Local Vertical Datum Research Articles

Heterogeneous data management and modeling for the gravimetric geoid model: a review study in Pakistan

The gravimetric geoid model can be used as vertical reference in surveying and other related technologies. It is being developed by NESCOM in collaboration with the Department of Earth sciences QAU, Survey of Pakistan and Directorate General of Petroleum Concessions (DGPC). The data collection, selection, and analysis to make the data suitable for this purpose are being carried out. About 77,834 land gravity observations along with leveling and 11,787 Bouguer/free-air anomalies from GTECH are available and readily accessible. While GPS/leveling data for the whole Pakistan region is required and is being collected from different sources, though its density and quantity is not good enough for better calibration of gravimetric geoid. This study involves the feasibility and application of different datasets for the development of geoid model of Pakistan. The SRTM30 digital elevation model has been selected for topographic corrections and reductions due to its relatively better statistical comparison with local elevation data. Both least square collocation and FFT methods have been applied for this study. Two realistic studies have been carried out for global geopotential model selection based on statistical findings and evaluation of geoid-quasigeoid separation term in Pakistan. Geoid-quasigeoid separation term is an integral part of “Restore step” for geoid modeling with the utilization of the solution of the Molodensiky’s geodetic boundary value problem. The digital elevation model comparison with local leveling data shows that SRMT30 model is relatively better in accuracy (in terms of mean and standard deviation) than other counterparts such as Globe30, GTOPO30, and ETOPO2, etc. The results of geoid modeling have revealed that there exists a height bias of −70 cm between local vertical datum and global mean sea level.

Analysis of a relative offset between vertical datums at the North and South Islands of New Zealand

The leveling networks realized by 13 different local vertical datums were jointly readjusted at the South and North Islands of New Zealand. The relation between these two leveling networks and the Word Height System was then defined using GPS-leveling data and the EGM08 global geopotential model. In this study, we investigate the relative offset between these two vertical datum realizations. This is done based on comparison of the geometric geoid/quasigeoid heights (obtained from GPS and newly adjusted leveling data) with the regional gravimetric geoid/quasigeoid solutions. Moreover, oceanographic and geodetic models of mean dynamic topography (MDT) are used to assess the relative offset between these two vertical datum realizations through the analysis of regional spatial variations of mean sea level (MSL). The comparison of GPS-leveling data with regional gravimetric solutions re- veals large systematic distortions (exceeding several deci- meters across New Zealand) between the geometric and gravimetric geoid/quasigeoid heights attributed mainly to systematic errors within regional gravimetric solutions. The presence of a significant offset between the vertical datum realizations at the North and South Islands is not confirmed. The MSL difference between tide gauges in Wellington and Dunedin of ∼24 cm is estimated based on the analysis of MDT models.

Estimating Canadian vertical datum offsets using GNSS/levelling benchmark information and GOCE global geopotential models

AbstractThe performance of GOCE-based geopotential models is assessed for the estimation of offsets for three regional vertical datums in Canada with respect to a global equipotential surface using the GNSS benchmarks from the first-order vertical control network. Factors that affect the computed value of the local vertical datum offset include the GOCE commission and omission errors, measurement errors, the configuration of the network of GNSS/levelling benchmarks, and systematic levelling errors and distortions propagated through the vertical control network. Among these various factors, the effect of the GOCE omission error on the datum offsets is investigated by extending the models with the high resolution gravity field model EGM2008 and by means of Canada’s official high resolution geoid model CGG2010. The effect of the GOCE commission error in combination with errors from the GNSS/levelling data is also examined, in addition to the effect of systematic levelling errors. In Canada, the effect of the GOCE omission error is at the dm-level when computing local vertical datum offsets. The effect of including accuracy information for the GNSS/levelling data and the GOCE geoid heights can be up to 4 cm over the Canadian mainland and at the dm-level for island regions. Lastly, the spatial tilts found in the levelling network can be modelled with a 2-parameter bias corrector model, which reduces the RMS of the adjusted geoid height differences by 4 cm when compared to the RMS of adjusted geoid height differences computed without the use of a bias corrector model. Thus, when computing local vertical datum offsets in Canada, it is imperative to account for GOCE commission and omission errors, ellipsoidal and levelling height errors, as well as the systematic levelling errors of the vertical control network.

