The contribution presents the representative research progress on global static gravity field modeling, regional geoid/quasigeoid determination, vertical datum study, as well as the theory, algorithm and software for gravity field study in China from 2019 to 2023, which are the highlights of the chapter 6"Progress in Earth Gravity Model and Vertical Datum"in the"2019—2023 China National Report on Geodesy"that submitted to the International Association of Geodesy ( IAG ) . In addition, suggestions are proposed to promote the research in the fields of earth gravity field, geoid/quasigeoid and vertical datumin China according to trends of international geodesy and related disciplines.

Abstract New bathymetry models in the northwestern Pacific Ocean are presented at 1 arc-minute and 15 arc-second resolution. The latest version of the altimetric vertical gravity gradient (VGG) anomalies from Scripps Institute of Oceanography, ∼7 million single-beam depths from the National Centers for Environmental Information, and ∼80 GB of multibeam grids from the Japan Agency for Marine-Earth Science and Technology are used. The ship-board depths are used to constrain bathymetry at wavelengths longer than 200 km, and calibrate the local topography to VGG ratio at 15–200 km wavelength bands. The VGG is used to predict bathymetry at 15 ∼ 200 km wavelength bands. The spectrum analysis results show that the 1 arc-minute model has more power than models predicted from gravity anomalies at wavelengths shorter than 100 km. The standard deviation of differences between the 1 arc-minute model and ship-board depths is 44.76 m, and it is 102.842 m comparing to the SIO topo_20.1.nc model. The accuracy of the new 1 arc-minute model has been improved significantly from our last bathymetry model, BAT_VGG, and has a better accuracy than that of the DTU18, GEBCO_08, and ETOPO1 models. The accuracy of the 15 arc-second model is consistent with that of SRTM + V2.1 and GEBCO_2020.

Gravitational detection for underwater vehicles (UV) is a potential non-acoustic detection technique, which is still at the stage of theoretical exploration at present. In this study, we derived analytic formula for the vertical components of gravity and gravity gradient of a vertical dipole, and analyzed characteristics of their spatial distribution. Based on the dipole model, a method to simulate anomalous gravitational field of UV was presented. An example was demonstrated to illustrate the effectiveness of the method and to analyze the spatial variation of gravity anomaly and gravity gradient of UV, as well as to estimate requirements for the accuracy of sensors and the stability of detection platform. The following conclusions can be drawn from the analysis results of the example. Gravity anomaly is not suitable to be used for the detection of UV. However, the detection technique based on gravity gradient is of practicable value and worthy to be studied further. The dipole model presented in this paper is a good tool for the theoretical study of gravitational detection of UV, which can be conveniently used to estimate the magnitude of the anomalous field derived from UV, accuracy requirements of detection platform and maximum detectable distance.

In this paper, a 1'×1' bathymetry model BAT_WHU2020 in the range of 75°S—70°N is constructed by using the latest version of the global gravity anomaly model derived from the multi-source satellite altimetry data and the shipboard depths. The accuracy of the model is analyzed and evaluated based on ship depths, existing models and multibeam soundings. The standard deviation of the difference between the proposed model and the ship depths in China Sea and its adjacent areas (104°E—160°E, 0°N—50°N) is about 70 m, which is equivalent to the accuracy of SIO V19.1 model, superior to ETOPO1, DTU10, GEBCO_08 model, and about 30% higher than the accuracy of BAT_VGG model published before, which shows that the method in this paper is reliable, and the data processing is accurate and the accuracy is high. The standard deviation of the differences between BAT_WHU2020 model and ship depths is about 50~65 m globally, and the ratio of the difference within ±200 m is greater than 95%. It is showed that the accuracy of BAT_WHU2020 model is equivalent to SIO V19.1, better than ETOPO1, DTU10, GEBCO_08 model, and improved about 27%~36% from the BAT_VGG model. Comparing to SIO V19.1 model, the standard deviation of the model differences is about 90~110 m, about 90% of the grid differences is within 200 m, and about 95% is within 300 m . Finally, the effects of crustal isostasy and high order terms in the Parker's formula on the accuracy of the results, the accuracy of the model compared to multibeam soundings, and the spatial resolution are discussed. It indicates that the spatial resolution of BAT_WHU2020 model is about 10~18 km, and the relative accuracy is about 5%~6% around the Mariana trench and Macquarie ridge.

