Review the status of Korean geoid model development since 2000s and future improvement plan

Korean geoid models have been continuously developed for more than 20 years. However, the precision of previous models was approximately 8–15 cm according to evaluations based on newly obtained Global Navigation Satellite System (GNSS)/Leveling data because of irregular distribution and low precision of the gravity and GNSS/Leveling data. Therefore, in 2008, NGII began to obtain new terrestrial gravity and GNSS/Leveling data and collected more than 12,000 points of gravity data and 4492 points of GNSS/Leveling data by the end of 2017. As a result, the newest model, Korean National Geoid 2018 (KNGeoid18), achieved a degree of fit (DOF) of 2.3 cm. The precision was significantly improved compared to previous models including KNGeoid14, but precision in the mountainous areas remained still lower than that of the plain areas. Also, inconsistent differences between the GNSS/Leveling data and KNGeoid18 remained as a problem that should be solved. Through KNGeoid project, the NGII observed a positive effect of supplementing fundamental data, so NGII is obtaining new terrestrial gravity data. Regarding GNSS/Leveling data, the installation of 3D control points was completed in 2019 and the adjustment of GNSS and leveling data is ongoing to allow for the application of verified and adjusted GNSS/Leveling data in the future. Therefore, a new geoid model will be developed until the end of 2023 by applying new terrestrial gravity and GNSS/Leveling data. Overall, it is expected that the precision will be improved to approximately 1–1.5 cm, except in the mountainous areas, owing to new data gathering efforts and the maintenance of the fundamental data.


Introduction
As a reference surface of the vertical position, a geoid is essential for establishing a local geodetic reference frame. A geoid represents the gravity field, making it necessary in both scientific and engineering applications, such as exploring underground resources, mean sea-level monitoring, and orbital determination of missiles or satellites. Recently, geoids have been the subject of attention to realize a world height system as well as determining (orthometric) heights based on Global Navigation Satellite System (GNSS) surveying. Thus, several countries are working to obtain fundamental data such as gravity and GNSS/Leveling data and to construct a precise local geoid model. Similar to the GEOID18 of the USA, Australia Geoid 2020 (AUSGEOID2020) of Australia, Geospatial Information Authority of Japan Geoid 2011 (GSIGEO2011) of Japan which have 1.27 cm, 3.8 cm, and 1.8 cm of precision, respectively (Ahlgren et al. 2020;Brown et al. 2018;Miyahara et al. 2014), a recent local geoid model is being developed with a few centimeters of precision. Currently, advanced countries have plans to improve the precision of the geoid to the sub-centimeter level of precision.
In Korea, various geoid models have been constructed by several universities and government organizations over the past 20 years. However, the precision of previous models developed until the middle of the 2000s remained

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Terrestrial, Atmospheric and Oceanic Sciences at approximately 15 cm because of the irregular distribution and low quality of their gravity and GNSS/Leveling data. Therefore, to overcome this problem, new gravity and GNSS/Leveling data are being collected since the late 2000s. Especially, airborne gravity data covering the entire Korean peninsula was collected in order to ensure the precision of the geoid model. As a result, the precision of geoid models developed after 2010 has been continuously updated. Currently, as new terrestrial gravity data are being obtained in mountainous areas and the local adjustment of GNSS/Leveling data is planning to be performed to improve its reliability, it is expected that the precision of the geoid model will improve to a few centimeter levels.
In this study, the data, modeling result, precision as well as limits of various studies and government projects aiming to develop a Korean geoid model were analyzed. In addition, the latest developed geoid model, Korean National Geoid 2018 (KNGeoid18), was introduced with a future plan to improve the precision of the current model.

