The data used in this study were collected at two sites: Beijing in north China and the Southern Great Plain (SGP) site in central US. The ASI data in Beijing were collected by an SRF-02 ASI manufactured by EKO. This imager lacks a solar occulting device, and representative clear-sky and cloudy-sky images from the Beijing_PKU ASI are shown in Fig. 1a and b, respectively. The ASI was installed at the School of Physics, Peking University (39°59^′ N, 116°18^′ E). Images were captured between April 2017 and January 2020, with a resolution of 2272 × 1704 pixels at 180 dpi, totalling approximately 200 000 images.

Representative clear-sky and cloudy-sky images from the SGP TSI are shown in Fig. 1c and d, respectively. The SGP site, operated by the U.S. Department of Energy's Atmospheric Radiation Measurement (ARM) program, serves as a key atmospheric observation station (Stokes and Schwartz, 1994). Sky conditions were monitored using the Total Sky Imager (TSI), Model TSI-660, developed by Yankee Environmental Systems (YES), Inc. To evaluate the model's performance under different climatic conditions and geographical contexts, data spanning from January to November 2024 were selected from the SGP site. This period is distinct from the Beijing dataset (2018–2020), providing an opportunity to assess the method's robustness across different environments.

The target AOD and SSA are obtained from collocated surface sun photometers, namely those at the “Beijing_PKU” and “ARM_SGP” sites of AERONET. AOD from direct measurements and SSA retrieved from diffuse sky measurements at four wavelengths (440, 675, 870, and 1020 nm) are used. The dataset covers the period from 2017 to 2021 for Beijing_PKU and from 2024 to 2025 for SGP. For the SGP site, we utilized the Version 3 Level 2.0 (cloud-screened and quality-assured) data products for both AOD and SSA. This dataset represents the highest quality standard of AERONET, providing a robust benchmark for model validation in cleaner atmospheric environments. For the Beijing_PKU site, AERONET Version 3 Level 2.0 SSA inversion products were not available during the period overlapping with the ASI observations, mainly because the post-deployment calibration required for Level 2.0 quality assurance could not be completed in time due to pandemic-related restrictions on international shipment and calibration. Therefore, Version 3 Level 1.5 inversion products were used as the reference targets for Beijing SSA retrieval. Although Level 1.5 products are cloud-screened, they have not undergone the full quality-assurance procedure applied to Level 2.0 products. To reduce the potential uncertainty associated with Level 1.5 SSA, we further applied additional quality-control criteria to the Beijing inversion records. Specifically, only SSA retrievals with solar zenith angle greater than 50° and sky residual less than 5 % were retained. These criteria remove less stable sky-radiance inversion cases associated with unfavorable observation geometry or relatively large fitting residuals, for which SSA retrievals are expected to be more uncertain. Consequently, the Beijing SSA validation should be interpreted as the agreement of the ASI-based retrievals with additionally quality-screened Level 1.5 AERONET inversion products, rather than with fully quality-assured Level 2.0 SSA.

The inversion algorithm developed in this study comprises four main components: clean-sky image processing, image feature extraction, data matching, and the machine learning model. The overall technical framework of the proposed ASI-based aerosol retrieval algorithm is illustrated in Fig. 2.

Clean-Sky Image Processing: upon acquiring time-stamped raw sky images, we first mask areas that interfere with the extraction of cloud-free sky radiance—namely buildings, clouds, and glare spots caused by the sun and lens artifacts. The specific steps are: a.

Masking buildings at the image periphery.

While the core retrieval algorithm remains consistent across both sites, a site-specific preprocessing step was implemented for the SGP dataset to account for instrument differences. Unlike the setup at the Beijing site, the Total Sky Imager (TSI) at the SGP site is equipped with a sun occultation system (a sun-blocking strip and support arm) to prevent sensor saturation. This physical structure introduces permanent non-sky artifacts into the field of view. To address this, we applied a fixed fan-shaped digital mask to the SGP raw images prior to cloud screening and feature extraction. This mask effectively assigns zero weights to the pixels occupied by the occultation arm, excluding them from subsequent calculations. Beyond this geometric masking, the entire downstream processing pipeline – including the extraction of statistical features (mean, standard deviation, and texture) and the XGBoost model architecture – remains identical to that applied at the Beijing site, ensuring methodological consistency.

