Global Geopotential Model Evaluations and Local Geoid in Indonesia: A Review

Geoid model was chosen as a vertical reference in Indonesia based on the Head of the Geospatial Information Agency Regulation (Perka BIG) No. 15 of 2013 concerning the Indonesian Geospatial Reference System (SRGI2013). Therefore, the development of local geoid models continues to be carried out to obtain good accuracy. The geoid is formed through three main components: long wave, short wave, and medium wave. One of the longwave components is the global geopotential model obtained from topographic, terrestrial, altimetry, and gravity satellite data. Along with the development of technology and gravity observation methods, the global model has many variations, so it is necessary to determine the global model that is most suitable for the geographical conditions in Indonesia. EGM2008 is often used in local geoid modeling in Indonesia based on research that compares several global models. Still, it does not rule out the possibility of a new global model that is more suitable for Indonesia.

Geoid Modelling of Kalimantan Island using Airborne Gravity Data and Global Geoid Model (EGM2008)

The availability of geoids, especially in survey and mapping activities, is useful for transforming the geometric heights obtained from observations of the Global Navigation Satellite System (GNSS) into orthometric heights that have real physical meanings such as those obtained from waterpass measurements. If a geoid is available, the orthometric heights of points on earth can be determined using the GNSS heighting method. The use of modern survey and mapping instruments based on satellite observations such as GNSS is more efficient in terms of time, effort, and cost compared to the accurate waterpass method. According to the Indonesian Geospatial Information Agency (BIG) it is stated that the application of geoid as a national Vertical Geospatial Reference System has an adequate and ideal category if the accuracy is higher than 15 cm. Recent studies have shown that it is possible to generate local geoid models with centimetre accuracy by utilizing airborne gravity data. We calculate free-air gravity anomaly data is calculated by processing airborne gravity and GNSS data using the Stokes Integral method on AGR software. Next a geoid model is created by calculating the contribution of three components, namely the long wave component represented by the EGM2008 global geoid data model, the shortwave component represented by the Shuttle Radar Topography Mission (SRTM) data and the medium wave component represented by the free-air gravity anomaly data. The geoid model validation was carried out using the geoid fitting method for geoid accuracy by calculating the difference between the gravimetric geoid and the geometric geoid and comparing it with the global geoid model EGM2008 degrees 2190. As a result, the total geoid model accuracy value was determined to be 49.4 cm on gravimetric geoid undulations with a standard deviation of 7.1 cm. Meanwhile, the results of the EGM2008 geoid undulation accuracy test at 2190 degrees resulted in an accuracy of 51.9 cm with a standard deviation of 9.9 cm. These results indicate that the local geoid model from airborne gravity measurement data produces a geoid model with a higher accuracy than the global geoid model EGM2008 degrees 2190. However, the accuracy of the resulting data is still below the BIG standard of 15 cm, so further research is needed to produce a geoid model which conforms to the standard.

On the determination of a locally optimized Ellipsoidal model of the Geoid surface in sea areas

Deriving a local geoid model has drawn much research interest in the last decade, in an endeavour to minimize the errors in orthometric heights calculations, inherited by the use of global geoid reference models. In most parts of the earth, the local geoid surface may be tens of meters away from the Global Reference biaxial Ellipsoid (WGS84), which create numerus problems in topographic, environmental and navigational applications. Several methods have been developed for optimizing the precision of the calculation of the geoid heights undulations and the accuracy of the corresponding orthometric heights calculations. The optimization refers either to the method used for data acquisition, or to the geometrical method used for the determination of the best fit local geoid model. In the present work, we focus on the reference ellipsoid used for the geometric and geoid heights determination and develop a method to provide the one that fits best to the local geoid surface. Moreover, we consider relatively small sea regions and near to coast areas, where the usual methods for data acquisition fail more or less, and we pay attention in two directions: To obtain accurate measured data and to have the best possible reference ellipsoid for the area at hand. In this due, we use the “GNSS-on-boat” methodology to obtain direct sea level data, which we induce in a Moore Penrose pseudoinverse procedure to calculate the best fit triaxial ellipsoid. This locally optimized reference ellipsoid minimizes the geometric heights in the region at hand. The method is applied in two closed sea areas in Greece, namely Corinthian and Patra’s gulf and also in four regions in the Ionian Sea, which exhibit significant geoid alterations. Taking into account all factors of uncertainty, the precision of the mean sea level surface, produced by the “GNSS on boat” methodology, had been estimated at 5.43 cm for the gulf of Patras, at 3.76 cm for the Corinthian gulf and at 3.31 for the Ionian and Adriatic Sea areas. The average difference of this surface and the local triaxial reference ellipsoid, calculated in this work, is found to be less than 15 cm, whereas the corresponding difference with respect to WGS84 is of the order of 30m.