Development of previous geoid models
Gravity surveying for geophysical or geoscientific exploration in Korea began in the 1960s for the analysis of underground resources or structures. Despite their relatively high density, the data were distributed only in the target area, making it somewhat inappropriate for geoid modeling. Therefore, in the late 1990s, several studies practically began to focus on geoid modeling. According to Lee et al. (2005), NORI05 was developed based on the Earth Gravitational Model 1996 (EGM96) by combining 13,493 points of terrestrial gravity data (Fig. 1a), approximately 1,720,000 points of shipborne gravity data obtained by NORI and KMS02 altimeter data developed by the National Survey and Cadastre-Denmark (KMS). For North Korea, gravity data was generated and included by digitizing the Bouguer anomaly map. Among the terrestrial gravity data, approximately 49,000 points were collected before introducing the GNSS in Korea so that the reliability of the dataset was quite low and exhibited an irregular distribution. The official precision evaluated by comparing the 182 points of GNSS/Leveling data was approximately 13.24 cm. For reference, 182 points of GNSS/Leveling data were applied to evaluate the precision of the geoid model. It means that the NORI05 is a gravimetric geoid, therefore, NORI05 showed a large difference in the inland and mountainous areas, as compared with the 1091 points of GNSS/Leveling data that were newly obtained by the NGII (Fig. 2a), and the standard deviation of the geoidal height difference was found to be 25 cm (Kwon et al. 2011). Another main reason for this large difference is presumed to be the result of the low distribution and reliability of the fundamental dataset.

Geoid modeling from 2001 to 2010
GMK09 was modeled by fitting a gravimetric geoid, which was developed by combining 1817 points of new terrestrial gravity data with the EGM2008 and 17,814 points of GNSS/Leveling data (Heo et al. 2009). Figures 1b and c show the distribution of terrestrial gravity and GNSS/Leveling data for the GMK09 modeling. For reference, among 17,814 points of GNSS/Leveling data, 16,409 points plotted with red dots are not used more due to low reliability. Other blue dots mean the newly obtained data since 2008. As only a portion of the terrestrial data obtained at the beginning of the gravity survey project from 2008 to 2009 were included, the GMK09 would be viewed as a model developed by fitting EGM08 to the local GNSS/Leveling data. According to Heo et al. (2009), the precision of GMK09 was found to be approximately 6 cm by comparing it to 44 points of GNSS/Leveling data obtained at the Continuous Operating Reference Station (CORS). However, it seems that the GNSS/Leveling data used to adjust the geopotential model caused local bias or distortion as some of the data obtained at triangulation points (TPs) or benchmarks (BMs) had reliability problem (i.e., BM 10-04-00-00 had a 92.9 cm difference compared with GMK09). Therefore, GMK09 was also compared with newly obtained GNSS/ Leveling data, and the standard deviation of the geoidal height difference was calculated to be approximately 14 cm (Kwon et al. 2011). As shown in Fig. 2b, GMK09 exhibited a large difference in the mountainous areas, and some points showed inconsistent differences to nearby located points.
The main factor degrading the precision of these geoid models is the irregular and low distribution of fundamental data. In particular, the use of inconsistent processing models for terrestrial gravity data and the possibility of bias existing on the fixed absolute gravity value cannot be ruled out. Therefore, the KLSP collected and re-processed terrestrial gravity data obtained in the Page 3 of 16 Lee and Kwon Terrestrial, Atmospheric and Oceanic Sciences (2022) 33:12 Fig. 1 a Terrestrial gravity data for NORI05 (Lee et al. 2005). b Terrestrial gravity data and c GNSS/Leveling data for GMK09 (Heo et al. 2009) Page 4 of 16 Lee and Kwon Terrestrial, Atmospheric and Oceanic Sciences (2022)  Page 5 of 16 Lee and Kwon Terrestrial, Atmospheric and Oceanic Sciences (2022) 33:12 2000s in cooperation with the help of the Korea Institute of Geoscience and Mineral Resources (KIGAM) and Pusan National University (PNU). As a result, a total of 10,862 points of terrestrial data were generated. However, these data still exhibited an irregular and regionally biased distribution because most data were obtained for geophysical or geoscientific purposes, as shown in Fig. 3a. Furthermore, the post-processing precision of the data remained to be 0.4 mGal because of the low-precise gravimeter used. Therefore, to compensate for the weak terrestrial gravity data, airborne gravity surveying was performed for the first time in Korea from December 2009 to January 2010 in cooperation with the Danish National Space Center (DNSC). This survey covered the entire Korean peninsula, including offshore regions, and the precision of data was estimated to be 1.5 mGal.
