Verification of the Jakarta Geoid Model from the Gravity Data of 2.5 km Resolution with Gravimetric Geoid

To use the Global Navigation Satellite System (GNSS) correctly, the height information should be transformed into orthometric height by subtracting geoid undulation from it. This orthometric height is commonly used for practical purposes. In 2015 geoid of Jakarta has been produced, and it has an accuracy of 0.076 m. In the year 2019, airborne gravimetry has been done for the entire Java Island. The area of DKI Province cannot be measured because there is inhibition from Airnav. For this reason, terrestrial gravimetric measurements are carried out in this region by adding points outside the previously measured area. To compute the geoid in the Jakarta region is needed the Global Geopotential Model (GGM). In this paper, the GMM used is gif48. The “remove and restore” method will be used in calculating the geoid in this Jakarta region. Besides that in this geoid calculation also uses Stokes kernel and FFT to speed up the calculation. The verification of the resulting geoid is carried with 11 points in DKI Jakarta Province. This verification produces a standard deviation of 0.116 m and a root mean square of 0.411 m.

Optic-fiber gravity frequency transfer network

<p>According to<strong> </strong>Einstein’s general relativity theory (GRT), a clock at a position with higher potential runs faster than a clock at a position with lower potential. Hence, inversely, one can determine the gravity potential (geopotential) and orthometric height based on precise clocks. If a clock with an accuracy of 10<sup>-18</sup> is used, the geopotential difference between two points can be determined with an accuracy of centimeters level.<strong> </strong>With the rapid development of science and technology, optical clocks achieve 10<sup>-18</sup> stability, which opens up opportunity for scientists to practically determine geopotential as well as orthometric height using optical clocks. One of the challenges of classical geodesic in the long time has been the unification of local hight systems. To complete this task is very difficult because each country has a regional high system. This problem can be solved if using a clock network, which overcomes the weaknesses of the spirit leveling method. Here we provide a formulation to establish a model of a network using optical clocks linked together by optical fibers for the purpose of determining the geopotential and establishing a unified world hight system at centimeter accuracy level. This study is supported by National Natural Science Foundation of China (NSFC) (grant Nos. 41721003, 42030105, 41631072, 41874023, 41804012), and Space Station Project (2020)228.</p><p><strong>Key words:</strong><strong> </strong>GRT, optical clocks network, frequency transfer, geopotential, orthometric height</p>

The worldwide physical height datum project

The definition of a common global vertical coordinate system is nowadays one of the key points in Geodesy. With the advent of GNSS, a coherent global height has been made available to users. The ellipsoidal height can be obtained with respect to a given geocentric ellipsoid in a fast and precise way using GNSS techniques. On the other hand, the traditional orthometric height is not coherent at global scale. Spirit levelling allows the estimation of height increments so that orthometric heights of surveyed points can be obtained starting from a benchmark of known orthometric heights. As it is well known, this vertical coordinate refers to the geoid, which is assumed to be coincident to the mean sea level. By means of a tide gauge, the mean sea level is estimated and thus a point of known orthometric height is defined. This assumption, which was acceptable in the past, became obsolete given the level of precision which is now required. Based on the altimetry observation, one can precisely quantify the existing discrepancy between geoid and mean sea level that can amount to 1 ÷ 2 m at global scale. Therefore, different tide gauges provide biased estimates of the geoid, given the discrepancy between this equipotential surface and the mean sea level. Also, in the last years, another vertical coordinate was used, the normal height that was introduced in the context of the Molodensky theory. In this paper, a review of the existing different height systems is given and the relationships among them are revised. Furthermore, an approach for unifying normal height referring to different tide gauges is presented and applied to the Italian test case. Finally, a method for defining a physical height system that is globally coherent is discussed in the context of the definition of the International Height Reference System/Frame, a project supported by the Global Geodetic Observing System of the International Association of Geodesy (IAG). This project was established in 2015 during the XXVI IAG General Assembly in Prague as described in IAG Resolution no. 1 that was presented and adopted there.

