}}), where h is the Planck’s constant, c is the speed of light and APE denotes the average photon energy in a spectrum (see e.g.³⁴). Table 1 displays the values of (Lambda_{m}), which all correspond to shades of red, and also the associated blue fraction BF values³⁴. APE and BF are defined in Appendix A. Since (Lambda_{m}) does not change significantly, the shades of red at the five wavelengths can hardly be distinguished by the standard human eye. Apparently, the variation of aerosols seems to have a minor influence on the spectral distribution of sunlight. And yet, aerosols deeply mark the spectral distribution of solar radiation, Fig. 3 shows the results of simulations of what an observer sees looking at the sky and the Sun when the atmosphere is successively loaded with each of the five types of aerosols. The simulations were performed estimating the direct-normal and diffuse solar spectral irradiances, which were then transformed into a representation of “what” the naked eye would see looking at the Sun or sky. For the purpose of this representation, the Sun’s brightness is considered low enough to observe its color, and the color of the sky is considered to be the same in all directions. The solar spectra utilized for the representation in Fig. 3 were generated with a step of 1 nm in the spectral band 360–830 nm. This range is defined in relation to the relative spectral sensitivity of human cone cells³⁵.
SMARTS2 simulated spectra for five different aerosol types: marine (MA), desert dust (DD), mixed (MX), urban-industrial (UI) and biomass burning (BB).
The colors seen by the normal human eye looking at the Sun (inner disk) and the sky (square area around the disk) under clear sky conditions. The simulations were made considering the atmosphere loaded with aerosols of five classes (marine (MA), desert dust (DD), mixed (MX), urban-industrial (UI) and biomass burning (BB). The following atmospheric parameters were considered: (a) atmospheric optical mass m = 2 and three values of the Ångström turbidity coefficient β = 0.03, 0.1, 0.3 and (b) m = 1.5, 3, 5 and β = 0.1. The other atmospheric parameters were kept at reference values.
Figure 3 gives the viewer a somewhat common picture of everyday experience: sunlight is white, and the sky is blue. As the atmospheric aerosol load increases, the solar disk becomes increasingly yellow and the sky a paler blue. Similarly, as the Sun descends toward the horizon, the color of the solar disk becomes yellow, orange, and near the horizon reddish. The merit of the simulation in Fig. 3 is that it shows us how different types of aerosols influence the color of sunlight. While marine aerosols and desert dust have a relatively small influence on the color of sunlight, the more absorbing aerosols of the urban-industrial and biomass burning classes have a much more pronounced influence. Changing the atmospheric load of aerosols causes significant changes in the color of the light. Even at moderate loading, β = 0.1, a simple visual inspection of Fig. 3b shows that changing the Sun elevation angle ((sin h{{ cong 1} mathord{left/ {vphantom {{ = 1} m}} right. kern-0pt} m})) causes a significant change of the colors of the Sun and the sky.
Let us now imagine that instead of the human eye we have a solar cell. This means that the relative spectral sensitivity of the eye is replaced with the relative spectral response of the PV cell. Extrapolating the previous analysis, it can be stated that just like the human eye a solar cell will perceive aerosol-induced changes in the solar radiation spectrum, with consequences in its performance. The results of our research on this topic are discussed next.
Before presenting these results, it is worth looking at the influence of the receiving surface’s tilt angle β_S on the spectral solar irradiance. The tilt angle is the angle between the solar collector surface and the horizontal plane. In particular, β_S is the angle at which a PV module is tilted with respect to the horizontal plane: β_S = 0° means that the PV module is placed horizontally while β_S = 90° means that the PV module is placed vertically. Figure 4 illustrates the solar total spectral irradiance estimated on tilted surfaces located at a latitude of 45°N, facing South, on the equinox day, at the Sun elevation angle h = 30°. The spectra are simulated under the following atmospheric conditions m = 2, l_O3 = 0.34 cm⋅atm, w = 1.42 g/cm², β = 0.2, α = 1.3 and SSA = 0.93. Figure 4 indicates that tilt angles in the 30°–60° range yield comparable spectral irradiance, while horizontal and vertical orientations result in pronounced spectral deviations. Figure 4 shows in its entirety that the spectral distribution of solar radiation is different on differently inclined surfaces. As a result, the tilt angle of the PV module must be considered in the SF analysis, and as will be seen below, it does have a substantial influence. This conclusion has been drawn before for monthly and yearly mean values of SF³⁶.