In addition, some new terrestrial data were obtained to complement the gravity signal in the mountainous areas, but the number of points was limited to 500 because of time and cost restraints. As shown in Fig. 3a, gray dots show the distribution of the KIGAM and PNU data, and blue dots represent the newly obtained data by KLSP. The distribution of airborne gravity data was plotted in Fig. 5a because it was also applied for the newest version of geoid modeling in Korea. The KLSP 2010 geoid was developed by combining the terrestrial and airborne gravity data with the shipborne gravity data obtained by Korea Hydrographic and Oceanographic Agency (KHOA) in the 1990s and early 2000s as well as the altimeter data, Danish National Space Center 2008 (DNSC08  Kwon et al. (2010).
In the same manner as NORI05 and GMK09, the precision of KLSP 2010 was re-evaluated based on 1091 points and the standard deviation of the geoidal height difference was calculated to be approximately 8 cm. As shown in Fig. 3c, the KLSP 2010 shows a relatively consistent variation because of the inclusion of re-processed terrestrial gravity data and airborne gravity data However, there exists a bias in the southwest region. According to NGII (2010a) and NGII (2010b) , the heights of the BMs and UCPs located in this bias region were corrected after development of KLSP 2010. Therefore, the local difference between the KLSP 2010 and GNSS/Leveling data occurred because the KLSP 2010 was caused by adjusting the gravimetric geoid to the previous heights. For reference, strictly speaking, Korean vertical datum is the normal-orthometric height system because heights of the BMs and UCPs were determined based on the spirit leveling without gravity surveying.

Geoid modeling since 2010 (KNGeoid development project and KNGeoid14)
Despite significant efforts in the 2000s, the irregular distribution and low quality of the fundamental data continued to be an issue. In addition, collected fundamental data such as terrestrial and GNSS/Leveling data were not broadly applied in the research because a cooperation system among the government, research projects, and universities had not been established. Thus, the NGII set a plan to combine various gravity data that were obtained and managed by different organizations in order to develop a geoid that covers the inland and ocean of Korea. According to Kwon et al. (2011), the key to this plan was to replace the existing terrestrial gravity data, which showed an irregular, biased distribution, and had low precision, with the new gravity data obtained at various control points (i.e., UCP, BM, and TP) by the gravity surveying project of NGII beginning in 2008; then, combine new terrestrial data with airborne, shipborne, and altimeter data. The distribution of the new terrestrial data is shown in Fig. 4a. Regarding shipborne gravity data, the KHOA had an independent re-processing plan to improve the reliability of the data, allowing shipborne data to be finally included in 2014. In a previous study, the SRTM was applied to calculate the terrain effect. However, the region of Korea was replaced by the NGII DEM because of the development of highresolution DEM, and the SRTM was only applied to North Korea and Japan. Finally, the GNSS/Leveling data were also replaced with the newly obtained data at the UCPs (Fig. 4b).
As a product of the research project from 2011 to 2014, the KNGeoid14 was developed in 2014 as below (Kwon et al. 2014). This model refers to the EGM2008 for its reference gravity field and combines 9455 points of terrestrial gravity data with 27,343 points of airborne data. Regarding the ocean, shipborne and Danish Technical University 2010 (DTU10) data were combined and resampled to 1 arcmin. When compared with the 1034 points of the GNSS/Leveling data, the precision of KNGeoid14 was found to be approximately 3.3 cm. By only counting the number of terrestrial gravity data, fewer data were applied for the KNGeoid14 modeling than that used for the NORI05 or KLSP2010. However, as shown in Fig. 4a, the new dataset had a homogeneous distribution, and the precision of the data was 0.05 mGal, which is more reliable. In addition, the GNSS/Leveling data showed Page 6 of 16 Lee and Kwon Terrestrial, Atmospheric and Oceanic Sciences (2022)  Page 9 of 16 Lee and Kwon Terrestrial, Atmospheric and Oceanic Sciences (2022) 33:12 a regular distribution, as compared with that of the KLSP2010. Figure 4c shows the difference between the KNGeoid14 and GNSS/Leveling data, which was applied as the fitting point for KNGeoid14 modeling. The results show a relatively homogenous trend over Korea. However, the mountainous region along the border to North Korea marked with red circles revealed a relatively large difference. Thus, according to the final report of KNGeoid14 development, both gravity and GNSS/Leveling data are necessary to improve the precision of the KNGeoid14. Note that the legend in Fig. 4c was adjusted compared with the previous models, as the precision was improved.

