Improved Clear Sky Model from In Situ Observations and Spatial Distribution of Aerosol Optical Depth for Satellite-Derived Solar Irradiance over the Korean Peninsula

Abstract

In solar resource assessment, the climatological environment of the target area is objectively quantified by the cloudiness or clear sky index, which is defined as the ratio of global horizontal irradiance to clear sky solar insolation. The clear sky model calculates incoming solar irradiance on the ground surface considering several atmospheric parameters such as water vapor and aerosol optical depth. This study investigated the importance of aerosol optical depth for deriving clear sky irradiance in radiative transfer models and examined its viability in a universal or community model for public use. The evaluation was conducted based on ground observations at the Korea Institute of Energy Research (KIER) station from January to December 2021. The original simulation was performed using the monthly mean of aerosol optical depth obtained from the Aerosol Robotic Network station; the mean absolute error was 29.9 W m⁻². When the daily mean of in situ observations at KIER was incorporated into the clear sky model, the mean absolute error was reduced to 9.7 W m⁻². Our results confirm that the clear sky model using gridded datasets of aerosol optical depth is suitable for use as a universal or community model.

1. Introduction

The increased contribution of renewable energy to the energy mix has mitigated global warming via low carbon and decarburization methods ([1,2]). Solar resource assessment with in situ observations or available gridded datasets (e.g., reanalysis) is necessary for the successful deployment, installation, and operation of solar power facilities (e.g., [3,4,5,6,7,8]). The spatial limitations of in situ measurements and relatively short historic records render satellite-derived solar irradiance an efficient way to asses solar resources, although ground observation is the most accurate and reliable approach ([9,10,11,12,13,14,15]).

Huang et al. [16] reviewed derivation models for estimating surface solar irradiance from satellite imagery and classified them into radiative transfer models and statistical models. Radiative transfer models calculate atmospheric transmittance from the top of the atmosphere (TOA) to the surface at a given vertical level. Spectral irradiance from radiative transfer models, such as MODerate resolution atmospheric TRANsmission (MODTRAN) and Santa Barbara DISORT Atmospheric Radiative Transfer (SBDART), is generated at a high numerical cost ([14,17,18]). To reduce the numerical burden, Pinker and Laszlo [19] employed a look-up table that was pre-compiled for discrete values of the following atmospheric parameters: aerosol optical depth, water vapor mixing ratio, ozone concentration, and surface albedo. When optical properties are parameterized in the radiative transfer model, solar irradiance can be obtained without a numerical burden at the global scale (e.g., [14,20,21,22]). For example, Habte et al. [15] developed the National Solar Radiation Database (NSRDB), which includes meteorological elements, as well as solar irradiance over the United States during the last two decades. The current version of the NSRDB is a gridded dataset with a 4 km resolution, developed using Physical Solar Model with Geostationary Operational Environmental Satellite data ([23]).

In contrast to physical models, statistical methods are based on the empirical relationship between visible reflectance at the TOA and the clear sky index, which is defined as the ratio of global horizontal irradiance (GHI) to clear sky GHI. A good example is the Heliosat method, which calculates atmospheric radiation based on a statistical method ([24,25,26]). The performance of statistical methods is highly dependent on the clear sky index; thus, the reliability of the clear sky model is a crucial factor in deriving solar irradiance from satellite imagery. Mazorra Aguiar et al. [27] compared solar irradiance estimates obtained from the Satellite Application Facility on Climate Monitoring and McClear model as a clear sky model against in situ observed GHI at 22 ground measurement stations in the Canary Islands. On an hourly time scale, Ineichen [28] evaluated direct normal irradiance (DNI) and GHI estimations at 22 locations in Europe and the Mediterranean region. In these studies, the McClear and REST2 and Solis models were selected as being the best, with a low bias and a standard deviation ranging from ±3% to ±5%, which can be largely attributed to inaccuracies inherent to the source aerosol optical depth. A review paper by Antonanzas-Torres et al. [29] examined 70 clear sky solar irradiance parametric models that simplify atmospheric attenuation with simple parameterization. They found that the uncertainties of aerosol optical properties drive the clear sky model in the wrong direction when calculating clear sky GHI. Sun et al. [30] investigated the performance of 75 clear sky models against 75 ground observations at the minute scale worldwide and identified the best models as REST2v9.1, MAC2, REST2v5, and CLS for equatorial, arid, temperate, cold, and polar climate zones, respectively. Sun et al. [31] broadened this evaluation study to compare DNI estimates at the minute scale. Thus, clear sky models estimate solar irradiance based on the Linke Turbidity factor, which is highly dependent on atmospheric conditions at a given place.

