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1.
N. J. Brown J. C. McCubbine W. E. Featherstone N. Gowans A. Woods I. Baran 《Journal of Geodesy》2018,92(12):1457-1465
AUSGeoid2020 is a combined gravimetric–geometric model (sometimes called a “hybrid quasigeoid model”) that provides the separation between the Geocentric Datum of Australia 2020 (GDA2020) ellipsoid and Australia’s national vertical datum, the Australian Height Datum (AHD). This model is also provided with a location-specific uncertainty propagated from a combination of the levelling, GPS ellipsoidal height and gravimetric quasigeoid data errors via least squares prediction. We present a method for computing the relative uncertainty (i.e. uncertainty of the height between any two points) between AUSGeoid2020-derived AHD heights based on the principle of correlated errors cancelling when used over baselines. Results demonstrate AUSGeoid2020 is more accurate than traditional third-order levelling in Australia at distances beyond 3 km, which is 12 mm of allowable misclosure per square root km of levelling. As part of the above work, we identified an error in the gravimetric quasigeoid in Port Phillip Bay (near Melbourne in SE Australia) coming from altimeter-derived gravity anomalies. This error was patched using alternative altimetry data. 相似文献
2.
W. E. Featherstone J. F. Kirby A. H. W. Kearsley J. R. Gilliland G. M. Johnston J. Steed R. Forsberg M. G. Sideris 《Journal of Geodesy》2001,75(5-6):313-330
The AUSGeoid98 gravimetric geoid model of Australia has been computed using data from the EGM96 global geopotential model,
the 1996 release of the Australian gravity database, a nationwide digital elevation model, and satellite altimeter-derived
marine gravity anomalies. The geoid heights are on a 2 by 2 arc-minute grid with respect to the GRS80 ellipsoid, and residual
geoid heights were computed using the 1-D fast Fourier transform technique. This has been adapted to include a deterministically
modified kernel over a spherical cap of limited spatial extent in the generalised Stokes scheme. Comparisons of AUSGeoid98
with GPS and Australian Height Datum (AHD) heights across the continent give an RMS agreement of ±0.364 m, although this apparently
large value is attributed partly to distortions in the AHD.
Received: 10 March 2000 / Accepted: 21 February 2001 相似文献
3.
J. F. Kirby 《Journal of Geodesy》2003,77(7-8):433-439
The geoid gradient over the Darling Fault in Western Australia is extremely high, rising by as much as 38 cm over only 2 km. This poses problems for gravimetric-only geoid models of the area, whose frequency content is limited by the spatial distribution of the gravity data. The gravimetric-only version of AUSGeoid98, for instance, is only able to resolve 46% of the gradient across the fault. Hence, the ability of GPS surveys to obtain accurate orthometric heights is reduced. It is described how further gravity data were collected over the Darling Fault, augmenting the existing gravity observations at key locations so as to obtain a more representative geoid gradient. As many of the gravity observations were collected at stations with a well-known GRS80 ellipsoidal height, the opportunity arose to compute a geoid model via both the Stokes and the Hotine approaches. A scheme was devised to convert free-air anomaly data to gravity disturbances using existing geoid models, followed by a Hotine integration to geoid heights. Interestingly, these results depended very weakly upon the choice of input geoid model. The extra gravity data did indeed improve the fit of the computed geoid to local GPS/Australian Height Datum (AHD) observations by 58% over the gravimetric-only AUSGeoid98. While the conventional Stokesian approach to geoid determination proved to be slightly better than the Hotine method, the latter still improved upon the gravimetric-only AUSGeoid98 solution, supporting the viability of conducting gravity surveys with GPS control for the purposes of geoid determination.
AcknowledgementsThe author would like to thank Will Featherstone, Ron Gower, Ron Hackney, Linda Morgan, Geoscience Australia, Scripps Oceanographic Institute and the three anonymous reviewers of this paper. This research was funded by the Australian Research Council. 相似文献
4.
