Nonlinear Drivers and Volatility of Solar Radiation Variability in Asian Megacities: A Functional Time-Series Approach

Nonlinear Drivers and Volatility of Solar Radiation Variability in Asian Megacities: A Functional Time-Series Approach | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Nonlinear Drivers and Volatility of Solar Radiation Variability in Asian Megacities: A Functional Time-Series Approach Md. Rakib Hasan Sarker, Farjana Akter This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7807830/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Solar radiation is a significant renewable energy source, but its variability in Asian megacities is driven by advanced meteorological drivers that are poorly represented by traditional linear models. This study employs a functional time series method to investigate the nonlinear drivers and volatility of solar variability in five typical cities Dhaka, New Delhi, Jakarta, Manila, and Kuala Lumpur from July 2016 to June 2025. Solar irradiance was represented as continuous daily curves with functional data analysis (FDA), and the first three components explained more than 97% of the variance with functional principal component analysis (FPCA). Seasonal clustering indicated monsoon-dominated regimes for New Delhi, Manila, and Dhaka, and equatorial stability for Kuala Lumpur and Jakarta. Threshold and nonlinear modelling indicated city-specific tipping points: rainfall (~43 mm) for Dhaka, humidity (~48%) for New Delhi, wind (~4 m/s) for Jakarta, and precipitation (~108 mm) for Manila. Volatility analyses via GARCH-family models confirmed clustering and persistence, with EGARCH capturing the asymmetric effects of negative shocks. VAR impulse–response functions demonstrate that precipitation shocks cause immediate but transitory reductions in solar returns. These findings demonstrate that solar variability over Asian megacities is controlled by nonlinear thresholds and clustered volatility and has implications for forecasting, grid integration, and climate-resilient energy planning. Solar radiation variability Functional data analysis (FDA) Functional principal component analysis (FPCA) GARCH-family models Volatility clustering Threshold autoregressive (TAR) models Smooth transition autoregressive (STAR) models Vector auto regression (VAR/VARX) Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Figure 15 Introduction Background and Context Solar radiation is the foundation of the Earth's climate system and one of the most promising renewable energy sources(Huang et al., 2021 ). Its variability determines energy system reliability, climate feedback mechanisms, and policy decisions regarding sustainable development(Krūmiņš & Kļaviņš, 2023). In Asia, where megacities are undergoing rapid urbanization and industrialization, solar radiation is influenced by multiple interacting drivers, such as air pollution, monsoon cycles, tropical cyclones, and regional climate variability(Huang et al., 2021 ; Qian et al., 2022 ). These factors create complex patterns that complicate the stability and predictability of solar energy production.(Hou et al., 2021 ). Consequently, the application of sophisticated statistical methodologies, such as functional time series models and generalized autoregressive conditional heteroskedasticity processes, becomes imperative for accurately characterizing these complex dynamics (Euán et al., 2022 ). Accurate characterization of solar variability is crucial not only for energy planning but also for climate risk analysis in highly populated regions(Huang et al., 2020 ). Traditional approaches, which rely on linear regression models or mean climatological approximations, fail to capture nonlinear dynamics, abrupt regime shifts, and volatility clustering under realistic meteorological conditions(Yu et al., 2020 ). This limitation promotes the integration of functional time series methods, where solar radiation is treated as continuous curves with nonlinear and volatility frameworks, which reveal threshold effects and uncertainty patterns(Huang et al., 2020 ). This approach offers a significant improvement over traditional metrics, which often fail to isolate stochastic fluctuations from deterministic trends, by providing a normalized, dimensionless measure of variability that accounts for temporal dependencies (Voyant et al., 2025). Our comparative analyses demonstrate that such sophisticated models proficiently encapsulate multi-scale fluctuations, addressing significant limitations inherent in traditional metrics (Voyant et al., 2025). Research Problem and Objectives Despite the growing body of literature on solar energy, there remains a critical gap in the representation of the nonlinear and functional characteristics of solar variability in Asian megacities(Pandey et al., 2022 ). Existing studies tend to disregard the daily functional form of solar radiation, neglect the nonlinear threshold behavior of meteorological drivers, and fail to adequately quantify volatility clustering in the presence of extreme weather events(Qian et al., 2022 ). Therefore, policymakers and energy planners do not have useful tools for high-resolution forecasting and risk planning(Huang et al., 2021 ). To address this gap, the present study pursues the following objectives: 1. Functional Representation of Solar Radiation Dynamics Solar radiation components are modelled as continuous daily curves (from sunrise to sunset), and dominant modes of variability across different climatic regimes via functional data analysis (FDA), functional principal component analysis (FPCA), and functional clustering. 2. Identification of Nonlinear and Threshold Drivers To examine how meteorological variables—including temperature, humidity, wind, precipitation, and pressure—act as nonlinear or threshold-dependent drivers of solar variability, threshold autoregressive (TAR), smooth transition autoregressive (STAR), and functional regression approaches are used. 3. Modelling the Volatility and Uncertainty in Solar Energy To capture volatility clustering and quantify uncertainty in solar radiation and energy production, particularly under monsoon conditions and extreme weather events, through GARCH-family models, VAR/VARX structures are used. Research Gap and Significance While the literature has provided excellent insights into mean solar trends and climatic effects(Huang et al., 2020 ), there are three important gaps. • Functional representation: Few studies have used the FDA to represent solar radiation as continuous curves, despite its apparent advantages in capturing intraday dynamics(Hou et al., 2021 ; Huang et al., 2020 ). • Nonlinear drivers: Nonlinear thresholds caused by meteorological variables, such as spikes in humidity during monsoons or sudden temperature drops during storms, are less studied(Bowden et al., 2023 ). • Uncertainty and volatility: Existing models inadequately represent volatility clustering, which is vital for solar energy planning in monsoon-variable and extreme weather-prone areas(Kim et al., 2021 ). By addressing these gaps, this study offers methodological novelty and practical relevance. These findings will enhance the predictive capacity for solar energy production and guide climate-resilience planning. In addition, the study focuses on five representative Asian megacities—New Delhi (India), Dhaka (Bangladesh), Jakarta (Indonesia), Manila (Philippines), and Kuala Lumpur (Malaysia)—chosen on the basis of their diverse climatic regimes, which span from monsoon-influenced to tropical and equatorial systems(Nik et al., 2020). The comparative multicity design ensures that the results are not only statistically reliable but also regionally relevant, making them more useful for energy policy and climate adaptation planning. Literature Review Review of Related Studies Solar radiation has been widely studied because of its central role in solar energy development, climate science, and atmospheric modelling(Gürel et al., 2023 ; Huang et al., 2021 ). Early research mainly employed statistical regression and climatological means to estimate the solar energy potential by region(Obaideen et al., 2023). Although these approaches provide adequate baseline information, they are incapable of capturing the intraday complexity and nonlinear dynamic characteristics of solar radiation variability(Quansah et al., 2022 ). Studies in South Asia and Southeast Asia have highlighted the extent to which seasonal monsoon regimes and tropical climatic conditions strongly affect solar radiation(Mol et al., 2023 ). For example, rainforests and humidity produced by monsoon-induced rains in cities such as Dhaka and Manila reduce solar irradiance significantly during rainy seasons(Yang et al., 2022 ), whereas air pollution and temperature variability in cities such as New Delhi further add variability(Tan et al., 2023 ). Experiments conducted in equatorial regions, such as Kuala Lumpur and Jakarta, emphasized the persistent influence of cloud cover in modulating solar cycles(Baghel & Chander, 2022 ). However, most such studies have utilized mean-value models and overlooked threshold effects and abrupt regime shifts in solar behavior(Correa et al., 2022 ). New technological developments in time series modelling have introduced ARIMA, ANN, and VAR-based solar forecasting models(Velásquez, 2022). These methods improve short-term forecasts but are still limited in handling the functional and nonlinear characteristics of solar data(Barhmi et al., 2024 ; Fara et al., 2021). Moreover, the dynamics of volatility clustering, where periods of high solar variability are followed by prolonged instability, have only recently begun to be Addressed, and some examples of GARCH-type models have appeared in renewable energy studies(Zaffar, 2021). More promising have been the series of literature streams that have resulted from the use of functional data analysis (FDA). The FDA allows solar radiation to be treated as continuous daily curves(Fara et al., 2021), allowing for the extraction of leading modes of variability with techniques such as functional principal component analysis (FPCA)(Jiao et al., 2023 ). In addition, threshold autoregressive (TAR) and Smooth Transition Autoregressive (STAR) models have been found to be useful in extracting nonlinear regime-dependent dynamics from environmental and energy systems(Hoffmann et al., 2020 ). However, the FDA, nonlinear drivers, and volatility modelling remain underdeveloped in the solar literature, particularly for Asian megacities with the most intense climatic variability(Pandey et al., 2022 ). Theoretical Framework The theoretical underpinning of this study is a multilayered theoretical framework that integrates functional, nonlinear, and volatility frameworks to fully account for solar variability. The three strands of this complementary framework are outlined as follows: 1. Functional Data Theory (FDA and FPCA) Solar radiation observations are operated as continuous curves rather than discrete points(Stefani et al., 2024 ). This study provides a means to identify leading patterns of intraday variability and compare climatic regions(David et al. 2016 ). Clustering of solar profiles, whereby days or regimes can be grouped, is provided(Santiago et al., 2021). 2. Nonlinear Time-Series Theory (TAR/STAR and Functional Regression) This is because solar variability is not linear but regime-dependent(Zafar et al., 2021 ). TAR models identify abrupt threshold effects, such as sharp radiation reductions during heavy precipitation(Zwaard et al., 2021). STAR models enable smooth transitions between states (e.g., from clear sky to overcast) in accordance with real atmospheric processes(Dash et al., 2023 ). Functional regression enables the linking of meteorological drivers (temperature, humidity, wind, precipitation, etc.) to solar radiation curves(Wang & Wen, 2022 ). 3. Volatility and uncertainty theory (GARCH and VAR/VARX Models) Models based on financial econometrics estimate time-varying conditional variance(Haputhanthri et al., 2021 ). They capture volatility clustering during extreme weather, monsoon onset, and prolonged cloudiness(Prasad & Kay, 2021 ). VAR/VARX models extend this by introducing exogenous meteorological drivers and monitoring lagged interactions between solar variability and weather(Vyas et al., 2022). By bringing together these strands, the theoretical framework ensures that the research captures structural patterns (the FDA), nonlinear drivers (TAR/STAR), and uncertainty dynamics (GARCH/VAR). This joined-up framework spans a critical research gap in solar radiation studies and strengthens the methodological foundation for policy-relevant energy forecasting. Materials and methods Five major Asian cities—Dhaka (Bangladesh), New Delhi (India), Jakarta (Indonesia), Manila (Philippines), and Kuala Lumpur (Malaysia)—were chosen to represent diverse climatic conditions, including monsoon-dominated, tropical, and equatorial climates(Romitti & Wing, 2022). The observations between July 01, 2016, and June 30, 2025, were taken from the NASA POWER Project. These datasets, in the CSV format, were made up of hourly solar radiation and meteorological data that were additionally merged into daily profiles for functional and time-series analysis. Each dataset included time data (YEAR, MO, DY, and HR) and significant solar radiation variables: All-sky surface shortwave downward irradiance (ALLSKY_SFC_SW_DWN), clear-sky surface shortwave downward irradiance (CLRSKY_SFC_SW_DWN), all-sky direct normal irradiance (ALLSKY_SFC_SW_DNI), all-sky diffuse irradiance (ALLSKY_SFC_SW_DIFF), and the all-sky insolation clearness index (ALLSKY_KT). Moreover, meteorological variables, which included the air temperature at 2 m (T2M), relative humidity at 2 m (RH2M), corrected total precipitation (PRECTOTCORR), surface pressure (PS), and wind speed at 10 m (WS10M)(Tercha et al., 2024 ). Data preprocessing involves the treatment of missing values and the application of linear and spline interpolation techniques(Park et al., 2019 ) for preserving time series continuity. The statistical analysis was performed via R version 4.5.1. The analysis technique utilized functional data analysis, nonlinear time series modelling, and volatility modelling. The FDA was utilized through the fda, fda.usc, and refund packages, whereas nonlinear dynamics were handled by threshold autoregressive (TAR) and smooth transition autoregressive (STAR) models under the tsDyn package. The uncertainty, volatility, and variability of solar energy were simulated via GARCH-family models via the rugarch package, whereas the multivariate interaction between solar energy and weather variables was explored via vector autoregression (VAR/VARX) via the vars package. Other packages such as dplyr, tidyr, and zoo, were employed for data preprocessing, whereas ggplot2 and corrplot were employed to visualize the data and conduct diagnostic testing. The research was conducted in three phases on the absis of the behavioral objectives. In phase one, solar irradiance hourly data were converted into effective daily curves for sunrise to sunset. Intrday variation modes were identified using functional principal component analysis (FPCA)(Gradwohl et al., 2021 ), and functional scores were categorized to partition the radiation regime classes into hourly intervals at the five stations. In the second phase, the drivers of nonlinear and threshold changes in solar radiation were determined(Tye et al., 2019 ). Daily averaging was used for the meteorological variables, and their associations with functional principal components were investigated(Bai et al., 2022 ). The TAR model and STAR model accounted for the regime-dependent impacts of temperature, humidity, precipitation, and wind, whereas the functional regression methods characterized the impacts of the predictors on the shape of the solar radiation curve(Costa et al., 2021 ). The final step addresses volatility and uncertainty by taking daily solar energy forecasts in terms of log returns and using GARCH-family models (GARCH, TGARCH, EGARCH, and APARCH) to check for evidence of volatility persistence and clustering(Sedai et al., 2023 ). The findings of volatility were checked against meteorological parameters, i.e., rain, relative humidity, and the clearness index, for causal effect interpretation, and VAR/VARX models were used to identify lagged interactions between weather and changes in solar radiation(Zhu et al., 2020 ). A number of procedures were used to evaluate model robustness and verification. Cross-validation was applied to handle missing data, and interannual cross-validation and seasonal cross-validation were used to test model performance across different climate conditions(Mishra et al., 2023). Robustness was also confirmed through the usage of varying numbers of function basis functions (13, 17, and 21) and taking into account the GARCH-family models on the basis of AIC and BIC tests(AlOmar et al., 2022 ; Killeen et al., 2024 ). This approach needs a multistep procedure that offers a combined treatment of structural shattering, nonlinear meteorological