This section discusses the performance of the model at both the Beijing and SGP sites, evaluating its robustness and reliability across different climatic conditions.

Figure 4 displays the scatter density plots of AOD and SSA retrieved by the algorithm versus AERONET observations at 675 nm for the Beijing and SGP sites over the entire study period.

The retrieved AOD agrees well with AERONET AOD, with all data points closely distributed around the 1:1 line. For both sites, the Pearson correlation coefficient (r) for AOD exceeds 0.87 across all wavelengths, demonstrating robust retrieval performance. The retrieval performance for SSA is lower compared to that of AOD, which is not surprising since SSA is highly sensitive to uncertainties in the diffuse measurements (Dubovik et al., 2000).

According to Table 1, for the Beijing site, the model demonstrated robust performance in retrieving AOD across all wavelengths, with r values ranging from 0.90 to 0.91 and RMSE values of 0.06–0.21. SSA retrieval at Beijing showed moderate but wavelength-dependent performance: the correlation was highest at 675 nm (r = 0.74) and decreased progressively toward longer wavelengths, reaching r = 0.480 at 1020 nm. Despite the low correlation, RMSE remained consistently low (≤ 0.04) across all bands, which may partly be attributed to the narrow dynamic range of SSA values at this site (Legates and McCabe, 1999).

We performed a Monte Carlo sensitivity experiment by adding Gaussian random perturbations to the AOD and SSA training labels. The results show that SSA retrievals are more sensitive to the assumed label uncertainty than AOD retrievals. Under the 0.03 perturbation scenario, SSA RMSE increased from 0.0266 to 0.0299, while under the conservative 0.06 scenario, it increased to 0.04. In contrast, AOD RMSE and correlation do not show a significant positive or negative trend. This indicates that the Beijing SSA retrieval uncertainty is partly constrained by the uncertainty of the Level 1.5 reference data (Fig. S2 in the Supplement).

To further interpret the wavelength-dependent SSA performance at the Beijing_PKU site, we examined the SSA distributions under the clean regime (AOD440 < 0.2; Fig. 5). The sample size is identical at all four wavelengths (N = 657), indicating that the observed differences are not caused by unequal sampling. As shown in Fig. 5a and c, the reference SSA values are concentrated within a relatively narrow high-SSA range, with only limited variation across wavelengths. The mean SSA decreases slightly toward longer wavelengths, while the interquartile range and 95 % confidence interval remain narrow. This range restriction helps explain why the Pearson correlation decreases at longer wavelengths: when the dynamic range of the reference SSA is small, even modest absolute deviations and retrieval uncertainty can lead to a substantial reduction in correlation. Therefore, the weaker long-wavelength SSA correlation at Beijing_PKU should be interpreted primarily as a consequence of limited SSA variability in the clean regime, rather than as evidence of a failure of the ASI-based retrieval to capture the overall SSA magnitude.

For the SGP site, the model achieved higher overall accuracy than at Beijing. AOD retrieval yielded r values of 0.87–0.92 with notably low RMSE (0.02–0.05), reflecting the more stable aerosol conditions at this site. SSA retrieval also showed improved performance compared to Beijing, with r increasing from 0.64 at 440 nm to 0.84 at 1020 nm and RMSE remaining below 0.09. These evaluation metrics indicate that the algorithm can effectively retrieve AOD and SSA with reasonable accuracy and stability throughout the observation period.

Existing SSA retrieval products provide useful references for assessing the capability and limitations of ASI-based SSA retrievals. AERONET Version 3 remains the ground-based benchmark and provides spectral SSA at 440, 675, 870, and 1020 nm; its Level 2 inversion framework targets an SSA uncertainty of about 0.03 under quality-controlled almucantar/hybrid conditions (Sinyuk et al., 2020). For PARASOL/POLDER-GRASP, which retrieves SSA at 443, 670, 865, and 1020 nm, the 670 nm SSA validation against AERONET gives R = 0.25–0.54 and RMSE = 0.05–0.07 depending on the GRASP configuration, while high-loading scenes (AOD > 1.5) improve to R = 0.814 and RMSE = 0.029 for GRASP/Models (Chen et al., 2020). The current GEMS aerosol product also retrieves SSA at 443 nm, with validation against AERONET SSA at 440 nm showing that, for AOD > 0.4, 42.76 % and 67.25 % of retrievals fall within the ±0.03 and ±0.05 error bounds, respectively, increasing to 56.61 % and 85.70 % for AOD > 1.0 (Cho et al., 2024). More recently, the Gaofen-5 DPC multi-angle polarimetric retrieval simultaneously derives AOD, SSA, and land DHR; for AOD443 > 0.4, the retrieved SSA has a correlation coefficient of approximately 0.3, RMSE of 0.05–0.08, and only about 40 %–45 % of retrievals fall within the ±0.03 error envelope (Zhang et al., 2026). Compared with existing SSA retrieval products, the ASI-based retrievals achieve a broadly comparable level of performance, particularly in terms of RMSE. However, because of differences in wavelength, viewing geometry, aerosol loading, reference data quality, and spatial representativeness, this comparison does not imply that ASI retrievals outperform established AERONET or satellite products. Instead, the results suggest that ASI observations can provide complementary, low-cost, high-temporal-resolution local SSA estimates, especially where dense sun-photometer or advanced satellite observations are unavailable.