Application of the BEM approach for a determination of the regional marine geoid model and the mean dynamic topography in the Southwest Pacific Ocean and Tasman Sea

Application of the BEM approach for a determination of the regional marine geoid model and the mean dynamic topography in the Southwest Pacific Ocean and Tasman SeaWe apply a novel approach for the gravimetric marine geoid modelling which utilise the boundary element method (BEM). The direct BEM formulation for the Laplace equation is applied to obtain a numerical solution to the linearised fixed gravimetric boundary-value problem in points at the Earth's surface. The numerical scheme uses the collocation method with linear basis functions. It involves a discretisation of the Earth's surface which is considered as a fixed boundary. The surface gravity disturbances represent the oblique derivative boundary condition. The BEM approach is applied to determine the marine geoid model over the study area of the Southwest Pacific Ocean and Tasman Sea using DNSC08 marine gravity data. The comparison of the BEM-derived and EGM2008 geoid models reveals that the geoid height differences vary within -25 and 18 cm with the standard deviation of 6 cm. The DNSC08 sea surface topography data and the new marine geoid are then used for modelling of the mean dynamic topography (MDT) over the study area. The local vertical datum (LVD) offsets estimated at 15 tide-gauge stations in New Zealand are finally used for testing the coastal MDT. The average value of differences between the MDT and LVD offsets is 1 cm.

A Re-Evaluation of the Offset in the Australian Height Datum Between Mainland Australia and Tasmania

The adoption of local mean sea level (MSL) at multiple tide-gauges as a zero reference level for the Australian Height Datum (AHD) has resulted in a spatially variable offset between the geoid and the AHD. This is caused primarily by sea surface topography (SSTop), which has also resulted in the AHD on the mainland being offset vertically from the AHD on the island of Tasmania. Errors in MSL observations at the 32 tide-gauges used in the AHD and the temporal bias caused by MSL observations over different time epochs also contribute to the offset, which previous studies estimate to be between ∼+100 mm and ∼+400 mm (AHD on the mainland above the AHD on Tasmania). This study uses five SSTop models (SSTMs), as well as GNSS and two gravimetric quasigeoid models, at tide-gauges/tide-gauge benchmarks to re-estimate the AHD offset, with the re-evaluated offset between −61 mm and +48 mm. Adopting the more reliable CARS2006 oceanographic-only SSTM, the offset is −12 ± 11 mm, an order of magnitude less than three previous studies that used geodetic data alone. This suggests that oceanographically derived SSTMs should be considered as a viable alternative to geodetic-only techniques when attempting to unify local vertical datums.

Estimation of the zero-height geopotential level W o LVD in a local vertical datum from inversion of co-located GPS, leveling and geoid heights: a case study in the Hellenic islands

The estimation of the zero-height geopotential level of a local vertical datum (LVD) is a key task towards the connection of isolated physical height frames and their unification into a common vertical reference system. Such an estimate resolves, in principle, the ‘ambiguity’ of a traditional crust-fixed LVD by linking it with a particular equipotential surface of Earth’s gravity field under the presence of an external geopotential model. The aim of this paper is to study the estimation scheme that can be followed for solving the aforementioned problem based on the joint inversion of co-located GPS and leveling heights in conjunction with a fixed Earth gravity field model. Several case studies with real data are also presented that provide, for the first time, precise estimates of the LVD offsets for a number of Hellenic islands across the Aegean and Ionian Sea.

Error propagation for three common height-system corrections to differential levelling

This paper investigates the propagation of input data errors through the application of Helmert orthometric, normal and normal-orthometric height corrections to differential levelling observations, these being the three principal height systems in practical use around the world. Height corrections are required to remove the systematic error resulting from the geometric non-parallelism of the Earth's equipotential surfaces, but different height systems propagate errors differently. These systematic errors are thus present within levelling networks and subsequently in local vertical datums. Here, we show that the Helmert orthometric correction is sensitive to errors in the mean value of gravity along the plumbline, particularly for heights above 1000 m. The normal correction is much less sensitive due to the use of normal gravity along the normal plumbline. The normal-orthometric correction of Rapp (1961) is largely insensitive to such errors, but it does not properly correct for the non-parallelism of the Earth's equipotential surfaces. Information showing the circumstances under which survey practitioners should apply height corrections to levelling lines is provided, demonstrating that normal-orthometric corrections only need be applied to class LC levelling lines that are to be used for large levelling networks extending in the north-south direction, particularly at high elevations.