The Korea Meteorological Administration (KMA) launched a first-generation meteorological geostationary satellite, named the Communication, Oceanic, and Meteorological Satellite (COMS), at 128.2°E on 27 June 2010. Based on a simple physical model, the KMA produces hourly mean GHI as a routine procedure ([32]). Zo et al. [33] introduced a single-layered radiative transfer model to derive solar irradiance from COMS imagery. The University of Arizona Solar Irradiance Based on Satellite KIER (UASIBS–KIER) model was also developed by the Korea Institute of Energy Research (KIER) to produce downwelling surface shortwave radiation ([34]). This model was then updated to incorporate the visible reflectance and brightness temperature from the second generation of COMS, GK–2A, which was launched on 5 December 2018. The new version of the UASIBS–KIER model produces clear sky GHI estimates with a root mean square error (RMSE), which is normalized to the ground observation within the range of 4.8–5.3% ([35]). Ineichen [28], Antonanzas-Torres et al. [29], and Kim et al. [35] showed that the bias can be traced to the monthly mean of aerosol optical depth that is amalgamated into the UASIBS–KIER model. Therefore, the effects of aerosol optical depth on the reliability of the clear sky model is of interest in this study and we further investigate the feasibility of using the clear sky model as a part of UASIBS–KIER to create a universal or community model, similar to the REST model. Section 2 explains the clear sky model used in this study. Section 3 describes the aerosol optical depth and ground observations. The numerical simulation design is presented in Section 4. Section 5 presents the results of the evaluation, and further analysis of aerosol optical depth effects and a feasibility study is presented in Section 6, while Section 7 is a summary of the major findings of this study.

2. Clear Sky Model

For a given pixel of satellite imagery, the UASIBS–KIER model ([34]) retrieves the atmospheric transmittance from the look-up, which is 5667compiled by the Goddard Space Flight Center (GSFC) radiative transfer model ([36]). Moreover, this model is used in the Weather Research and Forecast model as part of the physics parameterization ([37]). The radiative transfer model is described in detail in the preceding reference; only a brief overview of the model is provided here. Estimating the radiative properties accurately requires a high computational cost, owing to the complex calculation of spectral irradiance and angular integration. Instead, this model parameterizes radiative parameters at 11 spectral ranges to reduce the numerical burden. There are eight bands in the ultraviolet and visible regions (175–700 nm) and three in the infrared region (700–10,000 nm). Ozone was the most effective at absorbing solar energy at ultraviolet wavelengths. Reflection and transmission of a cloud and aerosol layer are computed using delta-Eddington approximation. Fluxes at each layer are calculated by using the two-stream adding approximation. In the visible and infrared bands, water vapor plays a substantial role in lowering solar irradiation. Rayleigh scattering was also parameterized for each spectral range. The effects of oxygen and carbon dioxide on absorbing solar irradiance were treated as secondary processes in the infrared bands. The extinction of clouds and aerosols was included in all bands. For example, the extinction coefficient of clouds was determined as a function of the effective radius based on previous research conducted by Slingo and Schrecker [38]. For elaborative simulation of interaction between cloud and radiation, a maximum-random approximation is adopted for the overlapping of clouds at different heights. In contrast to clouds, the radiative properties of aerosol optical depth and single scattering albedo were specified as a function of height and spectral band for the input variable, rather than being parameterized. As a result, the aerosol characteristics identified in the clear sky model in this investigation were sensitive to solar irradiation.