The accuracy of aerosol retrieval is typically associated with aerosol loading. To evaluate the performance of the algorithm more rigorously, we categorized the validation dataset into three regimes based on the reference 440 nm AOD: clean (AOD_440 nm < 0.2), moderate (0.2 ≤ AOD_440 nm < 0.4), and polluted (AOD_440 nm ≥ 0.4). Figure 6 illustrates the retrieval performance for 675 nm AOD and SSA across these regimes for both the Beijing and SGP sites. Note that the y-axis scales are unified to facilitate direct comparison.

At the Beijing_PKU site (Fig. 6a–b), the AOD retrieval error exhibits a clear dependence on aerosol loading. In the clean and moderate regimes, the RMSE for AOD remains low (< 0.05). However, in the polluted regime, the RMSE increases significantly to ∼ 0.13. This reflects the challenge of retrieving extremely high aerosol loads in complex urban environments using ASI, where the signal saturation effect may degrade its sensitivity to aerosol loading. However, the RMSE for SSA remains reasonable (< 0.05) across all regimes, confirming that the model correctly estimates the magnitude of absorption even when pixel-level correlation is limited by noise.

The SGP site (Fig. 6c–d) demonstrates superior stability. A striking contrast is observed in the polluted regime: while the AOD RMSE at Beijing surges to 0.13 when AOD > 0.4, the RMSE of AOD at the SGP site remains remarkably low at ∼ 0.035. This is likely related to the fact that the “polluted” conditions at SGP are still optically thinner and less complex than the haze events in Beijing that do not cause image saturation, thus allowing for more accurate retrievals. It should be noted that the relatively low r values observed in the moderate regime for SGP (AOD: r = 0.34, SSA: r = 0.35) may partly reflect a range restriction effect, as the sample size in this bin is limited (N = 15 in the test set), which can reduce statistical reliability (Jenkins and Quintana-Ascencio, 2020). Despite this, the consistently low RMSE (< 0.05 for AOD and < 0.08 for SSA) across all bins confirms the applicability of ASI in retrieving aerosol properties under cleaner atmospheric background of the Central US.

To further characterize the uncertainty of the SSA retrieval, we analyzed how retrieval errors depend on observing geometry, aerosol loading, season, and image brightness (Fig. 7). The residual error was evaluated using RMSE and MAE for SSA at 675 nm in the independent test set at the Beijing_PKU site. The results show that the SSA retrieval error is condition dependent rather than uniform across all samples. The error shows only a weak dependence on SZA between the 50–70 and 70–90° bins, suggesting that the model remains relatively stable over the solar-geometry range represented in the test data. In contrast, the dependence on aerosol loading is more pronounced: the clean regime shows the largest RMSE and MAE, while the moderate and polluted regimes show substantially smaller errors. This is consistent with the limited information content and narrow SSA dynamic range under low-aerosol-loading conditions.

The seasonal analysis further indicates that winter has the largest SSA retrieval error, whereas autumn, spring, and summer show lower and more comparable errors. This may reflect seasonal differences in aerosol type, illumination geometry, and surface-atmosphere conditions that are not fully represented by the current feature set. Image brightness also shows a clear error dependence, with the largest RMSE and MAE occurring in the low-brightness bin and progressively smaller errors under medium and high brightness conditions. This suggests that low image brightness reduces the radiometric contrast available to the model and increases the uncertainty of SSA retrieval. Overall, Fig. 7 indicates that the ASI-based SSA retrieval uncertainty depends on observing and aerosol conditions, which should be considered when extending the method to broader low-cost monitoring networks.

