1 Introduction

Solar geoengineering, which refers to the deliberate alteration of the Earth’s climate with the aim of countering human-induced climate change, has attracted considerable attention as a prospective remedy for the slow progress in reducing greenhouse gas emissions. Despite ongoing efforts to mitigate and adapt to climate change, concerns persist regarding insufficient reductions in emissions (Ming et al., 2014; Burnell, 2021). The primary goal of solar geoengineering is to mitigate climate change by redirecting some of the incoming solar radiation away from the Earth’s atmosphere, incorporating various methods like introducing aerosols into the stratosphere, brightening marine clouds, utilizing space-based approaches, altering surface albedo, and reducing cirrus clouds. Nevertheless, these techniques pose distinct challenges and uncertainties, including potential effects on the ozone layer, regional climates, and precipitation patterns. A crucial consideration is the potential impact on the generation of photovoltaic (PV) energy, particularly in regions like Nigeria that heavily rely on solar power (Niu et al., 2023). Previous research suggests that solar geoengineering has the potential to impact the production of PV energy by decreasing the amount of solar radiation that reaches the Earth’s surface. However, the extent of this impact varies depending on factors such as location, PV technology, and the specific geoengineering approach. While some regions may experience a modest reduction in PV energy output, the effects are complex and necessitate further research to better understand the risks and benefits associated with solar geoengineering in the study of energy transition and climate policy decisions (Mitchell & Finnegan, 2009; Murphy, 2009).

Several studies have explored the potential impacts of solar geoengineering on photovoltaic energy generation. Caldeira et al. (2013) revealed that solar geoengineering could reduce solar radiation reaching the Earth’s surface, thereby diminishing available energy for PV systems, with regional variations. Kravitz et al. (2013) proposed solar geoengineering as a means to mitigate climate risks associated with rising greenhouse gasses. Li et al. (2022) found mixed effects in China, with certain regions experiencing negative impacts on PV generation while others saw benefits. Irvine (Keith & Irvine, 2016; Irvine et al., 2017) highlighted the significant potential impact on PV energy, especially in high-solar-radiation regions, emphasizing the need for further research. MacMartin et al. (2018) showed that solar geoengineering could decrease solar radiation in the USA, affecting PV energy output, contingent on location, and PV technology. Ricke et al. (2013) stressed the necessity of additional research on solar geoengineering’s effects on energy systems. Irvine et al. (2019) used a global model to show that solar geoengineering would reduce solar radiation and PV energy output across regions, with variations. Meanwhile, recent studies such as Yasmeen et al. (2023b, 2023a); Shah et al. (2022, 2023a, 2023b, 2024) on transition of energy from 2020 and above mainly focused on energy efficiency, productivity, and sustainable development without exploring the impact of solar radiation management on the sustainable energy generation. While these studies contribute valuable insights, a comprehensive investigation specific to Nigeria is lacking. This research aims to fill this gap by focusing on the potential impacts of solar radiation management (SRM), specifically stratospheric aerosol injection, on PV energy in Nigeria.

The objectives of this present study include computing the PV energy potentials using observed and simulated solar radiation and temperature data, comparing the agreement between PV energy potentials from observed and simulated data under SRM scenarios using verifying metrics (the bias, correlation, index of agreement and root mean square errors), and evaluate the projecting impact of stratospheric aerosol injection on PV energy potentials from 2035 to 2069 in Nigeria. This will enhance the assessment of the degree of reduction in energy output and understanding regional variations. The innovative contribution of this study lies in its emphasis on a region that heavily relies on solar power and its potential to provide valuable discoveries for making energy and climate policy decisions. By providing a comprehensive understanding of the impacts of solar geoengineering on photovoltaic energy generation in Nigeria, the study will assist stakeholders in transitioning to sustainable energy systems and addressing the challenges of climate change. The findings are expected to have broader implications for regions that heavily depend on solar energy, contributing to a more comprehensive understanding of the intricate dynamics between solar geoengineering and renewable energy sources.

