NING Jinsheng, LI Jiancheng, LUO Zhicai, CHAO Dingbo and JIANG Weiping
School of Geodesy and Geomatics, Wuhan University, 129 Luoyu Road, Wuhan 430079, China
I. ESTABLISHMENT OF NFGN 2000
As same as the establishment of other geodetic control network, the gravity network is also set up by the way of step control. The national fundamental gravity network (NFGN) can provide the gravity datum and the highest order control of gravimetry for different purposes. The first NFGN in P.R.China, named NFGN 57, was established in 1957, its mean accuracy is ± . Afterwards, NFGN 85 was constructed in 1985 for the requirements of the national economic construction and the development of science and technology. The systematic error of Potsdam absolute gravimetric system was corrected for NFGN 85, more gravity fiducial points are available, and the density of absolute gravimetric point improved. So the mean accuracy of NFGN 85 is better than that of NFGN 57 by one order of magnitude, and can arrive at ± . Now the accuracy and the reliability of NFGN 85 cannot meet with the requirements of resource exploration, national defense construction, surveying and mapping, spaceflight technology, geoscience, etc., due to the lower observation accuracy and inhomogeneous distribution of absolute gravimetric points, not completely reasonable figure structure of NFGN 85, some gravity basic points destroyed, etc. For these purposes, NFGN 2000 covering the whole territory of China except for Taiwan was designed and measured since 1999. This network consists of 133 gravity points, and there are 17 fiducial points (absolute gravimetric points) and 116 basic points (relative gravimetric points) among these gravity points. Furthermore, one derived point was laid out for every point of 106 basic points, which were used as the spare point of basic point. NFGN 2000 has the following characteristics and improvements by comparing to NFGN 85:（1）17 high accuracy absolute gravimetric points were laid out reasonably and homogenously over the whole territory of China, which further improved the gravity datum of national fundamental gravity network.
（2）The figure structure of NFGN 2000 was designed optimally, and the observational figure structure and the figure strength of west China especially improved and enhanced, so the overall accuracy of NFGN 2000 was improved.（3）The calibration line of gravimeter (long base line) and the national high accuracy calibration site of gravimeter constant (short base line), were reconstructed and improved for the unification of gravimetric scale and the precise calibration of various gravimeter constants.
（4）NFGN 2000 was connected to NFGN 85, and joined together with the gravity basic network of national important scientific engineering “Monitoring Network of Crustal Movement in China”.The mobile absolute gravimeter FG-5 and LCR-G gravimeter were used in NFGN 2000. The effects of tide, pressure, polar movement, vertical gradient, etc., were corrected for the absolute gravimetric measurements of NFGN 2000. So the observation accuracy of gravity fiducial points is better than ± . For the relative gravimetric measurements, the effects of tide, pressure, height of instrument, zero drift, etc., were also corrected. The relative observation accuracy of gravity basic points is better than ± . Therefore, the standard error of NFGN 2000 is not larger than ± after adjustment. The heights of the gravity fiducial point, basic point and derived point are relative to China’s 1985 Yellow Sea Height Datum, and their planar coordinates with respect to Xi’an 80 coordinate system.
II．REFINEMENT OF LOCAL GEOID
The local or regional geoid with high resolution and high accuracy can provide the fundamental geo-spatial information not only for surveying and mapping, geophysics oceanography and geodynamics, but also for the construction of “digital China”, and now especially for applying GPS technique to determine orthometric or normal height in geodesy and surveying engineering. For these purposes, the new quasi-geoid model CQG2000 with the accuracy of decimeter level has been constructed, which covers the whole territory of China (Chen et al., 2001). The local quasi-geoid with the accuracy of centimeter level and the resolutions of 2¢.5 and 1km has also been determined respectively for Jiangsu Province and Shenzhen City, P.R.China. In future the local quasi-geoid with high accuracy for other provinces and developing regions in China will be determined continually. It is hopeful that the high accuracy quasi-geoid can be employed to the substitution of traditional third and fourth order spirit leveling, the large-scale digital mapping, etc. This will accelerate the construction of “digital city” and “digital China”.