thresholds, and volatility dynamics of the solar radiation changes in South Asia and Southeast Asian megacities of these predictors on the basis of the shape of the solar radiation curve(Aman et al., 2023 ; Kanga et al., 2022). The final step addresses volatility and uncertainty by casting daily solar energy forecasts to log returns and modelling GARCH-family models (GARCH, TGARCH, EGARCH, and APARCH) to search for evidence of volatility clustering and persistence(T et al., 2024). Volatility outcomes were also compared with meteorological drivers, that is, precipitation, relative humidity, and clearness index, for causal effect interpretation, and the VAR/VARX models were used to reveal lagged weather solar radiation change interactions(Hou et al., 2023 ). Robustness and model checking were achieved via several methods. The missing data treatments were cross-validated, and season and interannual cross-validations were conducted to check model performance under different climatic conditions(Wang & Shi, 2021 ). Robustness was verified by altering the number of function basis functions (13, 17, and 21) and comparing the GARCH-family models via the AIC and BIC(Szostek et al., 2024 ). Together, this calls for a multistep procedure that provides a composite methodology for revealing structural breaks, nonlinear meteorological thresholds, and volatility dynamics in solar radiation variations in South and Southeast Asian megacities. Results Functional Representation of Solar Variability Table 1 Summary of the FPCA results, clustering, correlations, robustness, and seasonality across five Asian megacities. City Var. (PC1 //PC2 //PC3, %) Cum. Var. (PC1–3) Clusters (n1 // n2 // n3) PC1–Met Corr. (RH // Rain // Wind // Temp) Robustness (nb = 13–21) ANOVA F (month) P_value Dhaka 84.1 // 9.4 // 3.5 97 1192 // 31 // 2064 -75.7575758 84.4 → 83.9 49.5 < 0.001 Jakarta 85.9 // 7.0 // 4.8 97.8 31 // 2132 // 1124 -1477.27273 84.4 → 83.9 42.6 < 0.001 Kuala Lumpur 86.4 // 6.8 // 4.5 97.8 2098 // 31 // 1158 1851.851852 84.4 → 83.9 34.4 < 0.001 Manila 85.8 // 9.2 // 3.2 98.2 1064 // 2192 // 31 -118.75 84.4 → 83.9 54.8 < 0.001 New Delhi 85.8 // 9.0 // 2.9 97.7 1512 // 1744 // 31 64.55083378 84.4 → 83.9 81.9 < 0.001 The FPCA decomposition revealed that the first three PCs explained nearly all the variability in the daily solar irradiance curves. Table 1 shows that PC1 explained 84–86% of the total variance among cities, and PC2 and PC3 explained 6–10% and 3–5%, respectively. The total variance in all the scenarios was greater than 97%, confirming that most of the variation in solar radiation was captured on a low-dimensional functional basis. The mean functional curves (Fig. 1 ) showed typical diurnal patterns, rising after sunrise, peaking at approximately midday, and dropping towards sunset. Kuala Lumpur and Manila recorded the highest midday peaks (> 700 W/m²), and Dhaka showed lower irradiance throughout the year owing to increased atmospheric attenuation by aerosols and cloud cover. Cluster analysis revealed three distinct regimes for each city (Fig. 2 ). Large clusters were mapped to standard clear-sky or partially cloudy days, and small clusters detected exceptional weather-driven extremes such as monsoon rain storms or storm events. The sub clusters capture the day-to-day heterogeneity of solar input and demonstrate the operationally useful value of unusual day modelling. The scree plots (Fig. 3 ) confirmed the pervasive dominance of PC1 in explaining variance. Robustness tests with different basis dimensions (nbasis = 13, 17, 21) resulted in very similar variances (Fig. 4 ), confirming that the FPCA results were methodology insensitive and thus extremely stable. The monthly boxplots (Fig. 5 ) revealed strong seasonality in Dhaka, Manila, and New Delhi, where the PC1 values were the highest in the dry season and the lowest during the monsoon season. Conversely, Kuala Lumpur and Jakarta presented flat seasonality in accordance with equatorial regimes. ANOVA confirmed significant seasonal effects in both cities (p < 0.001). Correlation analysis (Table 1 ) confirmed that PC1 was negatively correlated with relative humidity (− 0.18 to − 0.24) and rainfall (− 0.09 to − 0.20). Temperature was significantly positively correlated in New Delhi (+ 0.26), as anticipated, with cloudier skies and a wetter continental climate. Solar Variability Nonlinear and Threshold Drivers Nonlinear and threshold analyses revealed pronounced city-level trends in the meteorological regulation of solar energy variability. The heatmaps of correlations (Fig. 6 ) show that in Dhaka and Manila, solar irradiance is highly significantly negatively correlated with relative humidity and precipitation, which is consistent with the monsoon season. New Delhi had highly significant positive correlations with temperature, which is consistent with dry season dominance, whereas Jakarta and Kuala Lumpur had weaker but significant correlations with the pressure and diurnal temperature range. Table 2 Effects of key weather drivers and the GAM on solar energy production Generalized additive models (Table 2 ) confirmed these trends. The temperature range (T2M_range) was always a positive force across all cities, and precipitation (PRECTOT) was negative, most strongly in Dhaka, Manila and Kuala Lumpur. New Delhi is the only exception, where the mean temperature and humidity are positively influential, and where precipitation is highly negative. City Top Predictors (r) GAM Effects (Estimate ± SE, Effect) Dhaka RH2M − 0.20; T2M_max + 0.19 T2M_mean 0.195 ± 0.021 (Positive); PRECTOT − 0.00098 ± 0.00018 (Negative); T2M_range 0.181 ± 0.036 (Positive) Jakarta T2M_range + 0.25; RH2M − 0.19 T2M_range 0.633 ± 0.076 (Positive); PS − 1.38 ± 0.423 (Negative); T2M_mean − 0.184 ± 0.082 (Negative) Kuala Lumpur T2M_range + 0.18; T2M_max + 0.15 T2M_range 0.347 ± 0.051 (Positive); PRECTOT − 0.00056 ± 0.00025 (Negative) Manila T2M_range + 0.35; RH2M − 0.31 T2M_range 0.411 ± 0.054 (Positive); PRECTOT − 0.00064 ± 0.00016 (Negative); PS 1.10 ± 0.280 (Positive); WS10M_mean 0.502 ± 0.193 (Positive) New Delhi T2M_max + 0.29; T2M_mean + 0.23 T2M_mean 0.178 ± 0.018 (Positive); T2M_range 0.278 ± 0.029 (Positive); RH2M 0.030 ± 0.005 (Positive); PRECTOT − 0.00180 ± 0.00040 (Negative) Generalized additive models (Table 2) confirmed these trends. The temperature range (T2M_range) was always a positive force across all cities, and precipitation (PRECTOT) was negative, most strongly in Dhaka, Manila and Kuala Lumpur. New Delhi is the only exception, where the mean temperature and humidity are positively influential, and where precipitation is highly negative. Table 3 Comparison of TAR and STAR model fits with key coefficients, thresholds, and GAM-derived nonlinear drivers for solar energy production across Cities. City Model (Best / Type) AIC / BIC Ljung–Box p Low-Regime (Const / φ₁ / φ₂) High-Regime (Const / φ₁ / φ₂) Threshold (Value / Variable / GAM Variable / GAM Value) Dhaka TAR 946 / 965 0.969 100.0 / 0.740 / −0.516 −1441 / 2.17 / 7.48 150 / PRECTOT / PRECTOT / 43.4 Jakarta TAR 925 / 944 0.909 −994.0 / 7.92 / 0.135 64.7 / 0.55 / −0.009 134 / WS10M_max / WS10M_max / 4.02 Kuala Lumpur TAR 947 / 966 1.000 111.0 / 0.175 / 0.061 −1063 / 4.20 / 3.58 149 / T2M_mean / T2M_mean / 25.7 Manila STAR 927 / 948 0.995 78.4 / 0.691 / −0.186 −4175 / 8.22 / 12.2 204 / PRECTOT / PRECTOT / 108 New Delhi STAR 789 / 810 0.525 64.1 / 1.08 / −0.534 −6536 / 17.0 / 15.9 200 / RH2M / RH2M / 48.3 Threshold models (Table 3 ) highlight regime-dependent changes. Dhaka is said to possess a rainfall threshold (~ 43 mm) that demarcates high-irradiance and monsoon-dominant days. Jakarta has a wind threshold (~ 4 m/s), Kuala Lumpur has a temperature threshold (~ 25.7°C), Manila has a precipitation threshold (~ 108 mm), and New Delhi has a humidity threshold (~ 48%). All these thresholds confirm the existence of rapid drops in irradiance when specific climatic thresholds are reached. The variable importance plots (Fig. 7 ) revealed the largest contributions from T2M_range, precipitation, and pressure, with smaller contributions from wind speed (Manila) and surface pressure (Jakarta and Manila). Volatility and Uncertainty in Solar Energy Production The heteroskedasticity is further supported by autocorrelation analysis. The ACF of log-returns (Fig. 8 ) showed no serial correlation at the significance level, and the ACF of squared returns (Fig. 9 ) showed long-term positive autocorrelation, reflecting volatility clustering in the data. Plots of the time series of log returns (Fig. 10 ) further show recurrent peaceful and stormy intervals, with Dhaka and Manila having the highest peaks, especially during monsoons. The conditional volatility predictions from the GARCH, TGARCH, and EGARCH models (Fig. 11 ) capture these dynamics well. All three models replicated periods of high and low volatility, with EGARCH highlighting asymmetric effects, under which volatility spikes more strongly after negative shocks such as rain or cloud cover. The role of meteorological drivers was examined by overlaying precipitation and humidity on model-based volatility (Fig. 12 ). High volatility coincided with high rainfall and increased humidity, especially in Dhaka and Manila, confirming that extreme weather increases uncertainty. Scatterplots of σ against rainfall and humidity (Fig. 13 ) exhibited clear positive slopes, revealing increased variance with higher and more humid rainfall. An integrated multii-panel summary (Fig. 14 ) confirmed the results, with statistically significant correlations (p < 0.001) between conditional volatility and drivers across all cities. Precipitation consistently had the most significant effect, with relative humidity contributing to equatorial metropolises, such as Jakarta and Kuala Lumpur. Finally, the impulse–response functions derived from the VAR models (Fig. 15) show that precipitation shocks had an instantaneous negative impact on solar returns, after which partial recovery was observed after 3–5 days. Dhaka and Manila presented the most intense responses, whereas Jakarta and Kuala Lumpur presented somewhat more moderate responses, and New Delhi presented slightly longer persistence. Discussion The FPCA results indicate that a diurnal solar irradiance cycle exists, but its variability is governed by local climate regimes. Dhaka and Manila are governed by monsoonal cloudiness and precipitation with high seasonal cycles, whereas Jakarta and Kuala Lumpur have relatively uniform year-round irradiance regimes. New Delhi is governed by the temperature and humidity dynamics of continental climates. Cluster analysis reveals the differential regimes of the sun, distinguishing normal workdays from unusual weather days. This reinforces the need for regime-sensitive forecasting models with the capacity to predict unusual but substantial reductions in solar availability. Meteorological correlations underpin physical processes: rain and humidity reduce solar radiation uniformly, and dryness, particularly in New Delhi, increases availability. Robustness tests provide additional assurance that these outcomes are free from the artifacts of modelling assumptions. From a planning perspective, these outcomes highlight the importance of incorporating climate-sensitive and seasonal factors into solar power forecasting and grid-integration planning. The risk management of monsoon-based cities must consider the greater volatility in solar power availability than that of equatorial cities. These findings indicate that solar variations in Asian megacities are controlled by nonlinearities and climate-dependent thresholds but not by linear drivers. Solar suppression during the monsoon season is controlled by rainfall and humidity thresholds for Dhaka and Manila, but for New Delhi, the humidity temperature interaction controls the variation. Jakarta and Kuala Lumpur are subjected to storm-related thresholds involving wind and pressure. Linear models conventionally underestimate such abrupt changes. Nonlinear techniques, such as TAR and STAR, detect threshold levels and indicate the locations of tipping points, which results in irradiance collapse. This has policy implications for energy planning and predictions. Backup generation and storage are needed for Manila and Dhaka to buffer monsoon-driven variability. In New Delhi, adaptations must respond to seasonally varying monsoon and dry regimes. For Kuala Lumpur and Jakarta, now casting and very short-term storm forecasting are important for buffering variability. Cumulatively, the evidence from Figs. 6 and 7 and Tables 2 and 3 illustrates the utility of regime-sensitive, nonlinear models for solar forecasting. Threshold detection improves prediction accuracy and confidence in the integration of renewables into rapidly emerging urban energy grids. These results reaffirm that solar energy returns in Asian megacities exhibit volatility clustering and persistence, as seen in financial markets. GARCH-type models, particularly EGARCH, capture how both clustering and asymmetries are picked up and demonstrated that negative shocks (e.g., cloudiness and precipitation) have greater effects on volatility than positive shocks do. Rainfall was the leading source of volatility (Figs. 12 – 14 ), emphasizing the role played by monsoon and storm occurrences in destabilizing the solar supply. Relative humidity also contributes, notably in the tropics, where continuous high humidity generates clouds and attenuates radiation. The VAR-impulse–response analysis using the VAR (Fig. 15) shows that weather shocks are severe but short-lived and tend to dissipate within a week. This suggests that operational planning must focus on near-term volatility buffering through storage and backup arrangements, especially in monsoon-prone cities such as Dhaka and Manila. Overall, Objective 3 highlights the importance of climate-sensitive volatility modelling for secure solar energy integration. By categorically defining the linkages between volatility and precipitation and humidity, the results provide a means of creating more robust forecasting networks and energy management practices in rapidly growing urban environments. Conclusion This study aimed to reveal the nonlinear drivers of solar variability in Asian megacities from a functional time-series perspective. Through the integration of functional data analysis (FDA), nonlinear threshold models, and volatility paradigms, this study addresses three broad objectives: functional modelling of solar radiation, identification of nonlinear meteorological thresholds, and volatility modelling and uncertainty in solar energy generation. The conclusions clearly show that solar variability can only be understood in the manner that it is determined by climate-specific thresholds and the dynamics of volatility. Functional principal component analysis also revealed that the first three components accounted for more than 97% of the variance in daily irradiance, validating the FDA as a robust method for representing and classifying solar regimes. Threshold analyses also revealed city-specific tipping points, such as rainfall thresholds in Dhaka and Manila, humidity thresholds in New Delhi, and wind and temperature thresholds in Jakarta and Kuala Lumpur. These regime-sensitive dynamics demonstrate that linear models are inadequate, whereas nonlinear approaches can represent sudden variations in solar availability. GARCH-family volatility modelling techniques also highlight clustering and persistence, particularly during monsoons, and impulse–response analysis reveals that weather shocks, particularly rain, have short-term but considerable influences on solar returns. Collectively, these results underscore the methodological and practical significance of cross-integrating nonlinear, function-based, and volatility-based approaches. Methodologically, this study closes a significant gap in the solar energy literature by introducing a composite model with the potential for tracking structural trajectories, thresholds, and uncertainty dynamics. This evidence has important practical implications for energy system resilience planning and climate adaptation. In monsoon-dominant cities, such as Dhaka and Manila, the results highlight the urgent need for backup and storage systems to mitigate volatility. In continental climates, such as New Delhi, flexible planning must account for seasonal transitions, whereas in equatorial cities, such as Jakarta and Kuala Lumpur, improved prediction and now casting storms are needed to maintain grid stability. Overall, this study provides theoretical and practical insights into the field of renewable energy forecasting. By demonstrating the regulation of variability in solar radiation by nonlinear thresholds and volatility clusters, this study provides scientific knowledge and actionable intelligence for policymakers, urban energy planners, and decision-makers. Future research should build upon this effort by adding other climatic drivers, such as aerosols and cloud cover categories, expanding geographical sites beyond five cities, and exploring the integration of machine learning