2 Materials and methods

2.1 Data sources and acquisition

In this study, reference data (air temperature and solar radiation) were sourced from the Modern-Era Retrospective analysis for Research and Applications, version 2 (MERRA-2) database repository at a high-resolution grid system at 0.25 \(\times\) 0.25 resolution spanning 33 years (1990–2022) across four climatic regions in Nigeria as shown in Fig. 1. The detailed description of the MERRA-2 data repository can be found in Ojo (2023); Gelaro et al. (2017). Also, air temperature and solar radiation data simulated under stratospheric aerosol injection (SAI) solar geoengineering approach were obtained from the ARISE-SAI 1.5 model, spanning the period from 2035 to 2070. The Assessing Responses and Impacts of Solar Climate Intervention on the Earth System with Stratospheric Aerosol Injection (ARISE-SAI) initiative aims to simulate plausible SAI deployment and assess Earth system responses at a level approximately 1.5\(^{\circ }\)C above pre-industrial values, aligning with climate change mitigating objectives (Richter et al., 2022). The simulations involve introducing stratospheric aerosols at approximately 21 kilometers in 2035 at specified latitudes (15\(^{\circ }\)S, 15\(^{\circ }\)N, 30\(^{\circ }\)S, 30\(^{\circ }\)N) within a grid box at 180\(^{\circ }\) longitude and 21.6 km altitude, with annual injection amounts controlled by a sophisticated algorithm (MacMartin et al., 2014, 2018; Kravitz et al., 2013). The geographical location of the study, Nigeria, is situated within these specified geographical coordinates, thus rendering the study of utmost importance.

Fig. 1
figure 1

A climatic map of Nigeria (Ojo, 2021)

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2.2 Data analysis

Photovoltaic energy (PVE) was evaluated from the air temperature (Ta) and solar radiation obtained from MERRA-2 and ARISE-SAI-1.5 models using the empirical models given by Notton et al. (2005); Antonanzas et al. (2016) as:

$$\begin{aligned} PVE = G_S \times \eta _c \end{aligned}$$
(1)

where \(G_s\) is the surface solar radiation and \(\eta _c\) is the electrical resistance given as:

$$\begin{aligned} \eta = \eta _{\text {ref}} \left[ 1 - \beta _{\text {ref}} \left( T_{\text {c}} - T_{\text {ref}}\right) + \gamma \log _{10} G_s \right] \end{aligned}$$
(2)

\(\eta _{\text {ref}}\) is the electrical efficiency of the battery at a reference temperature of \(T_{\text {ref}}\) = 25\(^{\circ }\)C (Krauter et al., 1999) with solar irradiance of 1000 \(Wm^{-2}\); \(\beta _{\text {ref}}\) is the temperature coefficient given as:

$$\begin{aligned} \beta _{\text {ref}} = \frac{1}{{T_{\text {o}} - T_{\text {ref}}}} \end{aligned}$$
(3)

and \(T_o\) is the temperature when the electrical efficiency of the PV module is reduced to 0, and the value is 0.004 \(k^{-1}\) (Hegazy, 2000). \(T_c\) is the photovoltaic cell temperature determined by the external environment given as:

$$\begin{aligned} T_c = T_a + (T_{\text {noct}} - T_{(a, \text {noct})}) \times G_s \times G_{\text {noct}} \end{aligned}$$
(4)

\(T_(noct)\) is the standard cell temperature when the solar irradiance is 800 \(Wm^{-2}\), the wind speed is 1 m/s, ambient temperature is 25 \(^oC\), and \(\eta\) = 0; \(T_(a,noct)\) is 20 \(^oC\); \(\gamma\) is the radiation coefficient determined by the material properties, usually 0.12. Furthermore, the impact of solar radiation management (SRM) on photovoltaic energy potential (PVE) was evaluated using, correlation coefficient (R), index of agreement (d), mean bias error (MBE), and root of mean square errors (RMSE) between the MERRA-2 and ARISE-SAI 1.5 PVEs given by:

