The “Simple Model for Atmospheric Transmission of Sunshine”, or SMARTS for short, is a radiative transfer spectral model that has been under development since the early 1990s (Gueymard, 2001, 2005, 2019). SMARTS estimates the different clear-sky irradiance components (direct, diffuse, and global) at the surface over the entire short-wave solar spectrum (280–4000 nm), and has become an essential tool in various disciplines, most importantly in various solar energy applications (Bicer et al., 2022; Mouhib et al., 2022; Pelland and Gueymard, 2022), the development of spectral irradiance standards (Habte et al., 2020; Xue and Igari, 2023), and UV research (Habte et al., 2019; Apell and McNeill, 2019). The UV band under scrutiny here extends from 280 to 400 nm at 0.5 nm resolution.

The SMARTS computational flow is shown in Fig. 1. As visualized, single-image metadata is converted from planar to 3D at run time, thus significantly increasing the time cost of computation. To optimize the process, the model's Fortran code was reconstructed and converted to MATLAB^®. In that optimized implementation, the model can perform matrix operations in an efficient way.

The quality control of the measured UV data involves two parallel procedures: (i) quality control of the observations; and (ii) detection of the clear-sky periods in the observational time series (Fig. 2). The quality control of observation data can be divided into two parts: detection and elimination of systematic errors, and quality assessment of the observation data. The systematic errors include operator errors and sensor errors. Furthermore, many obvious errors and missing observations need to be eliminated. The quality assessment of observational data is conducted in successive steps. First, the observed surface broadband UV irradiance should be less than extraterrestrial UV radiation. Second, the ratio of UV radiation to total solar radiation should be in the range 0.02–0.08 (Liu et al., 2017).

It should be noted that, in the present investigation, the estimated UV radiation exclusively relates to clear-sky conditions. Therefore, it is necessary to conduct an efficient clear-sky screening of the observational time series, which needs to be done. The clearness index (Kt), which is the ratio between the surface global solar irradiance (G) measured at 1 hourly resolution and its extraterrestrial counterpart (G0), is employed as the primary screening tool in this study. Clear-sky conditions are identified as those for which Kt exceeds 0.7 (Qi et al., 2024). The global solar irradiance was obtained from the CERN site observations at 1 hourly temporal resolution and the extraterrestrial radiation was calculated using: 1G0=S×I×cos⁡Z where S is the sun–earth distance correction factor, I is the solar constant (1361.1 W m⁻²) (Gueymard, 2018), and Z is the solar zenith angle. At each instant, Z and S are provided by a precise sun position algorithm.

In the absence of spectral measurements, which would necessitate costly SRMs, the assessment of the accuracy of the clear-sky UV modeled estimates is done relatively to broadband measurements, as described in Sect. 3.1. The assessment uses conventional evaluation metrics (Gueymard, 2014), including mean bias error (MBE), root mean square error (RMSE), and correlation coefficient (R). MBE and RMSE are expressed both in absolute terms (W m⁻²) and relative percentage.

In addition, the probability density functions (PDFs) of the bias and the cumulative distribution functions (CDFs) of the absolute relative error (ARE) are used to compare the accuracy of the estimates with respect to various satellite products (Jiang et al., 2020). The PDFs and CDFs provide complementary information about the distribution of the deviations between different UV radiation products and station observations. In particular, the position and shape of the PDF peaks can offer insights into the temporal characteristics of the bias. The CDF curves of different UV radiation products also allow a visual comparison of their overall performance. The steeper the CDF curve, the more concentrated the error and the higher the accuracy of the product, whereas a flat curve indicates a dispersed error and lower precision.

The UV database collected from the China Ecosystem Research Network (CERN) observation sites is used to validate the accuracy of the UV radiation estimates obtained with the SMARTS model. Detailed information on CERN sites is provided in Table 1. CERN has established a network of ecosystem observatories throughout China to monitor the meteorological, environmental, and radiometric conditions over a widely diverse range of ecosystems, including nature reserves, forest ecosystems, grassland ecosystems, wetland ecosystems, and urban ecosystems. The observational database selected for this study comprises hourly UV and total solar irradiance data from all the 37 stations in mainland China over the 2005–2013 period. The CERN stations use the CM11 global radiometer (Kipp & Zonen, the Netherlands) to measure global radiation with a spectral range of 285–2800 nm, with an accuracy of 5 %. The CUV3 broadband radiometer (Kipp & Zonen, the Netherlands) is used to measure UV radiation, with a spectral range of 280–400 nm and an accuracy of 5 %, which meets the World Meteorological Organization's (WMO) measurement standards. As shown in Fig. 3, the CERN sites are relatively well distributed in the east. Due to the influence of topography, however, the density of sites in the west is much lower than in the east, which results in an uneven spatial distribution overall. The spatial coverage of this product is constrained by the continuous availability of ERA5 reanalysis data, resulting in the exclusion of certain coastal observation stations at CERN.

