Regional Gravimetric Geoid Model Research Articles

Utilizing Airborne LiDAR and UAV Photogrammetry Techniques in Local Geoid Model Determination and Validation

This investigation evaluates the performance of digital terrain models (DTMs) generated in different vertical datums by aerial LiDAR and unmanned aerial vehicle (UAV) photogrammetry techniques, for the determination and validation of local geoid models. Many engineering projects require the point heights referring to a physical surface, i.e., geoid, rather than an ellipsoid. When a high-accuracy local geoid model is available in the study area, the physical heights are practically obtained with the transformation of global navigation satellite system (GNSS) ellipsoidal heights of the points. Besides the commonly used geodetic methods, this study introduces a novel approach for the determination and validation of the local geoid surface models using photogrammetry. The numeric tests were carried out in the Bergama region, in the west of Turkey. Using direct georeferenced airborne LiDAR and indirect georeferenced UAV photogrammetry-derived point clouds, DTMs were generated in ellipsoidal and geoidal vertical datums, respectively. After this, the local geoid models were calculated as differences between the generated DTMs. Generated local geoid models in the grid and pointwise formats were tested and compared with the regional gravimetric geoid model (TG03) and a high-resolution global geoid model (EIGEN6C4), respectively. In conclusion, the applied approach provided sufficient performance for modeling and validating the geoid heights with centimeter-level accuracy.

Application of the one-step integration method for determination of the regional gravimetric geoid

The regional gravimetric geoid solved using boundary-value problems of the potential theory is usually determined in two computational steps: (1) downward continuing ground gravity data onto the geoid using inverse Poisson’s integral equation in a mass-free space and (2) evaluating geoidal heights by applying Stokes integral to downward continued gravity. In this contribution, the two integration steps are combined in one step and the so-called one-step integration method in spherical approximation is implemented to compute the regional gravimetric geoid model. Advantages of using the one-step integration method instead of the two integration steps include less computational cost, more stable numerical computation and better utilization of input ground gravity data (reduced in each integration step to avoid edge effects). A discrete form of the one-step integral equation is used to convert mean values of ground gravity anomalies into mean values of geoidal heights. To evaluate mean values of the integral kernel in the vicinity of the computation point, a fast and numerically accurate analytical formula is proposed using planar approximation. The proposed formula is tested to determine the regional gravimetric geoid of the Auvergne test area, France. Results show a good agreement of the estimated geoid with geoidal heights estimated at GNSS-levelling reference points, with the standard deviation for the difference of 3.3 cm. Considering the uncertainty of geoidal heights derived at the GNSS/levelling reference points, one can conclude the geoid models computed by the one-step and two-step integration methods have negligible differences. Thus, the one-step method can be recommended for regional geoid modelling with its methodological and numerical advantages.

A software package for computing a regional gravimetric geoid model by the KTH method

Nowadays, the geodetic community has aimed to determine 1-cm accuracy gravimetric geoid model, which satisfies the demands of most engineering applications. However, the gravimetric geoid determination is a difficult mission which needs an exclusive attention to obtain reliable results for this purpose. Today, Least-Squares Modification of Stokes (LSMS) formula which is so-called the KTH method (Swedish Royal Institute of Technology) has been performed in the regional geoid studies. Based upon the earlier investigations, the KTH method provides more reasonable results than the Remove Compute Restore technique, especially in roughly terrain with sparse terrestrial gravity data. Nevertheless, a compact and practical software package is now not available for users and researchers in geosciences. Thus, in this paper, a scientific software called “LSMSSOFT” is developed and presented by adding a new algorithm which speeds up the evaluation of Stokes’ integral. Afterwards, the LSMSSOFT is applied to a case study for the construction of a geoid model over the Auvergne test area in France. Consequently, the algorithm treated in the software and its results imply that the LSMSSOFT is an alternative software package for modelling the gravimetric geoid by the KTH method.

Evaluation of W0 in Canada using tide gauges and GOCE gravity field models

AbstractThe existing Canadian Geodetic Vertical Datum of 1928 (CGVD28) does not meet the needs of the modern user in terms of accuracy and accessibility. As a result, Canada plans to implement a geoid-based and global navigation satellite system (GNSS)-accessible vertical datum by 2013. One of the primary concerns in realizing this new vertical datum is to determine a W0 value that will represent the potential of the zero height surface. The objective of this study is to evaluate W0 by averaging the potential of points on the mean sea water surface utilizing tide gauge recordings and gravity field and steady-state ocean circulation explorer (GOCE)-based global geopotential models. In order to assess the performance of the GOCE-based models for the computation of W0, the models are extended with the high resolution gravitational model EGM2008. Regional gravimetric geoid models are also used for the estimation of W0. Additionally, local sea surface topography models are utilized in order to validate the W0 results at the tide gauges. Excluding the Arctic coast, the W0 values obtained from both tide gauges and oceanic sea surface topography models are not statistically different from the International Earth Rotation and Reference Systems Service (IERS) 2010 global conventional value 62636856.00 m2/s2.