approaches with functional time series models. These extensions will further increase the predictability, power, and resilience of solar power systems to rising climatic and urban pressures. Declarations Author Contribution Statement Md. Rakib Hasan Sarker conceived and designed the study, performed the data analysis, developed the models, interpreted the results, and prepared the final version of the manuscript. Farjana Akter contributed to data collection, literature review, methodological formulation, and manuscript editing. Both authors read and approved the final manuscript. Funding Statement This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. Conflict of Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Data Availability Statement The datasets analyzed during the current study are publicly available from the NASA POWER Project repository (https://power.larc.nasa.gov/). Processed data and analysis codes are available from the corresponding author upon reasonable request. Ethics Statement This study did not involve human participants, animals, or any personal or confidential data. All data used were obtained from publicly accessible sources (NASA POWER Project). Therefore, no ethical approval or informed consent was required. References Alomar, M. K., Khaleel, F., Aljumaily, M. M., Masood, A., Razali, S. F. M., AlSaadi, M. A., Al-Ansari, N., & Hameed, M. M. (2022). Data-driven models for atmospheric air temperature forecasting at a continental climate region. PLOS ONE , 17 (11), e0277079. https://doi.org/10.1371/journal.pone.0277079 Aman, N., Kasemsan Manomaiphiboon, Natchanok Pala-En, Bikash Devkota, Muanfun Inerb, & Eakkachai Kokkaew. (2023). A Study of Urban Haze and Its Association with Cold Surge and Sea Breeze for Greater Bangkok. International Journal of Environmental Research and Public Health , 20 (4), 3482–3482. https://doi.org/10.3390/ijerph20043482 Baghel, N. S., & Chander, N. (2022). Performance comparison of mono and polycrystalline silicon solar photovoltaic modules under tropical wet and dry climatic conditions in east-central India. Clean Energy , 6 (1), 929–941. https://doi.org/10.1093/ce/zkac001 Bai, J., Zong, X., Ma, Y., Wang, B., Zhao, C., Yang, Y., Guang, J., Cong, Z., Li, K., & Song, T. (2022). Long-Term Variations in Global Solar Radiation and Its Interaction with Atmospheric Substances at Qomolangma. International Journal of Environmental Research and Public Health , 19 (15), 8906. https://doi.org/10.3390/ijerph19158906 Barhmi, K., Heynen, C., Golroodbari, S., & van Sark, W. (2024). A Review of Solar Forecasting Techniques and the Role of Artificial Intelligence. Solar , 4 (1), 99–135. https://doi.org/10.3390/solar4010005 Bowden, C., Foster, T., & Parkes, B. (2023). Identifying links between monsoon variability and rice production in India through machine learning. Scientific Reports , 13 (1). https://doi.org/10.1038/s41598-023-27752-8 Correa, L. F., Folini, D., Boriana Chtirkova, & Wild, M. (2022). A Method for Clear‐Sky Identification and Long‐Term Trends Assessment Using Daily Surface Solar Radiation Records. Earth and Space Science , 9 (8). https://doi.org/10.1029/2021ea002197 Costa, L., McBreen, J., Ampatzidis, Y., Guo, J., Gahrooei, M. R., & Babar, M. A. (2021). Using UAV-based hyperspectral imaging and functional regression to assist in predicting grain yield and related traits in wheat under heat-related stress environments for the purpose of stable yielding genotypes. Precision Agriculture , 23 (2), 622–642. https://doi.org/10.1007/s11119-021-09852-5 Dash, S., Nandy, D., & Ilya Usoskin. (2023). Long-term forcing of the Sun’s coronal field, open flux, and cosmic ray modulation potential during grand minima, maxima, and regular activity phases by the solar dynamo mechanism. Monthly Notices of the Royal Astronomical Society , 525 (4), 4801–4814. https://doi.org/10.1093/mnras/stad1807 David, M., Ramahatana, F., Trombe, P. J., & Lauret, P. (2016). Probabilistic forecasting of the solar irradiance with recursive ARMA and GARCH models. Solar Energy , 133 , 55–72. https://doi.org/10.1016/j.solener.2016.03.064 Euán, C., Sun, Y., & Reich, B. J. (2022). Statistical analysis of multi‐day solar irradiance using a threshold time series model. Environmetrics , 33 (3). https://doi.org/10.1002/env.2716 Gradwohl, C., Vesna Dimitrievska, Pittino, F., Muehleisen, W., András Montvay, Franz Langmayr, & Kienberger, T. (2021). A Combined Approach for Model-Based PV Power Plant Failure Detection and Diagnostic. Energies , 14 (5), 1261–1261. https://doi.org/10.3390/en14051261 Gürel, A. E., Ağbulut, Ü., Bakır, H., Ergün, A., & Yıldız, G. (2023). A state of art review on estimation of solar radiation with various models. Heliyon , 9 (2,e13167), e13167. https://doi.org/10.1016/j.heliyon.2023.e13167 Haputhanthri, D., De Silva, D., Sierla, S., Alahakoon, D., Nawaratne, R., Jennings, A., & Vyatkin, V. (2021). Solar Irradiance Nowcasting for Virtual Power Plants Using Multimodal Long Short-Term Memory Networks. Frontiers in Energy Research , 9 . https://doi.org/10.3389/fenrg.2021.722212 Hoffmann, M., Kotzur, L., Stolten, D., & Robinius, M. (2020). A Review on Time Series Aggregation Methods for Energy System Models. Energies , 13 (3), 641. https://doi.org/10.3390/en13030641 Hou, X., Wild, M., Folini, D., Kazadzis, S., & Wohland, J. (2021). Climate change impacts on solar power generation and its spatial variability in Europe based on CMIP6. Earth System Dynamics , 12 (4), 1099–1113. https://doi.org/10.5194/esd-12-1099-2021 Huang, C., Zhao, Z., Wang, L., Zhang, Z., & Luo, X. (2020). Point and interval forecasting of solar irradiance with an active Gaussian process. IET Renewable Power Generation , 14 (6), 1020–1030. https://doi.org/10.1049/iet-rpg.2019.0769 Huang, L., Kang, J., Wan, M., Fang, L., Zhang, C., & Zeng, Z. (2021). Solar Radiation Prediction Using Different Machine Learning Algorithms and Implications for Extreme Climate Events. Frontiers in Earth Science , 9 . https://doi.org/10.3389/feart.2021.596860 Jiao, B., Su, Y., Li, Q., Manara, V., & Wild, M. (2023). An integrated and homogenized global surface solar radiation dataset and its reconstruction based on a convolutional neural network approach. Earth System Science Data , 15 (10), 4519–4535. https://doi.org/10.5194/essd-15-4519-2023 Killeen, P., Iluju Kiringa, Yeap, T., & Branco, P. (2024). Corn Grain Yield Prediction Using UAV-Based High Spatiotemporal Resolution Imagery, Machine Learning, and Spatial Cross-Validation. Remote Sensing , 16 (4), 683–683. https://doi.org/10.3390/rs16040683 Kim, B., Suh, D., Otto, M.-O., & Huh, J.-S. (2021). A Novel Hybrid Spatio-Temporal Forecasting of Multisite Solar Photovoltaic Generation. Remote Sensing , 13 (13), 2605. https://doi.org/10.3390/rs13132605 Krumins, J., & Klavins, M. (2023). Investigating the Potential of Nuclear Energy in Achieving a Carbon-Free Energy Future. Energies , 16 (9), NA–NA. https://doi.org/10.3390/en16093612 Mishra, D., Jena, S., Rudranarayan Senapati, Atman Panigrahi, & Surender Reddy Salkuti. (2023a). Global solar radiation forecast using an ensemble learning approach. International Journal of Power Electronics and Drive Systems , 14 (1), 496–496. https://doi.org/10.11591/ijpeds.v14.i1.pp496-505 Mishra, D., Jena, S., Rudranarayan Senapati, Atman Panigrahi, & Surender Reddy Salkuti. (2023b). Global solar radiation forecast using an ensemble learning approach. International Journal of Power Electronics and Drive Systems , 14 (1), 496–496. https://doi.org/10.11591/ijpeds.v14.i1.pp496-505 Mol, W. B., van Stratum, B. J. H., Knap, W. H., & van Heerwaarden, C. C. (2023). Reconciling Observations of Solar Irradiance Variability With Cloud Size Distributions. Journal of Geophysical Research: Atmospheres , 128 (5). https://doi.org/10.1029/2022jd037894 Mou Leong Tan, Liew Juneng, Heri Kuswanto, Hong Xuan Do, & Zhang, F. (2023). Impacts of Solar Radiation Management on Hydro-Climatic Extremes in Southeast Asia. Water , 15 (6), 1089–1089. https://doi.org/10.3390/w15061089 Pandey, A. K., Kalidasan, B., Reji Kumar, R., Rahman, S., Tyagi, V. V., Krismadinata, Said, Z., Salam, P. A., Juanico, D. E., Ahamed, J. U., Sharma, K., Samykano, M., & Tyagi, S. K. (2022). Solar Energy Utilization Techniques, Policies, Potentials, Progresses, Challenges and Recommendations in ASEAN Countries. Sustainability , 14 (18), 11193. https://doi.org/10.3390/su141811193 Park, Kim, Lee, Kim, Song, & Kim. (2019). Temperature Prediction Using the Missing Data Refinement Model Based on a Long Short-Term Memory Neural Network. Atmosphere , 10 (11), 718. https://doi.org/10.3390/atmos10110718 Phon Sheng Hou, Lokman Mohd Fadzil, Manickam, S., & Al-Shareeda, M. A. (2023). Vector Autoregression Model-Based Forecasting of Reference Evapotranspiration in Malaysia. Sustainability , 15 (4), 3675–3675. https://doi.org/10.3390/su15043675 Prasad, A. A., & Kay, M. (2021). Prediction of Solar Power Using Near-Real Time Satellite Data. Energies , 14 (18), 5865. https://doi.org/10.3390/en14185865 Qian, Y., Chakraborty, T. C., Li, J., Li, D., He, C., Sarangi, C., Chen, F., Yang, X., & Leung, L. R. (2022). Urbanization Impact on Regional Climate and Extreme Weather: Current Understanding, Uncertainties, and Future Research Directions. Advances in Atmospheric Sciences , 39 (6), 819–860. https://doi.org/10.1007/s00376-021-1371-9 Quansah, A. D., Dogbey, F., Asilevi, P. J., Boakye, P., Darkwah, L., Oduro-Kwarteng, S., Sokama-Neuyam, Y. A., & Mensah, P. (2022). Assessment of solar radiation resource from the NASA-POWER reanalysis products for tropical climates in Ghana towards clean energy application. Scientific Reports , 12 (1). https://doi.org/10.1038/s41598-022-14126-9 Rens van der Zwaard, Bergmann, M., Zender, J., Rangaiah Kariyappa, Giono, G., & Luc Damé. (2021). Segmentation of Coronal Features to Understand the Solar EUV and UV Irradiance Variability III. Inclusion and Analysis of Bright Points. Solar Physics , 296 (9). https://doi.org/10.1007/s11207-021-01863-9 Romitti, Y., & Sue Wing, I. (2022). Heterogeneous climate change impacts on electricity demand in world cities circa mid-century. Scientific Reports , 12 (1). https://doi.org/10.1038/s41598-022-07922-w Santiago, I., Esquivel-Martin, J. L., Trillo-Montero, D., Real-Calvo, R. J., & Víctor Pallarés-López. (2021a). Classification of Daily Irradiance Profiles and the Behaviour of Photovoltaic Plant Elements: The Effects of Cloud Enhancement. Applied Sciences , 11 (11), 5230–5230. https://doi.org/10.3390/app11115230 Santiago, I., Esquivel-Martin, J. L., Trillo-Montero, D., Real-Calvo, R. J., & Víctor Pallarés-López. (2021b). Classification of Daily Irradiance Profiles and the Behaviour of Photovoltaic Plant Elements: The Effects of Cloud Enhancement. Applied Sciences , 11 (11), 5230–5230. https://doi.org/10.3390/app11115230 Santiago, I., Esquivel-Martin, J. L., Trillo-Montero, D., Real-Calvo, R. J., & Víctor Pallarés-López. (2021c). Classification of Daily Irradiance Profiles and the Behaviour of Photovoltaic Plant Elements: The Effects of Cloud Enhancement. Applied Sciences , 11 (11), 5230–5230. https://doi.org/10.3390/app11115230 Sedai, A., Dhakal, R., Gautam, S., Dhamala, A., Bilbao, A., Wang, Q., Wigington, A., & Pol, S. (2023). Performance Analysis of Statistical, Machine Learning and Deep Learning Models in Long-Term Forecasting of Solar Power Production. Forecasting , 5 (1), 256–284. https://doi.org/10.3390/forecast5010014 Stefani, F., Horstmann, G. M., M. Klevs, G. Mamatsashvili, & Weier, T. (2024). Rieger, Schwabe, Suess-de Vries: The Sunny Beats of Resonance. Solar Physics , 299 (4). https://doi.org/10.1007/s11207-024-02295-x Szostek, K., Mazur, D., Drałus, G., & Kusznier, J. (2024). Analysis of the Effectiveness of ARIMA, SARIMA, and SVR Models in Time Series Forecasting: A Case Study of Wind Farm Energy Production. Energies , 17 (19), 4803. https://doi.org/10.3390/en17194803 Tercha, W., Tadjer, S. A., Chekired, F., & Canale, L. (2024). Machine Learning-Based Forecasting of Temperature and Solar Irradiance for Photovoltaic Systems. Energies , 17 (5), 1124. https://doi.org/10.3390/en17051124 Tye, M. R., Haupt, S. E., Gilleland, E., Kalb, C., & Jensen, T. (2019). Assessing Evidence for Weather Regimes Governing Solar Power Generation in Kuwait. Energies , 12 (23), 4409. https://doi.org/10.3390/en12234409 Wang, J., & Wen, X. (2022). Excess radiation exacerbates drought stress impacts on canopy conductance along aridity gradients. Biogeosciences , 19 (17), 4197–4208. https://doi.org/10.5194/bg-19-4197-2022 Wang, L., & Shi, J. (2021). A Comprehensive Application of Machine Learning Techniques for Short-Term Solar Radiation Prediction. Applied Sciences , 11 (13), 5808. https://doi.org/10.3390/app11135808 Yang, J., Yi, B., Wang, S., Liu, Y., & Li, Y. (2022). Diverse cloud and aerosol impacts on solar photovoltaic potential in southern China and northern India. Scientific Reports , 12 (1). https://doi.org/10.1038/s41598-022-24208-3 Yu, G., Wright, D. B., & Li, Z. (2020). The Upper Tail of Precipitation in Convection‐Permitting Regional Climate Models and Their Utility in Nonstationary Rainfall and Flood Frequency Analysis. Earth’s Future , 8 (10). https://doi.org/10.1029/2020ef001613 Zafar, R., Vu, B. H., Husein, M., & Chung, I.-Y. (2021). Day-Ahead Solar Irradiance Forecasting Using Hybrid Recurrent Neural Network with Weather Classification for Power System Scheduling. Applied Sciences , 11 (15), 6738. https://doi.org/10.3390/app11156738 Zhu, T., Guo, Y., Wang, C., & Ni, C. (2020). Inter-Hour Forecast of Solar Radiation Based on the Structural Equation Model and Ensemble Model. Energies , 13 (17), 4534–4534. https://doi.org/10.3390/en13174534 Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7807830","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":530274598,"identity":"da3a11ad-edeb-4c5e-bd90-e8aad424b1cf","order_by":0,"name":"Md. Rakib Hasan Sarker","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA5klEQVRIiWNgGAWjYFACNobDDAwHGBh4GBgfALk8fKRoYTYAaWEjRgszVAubBIRPAJi3H0s8XMBwh0G+5+yzyq85djJAIx4+uoFHi8yZtAOHZzA8YzA42252W3ZbMtBhbMbGOXi0SDCkNxzmAXrHgJ+N7bbkNmagFh42abxa+J9DtMj3s7EVS26rJ0KLBNBhIC0MZ9vYGD9uO0yMlmcJh2cYHOYxOHOMWZpx23EeNmZCfuFPM/5cUHFYTr4njfHjz23V9vzszQ8f49MCAQbAWAECZghJUDkSYPxBiupRMApGwSgYMQAAwR1AdgiWzrcAAAAASUVORK5CYII=","orcid":"","institution":"Comilla University","correspondingAuthor":true,"prefix":"","firstName":"Md.","middleName":"Rakib Hasan","lastName":"Sarker","suffix":""},{"id":530274599,"identity":"b3ff739b-33b0-4734-856e-51301dd3f8f6","order_by":1,"name":"Farjana Akter","email":"","orcid":"","institution":"Comilla University","correspondingAuthor":false,"prefix":"","firstName":"Farjana","middleName":"","lastName":"Akter","suffix":""}],"badges":[],"createdAt":"2025-10-08 12:23:14","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7807830/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7807830/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":93651207,"identity":"2e202946-a3ff-4fcd-b4c2-2e0bca15e141","added_by":"auto","created_at":"2025-10-16 05:51:18","extension":"docx","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":387338,"visible":true,"origin":"","legend":"","description":"","filename":"Manuscript.docx","url":"https://assets-eu.researchsquare.com/files/rs-7807830/v1/02a5ce46eedf9ac2efda9481.docx"},{"id":93649174,"identity":"c4ab3e0c-d7bd-476e-895b-f55ba260091f","added_by":"auto","created_at":"2025-10-16 05:19:18","extension":"json","order_by":1,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":4607,"visible":true,"origin":"","legend":"","description":"","filename":"960c0df7e25e4296a23c54f49d1ee3e5.json","url":"https://assets-eu.researchsquare.com/files/rs-7807830/v1/afafef278e40dd103733b094.json"},{"id":93649176,"identity":"d628e1d2-22dc-4717-8619-1e26f55f8fd1","added_by":"auto","created_at":"2025-10-16 05:19:18","extension":"xml","order_by":2,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":137787,"visible":true,"origin":"","legend":"","description":"","filename":"960c0df7e25e4296a23c54f49d1ee3e51enriched.xml","url":"https://assets-eu.researchsquare.com/files/rs-7807830/v1/e09c7988ac12f5f520b63209.xml"},{"id":93649168,"identity":"984ea4f9-e296-4545-a280-1bbe6966681e","added_by":"auto","created_at":"2025-10-16 05:19:18","extension":"png","order_by":3,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":12604,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-7807830/v1/58eea5d4c0118273d37bef87.png"},{"id":93649966,"identity":"3a46c860-bd1b-49f2-bf8e-07f4d34ace98","added_by":"auto","created_at":"2025-10-16 05:35:18","extension":"png","order_by":4,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":15995,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage10.png","url":"https://assets-eu.researchsquare.com/files/rs-7807830/v1/d165b42a40014a7afbc26a06.png"},{"id":93649967,"identity":"02043b41-425a-41b3-95b7-de7354470605","added_by":"auto","created_at":"2025-10-16 05:35:18","extension":"png","order_by":5,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":18465,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage11.png","url":"https://assets-eu.researchsquare.com/files/rs-7807830/v1/34237d69d0a8e4d92356a6ba.png"},{"id":93650798,"identity":"c5c8e2bc-dffd-45b5-a290-6891a2beae23","added_by":"auto","created_at":"2025-10-16 