3. Research Data

3.1. Aerosol Optical Depth

3.1.1. AERONET Data

This study used in situ measurements from Yonsei University station (Figure 1), which is a part of the Aerosol Robotic Network (AERONET) project, to determine the aerosol optical depth ([39]). Figure 2a shows the monthly mean of aerosol optical depth at Yonsei University with the Ångström exponent for the period 1993–2019. On average, aerosol optical depth is relatively higher in the spring season, which is attributed to the long-range transport of Asian dust and air pollutants from the Chinese continent ([40,41,42]). In contrast to the spring season, aerosol optical depth is lower in summer, owing to the Asian monsoon ([43,44]). Wet scavenging due to precipitation plays a significant role in improving air quality. Moreover, there is a decrease in the number of clear days when the aerosol optical depth can be retrieved in the summer season. The monthly Ångström exponent values are averaged over the year to be 1.1743 with a standard deviation of 0.1290. The monthly variation in the Ångström exponent is too small, and thus, it is ignored. The behavior of the Ångström exponent is consistent with a previous study by Michalsky et al. [45], which showed that continental aerosols have a typical value of 1.3 with a small seasonal variation. Yoon et al. [46] investigated temporal changes in aerosol optical depth based on AERONET measurements at Yonsei University station between 1993 and 2013 and showed that the diurnal variation of aerosol optical depth could differ from trends based on monthly and annual means. However, for the purpose of simplicity, we used the monthly mean of the aerosol optical depth measured from 1993 to 2019. The spectral aerosol optical depth, which was incorporated into the clear sky model in this study, can be derived by using the aerosol wavelength spectra with the Ångström exponent and aerosol optical depth at 550 nm, which were directly taken from the AERONET station.

3.1.2. POM-02 Skyradiometer

At the KIER station (Figure 1), aerosol optical properties were measured using a PREDE POM-02 skyradiometer, starting from December 2020. However, due to calibration issues at the National Oceanic and Atmospheric Administration Mauna Loa Observatory, the operation was halted for 2 months in March and April 2021. As the detailed principle of the operation and retrieval algorithm has already been explained in previous studies by Aoki and Fujiyoshi [47], Uchiyama et al. [48], and Che et al. [49], this study describes the direct and diffused measurements of the POM-02 skyradiometer. The skyradiometer instrument measures direct solar irradiance in 11 spectral bands (315, 340, 380, 400, 500, 670, 870, 940, 1020, 1600, and 2200 nm; [48]) to retrieve the spectral aerosol optical depth using the improved Langley method and Beer–Lambert–Bouguer law every minute after the diffused irradiance measurement is complete. The single scattering albedo can be derived from the sky radiation observed at 24 predefined scattering angles every 10 min. Figure 2b shows the monthly mean aerosol optical depth at 500 nm with Ångström exponent for the whole year of 2021. There were no observations in March and April, owing to calibration issues. With an Ångström exponent identical to that of the AERONET station, the skyradiometer catches the lower aerosol optical depth in the summer season. In the same manner as the AERONET measurement, the spectral aerosol optical depth, which is incorporated into the clear sky model in this study, can be derived by using the aerosol wavelength spectra with the Ångström exponent and aerosol optical depth at 500 nm, which are different wavelengths in the AERONET measurement (500 vs. 550 nm).

3.1.3. MODIS Products

The present study used the aerosol optical depth derived from the MODerate resolution Imaging Spectroradiometer (MODIS) onboard the Aqua satellite ([50]). The MODIS level-2 atmospheric aerosol product (MYD04_L2) provides full global coverage of aerosol properties using the Dark Target and Deep Blue algorithms. The latter algorithm has been preferred for this study, because a recent study by Choi et al. [51] showed that the RMSE is lower than that obtained in Korea by the Dark Target algorithm. The monthly mean of aerosol optical depth for the investigation period from January 2020 to December 2021 is shown in Figure 2c. The reduced aerosol optical depth in summer is consistent with the other in situ observations, but the retrieved aerosol optical depth is lower than that observed at the AERONET station. A similar behavior was observed by Nam et al. [52] who analyzed the spatial and temporal variations in aerosol optical depth near the Korean Peninsula.

