Improvement of Korea Meteorological Administration Solar Energy Resources Map Using Fine-Scale Terrain Data

Real-time solar energy resources mapping is crucial for the development and management of solar power facilities. This study analyzes the effects of the digital elevation model (DEM) resolution on the accuracy of the surface insolation (insolation hereafter) calculated by the Korea Meteorological Administration solar energy mapping system, KMAP-Solar, using two DEMs of different resolutions, 1.5 km and 100 m. It is found that KMAP-Solar yields smaller land-mean insolation with the fine-scale DEM than the coarse-scale DEM. The fine-scale DEM reduces biases by as much as 32 Wm− 2 for all observation sites, especially those in complex terrain and that the insolation error reduction is correlated with the difference in sky view factor (SVF) between the coarse- and fine-scale DEM. Both the coarse- and fine-scale DEMs generate the insolation-elevation and insolation-SVF relationship which is characterized by positive (negative) correlation between the insolation and the terrain altitude (SVF). However, the coarse-scale DEM substantially underestimates these relationships compared to the fine-scale DEM, mainly because the coarse-scale DEM underrepresents large terrain slopes and/or small SVFs, most seriously in high-altitude regions. The fine-scale DEM generates a more realistic insolation distribution than the coarse-scale DEM by incorporating a wider range of key terrain parameters involved in determining insolation. Improvements of insolation calculations in KMAP-Solar using a fine-scale DEM, especially in the areas of complex terrain, is of a practical value for Korea because the operational solar resources map from KMAP-Solar supports solar energy research, solar power plant installations, and real-time prediction and management of solar power within the power grid.


Introduction
Despite the worldwide increase in renewable energy production, the World Energy Lookout 2020 by the International Energy Agency (IEA) estimates that the share of renewable energy within the total energy production must increase from 9% in 2020 to 56% in 2050 to achieve carbon neutrality by 2050. Solar energy is the most viable resource towards meeting this goal considering that the solar energy reaching the earth's surface is about 23,000 TWyr -1 , much larger than other energy resources such as wind power and natural gas (Perez and Perez 2008). Despite the potential to become a major energy resource, solar power generation suffers from limitations due to high initial costs and site availability among others. Considering that solar power plants are costly to install and that, once installed, practically impossible to relocate, accurate surface insolation (insolation hereafter) data are sorely needed for cost-effectiveness in solar energy developments Lee et al. 2011;Ruiz-Arias et al. 2011;Kim 2013;Park et al. 2015;Lee et al. 2017).
A fine-scale solar energy map is highly useful not only for selecting solar power plant sites but also for real-time managements of power grids composed of multiple types of power plants. In-situ insolation measurements provide accurate values, but are not practical in building high-resolution solar energy maps over large areas because of the high costs for the installation and maintenance of instruments (Koo et al. 2019;Jee et al. 2017). Moreover, in-situ measurements cannot be used for solar energy forecasting. Solar radiation models can be a cost-effective alternative to high-density sensor networks for generating solar energy maps over large areas (Greeley and Batson 1997;George and Maxwell 1999;Perez et al. 2002;Lave and Kleissl 2011;Jee et al. 2011). Solar radiation models that compute insolation by explicitly considering the physical processes involved the atmospheresurface radiative transfer, are also the sole practical source of operational solar energy forecasts for supporting real-time power grid managements. Realizing the importance, the National Institute of Meteorological Sciences (NIMS)/Korea Meteorological Administration (KMA) has been operationally providing solar resources maps for South Korea (Korea hereafter) since 2010 to support various research institutes, government agencies, and private enterprises. The current solar radiation calculation at NIMS/KMA is based on a simple horizontal interpolation of surface insolation from a regional numerical weather prediction (NWP) model, the Local Data Assimilation and Prediction System (LDAPS) (NIMR, 2014(NIMR, , 2015(NIMR, , 2017. The solar energy forecast using LDAPS provides useful data for supporting various users, but has been suffering from large uncertainties due to the lack of horizontal resolutions necessary for representing fine-scale terrain effects on insolation (Hou et al. 2020).
Because solar energy generations are determined by local insolation, fine-scale terrain effects on insolation is of a particular concern. Hoch and Whiteman (2010) showed that terrain properties such as slope and azimuth greatly affect insolation to induce heterogeneous microclimate in a mountainous region. Wang et al. (2014) analyzed the insolation distribution around the Yangtze River using a 1 km-scale digital elevation model (DEM) in conjunction with surfacestation and satellite data to find that the total insolation varies according to topographic properties such as altitudes, latitudes, terrain slopes, and azimuth.