05:43:18","extension":"png","order_by":6,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":24726,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage12.png","url":"https://assets-eu.researchsquare.com/files/rs-7807830/v1/6f94d15846c5fae3e528f1ed.png"},{"id":93651208,"identity":"50b23669-ea4a-4401-854e-b9f1ca131b8d","added_by":"auto","created_at":"2025-10-16 05:51:18","extension":"png","order_by":7,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":18469,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage13.png","url":"https://assets-eu.researchsquare.com/files/rs-7807830/v1/b80f3945828b3ea23629c7f6.png"},{"id":93649731,"identity":"49b053d3-82cc-42fe-9d9d-8628675ef69b","added_by":"auto","created_at":"2025-10-16 05:27:18","extension":"png","order_by":8,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":27534,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage14.png","url":"https://assets-eu.researchsquare.com/files/rs-7807830/v1/b5218743dec49d5e56b1e141.png"},{"id":93649192,"identity":"f20b7422-67a5-4813-9146-cc53f7e76a28","added_by":"auto","created_at":"2025-10-16 05:19:19","extension":"png","order_by":9,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":14534,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage15.png","url":"https://assets-eu.researchsquare.com/files/rs-7807830/v1/280721a4d1bab5e335035d1c.png"},{"id":93649188,"identity":"d16e3f36-a2b3-4319-9f62-b2acaeb564cc","added_by":"auto","created_at":"2025-10-16 05:19:18","extension":"png","order_by":10,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":9552,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-7807830/v1/c94f653860e0f9f451acbaf5.png"},{"id":93649737,"identity":"76dd82bf-1bf0-433d-a026-464a84031fe1","added_by":"auto","created_at":"2025-10-16 05:27:18","extension":"png","order_by":11,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":11092,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-7807830/v1/f7c8cd4911d2f269305a4e2a.png"},{"id":93649189,"identity":"e68039c8-ceed-4259-a961-7c844a73806e","added_by":"auto","created_at":"2025-10-16 05:19:19","extension":"png","order_by":12,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":10539,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-7807830/v1/c624507e4bb87d4f0453b3c5.png"},{"id":93649205,"identity":"6aab10d4-aca7-483e-881e-6f4bfb98268c","added_by":"auto","created_at":"2025-10-16 05:19:19","extension":"png","order_by":13,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":13809,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-7807830/v1/f8ee5f04202bc8fc6951174f.png"},{"id":93649209,"identity":"2fcf18d6-dcdc-4685-bed1-1d3b1c59cdda","added_by":"auto","created_at":"2025-10-16 05:19:19","extension":"png","order_by":14,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":65541,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-7807830/v1/74ee2364fa69a5a0e7be5f84.png"},{"id":93649190,"identity":"dc557e92-7339-49a2-b313-59ed90dc775e","added_by":"auto","created_at":"2025-10-16 05:19:19","extension":"png","order_by":15,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":18861,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-7807830/v1/90a8cdf5f2a6caa6f2cde2c5.png"},{"id":93649215,"identity":"57cc8937-9127-4c9f-bc52-03a5bf982536","added_by":"auto","created_at":"2025-10-16 05:19:20","extension":"png","order_by":16,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":10998,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-7807830/v1/108803984be51d2bea9dd29d.png"},{"id":93649197,"identity":"49841e5b-5391-4a6d-9680-a189954d8900","added_by":"auto","created_at":"2025-10-16 05:19:19","extension":"png","order_by":17,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":11946,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage9.png","url":"https://assets-eu.researchsquare.com/files/rs-7807830/v1/82dd1d8578b91128916ac984.png"},{"id":93649746,"identity":"1b0671ac-456d-450b-807e-ef508174f806","added_by":"auto","created_at":"2025-10-16 05:27:20","extension":"png","order_by":18,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":12444,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-7807830/v1/604ea56e07339b2e11a4ae68.png"},{"id":93649199,"identity":"3f1ab38b-69d2-48f3-a27f-24d2b33a3171","added_by":"auto","created_at":"2025-10-16 05:19:19","extension":"png","order_by":19,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":15157,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage10.png","url":"https://assets-eu.researchsquare.com/files/rs-7807830/v1/f3c42d5e3a3e0f482f6a748a.png"},{"id":93649203,"identity":"ce9a1dac-f155-4a1b-90c5-283df29962a8","added_by":"auto","created_at":"2025-10-16 05:19:19","extension":"png","order_by":20,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":17537,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage11.png","url":"https://assets-eu.researchsquare.com/files/rs-7807830/v1/9a355d28d9ac534e298a57a3.png"},{"id":93649745,"identity":"08bca1e8-77ae-4e13-835d-e0497be38044","added_by":"auto","created_at":"2025-10-16 05:27:19","extension":"png","order_by":21,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":23217,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage12.png","url":"https://assets-eu.researchsquare.com/files/rs-7807830/v1/de020bf97d53b8efa2e3c03b.png"},{"id":93649198,"identity":"a6ce5bd1-b926-4ce7-b47e-88f808ef26d4","added_by":"auto","created_at":"2025-10-16 05:19:19","extension":"png","order_by":22,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":17832,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage13.png","url":"https://assets-eu.researchsquare.com/files/rs-7807830/v1/889939e592b61659fd16ef73.png"},{"id":93649196,"identity":"671bc792-e574-4888-ba53-d94c71749d1a","added_by":"auto","created_at":"2025-10-16 05:19:19","extension":"png","order_by":23,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":26916,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage14.png","url":"https://assets-eu.researchsquare.com/files/rs-7807830/v1/6f76ea615ca626590d2b323c.png"},{"id":93649194,"identity":"d57c33e9-7b34-4fe0-861d-c71f3b7b3575","added_by":"auto","created_at":"2025-10-16 05:19:19","extension":"png","order_by":24,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":13845,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage15.png","url":"https://assets-eu.researchsquare.com/files/rs-7807830/v1/2873c7b8545e4298ce9929d8.png"},{"id":93649195,"identity":"72b89d4f-b327-41b2-ad79-3332697f7206","added_by":"auto","created_at":"2025-10-16 05:19:19","extension":"png","order_by":25,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":8791,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-7807830/v1/f300c07e2a82e077248c5b99.png"},{"id":93649200,"identity":"d4590bc7-22f7-458d-8a21-571c8420a246","added_by":"auto","created_at":"2025-10-16 05:19:19","extension":"png","order_by":26,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":10752,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-7807830/v1/43ab15583880a6a34c73a824.png"},{"id":93649204,"identity":"0c343031-969e-4b20-a5d0-b1f116444c2a","added_by":"auto","created_at":"2025-10-16 05:19:19","extension":"png","order_by":27,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":11688,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-7807830/v1/783999fd6598d39a4dfb1829.png"},{"id":93649214,"identity":"b90cbf63-b387-4ba3-88c6-be801761fa80","added_by":"auto","created_at":"2025-10-16 05:19:20","extension":"png","order_by":28,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":13409,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-7807830/v1/b6b415b43b0fb34859a6276b.png"},{"id":93649975,"identity":"aa6ef2ac-6b78-4feb-acca-ccd91b3d7db8","added_by":"auto","created_at":"2025-10-16 05:35:19","extension":"png","order_by":29,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":25006,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-7807830/v1/89b40edee5fc6a80432c95ad.png"},{"id":93649974,"identity":"51571323-2c5a-4670-840a-a8ff53a11781","added_by":"auto","created_at":"2025-10-16 05:35:19","extension":"png","order_by":30,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":9754,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-7807830/v1/879d2589e71a9c8bcd96f8a7.png"},{"id":93649742,"identity":"2bf565cd-5e7c-416f-80d6-597517affb97","added_by":"auto","created_at":"2025-10-16 05:27:19","extension":"png","order_by":31,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":10568,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-7807830/v1/3e5fcc8f364e0f23ca38f4fe.png"},{"id":93649206,"identity":"0d5369a6-f332-47ba-a2eb-5ef1b0653542","added_by":"auto","created_at":"2025-10-16 05:19:19","extension":"png","order_by":32,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":11435,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage9.png","url":"https://assets-eu.researchsquare.com/files/rs-7807830/v1/d0c349b479f32f4ddd62e163.png"},{"id":93649207,"identity":"72504802-d71d-41af-87e5-3a11844dbf1e","added_by":"auto","created_at":"2025-10-16 05:19:19","extension":"xml","order_by":33,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":136170,"visible":true,"origin":"","legend":"","description":"","filename":"960c0df7e25e4296a23c54f49d1ee3e51structuring.xml","url":"https://assets-eu.researchsquare.com/files/rs-7807830/v1/c97d1fc5012b8f55cc5f8f22.xml"},{"id":93649212,"identity":"58dd83a9-f9af-45d4-8533-784eb6f7e2f4","added_by":"auto","created_at":"2025-10-16 05:19:20","extension":"html","order_by":34,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":144062,"visible":true,"origin":"","legend":"","description":"","filename":"earlyproof.html","url":"https://assets-eu.researchsquare.com/files/rs-7807830/v1/74274d623bb79da4d3be9821.html"},{"id":93649166,"identity":"7b245b8f-425f-45f0-9994-a37834009270","added_by":"auto","created_at":"2025-10-16 05:19:18","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":47351,"visible":true,"origin":"","legend":"\u003cp\u003eFunctional Mean Diurnal Solar Irradiance by City.Functional Mean Diurnal Solar Irradiance by City.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-7807830/v1/5a1b0a5404a65c801ad35e2a.png"},{"id":93649167,"identity":"40c4a6b9-172c-4b5d-a0c5-cde146b2daaa","added_by":"auto","created_at":"2025-10-16 05:19:18","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":28706,"visible":true,"origin":"","legend":"\u003cp\u003eExplained variance of FPCA Components across Cities\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-7807830/v1/f14dd6442ca14c77cf1c58fc.png"},{"id":93649963,"identity":"803b2ccb-a089-4348-ae8b-c9da01c8a833","added_by":"auto","created_at":"2025-10-16 05:35:18","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":40548,"visible":true,"origin":"","legend":"\u003cp\u003eFunctional Clustering of Mean Daily Irradiance Profiles\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-7807830/v1/18e2b7547e70a7b1a963d37f.png"},{"id":93649725,"identity":"32df9f8a-5e93-44e5-b65d-fa131c49e3be","added_by":"auto","created_at":"2025-10-16 05:27:18","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":35816,"visible":true,"origin":"","legend":"\u003cp\u003eRobustness of FPCA: Variance explained by principal components across different basis dimensions\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-7807830/v1/d6d7640315fb35f9bcfeb44c.png"},{"id":93649182,"identity":"9a6c2588-c8f9-4c90-bc19-e699e9c8e8b2","added_by":"auto","created_at":"2025-10-16 05:19:18","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":71941,"visible":true,"origin":"","legend":"\u003cp\u003eMonthly seasonality patterns in PC1 scores across cities\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-7807830/v1/fed55524bde3f8df88e7ca56.png"},{"id":93649735,"identity":"347662da-ec17-49d9-9ca3-a3ce2ef9c004","added_by":"auto","created_at":"2025-10-16 05:27:18","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":137138,"visible":true,"origin":"","legend":"\u003cp\u003eCorrelation matrices of solar irradiance and meteorological variables across cities.\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-7807830/v1/53fb19239223db3bf5f40b16.png"},{"id":93649729,"identity":"36e75cf5-3f70-4cf8-a500-2ce36800304a","added_by":"auto","created_at":"2025-10-16 05:27:18","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":46415,"visible":true,"origin":"","legend":"\u003cp\u003eKey Meteorological Predictors of Solar Irradiance Variability by City\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-7807830/v1/82a4660ebb2e66a05b012a0f.png"},{"id":93650796,"identity":"d496ee02-c512-4d60-b043-e8e7d4da7e37","added_by":"auto","created_at":"2025-10-16 05:43:18","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":60194,"visible":true,"origin":"","legend":"\u003cp\u003eAutocorrelation of daily log-returns of solar Irradiance across cities\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-7807830/v1/c02a5c47e730e02ca4ffdd1e.png"},{"id":93649970,"identity":"090de45d-9af9-4dfd-8f8f-54160cf803d6","added_by":"auto","created_at":"2025-10-16 05:35:18","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":65775,"visible":true,"origin":"","legend":"\u003cp\u003eAutocorrelation of squared daily log-returns of solar irradiance across cities\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-7807830/v1/25ff79a5cb831be4cc9ca8c2.png"},{"id":93649193,"identity":"29a18ab3-7f64-4595-a7a0-c19d56154b02","added_by":"auto","created_at":"2025-10-16 05:19:19","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":76887,"visible":true,"origin":"","legend":"\u003cp\u003eVolatility patterns in daily solar energy log-returns across cities\u003c/p\u003e","description":"","filename":"10.png","url":"https://assets-eu.researchsquare.com/files/rs-7807830/v1/4fd36dd515b34196e530d644.png"},{"id":93650800,"identity":"99c759d7-e56a-4ea9-8357-95ccdbee2f11","added_by":"auto","created_at":"2025-10-16 05:43:18","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":87900,"visible":true,"origin":"","legend":"\u003cp\u003eModeling conditional volatility of solar energy log-returns using GARCH family models\u003c/p\u003e","description":"","filename":"11.png","url":"https://assets-eu.researchsquare.com/files/rs-7807830/v1/92867c32ba5ad1ed4b1e6053.png"},{"id":93649184,"identity":"46269eb9-16fe-4e9a-af3a-651fb75c8887","added_by":"auto","created_at":"2025-10-16 05:19:18","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":99283,"visible":true,"origin":"","legend":"\u003cp\u003eVolatility dynamics of solar energy returns and the role of climate drivers\u003c/p\u003e","description":"","filename":"12.png","url":"https://assets-eu.researchsquare.com/files/rs-7807830/v1/93834e84d4373aa6079e345d.png"},{"id":93649743,"identity":"9f41d392-77df-4d30-9943-2ae48e6b266e","added_by":"auto","created_at":"2025-10-16 05:27:19","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":62848,"visible":true,"origin":"","legend":"\u003cp\u003eImpact of precipitation and humidity on conditional volatility of solar energy returns\u003c/p\u003e","description":"","filename":"13.png","url":"https://assets-eu.researchsquare.com/files/rs-7807830/v1/1115fcaebc33b01d7b201d84.png"},{"id":93649971,"identity":"3def1325-b719-4095-ad30-ae8f4c0ebc6d","added_by":"auto","created_at":"2025-10-16 05:35:19","extension":"png","order_by":14,"title":"Figure 14","display":"","copyAsset":false,"role":"figure","size":99877,"visible":true,"origin":"","legend":"\u003cp\u003eExplaining conditional volatility of solar energy returns through climatic drivers\u003c/p\u003e","description":"","filename":"14.png","url":"https://assets-eu.researchsquare.com/files/rs-7807830/v1/0628ddaf1257a200f6a7a33e.png"},{"id":93649741,"identity":"95e9deb0-b515-4d8b-9804-65ad4adbfa4c","added_by":"auto","created_at":"2025-10-16 05:27:19","extension":"png","order_by":15,"title":"Figure 15","display":"","copyAsset":false,"role":"figure","size":85914,"visible":true,"origin":"","legend":"\u003cp\u003eVAR-based dynamic responses of solar energy returns to shocks\u003c/p\u003e","description":"","filename":"15.png","url":"https://assets-eu.researchsquare.com/files/rs-7807830/v1/68b99711980c3bb72346ad58.png"},{"id":93682013,"identity":"86821081-9143-49f5-be80-f0f2c02d2f85","added_by":"auto","created_at":"2025-10-16 12:30:30","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1792759,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7807830/v1/e429279b-1d86-4918-9ee5-c4b4d9e4c9a2.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Nonlinear Drivers and Volatility of Solar Radiation Variability in Asian Megacities: A Functional Time-Series Approach","fulltext":[{"header":"Introduction","content":"\u003ch3\u003eBackground and Context\u003c/h3\u003e\n\u003cp\u003eSolar radiation is the foundation of the Earth\u0026apos;s climate system and one of the most promising renewable energy sources(Huang et al., \u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e). Its variability determines energy system reliability, climate feedback mechanisms, and policy decisions regarding sustainable development(Krūmiņ\u0026scaron; \u0026amp; Kļaviņ\u0026scaron;, 2023). In Asia, where megacities are undergoing rapid urbanization and industrialization, solar radiation is influenced by multiple interacting drivers, such as air pollution, monsoon cycles, tropical cyclones, and regional climate variability(Huang et al., \u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e; Qian et al., \u003cspan class=\"CitationRef\"\u003e2022\u003c/span\u003e). These factors create complex patterns that complicate the stability and predictability of solar energy production.