为了进一步提高高程基准面的精度,研究剩余地形模型(RTM)在近海区域高程基准面中的影响:利用陆海统一岩石等效地形(RET)构建近海区域RTM和残余高程异常;并联合多面函数拟合残余高程异常改正面,实现近海区域高程基准面模型精度的提高.实验结果表明:在近海区域,利用RTM高程异常可提高新技术改进后的欧洲地球重力联合模型(EIGEN-6C4)的精度约为3 mm;多面函数拟合后,可以将EIGEN-6C4模型的精度由9.0 cm提高到3.4 cm.

针对不同经验公式的断层参数对海啸数值模拟影响的问题,该文选择两种断层参数的经验公式,海啸初始阶段采用Okada模型,该模型将海底地形变化直接作为水面变化进行处理,利用COMCOT海啸传播模型分别对2013年2月6日发生在所罗门群岛海域的地震海啸进行数值模拟.将数值模拟结果与DART观测站的实际观测数据进行比较.结果 表明,JMA经验公式计算的断层长度、宽度和滑动量的海啸数值模拟结果更符合此次海啸的实际观测数据.研究结论对所罗门群岛及周边海域地震海啸数值模拟中断层参数的确定具有实际参考意义.

The accuracy of the geopotential value of the vertical datum is usually relies on the high-precision Global Geopotential Models (GGMs), which are critical for high-precision uniformity of global and regional vertical datums or height systems. The advent of the GOCE and GRACE missions during the last decade have brought significant improvement in modelling of the low frequency or rather medium-frequency part of the Earth's static gravity field. The GRACE/GOCE GGMs are extended from the degree and order n(max) +1 to 2190 using EGM2008 in order to evaluated the effect of the omission error on the computed geopotential value of the China vertical datum of 1985, and the effect of the GRACE/GOCE GGMs omission error is at dm-level for China. The effect of the GRACE/GOCE GGMs omission error on the geopotential can be effectively reduced by extending the model with the high-resolution gravity field model EGM2008 and the optimal extend degree and order is difference based on the difference GRACE/GOCE GGMs, for example, the extend degree and order is 180 and 220 for DIR-1 and DIR-5. The GRACE/GOCE GGMs extended by the EGM2008 with the optimal extend degree and order provide a significant, compared to EGM2008, improvement in the comparisons with the GPS/Levelling data, by as much as 18 cm, in terms of the standard deviation. The W-0(LVD) determined for the China local vertical datum was 62636853. 47 m(2) . s(2) and 62636853. 49 m(2) . s(2) for DIR-5 and TIM-5, and the accuracy both are 1. 51 m(2) . s(2). Lastly, the spatial tilts found in the levelling network can be modeled with a 2-parameter bias corrector model, the east-west tilt is about 9 cm, and the north-south tilt is about 1. 4 cm. Based on the DIR-5 or TIM-5 models, the accuracy of the geopotential value of the 1985 is improved about 0. 16 m(2) . s(2).

Satellite altimetry has been successfully applied to monitoring water level variation of global lakes. However, it is still difficult to retrieve accurate and continuous observations for most Tibetan lakes, due to their high altitude and rough terrain. Aiming to generate long-term and accurate lake level time series for the Tibetan lakes using multi-altimeters, we present a robust strategy including atmosphere delay corrections, waveform retracking, outlier removal and inter-satellite bias adjustment. Apparent biases in dry troposphere corrections from different altimeter products are found, and such correctios must be recalculated using the same surface pressure model. A parameter is defined to evaluate the performance of the retracking algorithm. The ICE retracker outperforms the 20% and 50% threshold retrackers in the case of Ngangzi Co, where a new wetland has been established. A two-step algorithm is proposed for outlier removal. Two methods are adopted to estimate inter-satellite bias for different cases of with and without overlap. Finally, a 25-year-long lake level time series of Ngangzi Co are constructed using the TOPEX/Poseidon-family altimeter data from October 1992 to December 2017, resulting in an accuracy of ~17 cm for TOPEX/Poseidon and ~10 cm for Jason-1/2/3. The accuracy of retrieved lake levels is on the order of decimeter. Because of no gauge data available, ICESat and SARAL data with the accuracy better than 7 cm are used for validation. A correlation more than 0.9 can be observed between the mean lake levels from TOPEX/Poseidon-family satellites, ICESat and SARAL. Compared to the previous studies and other available altimeter-derived lake level databases, our result is the most robust and has resulted in the maximum number of continuous samples. The time series indicates that the lake level of Ngangzi Co increased by ~8 m over 1998–2017 and changed with different rates in the past 25 years (-0.39 m/yr in 1992–1997, 1.03 m/yr in 1998–2002 and 0.32 m/yr in 2003–2014). These findings will enhance the understanding of water budget and the effect of climate change.

