Modification of the SUNFLUX Solar Radiation Scheme with a New Aerosol Parameterization and Its Validation Using Observation Network Data

Solar radiation at the Earth's surface is an important physical quantity in the Earth surface radiation budget. It is a major type of incoming energy driving land surface processes. The accuracy of latent and sensible heat fluxes simulated by land-surface models is largely dependent on the accuracy of the solar radiation (Kowalczyk et al., 2006). Solar radiation at the Earth's surface also plays a significant role in numerical weather prediction (NWP) and climate models due to its influence on land surface processes.

Furthermore, solar radiation is a renewable energy, and an accurate forecast of the quantity received by the Earth's surface is required by the solar energy industries (Troccoli and Morcrette, 2014). It has been widely recognized that NWP models are the preferred method for providing solar energy forecasting (Lorenz et al., 2009; Mathiesen and Kleissl, 2011; Ward, 2016). However, several deficiencies remain in current NWP models, as discussed by (Sun et al., 2012) and (Manners et al., 2009), which influence the accuracy of solar energy forecasts. To improve model performance in solar radiation calculations in an NWP system, Sun et al. (2012, 2014a) developed a fast surface radiation scheme (named SUNFLUX) that can be used to determine the surface solar radiation at high temporal resolution. SUNFLUX is a physical-based scheme. It treats the atmosphere as a single layer and requires a small number of input variables but rapidly determines the solar radiation in a compatible way with that determined by a full radiative transfer model. The variables requested by SUNFLUX can be provided by model forecasting products or from satellite retrieval. Therefore, it can be used either online within an NWP model or offline using data from other sources, such as satellites.

The performance of SUNFLUX has been evaluated using observational data from three U.S. Department of Energy atmospheric radiation measurement (ARM) stations (Sun et al., 2012, 2014a) and three stations on the Tibetan Plateau (Liang et al., 2012). The results show that the relative mean bias under clear-sky conditions is less than 4.3% for the ARM stations and less than 7% for the Tibetan Plateau stations. Although these evaluation results are encouraging, the number of stations is too small and the length of the evaluation too short. Since this scheme will be used globally, it is necessary to re-evaluate it using longer-term observations collected around the world. This is the main purpose of the present study. In addition, we have developed a new aerosol scheme for improving the aerosol modelling. In this paper, we further evaluate the performance of SUNFLUX using the solar radiation data observed at 14 Baseline Surface Radiation Network (BSRN) stations and 7 Surface Radiation Budget Network (SURFRAD) stations. The primary input data are obtained from the Aerosol Robotic Network (AERONET) and MODIS. The evaluations are conducted under clear-sky conditions using the BSRN data and all-sky conditions using the SURFRAD data.

SUNFLUX is a fast scheme for the determination of solar radiation, developed based on a detailed radiative transfer scheme, Sun——Edwards-Slingo (SES2; Sun, 2011). The details of the SUNFLUX scheme have been described by Sun et al. (2012, 2013, 2014a, 2014b). Only a brief description is given here.

SUNFLUX consists of two spectral bands: ultraviolet-visible (0.2-0.7 μm), and near-infrared (0.7-5.0 μm). The processes of absorption and scattering of solar radiation by major absorbing gasses, aerosols and clouds in the atmosphere are parameterized individually based on the modelled results determined using SES2. The effects of scattering due to clouds and aerosols are represented by their albedo, while the effects of absorption are expressed by their transmittances. The transmittance and albedo data for various atmospheric conditions are generated using the SES2 scheme and the results are parameterized using simplified functions.

In the original SUNFLUX scheme, the aerosol transmittance and albedo are determined using the parameterization scheme developed by (Kokhanovsky et al., 2005) (hereafter referred to as KOK). The KOK scheme assumes an aerosol single scattering albedo of ω=1 and the input variables required are total aerosol optical depth (AOD) and asymmetry factor. The advantage of this scheme is that it is simple and easy to use. The disadvantage is that the type of aerosol and aerosol absorption cannot be considered. Our earlier evaluation results (Sun et al., 2014a) have shown that the modelled clear-sky solar radiation is slightly overestimated, possibly due to ignoring the aerosol absorption. In this paper, we improve this deficiency by developing a new aerosol scheme that includes the effect of aerosol absorption. The scheme is developed separately for five aerosol species: black carbon (BC), organic carbon (OC), dust (DU), sulfate (SU) and sea salt (SEA). These are common types of aerosols distributed at different locations throughout the world and included in most climate models.