$$\begin{aligned} R = \frac{n\sum PVE_{\text {ref}} \cdot PVE_{\text {srm}} - (\sum PVE_{\text {ref}})(\sum PVE_{\text {srm}})}{\sqrt{n(\sum PVE_{\text {ref}}^2) - (\sum PVE_{\text {ref}})^2} \cdot \sqrt{n(\sum PVE_{\text {srm}}^2) - (\sum PVE_{\text {srm}})^2}} \end{aligned}$$
(5)
$$\begin{aligned} d = 1 - \frac{\sum \nolimits _{n-1}^{n} (PVE_{\text {srm}} - PVE_{\text {ref}})^2}{\sum \nolimits _{n-1}^{n} [(PVE_{\text {srm}} - \bar{PVE}_\text {ref}) + (PVE_{\text {ref}} - \bar{PVE}_\text {ref})]^2} \end{aligned}$$
(6)
$$\begin{aligned} MBE = \frac{1}{n} \sum \limits _{i=1}^n (PVE_{\text {srm}} - PVE_{\text {ref}}) \end{aligned}$$
(7)
$$\begin{aligned} RMSE = \sqrt{\frac{1}{n} \sum \limits _{i=1}^n (PVE_{\text {srm}} - PVE_{\text {ref}})^2} \end{aligned}$$
(8)

where \(PVE_{ref}\) is the photovoltaic energy generated from the MERRA-2 datasets in \(Wh/m^2\), \(PVE_{srm}\) is the photovoltaic energy stimulated from the ARISE-SAI-1.5 datasets in \(Wh/m^2\), and n is the number of observations. Bias quantifies disparities in photovoltaic energy potential (PVE) between MERRA-2 and ARISE-SAI-1.5 datasets, visually analyzed using box plots where a mid-line close to zero signifies minimal bias. mean bias Error (MBE) values being positive or negative indicate overestimation or underestimation of PVE due to solar radiation management (SRM). In contrast, the correlation coefficient assesses the strength and direction of the linear relationship between reference and stimulated PVE. A value of +1 indicates a perfect positive correlation, 0 indicates no correlation, and − 1 indicates a perfect negative correlation. The index of agreement evaluates the agreement between reference and stimulated PVE, with higher values indicating better agreement. Additionally, the root mean square error (RMSE) is used for predictive model accuracy, with RMSE sensitive to larger errors and outliers, and a zero value of RMSE is desirable or a lower value in case of comparison (Willmott et al., 2012; Ojo & Adeyemi, 2020; Pradeep et al., 2022).

3 Results and discussion

Figure 2a–d presents the bias distribution between solar radiation management (SRM) and referenced photovoltaic energy (PVE) across four climatic regions in Nigeria using boxplots. The middle line of the boxplot represents the mean bias errors (MBE) between SRM and referenced PV energy, with a desirable value of zero. In the Sahel region, all seventeen studied stations showed positive MBE, indicating an excess of photovoltaic energy if the SAI approach of SRM is implemented. Some stations, such as Biu, Birni-Nkonni, Gaya, Jega, Maradi, Sokoto, and the entire Sahel zone, demonstrate lower MBE values closer to zero, suggesting minimal deviation between SRM-predicted PVE and the reference data. Similarly, in the Guinea Savannah region, all stations have MBE values closer to zero, particularly Makurdi, Kanji, and Minna, which have almost zero values. This implies a strong agreement between SRM and reference PV energy in the region. In the rainforest region, all MBE values were positive, with stations like Abeokuta, Ibadan, and Lokoja showing almost zero values of MBE, indicating reasonable agreement between SRM and reference PV energy. However, in the coastal region, both positive and negative MBE values were observed. Among the nine studied stations, only three have positive MBE, with Asaba and Calabar having almost zero MBE values. Meanwhile, the remaining six stations have negative MBE values, with Aba, Uyo, and Yenegoa having slightly less than zero MBE values. This suggests that the ARISE-SAI-1.5 model generally provides relatively accurate PV energy predictions in those stations. However, the presence of outliers in the Sahel and coastal regional stations, in both positive and negative whiskers, highlights the need for appropriate regional bias-corrections to standardize the PV energy values from the ARISE-1.5 models. These findings contribute to the understanding of the impact of SRM on PV energy accuracy and regional variations.