The NZGeoid09 Model of New Zealand

The NZGeoid09 gravimetric quasigeoid model of New Zealand was computed through FFT-based Stokesian integration with a deterministically modified kernel and an iterative computation approach that accounts for offsets among New Zealand's 13 different local vertical datums (LVDs). NZGeoid09 is an improvement over the previous NZGeoid05 due to use of the EGM2008 and DNSC08GRA models, and due to improvements to the data processing strategy. The integration parameters of degree of kernel modification L=40 and cap radius ψ0=2.5° were determined empirically through a comparison with 1422 GPS/levelling observations, after the LVD offsets had been removed. The precision of NZGeoid09 was assessed using the same GPS/levelling dataset, yielding an overall standard deviation of 6.2 cm. NZGeoid09 performs better than NZGeoid05 and marginally better than EGM2008, but few data are available in the Southern Alps of New Zealand to give a better evaluation.

Combined approach for the unification of levelling networks in New Zealand

Combined approach for the unification of levelling networks in New ZealandThe unification of levelling networks in New Zealand is done using a combined approach. It utilises the joint levelling network adjustment and the geopotential-value approach. The levelling and normal gravity data are used for a joint adjustment of the levelling networks at the South and North Islands of New Zealand while fixing the heights of tide gauges in Dunedin and Wellington. The results reveal a good quality of levelling data; the STD of residuals is 2 mm for the whole country. The comparison of the newly determined and original normal-orthometric heights confirms the presence of large local vertical datum offsets and systematic levelling errors. Since the geopotential-value approach is based on the Molodensky's theory, the newly adjusted normal-orthometric heights are converted to the normal heights. This conversion is based on applying the cumulative normal to normal-orthometric height correction computed from levelling and gravity anomaly data. In the absence of the observed gravity data the gravity anomalies along levelling lines are generated fromEGM2008. The GPS-levelling data and EGM2008 are used to estimate the average offsets of the jointly adjusted levelling networks at the North and South Islands with respect to World Height System defined by the adopted geoidal geopotential value of W0 = 62636856 ± 0.5 m2s-2; the estimated offsets are 10.6 cm and 27.5 cm.

Assessment of the LVD offsets for the normal-orthometric heights and different permanent tide systems—a case study of New Zealand

The geopotential-value approach is utilized in this study to estimate the average offsets of local vertical datums (LVDs) in New Zealand realized in the system of normal-orthometric heights. The LVD offsets are taken relative to the World Height System (WHS). We adopt the geoidal geopotential value W 0 = 62,636,856 m2 s−2 for a definition of WHS. The conversion of heights between different permanent tide systems is taken into consideration. The geopotential-value approach utilizes Molodensky’s theory of the normal heights. The normal-orthometric heights at global positioning system (GPS)-leveling points are thus first converted to the normal heights. The normal to normal-orthometric height correction is computed and applied along the leveling lines using the leveling data, and the gravity disturbances are computed approximately from the EGM08 global geopotential model. The numerical study is conducted for 18 LVDs in the North and South Islands of New Zealand. The LVD offsets are estimated from EGM08 to GPS-leveling data. The estimated average LVD offsets vary between 1 cm (Wellington 1953 LVD) and 37 cm (One Tree Point 1964 LVD).