We use globally averaged aerosol mixing ratio profiles simulated by the Spectral Radiation-Transport Model for Aerosol Species (SPRINTARS) (Takemura et al., 2009) as an aerosol background. SPRINTARS is a numerical model developed by the Climate Change Science Section, Research Institute for Applied Mechanics, Kyushu University, for simulating the effects of atmospheric aerosols on the climate system and air pollution on the global scale. The model data used in this study are from SPRINTERS simulations for 2006-08. The global mean mixing ratios of the SPRINTARS aerosol climatology for the five species mentioned above are used in the SES2 model calculations to generate model reference data for the development of the parameterization. The aerosol optical scattering properties of these five species described by (Cusack et al., 1998), based on the complex indices of refraction and size distributions for each aerosol component (WMO, 1983) for a climate analysis, are used in the calculations. Table 1 lists the single-scattering albedo and asymmetry factor at 0.55 μm for the five aerosol components.

Figure 1.  Aerosol transmittance as a function of solar zenith angles and optical depths for the five aerosol species.

We determine the aerosol transmittance for global horizontal irradiance by \begin{equation} T_{{\rm a}_i}=\dfrac{F_{{\rm a}_i}^{\downarrow}}{\mu S_0} , \ \ (1)\end{equation} where F _ai^↓ represents the spectral band global horizontal irradiance at the surface due to the attenuation of aerosol absorption and scattering by species i, i represents the five aerosol species, μ is the cosine of the solar zenith angle, and S₀ is the solar constant. The solar irradiance for the coupled surface and aerosol atmosphere can be expressed by \begin{equation} F_{A}^{\downarrow}=\dfrac{F_{0}^{\downarrow}}{1-AR_{{\rm a}_i}} , \ \ (2)\end{equation} where F₀^↓ represents the downward solar irradiance without including the surface reflection, R _ai is the aerosol albedo for the upward transfer irradiance, A is the surface albedo, and F_A^↓ denotes the solar irradiance when the surface albedo is A. From Eq. (2), we can derive the aerosol albedo by \begin{equation} R_{{\rm a}_i}=\dfrac{F_{A}^{\downarrow}-F_{0}^{\downarrow}}{AF_{A}^{\downarrow}} .\ \ (3) \end{equation}

We run SES2 to calculate the solar irradiance for the AODs ranged between 0 and 4 and the solar zenith angles between 0^° and 89^°. The reference calculations are conducted for aerosol species only, i.e. no gasses and clouds are included. The varied AODs are integrated in the calculations by scaling profiles of the model background AOD so the scaled total optical depth is equal to the varied value. In this case, the single scattering albedo and asymmetry factor in each spectral band are fixed to the climatological values for each aerosol species. We do not explicitly include these two scattering parameters in the parameterization for the reasons that they are generally not available from observations, and their effects may be considered as a second order compared with the AOD.

Figure 1 shows the visible band transmittance as a function of the solar zenith angle and AOD for the five aerosol species determined using the Eq. (1). In general, the aerosol transmittance decreases with increasing AOD and solar zenith angle. Different aerosol species show quite different attenuation of solar radiation. The BC has the highest influence on the surface solar radiation due to its strong absorption, leading to the smallest transmittance for the same solar zenith angle and AOD. The SEA has the lowest effect for the same solar zenith angle and AOD. The DU aerosol has a comparable effect to the OC and SU aerosols.

Figure 2 presents the visible band albedo as a function of the AOD determined using Eq. (3). Note that the aerosol albedo defined by Eq. (3) is independent of the solar zenith angle because the reflected upward irradiances are all diffuse. It is apparent that the aerosol albedos for OC, DU and SEA are very similar, but those for BC and SU are different. The albedo of BC is very small due to the dominant influence of absorption. The albedos of SU are larger when the AOD is greater than 1.

Based on the results shown in Figs. 1 and 2, we propose the following parameterizations for the aerosol transmittance and albedo: \begin{eqnarray} T_{{\rm a}_i}&=&\exp(-a\mu^b\tau_{{\rm a}_i}) ;\ \ (4)\\ R_{{\rm a}_i}&=&\dfrac{\tau_{{\rm a}_i}}{c+d\tau_{{\rm a}_i}} .\ \ (5) \end{eqnarray} Here, τ _ai is the AOD and the coefficients a,b,c, and d are determined by fitting the results of T _ai and R _ai from Eqs. (1) and (3) for the five species separately. Table 2 lists the values of these coefficients.