3.1.4. MERRA2 Reanalysis

The gridded aerosol optical depth was obtained from Modern-Era Retrospective Analysis for Research and Applications Version 2 (MERRA-2), which is a reanalysis dataset assimilated by ground and satellite observations into the first guess model ([53]). The horizontal resolution is 0.625° × 0.5°, and the temporal resolution is 1 h. Mukkavilli et al. [54] evaluated the atmospheric aerosol products from MERRA-2 in Australia. When compared with the observations at the AERONET station, they investigated the Pearson correlation coefficient between MERRA-2 aerosol optical depth estimates and the observations, which was 0.725 with a mean bias error (MBE) of 0.02 on a monthly scale. Another study performed in China showed better performance of MERRA-2 products; Sun et al. [55] validated the monthly mean aerosol optical depth from the MERRA-2 datasets from 1980 to 2016 and found correlation coefficients of 0.80 to 0.88 throughout the year. We derived the climatological averages for the long-term period from 2000 to 2021 to build an aerosol optical depth database over the Korean Peninsula. Figure 2d shows the monthly variation in aerosol optical depth at 550 nm with the Ångström exponent at the KIER station. Despite the larger standard deviation of aerosol optical depth for each month, the monthly mean values of aerosol optical depth are similar to those from in situ measurements at the AERONET and KIER stations.

It is of interest to compare all aerosol optical depth datasets. The monthly mean of aerosol optical depth from the POM-02 skyradiometer at the KIER station is highly correlated with the other datasets, AERONET, MERRA-2, and MODIS products (Figure 3). Bright and Gueymard [56] conducted a study to compare the aerosol optical depth from ground observations with those from satellite observations at 452 AERONET stations for several climate zones. In their study, MODIS products were the worst in the equatorial climate, but the opposite was true in the temperate climate zone. Here, the RMSE between the MODIS estimates and observations from the POM-02 skyradiometer is 0.183, which is similar to the result of Bright and Gueymard [56].

3.2. Solar Irradiance Observations

The solar irradiance observation station is located on the KIER in Daejeon, Korea (Figure 1). GHI and DNI are observed by the CMP11 pyranometer and CHP1 pyrheliometer, respectively (both manufactured by Kipp & Zonen). These are installed on the Sun tracker, SOLYS2, with a shadow ball that is employed for detecting diffused horizontal irradiance (DHI). The temporal resolution is set at 1 min. Data quality control is conducted before evaluation according to the criteria presented by Gueymard and Ruiz-Arias [57]. The data points are accepted when all the following conditions are satisfied:

$${\theta }_s<{75}^{°}$$

(1)

$$\mathrm{GHI}>0 \mathrm{and} \mathrm{DHI}>0 \mathrm{and} \mathrm{DNI}\ge 0$$

(2)

$$\mathrm{DNI}<1100+0.03h$$

(3)

$$\mathrm{DNI}<S_{0n}$$

(4)

$$\mathrm{DHI}<0{.95S}_{0n}{\cos }^{1.2}h+50$$

(5)

$$\mathrm{GHI}<1{.50S}_{0n}{\cos }^{1.2}h+100$$

(6)

$$\left|\frac{{\mathrm{DNIcos}\theta }_s+\mathrm{DHI}-\mathrm{GHI}}{\mathrm{GHI}}\right|<0.05$$

(7)

$$\frac{\mathrm{DHI}}{\mathrm{GHI}}<1.05 \mathrm{when} \mathrm{GHI} > 50 \mathrm{and} {\theta }_s<{ 75}^{°}$$

(8)

$$\frac{\mathrm{DHI}}{\mathrm{GHI}}<1.10 \mathrm{when} \mathrm{GHI} > 50 \mathrm{and} {\theta }_s>{ 75}^{°}$$

(9)

where h is the terrain height set at 40 m above mean sea level, and S_0n is the extraterrestrial irradiance on a normal surface. In a given condition, Gueymard and Ruiz-Arias [57] set the threshold value for θ_s as 85°. However, we reduced this to 75° because the solar irradiance measured at low Sun elevations is occasionally contaminated by either solar reflection or beam blocking, owing to surrounding buildings at the KIER observing station.

