Combining Global Geopotential Models, Digital Elevation Models, and GNSS/Leveling for Precise Local Geoid Determination in Some Mexico Urban Areas: Case Study

This work shows improvements of geoid undulation values obtained from a high-resolution Global Geopotential Model (GGM), applied to local urban areas. The methodology employed made use of a Residual Terrain Model (RTM) to account for the topographic masses effect on the geoid. This effect was computed applying the spherical tesseroids approach for mass discretization. The required numerical integration was performed by 2-D integration with 1DFFT technique that combines DFT along parallels with direct numerical integration along meridians. In order to eliminate the GGM commission error, independent geoid undulations values obtained from a set of GNSS/leveling stations are employed. A corrector surface from the associated geoid undulation differences at the stations was generated through a polynomial regression model. The corrector surface, in addition to the GGM commission error, also absorbs the GNSS/leveling errors as well as datum inconsistencies and systematic errors of the data. The procedure was applied to five Mexican urban areas that have a geodetic network of GNSS/leveling points, which range from 166 to 811. Two GGM were evaluated: EGM2008 and XGM2019e_2159. EGM2008 was the model that showed relatively better agreement with the GNSS/leveling stations having differences with RMSE values in the range of 8–60 cm and standard deviations of 5–8 cm in four of the networks and 17 cm in one of them. The computed topographic masses contribution to the geoid were relatively small, having standard deviations on the range 1–24 mm. With respect to corrector surface estimations, they turned out to be fairly smooth yielding similar residuals values for two geoid models. This was also the case for the most recent Mexican gravity geoid GGM10. For the three geoid models, the second order polynomial regression model performed slightly better than the first order with differences up to 1 cm. These two models produced geoid correction residuals with a standard deviation in one test area of 14 cm while for the others it was of about 4–7 cm. However, the kriging method that was applied for comparison purposes produced slightly smaller values: 8 cm for one area and 4–6 cm for the others.

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).

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.

Determining the height of Mount Everest using the shallow layer method

<p>We proposed an alternative method to determine the height of Mount Everest (HME) based on the shallow layer method (SLM), which was put forward by Shen (2006). We use the precise external global Earth gravity field model (i.e., EGM2008 and EIGEN-6C4 models) as input information, and the digital topographic model (i.e., DTM2006.0) and crust models (i.e., CRUST2.0 and CRUST1.0 models) to construct the shallow layer model. There are four combined strategies：(1) EGM2008 and CRUST1.0 models, (2) EGM2008 and CRUST2.0 models, (3) EIGEN-6C4 and CRUST1.0 models, and (4) EIGEN-6C4 and CRUST2.0 models, respectively. We calculate the HME by two approaches: first approach, the HME is directly calculated by combining the geoid undulation (N) and geodetic height (h); second approach, we calculate the HME by the segment summation approach (SSA) using the gravity field inside the shallow layer determined by the SLM. Numerical results show that for four combined strategies, the differences between our results and the authoritatively released value 8848.86 m by the Chinese and Nepalese governments on December 8, 2020 are 0.448 m, -0.009 m, -0.295 m, and -0.741 m using first approach and 0.539 m, 0.083 m, -0.214 m, and -0.647 m using second approach. The combined calculation of the HME by the terrain model and gravity field model is more accurate than that by the gravity field model alone. This study is supported by the National Natural Science Foundations of China (NSFC) under Grants 42030105, 41721003, 41804012, 41631072, 41874023, Space Station Project (2020)228.</p>

The Deflection of the Vertical, from Bouguer to Vening-Meinesz, and Beyond – the unsung hero of geodesy and geophysics

<p>When thinking of gravity in geodesy and geophysics, one usually thinks of its magnitude, often referred to a reference field, the normal gravity.  It is, after all, the free-air gravity anomaly that plays the significant role in terrestrial data bases that lead to Earth Gravitational Models (such as EGM96 or EGM2008) for a multitude of geodetic and geophysical applications.  It is the Bouguer anomaly that geologists and exploration geophysicists use to infer deep crustal density anomalies.  Yet, it was also Pierre Bouguer (1698-1758) who, using the measured direction of gravity, was the first to endeavor a determination of Earth’s mean density (to “weigh the Earth”), that is, by observing the deflection of the vertical due to Mount Chimborazo in Ecuador.  Bouguer’s results, moreover, sowed initial seeds for the theories of isostasy.  With these auspicious beginnings, the deflection of the vertical has been an important, if not illustrious, player in geodetic history that continues to the present day.  Neglecting the vertical deflection in fundamental surveying campaigns in the mid to late 18<sup>th</sup> century (e.g., Lacaille in South Africa and Méchain and Delambre in France) led to errors in the perceived shape of the Earth, as well as its scale that influenced the definition of the length of a meter.  The vertical deflection, though generally excluded from modern EGM developments, nevertheless forms a valuable resource to validate such models.  It is also the vertical deflection that is indispensable for precision autonomous navigation (i.e., without external aids such as GPS) using inertial measurement units.  It is the deflection of the vertical that, measured solely along horizontal lines, would readily provide geoid undulation profiles, essential for the modernization of height systems (i.e., vertical geodetic control) without the laborious and traditional methods of spirit leveling.  But, measuring the deflection of the vertical is itself an arduous undertaking and this has essentially contributed to its neglect and/or underusage.  Even Vening-Meinesz’s formulas of convolution with gravity anomalies do not greatly facilitate its determination.  This presentation offers a review of the many roles the vertical deflection has, or could have, played over the centuries, how it has been measured or computed, and how gravity gradiometry might eventually awaken its full potential.</p>

Vegetation Height Estimation using Satellite Remote Sensing in Peat Land of Central Kalimantan

Vegetation height is an important parameter in monitoring peatlands. Vegetation height can be estimated using remote sensing. Vegetation height can be estimated by utilizing DSM and DTM. The data that can be used are LiDAR, X-SAR, and SRTM C. In this study, LiDAR data is used for DSM2018 and DTM2018 extraction. The purpose of this research is to detect the vegetation height in Central Kalimantan peatlands using remote sensing technology. The research location is in Bakengbongkei, Kalampangan, Central Kalimantan. The integration of X-SAR and SRTM C is used for DSM2000 and DTM2000 extraction. DSM2000, DTM2000, DSM2018, and DTM2018 performed height error correction with tolerance of 1.96? (95%). Then do the geoid undulation correction to EGM2008. The results obtained are DSM and DTM with a similar height reference field. If it meets these conditions it can be calculated the vegetation height estimation. Vegetation height can be obtained using the Differential DEM method. The Changing in vegetation height from 2000 to 2018 can be estimated from the difference in vegetation height from 2000 to vegetation height in 2018. Results of spatial information on vegetation height and its changes need to be tested for the accuracy. This accuracy-test includes a cross section test, height difference test, and comparison with measurements of vegetation height in the field. The results of this research can be used to monitor the changing the vegetation height in peatlands.

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.