Figure 2.  Aerosol albedo for upward irradiance as a function of AOD for the five aerosol species.

Figure 3.  Comparison of modelled solar irradiances using the new aerosol parameterization with those from the SES2 model results. The left-hand panel is a scattered data point density plot with gray-scale color bar representing the range of data point densities and the right-hand panel is a histogram of the difference. The statistical test results are given in Table 3.

The total aerosol transmittance for the mixture of all species can be determined by the product of the transmittance of the individual species, \begin{equation} T_{\rm a}=\prod_{i=1}^{i=5}T_{{\rm a}_i} . \ \ (6)\end{equation} The aerosol albedo is used to determine the multiple reflections between the surface and atmosphere. In (Sun et al., 2014a), we prove that this multiple reflection term can be expressed by \begin{equation} {\rm MR}=1-A\left[1-(1-r)(1-R_{\rm cld})\prod_{i=1}^{i=5}(1-R_{{\rm a}_i})\right] ,\ \ (7) \end{equation} where MR represents the multiple reflection, r is the Rayleigh albedo and R _cld is the cloud albedo. The term \(\prod_{i=1}^{i=5}(1-R_{a_i})\) represents the effect of aerosol albedo, which also satisfies the multiplying property. The total atmospheric transmittance can then be determined by \begin{equation} T=\dfrac{T_{\rm g}T_{\rm r}T_{\rm a}T_{\rm cld}}{\rm MR} ,\ \ (8) \end{equation} where T _g, T _r and T _cld are transmittances due to gaseous absorption, Rayleigh scattering and cloud extinction, respectively. Equation (2) will be used in sections 5 and 6 to evaluate SUNFLUX using the observational data. The following evaluations are performed by comparing the solar irradiances determined by the SES2 model with those by the SUNFLUX scheme for each aerosol species.

Figure 3 compares the parameterized irradiances and reference irradiances for all five aerosol species. Note the irradiances are calculated for each aerosol species separately, so the number of data points is large. It is more meaningful to plot the binned data point density than the scattered points themselves. Therefore, Fig. 3 presents such a density plot. It is apparent that the results from the parameterization are in very good agreement with those from the SES2 model. There are a total of 180 000 scattered data points and the highest densities are all distributed along the 1:1 diagonal line. The right-hand panel in Fig. 3 is a histogram of the irradiance difference.

For testing the accuracy of the parameterization, we use four statistical parameters defined by (Beyer et al., 2009); namely, mean bias (mb), relative mean bias (rmb), root-mean-square error (rms) and relative root-mean-square error (rrms), determined as follows: \begin{eqnarray} \label{eq1} {\rm mb}&=&\dfrac{\sum_{i=1}^n{(m_i-o_i)}}{n} ; \ \ (9)\end{eqnarray} $$ {rmb}=\dfrac{{mb}}{\sum_{i=1}^n{o_i/n}}\times 100\% ;\ \ (10) $$ $$ {rms}=\sqrt{\dfrac{\sum_{i=1}^n{(m_i-o_i)^2}}{n}} ;\ \ (11)$$ $$ { rrms}=\frac{{rms}}{\sum_{i=1}^n{\frac{o_i}{n}}}\times 100\% .\ \ (12) $$ Here, o_i represents the observed (or referenced here) values, m_i denotes the modelled values, and n is the number of samples. In addition, the correlation coefficients between the modelled and referenced values are also determined. The statistical test results are listed in Table 3. It is apparent that the rmb for all aerosol species is 5.92%, the rrms is 7.64%, and the correlation coefficient is 0.99.

To evaluate the SUNFLUX scheme with the new aerosol parameterization, data from five sources are collected. The first is the solar radiation data observed at BSRN stations.

Figure 4.  Geographic distribution of the BSRN and SURFRAD stations used in this study. The full name for each station code is given in Table 4.

The BSRN (Ohmura et al., 1998) stations provide 1-3-min averaged high-quality shortwave surface radiation fluxes. Currently, there are 58 BSRN stations distributed in different climatic zones, covering a latitudinal range from 80^°N to 90^°S. The BSRN data are quality-checked before they are archived. The quality control is carried out using the BSRN Toolbox, which is a software package supplied by the World Radiation Monitoring Centre (Schmithüsen et al., 2012). The data are checked for physically possible limits, extremely rare limits and cross-comparisons. The solar radiation data from the selected BSRN stations were downloaded from http://www.bsrn.awi.de/.