Fig. 2
figure 2

Distribution of bias between SRM and referenced data on photovoltaic energy in a Sahel, b Guinea, c rainforest, and d coastal over Nigeria

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Figure 3a–d illustrates the comparison of correlation coefficients between solar radiation management (SRM) stimulated and reference photovoltaic energy (PVE) across four climatic regions in Nigeria. The correlation coefficients indicate the extent of the linear relationship between SRM-stimulated PV energy and the reference data. The figures revealed that the correlation coefficient between SRM and reference PV energy is below 0.20 in all four climatic regions. These values signify that the linear relationship between SRM and reference PV energy is relatively weak in all regions, accounting for less than 20% of the variability of PV energy. This observation is supported by the presence of scattered noisy points in Fig. 4a–d instead of the expected linear and orderly patterns. It is essential to note that such low correlation coefficients suggest that the variations in PV energy are influenced by numerous factors going beyond linear relationships, including local climate, geographical attributes, and environmental dynamics. This observation further underscores the understanding that estimating PVE is a complex process, particularly under SRM scenarios, and cannot be solely ascribed to linear dependencies. Previous literature has also emphasized the limitations of linear models in capturing the intricate and multifaceted nature of PV energy variations (Perpiñán et al., 2008; Dirnberger et al., 2015; Boegli & Stauffer, 2017; Boretti et al., 2020). Consequently, these results show the need for more advanced and comprehensive modeling techniques that can account for non-linear factors and regional variations to enhance the accuracy of PVE predictions.

Fig. 3
figure 3

Comparison of photovoltaic energy in a Sahel, b Guinea Savannah, c rainforest, and d coastal region over Nigeria using the correlation coefficient

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Fig. 4
figure 4

Linear relationship of SRM and MERRA-2 photovoltaic energy in a Sahel, b Guinea Savannah, c rainforest, and d coastal region over Nigeria

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Figure 5a–d presents a comparison of the index of agreement (d) between solar radiation management (SRM) and referenced photovoltaic energy (PVE) across four climatic regions in Nigeria. The index of agreement is particularly valuable when assessing the relationship between two variables that exhibit non-linear behavior, as acknowledged by previous studies (Willmott et al., 2012; Ojo, 2023). The figures revealed that, in all the selected stations across the four regions, the values of index of agreement exceed 0.8, except in Lagos and Port Harcourt. Comparing Fig. 5a–d with Fig. 3a–d, it became evident that the index of agreement values is notably higher than those of the correlation coefficient. This observation supports the fact that the relationship between SRM and referenced photovoltaic energy is predominantly non-linear, with the index of agreement indicating substantial agreement between the two datasets, exceeding 80%. This shows the importance of considering non-linear relationships when evaluating the impact of SRM on photovoltaic energy predictions, especially in diverse climatic regions like Nigeria.

Fig. 5
figure 5

Comparison of SRM and historical photovoltaic energy in a Sahel, b Guinea, c rainforest, and d coastal over Nigeria using index of agreement

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Figure 6a–d presents a comparison of the root mean square error (RMSE) between solar radiation management (SRM) and referenced photovoltaic energy (PVE) across some selected stations in the four climatic regions in Nigeria. These RMSE values, measured in watts per squared meters, reveal show the accuracy of PV energy predicted by ARISE-SAI-1.5 model compared with the reference data, in which lower value is desirable. On a regional average assessment, observation showed average RMSE values of 16.50 in the Sahel region, 21.50 in the Guinea Savannah region, 20.50 in the rainforest, and 15.50 in the coastal region. These results reveal the importance of subjecting the SRM models to specific and appropriate error-correcting tests based on climatic conditions to optimize the accuracy of PV energy predictions under climate change control mechanisms.

