Figure 1 - uploaded by Ronald Ssengendo
Content may be subject to copyright.
Source publication
This study is devoted to the determination of a high resolution gravimetric geoid model for Uganda based on the optimal combination of terrestrial and satellite gravity anomalies using the method of Least Squares Modification of Stokes’ formula with additive corrections. Specifically the study investigates the current status of the existing Uganda...
Similar publications
William Sealy Gosset, otherwise known as "Student", was one of the pioneers in the development of modern statistical method and its application to the design and analysis of experiments. Although there were no computers in his time, he discovered the form of the "t distribution" by a combination of mathematical and empirical work with random number...
Citations
... In this study, the Tandem-X DEM with 12 and 30 m resolutions provided by DLR are used in the geoid computation as shown in Fig. 2. Prior to geoid computation, the Global Geopotential Model (GGM) is required in the gridding process of the gravity data. In this study, the geoid computation is performed through the LSMSA method, where the GGM is employed together with the terrestrial gravity data to produce approximate geoid heights (Ssengendo, 2015). Hence, the selection of the ideal GGM is crucial to produce a precise gravimetric geoid model. ...
... As stated by Sjöberg et al. (2015) and after numerous studies, the geoid model in their interest region has been successfully developed via this method. The regions include New Zealand (Abdalla and Tenzer, 2011), Turkey (Abbak et al., 2012), Uganda (Sjöberg et al., 2015;Ssengendo, 2015), Poland (Kuczynska-Siehien et al., 2016), Peninsular Malaysia (Sulaiman, 2016;Pa'suya et al., 2019Pa'suya et al., , 2021, etc. Figure 7 illustrates the computation processes of the gravimetric and hybrid geoid models over Peninsular Malaysia. Basically, the grid surface gravity anomalies and selected GGM are exploited to compute the approximate geoid undulation ( N ) by the Stokes integration, as follows (Sjöberg, 2003a): ...
We describe the development of a hybrid geoid model for Peninsular Malaysia, based on two approaches. The first approach is utilising an ordinary method fitting the gravimetric geoid to the geometric undulation derived from GNSS-levelling data; the second approach directly fits the gravimetric geoid to the reference mean sea level derived from the tide measurements of Port Klang tide gauge station. The hybrid geoid model fitted to Port Klang (PMHGG2020_PK) is produced by adding an offset of 0.446 m to the gravimetric geoid, based on the comparison at the tide gauge benchmark. To calculate the gravimetric geoid, a new model for Peninsular Malaysia (PMGG2020) has been developed based on Least-Squares Modification of Stokes’ Formula with Additive correction (LSMSA). Three different sources of gravity data which are terrestrial, airborne, and satellite altimetry-derived gravity anomaly (DTU17) have been combined to construct the geoid model. The height information has been extracted from the newly released global digital elevation model, TanDEM-X DEM. GO_CONS_GCF_2_SPW_R4 model derived from GOCE data provides long-wavelengths gravity field up to maximum degree and order 130. The gravity datasets are gridded by 3D Least-Squares Collocation method. The PMGG2020 model is consistent with the geometric geoid heights from 173 GNSS-levelling measurements, with a standard deviation of ±5.8 cm. Evaluation of the hybrid geoid model constructed from the first approach shows a significant improvement over the two existing hybrid geoid models. The accuracy of ±4.6 cm has been achieved after evaluating by 20 GNSS-levelling points, externally. Hybrid geoid model fitted to Port Klang has also been evaluated via 173 GNSS-levelling points, and the result shows that 71% of the total data exhibit height differences lower than 10 cm. The overall results indicate that the hybrid geoid model developed in this study can be valuable as an alternative to the current modern height system in Peninsular Malaysia for surveying and mapping.