The second dataset is SURFRAD, which consists of seven stations distributed in the United States. The SURFRAD network began collecting data from four stations in 1995, two more in 1998, and another one in 2003. In addition to the radiation data, ancillary measurements are taken to support this research; these include meteorological variables, solar spectral measurements, and fraction of sky cover. The AODs at five spectral regions are retrieved from solar spectral measurements (Augustine et al., 2003). The cloud optical depths are retrieved using shortwave solar spectral measurements (Barnard et al., 2008). There are analyses of clear-sky radiation data at these seven stations, which were derived by numerical fitting to the clear-sky observations (Long and Gaustad, 2004). These analyzed results are used to evaluate the modelled clear-sky calculations.

The third dataset is AERONET, which provides spectral AOD retrieved from ground-based sun photometer measurements (Dubovik et al., 2006). The AERONET level 2.0 optical depths, which have undergone cloud-screening and quality control, are used in this study. Since the AERONET AODs are only retrieved under cloud-free conditions, these AODs can be used as a clear-sky indicator, based on which the clear-sky radiation data from the BSRN stations are selected. AERONET also includes the total precipitable water (PW) amount, retrieved using Cimel CE-318-4 sunphotometers (Pèrez-Ramrez et al., 2014), and the total column ozone amount, from the Total Ozone Monitoring Instrument (https://ozoneaq.gsfc.nasa.gov/data/ozone/; last accessed 16 September 2016).

The fourth data source is the MODIS cloud fraction. Although the AOD data from AERONET can be used to eliminate radiation data from the BSRN stations under cloudy conditions, some data selected in this way remain contaminated by cloud. To remove the effect of cloud, the MODIS cloud fraction is used to further filter the radiation data. MODIS cloud fraction data are available twice a day and have a spatial resolution of 5 km × 5 km (Platnick et al., 2015). If the MODIS cloud fractions are greater than 10% for these two times, the radiation data from the BSRN stations on that day are removed from the input list.

The BSRN stations do not include reflected solar radiation measurements; the surface albedos at these stations must be alternatively determined. To solve this problem, the surface albedo data from the global Surface Radiation Budget (SRB; Stackhouse and Gupta, 2013) dataset are used. The SRB dataset contains both longwave and shortwave radiation data retrieved from satellite measurements. Surface albedos are derived internally in the shortwave radiation model developed by (Pinker and Laszlo, 1992). The monthly mean data at a 1^°× 1^° spatial scale are available for the 10-year period from 1986 to 1995. These data do not correspond to the period of the BSRN data used in this study. Therefore, we use the 10-year climatological mean values in the calculations. The grid values close to the BSRN stations are used to determine the surface albedo at the BSRN stations by linear interpolation. In this case, the albedo used in this study only represents a climatological background and is a source of uncertainty in the radiation calculations.

Since we need data from both BSRN and AERONET, only stations available in both networks can be selected. A total of 16 stations meet this requirement, but two of them are the same as in the SURFRAD network. Therefore, 14 stations are selected for use in this study. Their distributions, together with those from SURFRAD, are shown in Fig. 4, and the station information is listed in Table 4. Note that two SURFRAD stations BON and SXF also belong to BSRN, but they are grouped under SURFRAD as the data were downloaded from the SURFRAD website.

The last data source is the aerosol mass concentrations simulated by CAM-chem (Lamarque et al., 2012). This dataset was produced at NCAR using CAM3.5 with a bulk aerosol model driven by CMIP4 SST and RCP8.5 emissions (Riahi et al., 2011). We use this dataset to calculate the fractions of the five aerosol species used in this study from which the AOD for each species is estimated using the observed AOD and used in Eqs. (4) and (5) to determine the transmittance and albedo. The decadal average (2000-09) monthly mean aerosol mixing ratio profiles at the BSRN and SURFRAD stations from the historical run of CAM-chem between 1850 and 2009 are extracted and inputted into the SES2 radiation scheme to calculate the optical depth in the visible band for each of the five aerosol species, and the fraction of each species is determined by the ratio of AOD to the sum of the five species. This ratio is then used to determine the τ _ai used in Eqs. (4) and (5) by \begin{equation} \tau_{{\rm a}_i}=f_{{\rm a}_i}\tau , \ \ (13)\end{equation} where f _ai is the fraction of AOD for the aerosol species i, and τ is the total AOD.