A new gravimetric geoid model, USGG2009 (see Abbreviations), has been developed for the United States and its territories
including the Conterminous US (CONUS), Alaska, Hawaii, Guam, the Commonwealth of the Northern Mariana Islands, American Samoa,
Puerto Rico and the US Virgin Islands. USGG2009 is based on a 1′ × 1′ gravity grid derived from the NGS surface gravity data
and the DNSC08 altimetry-derived anomalies, the SRTM-DTED1 3′′ DEM for its topographic reductions, and the global geopotential
model EGM08 as a reference model. USGG2009 geoid heights are compared with control values determined at 18,398 Bench Marks
over CONUS, where both the ellipsoidal height above NAD 83 and the Helmert orthometric height above NAVD 88 are known. Correcting
for the ellipsoidal datum difference, this permits a comparison of the geoid heights to independent data. The standard deviation
of the differences is 6.3 cm in contrast to 8.4 cm for its immediate predecessor— USGG2003. To minimize the effect of long-wavelength
errors that are known to exist in NAVD88, these comparisons were made on a state-by-state basis. The standard deviations of
the differences range from 3–5 cm in eastern states to about 6–9 cm in the more mountainous western states. If the GPS/Bench
Marks-derived geoid heights are corrected by removing a GRACE-derived estimate of the long-wavelength NAVD88 errors before
the comparison, the standard deviation of their differences from USGG2009 drops to 4.3 cm nationally and 2–4 cm in eastern
states and 4–8 in states with a maximum error of 26.4 cm in California and minimum of −32.1 cm in Washington. USGG2009 is
also compared with geoid heights derived from 40 tide-gauges and a physical dynamic ocean topography model in the Gulf of
Mexico; the mean of the differences is 3.3 cm and their standard deviation is 5.0 cm. When USGG2009-derived deflections of
the vertical are compared with 3,415 observed surface astro-geodetic deflections, the standard deviation of the differences
in the N–S and E–W components are 0.87′′ and 0.94′′, respectively. 相似文献
5.
A data-driven approach to local gravity field modelling using spherical radial basis functions 总被引:3,自引:0,他引:3
We propose a methodology for local gravity field modelling from gravity data using spherical radial basis functions. The methodology
comprises two steps: in step 1, gravity data (gravity anomalies and/or gravity disturbances) are used to estimate the disturbing
potential using least-squares techniques. The latter is represented as a linear combination of spherical radial basis functions
(SRBFs). A data-adaptive strategy is used to select the optimal number, location, and depths of the SRBFs using generalized
cross validation. Variance component estimation is used to determine the optimal regularization parameter and to properly
weight the different data sets. In the second step, the gravimetric height anomalies are combined with observed differences
between global positioning system (GPS) ellipsoidal heights and normal heights. The data combination is written as the solution
of a Cauchy boundary-value problem for the Laplace equation. This allows removal of the non-uniqueness of the problem of local
gravity field modelling from terrestrial gravity data. At the same time, existing systematic distortions in the gravimetric
and geometric height anomalies are also absorbed into the combination. The approach is used to compute a height reference
surface for the Netherlands. The solution is compared with NLGEO2004, the official Dutch height reference surface, which has
been computed using the same data but a Stokes-based approach with kernel modification and a geometric six-parameter “corrector
surface” to fit the gravimetric solution to the GPS-levelling points. A direct comparison of both height reference surfaces
shows an RMS difference of 0.6 cm; the maximum difference is 2.1 cm. A test at independent GPS-levelling control points, confirms
that our solution is in no way inferior to NLGEO2004. 相似文献
6.