SMARTS2 simulated spectra showcasing the influence of a surface’s tilt angle β_S on the total spectral irradiance. The corresponding APE values are: 1.879 eV at β_s = 0°, 1.867 eV at β_s = 30°, 1.866 eV at β_s = 45° and β_s = 60°, and 1.871 eV at β_s = 90°.
Spectral factor can be viewed as a fairly accurate proxy for evaluating the influence of the solar radiation spectrum on the conversion efficiency of a PV module. In an intuitive representation, we have already shown that the atmospheric aerosol parameters significantly influence the in-plane components of the spectral solar irradiance. Taken together, these findings provide strong motivation for analyzing the dependence of SF on the atmospheric aerosols related to the atmospheric optical mass and the tilt angle of the PV module. We have conducted an extensive study on this topic; the main results being discussed below.
Figure 5 shows the impact of aerosol type on SF. The calculation was done assuming the mean Sun-Earth distance. The same typical values were considered for water vapor amount (w = 1.42 g/cm²) and ozone column content (l_O3 = 0.34 cm⋅atm). The two parameters α ((0.1 le alpha le 3)) and SSA ((0.6 le SSA le 1)) were uniformly discretized with a 30 × 30-node mesh. The two domains cover most of the possible physical values of SSA and α. The Ångström turbidity coefficient was assumed β = 0.2. While β seems quite high, this value was chosen to more noticeably illustrate the impact of the aerosol properties on SF. Figure 5 presents the results for six values of the atmospheric optical mass (m = 1, 1.5, 2, 3, 4, 5) and three inclinations of the PV module (horizontal, β_S = 45°, vertical). Regardless of the atmospheric optical mass, spectral losses are observed mainly on horizontal surfaces. As β_S increases, losses decrease. At β_S = 45°, the silicon solar cells are somehow spectrally immune, roughly recording neither spectral loss nor spectral gain (SF has values very close to 1). For vertical surfaces, significant spectral gain is observed, with a more pronounced effect at higher values of m. An important role in determining the magnitude of spectral gain/loss is played by the size of the aerosol particles. Thus, for a vertical PV module, at a given m, as coarse aerosol is replaced by fine aerosol (α increases), the spectral gain becomes increasingly greater. In the case of horizontal surfaces, the phenomenon is repeated but instead of gain, spectral loss is observed. This is a non-intuitive behavior, which can be expressed from another perspective as well: at some point, rotating a silicon PV module from horizontal to vertical position the spectral loss turns into gain and, the finer the aerosol, the greater the variation. Loading the atmosphere with desert dust (DD class) generally induces spectral losses. The aerosols from UI and BB classes influence SF in a more complex way, the gain or loss being determined by the other parameters (Fig. 5).
Contour plots showcasing the influence of single scattering albedo SSA and Ångström exponent α on the spectral factor SF in the case of a generic crystalline silicon PV cell²⁷. Each row corresponds to a tilt angle of the cell surface: β_{S =} 0°, 45° and 90°. In the first frame, the five classes of aerosols are roughly indicated in the (α, SSA) plane: marine (MA), desert dust (DD), mixed (MX), urban-industrial (UI) and biomass burning (BB).