The new aerosol parameterization introduced in this paper can be applied to the five species. This has a great advantage in large-scale NWP and climate models as the aerosol concentrations for different species are generally available in the aerosol component of these models. A question arises when the AODs retrieved using the sunphotometers or satellite measurements are used in the calculations and the results are compared with observations. These retrieved optical depths are the total values and cannot be classified to any single aerosol species. To solve this problem, we introduced a new variable of the fraction of AOD in the previous section, with which the total retrieved AOD can be converted into the AOD of the specified aerosol species.

In this section, we evaluate the clear-sky irradiances determined using the BSRN data. Both the old aerosol (KOK) scheme and new parameterization (NEW) are used in the calculations with the SUNFLUX scheme. The calculations with NEW are performed for the mixture of the five aerosol species. The statistical test results against the observations at each station are used to evaluate the two schemes. Table 5 lists the evaluation results for the 14 BSRN stations. It is seen that both the KOK and NEW schemes produce relatively good Global Horizontal Irradiance (GHI) results compared with the observations. For example, the total rmb for the KOK and NEW scheme is 2.28% and 0.48%, respectively. The rrms is 7.67% and 6.30%, respectively. It is clear that the test results using the NEW scheme are better than those with the KOK scheme. This is generally true for the test results from each BSRN station as well.

Figure 5.  Comparison of solar irradiances determined using the NEW and KOK aerosol schemes with observations at 14 BSRN stations. The left-hand panels are scattered data density plots with gray-scale color bar representing the range of densities. The right-hand panels are histograms of the irradiance difference. The statistical test results are given in Table 5.

Figure 5 shows the scattered data point density between modelled solar irradiances and observations for all 14 BSRN stations using the two aerosol schemes. It is apparent that the results from the two aerosol schemes are very similar and the higher number densities distribute along the 1:1 diagonal line, which demonstrates that the modelled results are in reasonable agreement with the observations. The histogram indicates that the results of the NEW scheme are better than those of the KOK scheme because their distribution is closer to a normal one.

All the input data required by SUNFLUX are available at a 1- or 3-min temporal resolution from the SURFRAD stations, except the total PW, which can be determined using the radiosonde data. If we use these radiosonde data, the number of samples in the evaluations will be reduced substantially, resulting in the loss of many valuable observed radiation data because the radiosonde data are only available twice a day. To maximize the use of the available data, we use the measurements of water vapor pressure at the surface to estimate the total PW. Such an approach has been used before by (Sun, 1987) and (Wang and Shen, 2012). (Wang and Shen, 2012) analyzed relationship between PW and water vapor pressure using data collected at meteorological measurement stations in China and obtained the following linear equation: \begin{equation} {\rm PW}=0.093+0.185(P/P_0)e . \ \ (14)\end{equation} Here, PW represents precipitable water, P and P₀ represent surface pressure and standard pressure (taken as 1013.25 hPa), and e is water vapor pressure in hPa. The PW data calculated using the radiosonde profile and water vapor pressure collected from seven SURFRAD stations are plotted in Fig. 6. One can see that the relationship in Eq. (13) can also be used to represent the SURFRAD data, but the numerical fitting results in slightly different coefficients: \begin{equation} {\rm PW}=0.2968+0.1539(P/P_0)e .\ \ (15) \end{equation}

Figure 6.  Scatterplot of PW against water vapor pressure using data from SURFRAD stations.

The correlation coefficient between the two variables is 0.904. Equation (14) is used to determine the PW at these SURFRAD stations.

All the observational data collected at the SURFRAD stations from 1995 to present are used to calculate the global solar radiation. The calculations are also made using the two aerosol schemes. Table 6 lists the statistical test results for the comparison between the modelled and observed irradiance under clear-sky conditions. Unlike those obtained using the BSRN data, the test results using the KOK scheme are better than those of the NEW scheme, but the difference between the two results is not significant (the reason for this will be discussed at the end of this section). The rmb for all test samples is 0.24% for the KOK scheme and -0.56% for the NEW scheme. The corresponding rrms values are 11.61% and 15.15%, respectively. So, the statistics are good for both schemes. We can see that the rmb values for the SURFRAD stations are better than those obtained using the BSRN data (mainly due to the cancellation between positive and negative biases), while the rrms values are clearly larger than those derived from the BSRN comparison. The reason for this difference is likely due to the use of Eq. (14) to estimate the total column water PW.

