| The geoid, defined as the equipotential surface that best approximates the mean sea level, is the most natural representation of the Earth’s figure and reflects not only the crustal structure but also the density inhomogeneities in the mantle. The geoid serves as vertical datum in many countries and can provide basic infor-mation for research on geoscience and economic development as well as the national defense. Geoid determination remains a major issue for more than a century in physical geodesy, it is still a common challenge today and attracts significant at-tention from the international geodetic and geophysical communities, since a main goal of physical geodesy is the determination of the geoid with high resolution and accuracy in21st century.The new theoretical method put forward by Shen (2006) is introduced in de-tail. This new method is quite different from the classic geoid modeling methods (Stokes’method, Molodensky’s method and Bjerhammar’s method) and it provides a solution, which does not depend on the Stokes’integral or Molodensky’s integral, from a new point of view that is based on the definition of the geoid.The detailed discussion on the evaluation of the gravitational potential of the shallow layer is presented, including the establishment of the3D spatial and density model and the modeling methods. The3D spatial model focuses on the geometry of the shallow layer, namely, the upper and lower surfaces. In this study, the upper surface of the shallow layer is finally established by combining DTM2006.0topographic database on land areas and DNSC08MSS on ocean surfaces, the lower surface is obtained by extending from the reference surface (i.e., EGM2008geoid) downward to a depth of150meters. The3D density model is provided by CRUST2.0model. Then the combined modeling method (prism model in direct vicinity and tesseroid model in other regions) are used to calculate the gravitational potential generated by the shallow layer. Owing to the high computation cost, an appropriate choice of computation strategies and the related fast algorithms to improve the efficiency of the entire evaluation are also introduced.Based on the newly released high-precision5’x5’global gravity model EGM2008, the high-resolution global digital topographic database DTM2006.0, the global crustal model CRUST2.0and the new theoretical method, a5’×5’geoid in the Xinjiang and Tibeta regions, which ranges from latitude25°～50°N and longitude70°～100°E, has been determined as a case study of the new theoretical method. The modeled5’×5’regional geoid is compared with the EGM2008geoid model in the same study area and validated by21GPS/leveling benchmarks (GPSBMs) distributed sparsely in the Xinjiang area. The results show that the accuracy of the calculated geoid and the EGM2008geoid is17.9cm and19.8cm, respectively. The calculated geoid agrees with the GPSBMs better2cm than the EGM2008geoid in the Xinjiang region. The EGM2008global gravity model is adopted in the calculations and the omission and commission errors of which will finally affect the accuracy of the calculated geoid. A solution is found to reduce these errors. Firstly, the low degree part of the calculated geoid is replaced by the geoid from the satellite-only gravity model with the same cut-off degree, in reduction of the commission error. The satellite-only gravity model is determined only from satel-lite gravity data, and is free of the long-wavelength errors in the terrestrial gravity data and altimetry-derived data which EGM2008suffers. We checked with different models (GOCO02S、EIGEN-6S、ITG-Grace2010s and GGM03S) and tested dif-ferent cut-off degrees, but found120to be optimal for each model. After replacing the low degree part with that from the satellite-only models, the accuracy of the calculated geoid reaches an accuracy of15.7cm in the Xinjiang area, which means～4cm better than the EGM2008geoid. Secondly, the residual terrain model (RTM) is introduced to reduce the omission errors. After applying the RTM method, the accuracy of the calculated geoid reaches14.6cm in the Xinjiang area.In consideration of the successful case study in the Xinjiang and Tibetan re-gions, further work has been carried out to extend the application of the new method to determining the5’×5’global geoid. GPS levelling comparisons are performed for the global calculated geoid and the EGM2008geoid. Four different regional GPS levelling data sets are applied for the comparison purposes, namely, the USA data sets, the Australian data sets, the European data sets and the Chi-nese data sets. The STD of the differences between the calculated geoid and the GPS/leveling-derived geoid is29.3cm over USA, sightly better than the29.6cm of the EGM2008geoid. If the test region is restricted to the western US (mainly the Rocky Mountains), the STD of the differences between the calculated geoid and the GPS/leveling-derived geoid reduces to18.6cm, about2cm better than the20.4cm of the EGM2008geoid. The STD of the differences between the calculated geoid and the GPS/leveling-derived geoid reaches19.6cm over Australia, almost identical to the EGM2008geoid. The STD over Europe is much larger, for the calculated geoid it is39.7cm while for the EGM2008geoid it is40.6cm. There are some long-wavelength errors existed in the GPS/leveling data sets over CONUS, Australia and Europe, but these errors do not affect the above comparisons. The accuracy of the EGM2008geoid is25.2cm in China, which is similar to the results reported by Zhang et al.(2009)(compared with7788GPSBMs) and Li et al.(2012)(compared with649GPSBMs). The calculated geoid reaches an accuracy of24.5cm in China, and it fits the GPSBMs better7mm than the EGM2008geoid.The error sources in the geoid determination using the new theoretical method is analysed thoroughly and solutions which may be used to reduce the influence of error sources are investigated. Errors in EGM2008, DTM2006.0and CRUST2.0nat-urally dominate errors in the calculated geoid.The influence of DNSC08MSS and the calculation methods are minor, which can be neglected under most circumstances. The influence of EGM2008is the largest, with a globally10cm-level contribution, but can be reduced by the low degree part replacement and the RTM methods. Errors in elevations may also introduce large errors in the geoidal heights. Two different geoid models, based on different DEMs, have been determined in the Xin-jiang and Tibetan regions and then compared with each other. The results shows that an STD error in height of the order of100meters introduces an STD error in geoid undulations of nearly10centimeters. Errors in CRUST2.0model also plays an import role. A geoid based on the new theoretical method and the constant density hypothesis (2670kg/m3for the rocks) has been determined in the Xinjiang and Tibetan regions and validated by21GPS/leveling benchmarks (GPSBMs) dis-tributed in the Xinjiang area. The results show that the calculated geoid (based on the constant density hypothesis) reaches an accuracy of19.5cm and agrees with the GPSBMs slightly better3mm than the EGM2008geoid in the same region. The above results have proved the validity and reliability, even the superiority of the new theoretical method since constant density hypothesis is also adopted in the de-velopment of the EGM2008geoid model. The calculated geoid based on CRUST2.0reaches an accuracy of17.9cm in the test region, it suggests that CRUST2.0does bring a noticeable improvement in geoid determinations in this area. The differences in geoid undulations in the Xinjiang region due to different density hypotheses can reach a magnitude of1.6cm, which is significant and could not be negligible in the precise geoid determination with centimeter accuracy. Our research is also helpful to the geoid determinations in other mountainous regions.The orthometric height of the Qomolangma Feng is also determined based on the5’x5’calculated geoid and EGM2008geoid in the Xinjiang and Tibetan regions. The results show that the height determined based on the calculated geoid is8844.58m while that determined based on the EGM2008geoid is8844.75m, the former is more close to the official value8844.43m published by the National Administration of Surveying, Mapping and Geoinformation in2005. The peeling algorithm to refine the crustal density structure based on the new theoretical method is put forward, which is concise but needs more verifications. The application of the calculated geoid based on the new method in height datum unification is also discussed. |
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