Comparative Analysis of Change between Ellipsoidal Height Differences and Equivalent Orthometric Height Difference

Height is an important component in the determination of the position of a point. The study aimed at performing a comparative analysis of change between ellipsoidal height differences and the equivalent orthometric height difference of points. A hi-target Differential Global Positioning System (DGPS) was used to acquire GPS data with an occupation period of thirty (30) minutes on each point, which were processed using Hi-target Geomatics Office (HGO) software to obtain the ellipsoidal heights. An automatic level instrument was used to acquire leveling data, which were processed using the height of collimation method to obtain the orthometric heights. A total of fifty (50) points were occupied as common points for both the GPS and levelling observations at 20-meter intervals. The accuracy of the height difference was determined using standard deviation with the ellipsoidal height difference as 53.59cm and the orthometric height as 53.07cm respectively. A Root Mean Square Error value of 0.0621m was obtained as the accuracy of the change between the two height differences. Statistical analysis using the independent-sample Z test was used to analyze the data at a 5% significant level. The result shows no significant difference in the performance of the two height systems. It is worthy to note that GPS and spirit levelling height differences can be used interchangeably for any heighting in short distances for surveying and engineering applications.

Impact of different centroid means on the accuracy of orthometric height modelling by geometric geoid method

<p class="abstract"><strong>Background:</strong> Orthometric height, as well as geoid modelling using the geometric method, requires centroid computation. And this can be obtained using various models, as well as methods. These methods of centroid mean computation have impacts on the accuracy of the geoid model since the basis of the development of the theory of each centroid mean type is different. This paper presents the impact of different centroid means on the accuracy of orthometric height modelling by geometric geoid method.</p><p class="abstract"><strong>Methods:</strong> DGPS observation was carried out to obtain the coordinates and ellipsoidal heights of selected points. The centroid means were computed with the coordinates using three different centroid means models (arithmetic mean, root mean square and harmonic mean). The computed centroid means were entered accordingly into a Microsoft Excel program developed using the Multiquadratic surface to obtain the model orthometric heights at various centroid means. The root means square error (RMSE) index was applied to obtain the accuracy of the model using the known and the model orthometric heights obtained at various centroid means. </p><p class="abstract"><strong>Results:</strong> The computed accuracy shows that the arithmetic mean method is the best among the three centroid means types.</p><p class="abstract"><strong>Conclusions:</strong> It is concluded that the arithmetic mean method should be adopted for centroid computation, as well as orthometric height modelling using the geometric method.</p>

Assessment of ArcGIS based extraction of geoidal undulation compared to National Geospatial Intelligence Agency (NGA) model – A case study

Global Navigation Satellite System (GNSS) and remote sensing Digital Elevation Models (DEMs) represent earth’s surface elevation with reference to ellipsoid and orthometric heights. Proper estimation of the geoid (difference of ellipsoid and orthometric heights) is necessary before comparing data referenced to the different vertical datum. In this paper, an error in estimating EGM96 orthometric height is highlighted, verified by NGA/NASA developed model and MATLAB®. A significant error was found in the ArcGIS derived EGM96 orthometric heights range between ±6.9 meters. In addition, interpolation of low-resolution geoid data also produces significant biases depending on geographic location and the number of the interpolation data point. The bias was maximum negative in the central part of Tibetan Plateau and Himalaya. Therefore, estimation of orthometric height similar to NGA/NASA model precision is necessary for comparison of DEMs for natural resources management, 3D modelling and glaciers mass balance mainly in the mountainous regions.

Geoid heights in Costa Rica, Case of Study: Baseline Along the Central Pacific Zone

A precise orthometric height (H) and orthometric height difference (ΔH) determination is required in many fields like construction, geodesy and geophysics. H is often obtained from an ellipsoidal height (h) and geoid height (N) of a geoid model (GM) because this computation does not have the spirit leveling restrictions on long distances. However, the H accuracy depends on the GM local area adaptation, and current global geoid models (GGMs) have not been yet evaluated for Costa Rica. Therefore, this paper aims to determine which GGM maintains a better fit with a GPS/levelling baseline that contains the gravity full spectrum. A 74 km baseline was measured using GPS, spirit leveling and gravity measurements to validate the N computed from EGM2008, EIGEN-6C4, GECO, EGM96, GGM05C and GOCO05C. First, an absolute N assessment was made, where geoid height from the GGMs (NGGM) were directly compared to the geometric geoid heights (Ngeo) obtained from GPS and spirit levelling. A bias fit (Nbias) of about 2 m was computed from this comparison for most GGMs with respect to the local vertical reference surface (W0). By subtracting the Nbias, a relative geoid height (ΔN) assessment was designed to compare the differences between GGM relative geoid height (ΔNGGM) and geometric relative geoid height (ΔNgeo) on segments along the baseline. The ΔN comparison shows that EGM2008, EIGEN-6C4 and GECO better represent the Costa Rican Central Pacific Coastal Zone and over long distances, ΔH can be computed with a decimeter to centimeter precision.