Results of comparing astronomical-geodetic and navigational-geodetic methods of determining the components of the deflection of vertical

The authors present the results of comparing the components of deflection of vertical obtained through astronomical-geodetic and navigational-geodetic methods. The first one is based on comparing astronomical and geodetic coordinates of a location. This method has recently been widely implemented in a digital zenith camera systems using a small-sized digital telescope with an astronomical camera based on CCD or CMOS technologies, a high-precision inclinometer and satellite navigation system receiver. In this case, the combination of a telescope, an astronomical camera and an inclinometer enables determining the local direction of the plumb line, expressed by astronomical coordinates, from observations of stars at the zenith and using high-precision star catalogs. The navigational-geodetic method is based on comparing the results of the normal heights’ increments, defined through geometric leveling, and geodetic heights, computed with the relative method of satellite coordinate determinations. For each method, random and systematic components of the error and its confidence bounds were calculated; the absolute values of the deflection of vertical components at two geographically separated points were compared.

Strategy for Connecting to the IHRF: Case Study for the Tide Gauge of Cananeia-SP

In July 2018, IBGE launched the new heights of the Brazilian Geodetic System (BGS), the normal height, which has associated gravity. These new heights are replacing the old normal-orthometric ones, in which there was only the non-parallelism correction. The IBGE informs that the values farther from the origin, have less accuracy. This lower accuracy may interfere in the future, the connection of the local tide gauges to IHRF (International Reference Frame Height). Thus, this paper proposes the integration of the local tide gauge of Cananeia-SP to the IHRF. In order to validate the methodology, the normal, Helmert, and rigorous orthometric heights using two distinct references: the Imbituba-SC tide gauge, as the origin of the BGS and the Cananeia-SP tide gauge, as a local tide gauge to be integrated into the IHRF. Calculating the three heights through these two origins, we analyzed the discrepancies in comparison to the heights calculated by IBGE. Numerical tests indicate that there was an improvement in terms of a mean and standard deviation when using the Cananeia gauge as origin in the calculation of normal, Helmert, and rigorous heights. In the congruence analysis, the calculations indicate that the highest standard deviation is presented when using IBGE normal heights. Thus, we have a new origin that is reliable and functional, can be integrated with the IHRF, where the Helmert and rigorous orthometric heights have the best statistical results.

On the dynamics of physical heights and their use for the determination of accurate orthometric/normal heights

<p>Physical heights, e.g. orthometric and normal heights, are, so far, practically considered as static heights in the majority of land areas over the world. They were traditionally determined without considering the dynamic processes of the Earth induced from temporal mass variations within the Earth’s system. The Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On (GRACE-FO) satellite missions provided unique data that allow the estimation of temporal variations of geoid heights and vertical deformations of the Earth’s surface, and thereby the dynamics of physical heights. They revealed that for the large river basin of a strong hydrological signal (e.g. the Amazon river basin), peak to peak variations of orthometric/normal height changes reach 8 cm. The objective of this research is to discuss the need of considering the dynamics of physical heights for the determination of accurate orthometric/normal heights. An approach to determine the dynamics of physical heights using the release 6 (RL06) GRACE-based Global Geopotential Models (GGMs) as well as load Love numbers from the Preliminary Reference Earth Model (PREM) was proposed. Then, the dynamics of orthometric/normal heights was modelled and predicted using the seasonal decomposition (SD) method. The proposed approach was tested over the area of Poland. The main findings reveal that the dynamics of orthometric/normal heights over the area investigated reach the level of a couple of centimetres and can be modelled and predicted with a millimetre accuracy using the SD method. Accurate orthometric/normal heights can be obtained by combining modelled dynamics of orthometric/normal heights with static orthometric/normal heights referred to a specific reference epoch.</p><p><strong>Keywords:</strong> dynamics of physical heights, GRACE, accurate orthometric/normal heights, temporal variations of geoid/quasigeoid heights, vertical deformations of the Earth’s surface</p>