... Among the available methods, three popular methods are commonly applied in geoid determination: (1) the removal-compute-restore (RCR) (Forsberg and Tscherning 1981;Schwarz et al. 1990), (2) Stokes-Helmert (Vaníček and Sjöberg 1991), and (3) the least square modification of Stokes with additive correction (LSMSA), also called the KTH method (Sjöberg 1984(Sjöberg , 1991(Sjöberg , 2003a(Sjöberg , 2003b. The RCR method developed at the University of Copenhagen in Denmark is an excellent method that is widely used for geoid computation in most parts of the world, including Canada (Véronneau et al. 2006;Huang and Véronneau 2013), Malaysia (Nordin et al. 2005), South Korea (Bae et al. 2012;Lee and Kim 2012;Lee 2018), East Malaysia (Jamil et al. 2017), China (Jiang 2018), Argentina (Piñón et al. 2018), Vietnam (Vu et al. 2019), Taiwan (Hsiao et al. 2017;Hwang et al. 2020), Colorado , Nigeria (Odumosu and Nnam 2020), Japan (Matsuo and Kuroishi 2020), and Turkey (Erol et al. 2020 Meanwhile, the KTH method developed at the Royal Institute of Technology has become an alternative method for the computation of the geoid model and has also been implemented in numerous countries, including Sweden (Ågren and Sjöberg 2014), Iran (Kiamehr 2007;Kiamehr and Sjöberg 2005), Tanzania (Ulotu 2009), Central Turkey (Abbak et al. 2012a), Uganda (Sjöberg et al. 2015;Ssengendo 2015), and Peninsular Malaysia (Sulaiman 2016;Pa'suya et al. 2019a). However, there is no consensus regarding the ideal method to contribute to the optimal results between the RCR and KTH methods; they differ in computation steps but have similar computation processes (Varga 2018). ...
... A cross-validation approach was implemented to identify any outliers in the database. Introduced by Geisser and Eddy (1979), this method has been employed in various studies to identify the quality of terrestrial gravity data (Danila 2012;Ssengendo 2015;Sulaiman 2016); details about the cross-validation procedures have been discussed by Kiamehr (2007). Through visual inspection and cross-validation, a total of 461 points were eliminated due to erroneous positions and duplicate points, representing 5.4% of the original number of points (8474 points). ...
We compute a new gravimetric geoid model for Peninsular Malaysia (PMGG2020) based on the Royal Institute of Technology (KTH) method. The PMGG2020 was computed from 8474 terrestrial gravity points, satellite altimetry-derived gravity anomaly (DTU17), 24,855 airborne gravity data, and the TanDEM-X Digital Elevation Model. All the gravity datasets were combined and gridded onto a 1-min resolution using the 3D Least Square Collocation (LSC) method with EIGEN-6C4 as the reference field. GO_CONS_GCF_2_SPW_R4 was used to provide long wavelengths of gravity field up to 130 maximum degrees and order in the geoid computation. Based on an evaluation using 173 Global Navigation Satellite System (GNSS)-levelling points distributed over Peninsular Malaysia, the precision of the PMGG2020 was 0.058 m. It is almost identical to the accuracy of the official Peninsular Malaysia gravimetric geoid, WMG03A. Using airborne gravity, the precision of PMGG2020 showed a significant improvement of ~4 cm over the existing KTH-derived geoid model, PMSGM2014. These results highlight the significant effect of airborne gravity data on the accuracy of the geoid model.
... The relationship between the orthometric height, ellipsoidal height, and geoid height[96]. ...
Determining the correct height of mountain peaks is vital for tourism, but it is also important as a reference point for devices equipped with GPS (e.g. watches or car navigation systems). The peak altitude data is part of the geographic and geodetic information. As more modern technologies and equipment become available, their precision should increase. However, verification of peak heights is usually only conducted for the highest, well-known mountains, and lower peaks or mountain passes are rarely verified. Therefore, this study focused on an investigation of 12 alti-tude points on a section of the longest and most famous touristic trail in Poland (the Main Beskid Trail), located in the Orava-Żywiec Beskids Mts. The aim of this research was to measure and verify the heights of the 12 selected mountain peaks, in addition to evaluating the chosen methods based on the quality of the obtained data and determining their suitability and oppor-tunity for use in further research. Measurements were obtained at the most specific height-points – on the 12 highest points of the summits. This study compared two modern measurement techniques: the Global Navigation Satellite Systems (GNSS) and light detection and ranging (LiDAR). The obtained results were later compared with those widely used on the internet and in printed materials (period covered: 1884–2015). This analysis demonstrated that lesser-known objects are rarely the subject of remeasurement and significant altitude errors may occur, pri-marily because the heights originate from a source in the past when modern methods were not available. Our findings indicate that the heights of the peaks presented in cartographic materials are inaccurate. The assumed heights should be corrected by direct measurement using modern techniques.