4. Numerical Simulation Design

This study determined the investigation period as the whole year of 2021, except for March and April, according to the data availability of the POM-02 skyradiometer. It is important to distinguish between clear and cloudy skies. A clear sky day is defined when the cloudiness is lower than 0.1 for all times from sunrise to sunset. The study detects the cloudiness by using the sky imager, VIS-J1006, made by CMS–ING. GmbH. Clear and cloudy sky images are shown in Figure 4a,b, respectively. For clear sky, no cloud patches are taken by the sky imager. The individual images can be converted into a cloudiness distribution over the sky using the software provided by the CMS–ING. The white pixels in Figure 4c are ascribed to circumsolar irradiance in the field of view, which corresponds to the bright pixels in Figure 4a. Contrary to clear sky, a cloud layer covers the zenith of the sky imager, implying overcast conditions (Figure 4d). Figure 5 shows the time series of cloudiness for the clear and cloudy skies. Even if cloudiness reaches 0.4 toward sunset, daytime cloudiness of less than 0.1 is a good indicator to choose clear days. A cloudy sky represents obviously higher cloudiness throughout the day. Consequently, 24 clear sky days were selected based on the above measurements for the investigation period.

In addition to the aerosol optical depth, atmospheric transmittance on the ground surface relies on the vertical profiles of air temperature and water vapor. The rawinsonde data at the Osan station (Figure 1) were obtained at 09:00 Local Standard Time (LST = 9 + UTC, Universal Time Coordinate) for the individual clear day. The initial vertical profiles were interpolated into a grid of 59 layers in the clear sky model. The monthly average of the total ozone column concentration from the climatological background ([58]) was incorporated into the model to account for the effects of ozone on solar irradiance in the ultraviolet region. The aerosol optical depth introduced in the previous section is the vertically integrated column concentration; therefore, it was redistributed at each vertical level to parameterize the aerosol extinction coefficient profile in the clear sky model using an exponential distribution with a scale height ([59]). Surface albedo was obtained from the MODIS product MCD43B3, a 16-day composite product of albedo containing white sky (bi-hemispherical) albedo and black sky (directional hemispherical) albedo at a spatial resolution of 1 km.

Table 1. Numerical simulation design for sensitivity tests of the aerosol optical depth. Sensitivity tests, i.e., S1 to S5 are performed for the different datasets of aerosol optical depth.

	Control	S1	S2	S3	S4	S5
Dataset a	AERONET	POM-02	AERONET	MODIS	MERRA-2	MERRA-2
Time Scale	Monthly Mean	Daily mean	Daily mean	Daily mean	Daily mean	Julian Daily mean

^a Abbreviations: AERONET, Aerosol Robotic Network; MODIS, MODerate resolution imaging spectroradiometer; MERRA-2, Modern-Era Retrospective Analysis for Research and Applications Version 2.

lists the outline of the sensitivity test for the aerosol optical depth. All simulations were performed every 10 min from sunrise to sunset for a given clear day, assuming that the diurnal variations of atmospheric conditions (i.e., water vapor, air temperature, and aerosol optical depth) were ignored within a single day. The control run was performed using the climatological monthly mean aerosol optical depth at the AERONET station. There were four simulations with different datasets of aerosol optical depth at the KIER station: S1 with in situ measurement by the POM-02 skyradiometer, S2 with the daily mean of aerosol optical depth obtained from the AERONET station, S3 with MODIS L2 Aqua data (Deep Blue algorithm), and S4 with a daily average of MERRA2 reanalysis for a given day. An additional run, S5, was carried out to compare the performance when the clear sky model was operated by the daily average of the MERRA2 reanalysis from 2000 to 2021, which corresponds to the Julian date of a given day.