利用Okada模型计算2018-01-23 09:31（UTC）阿拉斯加湾7.9级地震引发的海啸的初始场信息,利用COMCOT模型模拟海啸传播。比较海啸首波振幅和到达时间模拟值与实测值显示,振幅差异在4 cm以内,时间差异在4 min以内。模拟结果与观测资料吻合,揭示阿拉斯加地震引发的海啸强度弱,同时反映海啸初始场参数的选择合理有效,海啸模拟计算结果真实可靠。

Estimation of the zero-height geopotential value W0LVD for the CVD (China Vertical Datum) plays a fundamental role in the connection of traditional height reference systems into a global height system. Estimation the W0LVD of China is based on the computation of the mean geopotential offset between the value W0 = 62636856.0 m2s−2, selected as reference in this study, and the unknown geopotential value W0LVD. This estimation is based on the combination of ellipsoidal heights, levelled heights (referring to the CVD), and some physical parameters, such as geopotential values, gravity values, and geoid undulations. The geoid undulations derived from the GGM (Global Geopotential Models). This combination is performed through three approaches: The first one is based on the theory of Molodensky, and the second one compares levelled heights and geopotential values derived from the GGMs, while the third one analyses the differences between GPS/Levelling and GGMs geoid undulations. The approaches are evaluated at 65 benchmarks (BMs) covered around Qingdao where the tide gauge is used to observe the local mean sea level of China. The results from three approaches are very similar. Furthermore, the W0LVD determined for the China local vertical datum was 62636852.9462 m2s−2, indicates a bias of about 3.0538 m2/s−2 compared to the conventional value of 62636856.0 m2s−2.

The unification of the global height datum is a key problem to be solved for geodesy after the unification of global geodetic coordination system and three-dimension spatial datum,and the basis of global spatial information sharing and exchange.In this paper,the theoretical and practical problems of vertical datum offset between the regional height datum and the global height datum are studied.Based on the classical theory of the height system in physical geodesy,the definition of the height datum vertical offset is given,and the rigorous formulas for calculating the vertical offset are derived.The formulas can be used to deduce the three methods of the height datum vertical offset determination.On that basis,the influences of different reference system and reference ellipsoid parameters on the calculation of the vertical offset are analyzed.The results show that the reference system and the ellipsoid parameter conversion are very necessary.At the same time,the height anomaly differences method needs to consider the degree zero correction caused by the inconsistency between gravity potential of the global height datum and the one computed by the model.Based on potential difference approach and the height anomaly difference method,the vertical offset between the China 1985 national height datum and the global height datum corresponding to the normal gravity potential U0 of GRS80,WGS-84 and CGCS2000 reference ellipsoidal from the 152 GPS/ leveling points near the origin of Qingdao height origin and the EGM2008,EIGEN-6C4 and SGG-UGM-1 model.The regional datum is 23.1 cm lower than the global datum based on EIGEN-6C4 and WGS-84.When the Gauss-Listing geoid (mean sea surface) is selected as the global height datum,the China 1985 national height datum is 21.0 cm higher than the global height datum.The results also show that there are still large differences among the accuracies of the current gravity field models on these GPS/Levelling points around Qingdao,which will lead to big differences in estimating the vertical datum offset between the China 1985 national height datum and the global height datum with respect to different selected data sets.Therefore,the accuracy and reliability of the current global gravity field models needs to be further improved if they were used for the height datum vertical offset determination.The theoretical and practical results of this paper could be used for the realization of the unification of the regional height datum and the global height datum.