With remove-restore technique Wuhan University calculated the quasi-geoid of Jiangsu Province using the following data: (1) 8756 discrete gravity data on land; (2) marine gravity anomalies on 422475 cross points derived from the multi-satellite altimetric data of version 3 T/P (cycle 1 to cycle 249), Geosat/GM/ERM, ERS-1, ERS-1/168 days, and ERS-2 (cycle 0 to cycle 52); (3) digital terrain model (DTM) with resolution of 18².75´28².125 covering the whole territory of Jiangsu Province, 2¢´2¢ global DTM2000 provided by NASA/NIMA; (4) high quality GPS/leveling data; and (5) WDM94 and EGM96 geo-potential models. Moreover, all integral computations such as terrain correction, first term correction of Molodensky solution, etc., were carried out by rigorous 1-D FFT technique. The resolution of the quasi-geoid is 2¢.5´2¢.5, and its accuracy is better than ±0.078 m.
With the fast development of science and technology, and the requirements of economic construction in Shenzhen City, the land planning department of Shenzhen decided to construct the Shenzhen quasi-geoid with the resolution of 1km and the accuracy of centimeter level in 2000. For
this purpose, the GPS/leveling network consisting of 73 control points was laid out in 2001, and 4870 discrete gravity points were also collected using Lacoste & Romberg model ‘G’ and “D” land gravimeter and model ‘S’ marine gravimeter. And then with almost the same method as that computing the quasi-geoid of Jiangsu Province, Wuhan University calculated the Shenzhen quasi-geoid with the resolution of 1km, using 65 high accuracy GPS/leveling data, 5213 discrete gravity data, digital topographic model with the resolution of 100 m which covers the whole territory of Shenzhen and its neighboring region, and WDM94 geo-potential model. The geoid covers the area of 8 km to 60 km along south-north direction and 79 km to 179 km along west-east direction in Shenzhen local grid coordinate system. Finally, the modeled geoid heights and geoid height differences were compared to those from 29 high precision GPS/leveling data that not used to the calculation of the geoid. And the check results show that the accuracies (standard deviations) of the geoid height and geoid height difference are ±0.014 m and ±0.019 m, respectively, and its overall relative accuracy is better than 1ppm.
Chinese geodesists have always investigated the methods for transferring the height within long distance across sea. Up to now there are four methods used to the height transference, such as static leveling, dynamic leveling, GPS/leveling and conventional geodetic method. The conventional height transferring methods are not practical due to the time-consuming and labour-intensive. Wuhan University studied the method of the height transference within long distance across sea by combining the ellipsoidal height from GPS and the precise gravimetric geoidal height. Using this method the China’s 1985 Yellow Sea Height Datum is transferred to Yangshan Island, which is 30 km far away from Shanghai. The transferred heights are then compared with those determined from two independent sets of gauge records, and the differences are 1.0 cm and 5.0 cm respectively. Moreover, the transferred height differences on the island are also compared with those derived from third order precise spirit leveling, which indicates that the differences are 0.2 cm and 0.7 cm respectively. These test results show that the method is inexpensive, very effective and reliable for the height transference within long distance across sea.
III. SATELLITE ALTIMETRY
Since 1970s, the marine gravity field derived from multi-satellite altimetry missions has rapidly been developed. Combining processing the altimeter data of TOPEX/Poseidon (9-249 cycle), ERS2 (0-44 cycle), Geosat/GM(1-25 cycle) and Geosat/ERM (1-66 cycle), it was solved out for crossover points of respective satellite altimetric mission and the deflection of the vertical along altimetric track profiles, and then the marine gravity anomalies gridded in 2.5¢×2.5¢ size over the South China Sea were determined using inverse Vening-Meinesz formula. Comparing the gravity anomalies derived from the altimeter data with 600 000 gravity anomalies measured by marine gravimeter, it shows that RMS and STD of the difference between them are ± 9.4 mGal and ±9.3 mGal respectively. A new gravity recovery method with along-track vertical deflections is developed independently on the basis of the Laplace’s equation in Cartesian system. The method can be easily approached with 1D Hilbert transform and the along-track gravity anomalies can be derived directly from the along-track slopes of sea surface height (SSH). In other words, only along-track slope of SSH needs to be calculated other than two slopes of along-track and cross track at crossover point（Li et al., 2001; Wang et al., 2001; Huang et al., 2001）.