Development of regional gravimetric geoid model and comparison with EGM2008 gravity-field model over Korea

We constructed a regional geoid model and compared it with the EGM2008 global gravity-field model to evaluate the performance of EGM2008 for Korea. By using the Remove–Compute–Restore (RCR) technique, we developed an improved gravimetric geoid model JNUGEOID2010 on a 1 × 1′ grid by combining the EIGEN-GL04C global geopotential model (GGM), 8316 land-gravity data, an altimetry-derived marine gravity model DNSC08, and the Shuttle Radar Topography Mission (SRTM) digital elevation model (DEM). The computations were done using a two-dimensional four-band spherical fast Fourier transform (FFT) with 100% zero padding. In addition, we compared the Korean national gravimetric geoid model KGEOID98 to EGM2008. For the comparison, geometric geoid heights derived from 735 GPS-levelling stations were used. The smallest standard deviation of geoid height differences is ± 0.163 m for EGM2008 to degree and order 2190. Thus, we conclude that the new model EGM2008 is superior to the two regional gravimetric geoid models, JNUGEOID2010 and KGEOID98, for Korea. Key words: Regional geoid model, EGM2008, Global geopotential models, GPS-levelling, geoid height, Korea.

Yet more evidence for a North‐South slope in the Australian Height Datum

The results here add to the body of evidence for a systematic north‐south error in the Australian Height Datum (AHD). Previous studies based solely on Global Positioning System (GPS) and a gravimetric geoid model have suffered from the ‘inseparability problem’, where it is not possible to discriminate between errors in the AHD and geoid. Instead, this study compares horizontal gradients of the AUSGeoid98 regional gravimetric geoid model with totally independent astrogeodetically observed vertical deflections at 741 Laplace stations across Australia. These comparisons do not show any significant latitude‐dependent residuals, thus significantly reducing the likelihood of a north‐south slope in AUSGeoid98. Subsequently using GPS and AUSGeoid98, now that the inseparability problem has been addressed, there is very compelling evidence for a real north‐south slope of ∼1.5m in the AHD.

The relation between rigorous and Helmert’s definitions of orthometric heights

Following our earlier definition of the rigorous orthometric height [J Geod 79(1-3):82–92 (2005)] we present the derivation and calculation of the differences between this and the Helmert orthometric height, which is embedded in the vertical datums used in numerous countries. By way of comparison, we also consider Mader and Niethammer’s refinements to the Helmert orthometric height. For a profile across the Canadian Rocky Mountains (maximum height of ~2,800 m), the rigorous correction to Helmert’s height reaches ~13 cm, whereas the Mader and Niethammer corrections only reach ~3 cm. The discrepancy is due mostly to the rigorous correction’s consideration of the geoid-generated gravity disturbance. We also point out that several of the terms derived here are the same as those used in regional gravimetric geoid models, thus simplifying their implementation. This will enable those who currently use Helmert orthometric heights to upgrade them to a more rigorous height system based on the Earth’s gravity field and one that is more compatible with a regional geoid model.

A strategy for determining the regional geoid by combining limited ground data with satellite-based global geopotential and topographical models: a case study of Iran

The computation of regional gravimetric geoid models with reasonable accuracy, in developing countries, with sparse data is a difficult task that needs great care. Here we investigate the procedu ...

Comparison of the qualities of recent global and local gravimetric geoid models in Iran

A number of regional gravimetric geoid models have recently been determined for the Iran area, and a common problem is to select the best model, e.g. for engineering applications. A related probl ...

EXPERIMENTS WITH TWO DIFFERENT APPROACHES TO GRIDDING TERRESTRIAL GRAVITY ANOMALIES AND THEIR EFFECT ON REGIONAL GEOID COMPUTATION

This paper compares the gridding of two types of terrestrial gravity anomaly prior to the computation of regional gravimetric geoid models over Australia. The aim is to investigate the effects of high-frequency components (by way of the terrain correction) on the resulting grid of mean gravity anomalies, and hence the geoid. The gravity anomaly types investigated comprise simple Bouguer anomalies and refined Bouguer anomalies, both computed using a constant topographic mass density. Irrespective of which anomaly type is used for gridding, the relevant additional correction terms are applied to yield an approximation of the mean Helmert anomaly. Regional gravimetric geoid models are then computed over Australia and compared with one another and with GPS-levelling points on the Australian Height Datum. This shows that the application of terrain corrections before or after gravity gridding has only a relatively small effect on the computed geoid in Australia.

EXPERIMENTS WITH TWO DIFFERENT APPROACHES TO GRIDDING TERRESTRIAL GRAVITY ANOMALIES AND THEIR EFFECT ON REGIONAL GEOID COMPUTATION

This paper compares the gridding of two types of terrestrial gravity anomaly prior to the computation of regional gravimetric geoid models over Australia. The aim is to investigate the effects of high-frequency components (by way of the terrain correction) on the resulting grid of mean gravity anomalies, and hence the geoid. The gravity anomaly types investigated comprise simple Bouguer anomalies and refined Bouguer anomalies, both computed using a constant topographic mass density. Irrespective of which anomaly type is used for gridding, the relevant additional correction terms are applied to yield an approximation of the mean Helmert anomaly. Regional gravimetric geoid models are then computed over Australia and compared with one another and with GPS-levelling points on the Australian Height Datum. This shows that the application of terrain corrections before or after gravity gridding has only a relatively small effect on the computed geoid in Australia.