ADAPTATION OF THE GLOBAL GEOID MODEL EGM2008 ON CAMPANIA REGION (ITALY) BASED ON GEODETIC NETWORK POINTS

The knowledge of the geoid undulation, the height of the geoid relative to a given ellipsoid of reference, is fundamental to transform the ellipsoidal heights into orthometric heights. Global geoid undulation models developed from satellite gravity measurements appropriately integrated with other data, are free accessible in internet, but their accuracy may be inadequate for specific applications. Earth Gravitational Model 2008 (EGM2008) is one of those: usually available in grid form 2.5’ × 2.5’ (a geotif is developed by Agisoft with resolution 1’ × 1’), it defines the difference between the WGS84 ellipsoid height and the mean sea level, but in some areas the discrepancies between these geoid undulations and local correspondent measured values are on the order of various decimetres. For consequence, more accurate models are necessary. This article aims to determine a geoid undulation model suitable for Campania Region (Italy), starting from the global model EGM2008 (1’ × 1’) that is locally adjusted by using geodetic network points (GNPs) and GIS interpolation functions. Three different datasets are considered including respectively 20, 40 and 60 GNPs and three deterministic interpolators are applied in global way to generate geoid undulation grids: Inverse Distance Weight (IDW), Global Polynomial 1st order (GP1), Global Polynomial 2nd order (GP2). The resultant 9 models are tested on 20 additional GNPs. The experiments demonstrate that local geoid can be produced on a little area adapting global geoid by means of GNPs: the model obtained using GP2 and 60 GNPs, the most accurate one, fits the data with ±3.2 cm root mean square error (RMSE).

Validation of the GPS leveling method through the gradient analysis of the geoidal wave. Case study of Ecuador

We validated the GPS leveling as an alternative to the traditional geometric leveling method. Validation compares the geometric slopes derived from the GNSS positioning technique, heights resulting from geometric leveling campaigns and geoid undulations extracted from the Global Geopotential Model EGM08. This analysis was performed in the Ecuadorian mainland, where we identified areas in which the gradient of the geoidal undulation is less pronounced. The spatialization of the gradient or variation-based methods allowed to analyze the performance of the GPS leveling method, under the hypothesis that less variability in geoid undulation implies less discrepancies in the GPS unevenness. GNSS observations were determined on the leveling plates belonging to the Basic Vertical Control Network. The results of the study are given based on the relative error resulting from the comparison of the traditional differential leveling method with the corresponding values obtained from the GNSS positioning, considering different distances for the spread of unevenness.

Validation of the GPS leveling method through the gradient analysis of the geoidal wave. Case study of Ecuador.

We validated the GPS leveling as an alternative to the traditional geometric leveling method. Validation compares the geometric slopes derived from the GNSS positioning technique, heights resulting from geometric leveling campaigns and geoid undulations extracted from the Global Geopotential Model EGM08. This analysis was performed in the Ecuadorian mainland, where we identified areas in which the gradient of the geoidal undulation is less pronounced. The spatialization of the gradient or variation-based methods allowed to analyze the performance of the GPS leveling method, under the hypothesis that less variability in geoid undulation implies less discrepancies in the GPS unevenness. GNSS observations were determined on the leveling plates belonging to the Basic Vertical Control Network. The results of the study are given based on the relative error resulting from the comparison of the traditional differential leveling method with the corresponding values obtained from the GNSS positioning, considering different distances for the spread of unevenness.

EVALUATION OF THE RECENT HIGH-DEGREE COMBINED GLOBAL GRAVITY-FIELD MODELS FOR GEOID MODELLING OVER KENYA

This study carries out an evaluation of the recent high-degree combined global gravity-field models (EGM2008, EIGEN-6C4, GECO and SGG-UGM-1) over Kenya. The evaluation is conducted using observed geoid undulations (18 data points, mainly in Nairobi area) and free-air gravity anomalies (8,690 data points, covering the whole country). All the four models are applied at full spherical harmonic degree expansion. The standard deviations of the differences between observed and GGMs implied geoid undulations at 18 GPS/levelling points over Nairobi area are ±11.62, ±11.48, ±12.51 and ±11.75 cm for EGM2008, EIGEN-6C4, GECO and SGG-UGM-1, respectively. On the other hand, standard deviations of the differences between observed and GGMs implied free-air gravity anomalies at 8,690 data points over Kenya are ±10.11, ±10.03, ±10.19 and ±10.00 mGal for EGM2008, EIGEN-6C4, GECO and SGG-UGM-1, respectively. These results indicate that the recent high-degree global gravity-field models generally perform at the same level over Kenya. However, EIGEN6C4 performs slightly better than EGM2008, GECO and SGG-UGM-1, considering the independent check provided by GPS/levelling data (admittedly over a small area). These results further indicate a good prospect for the development of a precise gravimetric geoid model over Kenya using EIGEN-6C4 by integrating local terrestrial gravity data in a removecompute-restore scheme.