The first Australian gravimetric quasigeoid model with location-specific uncertainty estimates 总被引:1,自引:1,他引:0
W. E. Featherstone J. C. McCubbine N. J. Brown S. J. Claessens M. S. Filmer J. F. Kirby 《Journal of Geodesy》2018,92(2):149-168
We describe the computation of the first Australian quasigeoid model to include error estimates as a function of location that have been propagated from uncertainties in the EGM2008 global model, land and altimeter-derived gravity anomalies and terrain corrections. The model has been extended to include Australia’s offshore territories and maritime boundaries using newer datasets comprising an additional \({\sim }\)280,000 land gravity observations, a newer altimeter-derived marine gravity anomaly grid, and terrain corrections at \(1^{\prime \prime }\times 1^{\prime \prime }\) resolution. The error propagation uses a remove–restore approach, where the EGM2008 quasigeoid and gravity anomaly error grids are augmented by errors propagated through a modified Stokes integral from the errors in the altimeter gravity anomalies, land gravity observations and terrain corrections. The gravimetric quasigeoid errors (one sigma) are 50–60 mm across most of the Australian landmass, increasing to \({\sim }100\) mm in regions of steep horizontal gravity gradients or the mountains, and are commensurate with external estimates. 相似文献
7.
The effect of EGM2008-based normal, normal-orthometric and Helmert orthometric height systems on the Australian levelling network 总被引:4,自引:4,他引:0
This paper investigates the normal-orthometric correction used in the definition of the Australian Height Datum, and also computes and evaluates normal and Helmert orthometric corrections for the Australian National Levelling Network (ANLN). Testing these corrections in Australia is important to establish which height system is most appropriate for any new Australian vertical datum. An approximate approach to assigning gravity values to ANLN benchmarks (BMs) is used, where the EGM2008-modelled gravity field is used to ‘re-construct’ observed gravity at the BMs. Network loop closures (for first- and second-order levelling) indicate reduced misclosures for all height corrections considered, particularly in the mountainous regions of south eastern Australia. Differences between Helmert orthometric and normal-orthometric heights reach 44 cm in the Australian Alps, and differences between Helmert orthometric and normal heights are about 26 cm in the same region. Normal-orthometric heights differ from normal heights by up to 18 cm in mountainous regions >2,000 m. This indicates that the quasigeoid is not compatible with normal-orthometric heights in Australia. 相似文献
8.
A detailed gravimetric geoid in the North Atlantic Ocean, named DGGNA-77, has been computed, based on a satellite and gravimetry
derived earth potential model (consisting in spherical harmonic coefficients up to degree and order 30) and mean free air
surface gravity anomalies (35180 1°×1° mean values and 245000 4′×4′ mean values). The long wavelength undulations were computed
from the spherical harmonics of the reference potential model and the details were obtained by integrating the residual gravity
anomalies through the Stokes formula: from 0 to 5° with the 4′×4′ data, and from 5° to 20° with the 1°×1° data. For computer
time reasons the final grid was computed with half a degree spacing only. This grid extends from the Gulf of Mexico to the
European and African coasts.
Comparisons have been made with Geos 3 altimetry derived geoid heights and with the 5′×5′ gravimetric geoid derived byMarsh andChang [8] in the northwestern part of the Atlantic Ocean, which show a good agreement in most places apart from some tilts which
porbably come from the satellite orbit recovery. 相似文献
9.
2020珠峰高程测量,首次确定并发布了基于国际高程参考系统(IHRS)的珠峰正高。在珠峰地区实现国际高程参考系统,采用的方案是建立珠峰区域高精度重力大地水准面。利用地球重力场谱组合理论和基于数据驱动的谱权确定方法,测试优选参考重力场模型及其截断阶数和球冠积分半径等关键参数,联合航空和地面重力等数据建立了珠峰区域重力似大地水准面模型,61点高精度GNSS水准高程异常检核表明,模型精度达3.8 cm,加入航空重力数据后模型精度提升幅度达51.3%。提出顾及高差改正的峰顶高程异常内插方法,采用顾及地形质量影响的高程异常——大地水准面差距转换改正严密公式,使用峰顶实测地面重力数据,基于国际高程参考系统定义的重力位值W0和GRS80参考椭球,最终确定了国际高程参考系统中的高精度珠峰峰顶大地水准面差距。 相似文献
10.