The inputs to SMARTS are derived primarily from key products generated by the ERA5 and MERRA2 reanalysis over the period 1981–2023. ERA5 (ECMWF Reanalysis: Fifth generation) is an atmospheric reanalysis dataset published by the European Centre for Medium-Range Weather Forecasts (ECMWF) to describe the state and variability of the Earth's atmospheric system (Muñoz-Sabater et al., 2021). The data employed in this study comprise ERA5_Land, ERA5_Pressure levels, and ERA5_Single levels. ERA5_Land has a spatial resolution of 0.1°×0.1°, whereas ERA5_Pressure levels and ERA5_Single levels have a spatial resolution of 0.25°×0.25°. Consequently, that coarser grid is resampled to achieve a unified spatial resolution of 0.1°×0.1° or ≈10 km. The forecast albedo (FAL) from the ERA5-Land product is a land-specific parameter, as its values over ocean and lake surfaces are systematically set to NAN, making it suitable for continental-scale analysis.

MERRA-2 (Modern-Era Retrospective analysis for Research and Applications, Version 2) is an atmospheric reanalysis dataset released by NASA (Gelaro et al., 2017). MERRA-2 provides a long time series of AOD data (1980–present) with reasonable accuracy (Gueymard and Yang, 2020; Ou et al., 2022). The coarse resolution (0.5°×0.625°) of the MERRA2 AOD data requires bilinear resampling to 0.1°×0.1°, however. Table 2 shows the summarized information pertaining to all input variables. The position of each grid cell (latitude, longitude, and elevation) is also necessary to operate the radiation model.

CERES (Clouds and the Earth's Radiant Energy System) is a project initiated by NASA with the objective of conducting long-term monitoring and research on the Earth's radiant energy balance. In particular, CERES SYN1deg is a synthetic data base that provides various products related to the surface radiant field including radiative fluxes, cloudiness, and temperature. The SYN1deg database provides global coverage at a horizontal resolution of 1°×1°, with hourly temporal resolution (Wielicki et al., 1998). Here, the hourly UVA and UVB estimates from SYN1deg are used as a benchmark against which the present model's estimates can be assessed.

Figure 4 presents the validation results of the hourly clear-sky UV radiation model estimates. Out of the 196 original observed data points from 37 CERN stations during 2005–2013, 170 were selected after applying the clear-sky screening procedure described in Sect. 2.2. Overall, the estimated hourly clear-sky broadband UV irradiance exhibits satisfactory accuracy, as evidenced by Fig. 4a, with an R of 0.919, an RMSE of 5.07 W m⁻², and an MBE of -0.07 W m⁻². The density scatter plot shows that the model performs well across most UV radiation levels, particularly in the range of 20–40 W m⁻², where the highest density of points is observed. However, at lower (<10 W m⁻²) and higher (>50 W m⁻²) UV radiation levels, the scatter points become more dispersed, indicating increased model uncertainty under these extreme conditions. Notably, the regression slope of 1.009 and a negative intercept (-0.319) suggest a slight systematic underestimation under low UV radiation conditions, possibly due to factors like local atmospheric characteristics not fully captured by the model. In addition, the upper and lower boundaries of the scatter points reveal distinct patterns: overestimation occurs predominantly under high UV conditions, whereas underestimation is more frequent at low to moderate radiation levels. The broader scatter at extreme values also suggests that the model's performance might be sensitive to solar zenith angles, particularly during sunrise and sunset.

In addition, boxplots of R, MBE and RMSE for all stations combines are shown in Fig. 4b. In particular, the RMSE for the majority of stations ranges between 3.9 and 5.6 W m⁻², with a mean value of 4.98 W m⁻² and a maximum value not exceeding 9 W m⁻². The mean and median MBE values are -0.13 and 0.27 W m⁻², respectively, indicating a small overall error. The R value at most sites is greater than 0.9. The median value is notably elevated, approaching the upper quartile, which collectively suggests that the overall R value remains satisfactory and that the model's performance has strong spatial consistency and robustness, even in regions with varying climatic conditions. Figure 4c and d displays the RMSE and MBE results, respectively, for each station. About half of the stations are affected by only low RMSEs below 5 W m⁻². The two most challenging stations are Taihu (TAL) and Aksu (AKA). The Taihu (TAL) station, located in the humid, cloud-prone region of eastern China, exhibits significant errors, with RMSE and MBE reach 8.82 and -7.59 W m⁻², respectively. These errors are likely influenced by high humidity and the reflective surface of the Taihu Lake, which complicates the estimation of clear-sky UV radiation. The Aksu (AKA) station, situated in the arid desert region of northwestern China, also stands out with RMSE = 6.40 W m⁻², MBE = -3.09 W m⁻², and R=0.877. The larger errors at AKA may be attributed to several factors, including the high aerosol loading in the region, where mineral dust particles from the surrounding deserts can significantly scatter and absorb UV radiation. Additionally, the reflective properties of the desert surface, extreme climatic conditions, and local meteorological variations could further complicate the accurate estimation of clear-sky UV radiation, leading to the observed discrepancies. These unique atmospheric conditions, combined with the station's extreme climatic environment, likely reduce the model's estimation accuracy (Wu et al., 2022b).

