Introduction to the special issue on gravity and geoid in the Asia Pacific

This special issue (SI) includes papers related to some recent efforts on geoid modeling in the Asia-Pacific region. In total, twelve papers were submitted to this SI, covering geoid models in Australia, mainland China, India, Indonesia, South Korea, Malaysia, Nepal, the Philippines, Taiwan and Thailand. The methods for geoid modeling are rather diversified, with different considerations in gravity data processing and terrain effects. It is suggested that a mechanism for gravity data sharing should be developed and software packages can be freely distributed to geoid modelers. Observed GNSS/leveling along a route over varying terrains across Taiwan are released for testing geoid modeling methods and for accuracy assessments.

Specifically, this SI accepts papers that show the latest geoid models in Australia (McCubbine et al., 2021), mainland China (Xie et al., 2021), India (Goyal et al., 2021), Indonesia (Bramanto et al., 2021), South Korea (Lee et al., 2021), Malaysia (Tugi et al., 2021), Nepal (Timilsina et al., 2021), the Philippines (Gatchalian et al., 2021), Taiwan (Huang et al., 2021) and Thailand (Dumrongchai et al., 2021). Some of the papers are not directly involved with national geoid models. For example, Bramanto et al. (2021) show a software package that can efficiently process airborne gravity data in Java, Indonesia. Xue et al. (2021)  The cover image of this SI shows the free-air gravity anomalies and geoidal heights from the global gravitational model EGM 2008 (Pavlis et al., 2012), based on the geopotential coefficients in this model complete to harmonic degree 2160 with the incomplete higher coefficients beyond degree 2160. A geoid model from EGM2008 is most likely very useful for any given country,, but the model may lack high wavenumber geoidal components in mountainous areas.
To model a geoid in a given country, most likely trans-national gravity data around the country are needed. An important activity of IAG-SC2.4e is to encourage gravity data sharing between the members of this commission. A suggested method for sharing is that individual countries contribute gravity data to an IAG service such as the International Bureau of Gravity (BGI) and then retreat the needed transnational gravity measurements from this service. Fig. 1 shows the distribution of land gravity measurements from BGI in the Asia-Pacific region. Except Australia, New Zealand, South Korea and Japan, most countries are covered with sparse gravity data.
There are about 48 countries in the Asia-Pacific region. Many countries in the < A c c e p t e d M a n u s c r i p t > 5 region have invested considerable resources on improved geoid models. Recent progress in satellite altimetry greatly increases coastal marine gravity accuracy.
Satellite remote sensing data have been used to generate digital elevation models that are needed for geoid modeling. Many countries now also increase their GNSS/leveling observation campaigns to collect data to assess and to control the qualities of national geoid models. All such datasets may be used to improve the accuracies of geoid models in the Asia-Pacific region. Since the publication of the lecture notes "Geodetic Boundary Value Problems in View of the One Centimeter Geoid" (Sanso and Rummel, 1997), cm-level accuracy has been the ultimate goal pursued by geoid modelers around the world. As an example of promoting this cm geoid goal, the National Geodetic Survey of the USA released its gravity and elevation data in Colorado, where 14 international teams constructed their individual Colorado geoid models. According to Wang et al. (2021), the accuracy of the 14 Colorado geoid models may reach 2 cm, based on the assessments with the observed geoidal heights from GNSS/leveling along a profile (highway) in Colorado (GSVS17).
Following the Colorado experiment described by Wang et al. (2021), this SI announces that gravity data and elevation data for geoid modeling in Taiwan (Huang et

< A c c e p t e d M a n u s c r i p t >
al., 2021) can be freely used for experiments by sending your request to the executive author of SI (C Hwang). Fig. 2a shows a LiDAR-derived digital elevation model (DEM) in Taiwan, which features varying terrains from low-lying coastal areas to high mountains up to 3952 m. Fig. 2b shows the elevation differences between the LiDarderived DEM and the 15" SRTM DEM. Elevation data are essential for removing or condensing the terrain mass external from or to the geoid, and the DEM accuracy has an immediate impact on the geoid model accuracy. Fig. 2b suggests that the two DEMs differ by up to several hundred meters in the mountainous areas of Taiwan. 2. Stochastic approach: based on least-squares collocation (LSC) for transforming gravity anomalies (usually residual gravity anomalies) to (residual) geoid heights.
One feature of LSC is that it considers the heights of gravity data points using covariance functions In both approaches, the terrain effect and its indirect effect on the geoid must be considered. In some cases, height anomalies are computed first and geoidal heights are < A c c e p t e d M a n u s c r i p t > 8 obtained by corrections using heights or Bouguer anomalies. All numerical methods for geoid modeling use the remove-restore-compute procedure because it is not possible to carry out a global integration when computing a geoidal height or height anomaly at a given location. It is not uncommon that gravimetric-only geoidal heights can vary with the integration cap size, the reference field and other factors. Thus, only relative geoidal heights are often assessed against observed relative geoidal heights. When a gravimetric-only geoid model is "adjusted" by a shift to a local mean sea level, or by blending with observed geoidal heights, the resulting geoid is a "hybrid" geoid that may be directly used in orthometric heighting. But observed geoidal heights are not necessarily correct because of the uncertainties in the heights from GNSS and from leveling. For example, vertical tectonic motions in Taiwan can introduce errors in the observed geoidal height at a benchmark if the times of the GNSS observation and the leveling observation s at the benchmark are not the same.
In summary, modeling a 1 cm-geoid is an unfinished task in the geodetic community. The papers presented in this SI highlight this continual effort only in the countries related to these papers.