The main purpose of this paper is to estimate the zero height geopotential value for the China Local Vertical Datum.The method used is based on a gravimetric approach and benefits from the significant improvements in the determination of the global gravity field by the recent satellite gravity missions such as GRACE and GOCE.The performance of GOCE-based or GRACE/GOCE-based Global Geopotential Models (GGMs) is assessed for estimation of geopotential of the regional vertical datum of China using the GPS/Levelling BMs (benchmarks) from vertical control network.We should conver the normal height to orthometric height.From the evaluation with the GPS/Levelling BMs, it is concluded that the GOCE-based or GRACE/GOCE-based GGMs provide an absolute accuracy at of 40cm, up to their maximum degree and order.Factors that affect the geopotential value of vertical datum include the GOCE commission and omission errors.Among these factors, the effect of the GOCE omission error is investigated by extending the models with the high resolution gravity field model EGM2008.When extending the GOCE-based or GRACE/GOCE-based models with the high resolution gravity field model EGM2008, we should provide the same parameters.At the same time we should unify the frame and tide system between the GGMs and GPS/Levelling dataset.The result shows that, the effect of the GOCE omission error is at the level of 1.6 m2s-2 (about 16 cm), in China, is at decimetre-level when computing local vertical datum geopotential, the effect of the tide system is about 4-6cm.The vertical datum geopotential of China is estimated as 62 636 852.704 5 m2s-2.

卫星记录的测高数据是离散的,格网化后才能得到规则的海平面.采用连续曲率张力样条方法对卫星测高数据格网化,并与Shepard算法进行比较.结果表明,连续曲率张力样条方法可以用于测高数据格网化,而且精度更好.

The mean geopotential value of the global mean sea surface,62 636 856.550 7 m2s-2,is determined based on the global gravity model(EIGEN-6C4、EGM2008)and global mean sea surface height model(DNSC08、DTU10、DTU13).The geoidal potential (62 636 858.179 0 m2 s-2 )can be obtained by subtracting the mean sea surface topography from the mean sea surface height.Then,649 GPS/leveling data,distributed evenly over the mainland of China,are selected to calculate the 1985 national height datum geopotential and the vertical shift using three methods,combined with the global gravity model EGM2008.The vertical shift value is improved by weighting,and utilizing two methods to verify the rationality and correctness after weighting.The final results demonstrate that the 1985 national height datum is 0.298 0 and 0.464 2 m above the mean sea level and the global geoid,respectively.

The cryosat-2 satellite recently published its first altimeter dataincluding periodically drifting orbit and dense ground tracks.These data can be used to improve the accuracy and resolution of the marine gravity field.In this paper,we constructs auto-regressive models of the altimeter data series by considering two aspects of signal and noise,and propose a new method called the signal-to-noise ratio analytical method for estimating the resolution capability of Cryosat-2 data.in five test cases,this new method offers a consistent alternative to the traditional spectral correlation method.The resolution capability of Cryostat-2 altimeter data from single cycle is in the range of 23 km～33 km,with an average value of 27 kn,and better than 38 km,43 km and 37 km of the Geosat/ERM,ERS 1/ERM and T/P data.This result shows that the Cryosat 2 altimeter data has a lower noise level and a higher geoid signal recognition.Therefore,it is reasonable to believe that the Cryostat-2 could provide shorter wavelength information for the construction of marine gravity field with higher resolution.

Based on variation characters of sea surface height and parameters of ICESat return pulse waveform,a method is proposed for estimating Arctic sea ice freeboard with ICESat observation.This proposed method is compared with the common ‘lowest-level’method.The results show that the lowest-level method is vulnerable to gross errors and present systematic errors in spatial distribution of freeboard. But the proposed method is more rel iable than the lowest-level method.The lowest-level method is improved by the employ of an elevation standard deviation threshold and combined with the proposed method to estimate sea ice freeboard for six ICESat campaigns between 2005 and 2006 to review the seasonal variabi l ity.The results show that the abnormal cl imate in the summer of 2005 have a profound impact on arctic sea ice,which caused the decrease of freeboard and changed the constituent of sea ice as wel l.

针对不同时空分辨率测高数据对测高垂线偏差计算结果的影响,联合使用Jason1波形数据和Cryosat数据,在对波形重跟踪处理和海面时变效应消弱预处理后,采用Sandwell方法和加权最小二乘法计算了三个典型区域的垂线偏差分量.研究结果与EGM2008模型检核表明,低轨道倾角的Jason1大地测量任务数据能有效提取垂线偏差东西分量信息,联合高轨道倾角的Cryosat测高数据可以提升垂线偏差计算精度,而引入重力场模型作为参考场可以进一步改进垂线偏差计算结果.