Fundamental data
The newest Korean geoid model, KNGeoid18, is the updated version of KNGeoid14. Since 2014, three big changes in terms of the fundamental data for geoid modeling in Korea occurred. First, various global geopotential models based on the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) satellite observations were newly developed (ICGEM 2021), making it possible to select a more precise model than EGM2008 for the target area. Second, the NGII obtained more than 3000 points of GNSS/Leveling data by establishing new control points called 2nd UCPs. With this development, the spatial resolution of the GNSS/Leveling data improved from approximately 10 km to 3-5 km. Finally, more than 2500 points of terrestrial gravity data were collected in the mountainous areas of Korea and at the 2nd UCPs. The fundamental data for the KNGeoid18 modeling reflecting these changes are as follows.
Before 2014, the EGM2008 was broadly applied as a reference gravity field, however various geopotential models, including the European Improved Gravity Field of the Earth by New techniques-6C4 (EIGEN-6C4), GOCE and EGM2008 Combined model (GECO), Experimental Gravity Field Model 2016 (XGM2016), and SGG-UGM-1, developed including GOCE satellite observations were newly developed and announced. By comparing these models and the EGM2008 to approximately 4600 points of Korean GNSS/Leveling data, the XGM2016 achieved the minimum difference, and thus replaced the EGM2008 for the KNGeoid18 modeling. Regarding the DEM, a version constructed by combining the NGII DEM in Korea and the SRTM for North Korea and Japan was used, which is the same as that used in KNGeoid14.
Regarding gravity data, airborne and ocean (shipborne + DTU10) data were applied in the same manner as KNGeoid14 (Fig. 5a). However, the terrestrial gravity data exhibited differences in terms of resolution and precision. As shown in Fig. 5b, more than 2500 points of new gravity data were included. The gray dots show the distribution of the terrestrial gravity data and the new gravity data (blue dots) reveal the supplemental information in the mountainous areas as well as middle of Korea where the 2nd UCPs are located. Free-air anomalies submitted as surveying products were applied in the KNGeoid14 modeling, but biases were found in the dataset because of inconsistencies on the fixed absolute station and processing models. Therefore, gravity data obtained between 2008 and 2017 were re-calculated by processing with the same model and absolute stations to minimize the processing error. As a result, free-air anomalies at a total of 12,117 points of terrestrial gravity data were generated, and the estimated error of post-processing was calculated to be 0.015 mGal. For North Korea (up to latitude 39°), the gravity data were supplemented based on the EGM2008 with the maximum degree and order in order to minimize modeling error at the border.
Moreover, the GNSS/Leveling data showed a large difference in the resolution, as compared with the previous data. Thus, the installation of 2nd UCPs began in 2011 to support public and cadastre surveys, but they only covered the middle of Korea in 2014. Thus, only 1st UCPs were applied for KNGeoid14 modeling. Since then, more than 3000 points of GNSS/Leveling data were newly established, allowing 4492 points (after removing outliers and points located in islands) to be applied for KNGeoid18 modeling. The gray and blue dots indicate the 1st UCPs and 2nd UCPs in Fig. 5c. For reference, the Korean peninsula has moved to the east, ranging from 1.2 to 5.6 cm due to the 2011 Tohoku earthquake (Kim and Bae 2012). Therefore, positions of 1st UCPs installed before 2011 were re-calculated and published in 2014. The vertical datum in Korea has been separated into inland and islands. The vertical origin of Korea located in the Inha Technical College was determined by leveling surveying from a tide gauge at Incheon Bay, and benchmarks and UCPs located inland were calculated by fixing the origin. On the other hand, control points located on Jeju island refer local mean sea level. In addition, heights of control points were determined based on the spirit leveling, and normal-orthometric corrections were applied. Because it was found that the vertical variation due to the 2011 Tohoku earthquake was smaller than 5 mm (Kim and Bae 2012), the heights of benchmarks and UCPs were not updated, unlike GNSS data.