Fig. 6
figure 6

Comparison of SRM and historical photovoltaic energy in a Sahel, b Guinea, c rainforest, and d coastal over Nigeria using the root of mean square errors

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Figure 7a–d shows the projected future changes in photovoltaic energy potential (PVE) predicted between 2035 and 2070 by the ARISE-SAI-1.5 model under the solar radiation management (SRM) scenario across four climatic regions in Nigeria. These changes were assessed by evaluating the differences between SRM-simulated PV energy and historical PV energy values in watts per squared meters, to investigate the potential impacts of stratospheric aerosol injection (SAI) as an approach for mitigating climate change in those regions. Positive and negative values of projected changes indicate increases and decreases in PV energy values resulting from SRM implementation respectively. Notably, the figures revealed positive projected change values in PV energy across all selected stations and the entire Sahel region, with a maximum change of 8.7 ± 1.5 observed in Mubi and a minimum change of 1.0 ± 1.5 in Gaya, yielding a regional average change of 5.0 ± 1.2 (Fig. 7a). In the Guinea Savannah region, positive changes in PV energy are predominant, particularly in Jos with a maximum change of 16.5 ± 2.0 and a regional average change of 3.5 ± 2.0, although Kanji and Minna exhibited negative changes of − 1.5 ± 2.0 and − 2.5 ± 2.0, respectively (Fig. 7b). Meanwhile, the rainforest region showed uniformly positive PV energy changes across all its stations, with Ido-Ekiti showing the highest change of 6.8 ± 1.9 and Abeokuta having the lowest change value of 0.5 ± 1.3, contributing to a regional average change of 3.0 ± 1.8 (Fig. 7c). In contrast, the coastal region showed more diverse patterns, with positive PV energy changes in some stations like Asaba, Calabar, and Ebonyi, with Ebonyi showing the highest positive change of 4.0 ± 2.0. However, six stations and the entire coastal region exhibited negative projected changes, with Port Harcourt recording the highest negative change value of − 11.2 ± 1.3 and an overall regional average change of − 3.0 ± 1.4 (Fig. 7d). These analyses collectively suggest that while SRM application may lead to PV energy increases in the Sahel, Guinea Savannah, and rainforest regions, it could also result in PV energy decrease in several other coastal stations, indicating the importance of region-specific strategies when considering implications of solar radiation management for photovoltaic energy potential in Nigeria.

Fig. 7
figure 7

Projected impact of Solar Geoengineering on photovoltaic energy in a Sahel, b Guinea, c rainforest, and d coastal over Nigeria

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4 Conclusion

The study extensively investigated the performance of the ARISE-SAI-1.5 model in evaluating the effects of solar radiation management (SRM) on the potential of photovoltaic energy (PVE) in Nigeria. The analysis revealed variations in PV energy estimation specific to each region, indicating the potential impact of SRM implementation on solar energy production as an approach for climate change mitigation efforts. The index of agreement consistently demonstrated a strong correlation between SRM-simulated and reference PV energy in several regions, although complexities were observed in the coastal region, highlighting the importance of tailored SRM strategies for oceanic areas. The findings from the root mean square error analysis also pointed out regional differences in prediction accuracy. Future projections under SRM scenarios showed potential increase in the Sahel, Guinea Savannah, rainforest, and some selected coastal areas, emphasizing the need to consider regional variability. These findings have significant implications for Nigeria’s renewable energy sector, suggesting that SRM could be a promising approach to enhance PV energy generation in the face of changing climate conditions. However, the study acknowledges its limitations in terms of regional focus and recommends extending research to other African countries. It also shows the importance of incorporating local factors that influence photovoltaic energy potential and assessing the broader socio-economic and environmental impacts of solar radiation management strategies. Furthermore, the study proposes conducting long-term spatial variation studies to evaluate the sustained benefits and potential risks of SRM by providing valuable information for informed decision-making in Nigeria’s sustainable advancement of renewable energy utilization.