The influence of water vapor w and the Ångström turbidity coefficient β on SF has been investigated too. Figure 6 illustrates the results for an atmosphere loaded with characteristic aerosols (SSA = 0.93 and α = 1.3), i.e. an aerosol located in the fuzzy area of overlap between the MX and UI classes. The variation domains of β (ranging from 0 to 0.5) and w (ranging from 0 to 5) were uniformly discretized with a 30 × 30-node mesh. The two ranges encompass most of the physically possible values of these two parameters. A quick look at Fig. 6 shows a similar picture to that in Fig. 5: horizontal surfaces record spectral losses (SF < 1), as β_S increases, the losses turn into spectral gain (SF > 1), reaching maximum in the case of vertical surfaces. For a horizontal PV module and lower values of m, w has the most significant effect on SF. For increasingly higher m, β begins to have a stronger effect. For a vertical PV module, the influence is contrary. At low values of m, β is the most influential parameter. As m increases, β’s dominance falls in favor of w.
Contour plots showcasing the influence of the Ångström turbidity coefficient β and the water vapor column content w[g/cm²] on the spectral factor SF. Each row corresponds to a tilt angle of the cell surface β_{S =} 0°, 45° and 90°.
A possible reason for the spectral gain being more pronounced for vertical surfaces is the shift in the direct-to-diffuse ratio of solar radiation components. Another contributing factor is the increased role of reflected irradiance. However, in the present model, the relationship between the spectral factor and the direct-to-diffuse ratio is complex and beyond the scope of this study.
Equation (3) suggests a pragmatic way to use SF in assessing the impact of atmospheric conditions on the efficiency of a PV module due to spectral mismatch. In the following, we present the results of our study on the influence of the position of the Sun in the sky (with atmospheric optical mass m as variable), the tilt angle of the module surface β_S, and atmospheric conditions (defined by the atmospheric water vapor and aerosol amount and type) on the efficiency of a PV module operating under clear sky conditions. Geographic location plays an important role in analysis. Latitude ϕ limits the range of variation of the Sun zenith angle and determines the azimuthal angle of the Sun at a given time, with consequences on SF.
The virtual experiment was conducted as follows. For the same generic PV module (with η_STC = 20%.), based on Eq. (3), the conversion efficiency under real operating conditions was approximated as a function of seven variables:
η was computed in 890,400 states from the 7D space, varying the model parameters to cover open-air operating conditions at four geographical latitudes: ϕ = 0° (267,120 states), 30° (222,600 states), 45° (222,600 states) and 60° (178,080 states). The values and ranges of the parameters in Eq. (4) are the following: β_S = 0…90° with 15° sampling; m = 1, 1.5, 2, 3, 4, 5; w = 0.1, 1, 2, 3, 4, 5 g/cm²; β = 0.001…0.2 with 0.022 sampling. The range (α, SSA), α = 0…2.5 and SSA = 0.72…1, was uniformly discretized with a rectangular mesh comprising 15 × 15 nodes. Each aerosol class was identified in the (α, SSA) plane, considering only disjoint sets. The ozone column content and aerosol asymmetry factor were considered constant at l_O3 = 0.34 cm⋅atm and g = 0.7, respectively. All 890,400 spectra were generated on the day of the equinox, at the average Earth-Sun distance.
Table 2 presents an elementary statistic of the PV module efficiency across aerosol classes. For each aerosol class, Fig. 7 summarizes the results in a boxplot representation. Each frame corresponds to one of the four latitudes. As the resulting boxplots exhibit a high degree of similarity, we investigated whether the mean efficiencies corresponding to the five considered aerosol classes differ significantly. To this end, we applied a one-way ANOVA test, which assesses the equality of means by comparing the variance between groups with the variance within groups. The results, summarized in Table 3, indicate that the mean efficiencies are not equal, thus confirming the presence of statistically significant differences among the aerosol classes. In all cases, the null hypothesis of equal means across aerosol classes is rejected (p < 0.001). To further identify which pairs of classes differ from each other, we performed Tukey’s post-hoc test, the results of which are provided in Table 4. The Tukey HSD test revealed that the differences in mean efficiencies between all aerosol-class pairs are statistically significant, with one exception: the pair MA—DD. A possible explanation for this may lie in the fact that both marine aerosol and desert dust belong to the coarse aerosol category, differing primarily in their optical properties, namely their non-absorbing vs. absorbing characteristics. The occurrence of coarse aerosols of marine and desert dust origin enhances performance at latitudes 30°, 45°, and 60°, such that the values of the three upper quartiles all surpass 20%. Conversely, at the equator (latitude 0°), the occurrence of fine aerosols originating from urban-industrial activities and biomass burning contributes to increased efficiencies.