Since the installation project was finished in 2019, the GNSS/Leveling data do not have a completely homogeneous distribution. Thus, only part of the GNSS/Leveling data were applied to develop the hybrid geoid, and the rest were used for evaluation. Because the GNSS/ Leveling data adjustment has not been performed, the precision of GNSS/Leveling data could not be affirmed.
Page 10 of 16 Lee and Kwon Terrestrial, Atmospheric and Oceanic Sciences (2022) 33:12 However, GNSS and levelling surveying were performed to meet 5 mm + 1.0 ppm ∑D (where D is a sum of baselines) and 2.5 mm √S (where S is the distance between two points), respectively. In addition, the horizontal precision of GNSS data is known to be ± 3 cm (NGII 2010b) and the vertical precision of the normal-orthometric height was estimated to be ± 2-3 cm in the local network adjustment . Thus, it is expected that the precision of GNSS/Leveling data would be approximately ± 5 cm.

Geoid modeling
Reflecting the fundamental data updates, KNGeoid18 was developed using a "remove and restore" technique. Theoretically, gravity data located over the world is necessary for geoid modeling, but it is not practical. Thus, an optimal Stokes' radius and Wong-Gore kernel should be determined for local geoid modeling. In this study, various combinations were tested by setting the maximum degree and order of the geopotential model to 360 and 720, setting the Stokes' integral radius to 0.3°, 0.5°, and 1°, and setting the Wong-Gore kernel degree to 110-120 and 170-180, respectively. The optimal values were selected when the gravimetric geoid reached a minimum difference compared with the GNSS/Leveling data. As a result of the tests, the maximum degree of the XGM2016, Stokes' radius, and Wong-Gore kernel degree were set to 360, 0.5°, and 110-120. Other modeling parameters, such as the maximum radius for the terrain effect calculation, Bejerhammar sphere depth, and attenuation factor for the downward continuation of airborne gravity, remained the same as those used in KNGeoid14 because they were already optimized (Lee and Kwon 2009;Kwon et al. 2014).
For the practical use of geoids in the surveying field, a gravimetric geoid was fitted to the local GNSS/Leveling data. As previously mentioned, even though the amount of GNSS/Leveling data increased, the distribution varied depending on the region. Thus, 2791 points located near the center of the 5 km grid were applied as fitting points, and 1071 points were used for a geoid precision evaluation. The precision of the GNSS/Leveling data was assumed to be 5 cm in adjusting gravimetric geoid. Figure 6 illustrates the steps of geoid modeling and the applied parameters, and KNGeoid18 is shown in Fig. 7. As listed in Table 1, the Korean geoidal height has a range of 15.05-33.61 m, with an average of approximately 25 m. For more details of the fundamental data and modeling, please see Kwon et al. (2018).

Precision evaluation
The precision of KNGeoid18 was evaluated in terms of degree of fit (DOF) and precision. DOF refers to the standard deviation between the KNGeoid18 and GNSS/ Leveling data, which were applied to adjust the gravimetric geoid, whereas precision indicates the standard deviation between KNGeoid18 and the remaining GNSS/ Leveling data. As a result, the DOF based on 2791 points was calculated to be 2.3 cm (Fig. 8a), and the precision of the remaining 1701 points was 2.5 cm. When comparing the 4492 points, which include the fitting and verification points, the standard deviation of the geoidal height was 2.4 cm ( Fig. 8b; Kwon et al. 2018).