To further test whether the retrieval skill could be influenced by short-term temporal autocorrelation, we conducted an additional sensitivity experiment using a day-block temporal split. In this experiment, matched ASI and AERONET samples were grouped by calendar day, and all observations from the same day were assigned exclusively to either the training set or the test set. Approximately two-thirds of the days were used for training and the remaining one-third for testing. The model architecture, input features, and hyperparameters were kept unchanged. The evaluation criteria and aerosol-loading bins were kept identical to those used in Fig. 7, allowing a direct comparison between the baseline within-month chronological split and the day-block split.

Compared with the baseline chronological split in Fig. 6, the day-block split in Fig. 8 yields broadly consistent retrieval performance. At the Beijing_PKU site, AOD remains robust across aerosol-loading regimes, although the polluted-bin correlation decreases slightly under the stricter split. SSA shows larger variability, particularly in the polluted regime, which is expected given its narrower dynamic range and stronger sensitivity to sample size. At SGP, the model continues to show strong cross-day generalization, with high correlations and low RMSE for both AOD and SSA. Overall, these results demonstrate that the proposed model retains meaningful predictive capability even under a more stringent temporal validation strategy, supporting the conclusion that the retrieval skill is not primarily caused by local temporal leakage.

A major advantage of ASI is the capability to retrieve aerosol properties with high temporal resolution, thus allowing for the representation of aerosol diurnal cycle. Here we first selected 15 June 2017 at Beijing site as a representative case since AOD on this day exhibited significant intra-day variation, providing an ideal condition for testing the model performance.

As shown in the time series (Fig. 9a), the ASI retrieved AOD demonstrates remarkable consistency with ground-based AERONET observations. Note that a 5 min time window smoothing technique was applied to the ASI AOD curve (red line) to filter out high-frequency retrieval noise. However, all statistical metrics reported in this study were calculated using the original, unsmoothed retrieval results to ensure rigorous validation. The ASI retrievals accurately capture the trend of AOD diurnal variability. AOD gradually increased and fluctuated from 15:00 to 18:00 LST, and then stabilized, which is well captured by the ASI. While the observations showed a “stepped” pattern due to instrument sampling characteristics, the model retrieval (solid red line) successfully fitted the central tendency of these discrete points. Moreover, the model responds sensitively to rapid changes, demonstrating its sensitivity to short-term high-frequency variations in atmospheric aerosols.

The statistical metrics (Fig. 9c) further confirm the retrieval accuracy. With 58 sample points, the correlation coefficient (R) reached 0.95, and the Root Mean Square Error (RMSE) was only 0.03.

The bias analysis (Fig. 9b) shows that the deviations for most data points were confined within ±0.03. Although minor overestimation occurred in the low-value period around 14:30 and 18:30, the overall bias distribution remained balanced without significant systematic errors.

The 5 min moving average in Fig. 9 was used only for visual clarity, whereas the statistical metrics were calculated from the unsmoothed ASI retrievals. To quantify the smoothing effect, we calculated the difference between the raw ASI retrievals and the 5 min moving average for the case (Fig. S1). The mean difference was 0.0008, indicating no systematic bias introduced by smoothing. The standard deviation of the difference was 0.01, the mean absolute difference was 0.0076, and the 95th percentile absolute difference was 0.03. These values are much smaller than the daytime AOD variation shown in Fig. 9, suggesting that the 5 min smoothing mainly suppresses high-frequency noise while preserving the diurnal variation pattern.

It is worth noting that a similar high-frequency diurnal analysis was not performed for SSA. Unlike AOD, which is derived from high-frequency direct sun measurements, SSA is retrieved from the much less frequent almucantar sky scans. This significantly reduces the number of valid SSA data points, making it unfeasible to characterize continuous intra-day variations. Similarly, such high-frequency analysis is also not available at the SGP site for either parameter.