A number of studies analyzed the effects of terrain properties such as elevation, slope, azimuth, and sky-view factors, on calculating insolation using DEMs of various resolutions (e.g., Dozier and Frew 1990;Dubayah 1994;Rich et al. 1994;Zhang et al. 2015). Kumar et al. (1997) found that the accuracy of the calculated insolation over the Nullica Eden Mountain, Australia is affected by the errors in terrain altitudes and slopes. Tovar-Pescador et al. (2006) analyzed the sensitivity of insolation calculations to the DEM scale using a Geographic Information System (GIS) Solar analyst model for the Ciara Nevada Park in Spain to show that the errors in calculating insolation are larger over complex terrains than flat terrains and are sensitive to the DEM scale. Olson and Rupper (2019) and Hopkinson et al. (2010) found that the insolation calculated over complex terrains vary following the DEM resolution in such a way that coarser resolution DEMs tend to yield larger values. Klok and Oerlemans (2002) and Arnold et al. (2006) found that topographical shading affects strongly the insolation in the regions surrounded by high terrain as manifested in local ice mass variations.
The terrain effect on local insolation is of a great concern in developing solar energy in Korea as over 70% of Korea is covered with mountainous terrains. The average slope over Korea is 14.3° with terrains of slopes > 20° cover over 30% of Korea (Park et al. 2015). Thus, accurate accounting of the fine-scale terrain effects on insolation is important for calculating insolation over Korea. A number of studies examined the characteristics of insolation over various regions in Korea (e.g., Kim et al. 2008;Zo et al. 2010, 2017Lee et al. 2011). Jee et al. (2011Jee et al. ( , 2017 analyzed the insolation in the Gangwon-do province and Seoul with multiple DEMs of varying scales to find that the calculated maximum expected power generation amount decreases with increasing DEM resolutions. The existing studies for Korea, however, deals only with limited areas and scopes, hence are not applicable to the generation of nationwide solar energy resources maps required by various governmental, academic, and private institutions. This study presents the KMA solar resources mapping system (KMAP-Solar) and the results from an analysis of the sensitivity of insolation calculation to the DEM resolution. Section 2 presents the descriptions of KMAP-Solar as well as the data and analysis methods employed in the study. Section 3 presents the evaluation and analysis of the insolation calculated using KMAP-Solar and the sensitivity of the calculated insolation to the DEM resolutions. The summary and conclusion of this study are presented in Section 4.

KMA Post-Processing Solar Resources Map (KMAP-Solar) System
KMA solar resources maps provide fine-scale insolation data over Korea using KMAP-Solar in conjunction with the KMA regional NWP model, the Local Data Assimilation and Prediction System (LDAPS  (2011) and Lewis et al. (2015). KMAP downscales the 1.5 km-scale LDAPS operational forecast data by considering the effects of fine-scale terrain to produce forecast data including insolation at the KMAP resolution. For insolation, the current KMAP generates 100 m-resolution 3-hourly (06, 09, 12, and 18 KST) insolation forecasts (Choi et al. 2020) by bi-linearly interpolating the insolation in the LDAPS forecasts to the KMAP grid nest (Fig. 1, dashed arrows). Because LDAPS calculates insolation using the terrain parameters computed from a 1.5 km-resolution DEM, the bi-linear interpolation alone cannot capture the effects of the fine-scale KMAP terrain on local insolation.
The solar module in KMAP-Solar (NIMS, 2018) downscales the LDAPS insolation onto the KMAP grid nest using the terrain parameters involved in determining insolation that are derived from the KMAP-scale DEM (solid arrows in Fig. 1). First, the direct (DIR) and diffuse (DFF) insolation on the slant surface of LDAPS (K S and D S , respectively) are converted into the DIR and DFF on the horizontal surface (K H and D H , respectively) using the LDAPS-scale terrain parameters for DIR and DFF (F K and F D , respectively) following Eqs. (1-5) below: where β is the terrain slope angle, ζ is the solar zenith angle, c is the solar incident angle, and ψ is the sky-view factor (SVF) of each grid calculated from the horizontal surface (indicated by the subscript 'H') (Manners et al. 2012). The solar incident angle on the slant plain is calculated as: where φ is the solar azimuth angle and γ is the terrain azimuth angle (Pielke and Roger 2002). Note that the topographic parameters in Eqs. (1-5) are calculated using the LDAPS-scale DEM.