Four-year altimeter data from T/P and one-year altimeter data from ERS-1 in the China sea and its vicinity are used to determine the mean sea surface (MSS) with stacking method along the satellite repeated collinear tracks. After the contributions of sea surface topography are reduced from the MSS, the 30’´30’ geoid undulations are obtained, and the accuracy of geoid is 8.5 cm (RMS) (Xu et al., 1999). The marine deflection of the vertical is computed from the altimeter data of Topex/Poseidon, ERS-2 and Geosat/GM ERM, in which 2.5’´2.5’ grids for calculation are used, and then 5.0¢´5.0¢ geoid determination of China Sea Area is carried out by Molodensky method. In order to check the computed results, the geoid which is directly solved out by Molodensky formula mentioned above is compared with that computed by Stokes formula using the deflection-inversed gravity anomaly data as an inner examination, and the standard deviation is ±0.025 m. Considering the reality that there is lack of gravity data in China coast area, an extending method is advanced for piecing the two types of geoid determined by different principle and data set. Finally, the continent-marine gravity geoid after piecing together is then fitted with quasi-geoid determined by National GPS leveling network, and the corrected gravity geoid called CQG2000 is obtained (Chen et al., 2001).
The method for determining mean sea surface (MSS) by using multi-altimetric data is developed. The data used to compute WHU2000 MSS include 7 years of Topex/Poseidon data (cycle 11 to 249), 2 years of Geosat ERM data (cycle 1 to 44), 5 years of ERS2 data (cycle 1 to 52) and all ERS-1 168-day data. The WHU2000 MSS is determined with resolution of 2¢´2¢ within the ±82° latitude and its precision is better than 0.05 m. Comparing WHU 2000MSS with 3.75¢×3.75¢ CLS-SHOM98.2 MSS, 3¢×3¢ GFZ MSS95A and 3.75¢×3.75¢ OSU MSS95, as an external check, the corresponding STDs of their differences are 0.090 m, 0.211 m and 0.079m respectively (Jiang et al., 2002； Li et al.，2001).
The collinear method is used to determine MSS heights and their variations in the regions of China seas including Yellow Sea, East China Sea and South China Sea with T/P and ERS-1 altimeter data during the period from October of 1992 to June of 1998. After having done the corrections of T/P altimeter instruments bias, and geophysical environment corrections of tide, ionosphere, troposphere, sea-state bias and inverse barometry, we find that rising rates vary in different regions. Compared with global annual sea level ring rate (+2.1±1.3) mm/a, the annual rising rate in Yellow Sea, East China Sea and South China Sea is (+3.44±0.61) mm/a, (+3.12±0.47) mm/a and (-1.41±0.48) mm/a, respectively. From sea level anomalies, it can be seen clearly that the influences of El Nino in 1993, 1994, and 1997-1998 are greatest in South China Sea, less in East China Sea and least in Yellow Sea (Hu et al., 2001; Wang et al., 2000).
Based on the characteristic of the perfect spatial distribution of the T/P altimeter data, a spatial analysis method is performed, which transfers the constituents harmonic constant H and g into a pair of orthogonal parameters U and V, and then expresses each of them with a polynomial function. As parameters, the polynomial coefficients are derived with altimeter data on the least squares criteria. Thus the models of the main tidal wave in south sea are established. 72 weeks T/P data through weeks 11 to 82 are included in the calculation. The models are evaluated with different approaches and data set. The conclusion is that the tide models can provide partial tide amplitudes with 3cm accuracy, phase lags deviation of those amplitudes which are larger over 10 cm are within ±10°, and the tide models derived are better than those of Schwiderski and SR95.1 (Bao et al., 1999; Bao et al., 2000).