Figure 5 presents similar results as in Fig. 4, but on a daily mean basis. From Fig. 5a, the overall validation results are satisfactory, with an R of 0.907, an RMSE of 3.37 W m⁻², and an MBE of 0.14 W m⁻². The box plots in Fig. 5b show that most stations have RMSE values below 4 W m⁻², reflecting consistent performance across regions. The MBE values are tightly clustered around zero, indicating minimal biases overall. Additionally, R values for most stations range between 0.88 and 0.95, demonstrating the model's strong spatial consistency and reliable performance. The spatial distributions of RMSE and MBE in Fig. 5c and d reveal patterns similar to those observed with the hourly estimates. Whereas most stations maintain low RMSE and near-zero MBE, the same two stations as before, TAL and AKA exhibit notable discrepancies again. For instance, the daily-mean RMSE, MBE, and R at AKA are 7.07 W m⁻², -6.16 W m⁻², and 0.783, respectively.

Overall, the validation results demonstrate that the model reliably captures hourly and daily mean clear-sky UV radiation across diverse environments, maintaining high accuracy and minimal bias at all 37 sites, with the possible exception of two challenging stations. The strong agreement between the model estimates and observations underscores its robustness. These findings support the reliability of the SMARTS model in estimating clear-sky UV radiation. A supplementary quantile binning analysis was conducted to guard against regression bias from uneven data density in our large sample. The results, shown in Fig. A2, align with Figs. 4 and 5, confirming the model's excellent overall performance and offering a more robust characterization of its behavior at the extremes.

A comparison between the present hourly UV estimates and those from CERES SYN1deg is desirable as a form of benchmarking, owing to the important status of the latter as a reference global database. Using CERN observations in 2013, the results in Fig. 6 demonstrate that the present UV product significantly outperforms SYN1deg in terms of overall accuracy. As shown in Fig. 6a and b, the estimated hourly clear-sky UV radiation achieves an R of 0.923, an RMSE of 4.92 W m⁻², and an MBE of 0.04 W m⁻², which are substantially better than the CERES product (R=0.825, RMSE = 10.61 W m⁻², MBE = 4.68 W m⁻²). Notably, SYN1deg exhibits systematic biases, with overestimation at high UV values and underestimation at low UV values, whereas the newly proposed product aligns more closely with the observed values. The distribution of the PDF (Fig. 6c) further highlights the differences between the two products. The bias distribution of the newly proposed product closely resembles a Gaussian curve, with a sharp peak near zero, indicating small and stable deviations across most data points. In contrast, SYN1deg displays a broader and flatter PDF curve, suggesting larger and more widely distributed errors, hence lower precision than the new SMARTS-derived product. Figure 6d reinforces this conclusion: the CDF curve for ARE is steeper for the newly proposed product, reaching the 95 % threshold for a much lower mean error than SYN1deg. This confirms that a larger fraction of the estimated product's deviations is confined to smaller bias ranges.

Figure 7 is similar to Fig. 6, but on a coarser daily-mean resolution. The R value for the new UV radiation product, 0.911, is markedly higher than the CERES product (0.763). In parallel, the RMSE and MBE for the new product, 3.18 and 0.09 W m⁻², respectively, are much lower than their CERES counterparts (8.84 and 6.39 W m⁻²). From Fig. 7b, it is evident that the CERES product systematically overestimates UV radiation, as indicated by the positive deviation of its best-fit line from the 1:1 line in almost all cases. In contrast, the estimated product aligns much more closely with the observations. The PDF and CDF in Fig. 7c and d further emphasize the differences between the two products, and confirm the results in Fig. 6c and d.

In summary, the hourly and daily mean clear-sky UV radiation product proposed here demonstrates significantly better performance than the CERES SYN1deg product in terms of accuracy, stability, and error distribution. As shown in the binned fitting results in Fig. A3, both products exhibit distribution characteristics similar to those described previously. The CERES SYN1deg product exhibits systematic biases in its representation of UV radiation, overestimating at high values and underestimating at low values. This results in a border and flatter probability density function compared to the new CHUV product, which indicates larger errors and lower overall precision. Consequently, the SYN1deg product also demonstrates a significantly weaker agreement with daily mean observations than the CHUV product.