Comparison of global geopotential models from the champ and grace missions for regional geoid modelling in Turkey

The continuous efforts on establishment and modernization of the geodetic control in Turkey include a number of regional geoid models that have been determined since 1976. The recently released gravimetric Geoid of Turkey, TG03, is used in geodetic applications where GPS-heights need to be converted to the local vertical datum. To reach a regional geoid model with improved accuracy, the selection of the appropriate global geopotential model is of primary importance. This study assesses the performance of a number of recent satellite-only and combined global geopotential models (GGMs) derived from CHAMP and GRACE missions’ data in comparison to the older EGM96 model, which is the underlying reference model for TG03. In this respect, gravity anomalies and geoid heights from the global geopotential models were compared with terrestrial gravity data and low-pass filtered GPS/levelling data, respectively. Also, five new gravimetric geoid models, computed by the Fast Fourier Transform technique using terrestrial gravity data and the geopotential models, were validated at the GPS/levelling benchmarks. The findings were also compared with the validation results of the TG03 model.

Mapping the geoid for Iberia and the Macaronesian Islands using multi-sensor gravity data and the GRACE geopotential model

A new gravimetric geoid model (ICAGM07) has been determined for the North-East Atlantic Ocean, Iberia, and the Macaronesian Islands using multi-sensor gravity data and a GRACE derived Earth geopotential model. A high resolution gravity model, determined using least squares optimal interpolation of marine, land, and satellite derived gravity anomalies, was used to resolve the medium and short wavelengths of the geoid. Long wavelengths of the geoid were provided by the GRACE derived Earth geopotential model. The topographic effects were computed in the spectral domain using a high resolution (100 m) digital terrain model derived from SRTM mission data and cartographic charts. The remove–restore technique was used to compute the geoid model on a 1.5′ grid, and the residual geoid height was computed using spherical FFT and a modified Stokes’ kernel. The effects of different Earth tide models on the geoid were computed and analysed. Comparison over the sea with an oceanographic geoid determined from CLS01 MSSH and Rio05 MDT yield a relative accuracy of 8 cm, with larger differences close to the shoreline. Over land, comparisons with 1646 GPS/levelling marks indicate an overall precision of 8–10 cm and relative vertical datum offsets of up to 2 m. This new geoid model represents a significant improvement over existing geoid models, with a homogeneous relative accuracy of 8–10 cm over both marine and land areas, and exposes the inaccuracies of local vertical datums as references for studies of vertical deformation.

GNSS‐based heighting in Australia: Current, emerging and future issues

Ellipsoidal heights, i.e., w.r.t. a geometrical Earth figure, determined from Global Navigation Satellite Systems (GNSS) are inherently their least accurate coordinate, due mainly to satellite geometry and atmospheric refraction. For most practical purposes, however, these GNSS‐derived ellipsoidal heights have to be transformed to heights that relate to the Earth's gravity field, which generally adds further uncertainty. The reduction in accuracy of the transformed height is due to errors in gravimetric quasi/geoid models, but this is compounded yet further in Australia and elsewhere because of the imperfect realisation of local vertical datums. This paper comments upon current, emerging and future issues with height determination on the Australian Height Datum (AHD) using GNSS. This comprises the reference frame used for GNSS ellipsoidal heights, theory‐ and data‐driven inaccuracies in modelling the quasi/geoid, and deficiencies in the realisation of the AHD. While some of these issues will be redressed, in part, by the production of AUSGeoid2008 that is fitted to the AHD, there will always be the need to routinely apply checks on GNSS‐derived heights in Australia, and elsewhere.

Height datum unification between Shenzhen and Hong Kong using the solution of the linearized fixed-gravimetric boundary value problem

The paper proposes a new algorithm to unify height datums in different regions, which is based on the solution of the linearized fixed-gravimetric boundary value problem. Compared with traditional methods, this method uses GPS ellipsoidal height and gravity disturbances on the surface of the earth to obtain a quasigeoid, which is not related to any local vertical datums. As an example, we calculate the height datum difference between Shenzhen and Hong Kong by applying this new method. The result shows that the height difference obtained by this new method is consistent with the ground leveling result to a few centimeters.

Unification of New Zealand’s local vertical datums: iterative gravimetric quasigeoid computations

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.