... The current GGMs, representing the Earth's gravitational field, can be classified into three groups: satellite-only, combined and tailored gravity field models. The satellite only GGMs are derived from the tracking and analysis of the orbits of artificial Earth satellites only [20]. The combined GGMs include satellite gravity data, terrestrial gravity data and satellite altimetry data. ...
The use of GNSS to determine the orthometric
height requires a geoid model which is used as a
transformation linkage between ellipsoidal height and
orthometric height. GNSS derived ellipsoidal height is purely
mathematical, having no physical meaning. So, in most of the
geodetic applications, it is necessary to use physically defined
orthometric height. Orthometric height can be obtained
accurately from traditional spirit levelling which is laborintensive,
tedious and costly. Conversion of GNSS-derived
ellipsoidal height into orthometric height is the popular
surveying technique in GNSS user community. This
approach is required to integrate a geoid model which
provides separation of geoid with reference ellipsoid. The
EGM2008, a global geoid model is widely employed for the
purpose yielding sub-meter accuracy. This paper evaluated
the orthometric height derived from GNSS measurements
and Global Geo-potential Model, EGM2008 in Bangladesh.
GNSS Survey as well as spirit levelling was carried out
connecting fifteen points distributed in the area. GNSS
observations were taken using dual frequency geodetic
receivers in differential static mode and levelling works were
carried out using digital levels. The geoidal undulation for
the corresponding points were obtained using the EGM2008
Geoid model. The orthometric height of these points are
computed using ellipsoidal height and the geoid undulation.
These heights are compared with the orthometric heights
obtained from levelling. The difference in these two, was
used to compute the root mean square error, mean and
standard deviation which are found 17.57 cm, 17.18 cm and
3.76 cm, respectively. The results show that EGM2008 model
is appropriate with root mean square errors. It is proven
that orthometric height can be obtained at centimeter level
accuracy by this method for any Engineering, Surveying or
Mapping works where rapid heights are required.
... However, the accuracy of GGMs and GDEMs should be analyzed in order to choose the optimum GGMs and GDEMs for the geoid modelling. According to Ssengendo (2015), any error in the GDEMs will affect the accuracy of the geoid model. Thus, the goal of this study is to evaluate the accuracy of several GDEMs and GGMs using GNSS and levelling data in the southern part of the Peninsular Malaysia as shown in Fig. 1. ...
In modeling of geoid model, global digital elevation models (GDEMs) and global geopotential models (GGMs) involve in most part of the geoid computation process. Any errors in GDEMs and GGMs will introduce errors directly in geoid computation. Therefore, this study aims to evaluate the six recent GGMs and new digital elevation model from TanDEM-X, as well as the previously available GDEMs, SRTM GDEMs, over the southern region of Peninsular Malaysia. The evaluation of GDEMs has been performed with the use of high-precision Global Navigation Satellite System (GNSS) and EGM96 as vertical reference consisting of 277 stations. Meanwhile, the evaluation of GGMs is carried out using sixty-two (62) collocated GPS/leveling benchmarks (BMs). Based on the statistical analysis, it is shown that the improvement of DEM from TanDEM-X data is compared to the previously available DEMs, SRTM GDEMs. DEM from TanDEM-X of 30-m arc resolution is much better than TanDEM-X of 12-m arc resolution, as well as SRTM 30m and 90m. Comparison of GGMs with GNSS leveling shows that geoid height from GOCO05c fits well with the local geoid model.
... GNSS can provide three- dimensional coordinates (latitude, longitude, and heights) anytime and anywhere in the world. However, the GNSS-determined heights are geometrical heights, which cannot be used in surveying and engineering projects as these do not define hydraulic head (Ssengendo, 2015). Horizontal datum is one which is used to describe the two-dimensional position or the so- called x, y position of a point on earth. ...
India, whose vertical datum dates back to 1905, has an urgent need for an accurate geoid model with a basic aim to redefine the vertical datum. Researchers from various organizations of the country have tried to develop regional/local gravimetric geoid models. Survey of India has recently launched geoid model for the country. This paper aims at reviewing the status of efforts in developing geoid models for various parts of the country. Different prevailing methods of geoid computation are discussed. The paper throws light on the importance of various datasets needed for computation of a precise geoid and briefly discusses corrections incorporated during the computation. The paper concludes with some suggestions for developing the high precision geoid model.