(Hou et al., \u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e). Consequently, the application of sophisticated statistical methodologies, such as functional time series models and generalized autoregressive conditional heteroskedasticity processes, becomes imperative for accurately characterizing these complex dynamics (Eu\u0026aacute;n et al., \u003cspan class=\"CitationRef\"\u003e2022\u003c/span\u003e).\u003c/p\u003e\n\u003cp\u003eAccurate characterization of solar variability is crucial not only for energy planning but also for climate risk analysis in highly populated regions(Huang et al., \u003cspan class=\"CitationRef\"\u003e2020\u003c/span\u003e). Traditional approaches, which rely on linear regression models or mean climatological approximations, fail to capture nonlinear dynamics, abrupt regime shifts, and volatility clustering under realistic meteorological conditions(Yu et al., \u003cspan class=\"CitationRef\"\u003e2020\u003c/span\u003e). This limitation promotes the integration of functional time series methods, where solar radiation is treated as continuous curves with nonlinear and volatility frameworks, which reveal threshold effects and uncertainty patterns(Huang et al., \u003cspan class=\"CitationRef\"\u003e2020\u003c/span\u003e). This approach offers a significant improvement over traditional metrics, which often fail to isolate stochastic fluctuations from deterministic trends, by providing a normalized, dimensionless measure of variability that accounts for temporal dependencies (Voyant et al., 2025). Our comparative analyses demonstrate that such sophisticated models proficiently encapsulate multi-scale fluctuations, addressing significant limitations inherent in traditional metrics (Voyant et al., 2025).\u003c/p\u003e\n\u003ch3\u003eResearch Problem and Objectives\u003c/h3\u003e\n\u003cp\u003eDespite the growing body of literature on solar energy, there remains a critical gap in the representation of the nonlinear and functional characteristics of solar variability in Asian megacities(Pandey et al., \u003cspan class=\"CitationRef\"\u003e2022\u003c/span\u003e). Existing studies tend to disregard the daily functional form of solar radiation, neglect the nonlinear threshold behavior of meteorological drivers, and fail to adequately quantify volatility clustering in the presence of extreme weather events(Qian et al., \u003cspan class=\"CitationRef\"\u003e2022\u003c/span\u003e). Therefore, policymakers and energy planners do not have useful tools for high-resolution forecasting and risk planning(Huang et al., \u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e\n\u003cp\u003eTo address this gap, the present study pursues the following objectives:\u003c/p\u003e\n\u003cp\u003e\u003cspan\u003e\u003c/span\u003e\u003c/p\u003e\n\u003cp\u003e1. Functional Representation of Solar Radiation Dynamics\u003c/p\u003e\n\u003cp\u003e\u003c/p\u003e\n\u003cdiv class=\"BlockQuote\"\u003e\n \u003cp\u003eSolar radiation components are modelled as continuous daily curves (from sunrise to sunset), and dominant modes of variability across different climatic regimes via functional data analysis (FDA), functional principal component analysis (FPCA), and functional clustering.\u003c/p\u003e\n\u003c/div\u003e\n\u003cp\u003e\u003cspan\u003e\u003c/span\u003e\u003c/p\u003e\n\u003cp\u003e2. Identification of Nonlinear and Threshold Drivers\u003c/p\u003e\n\u003cp\u003e\u003c/p\u003e\n\u003cdiv class=\"BlockQuote\"\u003e\n \u003cp\u003eTo examine how meteorological variables\u0026mdash;including temperature, humidity, wind, precipitation, and pressure\u0026mdash;act as nonlinear or threshold-dependent drivers of solar variability, threshold autoregressive (TAR), smooth transition autoregressive (STAR), and functional regression approaches are used.\u003c/p\u003e\n\u003c/div\u003e\n\u003cp\u003e\u003cspan\u003e\u003c/span\u003e\u003c/p\u003e\n\u003cp\u003e3. Modelling the Volatility and Uncertainty in Solar Energy\u003c/p\u003e\n\u003cp\u003e\u003c/p\u003e\n\u003cdiv class=\"BlockQuote\"\u003e\n \u003cp\u003eTo capture volatility clustering and quantify uncertainty in solar radiation and energy production, particularly under monsoon conditions and extreme weather events, through GARCH-family models, VAR/VARX structures are used.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\n \u003ch2\u003eResearch Gap and Significance\u003c/h2\u003e\n \u003cp\u003eWhile the literature has provided excellent insights into mean solar trends and climatic effects(Huang et al., \u003cspan class=\"CitationRef\"\u003e2020\u003c/span\u003e), there are three important gaps.\u003c/p\u003e\n \u003cp\u003e\u0026bull; Functional representation: Few studies have used the FDA to represent solar radiation as continuous curves, despite its apparent advantages in capturing intraday dynamics(Hou et al., \u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e; Huang et al., \u003cspan class=\"CitationRef\"\u003e2020\u003c/span\u003e).\u003c/p\u003e\n \u003cp\u003e\u0026bull; Nonlinear drivers: Nonlinear thresholds caused by meteorological variables, such as spikes in humidity during monsoons or sudden temperature drops during storms, are less studied(Bowden et al., \u003cspan class=\"CitationRef\"\u003e2023\u003c/span\u003e).\u003c/p\u003e\n \u003cp\u003e\u0026bull; Uncertainty and volatility: Existing models inadequately represent volatility clustering, which is vital for solar energy planning in monsoon-variable and extreme weather-prone areas(Kim et al., \u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e\n \u003cp\u003eBy addressing these gaps, this study offers methodological novelty and practical relevance. These findings will enhance the predictive capacity for solar energy production and guide climate-resilience planning. In addition, the study focuses on five representative Asian megacities\u0026mdash;New Delhi (India), Dhaka (Bangladesh), Jakarta (Indonesia), Manila (Philippines), and Kuala Lumpur (Malaysia)\u0026mdash;chosen on the basis of their diverse climatic regimes, which span from monsoon-influenced to tropical and equatorial systems(Nik et al., 2020). The comparative multicity design ensures that the results are not only statistically reliable but also regionally relevant, making them more useful for energy policy and climate adaptation planning.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"Literature Review","content":"\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\n \u003ch2\u003eReview of Related Studies\u003c/h2\u003e\n \u003cp\u003eSolar radiation has been widely studied because of its central role in solar energy development, climate science, and atmospheric modelling(G\u0026uuml;rel et al., \u003cspan class=\"CitationRef\"\u003e2023\u003c/span\u003e; Huang et al., \u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e). Early research mainly employed statistical regression and climatological means to estimate the solar energy potential by region(Obaideen et al., 2023). Although these approaches provide adequate baseline information, they are incapable of capturing the intraday complexity and nonlinear dynamic characteristics of solar radiation variability(Quansah et al., \u003cspan class=\"CitationRef\"\u003e2022\u003c/span\u003e).\u003c/p\u003e\n \u003cp\u003eStudies in South Asia and Southeast Asia have highlighted the extent to which seasonal monsoon regimes and tropical climatic conditions strongly affect solar radiation(Mol et al., \u003cspan class=\"CitationRef\"\u003e2023\u003c/span\u003e). For example, rainforests and humidity produced by monsoon-induced rains in cities such as Dhaka and Manila reduce solar irradiance significantly during rainy seasons(Yang et al., \u003cspan class=\"CitationRef\"\u003e2022\u003c/span\u003e), whereas air pollution and temperature variability in cities such as New Delhi further add variability(Tan et al., \u003cspan class=\"CitationRef\"\u003e2023\u003c/span\u003e). Experiments conducted in equatorial regions, such as Kuala Lumpur and Jakarta, emphasized the persistent influence of cloud cover in modulating solar cycles(Baghel \u0026amp; Chander, \u003cspan class=\"CitationRef\"\u003e2022\u003c/span\u003e). However, most such studies have utilized mean-value models and overlooked threshold effects and abrupt regime shifts in solar behavior(Correa et al., \u003cspan class=\"CitationRef\"\u003e2022\u003c/span\u003e).\u003c/p\u003e\n \u003cp\u003eNew technological developments in time series modelling have introduced ARIMA, ANN, and VAR-based solar forecasting models(Vel\u0026aacute;squez, 2022). These methods improve short-term forecasts but are still limited in handling the functional and nonlinear characteristics of solar data(Barhmi et al., \u003cspan class=\"CitationRef\"\u003e2024\u003c/span\u003e; Fara et al., 2021). Moreover, the dynamics of volatility clustering, where periods of high solar variability are followed by prolonged instability, have only recently begun to be Addressed, and some examples of GARCH-type models have appeared in renewable energy studies(Zaffar, 2021).\u003c/p\u003e\n \u003cp\u003eMore promising have been the series of literature streams that have resulted from the use of functional data analysis (FDA). The FDA allows solar radiation to be treated as continuous daily curves(Fara et al., 2021), allowing for the extraction of leading modes of variability with techniques such as functional principal component analysis (FPCA)(Jiao et al., \u003cspan class=\"CitationRef\"\u003e2023\u003c/span\u003e). In addition, threshold autoregressive (TAR) and Smooth Transition Autoregressive (STAR) models have been found to be useful in extracting nonlinear regime-dependent dynamics from environmental and energy systems(Hoffmann et al., \u003cspan class=\"CitationRef\"\u003e2020\u003c/span\u003e). However, the FDA, nonlinear drivers, and volatility modelling remain underdeveloped in the solar literature, particularly for Asian megacities with the most intense climatic variability(Pandey et al., \u003cspan class=\"CitationRef\"\u003e2022\u003c/span\u003e).\u003c/p\u003e\n\u003c/div\u003e\n\u003ch3\u003eTheoretical Framework\u003c/h3\u003e\n\u003cp\u003eThe theoretical underpinning of this study is a multilayered theoretical framework that integrates functional, nonlinear, and volatility frameworks to fully account for solar variability. The three strands of this complementary framework are outlined as follows:\u003c/p\u003e\n\u003cp\u003e1. Functional Data Theory (FDA and FPCA)\u003c/p\u003e\n\u003cul\u003e\n \u003cli\u003e\n \u003cp\u003eSolar radiation observations are operated as continuous curves rather than discrete points(Stefani et al., \u003cspan class=\"CitationRef\"\u003e2024\u003c/span\u003e).\u003c/p\u003e\n \u003c/li\u003e\n \u003cli\u003e\n \u003cp\u003eThis study provides a means to identify leading patterns of intraday variability and compare climatic regions(David et al. \u003cspan class=\"CitationRef\"\u003e2016\u003c/span\u003e).\u003c/p\u003e\n \u003c/li\u003e\n \u003cli\u003e\n \u003cp\u003eClustering of solar profiles, whereby days or regimes can be grouped, is provided(Santiago et al., 2021).\u003c/p\u003e\n \u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003e2. Nonlinear Time-Series Theory (TAR/STAR and Functional Regression)\u003c/p\u003e\n\u003cul\u003e\n \u003cli\u003e\n \u003cp\u003eThis is because solar variability is not linear but regime-dependent(Zafar et al., \u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e\n \u003c/li\u003e\n \u003cli\u003e\n \u003cp\u003eTAR models identify abrupt threshold effects, such as sharp radiation reductions during heavy precipitation(Zwaard et al., 2021).\u003c/p\u003e\n \u003c/li\u003e\n \u003cli\u003e\n \u003cp\u003eSTAR models enable smooth transitions between states (e.g., from clear sky to overcast) in accordance with real atmospheric processes(Dash et al., \u003cspan class=\"CitationRef\"\u003e2023\u003c/span\u003e).\u003c/p\u003e\n \u003c/li\u003e\n \u003cli\u003e\n \u003cp\u003eFunctional regression enables the linking of meteorological drivers (temperature, humidity, wind, precipitation, etc.) to solar radiation curves(Wang \u0026amp; Wen, \u003cspan class=\"CitationRef\"\u003e2022\u003c/span\u003e).\u003c/p\u003e\n \u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003e3. Volatility and uncertainty theory (GARCH and VAR/VARX Models)\u003c/p\u003e\n\u003cul\u003e\n \u003cli\u003e\n \u003cp\u003eModels based on financial econometrics estimate time-varying conditional variance(Haputhanthri et al., \u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e\n \u003c/li\u003e\n \u003cli\u003e\n \u003cp\u003eThey capture volatility clustering during extreme weather, monsoon onset, and prolonged cloudiness(Prasad \u0026amp; Kay, \u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e\n \u003c/li\u003e\n \u003cli\u003e\n \u003cp\u003eVAR/VARX models extend this by introducing exogenous meteorological drivers and monitoring lagged interactions between solar variability and weather(Vyas et al., 2022).\u003c/p\u003e\n \u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eBy bringing together these strands, the theoretical framework ensures that the research captures structural patterns (the FDA), nonlinear drivers (TAR/STAR), and uncertainty dynamics (GARCH/VAR). This joined-up framework spans a critical research gap in solar radiation studies and strengthens the methodological foundation for policy-relevant energy forecasting.\u003c/p\u003e"},{"header":"Materials and methods","content":"\u003cp\u003eFive major Asian cities\u0026mdash;Dhaka (Bangladesh), New Delhi (India), Jakarta (Indonesia), Manila (Philippines), and Kuala Lumpur (Malaysia)\u0026mdash;were chosen to represent diverse climatic conditions, including monsoon-dominated, tropical, and equatorial climates(Romitti \u0026amp; Wing, 2022). The observations between July 01, 2016, and June 30, 2025, were taken from the NASA POWER Project. These datasets, in the CSV format, were made up of hourly solar radiation and meteorological data that were additionally merged into daily profiles for functional and time-series analysis.\u003c/p\u003e\u003cp\u003eEach dataset included time data (YEAR, MO, DY, and HR) and significant solar radiation variables: All-sky surface shortwave downward irradiance (ALLSKY_SFC_SW_DWN), clear-sky surface shortwave downward irradiance (CLRSKY_SFC_SW_DWN), all-sky direct normal irradiance (ALLSKY_SFC_SW_DNI), all-sky diffuse irradiance (ALLSKY_SFC_SW_DIFF), and the all-sky insolation clearness index (ALLSKY_KT). Moreover, meteorological variables, which included the air temperature at 2 m (T2M), relative humidity at 2 m (RH2M), corrected total precipitation (PRECTOTCORR), surface pressure (PS), and wind speed at 10 m (WS10M)(Tercha et al., \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). Data preprocessing involves the treatment of missing values and the application of linear and spline interpolation techniques(Park et al., \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2019\u003c/span\u003e) for preserving time series continuity. The statistical analysis was performed via R version 4.5.1. The analysis technique utilized functional data analysis, nonlinear time series modelling, and volatility modelling. The FDA was utilized through the fda, fda.usc, and refund packages, whereas nonlinear dynamics were handled by threshold autoregressive (TAR) and smooth transition autoregressive (STAR) models under the tsDyn package. The uncertainty, volatility, and variability of solar energy were simulated via GARCH-family models via the rugarch package, whereas the multivariate interaction between solar energy and weather variables was explored via vector autoregression (VAR/VARX) via the vars package. Other packages such as dplyr, tidyr, and zoo, were employed for data preprocessing, whereas ggplot2 and corrplot were employed to visualize the data and conduct diagnostic testing.\u003c/p\u003e\u003cp\u003eThe research was conducted in three phases on the absis of the behavioral objectives.\u003c/p\u003e\u003cp\u003eIn phase one, solar irradiance hourly data were converted into effective daily curves for sunrise to sunset. Intrday variation modes were identified using functional principal component analysis (FPCA)(Gradwohl et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2021\u003c/span\u003e), and functional scores were categorized to partition the radiation regime classes into hourly intervals at the five stations.