The DIR and DFF of LDAPS for the horizontal surface are bi-linearly interpolated onto the KMAP grid nest to obtain the DIR ( K (4) F D = cos .
where cosc cos is the factor for converting DIR from the horizontal surface to the slant surface and ψ is the SVF calculated from the KMAP DEM. When the solar inclination angle is small enough to cause shading by itself (c > 90; 'self-shading') or by surrounding terrain (H > ζ; 'surrounding-shading'), DIR is set to 0. The total insolation on the slant KMAP-Solar surface is calculated as the sum of K DS and D DS . In order to reduce the uncertainty in calculating insolation caused by a large solar zenith angle (LI-COR 2005;Nottrot and Kleissl, 2010;Blane and Wald 2016), the terrain effects on insolation are not applied when the solar zenith angle exceeds 80°.  onto the 100 m-scale KMAP grid nest. Figure 2 compares the four topographic parameters (elevation, slope, azimuth, SVF) in the current KMAP (KM) and KMAP-Solar (KS) from the LDAPS and the KMAP DEM, respectively. Both the LDAPS (1.5 km scale) and KMAP (100 m scale) DEM represent the overall terrain shape, but they yield substantially different topographic parameters from each other. Most notably, the LDAPS DEM generates much smaller slope angles (Fig. 2b) and larger SVFs (Fig. 2d) than the fineresolution KS DEM (Fig. 2f, h, respectively). The KS DEM also yields much finer-scale azimuth angle variations than the LDAPS DEM (Fig. 2c).

Ground Insolation Observation Data
The KMA insolation data used for evaluating the effect of DEM resolutions on the insolation calculation are obtained from 42 Automated Synoptic Observation System (ASOS) sites (Table 1) at which the data are collected for 40% or more of the evaluation period, July 2016 -June 2020 ( Table 1). The radiometers at the KMA ASOS sites are installed to measure the insolation incident onto the horizontal surface. Thus, the ASOS insolation data reflect only the effect of SVFs among the four topographic parameters. The hourly ASOS data provides the total (the sum of DIR Fig. 3 The insolation from a KM and b KS, as well as the difference between KS and KM over Korea. d is the PDF of insolation generated in KM (black) and KS (red) and DFF) all-sky insolation averaged for the one-hour period prior to the time of report. In this study, only the ASOS data at 06, 09, 12, 15, and 18 KST are used to evaluate the 3-hourly KM and KS insolation outputs.

Evaluation Methods
Because only the insolation on the horizontal surface is observed, the KM and KS insolation values on the horizontal surface ( K H , D H for KM; K f H , and D f H for KS) modified only by the SVF effect are evaluated against the observations (boxes d5 and d6 in Fig. 1). The evaluation is performed using the following metrics; the mean bias error (MBE; Eq. 8), the root mean square error (RMSE; Eq. 9), percent MBE (%MBE) (Eq. 10), and percent RMSE (%RMSE) (Eq. 11). In addition, the added values (AVs) in terms of MBE (Eq. 12) and RMSE (Eq. 13) are analyzed:  Figure 3 compares the annual-mean insolation over the Korea domain from KM and KS during the evaluation period. Because KM (Fig. 3a) and KS (Fig. 3b)  Although KS yields similar annual-mean insolation (285.5 W m -2 ) as KM (294.2 W m -2 ) over the land, the different DEM resolution in KS results in notably different insolation distributions from KM. KS generates smaller insolation than KM over much of the land region, and the most outstanding insolation difference between KM and KS occurs in mountainous regions (Fig. 3c). The insolation calculated in KM is confined within a much narrower range (286-321 W m -2 ) than that in KS (192-343 W m -2 ) (Fig. 3d).

Evaluation of the Effect of DEM Resolution on the Insolation Calculation
The effect of DEM resolutions on calculating insolation is evaluated in terms of the BIAS and RMSE of the insolation calculated in KM (coarse-scale DEM) and KS (fine-scale DEM) against the observed values at the 42 ASOS stations at the five local time levels (06,09,12,15,and 18 KST).