The results above indicate that the SMARTS-based UV estimates are satisfactory in general, but are nevertheless affected by reduced accuracy at a few sites where challenging situations are likely to impact the model's inputs. It is thus desirable to evaluate the sensitivity of the modeled UV estimates to discrepancies in the atmospheric inputs. To that effect, a series of scaling factors (0.5, 0.9, 1.1, and 1.5) are applied to three key input variables as way to analyze the intrinsic model's sensitivity to them. These inputs are the aerosol optical depth (AOD), the total column ozone (TCO3), and the forecast albedo (FAL). In all cases, the clear-sky UV irradiances estimated using the original input data are used as the baseline reference. As shown in Fig. 8, the 37-station mean clear-sky UV irradiance thus obtained exhibits a typical unimodal distribution, peaking in summer and reaching a minimum in winter, as could be expected. This seasonal variation is closely tied to changes in solar zenith angle. Among the four input parameters tested here, AOD induces the most significant impact on clear-sky UV radiation (Fig. 8a). As AOD increases, the UV irradiance decreases substantially, highlighting the strong attenuation effect of aerosols in the UV. The sensitivity analysis revealed a strong negative relationship between AOD and surface UV irradiance. Specifically, a one-unit increase in AOD was associated with a fractional reduction in UV irradiance ranging from -50.06 % to -40.90 %. This is consistent with the physical properties of aerosols, which scatter and absorb radiation mostly in the UV spectrum. As TCO3 increases incrementally relative to its original value, the clear-sky UV radiation decreases progressively (Fig. 8b), which reflects the strong absorption of ozone in the UV spectrum, although this is confined to wavelengths below ≈340 nm only. Surface albedo (FAL) is shown to enhance UV radiation when it increases (Fig. 8c). Higher albedo values, such as those from snow-covered surfaces, amplify the reflection of UV radiation back into the atmosphere, which can subsequently increase the downward UV irradiance through the atmospheric backscattering effect (Shine et al., 2012).

A key limitation in this study arises from the selection of the aerosol model in the SMARTS radiative transfer simulations. To maintain consistency with the continental focus of our work, the built-in “Continental” aerosol model was employed. While this model is representative of typical inland aerosol species such as sulfates, nitrates, black carbon, and dust, it does not include an explicit parameterization for sea salt aerosols. This discrepancy could introduce systematic biases in simulated UV radiation in coastal regions and inland areas subject to marine air mass advection, as sea salt aerosols differ significantly from continental types in their size distribution, and scattering efficiency (Zhu et al., 2022; Kouvarakis et al., 2002; Chatzopoulou et al., 2025). Future research should aim to integrate a more sophisticated hybrid or maritime aerosol model and couple it with higher-resolution aerosol reanalysis or observational data to better constrain the aerosol-type dependence and improve the accuracy of UV estimates in complex coastal-continental transition zones.

Figure 9 presents the validation results of the SMARTS model's clear-sky UV radiation estimates against station observations under different scaling factors. For AOD, as the scaling factor increases from 0.5 to 1.5, the R value decreases from 0.943 to 0.918, indicating a slight decline in the model's correlation with observations. The MBE shifts from 1.83 to -1.51 W m⁻², suggesting that the model overestimates UV radiation at lower scaling factors and underestimates it at higher scaling factors. The RMSE initially decreases from 5.08 to 4.87 W m⁻² (scaling factors 0.5–0.9), and subsequently increases to 5.44 W m⁻² when the scaling factor exceeds 1, demonstrating a reduction in the model's predictive capability with increasing AOD scaling factors. As the scaling factor for TCO3 increases, the R value remains stable between 0.932 and 0.934, showing minimal variation. The MBE decreases from 1.19 to -0.74 W m⁻², indicating a transition from overestimation to underestimation. Meanwhile, the RMSE decreases from 5.21 to 4.69 W m⁻², suggesting that the model's prediction error is reduced at higher TCO3 scaling factors. When the FAL scaling factor reaches 1.5, the model exhibits the lowest overall accuracy, with an R value of 0.929, MBE of 1.05 W m⁻², and RMSE of 5.29 W m⁻², indicating that increasing FAL scaling factors significantly amplify the model's prediction error. The MBE shifts from -0.98 to 1.05 W m⁻², demonstrating that the model underestimates at lower scaling factors and overestimates at higher scaling factors. These results reveal the complex influence of different input parameters on UV radiation estimation and provide critical insights for optimizing model performance.