New geoid models computation in the Southeast part of Brazil

<p>In the last decade, big efforts have been undertaken in terms of gravity surveys in the Southeast part of Brazil. First of all, São Paulo state has gravity data coverage quite completed in terms of 5’ resolution. Second, in the last few years, some field works have been carried out in Minas Gerais state. The purpose of gravity densification is not only to improve the quality of geoid (quasi-geoid) models in Brazil, but also to contribute to the geodetic infrastructure, in particular, at the moment, for the establishment of the International Height Reference Frame, where two of six planned stations are located in the densification area. These efforts resulted in the computation of two quasi-geoid models in the Southeast region of Brazil. The decision is to compute a quasi-geoid instead of a geoid model, once since 2018, the Brazilian vertical system is based on normal heights. The Minas Gerais model was computed using Least Squares Collocation, via Fast Collocation. The spectral decomposition was employed in the technique for quasi-geoid model computation, where the reference field was represented by XGM2019 up to degree and order 200. The model was compared with GNSS/leveling in order to check the consistency of two different data sets. Two quasi-geoidal models for the São Paulo state have been computed. Numerical integration through the Fast Fourier Transform (FFT) was used to perform the integral. The Molodensky gravity anomaly was determined in a 5’ grid, reduced and restored using the Residual Terrain Model (RTM) technique and the XGM2019 with the degree and order 250 and 720. The validation for the São Paulo quasi-geoid model is based on the GNSS measurements in the leveling network too.  The Digital Terrain Model SRTM15 plus was used in the continent and the ocean areas in both states.</p>

Creating and updating of topographic maps height base in the new national spatial coordinate system: case Fergana valley

The use of high-precision technology of the global navigation satellite system (GNSS) has put forward the task of developing the methods for the creation and the use of a new national open coordinate system in the Republic of Uzbekistan. In the country, up to now the CS42 coordinate system, based on the Krasovsky ellipsoid used for geodetic works. The Baltic normal system of heights (1977), tied to the mean sea level with the zero mark of the Kronstadt tide gauge, was adopted as a height datum. Due to lack geoid information for the territory of the country determined by modern methods, the realization of a height reference datum becomes an urgent task. The results of GPS measurements usually presented in a coordinate system relative to the WGS-84 ellipsoid, and have to convert to national, local coordinate systems to solve practical problems. The horizontal GPS coordinates can directly use for computational work, but the geodetic heights have to convert to orthometric (or normal) heights for a given area using geoid information. In this work, a study was made of methods for updating the height reference datum of topographic maps at a scale of 1:200,000 using a deformation matrix between two reference coordinate systems for the territory of the Fergana Valley. To convert between geodetic and normal heights between the CS42 and WGS84 coordinate systems, a vertical deformation matrix in the GTX format of the National oceanic and Atmospheric Administration of Canada (NOAA) have created. To create a file of elevation displacements, the results of classical leveling and satellite GPS measurements have used at 144 “common” points of the entire network of the country with known coordinates in two systems. The difference between the “real” values of geodetic heights obtained from GPS measurements and “modeled” ranges from -0.13 m to 0.67 m. It has revealed that the maximum differences in heights are in the area of the Fergana basin itself and may be a consequence of both an anomalous gravitational field in this part of the territory, and an insufficient density of stations of the GPS network in the northeastern part of the area. The normal height values for the updated topographic map in WGS84 have computed using the EGM2008 high precision geopotential model. The discrepancy between the values of heights in CS42 and WGS84 is in the range of -3.93 m and 0.31 m.

HIGH-PRECISION SATELLITE LEVELING AND INVESTIGATION OF THE LOCAL GEOID MODEL IN THE TERRITORY OF KASHKADARYA REGION

In this paper, a study of the accuracy of obtaining normal heights using Global Geopotential Models EGM2008, EIGEN-6C4, GECO and GNSS measurements for the territory of the Kashkadarya region in Uzbekistan is carried out. The heights obtained by the classical leveling in Baltic reference system were used as reference data. EIGEN-6C4 and GECO models were recommended for definition a preliminary quasi  geoid model of the region. KEYWORDS: GNSS and classical leveling, Global Geopotential Model, height anomaly

On the uncertainty of height anomaly differences predicted by least-squares collocation

A network of pointwise available height anomalies, derived from levelling and GPS observations, can be densified by adjusting a gravimetric quasigeoid using least-squares collocation. The resulting type of Corrector Surface Model (CSM) is applied by Norwegian surveyors to convert ellipsoidal heights to normal heights expressed in the official height system NN2000. In this work, the uncertainty related to the use of a CSM to predict differences in height anomaly was sought. As previously, the application of variograms to determine the local statistical properties of the adopted collocation model led to predictions that were consistent with their computed uncertainties. For the purpose of predicting height anomaly differences, the effect of collocation was seen to be moderate in general for the small spatial separations considered (< 10 km). However, the relative impact of collocation could be appreciable, and increasing with distance, near the network. At last, it was argued that conservative uncertainties of height anomaly differences may be obtained by rescaling output of a grid interpolation by \sqrt \Delta, where Δ is the spatial separation of the two locations for which the difference is sought.