为解决世界各国高程基准差异的问题,提出联合卫星重力场模型、地面重力数据、GNSS大地高、局部高程基准的正高或正常高,按大地边值问题法确定局部高程基准重力位差的方法。首先推导了利用传统地面"有偏"重力异常确定高程基准重力位差的方法;接着利用改化Stokes核函数削弱"有偏"重力异常的影响,并联合卫星重力场模型和地面"有偏"重力数据,得到独立于任何局部高程基准的重力水准面,以此来确定局部高程基准重力位差;最后利用GNSS+水准数据和重力大地水准面确定了美国高程基准与全球高程基准W0的重力位差为-4.82±0.05 m2s-2。 相似文献
11.
Local geoid determination combining gravity disturbances and GPS/levelling: a case study in the Lake Nasser area, Aswan, Egypt 总被引:1,自引:0,他引:1
C. C. Tscherning Awar Radwan A. A. Tealeb S. M. Mahmoud M. Abd El-Monum Ramdan Hassan I. El-Syaed K. Saker 《Journal of Geodesy》2001,75(7-8):343-348
The use of GPS for height control in an area with existing levelling data requires the determination of a local geoid and
the bias between the local levelling datum and the one implicitly defined when computing the local geoid. If only scarse gravity
data are available, the heights of new data may be collected rapidly by determining the ellipsoidal height by GPS and not
using orthometric heights. Hence the geoid determination has to be based on gravity disturbances contingently combined with
gravity anomalies. Furthermore, existing GPS/levelling data may also be used in the geoid determination if a suitable general
gravity field modelling method (such as least-squares collocation, LSC) is applied. A comparison has been made in the Aswan
Dam area between geoids determined using fast Fourier transform (FFT) with gravity disturbances exclusively and LSC using
only the gravity disturbances and the disturbances combined with GPS/levelling data. The EGM96 spherical harmonic model was
in all cases used in a remove–restore mode. A total of 198 gravity disturbances spaced approximately 3 km apart were used,
as well as 35 GPS/levelling points in the vicinity and on the Aswan Dam. No data on the Nasser Lake were available. This gave
difficulties when using FFT, which requires the use of gridded data. When using exclusively the gravity disturbances, the
agreement between the GPS/levelling data were 0.71 ± 0.17 m for FFT and 0.63 ± 0.15 for LSC. When combining gravity disturbances
and GPS/levelling, the LSC error estimate was ±0.10 m. In the latter case two bias parameters had to be introduced to account
for a possible levelling datum difference between the levelling on the dam and that on the adjacent roads.
Received: 14 August 2000 / Accepted: 28 February 2001 相似文献
12.
Four different implementations of Stokes' formula are employed for the estimation of geoid heights over Sweden: the Vincent
and Marsh (1974) model with the high-degree reference gravity field but no kernel modifications; modified Wong and Gore (1969)
and Molodenskii et al. (1962) models, which use a high-degree reference gravity field and modification of Stokes' kernel;
and a least-squares (LS) spectral weighting proposed by Sj?berg (1991). Classical topographic correction formulae are improved
to consider long-wavelength contributions. The effect of a Bouguer shell is also included in the formulae, which is neglected
in classical formulae due to planar approximation. The gravimetric geoid is compared with global positioning system (GPS)-levelling-derived
geoid heights at 23 Swedish Permanent GPS Network SWEPOS stations distributed over Sweden. The LS method is in best agreement,
with a 10.1-cm mean and ±5.5-cm standard deviation in the differences between gravimetric and GPS geoid heights. The gravimetric
geoid was also fitted to the GPS-levelling-derived geoid using a four-parameter transformation model. The results after fitting
also show the best consistency for the LS method, with the standard deviation of differences reduced to ±1.1 cm. For comparison,
the NKG96 geoid yields a 17-cm mean and ±8-cm standard deviation of agreement with the same SWEPOS stations. After four-parameter
fitting to the GPS stations, the standard deviation reduces to ±6.1 cm for the NKG96 geoid. It is concluded that the new corrections
in this study improve the accuracy of the geoid. The final geoid heights range from 17.22 to 43.62 m with a mean value of
29.01 m. The standard errors of the computed geoid heights, through a simple error propagation of standard errors of mean
anomalies, are also computed. They range from ±7.02 to ±13.05 cm. The global root-mean-square error of the LS model is the
other estimation of the accuracy of the final geoid, and is computed to be ±28.6 cm.