Figure 7.  Comparison of modelled and observed global solar radiation under clear-sky conditions for seven SURFRAD stations. The left-hand panels (a) are scattered data density plots. The histogram plots on the right-hand panels (b) show the distribution of the relative frequency of the difference between the model and observation. The model results are determined using the NEW aerosol scheme. The statistical test results are given in Table 6.

The test results for all-sky conditions are listed in Table 7. Again, the KOK scheme produces the best results. The rmb and rms values for all samples from the KOK scheme are -6.71% and 17.51%, respectively, while those from the NEW scheme are -9.64% and 22.91%.

Figure 7 shows the evaluation results for each of the SURFRAD stations under clear-sky conditions. The model results determined using the NEW aerosol scheme are used in the plots. We can see that the modelled results are reasonably accurate compared with observations.

Figure 8 shows the evaluation results for all-sky conditions. The model results are also from using the NEW scheme. Compared with the clear-sky results presented in Fig. 7, the all-sky results are more scattered, but the linear relationships between the modelled and observed values are better than those of clear-sky conditions. This can be seen from the scatter plots and statistical test results listed in Table 7. The correlation coefficients for the all-sky results are slightly higher than those of the clear-sky results. The reason for these better correlation coefficients could be due to the slightly better agreement between the modelled results and observations of the higher values of irradiance. The histograms show that the maximum frequencies correspond to modelled results of -25 W m^-2, and this is opposite to the clear-sky results. The statistics listed in Table 7 also show that the rmb values of the all-sky results are negative. The possible reason for these negative biases could be due to the overlapping absorption between aerosols and clouds, which is not considered in the parameterizations. When considering the overlapping absorption, the total transmittance involving cloud and aerosol may be determined by \begin{equation} T=T_{\rm cld}T_{\rm a}+\Delta T_{\rm cld}\Delta T_{\rm a} , \ \ (16)\end{equation} where the second term in the above equation represents the correlation absorption between the cloud and aerosol. This term will vanish if the absorption of the cloud and aerosol are uncorrelated, but this is not true in real conditions. The total transmittance T should therefore be greater than the first term. Thus, the transmittance involving the cloud and aerosol in this study may be underestimated, leading to negative biases. This is an area that needs further improving.

Combined with the results from the BSRN stations, we can see that the performance of the new aerosol parameterization is not uniform. The results produced by the NEW scheme with the data from BSRN stations are better than the old scheme, while those with the data from SURFRAD stations are slightly worse. This behavior is concerning, and we suspect it could be due to the input of data sources. The sources of AOD and PW vapor amount are different in the BSRN and SURFRAD networks, but it is difficult to directly compare these input data because of the difference in the available time period and the method for choosing clear-sky data. Fortunately, we have two stations (BON and SXF) that overlap in the BSRN and SURFRAD networks, as mentioned previously, so we can swap the input datasets to test if the input data cause the different behavior. Originally, these two stations were grouped in the SURFRAD network. Now, we use the datasets from the BSRN network to repeat the calculations for these two stations, and the statistics are listed in the last two rows of Table 5. It can be seen that the mb and rmb for the two schemes using the BSRN input data are not as good as those from using the SURFRAD data, but the rms and rrms are both better than those from SURFRAD. Furthermore, the results from the NEW aerosol scheme are all better than the old one. This makes the comparison consistent with all other stations in the BSRN network. Based on these comparisons, we may conclude that the new aerosol scheme is generally better than the old KOK scheme under clear-sky conditions, but it needs further modification to consider the effect of overlapping absorption between cloud and aerosol.

Figure 8.  Comparison of modelled and observed global solar radiation at seven SURFRAD stations under all-sky conditions. The left-hand panels (a) are scattered data density plots. The histogram plots on the right-hand panels (b) show the distribution of the relative frequency of the difference between the model and observation. The model results are determined using the NEW aerosol scheme. The statistical test results are given in Table 7.