After the geoid is determined, the dynamic ocean topography with 15¢´15¢ grid over China oceans is separated from MSS heights. The RMS of difference between the computed dynamic topography and EGM96 SST model is 0.220 m (Jiang, 2001). The method that hydrodynamic models are reconciled with observation, e.g. altimeter and oceanographic data, is called as data assimilation. Observational equations are formed using finite difference method from the elevation-mode of steady current and its solid boundary condition with stationary sea surface topography as observation values and the square root of onflow friction coefficient as parameter, and the combination problem is solved with parameter adjustment. In the end, stationary sea surface topography of East China Sea, in 22°-41° and 116°-131°E, is calculated with T/P and ERS-2 altimeter and oceanographic data (Zhang et al., 2000).
Besides, the bathymetry model in South China Sea is calculated from gravity anomalies derived from altimteric data, and the interpretation on the characteristics of gravity anomalies is implied by the tectonic block boundaries and their inner structures using the 2.5¢´2.5¢ free air gravity anomalies derived with satellite altimetry data (Yao et al., 2001).
IV. HIGH DEGREE GEOPOTENTIAL MODELS
Since high resolution gravity anomaly data derived from satellite altimetry over global oceans are available now, it is possible for us to develop some ultra-high degree (n>360) geo-potential models. Recent three years, several research institutes in China have presented some such geo-potential models which include MOD99b/c/d, WDM2001, IGG-SCS00A/P and DQM2000A/B/C/D.
The maximum degree-orders of MOD99b/c/d series are 720 (b) and 1800 (c/d) respectively (Huang et al., 2001). In the development of the model series, the gravity data acquired in the continent of China and the global altimeter-derived 2’×2’ gridded marine gravity anomalies are used, and EGM96/GPM98CR are taken as the reference models. Based on the data tailor method, however, it only acts as a local improvement upon an existing global model. Unfortunately, it is possible for such local improved model to present some fluctuations in stairs-form around the boundary of tailoring area. In order to overcome this weakness of the method and to make the reference model used smoothly fitted with the local data, the idea on a local improving of reference model by tailoring is extended into a global improving procedure. Based on the global data file of gravity anomalies computed from the reference models, the model-derived anomaly data within the continent of China and the global oceans are updated by a new higher quality data set acquired from terrestrial gravity measurements and a global altimeter-derived marine gravity anomaly data set, and then the coefficients of the models to be developed are corrected by a global integral process. The geoidal undulations computed by MOD99b/c/d have been computed with those of 72 GPS leveling points and the altimeter-derived ones in 12 ocean areas respectively. The RMS of the differences between the MOD99 series-derived undulations and GPS leveling–measured ones is about 0.6 m, and the interval distribution of RMS of the differences between the models-derived undulations and the altimeter-derived ones is ±0.02 m - ±0.26 m in the oceans.
The maximum degree-order of WDM2001 is 720 (Li, 2000). 420 000 terrestrial gravity values acquired in the continent of China are adopted to form 15’×15’ gridded data set of gravity anomalies after data reduction processing. Using altimeter data set including the GRDs of T/P, ERS1/2, and Geosat/GM/ERM in the new edition, the deflection of the vertical is computed at crossover points of respective ground tracks, and then transferred into the gravity anomalies by the inverse Vening-Meinesz formula given by Molodensky. The resulting global marine gravity anomaly data along tracks are reduced in 15’×15’ gridded data set by interpolating and fitting procedure. The terrestrial gravity anomalies computed from EGM96 are used in the land outside the continent of China. Combining all the above three types of gravity anomaly data, a global 15’×15’ gridded data set is formed as the basic input data in the model computation. In addition, the satellite geo-potential model GRIM5-S1 with maximum degree 36 is also taken into account as a priori information of the low degree for developing the model. The geo-potential coefficients of WDM2001 are determined by use of rigorous spherical harmonic analyses and combined adjustment. The geoid undulations computed from this model are compared with those of 631 GPS leveling points, and the standard deviation of the differences in the comparison is ±0.56 m. The model is also compared with EGM96 and WDM94, and the corresponding results of the comparison in geoidal undulations are ±0.57 m and ±0.78 m respectively.