We continue to explore the averaged diurnal cycles of AOD and SSA retrieved by ASI. We select the Beijing_PKU site using data from May 2017 to May 2018. This 1-year period was selected to ensure complete seasonal coverage while maintaining sufficient sample size within each seasonal group. All matched data from the independent test set within this period were grouped by season – Spring (March–May), Summer (June–August), Autumn (September–November), and Winter (December–February) – and the hourly mean and standard deviation of both AERONET observations and model retrievals were calculated within each seasonal group. All timestamps were converted from UTC to Beijing Local Standard Time (LST, UTC+8) prior to analysis. It should be noted that the diurnal coverage is confined to approximately 12:00–18:00 LST, corresponding to the period of direct solar illumination required for valid AERONET almucantar sky scan retrievals, which limits the representativeness of the full diurnal cycle but still captures the afternoon period.

Figure 10 presents the averaged diurnal cycles of AOD at 440 nm at the Beijing_PKU site across four seasons (12:00–18:00 LST). A clear seasonal contrast is observed in the AOD magnitude, with summer exhibiting the highest loading and the largest diurnal variability, while winter shows the lowest values and the most stable diurnal pattern. In spring, both the observed and retrieved AOD display a slight decreasing trend from 15:00 to 18:00 LST, and the model closely follows the observed afternoon evolution. In summer, AOD decreases gradually from the early afternoon toward 18:00 LST, and the model captures the overall downward tendency, although a small underestimation appears around the late-afternoon period. In autumn, AOD increases sharply from 12:00 to 13:00 LST and then remains relatively stable through most of the afternoon before decreasing slightly at 17:00 LST; the model reproduces this pattern well, including the elevated values around 13:00 LST. In winter, the diurnal cycle is weak, with AOD increasing slowly and smoothly from noon to 16:00 LST, and the model remains in good agreement with the observations throughout the period. Overall, the retrievals successfully reproduce the seasonal differences in both magnitude and afternoon variability, with observation and model uncertainty ranges overlapping in most time bins.

Figure 11 shows the corresponding diurnal cycles of SSA at 440 nm. SSA exhibits smaller diurnal variation compared to AOD across all seasons. In spring, the model systematically overestimates SSA by approximately 0.03, indicating a tendency to underestimate aerosol absorption. Summer shows similar underestimation behavior in the early afternoon. Winter performance is the best among all seasons, with the model mean closely tracking observations throughout the afternoon. Autumn shows the largest retrieval uncertainty and a diverging trend between observations and model after 16:00 LST, though the wide uncertainty bands suggest this may partly reflect high day-to-day variability rather than a systematic model bias.

While Sect. 3.5 focuses on daily scale consistency, the following section further examines the temporal stability of the retrievals at seasonal scales for the Beijing and SGP sites, respectively.

Figure 12 presents the monthly mean validation of AOD and SSA at 440 nm for both the Beijing_PKU and SGP sites. Overall, the model reproduces the seasonal cycles of both parameters at both sites reasonably well, with the monthly means generally tracking the observed values throughout the year.

For AOD at the Beijing site (Fig. 12a), the seasonal cycle is well captured, with relatively low values in winter and spring, a pronounced enhancement in early summer, and the highest monthly mean in August. The model agrees well with the observations during most months, but it tends to underestimate the summer peak, especially in June and August, and slightly smooths the sharp month-to-month transition from summer to early autumn. For SSA at Beijing (Fig. 12b), the model follows the observed seasonal evolution, with high SSA values from spring to summer and a decrease in early autumn. However, the model is less sensitive to the abrupt SSA reduction around September and shows a smoother monthly cycle than the observations, indicating that the most rapid month-to-month changes are only partially captured.

At the SGP site, both AOD and SSA show good seasonal consistency between model and observations for most of the year. For AOD (Fig. 12c), the model closely follows the observed seasonal peak in summer and the low values in winter, with only a slight underestimation of 0.02–0.05 during January–April. It is worth noting that June exhibits negligible variability in both observations and model retrievals (indicated by the near-absent shading), which is attributable to the extremely limited number of valid matched samples in that month – with only a single observation day available – rather than reflecting genuinely low aerosol variability. This should be considered when interpreting the June monthly mean. For SSA (Fig. 12d), the model performs well from June to December, with the two lines nearly overlapping and the uncertainty ranges mutually covering each other. However, a notable overestimation is observed in January, where the model predicts ∼ 0.80 while the observed SSA is only ∼ 0.68. Overall, the monthly means demonstrate that the method captures the broad seasonal evolution of both AOD and SSA at both sites, although the retrievals are less sensitive to abrupt month-to-month transitions and low-sample months.