Since 2006, several different groups have computed geoid and/or quasigeoid (quasi/geoid) models for the Auvergne test area in central France using various approaches. In this contribution, we compute and compare quasigeoid models for Auvergne using Curtin University of Technology's and the Swedish Royal Institute of Technology's approaches. These approaches differ in many ways, such as their treatment of the input data, choice of type of spherical harmonic model (combined or satellite-only), form and sequence of correction terms applied, and different modified Stokes's kernels (deterministic or stochastic). We have also compared our results with most of the previously reported studies over Auvergne in order to seek any improvements with respect to time [exceptions are when different subsets of data have been used]. All studies considered here compare the computed quasigeoid models with the same 75 GPS-levelling heights over Auvergne. The standard deviation for almost all of the computations (without any fitting) is of the order of 30-40 mm, so there is not yet any clear indication whether any approach is necessarily better than any other nor improving over time. We also recommend more standardisation on the presentation of quasi/geoid comparisons with GPS-levelling data so that results from different approaches over the same areas can be compared more objectively.
******* THESIS+PRESENTATION (complete pdf versions below).********
One of the ultimate goals in geodesy, a 1 cm geoid model, is still unreachable for most of the areas worldwide. Several theoretical, methodological, numerical and data problems will have to be resolved in order to achieve it. The main motivation of this research is in making methodological and empirical contribution towards resolving some of the open problems in the regional gravity field and geoid modeling.
Topographic and density effects which affect short and very-short wavelengths of the gravity field have been traditionally modelled using the constant parameters of the Earth’s crust. As such parameters are only an approximation, this has been a limitation in more accurate filtering and reduction of the gravity data. Therefore, a methodology was developed which allows inclusion of surface and three dimensional crustal models in all steps of geoid determination. Prior to this, surface crustal density models were developed based on the inversion methods according to Pratt-Hayford, Airy-Heiskanen, and Parasnis-Nettleton. Additionally, three-dimensional crustal models EPcrust and CRUST1.0 were included in the computations. As a result of including crustal density models, the accuracy of developed gravimetric geoid models was improved from 1 to 3 cm.
The second major focus of research was related to the problem of the diversity of possible geoid computation methods and dozens of ways to perform reduction of the gravity field. The comparison of two widely used geoid modelling approaches was performed: Royal Institute of Technology (KTH) and Remove-Compute-Restore (RCR). Furthermore, compute step in RCR approach may be performed using several spectral and spatial methods. Therefore, different geoid computation methods were compared, including analytic Stokes integration using different deterministic modifications of the Stokes’ kernels, planar and spherical Fast Fourier Technique (FFT), flat-Earth and 3D least squares collocation (LSC). KTH approach, being a relatively straightforward geoid modelling approach compared to the RCR, was used for the analysis of the influence of all input models and parameters on the accuracy computed geoid models. From the large number of computed geoid solutions, two final gravimetric and hybrid geoid models for Croatia were selected HRG2018-RCR and HRG2018-KTH having standard deviation of ±3.0 cm and ±3.5 cm. The accuracy of geoid models was validated on GNSS/levelling points with seven parametric models using a unique cross-validation fitting methodology. Few other aspects of regional gravity field modeling were researched: i) investigation of the influence of input models and parameters in obtaining residual gravity field used in the RCR approach, ii) validation of the accuracy of global geopotential models, and iii) validation of gridding methods for several types of gravity anomalies.
In this chapter, geoid determination by the remove-compute-restore (RCR
) technique and Least Squares Modification of Stokes’ formula with Additive corrections
(LSMSA
) are briefly presented. The basic formulas of each method are developed, followed by a theoretical comparison. The advantages of the LSMSA method include: (a) a unique spectral least squares
matching of errors of gravity and EGM
data, as well as truncation of the integration
area to a cap; (b) additive corrections that are easier to compute than direct and indirect effects; (c) the downward continuation effect is more stable; (d) the bias in the atmospheric
effect in the standard IAG formula is avoided; and (e) each additive correction is easily updated whenever new data is available. The chapter ends with some case studies with numerical results. In most cases, even in international comparisons with other techniques, the LSMSA method provides the best agreement with geoid determination by the independent GPS
-levelling
technique.