Analyzing Precision and Efficiency of Global Navigation Satellite System-Derived Height Determination for Coastal and Island Areas

The global navigation satellite system (GNSS)-derived height determination technique is applied in the field of surveying owing to the broad use of GNSS and the development of precise local geoid models. In Korea, this technique was officially adopted in 2020 for public surveying, such as urban facility mapping; it is also treated as an efficient way to unify the vertical datum of the inland and island areas of Korea. Here, GNSS surveying was conducted on 19 stations located in Korea’s coastal regions and islands, and GNSS-derived elevations were determined. When each GNSS-derived elevation was compared with elevations from spirit leveling, all stations showed differences of less than 3 cm when GNSS surveying was conducted for 4 h/day over two days; they were smaller than 5 cm with 2 h of surveying. These differences meet the standards of GNSS-derived elevations in Korea. In addition, GNSS-derived elevations were compared with those obtained via sea-crossing leveling in two regions, showing differences smaller than 1 cm. Sea-crossing leveling takes longer than GNSS-derived height determination, and its accuracy can be significantly affected by various environments, such as sea fog. Thus, GNSS-derived height determination represents a practical and useful technique.

On Downward Continuing Airborne Gravity Data for Local Geoid Modeling

<p>The theories of downward continuation (DC) have been extensively studied for many decades, during which many different approaches were developed. In real applications, however, researchers often just use one method, probably due to resource limitations or to finish their work, without a rigorous head-to-head comparison with other alternatives. Considering that different methods perform quite differently under various conditions, comparing results from different methods can help a lot for identifying potential problems when dramatic differences occur, and for confirming the correctness of the solutions when results converge together, which is extremely important for real applications such as building official national vertical datums. This paper gives exactly such a case study by recording the collective wisdom recently developed within  the IAG’s study group SC2.4.1. A total of six normally used DC methods, which are SHA (NGS), LSC (DTU Space), Poisson and ADC (NRCan), RBF (DU Delft), and RLSC (TUM), are applied to both simulated data (in the combination of two sampling strategies with three noise levels) and real data in a Colorado-area test bed. The data are downward continued to both surface points and to the reference ellipsoid surface. The surface points are directly evaluated with the observed gravity data on the topography. The ellipsoid points are then transformed into geoid heights according to NRCan’s Stokes-Helmert’s scheme and eventually evaluated at the GNSS/Leveling benchmarks. In this presentation, we will summarize the work done and results obtained by the aforementioned workgroup.</p>

Optimum Combinations of GGM and GDEM Models for Precise National Geoid Modelling

This study aims to develop a Local Geoid Model (LGM) for Egypt to determine the optimal combinations of global models with Global Navigation Satellite Systems (GNSS/Levelling) data. A precise national geodetic dataset, four Global Geopotential Models (GGMs), and three global Digital Elevation Models (DEMs) have been utilized. Hence, twelve gravimetric LGMs have been developed using the Least-Square Collocation (LSC) method fitted to GNSS/Levelling data and judged over 100 checkpoints. Results revealed that improvements in local geoid accuracy are attributed mainly to GGMs models representing the long wavelength of the Earth's gravitational field. Regarding DEMs, the accuracy of LGMs does not significantly depend on the utilized DEM. Based on the available data, the attained optimum geoid of Egypt has been developed with a standard deviation, equals 0.129 m.