\u003c/p\u003e\u003cp\u003eIn the second phase, the drivers of nonlinear and threshold changes in solar radiation were determined(Tye et al., \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Daily averaging was used for the meteorological variables, and their associations with functional principal components were investigated(Bai et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). The TAR model and STAR model accounted for the regime-dependent impacts of temperature, humidity, precipitation, and wind, whereas the functional regression methods characterized the impacts of the predictors on the shape of the solar radiation curve(Costa et al., \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eThe final step addresses volatility and uncertainty by taking daily solar energy forecasts in terms of log returns and using GARCH-family models (GARCH, TGARCH, EGARCH, and APARCH) to check for evidence of volatility persistence and clustering(Sedai et al., \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). The findings of volatility were checked against meteorological parameters, i.e., rain, relative humidity, and the clearness index, for causal effect interpretation, and VAR/VARX models were used to identify lagged interactions between weather and changes in solar radiation(Zhu et al., \u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2020\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eA number of procedures were used to evaluate model robustness and verification. Cross-validation was applied to handle missing data, and interannual cross-validation and seasonal cross-validation were used to test model performance across different climate conditions(Mishra et al., 2023). Robustness was also confirmed through the usage of varying numbers of function basis functions (13, 17, and 21) and taking into account the GARCH-family models on the basis of AIC and BIC tests(AlOmar et al., \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Killeen et al., \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). This approach needs a multistep procedure that offers a combined treatment of structural shattering, nonlinear meteorological thresholds, and volatility dynamics of the solar radiation changes in South Asia and Southeast Asian megacities of these predictors on the basis of the shape of the solar radiation curve(Aman et al., \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Kanga et al., 2022). The final step addresses volatility and uncertainty by casting daily solar energy forecasts to log returns and modelling GARCH-family models (GARCH, TGARCH, EGARCH, and APARCH) to search for evidence of volatility clustering and persistence(T et al., 2024). Volatility outcomes were also compared with meteorological drivers, that is, precipitation, relative humidity, and clearness index, for causal effect interpretation, and the VAR/VARX models were used to reveal lagged weather solar radiation change interactions(Hou et al., \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2023\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eRobustness and model checking were achieved via several methods. The missing data treatments were cross-validated, and season and interannual cross-validations were conducted to check model performance under different climatic conditions(Wang \u0026amp; Shi, \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Robustness was verified by altering the number of function basis functions (13, 17, and 21) and comparing the GARCH-family models via the AIC and BIC(Szostek et al., \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). Together, this calls for a multistep procedure that provides a composite methodology for revealing structural breaks, nonlinear meteorological thresholds, and volatility dynamics in solar radiation variations in South and Southeast Asian megacities.\u003c/p\u003e"},{"header":"Results","content":"\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e\n \u003ch2\u003eFunctional Representation of Solar Variability\u003c/h2\u003e\n \u003cdiv class=\"gridtable\"\u003e\n \u003cdiv align=\"char\" class=\"colspec\"\u003e\u003cbr\u003e\u003c/div\u003e\n \u003ctable id=\"Tab1\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eSummary of the FPCA results, clustering, correlations, robustness, and seasonality across five Asian megacities.\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eCity\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eVar. (PC1 //PC2 //PC3,\u003c/p\u003e\n \u003cp\u003e%)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eCum. Var. (PC1\u0026ndash;3)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eClusters (n1 // n2 // n3)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003ePC1\u0026ndash;Met Corr. (RH // Rain // Wind // Temp)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eRobustness (nb\u0026thinsp;=\u0026thinsp;13\u0026ndash;21)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eANOVA\u003c/p\u003e\n \u003cp\u003eF (month)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eP_value\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eDhaka\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e84.1 // 9.4 // 3.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e97\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1192 // 31 // 2064\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-75.7575758\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e84.4 \u0026rarr; 83.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e49.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eJakarta\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e85.9 // 7.0 // 4.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e97.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e31 // 2132 // 1124\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-1477.27273\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e84.4 \u0026rarr; 83.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e42.6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eKuala Lumpur\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e86.4 // 6.8 // 4.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e97.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2098 // 31 // 1158\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1851.851852\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e84.4 \u0026rarr; 83.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e34.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eManila\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e85.8 // 9.2 // 3.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e98.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1064 // 2192 // 31\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-118.75\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e84.4 \u0026rarr; 83.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e54.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNew Delhi\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e85.8 // 9.0 // 2.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e97.7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1512 // 1744 // 31\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e64.55083378\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e84.4 \u0026rarr; 83.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e81.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n \u003cp\u003eThe FPCA decomposition revealed that the first three PCs explained nearly all the variability in the daily solar irradiance curves. Table \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e shows that PC1 explained 84\u0026ndash;86% of the total variance among cities, and PC2 and PC3 explained 6\u0026ndash;10% and 3\u0026ndash;5%, respectively. The total variance in all the scenarios was greater than 97%, confirming that most of the variation in solar radiation was captured on a low-dimensional functional basis.\u003c/p\u003e\n \u003cp\u003eThe mean functional curves (Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e) showed typical diurnal patterns, rising after sunrise, peaking at approximately midday, and dropping towards sunset. Kuala Lumpur and Manila recorded the highest midday peaks (\u0026gt;\u0026thinsp;700 W/m\u0026sup2;), and Dhaka showed lower irradiance throughout the year owing to increased atmospheric attenuation by aerosols and cloud cover.\u003c/p\u003e\n \u003cp\u003eCluster analysis revealed three distinct regimes for each city (Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e). Large clusters were mapped to standard clear-sky or partially cloudy days, and small clusters detected exceptional weather-driven extremes such as monsoon rain storms or storm events.\u003c/p\u003e\n \u003cp\u003eThe sub clusters capture the day-to-day heterogeneity of solar input and demonstrate the operationally useful value of unusual day modelling. The scree plots (Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e) confirmed the pervasive dominance of PC1 in explaining variance.\u003c/p\u003e\n \u003cp\u003eRobustness tests with different basis dimensions (nbasis\u0026thinsp;=\u0026thinsp;13, 17, 21) resulted in very similar variances (Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e), confirming that the FPCA results were methodology insensitive and thus extremely stable.\u003c/p\u003e\n \u003cp\u003eThe monthly boxplots (Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e) revealed strong seasonality in Dhaka, Manila, and New Delhi, where the PC1 values were the highest in the dry season and the lowest during the monsoon season. Conversely, Kuala Lumpur and Jakarta presented flat seasonality in accordance with equatorial regimes. ANOVA confirmed significant seasonal effects in both cities (p\u0026thinsp;\u0026lt;\u0026thinsp;0.001). Correlation analysis (Table \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e) confirmed that PC1 was negatively correlated with relative humidity (\u0026minus;\u0026thinsp;0.18 to \u0026minus;\u0026thinsp;0.24) and rainfall (\u0026minus;\u0026thinsp;0.09 to \u0026minus;\u0026thinsp;0.20). Temperature was significantly positively correlated in New Delhi (+\u0026thinsp;0.26), as anticipated, with cloudier skies and a wetter continental climate.\u003c/p\u003e\n\u003c/div\u003e\n\u003ch3\u003eSolar Variability Nonlinear and Threshold Drivers\u003c/h3\u003e\n\u003cp\u003eNonlinear and threshold analyses revealed pronounced city-level trends in the meteorological regulation of solar energy variability.\u003c/p\u003e\n\u003cp\u003eThe heatmaps of correlations (Fig. \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e) show that in Dhaka and Manila, solar irradiance is highly significantly negatively correlated with relative humidity and precipitation, which is consistent with the monsoon season. New Delhi had highly significant positive correlations with temperature, which is consistent with dry season dominance, whereas Jakarta and Kuala Lumpur had weaker but significant correlations with the pressure and diurnal temperature range.\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n \u003ctable id=\"Tab2\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eEffects of key weather drivers and the GAM on solar energy production Generalized additive models (Table \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e) confirmed these trends. The temperature range (T2M_range) was always a positive force across all cities, and precipitation (PRECTOT) was negative, most strongly in Dhaka, Manila and Kuala Lumpur. New Delhi is the only exception, where the mean temperature and humidity are positively influential, and where precipitation is highly negative.\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eCity\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eTop Predictors (r)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eGAM Effects (Estimate\u0026thinsp;\u0026plusmn;\u0026thinsp;SE, Effect)\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eDhaka\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRH2M \u0026minus;\u0026thinsp;0.20; T2M_max\u0026thinsp;+\u0026thinsp;0.19\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eT2M_mean 0.195\u0026thinsp;\u0026plusmn;\u0026thinsp;0.021 (Positive); PRECTOT \u0026minus;\u0026thinsp;0.00098\u0026thinsp;\u0026plusmn;\u0026thinsp;0.00018 (Negative); T2M_range 0.181\u0026thinsp;\u0026plusmn;\u0026thinsp;0.036 (Positive)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eJakarta\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eT2M_range\u0026thinsp;+\u0026thinsp;0.25; RH2M \u0026minus;\u0026thinsp;0.19\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eT2M_range 0.633\u0026thinsp;\u0026plusmn;\u0026thinsp;0.076 (Positive); PS \u0026minus;\u0026thinsp;1.38\u0026thinsp;\u0026plusmn;\u0026thinsp;0.423 (Negative); T2M_mean \u0026minus;\u0026thinsp;0.184\u0026thinsp;\u0026plusmn;\u0026thinsp;0.082 (Negative)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eKuala Lumpur\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eT2M_range\u0026thinsp;+\u0026thinsp;0.18; T2M_max\u0026thinsp;+\u0026thinsp;0.15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eT2M_range 0.347\u0026thinsp;\u0026plusmn;\u0026thinsp;0.051 (Positive); PRECTOT \u0026minus;\u0026thinsp;0.00056\u0026thinsp;\u0026plusmn;\u0026thinsp;0.00025 (Negative)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eManila\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eT2M_range\u0026thinsp;+\u0026thinsp;0.35; RH2M \u0026minus;\u0026thinsp;0.31\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eT2M_range 0.411\u0026thinsp;\u0026plusmn;\u0026thinsp;0.054 (Positive); PRECTOT \u0026minus;\u0026thinsp;0.00064\u0026thinsp;\u0026plusmn;\u0026thinsp;0.00016 (Negative); PS 1.10\u0026thinsp;\u0026plusmn;\u0026thinsp;0.280 (Positive); WS10M_mean 0.502\u0026thinsp;\u0026plusmn;\u0026thinsp;0.193 (Positive)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNew Delhi\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eT2M_max\u0026thinsp;+\u0026thinsp;0.29; T2M_mean\u0026thinsp;+\u0026thinsp;0.23\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eT2M_mean 0.178\u0026thinsp;\u0026plusmn;\u0026thinsp;0.018 (Positive); T2M_range 0.278\u0026thinsp;\u0026plusmn;\u0026thinsp;0.029 (Positive); RH2M 0.030\u0026thinsp;\u0026plusmn;\u0026thinsp;0.005 (Positive); PRECTOT \u0026minus;\u0026thinsp;0.00180\u0026thinsp;\u0026plusmn;\u0026thinsp;0.00040 (Negative)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eGeneralized additive models (Table 2) confirmed these trends. The temperature range (T2M_range) was always a positive force across all cities, and precipitation (PRECTOT) was negative, most strongly in Dhaka, Manila and Kuala Lumpur. New Delhi is the only exception, where the mean temperature and humidity are positively influential, and where precipitation is highly negative.\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n \u003ctable id=\"Tab3\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eComparison of TAR and STAR model fits with key coefficients, thresholds, and GAM-derived nonlinear drivers for solar energy production across Cities.\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eCity\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eModel (Best / Type)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eAIC / BIC\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eLjung\u0026ndash;Box \u003cem\u003ep\u003c/em\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eLow-Regime (Const / \u0026phi;₁ / \u0026phi;₂)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eHigh-Regime (Const / \u0026phi;₁ / \u0026phi;₂)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eThreshold (Value / Variable / GAM Variable / GAM Value)\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eDhaka\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eTAR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e946 / 965\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.969\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e100.0 / 0.740 / \u0026minus;0.516\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u0026minus;1441 / 2.17 / 7.48\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e150 / PRECTOT / PRECTOT / 43.4\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eJakarta\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eTAR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e925 / 944\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.909\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026minus;994.0 / 7.92 / 0.135\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e64.7 / 0.55 / \u0026minus;0.009\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e134 / WS10M_max / WS10M_max / 4.02\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eKuala Lumpur\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eTAR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e947 / 966\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e111.0 / 0.175 / 0.061\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u0026minus;1063 / 4.20 / 3.58\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e149 / T2M_mean / T2M_mean / 25.7\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eManila\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSTAR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e927 / 948\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.995\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e78.4 / 0.691 / \u0026minus;0.186\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u0026minus;4175 / 8.22 / 12.