5. Results

The clear sky GHI derived from the clear sky model every 10 min was evaluated against that observed at the KIER observing station. The error statistics employed in this study are as follows:

$$\mathrm{MBE}=\frac{1}{N}{\displaystyle \sum _{i=1}^N\left(E_i-O_i\right)}$$

(10)

$$\mathrm{MAE}=\frac{1}{N}{\displaystyle \sum _{i=1}^N\left|E_i-O_i\right|}$$

(11)

$$\mathrm{Skill} \mathrm{Score}=\frac{{\mathrm{MAE}}_{\mathrm{CTL}}-{\mathrm{MAE}}_{\mathrm{S}}}{{\mathrm{MAE}}_{\mathrm{CTL}}}\times 100$$

(12)

In Equations (10) and (11), E_i, O_i, and N represent the estimates, observations, and number of samples, respectively. The simulations were made every 10 min; and therefore, the number of samples was 923 for 24 clear sky days. MAE_CTL and MAE_S in Equation (12) represent the MAE values from the control and sensitivity runs, respectively. Figure 6 shows the results of the control run. Out of the 24 clear days, positive biases are found for only 4 days, which result in an average negative bias. As shown in Figure 7, the higher correlation coefficient between the bias of GHI estimate and the aerosol optical depth anomaly (=climatological mean − daily mean) is good evidence to indicate that the GHI observations could be underestimated by the large positive bias of climatological aerosol optical depth from the daily averages. A similar result was observed by Kim et al. [34] who observed a positive bias in aerosol optical depth that led to the underestimation of clear sky GHI observations. On 23 December 2021, long-range transport of air pollutants from China influenced air quality over the Korean Peninsula, resulting in an extremely high aerosol optical depth (Figure 8a). Figure 8b also shows that the aerosol optical depth measured by the POM-02 skyradiometer is much larger than the climatological mean originally ingested in the clear sky model. Consequently, the GHI is overestimated in the control run with the AERONET dataset on 23 December 2021.

Table 2. Simulation mean bias error (MBE) and mean absolute error (MAE) presented as the average ± standard deviation.

	Control	S1	S2	S3	S4	S5
MBE	−25.2 ± 18.7	1.5 ± 7.2	−5.6 ± 22.2	2.9 ± 17.9	4.1 ± 16.1	−4.3 ± 15.1
MAE	29.9 ± 10.2	9.7 ± 3.0	17.4 ± 16.5	17.0 ± 9.0	16.8 ± 8.8	15.7 ± 7.2
Skill Score	-	57.9 ± 35.4	28.6 ± 65.1	31.1 ± 52.6	34.6 ± 58.4	31.8 ± 62.0

summarizes the error statistics for all the runs. The control run results in MAE values that are averaged over all clear days as 29.9 W m⁻² with a standard deviation of 10.2 W m⁻². Simulations using the in situ observations, S1 and S2, reduced the MBE to 1.5 and −5.6 W m⁻², respectively. Corresponding to the improvement in the bias error, the MAE values are also reduced for the S1 and S2 runs. Even if both S1 and S2 runs are made based on the in situ measurement, the bias characteristics are different: positive in the S1 run, but the opposite is true for S2. The difference between the two runs originates from observations made at different locations. The aerosol optical depth measured at the AERONET station, approximately 135 km away from the KIER station, is the major source for creating a clear sky GHI with the largest MAE in the S2 run. When compared with the S3 run, runs S4 and S5 yield better results, i.e., the MAEs in runs S4 and S5 are lower than that of the S3 run. This may imply that using reanalysis datasets is a good alternative for producing clear sky GHI as a universal clear sky model; this is discussed in detail in the next section. To investigate the extent to which the results are improved in the sensitivity runs, the skill scores, calculated using Equation (12), are listed in Table 2. In Equation (12), a large positive value of the skill score indicates a larger improvement. The skill scores from the sensitivity tests indicate that updating the aerosol optical depth plays a role in improving the results of clear sky GHI estimates. In particular, S5 was run by the climatological mean of the MERRA2 aerosol product, but the modeling output improved by 31.8% when compared with the control run. Although the control and S5 runs were both carried out by using climatological monthly averages, the aerosol optical depth obtained from the reanalysis data at the KIER station is more reliable when the clear sky model derives the GHI observations. Of the five sensitivity runs, the largest skill score is found in the S1 run. This is because it was made using in situ observations at the KIER observation station.