Because the radiometers at these ASOS stations are installed  Table 3 to measure the insolation on the horizontal plain, only the effect of elevations and SVFs on insolation is accounted for in the evaluation.  (Fig. 4a) and 13 W m -2 (Fig. 4b), respectively, at some sites. The difference in MBE and RMSE between KM and KS (dMBE and dRMSE, respectively) that corresponds to the improvement in the accuracy of the calculated insolation by using the finescale DEM, generally increases with the increase in the SVF difference between KM and KS (dSVF) (Fig. 4a, b). This implies that the fine-scale DEM in KS generates more accurate local SVFs than the coarse-scale DEM used in KM to result in improved insolation calculations. The AV due to the use of the fine-scale DEM also increases with increasing dSVF for both MBE (Fig. 4c) and RMSE (Fig. 4d), with the largest values at the earliest and latest hours (6 and 18 KST, respectively) when the solar elevation is smallest and the terrain shading effects are largest (Fig. 4e). DEM resolutions also affect the calculation of other topographic parameters such as slope and azimuth that are important for determining insolation on slant surfaces. Because of the lack of insolation observations on slant surfaces, the evaluation of the effects of the DEM scale on the accuracy of insolation calculation is limited to the effects of SVFs in this study. The effect of DEM scales on calculating insolation due to other terrain parameters are analyzed by relating the insolation differences between KM and KS to the differences in the terrain parameters between KM and KS in the following section.

Effects of DEM Resolutions on Calculating
Insolation Via Topographic Parameters Figure 5 summarizes the effect of DEM resolutions on the four topographic parameters (Table 3) related to the insolation differences between KS and KM. Both KM and KS covers the same elevation range (Fig. 5a). The fine-scale DEM (KS) yields a larger fraction in the lowest (< 200 m) and highest (> 1000 m) categories than the coarse-scale DEM (KM) while KM yields a larger faction in the second lowest category (200-400 m); however, the overall elevation distribution in KS is similar to that in KM. Despite the similar terrain elevation distribution, the insolation-elevation relationship in KS notably differ from that in KM. The calculated insolation decreases with increasing elevation for both KM and KS, but KS generates a much larger rate of decrease than KM; i.e., the insolation-elevation relationship calculated using the fine-scale DEM is much stronger than that from the coarse-scale DEM (Fig. 5b). The insolation difference between KM and KS increases with increasing altitudes to become nearly 40 Wm -2 for the highest (> 1000 m) elevation category. KS and KM also generate similar terrain azimuth distributions (Fig. 5c), but the insolation-azimuth relationship in KS is substantially different from that in KM (Fig. 5d). For both KS and KM, insolation is largest and smallest on the southfacing and north-facing slope, respectively, but the insolation difference between the north-and south-facing slope is notably larger in KS (~ 40 Wm -2 ) than in KM (~ 15 Wm -2 ).
The fine-scale DEM in KS generates terrain slopes over a much wider range than the coarse-scale DEM in KM (up to > 30° in KS and up to 20° in KM;Fig. 5e). Hence, KS accounts for the effect of large slope angles in calculating insolation much better than KM. Both KM and KS show that the insolation decreases with increasing slope angle ( Fig. 5f) but the insolation-slope angle relationship is much stronger in KS; the insolation difference between the smallest and largest slope category is over 40 W m -2 for KS (between S1 and S7) and is about 8 W m -2 for KM (between S1 and S4). Because of the underrepresentation of large slope angles in KM, the KM insolation is limited to the four smallest slope angle categories to result in larger land-mean insolation than in KS. Similar to the slope angle, KS covers SVF over a much wider range, < 0.9-1, than KM, 0.96-1 (Fig. 5g). Thus, compared to KS, KM substantially underrepresents the SVF effect on insolation in small SVF ranges. The insolation decreases as SVF decreases in both KM and KS (Fig. 5h), but the insolation difference between the smallest and largest SVF categories in KS is over 40 W m -2 while that in KM is less than 10 Wm -2 . The smaller the SVF, the larger the terrain shading effects resulting in smaller insolation, especially in the early morning and late evening when the solar elevation is small (Olson and Rupper 2019). Because of the failure to account for the effect of small SVFs on insolation, KM overestimates the land-mean insolation and generates larger errors in the early morning and late evening hours (Fig. 4e).