In this section, we conduct sensitivity tests to investigate the error responses of SUNFLUX to the uncertainty of the input variables. Two sets of sensitivities are performed: one for the SURFRAD stations and one for the BSRN stations. For the SURFRAD stations, six input variables are investigated. The solar irradiance results at the seven SURFRAD stations determined by the normal input data are used as the benchmarks. The new aerosol scheme is used in the calculations. The input variables of water vapor, ozone, surface albedo, AOD, water and ice cloud optical depth are perturbed by 10% to 20%, respectively. The results obtained using the perturbed input data are compared with the benchmarks. The statistical test results from these sensitivity calculations are listed in Table 8. It is apparent that the scheme is relatively sensitive to the surface albedo, aerosol and cloud optical depths: 10%-20% uncertainties in these variables can cause errors of 3%-10% in the irradiance calculations. The effect of the uncertainty due to the water cloud optical depth is the most significant. The scheme is not sensitive to the water vapor and ozone: 20% errors in these input data only lead to errors of less than 0.7% in the calculations.

For the BSRN stations, we focus our attention on the sensitivity of SUNFLUX to the surface albedo. This is because the surface albedos used in the calculations for these stations are the climatological mean values. These sensitivity tests can reveal the effects of an uncertain surface albedo on the estimated radiation. We use a ratio of the standard deviation to the mean of the surface albedo determined by all SRB data as an estimation of the uncertainty of the surface albedo. This ratio is 0.62. This means that the uncertainty in the surface albedo is about 62% if we use the 10-year averaged surface albedo to replace the monthly mean value. Uncertainty also comes from the temporal and spatial differences between the observations at the BSRN stations and satellite measurements. Therefore, the actual uncertainty could be much larger than this ratio. For this reason, we perturb the surface albedo from 10% to 100%. The results determined from the perturbed albedos are compared with those from the climatological values. Table 9 lists the statistics from the 100% perturbation of the surface albedo. It is found that the model sensitivities to the surface albedo are much smaller than those found for the SURFRAD stations. Even when the albedo is doubled, the maximum relative error is only 4.06% at XIA station. The less sensitive results at the BSRN stations are mainly due to the fact that they are under clear-sky conditions, while those at the SURFRAD stations are under all-sky conditions. The interactions between the surface and clouds make the model more sensitive to the surface albedo under all-sky conditions than under clear-sky conditions.

In this paper, we further improve the SUNFLUX scheme in terms of new parameterizations for aerosol transmittance and albedo. The new aerosol scheme is developed for five aerosol species, based on detailed radiative transfer calculations for the aerosol atmospheres. The effects of aerosol scattering and absorption are included in the new parameterization. The solar radiation determined by the detailed radiative transfer scheme can be reproduced well using the SUNFLUX scheme together with this new and simple aerosol parameterization. We then evaluate the SUNFLUX scheme using the observations from 14 BSRN stations and 7 SURFRAD stations. The original aerosol scheme (KOK) and the new scheme (NEW) are used in the calculations. The aerosol concentrations simulated by CAM-chem are used to generate the fraction of aerosol species, which are then used to convert the total AOD into the portion of individual species for determining the aerosol transmittance and albedo. We discuss how to mix these aerosol species to calculate the overall transmittance and albedo and are able to evaluate the new scheme properly using the observational data.

The evaluations conducted using the data from the 14 BSRN stations under clear-sky conditions show that SUNFLUX can produce relatively accurate GHI using both the KOK and NEW aerosol schemes, but the results from the NEW scheme are better. The evaluation results for the SURFRAD stations are slightly the opposite. The reason is probably because of the differences in the input data, and this is backed up by the results using the two datasets available at the BON and SXF stations. The evaluations under all-sky conditions are only available for the SURFRAD stations and the results from using the KOK scheme are better than those from the NEW scheme. The rmb values for all stations using KOK scheme are -6.7% and -9.6% using the NEW scheme. The statistical analysis also shows that the evaluation results are very uniform among these stations. The worse results under all-sky are most likely due to the overlapping absorption between cloud and aerosol, which needs further improvement in the future.

Sensitivity tests are conducted to investigate the possible errors of the SUNFLUX scheme in response to the uncertainties in the input data. The results show that the scheme is relatively sensitive to the surface albedo, aerosol and cloud optical depths under all-sky conditions. Errors of 20% from these variables can cause errors in the modelled results of between 3% (surface albedo, aerosol and ice cloud optical depth) and 10% (water cloud optical depth). The scheme is insensitive to the water vapor and ozone. The errors of 20% for water vapor and ozone amounts only result in errors of less than 0.7% in the calculations. The scheme is also insensitive to the surface albedo under clear-sky conditions. Doubled surface albedos only lead to a maximum relative error of 4.06% in the calculations.