To determine the regional precision, mountainous and plain areas were extracted considering the heights of the UCPs. As shown in Fig. 8b, the mountainous and plain areas are marked with red and blue boxes, respectively. For the standard for selecting mountainous and plain regions, larger than 400 m and 100-400 m of the Fig. 6 Procedures for KNGeoid18 modeling and determined parameters Page 11 of 16 Lee and Kwon Terrestrial, Atmospheric and Oceanic Sciences (2022) 33:12 average of height were applied, respectively. Among the 4492 points, 553 points located in the mountainous areas had a precision of approximately 2.6 cm. Meanwhile, 550 points located in the plain areas showed a precision of approximately 2.1 cm. Thus, the precision in the mountainous areas is lower than that of the plain areas, but both remain acceptable as the magnitudes of standard deviation did not exceed 3 cm. As mentioned, the establishment of 2nd UCPs were finished in 2019. When applying all the available GNSS/ Leveling data, which includes 5591 points installed until the end of 2019, the precision was calculated to be 2.6 cm. This is not a large difference from the DOF of KNGeoid18 considering a large portion of the new GNSS/Leveling data was added in the mountainous areas, thus, it would be said that KNGeoid18 is quite reliable. Nevertheless, a problem is that the differences between GNSS/Leveling data and KNGeoid18 are not completely homogeneous. As shown in Fig. 8b, some points have inconsistent differences, except for those in the plain areas. These inconsistencies could be caused by bias or errors in the GNSS/Leveling data when fixing the existing UCPs during the regional adjustment. Therefore, a way to improve the precision must be developed in the future. Note that the precision evaluated considering the GNSS/Leveling data group and region are summarized in Table 2.
To identify improvements from KNGeoid14, two comparisons were conducted. First, KNGeoid18 was compared with 1034 GNSS/Leveling data used for KNGeoid14 modeling. As a result of the comparison, the standard deviation of the difference was calculated to be 2.65 cm (Fig. 9a). This is an approximately 20% improvement in precision, as compared with the KNGeoid14 precision of 3.3 cm. For reference, regarding KNGeoid14, 1034 points of all available GNSS/Leveling data were applied for hybrid geoid modeling and evaluation of its precision so that only DOF was available. Second, 4489 points of GNSS/Leveling data used to evaluate the KNGeoid18 precision were compared with the KNGeoid14 (Fig. 9b). Among 4,492 points, 3 points were removed because KNGeoid14 covers up to 131° of longitude. It was found that the standard deviation was 5.4 cm, which is more than two times larger than that of the KNGeoid18. As shown in Fig. 9b, the KNGeoid14 shows a large difference in the mountainous areas and border of North Korea. Thus, it is believed that the new data helped improve the precision.   Lee and Kwon Terrestrial, Atmospheric and Oceanic Sciences (2022)  Page 13 of 16 Lee and Kwon Terrestrial, Atmospheric and Oceanic Sciences (2022) 33:12 In addition, a positive effect was found based on 16 points located in the mountainous areas, marked with black circles in Fig. 9b. As summarized in Table 3, the differences between the GNSS/Leveling data and geoid models (KNGeoid14 and KNGeoid18) show that most points had better precision in KNGeoid18. In particular, A2, a point located at the top of the mountain, with a height of 1091 m, was significantly improved from a 14.3 cm difference in KNGeoid14 to 1.5 cm in KNGeoid18, confirming the positive effect in the mountainous areas (Kwon et al. 2018).

Geoid model improvement plan
The newest Korean geoid model, KNGeoid18, achieved better precision than previous models, including KLSP2010 and KNGeoid14, because of changes in the geopotential model as well as new terrestrial and GNSS/ Leveling data. However, both the lower precision in a mountainous areas and inconsistent differences in the plain areas are still problems. To solve these problems, the NGII proposed an annual plan as follows (NGII 2021).
To improve the precision of the geoid, the NGII will continue to perform terrestrial gravity surveying, especially in the mountainous areas. According to Jekeli et al. (2009), gravity data with a 2 arcmin resolution are required to develop a geoid model that is more precise than 2 cm when the precision of gravity data is assumed to be 1 mGal. The precision of the current gravity data in Korea was already sufficient thus the NGII plan was derived focusing on improving the gravity data resolution. The planned average resolution considering the target precision of the new geoid model was 3 km. When dividing Korea into 3 km interval grids, the gravity data used in the development of KNGeoid18 comprised approximately 70%. Therefore, additional gravity surveying was performed at the national control points where gravity information did not exist. More than 2800 points of gravity data were obtained by the end of 2019, and additional surveying will be done by the end of 2022. When comparing the adjusted terrestrial gravity data used in KNGeoid18 modeling with the newly obtained data from 2018 to 2019, the differences at the same control points do not exceed 0.05 mGal (Choi et al. 2020), indicating that gravity surveying in Korea has stabilized, allowing the new gravity obtained with high resolution and quality to contribute to the improvement of the geoid. In addition, the KIGAM and KHOA have been obtaining new terrestrial and shipborne gravity data since late 2010, and their data will be shared in cooperation with the NGII for updating geoid. Thus, it is expected that 30% of blank areas would be filled.