Vertical Gravity Gradient Modeling by 3-D Least Squares Collocation and its impact on quasigeoid-geoid separation term

<p>For the quasi-geoid determination by 3-D Least Squares Collocation (LSC) in the context of Molodensky’s approach, there is no need to measured or modelled vertical gravity gradient (VGG) as the 3-D LSC takes the varying heights of the gravity observation points into account. However, the use of measured or modelled VGG instead of the thereotical value is expected to improve the quasigeoid-geoid separation term particularly in mountainous areas. The VGG measurements are found to be different from the theoretical value in the range of - % 25 and + % 39 in western Turkey. Previously there has been no study using modelled VGGs for gravimetric geoid modelling in Turkey. VGGs are modelled by 3-D Least Squares Collocation (LSC) in remove-restore approach and validated by terrestrial VGG measurements in western Turkey. The effect of using modelled VGG instead of the theoretical one in quasigeoid-to-geoid separation term is found to be significant. The quasi-geoid computed by 3-D LSC in western Turkey is converted to geoids using theoretical or modelled VGG values and compared with GPS/levelling geoid-undulations.</p><p> </p>

Construction of regional geoid using a virtual spherical harmonics model

The spherical cap harmonics (SCH) method can be used in regional geoid modeling. The core of this approach is the computation of its associated Legendre functions (ALF) with non-integer degree. However, it is unlikely to obtain a large number of zero-root values for the non-integer ALF. To overcome this problem, a new approach called virtual spherical harmonics (VSH) is proposed in this paper to transform the cap range into the whole sphere so that unlimited numbers of zero-root values can be obtained. The new approach was tested using four cap ranges with the radii of {30^{\circ }}, {15^{\circ }}, {10^{\circ }} and {5^{\circ }}, and geoid undulations for each of the regions are calculated from EGM2008. For each of the regions, the geoid undulations were used to construct three models with three different degrees of 20, 30 and 40. Numerical results showed that with the increase in the degree of the VSH model, the value of the maximum error decreases; and the maximum error of the model was less than 1 mm while the maximum degree is 40.

ERRORS MEASUREMENT OF INTERPOLATION METHODS FOR GEOID MODELS: STUDY CASE IN THE BRAZILIAN REGION

The geoid is an equipotential surface regarded as the altimetric reference for geodetic surveys and it therefore, has several practical applications for engineers. In recent decades the geodetic community has concentrated efforts on the development of highly accurate geoid models through modern techniques. These models are supplied through regular grids which users need to make interpolations. Yet, little information can be obtained regarding the most appropriate interpolation method to extract information from the regular grid of geoidal models. The use of an interpolator that does not represent the geoid surface appropriately can impair the quality of geoid undulations and consequently the height transformation. This work aims to quantify the magnitude of error that comes from a regular mesh of geoid models. The analysis consisted of performing a comparison between the interpolation of the MAPGEO2015 program and three interpolation methods: bilinear, cubic spline and neural networks Radial Basis Function. As a result of the experiments, it was concluded that 2.5 cm of the 18 cm error of the MAPGEO2015 validation is caused by the use of interpolations in the 5'x5' grid.

Assessing the quality of GEOID12B model through field surveys

Elevation differences have been determined through conventional ground surveying techniques for over a century. Since the mid-80s GPS, GLONASS and other satellite systems have modernized the means by which elevation differences are observed. In this article, we assessed the quality of GEIOD12B through long-occupation GNSS static surveys. A set of NGS benchmarks was occupied for at least one hour using dual-frequency GNSS receivers. Collected measurements were processed using a single CORS station at most 24 kilometers from the benchmarks. Geoid undulation values were driven by subtracting measured ellipsoidal heights from the orthometric heights posted on the NGS website. To assess the quality of GEOID12B, we compared our computed vertical shifts at the benchmarks with those estimated from GEOID12B published by NGS. In addition, Kriging model was used to interpolate local maps for the geoid undulations from the benchmark heights. The maps were compared with corresponding parts of GEOID12B. No biases were detected in the results and only shifts due to random errors were found. Discrepancies in the range of ten centimetres were noticed between our geoid undulation and the values available from NGS.