IGG-SCS00A (Lu et al., 2001a) is a regional ultra-high degree geo-potential model with a maximum degree-order of 3600, computed from 3’×3’ gridded altimeter-derived marine gravity anomalies in South China Sea and vicinity (105°-122°E, 0°-25°N) based on the integral formula for spherical harmonic expansion and using local integrals of spherical harmonics. For the start of the iteration procedure, geo-potential model GPM98C is used. The model gravity anomalies of IGG-SCS00A have been compared with the marine ones in South China Sea, and the RMS of discrepancies between them is ±3.2 mGal, and the geoidal undulations of the model have also been compared with 3’×3’ altimeter-derived marine ones, which shows that the RMS of the discrepancies between them is about ±0.2 m. Using 2’×2’ gridded altimeter-derived gravity anomalies in the same area as mentioned above, the computation of the model IGG-SCS-P is based on the Pseudo-Harmonic Regional Analysis (PHRA) method taking a scale factor as 5 and expanded to 1080 degree and order that really corresponds to 5400 degree and order in common spherical harmonic expansion (Lu et al., 2001b). A similar comparison to the above, but at 2’×2’ resolution level, shows that the corresponding RMS is ±2.4 mGal and ±0.19 m respectively.
The maximum degree-order of the model series DQM2000A/B/C/D is 540 (A), 720 (B), 1080 (C) and 2160 (D) respectively (Surveying and Mapping Institute of Xi’an, 2001). In the development of the models, EGM96 is taken as a basic reference model, and 200692 5’×5’ terrestrial gravity anomalies acquired in the continent of China are used as the basic input data. The method for computing the model series is based on a local spectrum-weighted integral improving procedure to the reference model used. The accuracies of DQM2000A/B/C/D used in computing the terrestrial gravity anomaly in the area of the continent of China are ±10.4 (A), ±10.6 (B), ±13.3 (C) and ±18.6 (D) (unit: mGal) respectively, and the accuracy of computing geoidal undulations from the models in the same area is ±0.5 m— ±0.7 m.
V. SATELLITE GRAVITY GRADIOMETRY
At the beginning of 21st century, satellite gravity gradiometry or satellite-to-satellite tracking (SST) is known as one of the most promising techniques for the future progress in studying the earth’s gravity field. One of the primary scientific objective of ongoing satellite missions like GOCE is to provide with unprecedented accuracy, global and high-resolution estimates of the constant and time-variable part of the Earth’s gravity field. In recent years, Chinese scholars always track the progress of these techniques, and focus on studying their fundamental theories and methods. Wuhan University studied the principle, technical mode, error sources and their characteristics about SGG and SST, and discussed the technical scheme and possibility for developing SGG and SST in China. In theory, the determination of the earth’s gravity field using satellite gravity gradiometry data, is reduced to resolve satellite gravity gradiometry boundary value problem. The stochastic satellite gravity gradiometry boundary value problem was presented by Wuhan University, and corresponding practical computational models are derived. The generalized spherical harmonic series representation of the global and local gradient components for the full gravity tensor was given by Zhang et al. (2000), as well as the relationship between the generalized spherical harmonic function and the spherical harmonic function. A set of formulae for computing the geoid, gravity disturbance, gravity anomaly and deflection of the vertical from the second radial derivative of the disturbing potential are derived in detail using the basic differential equation with spherical approximation in physical geodesy and the modified Poisson integral formula. The derived integral in the space domain, expressed by a spherical geometric quantity, is then converted to a convolution form in the local planar rectangular coordinate system tangent to the geoid at the computing point, and the corresponding spectral formulae of 1-D FFT and 2-D FFT are presented for numerical computation (Li, 2002). It is hopeful that these achievements would be employed to recover the Earth’s gravity field and to compute the gravity quantities in practice using satellite gravity gradiometry data.
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