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e204 / PRECTOT / PRECTOT / 108\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNew Delhi\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSTAR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e789 / 810\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.525\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e64.1 / 1.08 / \u0026minus;0.534\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u0026minus;6536 / 17.0 / 15.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e200 / RH2M / RH2M / 48.3\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eThreshold models (Table \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e) highlight regime-dependent changes. Dhaka is said to possess a rainfall threshold (~\u0026thinsp;43 mm) that demarcates high-irradiance and monsoon-dominant days. Jakarta has a wind threshold (~\u0026thinsp;4 m/s), Kuala Lumpur has a temperature threshold (~\u0026thinsp;25.7\u0026deg;C), Manila has a precipitation threshold (~\u0026thinsp;108 mm), and New Delhi has a humidity threshold (~\u0026thinsp;48%). All these thresholds confirm the existence of rapid drops in irradiance when specific climatic thresholds are reached.\u003c/p\u003e\n\u003cp\u003eThe variable importance plots (Fig. \u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e) revealed the largest contributions from T2M_range, precipitation, and pressure, with smaller contributions from wind speed (Manila) and surface pressure (Jakarta and Manila).\u003c/p\u003e\n\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\n \u003ch2\u003eVolatility and Uncertainty in Solar Energy Production\u003c/h2\u003e\n \u003cp\u003eThe heteroskedasticity is further supported by autocorrelation analysis. The ACF of log-returns (Fig. \u003cspan class=\"InternalRef\"\u003e8\u003c/span\u003e) showed no serial correlation at the significance level, and the ACF of squared returns (Fig. \u003cspan class=\"InternalRef\"\u003e9\u003c/span\u003e) showed long-term positive autocorrelation, reflecting volatility clustering in the data.\u003c/p\u003e\n \u003cp\u003ePlots of the time series of log returns (Fig. \u003cspan class=\"InternalRef\"\u003e10\u003c/span\u003e) further show recurrent peaceful and stormy intervals, with Dhaka and Manila having the highest peaks, especially during monsoons.\u003c/p\u003e\n \u003cp\u003eThe conditional volatility predictions from the GARCH, TGARCH, and EGARCH models (Fig. \u003cspan class=\"InternalRef\"\u003e11\u003c/span\u003e) capture these dynamics well.\u003c/p\u003e\n \u003cp\u003eAll three models replicated periods of high and low volatility, with EGARCH highlighting asymmetric effects, under which volatility spikes more strongly after negative shocks such as rain or cloud cover. The role of meteorological drivers was examined by overlaying precipitation and humidity on model-based volatility (Fig. \u003cspan class=\"InternalRef\"\u003e12\u003c/span\u003e).\u003c/p\u003e\n \u003cp\u003eHigh volatility coincided with high rainfall and increased humidity, especially in Dhaka and Manila, confirming that extreme weather increases uncertainty. Scatterplots of \u0026sigma; against rainfall and humidity (Fig. \u003cspan class=\"InternalRef\"\u003e13\u003c/span\u003e) exhibited clear positive slopes, revealing increased variance with higher and more humid rainfall.\u003c/p\u003e\n \u003cp\u003eAn integrated multii-panel summary (Fig. \u003cspan class=\"InternalRef\"\u003e14\u003c/span\u003e) confirmed the results, with statistically significant correlations (p\u0026thinsp;\u0026lt;\u0026thinsp;0.001) between conditional volatility and drivers across all cities. Precipitation consistently had the most significant effect, with relative humidity contributing to equatorial metropolises, such as Jakarta and Kuala Lumpur.\u003c/p\u003e\n \u003cp\u003eFinally, the impulse\u0026ndash;response functions derived from the VAR models (Fig.\u0026nbsp;15) show that precipitation shocks had an instantaneous negative impact on solar returns, after which partial recovery was observed after 3\u0026ndash;5 days. Dhaka and Manila presented the most intense responses, whereas Jakarta and Kuala Lumpur presented somewhat more moderate responses, and New Delhi presented slightly longer persistence.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"Discussion","content":"\u003cp\u003eThe FPCA results indicate that a diurnal solar irradiance cycle exists, but its variability is governed by local climate regimes. Dhaka and Manila are governed by monsoonal cloudiness and precipitation with high seasonal cycles, whereas Jakarta and Kuala Lumpur have relatively uniform year-round irradiance regimes. New Delhi is governed by the temperature and humidity dynamics of continental climates. Cluster analysis reveals the differential regimes of the sun, distinguishing normal workdays from unusual weather days. This reinforces the need for regime-sensitive forecasting models with the capacity to predict unusual but substantial reductions in solar availability. Meteorological correlations underpin physical processes: rain and humidity reduce solar radiation uniformly, and dryness, particularly in New Delhi, increases availability. Robustness tests provide additional assurance that these outcomes are free from the artifacts of modelling assumptions. From a planning perspective, these outcomes highlight the importance of incorporating climate-sensitive and seasonal factors into solar power forecasting and grid-integration planning. The risk management of monsoon-based cities must consider the greater volatility in solar power availability than that of equatorial cities.\u003c/p\u003e\u003cp\u003eThese findings indicate that solar variations in Asian megacities are controlled by nonlinearities and climate-dependent thresholds but not by linear drivers. Solar suppression during the monsoon season is controlled by rainfall and humidity thresholds for Dhaka and Manila, but for New Delhi, the humidity temperature interaction controls the variation. Jakarta and Kuala Lumpur are subjected to storm-related thresholds involving wind and pressure.\u003c/p\u003e\u003cp\u003eLinear models conventionally underestimate such abrupt changes. Nonlinear techniques, such as TAR and STAR, detect threshold levels and indicate the locations of tipping points, which results in irradiance collapse. This has policy implications for energy planning and predictions.\u003c/p\u003e\u003cp\u003eBackup generation and storage are needed for Manila and Dhaka to buffer monsoon-driven variability. In New Delhi, adaptations must respond to seasonally varying monsoon and dry regimes. For Kuala Lumpur and Jakarta, now casting and very short-term storm forecasting are important for buffering variability. Cumulatively, the evidence from Figs.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e and \u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e and Tables\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e and \u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e illustrates the utility of regime-sensitive, nonlinear models for solar forecasting. Threshold detection improves prediction accuracy and confidence in the integration of renewables into rapidly emerging urban energy grids.\u003c/p\u003e\u003cp\u003eThese results reaffirm that solar energy returns in Asian megacities exhibit volatility clustering and persistence, as seen in financial markets. GARCH-type models, particularly EGARCH, capture how both clustering and asymmetries are picked up and demonstrated that negative shocks (e.g., cloudiness and precipitation) have greater effects on volatility than positive shocks do.\u003c/p\u003e\u003cp\u003eRainfall was the leading source of volatility (Figs.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e\u0026ndash;\u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e14\u003c/span\u003e), emphasizing the role played by monsoon and storm occurrences in destabilizing the solar supply. Relative humidity also contributes, notably in the tropics, where continuous high humidity generates clouds and attenuates radiation. The VAR-impulse\u0026ndash;response analysis using the VAR (Fig.\u0026nbsp;15) shows that weather shocks are severe but short-lived and tend to dissipate within a week. This suggests that operational planning must focus on near-term volatility buffering through storage and backup arrangements, especially in monsoon-prone cities such as Dhaka and Manila. Overall, Objective 3 highlights the importance of climate-sensitive volatility modelling for secure solar energy integration. By categorically defining the linkages between volatility and precipitation and humidity, the results provide a means of creating more robust forecasting networks and energy management practices in rapidly growing urban environments.\u003c/p\u003e"},{"header":"Conclusion","content":"\u003cp\u003eThis study aimed to reveal the nonlinear drivers of solar variability in Asian megacities from a functional time-series perspective. Through the integration of functional data analysis (FDA), nonlinear threshold models, and volatility paradigms, this study addresses three broad objectives: functional modelling of solar radiation, identification of nonlinear meteorological thresholds, and volatility modelling and uncertainty in solar energy generation.\u003c/p\u003e\u003cp\u003eThe conclusions clearly show that solar variability can only be understood in the manner that it is determined by climate-specific thresholds and the dynamics of volatility. Functional principal component analysis also revealed that the first three components accounted for more than 97% of the variance in daily irradiance, validating the FDA as a robust method for representing and classifying solar regimes. Threshold analyses also revealed city-specific tipping points, such as rainfall thresholds in Dhaka and Manila, humidity thresholds in New Delhi, and wind and temperature thresholds in Jakarta and Kuala Lumpur. These regime-sensitive dynamics demonstrate that linear models are inadequate, whereas nonlinear approaches can represent sudden variations in solar availability. GARCH-family volatility modelling techniques also highlight clustering and persistence, particularly during monsoons, and impulse\u0026ndash;response analysis reveals that weather shocks, particularly rain, have short-term but considerable influences on solar returns.\u003c/p\u003e\u003cp\u003eCollectively, these results underscore the methodological and practical significance of cross-integrating nonlinear, function-based, and volatility-based approaches. Methodologically, this study closes a significant gap in the solar energy literature by introducing a composite model with the potential for tracking structural trajectories, thresholds, and uncertainty dynamics. This evidence has important practical implications for energy system resilience planning and climate adaptation. In monsoon-dominant cities, such as Dhaka and Manila, the results highlight the urgent need for backup and storage systems to mitigate volatility. In continental climates, such as New Delhi, flexible planning must account for seasonal transitions, whereas in equatorial cities, such as Jakarta and Kuala Lumpur, improved prediction and now casting storms are needed to maintain grid stability.\u003c/p\u003e\u003cp\u003eOverall, this study provides theoretical and practical insights into the field of renewable energy forecasting. By demonstrating the regulation of variability in solar radiation by nonlinear thresholds and volatility clusters, this study provides scientific knowledge and actionable intelligence for policymakers, urban energy planners, and decision-makers. Future research should build upon this effort by adding other climatic drivers, such as aerosols and cloud cover categories, expanding geographical sites beyond five cities, and exploring the integration of machine learning approaches with functional time series models. These extensions will further increase the predictability, power, and resilience of solar power systems to rising climatic and urban pressures.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAuthor Contribution Statement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eMd. Rakib Hasan Sarker\u003c/strong\u003e conceived and designed the study, performed the data analysis, developed the models, interpreted the results, and prepared the final version of the manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFarjana Akter\u003c/strong\u003e contributed to data collection, literature review, methodological formulation, and manuscript editing.\u003c/p\u003e\n\u003cp\u003eBoth authors read and approved the final manuscript.\u003c/p\u003e\n\u003ch3\u003e\u003cstrong\u003eFunding Statement\u003c/strong\u003e\u003c/h3\u003e\n\u003cp\u003eThis research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.\u003c/p\u003e\n\u003ch3\u003e\u003cstrong\u003eConflict of Interest\u003c/strong\u003e\u003c/h3\u003e\n\u003cp\u003eThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\u003c/p\u003e\n\u003ch3\u003e\u003cstrong\u003eData Availability Statement\u003c/strong\u003e\u003c/h3\u003e\n\u003cp\u003eThe datasets analyzed during the current study are publicly available from the \u003cstrong\u003eNASA POWER Project\u003c/strong\u003e repository (https://power.larc.nasa.gov/). Processed data and analysis codes are available from the corresponding author upon reasonable request.\u003c/p\u003e\n\u003ch3\u003e\u003cstrong\u003eEthics Statement\u003c/strong\u003e\u003c/h3\u003e\n\u003cp\u003eThis study did not involve human participants, animals, or any personal or confidential data. All data used were obtained from publicly accessible sources (NASA POWER Project). Therefore, no ethical approval or informed consent was required.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eAlomar, M. K., Khaleel, F., Aljumaily, M. M., Masood, A., Razali, S. F. M., AlSaadi, M. A., Al-Ansari, N., \u0026amp; Hameed, M. M. (2022). Data-driven models for atmospheric air temperature forecasting at a continental climate region. \u003cem\u003ePLOS ONE\u003c/em\u003e, \u003cem\u003e17\u003c/em\u003e(11), e0277079. https://doi.org/10.1371/journal.pone.0277079\u003c/li\u003e\n\u003cli\u003eAman, N., Kasemsan Manomaiphiboon, Natchanok Pala-En, Bikash Devkota, Muanfun Inerb, \u0026amp; Eakkachai Kokkaew. (2023). A Study of Urban Haze and Its Association with Cold Surge and Sea Breeze for Greater Bangkok. \u003cem\u003eInternational Journal of Environmental Research and Public Health\u003c/em\u003e, \u003cem\u003e20\u003c/em\u003e(4), 3482\u0026ndash;3482. https://doi.org/10.3390/ijerph20043482\u003c/li\u003e\n\u003cli\u003eBaghel, N. S., \u0026amp; Chander, N. (2022). Performance comparison of mono and polycrystalline silicon solar photovoltaic modules under tropical wet and dry climatic conditions in east-central India. \u003cem\u003eClean Energy\u003c/em\u003e, \u003cem\u003e6\u003c/em\u003e(1), 929\u0026ndash;941. https://doi.org/10.1093/ce/zkac001\u003c/li\u003e\n\u003cli\u003eBai, J., Zong, X., Ma, Y., Wang, B., Zhao, C., Yang, Y., Guang, J., Cong, Z., Li, K., \u0026amp; Song, T. (2022). Long-Term Variations in Global Solar Radiation and Its Interaction with Atmospheric Substances at Qomolangma. \u003cem\u003eInternational Journal of Environmental Research and Public Health\u003c/em\u003e, \u003cem\u003e19\u003c/em\u003e(15), 8906. https://doi.org/10.3390/ijerph19158906\u003c/li\u003e\n\u003cli\u003eBarhmi, K., Heynen, C., Golroodbari, S., \u0026amp; van Sark, W. (2024). A Review of Solar Forecasting Techniques and the Role of Artificial Intelligence. \u003cem\u003eSolar\u003c/em\u003e, \u003cem\u003e4\u003c/em\u003e(1), 99\u0026ndash;135. https://doi.org/10.3390/solar4010005\u003c/li\u003e\n\u003cli\u003eBowden, C., Foster, T., \u0026amp; Parkes, B. (2023). Identifying links between monsoon variability and rice production in India through machine learning. \u003cem\u003eScientific Reports\u003c/em\u003e, \u003cem\u003e13\u003c/em\u003e(1). https://doi.org/10.1038/s41598-023-27752-8\u003c/li\u003e\n\u003cli\u003eCorrea, L. F., Folini, D., Boriana Chtirkova, \u0026amp; Wild, M. (2022). A Method for Clear‐Sky Identification and Long‐Term Trends Assessment Using Daily Surface Solar Radiation Records. \u003cem\u003eEarth and Space Science\u003c/em\u003e, \u003cem\u003e9\u003c/em\u003e(8). https://doi.org/10.1029/2021ea002197\u003c/li\u003e\n\u003cli\u003eCosta, L., McBreen, J., Ampatzidis, Y., Guo, J., Gahrooei, M. R., \u0026amp; Babar, M. A. (2021). Using UAV-based hyperspectral imaging and functional regression to assist in predicting grain yield and related traits in wheat under heat-related stress environments for the purpose of stable yielding genotypes. \u003cem\u003ePrecision