Meanwhile, the inconsistency problem must be solved in a different manner because it is an intrinsic problem of the GNSS/Leveling data. When constructing KNGeoid18, the GNSS/Leveling data were under installation, meaning their latitudes, longitudes, ellipsoidal heights were computed by fixing existing local control points. In this scenario, local bias or error on the fixing point affects the horizontal and vertical solutions of the new point. Especially, among the GNSS/Leveling data, some points were identified as outliers and removed, meaning that existing bias or error in the GNSS/Leveling data could not be ruled out. Thus, similar to the gravity data, the NGII has a plan to maintain GNSS/ Leveling data. First, leveling surveying will be performed for 2-3 years in regions where the height shows a large difference when comparing with the results of leveling network adjustments of 2020. Second, the GNSS data obtained since 2008 will be combined and re-processed by fixing the CORS in Korea, and a new survey will be done for 2 years to improve the reliability. Finally, the verified GNSS/Leveling data will be applied for hybrid geoid modeling and validating the precision. In addition, the update of local DEM is undergoing, aiming 1 m resolution.
These plans will be finished at the end of 2022, meaning the new hybrid geoid is expected to be developed in 2023. The target precision of this new geoid model is 1-1.5 cm in the plain areas and approximately 2 cm in the mountainous areas.

Conclusions
In this study, the status of geoid model development in Korea since the 2000s, and the merits and limitations of each developed model were summarized, and a future plan for updating geoid modeling was discussed.
NORI05, GMK09, and KLSP 2010 are representative geoid models developed in the 2000s by the NORI, KHOA, and KLSP, respectively. However, the precision of NORI05 and GMK09, based on approximately 1090 points of GNSS/Leveling data obtained since 2008, were found to be 24 cm and 15 cm, respectively, as a result of irregular and low-quality terrestrial and GNSS/Leveling data. Conversely, KLSP 2010 showed better precision Page 15 of 16 Lee and Kwon Terrestrial, Atmospheric and Oceanic Sciences (2022) 33:12 than NORI05 and GMK09 because of the inclusion of airborne gravity data covering the entire Korean peninsula. However, the irregular distribution and low quality of the fundamental data still degraded the precision.
To solve the lack of fundamental data, the NGII began to obtain new terrestrial gravity and GNSS/Leveling data in 2008 and collected additional gravity data in cooperation with agencies in Korea. As a result, terrestrial gravity and GNSS/Leveling data with homogeneous distribution and high-quality were obtained and a new geoid model, KNGeoid14, with a DOF of 3.3 cm was developed. Since then, the NGII continued to collect new fundamental data and new geopotential models were developed. Thus, the latest Korean gravimetric geoid model, KNGeoid18, was developed based on XGM2016 and includes more than 12,000 points of terrestrial, airborne, and ocean gravity data. This hybrid geoid model was fitted to 2791 points of GNSS/Leveling data, and its DOF was improved to approximately 2.3 cm, verifying the positive effect of the improved fundamental data on the precision of the geoid model.
Nevertheless, the precision in the mountainous areas is still lower than that of the plain areas, and inconsistent differences remain in some areas. A lack of gravity data in the mountainous areas and the possibility of bias or error in the GNSS/Leveling data and their irregular distribution may be the reason for the precision degradation of the geoid model. Therefore, the NGII has a plan to obtain new terrestrial gravity data in the mountainous areas and collect gravity data in cooperation with other agencies. In addition, GNSS/Leveling data will be re-calculated including the re-surveying to improve the reliability, and DEM is being updated. The efforts of NGII improving the fundamental data will continue until the end of 2022, thus, it is expected that the precision will be improved to 1-1.5 cm and 2 cm in the plain and mountainous areas in geoid models developed in 2023.