Boxplot of the PV module efficiency across the whole dataset stratified according to the aerosol class (MA—marine, DD—desert dust, MX—mixed, UI—urban-industrial and BB—biomass burning) and geographical latitude: (a) (phi = 0^circ), (b) (phi = 30^circ), (c) (phi = 45^circ) and (d) (phi = 60^circ).
Naturally, we would be interested in identifying potential trends in the results. By examining Fig. 7 and Table 2, a slight increase in mean efficiency with latitude can be observed for MA, DD, and MX aerosols. In contrast, for fine aerosols such as UI and BB, a slight decrease in efficiency with latitude is noticeable. For these two aerosol classes (UI and BB), a larger dispersion in the PV efficiency is also observed, as indicated by the consistently higher standard deviation values (Fig. 7 and Table 2).
Finally, it is worth mentioning that the results of this study lend themselves to regional or even local assessments of the spectral mismatch consequence. China could serve as a good case study illustration. Recent data indicates that China accounts for about 60% of new global PV capacity installed in 2024³⁷. The findings of this study show that at latitudes between 30° and 60°, higher turbidity caused by fine urban-industrial and biomass burning aerosols leads to reduced efficiency. Considering China’s geographic location, and the occurrence of pollution episodes, aerosols of the biomass burning and urban-industrial classes can be relevant in describing the operation of large PV plants. Increasing turbidity correlates with a reduction in PV efficiency, therefore during pollution episodes, a generic PV plant will also have reduced efficiency coupled with a lower amount of solar irradiance. Results also show that increasing the receiving surface tilt angle generally corresponds to higher PV efficiency values. This is particularly relevant for BIPV facades, usually vertical or near vertical surfaces, where higher spectral gain is mostly accompanied by lower PV power production. A higher spectral gain for a bandgap similar to that of silicon, corresponding to a vertical facade compared to 35° tilt angle, has been reported in ³⁶ for the annual mean as well as for most monthly averages, based on radiometric data from Berlin in 2020.
A PV module normally operates in an open-air environment, where the solar radiation spectrum rarely meets the standard AM1.5G characteristics (spectral mismatch). Since the composition of the atmosphere is constantly changing, the efficiency of PV modules operating open-air is also constantly changing, becoming a hidden source of uncertainty in the evaluation of PV plants’ performance. This study evaluated a possible impact of spectral mismatch on PV performance. Since silicon PV modules dominate the current market, the study focused on this technology. In the first part, the effect of spectral mismatch was studied through the spectral factor SF. In the second part, the direct effect on PV efficiency was evaluated.
In general, all parameters from location, position of the Sun in the sky to the atmospheric content influence SF more or less, leading to spectral gain or loss. Spectral losses are observed mainly when PV modules are placed on horizontal surfaces. As the PV module inclination angle β_S increases, losses decrease. For vertical surfaces, significant spectral gains (up to 15%) are observed under certain atmospheric conditions. When the atmosphere is loaded with mixed aerosol, SF appears less affected by changes in β_S and m. For quantitative details, the reader is pointed to the Supplementary Information file. Loading the atmosphere with desert dust largely induces spectral losses at low atmospheric optical mass (according to Fig. 5, roughly m < 2) or lower latitudes (close to equator, according to Table 2). Finer aerosols from urban-industrial and biomass burning classes intricately influence SF, the spectral gain/loss being determined by the combination with other atmospheric parameters. The analysis performed highlights non-intuitive effects. The spectral loss turns into gains as the rotation of a silicon PV module changes from horizontal to vertical position, the finer the aerosol, the greater the variation in SF. This preliminary study suggests that the ratio between the diffuse and direct components of solar radiation may act as a proxy in the relationship between the tilt angle and the spectral factor. Future work will focus on a more detailed analysis of this correlation.