The origins of the difference in the insolation-elevation relationship between KM and KS (Fig. 5b) are further explored using the insolation-slope (Fig. 5f) and insolation-SVF relationships (Fig. 5h). Figure 6a shows that both KM and KS show the category-mean slope angle increases with increasing elevation, but the slope angle as well as the rate of the slope angle increase with increasing altitudes are much smaller in KM than in KS. The slope angle difference between KM and KS increases with increasing altitudes (dashed line in Fig. 6a). Because the insolation tends to decrease with increasing slope angle (Fig. 5f), the altitude-dependence of the slope angle difference between KM and KS is consistent with the increase in the insolation difference with increasing heights (Fig. 5b). The mean SVF of the elevation category also decreases with increasing height. Similar to the slope angle, the decrease of SVF with increasing height is much smaller in KM than in KS (Fig. 6b). The SVF difference between KM and KS (dashed line in Fig. 6b) also increases with increasing heights, first rapidly from the lowest (E1) to the second lowest (E2) category, then more gradually from the second lowest (E2) to the highest (E6) category. This is consistent with the increase of the insolation difference between KM and KS with increasing altitude (Fig. 5) because the larger the SVF is, the smaller the insolation (Fig. 5h). In summary, the difference in the insolation-elevation relationship between KM and KS (Fig. 5b) results from the difference of the slope angle and SVF caused by different DEM resolutions.
The difference in representing the slope and SVF between KM and KS cannot explain the insolationazimuth relationship difference between KM and KS (Fig. 5d). The difference in the insolation-elevation relationship between KM and KS vary strongly according to the azimuth (Fig. 7). For the south-facing slope, KM and KS generate nearly identical insolation-elevation relationship (Fig. 7c) while KM yields a notably weaker insolation-elevation relationship than KS for the north-facing  (Fig. 7a). The variation of the insolation-elevation relationship difference between KM and KS following the azimuth (Fig. 7) coincides with the insolation-azimuth relationship difference between KM and KS (Fig. 5d).

Conclusion
NIMS/KMA has been providing real-time solar energy resource maps using KMAP-Solar in order to support the development and real-time management of the solar power in Korea. This study analyzes the sensitivity of the insolation calculated by KMAP-Solar to DEM scales using insolation calculated by KMAP-Solar based on two DEMs of different scales. The DEM scale in the control (KM) and sensitivity (KS) calculation is 1.5 km and 100 m, respectively, for the period from July 2016 to June 2020.
Averaged for the entire land grids of the KMAP-Solar domain, the fine-scale DEM (KS) yields smaller insolation than the coarse-scale DEM (KM) by 8.7 Wm -2 (3% of the KM insolation), as found in earlier studies (Olson and Rupper 2019;Hopkinson et al. 2010). Evaluation of the KMAP-Solar insolation against the observations at 42 KMA ASOS sites shows that the fine-scale DEM in KS reduces both the BIAS and RMSE of KM throughout a day for all seasons. For individual sites, the reduction in the BIAS (RMSE) due to the use of fine-scale DEM is as large as 30 Wm -2 (14 Wm -2 ); it increases with increasing SVF differences between KM and KS, primarily in highelevation mountainous areas.
The insolation difference between KS and KM, as well as the improvement of the insolation calculation by using the fine-scale DEM, are related to better representations of the topographic parameters that affect insolation. KM and KS yield the same relationship between the insolation and four topographic parameters (elevation, slope, azimuth, and SVF), but these relationships in KM are either much weaker or limited to narrower parameter ranges that those in KS. For example, both KM and KS generate negative (positive) insolation-elevation (insolation-SVF) relationship, but the difference between the maximum and minimum insolation range in KM (15 Wm -2 for both elevation and azimuth) is much smaller than that in KS (40 Wm -2 for both elevation and azimuth). The coarse-scale DEM in KM produces only the four smallest slope categories (up to 20 o ) and two largest SVF categories (0.96 − 1.0) whereas the fine-scale DEM in KS generates slopes and SVFs for a much larger range, up to > 30 o for the slope and from 0.9 to 1.0 for the SVF. Because of the absence of large slopes and small SVFs due to the coarse-scale DEM, KM overestimates the insolation than KS, especially over complex terrains where most of the large slope and small SVF occur. The insolation-elevation and insolation-azimuth relationship show that the lack of large slope angles and small SVFs in KM is most serious in high-elevation regions and the north-facing slopes.
The results of this study show that the use of fine-scale DEMs in KMAP-Solar can result in meaningful improvements in the accuracy of local insolation, especially in mountainous regions. Operational solar energy maps based on the KMAP-Solar system are useful for supporting the development of solar power plant sites, real-time management, and prediction of solar power (Voyant et al. 2012), as well as for various research related to solar power (e.g., McArthur 2005). Further improvements in the accuracy of KMA solar energy maps using KMAP-Solar will be possible with the progress in KMA LDAPS, the operational numerical weather prediction system that provides the input insolation to KMAP-Solar.