Assessment of Temporal Variations of Orthometric/Normal Heights Induced by Hydrological Mass Variations over Large River Basins Using GRACE Mission Data

Almost half of the Earth’s land is covered by large river basins. Temporal variations of hydrological masses induce time-varying gravitational potential and temporal mass loading that deforms the Earth’s surface. These phenomena cause temporal variations of geoid/quasigeoid and ellipsoidal heights that result in temporal variations of orthometric/normal heights ΔH/ΔH*. The aim of this research is to assess ΔH/ΔH* induced by hydrological masses over large river basins using the Gravity Recovery and Climate Experiment (GRACE) satellite mission data. The results obtained reveal that for the river basin of a strong hydrological signal, ΔH/ΔH* reach 8 cm. These ΔH/ΔH* would be needed to reliably determine accurate orthometric/normal heights. The ΔH/ΔH* do not exceed ±1 cm in the case of the river basin of the weak hydrological signal. The relation between hydrological mass changes and ΔH/ΔH* was investigated. Correlations between ΔH/ΔH* and temporal variations of equivalent water thickness were observed in 87% of river basins subareas out of which 45% exhibit strong correlations. The ΔH/ΔH* determined over two river basins that characterize with the strongest and weakest temporal variations were analysed using the Principal Component Analysis method. The results obtained reveal that ΔH/ΔH* in subareas of the same river basin can significantly differ (e.g., ±2 cm in the Amazon basin) from each other, and are strongly associated with different spatio-temporal patterns of the entire river basin.

EVALUATION AND TAILORING OF GLOBAL GEOPOTENTIAL MODELS IN THE DETERMINATION OF GRAVITY FIELD IN SERBIA

Within this paper, we evaluated the quality of three Global Geopotential Models entitled: EGM96,EGM2008, and GOCO05c. The models were evaluated by using 1001 terrestrial discrete values ofheight anomalies determined by Global Navigation Satellite Systems and normal heights, which weconsidered to be true values within this research. In addition to the quality evaluation, we tailoredthe models by using more than 80000 free air anomalies. The results obtained from the evaluationand tailoring indicate that by using the GOCO05c it is possible to determine a set of anomaly heightsacross Serbia, which are in agreement with terrestrial values with an average value of -7 cm, thestandard deviation of ±9 cm and with the range of 44 cm.

Development of a precise local quasigeoid model for the city of Krakow – QuasigeoidKR2019

A geoid or quasigeoid model allows the integration of satellite measurements with ground levelling measurements in valid height systems. A precise quasigeoid model has been developed for the city of Krakow. One of the goals of the model construction was to provide a more detailed quasigeoid course than the one offered by the national model PL-geoid2011. Only four measurement points in the area of Kraków were used to build a national quasigeoid model. It can be assumed that due to the small number of points and their uneven distribution over the city area, the quasigeoid can be determined less accurately. It became the reason for developing a local quasigeoid model based on a larger number of evenly distributed points. The quasigeoid model was based on 66 evenly distributed points (from 2.5 km to 5.0 km apart) in the study area. The process of modelling the quasigeoid used height anomalies determined at these points on the basis of normal heights derived through levelling and ellipsoidal heights derived through GNSS surveys. Height anomalies coming from the global geopotential model EGM2008 served as a long-wavelength trend in those derived from surveys. Analyses showed that the developed height anomaly model fits the empirical data at the level of single millimetres – mean absolute difference 0.005 m. The developed local model QuasigeoidKR2019, similar to the national model PL-geoid2011, are models closely related to the reference and height systems in Poland. Such models are used to integrate GNSS and levelling observations. A comparison of the local QuasigeoidKR2019 and national PL-geoid2011 model was made for the reference frame PL-ETRF2000 and height datum PL-KRON86-NH. The comparison of the two models with respect to GNSS/levelling height anomalies shows a triple reduction in the values of individual quartiles and a mean absolute difference for the developed local model. These summary statistics clearly indicate that the accuracy of the local model for the city of Krakow is significantly higher than that of the national one.