Agriculture\u003c/em\u003e, \u003cem\u003e23\u003c/em\u003e(2), 622\u0026ndash;642. https://doi.org/10.1007/s11119-021-09852-5\u003c/li\u003e\n\u003cli\u003eDash, S., Nandy, D., \u0026amp; Ilya Usoskin. (2023). Long-term forcing of the Sun\u0026rsquo;s coronal field, open flux, and cosmic ray modulation potential during grand minima, maxima, and regular activity phases by the solar dynamo mechanism. \u003cem\u003eMonthly Notices of the Royal Astronomical Society\u003c/em\u003e, \u003cem\u003e525\u003c/em\u003e(4), 4801\u0026ndash;4814. https://doi.org/10.1093/mnras/stad1807\u003c/li\u003e\n\u003cli\u003eDavid, M., Ramahatana, F., Trombe, P. J., \u0026amp; Lauret, P. (2016). Probabilistic forecasting of the solar irradiance with recursive ARMA and GARCH models. \u003cem\u003eSolar Energy\u003c/em\u003e, \u003cem\u003e133\u003c/em\u003e, 55\u0026ndash;72. https://doi.org/10.1016/j.solener.2016.03.064\u003c/li\u003e\n\u003cli\u003eEu\u0026aacute;n, C., Sun, Y., \u0026amp; Reich, B. J. (2022). Statistical analysis of multi‐day solar irradiance using a threshold time series model. \u003cem\u003eEnvironmetrics\u003c/em\u003e, \u003cem\u003e33\u003c/em\u003e(3). https://doi.org/10.1002/env.2716\u003c/li\u003e\n\u003cli\u003eGradwohl, C., Vesna Dimitrievska, Pittino, F., Muehleisen, W., Andr\u0026aacute;s Montvay, Franz Langmayr, \u0026amp; Kienberger, T. (2021). A Combined Approach for Model-Based PV Power Plant Failure Detection and Diagnostic. \u003cem\u003eEnergies\u003c/em\u003e, \u003cem\u003e14\u003c/em\u003e(5), 1261\u0026ndash;1261. https://doi.org/10.3390/en14051261\u003c/li\u003e\n\u003cli\u003eG\u0026uuml;rel, A. E., Ağbulut, \u0026Uuml;., Bakır, H., Erg\u0026uuml;n, A., \u0026amp; Yıldız, G. (2023). A state of art review on estimation of solar radiation with various models. \u003cem\u003eHeliyon\u003c/em\u003e, \u003cem\u003e9\u003c/em\u003e(2,e13167), e13167. https://doi.org/10.1016/j.heliyon.2023.e13167\u003c/li\u003e\n\u003cli\u003eHaputhanthri, D., De Silva, D., Sierla, S., Alahakoon, D., Nawaratne, R., Jennings, A., \u0026amp; Vyatkin, V. (2021). Solar Irradiance Nowcasting for Virtual Power Plants Using Multimodal Long Short-Term Memory Networks. \u003cem\u003eFrontiers in Energy Research\u003c/em\u003e, \u003cem\u003e9\u003c/em\u003e. https://doi.org/10.3389/fenrg.2021.722212\u003c/li\u003e\n\u003cli\u003eHoffmann, M., Kotzur, L., Stolten, D., \u0026amp; Robinius, M. (2020). A Review on Time Series Aggregation Methods for Energy System Models. \u003cem\u003eEnergies\u003c/em\u003e, \u003cem\u003e13\u003c/em\u003e(3), 641. https://doi.org/10.3390/en13030641\u003c/li\u003e\n\u003cli\u003eHou, X., Wild, M., Folini, D., Kazadzis, S., \u0026amp; Wohland, J. (2021). Climate change impacts on solar power generation and its spatial variability in Europe based on CMIP6. \u003cem\u003eEarth System Dynamics\u003c/em\u003e, \u003cem\u003e12\u003c/em\u003e(4), 1099\u0026ndash;1113. https://doi.org/10.5194/esd-12-1099-2021\u003c/li\u003e\n\u003cli\u003eHuang, C., Zhao, Z., Wang, L., Zhang, Z., \u0026amp; Luo, X. (2020). Point and interval forecasting of solar irradiance with an active Gaussian process. \u003cem\u003eIET Renewable Power Generation\u003c/em\u003e, \u003cem\u003e14\u003c/em\u003e(6), 1020\u0026ndash;1030. https://doi.org/10.1049/iet-rpg.2019.0769\u003c/li\u003e\n\u003cli\u003eHuang, L., Kang, J., Wan, M., Fang, L., Zhang, C., \u0026amp; Zeng, Z. (2021). Solar Radiation Prediction Using Different Machine Learning Algorithms and Implications for Extreme Climate Events. \u003cem\u003eFrontiers in Earth Science\u003c/em\u003e, \u003cem\u003e9\u003c/em\u003e. https://doi.org/10.3389/feart.2021.596860\u003c/li\u003e\n\u003cli\u003eJiao, B., Su, Y., Li, Q., Manara, V., \u0026amp; Wild, M. (2023). An integrated and homogenized global surface solar radiation dataset and its reconstruction based on a convolutional neural network approach. \u003cem\u003eEarth System Science Data\u003c/em\u003e, \u003cem\u003e15\u003c/em\u003e(10), 4519\u0026ndash;4535. https://doi.org/10.5194/essd-15-4519-2023\u003c/li\u003e\n\u003cli\u003eKilleen, P., Iluju Kiringa, Yeap, T., \u0026amp; Branco, P. (2024). Corn Grain Yield Prediction Using UAV-Based High Spatiotemporal Resolution Imagery, Machine Learning, and Spatial Cross-Validation. \u003cem\u003eRemote Sensing\u003c/em\u003e, \u003cem\u003e16\u003c/em\u003e(4), 683\u0026ndash;683. https://doi.org/10.3390/rs16040683\u003c/li\u003e\n\u003cli\u003eKim, B., Suh, D., Otto, M.-O., \u0026amp; Huh, J.-S. (2021). A Novel Hybrid Spatio-Temporal Forecasting of Multisite Solar Photovoltaic Generation. \u003cem\u003eRemote Sensing\u003c/em\u003e, \u003cem\u003e13\u003c/em\u003e(13), 2605. https://doi.org/10.3390/rs13132605\u003c/li\u003e\n\u003cli\u003eKrumins, J., \u0026amp; Klavins, M. (2023). Investigating the Potential of Nuclear Energy in Achieving a Carbon-Free Energy Future. \u003cem\u003eEnergies\u003c/em\u003e, \u003cem\u003e16\u003c/em\u003e(9), NA\u0026ndash;NA. https://doi.org/10.3390/en16093612\u003c/li\u003e\n\u003cli\u003eMishra, D., Jena, S., Rudranarayan Senapati, Atman Panigrahi, \u0026amp; Surender Reddy Salkuti. (2023a). Global solar radiation forecast using an ensemble learning approach. \u003cem\u003eInternational Journal of Power Electronics and Drive Systems\u003c/em\u003e, \u003cem\u003e14\u003c/em\u003e(1), 496\u0026ndash;496. https://doi.org/10.11591/ijpeds.v14.i1.pp496-505\u003c/li\u003e\n\u003cli\u003eMishra, D., Jena, S., Rudranarayan Senapati, Atman Panigrahi, \u0026amp; Surender Reddy Salkuti. (2023b). Global solar radiation forecast using an ensemble learning approach. \u003cem\u003eInternational Journal of Power Electronics and Drive Systems\u003c/em\u003e, \u003cem\u003e14\u003c/em\u003e(1), 496\u0026ndash;496. https://doi.org/10.11591/ijpeds.v14.i1.pp496-505\u003c/li\u003e\n\u003cli\u003eMol, W. B., van Stratum, B. J. H., Knap, W. H., \u0026amp; van Heerwaarden, C. C. (2023). Reconciling Observations of Solar Irradiance Variability With Cloud Size Distributions. \u003cem\u003eJournal of Geophysical Research: Atmospheres\u003c/em\u003e, \u003cem\u003e128\u003c/em\u003e(5). https://doi.org/10.1029/2022jd037894\u003c/li\u003e\n\u003cli\u003eMou Leong Tan, Liew Juneng, Heri Kuswanto, Hong Xuan Do, \u0026amp; Zhang, F. (2023). Impacts of Solar Radiation Management on Hydro-Climatic Extremes in Southeast Asia. \u003cem\u003eWater\u003c/em\u003e, \u003cem\u003e15\u003c/em\u003e(6), 1089\u0026ndash;1089. https://doi.org/10.3390/w15061089\u003c/li\u003e\n\u003cli\u003ePandey, A. K., Kalidasan, B., Reji Kumar, R., Rahman, S., Tyagi, V. V., Krismadinata, Said, Z., Salam, P. A., Juanico, D. E., Ahamed, J. U., Sharma, K., Samykano, M., \u0026amp; Tyagi, S. K. (2022). Solar Energy Utilization Techniques, Policies, Potentials, Progresses, Challenges and Recommendations in ASEAN Countries. \u003cem\u003eSustainability\u003c/em\u003e, \u003cem\u003e14\u003c/em\u003e(18), 11193. https://doi.org/10.3390/su141811193\u003c/li\u003e\n\u003cli\u003ePark, Kim, Lee, Kim, Song, \u0026amp; Kim. (2019). Temperature Prediction Using the Missing Data Refinement Model Based on a Long Short-Term Memory Neural Network. \u003cem\u003eAtmosphere\u003c/em\u003e, \u003cem\u003e10\u003c/em\u003e(11), 718. https://doi.org/10.3390/atmos10110718\u003c/li\u003e\n\u003cli\u003ePhon Sheng Hou, Lokman Mohd Fadzil, Manickam, S., \u0026amp; Al-Shareeda, M. A. (2023). Vector Autoregression Model-Based Forecasting of Reference Evapotranspiration in Malaysia. \u003cem\u003eSustainability\u003c/em\u003e, \u003cem\u003e15\u003c/em\u003e(4), 3675\u0026ndash;3675. https://doi.org/10.3390/su15043675\u003c/li\u003e\n\u003cli\u003ePrasad, A. A., \u0026amp; Kay, M. (2021). Prediction of Solar Power Using Near-Real Time Satellite Data. \u003cem\u003eEnergies\u003c/em\u003e, \u003cem\u003e14\u003c/em\u003e(18), 5865. https://doi.org/10.3390/en14185865\u003c/li\u003e\n\u003cli\u003eQian, Y., Chakraborty, T. C., Li, J., Li, D., He, C., Sarangi, C., Chen, F., Yang, X., \u0026amp; Leung, L. R. (2022). Urbanization Impact on Regional Climate and Extreme Weather: Current Understanding, Uncertainties, and Future Research Directions. \u003cem\u003eAdvances in Atmospheric Sciences\u003c/em\u003e, \u003cem\u003e39\u003c/em\u003e(6), 819\u0026ndash;860. https://doi.org/10.1007/s00376-021-1371-9\u003c/li\u003e\n\u003cli\u003eQuansah, A. D., Dogbey, F., Asilevi, P. J., Boakye, P., Darkwah, L., Oduro-Kwarteng, S., Sokama-Neuyam, Y. A., \u0026amp; Mensah, P. (2022). Assessment of solar radiation resource from the NASA-POWER reanalysis products for tropical climates in Ghana towards clean energy application. \u003cem\u003eScientific Reports\u003c/em\u003e, \u003cem\u003e12\u003c/em\u003e(1). https://doi.org/10.1038/s41598-022-14126-9\u003c/li\u003e\n\u003cli\u003eRens van der Zwaard, Bergmann, M., Zender, J., Rangaiah Kariyappa, Giono, G., \u0026amp; Luc Dam\u0026eacute;. (2021). Segmentation of Coronal Features to Understand the Solar EUV and UV Irradiance Variability III. Inclusion and Analysis of Bright Points. \u003cem\u003eSolar Physics\u003c/em\u003e, \u003cem\u003e296\u003c/em\u003e(9). https://doi.org/10.1007/s11207-021-01863-9\u003c/li\u003e\n\u003cli\u003eRomitti, Y., \u0026amp; Sue Wing, I. (2022). Heterogeneous climate change impacts on electricity demand in world cities circa mid-century. \u003cem\u003eScientific Reports\u003c/em\u003e, \u003cem\u003e12\u003c/em\u003e(1). https://doi.org/10.1038/s41598-022-07922-w\u003c/li\u003e\n\u003cli\u003eSantiago, I., Esquivel-Martin, J. L., Trillo-Montero, D., Real-Calvo, R. J., \u0026amp; V\u0026iacute;ctor Pallar\u0026eacute;s-L\u0026oacute;pez. (2021a). Classification of Daily Irradiance Profiles and the Behaviour of Photovoltaic Plant Elements: The Effects of Cloud Enhancement. \u003cem\u003eApplied Sciences\u003c/em\u003e, \u003cem\u003e11\u003c/em\u003e(11), 5230\u0026ndash;5230. https://doi.org/10.3390/app11115230\u003c/li\u003e\n\u003cli\u003eSantiago, I., Esquivel-Martin, J. L., Trillo-Montero, D., Real-Calvo, R. J., \u0026amp; V\u0026iacute;ctor Pallar\u0026eacute;s-L\u0026oacute;pez. (2021b). Classification of Daily Irradiance Profiles and the Behaviour of Photovoltaic Plant Elements: The Effects of Cloud Enhancement. \u003cem\u003eApplied Sciences\u003c/em\u003e, \u003cem\u003e11\u003c/em\u003e(11), 5230\u0026ndash;5230. https://doi.org/10.3390/app11115230\u003c/li\u003e\n\u003cli\u003eSantiago, I., Esquivel-Martin, J. L., Trillo-Montero, D., Real-Calvo, R. J., \u0026amp; V\u0026iacute;ctor Pallar\u0026eacute;s-L\u0026oacute;pez. (2021c). Classification of Daily Irradiance Profiles and the Behaviour of Photovoltaic Plant Elements: The Effects of Cloud Enhancement. \u003cem\u003eApplied Sciences\u003c/em\u003e, \u003cem\u003e11\u003c/em\u003e(11), 5230\u0026ndash;5230. https://doi.org/10.3390/app11115230\u003c/li\u003e\n\u003cli\u003eSedai, A., Dhakal, R., Gautam, S., Dhamala, A., Bilbao, A., Wang, Q., Wigington, A., \u0026amp; Pol, S. (2023). Performance Analysis of Statistical, Machine Learning and Deep Learning Models in Long-Term Forecasting of Solar Power Production. \u003cem\u003eForecasting\u003c/em\u003e, \u003cem\u003e5\u003c/em\u003e(1), 256\u0026ndash;284. https://doi.org/10.3390/forecast5010014\u003c/li\u003e\n\u003cli\u003eStefani, F., Horstmann, G. M., M. Klevs, G. Mamatsashvili, \u0026amp; Weier, T. (2024). Rieger, Schwabe, Suess-de Vries: The Sunny Beats of Resonance. \u003cem\u003eSolar Physics\u003c/em\u003e, \u003cem\u003e299\u003c/em\u003e(4). https://doi.org/10.1007/s11207-024-02295-x\u003c/li\u003e\n\u003cli\u003eSzostek, K., Mazur, D., Drałus, G., \u0026amp; Kusznier, J. (2024). Analysis of the Effectiveness of ARIMA, SARIMA, and SVR Models in Time Series Forecasting: A Case Study of Wind Farm Energy Production. \u003cem\u003eEnergies\u003c/em\u003e, \u003cem\u003e17\u003c/em\u003e(19), 4803. https://doi.org/10.3390/en17194803\u003c/li\u003e\n\u003cli\u003eTercha, W., Tadjer, S. A., Chekired, F., \u0026amp; Canale, L. (2024). Machine Learning-Based Forecasting of Temperature and Solar Irradiance for Photovoltaic Systems. \u003cem\u003eEnergies\u003c/em\u003e, \u003cem\u003e17\u003c/em\u003e(5), 1124. https://doi.org/10.3390/en17051124\u003c/li\u003e\n\u003cli\u003eTye, M. R., Haupt, S. E., Gilleland, E., Kalb, C., \u0026amp; Jensen, T. (2019). Assessing Evidence for Weather Regimes Governing Solar Power Generation in Kuwait. \u003cem\u003eEnergies\u003c/em\u003e, \u003cem\u003e12\u003c/em\u003e(23), 4409. https://doi.org/10.3390/en12234409\u003c/li\u003e\n\u003cli\u003eWang, J., \u0026amp; Wen, X. (2022). Excess radiation exacerbates drought stress impacts on canopy conductance along aridity gradients. \u003cem\u003eBiogeosciences\u003c/em\u003e, \u003cem\u003e19\u003c/em\u003e(17), 4197\u0026ndash;4208. https://doi.org/10.5194/bg-19-4197-2022\u003c/li\u003e\n\u003cli\u003eWang, L., \u0026amp; Shi, J. (2021). A Comprehensive Application of Machine Learning Techniques for Short-Term Solar Radiation Prediction. \u003cem\u003eApplied Sciences\u003c/em\u003e, \u003cem\u003e11\u003c/em\u003e(13), 5808. https://doi.org/10.3390/app11135808\u003c/li\u003e\n\u003cli\u003eYang, J., Yi, B., Wang, S., Liu, Y., \u0026amp; Li, Y. (2022). Diverse cloud and aerosol impacts on solar photovoltaic potential in southern China and northern India. \u003cem\u003eScientific Reports\u003c/em\u003e, \u003cem\u003e12\u003c/em\u003e(1). https://doi.org/10.1038/s41598-022-24208-3\u003c/li\u003e\n\u003cli\u003eYu, G., Wright, D. B., \u0026amp; Li, Z. (2020). The Upper Tail of Precipitation in Convection‐Permitting Regional Climate Models and Their Utility in Nonstationary Rainfall and Flood Frequency Analysis. \u003cem\u003eEarth\u0026rsquo;s Future\u003c/em\u003e, \u003cem\u003e8\u003c/em\u003e(10). https://doi.org/10.1029/2020ef001613\u003c/li\u003e\n\u003cli\u003eZafar, R., Vu, B. H., Husein, M., \u0026amp; Chung, I.-Y. (2021). Day-Ahead Solar Irradiance Forecasting Using Hybrid Recurrent Neural Network with Weather Classification for Power System Scheduling. \u003cem\u003eApplied Sciences\u003c/em\u003e, \u003cem\u003e11\u003c/em\u003e(15), 6738. https://doi.org/10.3390/app11156738\u003c/li\u003e\n\u003cli\u003eZhu, T., Guo, Y., Wang, C., \u0026amp; Ni, C. (2020). Inter-Hour Forecast of Solar Radiation Based on the Structural Equation Model and Ensemble Model. \u003cem\u003eEnergies\u003c/em\u003e, \u003cem\u003e13\u003c/em\u003e(17), 4534\u0026ndash;4534. https://doi.org/10.3390/en13174534\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Solar radiation variability, Functional data analysis (FDA), Functional principal component analysis (FPCA), GARCH-family models, Volatility clustering, Threshold autoregressive (TAR) models, Smooth transition autoregressive (STAR) models, Vector auto regression (VAR/VARX)","lastPublishedDoi":"10.21203/rs.3.rs-7807830/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7807830/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003e\u003cem\u003eSolar radiation is a significant renewable energy source, but its variability in Asian megacities is driven by advanced meteorological drivers that are poorly represented by traditional linear models. This study employs a functional time series method to investigate the nonlinear drivers and volatility of solar variability in five typical cities Dhaka, New Delhi, Jakarta, Manila, and Kuala Lumpur from July 2016 to June 2025. Solar irradiance was represented as continuous daily curves with functional data analysis (FDA), and the first three components explained more than 97% of the variance with functional principal component analysis (FPCA). Seasonal clustering indicated monsoon-dominated regimes for New Delhi, Manila, and Dhaka, and equatorial stability for Kuala Lumpur and Jakarta. Threshold and nonlinear modelling indicated city-specific tipping points: rainfall (~43 mm) for Dhaka, humidity (~48%) for New Delhi, wind (~4 m/s) for Jakarta, and precipitation (~108 mm) for Manila. Volatility analyses via GARCH-family models confirmed clustering and persistence, with EGARCH capturing the asymmetric effects of negative shocks. VAR impulse–response functions demonstrate that precipitation shocks cause immediate but transitory reductions in solar returns. These findings demonstrate that solar variability over Asian megacities is controlled by nonlinear thresholds and clustered volatility and has implications for forecasting, grid integration, and climate-resilient energy planning.\u003c/em\u003e\u003c/p\u003e","manuscriptTitle":"Nonlinear Drivers and Volatility of Solar Radiation Variability in Asian Megacities: A Functional Time-Series Approach","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-10-16 05:19:13","doi":"10.21203/rs.3.rs-7807830/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"e634f9f3-a8e5-4cdc-b473-c7e2b3ab51cb","owner":[],"postedDate":"October 16th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-11-02T18:53:02+00:00","versionOfRecord":[],"versionCreatedAt":"2025-10-16 05:19:13","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7807830","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7807830","identity":"rs-7807830","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}