A Global Vertical Reference Frame Based on Four Regional Vertical Datums

A Global Vertical Reference Frame (GVRF) has been realized by means of several regional and local vertical datums (LVD) distributed world-wide: the North American Vertical Datum 1988 (NAVD 88), Australian Height Datum 1971 (AHD 71), LVD France, Institute Geographique National 1969 (IGN 69) and Brazilian Height Datum 1957 (BHD 57). The vertical shifts of the above LVD origins have been related to the adopted reference geopotential value W 0 = (62 636 856.0 ± 0.5) m2s−2 and they were determined at the 5 cm level. However, the W 0 reference value can be chosen arbitrarily, the methodology, which was developed here, does not require that the above value be adopted.

Absolute and relative testing of gravimetric geoid models using Global Positioning System and orthometric height data

The verification of gravimetric geoid models on land is presented using co-located Global Positioning System (GPS) and orthometric heights. This is undertaken in an absolute sense, which also constrains the zero-degree term in the geoid, and in a relative sense, which indicates the appropriateness of the gravimetric geoid model for transforming GPS-derived ellipsoidal heights to the local vertical datum. Two computer programs are presented for these purposes, which can also be used for comparing other types of discrete and gridded data. A case study is used to illustrate the use of these approaches and software to validate gravimetric geoid models in Western Australia.

Determination of Geopotential Differences between Local Vertical Datums and Realization of a World Height System

The methodology developed for connecting Local Vertical Datums (LVD) was applied to the Australian Height Datum (AHD) and the North American Vertical Datum (NAVD88). The geopotential values at AHD and NAVD88 were computed and the corresponding vertical offset of 974 mm with rms 51 mm was obtained between the zero reference surfaces defined by AHD and NAVD88. The solution is based on the four primary geodetic parameters, the GPS/levelling sites and the geopotential model EGM96. The Global Height System (or the Major Vertical Datum) can be defined by a geoidal geopotential value used in the solution as the reference value, or by the geopotential value of the LVD, e.g. NAVD88.

On the adjustment of combined GPS/levelling/geoid networks

A detailed and statistically rigorous treatment of adjustment problems in combined GPS/levelling/geoid networks is given in this paper. The two main types of ”unknowns” in this kind of multi-data ID networks are the gravimetric geoid accuracy and a 2D spatial field that describes all the systematic distortions among the available height data sets. An accurate knowledge of the latter becomes especially important when we consider employing GPS techniques for levelling purposes with respect to a local vertical datum. Various modeling alternatives for the correction field are presented, namely a pure discrete deterministic model, a hybrid deterministic and stochastic model, and finally a pure stochastic model. Variance component estimation is also introduced as an important tool for assesing the actual geoid noise level, and checking a-priori given geoid error models. In addition, theoretical comparisons are made with some of the already established adjustment models that have been used in practice. The problem of statistical testing of various model components (data noise, deterministic model, stochastic model) in such networks is also discussed. Finally, some conclusions are drawn and a few recommendations for further study are pointed out.

GEOIDAL GEOPOTENTIAL AND WORLD HEIGHT SYSTEM

The geoidal geopotential value of W 0 = 62 636 856.0 ± 0.5m 2 s −2 , determined from the 1993 –1998 TOPEX/POSEIDON altimeter data, can be used to practically define and realize the World Height System. The W 0 -value can also uniquely define the geoidal surface and is required for a number of applications, including General Relativity in precise time keeping and time definitions. Furthermore, the W 0 -value provides a scale parameter for the Earth that is independent of the tidal reference system. All of the above qualities make the geoidal potential W 0 ideally suited for official adoption as one of the fundamental constants, replacing the currently adopted semi-major axis a of the mean Earth ellipsoid. Vertical shifts of the Local Vertical Datum (LVD) origins can easily be determined with respect to the World Height System (defined by W 0 ), in using the recent EGM96 gravity model and ellipsoidal height observations (e.g. GPS) at levelling points. Using this methodology the LVD vertical displacements for the NAVD88 (North American Vertical Datum 88), NAP (Normaal Amsterdams Peil), AMD (Australian Height Datum), KHD (Kronstadt Height Datum), and N60 (Finnish Height Datum) were determined with respect to the proposed World Height System as follows: −55.1 cm, −11.0 cm, +42.4 cm, −11.1 cm and +1.8 cm, respectively.