6. Discussion

6.1. Effect of Diurnal Variation in Aerosol Optical Depth

The daily mean of the in situ observation of aerosol optical depth at the KIER station raised the skill of the clear sky model in deriving the GHI estimates, as previously discussed. However, there was a small number of cases where the ingestion of in situ observations into the GSFC model did not improve the clear sky GHI estimates. Figure 9 shows a time series of observations and estimations on 14 January 2021; the behavior of MBE changes with time (negative MBE in the early morning, but positive MBE dominant in the afternoon). The aerosol optical depth measured by the POM-02 skyradiometer in the morning is lower than the climatological mean, which is employed in the control run (Figure 9). In the afternoon, however, the air quality becomes worse when compared with the AERONET data. Note the variability defined as the deviation of the instantaneous aerosol optical depth from the daily mean in Figure 9. Although there is a large diurnal variation in the aerosol optical depth, the S1 run prescribed the aerosol optical depth as a constant (the daily mean value of 0.2716 at the KIER ground station). Thus, the improvement cannot be recognized in the S1 run.

A good example of this improvement is shown in Figure 10. The bias values are all negative, which indicates that the GHI estimates in the control run are lower than those observed, owing to the larger aerosol optical depth in the clear sky model. On 19 January 2021, the POM-02 skyradiometer measured lower values of aerosol optical depth than the AERONET dataset. The daily mean aerosol optical aerosol optical depth was 0.0923; furthermore, its variability was smaller than that on 14 January 2021. Therefore, the S1 run corrects the bias in the GHI estimates resulting from the control run.

This study attempts an objective analysis to investigate the relationship between diurnal variation in MBE and the skill score of S1 runs. The bias sign index (BSI) is defined as follows:

$$\mathrm{BSI}=\frac{\mathrm{MAE}-\left|\mathrm{MBE}\right|}{\mathrm{MAE}}$$

(13)

If the signs of the bias at instantaneous GHI estimates are the same for a single day in Equation (13), the MAE and absolute value of MBE are exactly the same, implying that the BSI is zero. In contrast, the non-zero value of BSI indicates that the behavior of the bias changes during the course of the day, as shown in Figure 9, where the BSI is −0.5217. The BSI on 19 January 2021 is zero because the MAE and MBE values are 40.8 and −40.8 W m⁻², respectively. The relationship between the BSI and skill score appears to be more visible when the BSI is extended for all 24 clear sky days (Figure 11). Positive skill score values are distributed in the bin between −0.1 and 0. As the BSI decreases negatively, the results from the S1 run cannot be improved. To account for the diurnal variation in the aerosol optical depth, the clear sky model has to assimilate the aerosol optical depth observed at an hourly time scale. However, it is difficult to resolve such data during operation because of the lack of in situ measurements.

6.2. Applications for the Community Model

Solar resource assessments and solar power forecasting require a reliable clear sky model. With in situ observations, sufficiently reliable clear sky GHI can be derived. Nevertheless, depending on the local meteorological characteristics is to an extent burdened when the model is applied to universal or community models for public use. Table 2 lists the successful simulations of the clear sky model with MODIS products and MERRA2 reanalysis, which implies that the UASIBS–KIER model is feasible as a universal model. The clear sky model as a universal model must include information on the aerosol optical properties, vertical profiles of air temperature and water vapor, and surface albedo. Surface albedo is derived from MODIS Land products, as introduced in Section 4. Vertical profiles of air temperature and water vapor are obtained using rawinsonde measurements. For the aerosol optical properties, the Julian daily averages of the MERRA2 reanalysis datasets employed in the S5 run are sufficient to provide the aerosol optical depth and single scattering albedo for the vertical grids. During operation, the radiative properties in a single column can be easily generated by the GSFC radiative transfer model without numerical burden. However, the numerical cost must be considered when the GSFC radiative transfer model is extended to a two-dimensional domain. Therefore, we employed the look-up table approach in the same manner as the UASIBS–KIER model, assuming that the initial profile of air temperature and water vapor is the same for the designated domain because the domain area is not broad. The GSFC radiative transfer model generates a look-up table at discrete values of surface albedo, solar zenith angle, column-integrated aerosol optical depth, and Ångström exponent. The clear sky model determines the atmospheric transmittance corresponding to the surface albedo, solar zenith angle, and aerosol optical properties from the MERRA2 reanalysis datasets. Then, the clear sky GHI is finally derived using the atmospheric transmittance, solar constant, and Sun–Earth distance correction factor.