Received: 15 September 1999 / Accepted: 6 November 2000 相似文献
13.
Essam Ghanem 《地球空间信息科学学报》2001,4(1):19-23
1 IntroductionDifferentgeoidsolutionswerecarriedoutforE gyptusingheterogeneousdataanddifferentmethodologies (El_Tokhey ,1 993) .ThemaingoalofthispaperistodetermineamostaccuratenewgeoidforEgypttakingadvantageofanewupdatedgravitydatabase,theinformationgivenby… 相似文献
14.
Combining EGM2008 and SRTM/DTM2006.0 residual terrain model data to improve quasigeoid computations in mountainous areas devoid of gravity data 总被引:6,自引:4,他引:2
A global geopotential model, like EGM2008, is not capable of representing the high-frequency components of Earth’s gravity
field. This is known as the omission error. In mountainous terrain, omission errors in EGM2008, even when expanded to degree
2,190, may reach amplitudes of 10 cm and more for height anomalies. The present paper proposes the utilisation of high-resolution
residual terrain model (RTM) data for computing estimates of the omission error in rugged terrain. RTM elevations may be constructed
as the difference between the SRTM (Shuttle Radar Topography Mission) elevation model and the DTM2006.0 spherical harmonic
topographic expansion. Numerical tests, carried out in the German Alps with a precise gravimetric quasigeoid model (GCG05)
and GPS/levelling data as references, demonstrate that RTM-based omission error estimates improve EGM2008 height anomaly differences
by 10 cm in many cases. The comparisons of EGM2008-only height anomalies and the GCG05 model showed 3.7 cm standard deviation
after a bias-fit. Applying RTM omission error estimates to EGM2008 reduces the standard deviation to 1.9 cm which equates
to a significant improvement rate of 47%. Using GPS/levelling data strongly corroborates these findings with an improvement
rate of 49%. The proposed RTM approach may be of practical value to improve quasigeoid determination in mountainous areas
without sufficient regional gravity data coverage, e.g., in parts of Asia, South America or Africa. As a further application,
RTM omission error estimates will allow refined validation of global gravity field models like EGM2008 from GPS/levelling
data. 相似文献
15.
The separation between the reference surfaces for orthometric heights and normal heights—the geoid and the quasigeoid—is typically
in the order of a few decimeters but can reach nearly 3 m in extreme cases. The knowledge of the geoid–quasigeoid separation
with centimeter accuracy or better, is essential for the realization of national and international height reference frames,
and for precision height determination in geodetic engineering. The largest contribution to the geoid–quasigeoid separation
is due to the distribution of topographic masses. We develop a compact formulation for the rigorous treatment of topographic
masses and apply it to determine the geoid–quasigeoid separation for two test areas in the Alps with very rough topography,
using a very fine grid resolution of 100 m. The magnitude of the geoid–quasigeoid separation and its accuracy, its slopes,
roughness, and correlation with height are analyzed. Results show that rigorous treatment of topographic masses leads to a
rather small geoid–quasigeoid separation—only 30 cm at the highest summit—while results based on approximations are often
larger by several decimeters. The accuracy of the topographic contribution to the geoid–quasigeoid separation is estimated
to be 2–3 cm for areas with extreme topography. Analysis of roughness of the geoid–quasigeoid separation shows that a resolution
of the modeling grid of 200 m or less is required to achieve these accuracies. Gravity and the vertical gravity gradient inside
of topographic masses and the mean gravity along the plumbline are modeled which are important intermediate quantities for
the determination of the geoid–quasigeoid separation. We conclude that a consistent determination of the geoid and quasigeoid
height reference surfaces within an accuracy of few centimeters is feasible even for areas with extreme topography, and that
the concepts of orthometric height and normal height can be consistently realized and used within this level of accuracy. 相似文献
16.