In general, for a crystalline silicon PV module, depending on the tilt angle, the aerosol-induced spectral mismatch causes a gain or loss in PV efficiency, within a rough margin of 10%. Marginal loss can be recorded under even mild conditions: small tilt angle, the Sun close to the horizon and an atmosphere moderately loaded with fine absorbing aerosol.
A deeper analysis of the results would be beyond the scope of this paper. Those interested in the impact of spectral mismatches on PV performance under specific atmospheric and environmental conditions may find answers in the detailed statistics analysis from the Supplementary Information file.
The results regarding the impact of atmospheric aerosols on the spectral factor are of a general nature, as the study was conducted without introducing simplifying assumptions. With respect to the application of these results to PV performance, the analysis was performed under the assumption that the voltage at the maximum power point of a solar cell current–voltage characteristic varies negligibly with changes in the solar spectrum. In the near future, a dedicated study will be conducted to analyze the detailed impact of spectral mismatch on both the conversion efficiency and output power of a PV power plant, without relying on this simplifying assumption. As in the present study, the analysis will be carried out as a function of atmospheric parameters, with an emphasis on aerosol-related properties. Another limitation worth noting is that the present study considered only crystalline silicon technology, which currently represents the dominant share of the PV market. Future work will extend the present analysis to other emerging PV technologies.
The datasets generated and analyzed during the current study are available from the corresponding author on reasonable request.
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Faculty of Physics, West University of Timisoara, 300223, Timisoara, Romania
Sergiu-Mihai Hategan, Eugenia Paulescu & Marius Paulescu
Institute for Advanced Environmental Research, West University of Timisoara, 300086, Timisoara, Romania
Sergiu-Mihai Hategan
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S-M.H. and M.P. developed the research concept, S-M.H., E.P. and M.P. performed data analysis and interpretations, S-M.H. prepared computer codes, tables and figures, S-M.H., E.P. and M.P. wrote the main manuscript text. All authors reviewed the manuscript.
Correspondence to Eugenia Paulescu.
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The average photon energy (APE) is expressed as:
where (Gleft( lambda right)) [W/m²µm] is the spectral irradiance in the wavelength interval (left[ {lambda_{1} ,,lambda_{2} } right]) and (Phi left( lambda right) = {{lambda Gleft( lambda right)} mathord{left/ {vphantom {{lambda Gleft( lambda right)} {hc}}} right. kern-0pt} {hc}}) is the spectral photon flux density. q [C] denotes the elementary charge, h [Js] denotes Planck’s constant and c [m/s] is the speed of light. For crystalline silicon, the wavelength interval [0.35 µm, 1.05 µm] was considered in APE calculation.
The blue fraction (BF) is expressed as:
where (lambda_{B}) delimit the bluer and the redder parts of the solar radiation spectrum in the wavelength interval (left[ {lambda_{1} ,,lambda_{2} } right]). The standard value for crystalline silicon is considered (lambda_{B} = 0.65;{mu m}).
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Hategan, SM., Paulescu, E. & Paulescu, M. Atmospheric aerosol effects on spectral mismatch and the resulting uncertainty in photovoltaic performance. Sci Rep 16, 5339 (2026). https://doi.org/10.1038/s41598-026-36144-7
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Received: 01 July 2025
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Published: 16 January 2026
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DOI: https://doi.org/10.1038/s41598-026-36144-7
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