Figure 12 is the horizontal distribution of aerosol optical depth on Julian day 33 (i.e., 2 February 2021). Air quality is good along the Korean Peninsula, but the aerosol optical depth is relatively high over the Yellow Sea, owing to air pollutants originating from the Chinese continent. Moreover, the aerosol optical depth over the southern coast of the Korean Peninsula increased. The comparison between the control and S5 runs implies the importance of spatial distribution in the aerosol optical depth (Table 2). When the aerosol optical properties are treated as constant over the entire domain, the spatial distribution of the clear sky GHI depends only on the solar zenith angle and surface albedo. Good evidence is provided in Figure 13a, which shows that solar irradiance decreases with latitude. In contrast, the clear sky model improves the derivation of the clear sky GHI by taking into account the spatial distribution of aerosol optical depth. In Figure 13b, the clear sky GHI is distributed in accordance with the aerosol optical depth distribution shown in Figure 12.

7. Conclusions

The clear sky index, which is defined as the ratio of GHI to clear sky GHI, is the reference measure to indicate cloudiness for solar resource assessment and solar power forecasting. In addition, solar irradiance is derived from the clear sky index with the visible reflectance obtained from satellite imagery. Thus, the clear sky model is crucial for determining the clear sky GHI for a reliable clear sky index. Of the several parameters in the clear sky model, the aerosol optical depth is most effective in deriving the solar irradiance in the model, owing to the complexity of the relationship between shortwave radiation and aerosol optical depth. This study attempted to investigate the impact of aerosol optical depth on the derivation of clear sky GHI and to determine the feasibility of the clear sky model as a universal or community model. The GSFC radiative transfer model, which is a part of UASIBS–KIER, was employed as the clear sky model. In the original model configuration, the monthly average of aerosol optical properties at the AERONET station was assimilated into the clear sky model for the sake of simplicity. In this study, we obtained in situ measurements using a POM-02 skyradiometer, MODIS aerosol products, and MERRA2 reanalysis data; the performance of calculating the clear sky GHI was evaluated against ground observations at the KIER station.

The monthly variation of aerosol optical depth was similar for all individual datasets. The aerosol optical depth decreased in the summer, but the opposite was true in spring. This is because the Asian monsoon causes heavy precipitation in summer, and air quality in the spring is highly dependent on long-distance transit of fine particulate matter from China. The variability of the Ångström exponent for each month was relatively smaller than that of the aerosol optical depth. The control run that was performed using the monthly mean aerosol optical depth from the AERONET station resulted in an MAE of 29.9 W m⁻². When simulated by the aerosol optical properties measured by the POM-02 skyradiometer at the KIER station, the S1 run had the lowest MAE, implying the skill score to be the highest. Owing to data availability, the simulations were based on MODIS products and MERRA2 reanalysis. These runs also resulted in better performance than the control run: skill scores of the S3 and S4 runs were 31.1% and 34.6%, respectively.

Finally, the feasibility of applying the clear sky model to universal or community models without the dependence of local meteorological characteristics, such as in situ observations of aerosol optical depth, was investigated. The MERRA2 reanalysis was employed to generate the daily average aerosol optical depth and Ångström exponent for Julian dates between 2000 and 2021. The S5 run was carried out using the Julian daily average of the MERRA2 reanalysis, which corresponded to the target day. The skill score of the S5 run was relatively lower than that of the S4 run but was similar to that of the S3 run. In the original configuration of the clear sky model, aerosol optical properties are prescribed as constant over the entire domain when solar irradiance is derived from satellite imagery. The clear sky GHI is only a function of the solar zenith angle and surface albedo under a given atmospheric condition. The incorporation of the MERRA2 reanalysis into the radiative transfer model enables the clear sky model to produce the spatial distribution of clear sky GHI in accordance with the aerosol optical depth. Therefore, the radiative transfer model improved by the aerosol optical depth can be operated within the UASIBS–KIER model to derive the solar irradiance from geostationary satellite imagery. As a result, the ability to assess solar resources and forecast solar power is likely to be improved.