Fitting gravimetric geoid models to vertical deflections 总被引:2,自引:2,他引:0
Regional gravimetric geoid and quasigeoid models are now commonly fitted to GPS-levelling data, which simultaneously absorbs
levelling, GPS and quasi/geoid errors due to their inseparability. We propose that independent vertical deflections are used
instead, which are not affected by this inseparability problem. The formulation is set out for geoid slopes and changes in
slopes. Application to 1,080 astrogeodetic deflections over Australia for the AUSGeoid98 model shows that it is feasible,
but the poor quality of the historical astrogeodetic deflections led to some unrealistic values. 相似文献
17.
This paper addresses implementation issues in order to apply non-stationary least-squares collocation (LSC) to a practical
geodetic problem: fitting a gravimetric quasigeoid to discrete geometric quasigeoid heights at a local scale. This yields
a surface that is useful for direct GPS heighting. Non-stationary covariance functions and a non-stationary model of the mean
were applied to residual gravimetric quasigeoid determination by planar LSC in the Perth region of Western Australia. The
non-stationary model of the mean did not change the LSC results significantly. However, elliptical kernels in non-stationary
covariance functions were used successfully to create an iterative optimisation loop to decrease the difference between the
gravimetric quasigeoid and geometric quasigeoid at 99 GPS-levelling points to a user-prescribed tolerance. 相似文献
18.
I. N. Tziavos 《Journal of Geodesy》1987,61(2):177-197
Mean gravity anomalies, deflections of the vertical, and a geopotential model complete to degree and order180 are combined in order to determine geoidal heights in the area bounded by [34°≦ϕ≤42°, 18°≦λ≦28°]. Moreover, employing point
gravity anomalies simultaneously with the above data, an attempt is made to predict deflections of the vertical in the same
area. The method used in the computations is least squares collocation. Using empirical covariance functions for the data,
the suitable errors for the different sources of observations, and the optimum cap radius around each point of evaluation,
an accuracy better than±0.60m for geoidal heights and±1″.5 for deflections of the vertical is obtained taking into account existing systematic effects. This accuracy refers to the
comparison between observed and predicted values. 相似文献
19.
Two numerical techniques are used in recent regional high-frequency geoid computations in Canada: discrete numerical integration
and fast Fourier transform. These two techniques have been tested for their numerical accuracy using a synthetic gravity field.
The synthetic field was generated by artificially extending the EGM96 spherical harmonic coefficients to degree 2160, which
is commensurate with the regular 5′ geographical grid used in Canada. This field was used to generate self-consistent sets of synthetic gravity anomalies and
synthetic geoid heights with different degree variance spectra, which were used as control on the numerical geoid computation
techniques. Both the discrete integration and the fast Fourier transform were applied within a 6∘ spherical cap centered at each computation point. The effect of the gravity data outside the spherical cap was computed using
the spheroidal Molodenskij approach. Comparisons of these geoid solutions with the synthetic geoid heights over western Canada
indicate that the high-frequency geoid can be computed with an accuracy of approximately 1 cm using the modified Stokes technique,
with discrete numerical integration giving a slightly, though not significantly, better result than fast Fourier transform.
Received: 2 November 1999 / Accepted: 11 July 2000 相似文献
20.
Unification of New Zealand’s local vertical datums: iterative gravimetric quasigeoid computations 总被引:2,自引:2,他引:0
New Zealand uses 13 separate local vertical datums (LVDs) based on geodetic levelling from 12 different tide-gauges. We describe
their unification using a regional gravimetric quasigeoid model and GPS-levelling data on each LVD. A novel application of
iterative quasigeoid computation is used, where the LVD offsets computed from earlier models are used to apply additional
gravity reductions from each LVD to that model. The solution converges after only three iterations yielding LVD offsets ranging
from 0.24 to 0.58 m with an average standard deviation of ±0.08 m. The so-computed LVD offsets agree, within expected data
errors, with geodetically levelled height differences at common benchmarks between adjacent LVDs. This shows that iterated
quasigeoid models have a role in vertical datum unification. 相似文献