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Sri Lanka is still in need of a well-defined local geoid model. This geoidal void has made present-day Global Navigation Satellite System (GNSS) surveys heavily dependent on Global Geopotential Models (GGMs) for height determination. Further, in many instances, the accuracy of GGMs have shown drawbacks in elevation determination over Sri Lanka. Therefore, the study focused on developing a hybrid geoid model (HGM) for Sri Lanka by integrating the available GGMs. Five high-resolution (2190°) GGMs; EGM2008, EIGEN-6C4, GECO, XGM2019e-2159, and SGG-UGM2 were employed to extract GGM-derived geoid undulation for 21 Fundamental Benchmarks (FBMs). The residuals (geoid height deviation) were calculated relative to the observed geoid undulation using GNSS/leveling on the FBMs. The data set was clustered based on topography, and residuals were adjusted using weighted least squares adjustment (LSA). The uneven distribution of the FBMs promotes topography-based clustering. EIGEN-6C4 is found to be the robust GGM for Sri Lanka to develop a hybrid approach, with a 0.001 m RMS value of estimated residuals in LSA. The resulting HGM was interpolated at 1 arc-second grid resolution (30 m × 30 m) using the Inverse Distance Weighted Interpolation. Regression lines were generated for the interpolated HGM with respect to the interpolated observed geoid undulation for 9 transects along the parallel passing through Mount Pedro and for the 16 transects along the meridian. The coefficient of determination on both lines is 0.999. HGM generated by EIGEN-6C4 has shown reliable RMS gradient and intercept values of 8.860078 × 10−9 and 0.0039239, respectively, in first-order polynomial fitting. [ABSTRACT FROM AUTHOR]

Engineering uses digital elevation models to perform calculations and modeling phenomena, since it allows determining the scale at which they can be used and the quality of the by-products obtained. Two groups of models were evaluated, the digital terrain models (DTMs): Shuttle Radar Topography Mission (SRTM), ASTER Global Digital Elevation Map (ASTER GDEM), ALOS PALSAR and the DTM generated by the Instituto Geográfico Militar del Ecuador (IGM), and the geopotential models (GMs): EGM96, EGM08 and the GM created by the IGM. For the evaluation, the geometric leveling points and ellipsoidal height raised in one of the IGM projects were used to determine atypical values, calculate the mean square error (RMSE) and define the precision and scale at which the different ones can be used. The heights between the DTMs were compared to know their difference. It was determined that the SRTM 30, ALOS PALSAR and IGM DMTs can be used for jobs that require an accuracy of less than 10 meters. The GM EGM08 together with high precision ellipsoidal heights could generate elevation models that can reach an accuracy of 1.25 meters, while the GMs EGM96 and IGM can generate models that achieve an accuracy of 2.5 meters. The ellipsoidal heights of the SRTM 30, ALOS PALSAR and IGM DTMs obtained with the EGM 96 and EGM 08 GMs can only be used in jobs that require an accuracy of less than 10 meters. [ABSTRACT FROM AUTHOR]

Geoid undulation model is typically used for the conversion between GNSS obtained ellipsoidal heights and their orthometric counterparts. In this study, an adaptive approach for optimizing regional geoid model based on global geoid model and local GNSS/leveling measurements is presented. A rigorous sequential least squares approach coupled with an adjustable criterion is used for identifying appropriate observables so that an optimized model that fulfills a predefined quality level can be automatically produced. It has been demonstrated that a city scale geoid undulation model with a quality level around ± 14 mm km can be obtained by applying the proposed approach. [ABSTRACT FROM AUTHOR]

Engineering applications viz. flood inundation, hydrological modelling, canal alignment, pipeline alignment studies, etc. often require precise Orthometric heights. Airborne Light Detection and Ranging (LiDAR) sensor (ALS) provides precise terrain heights with decimetre accuracy in point form with reference to the WGS84 datum. To meet the requirement of the aforementioned applications, LiDAR heights are to be converted into Orthometric heights using geoid undulations having accuracy better than decimetre from the WGS84 datum. Accuracies of Geoid undulations that are available in the public domain (EGM2008, EGM96, CGM, etc.) are very coarse (meters) and are not suitable for the derivation of precise MSL heights. Hence often field surveys are conducted to derive precise geoid undulations at particular sampling spacing at the same location using accurate GNSS & Levelling instruments to obtain centimetre accurate WGS84 and MSL heights. Further Geometric method is used to derive the geoid undulations at each location using GNSS & MSL Heights collected in the field. To derive continuous surface of geoid undulations using field sample geoid undulation data which is collected at large irregular spacing depending on accessibility, spatial interpolation techniques are used. The accuracy of a derived continuous surface of precise geoid undulations mostly depends on the selection of interpolation technique, right field spatial sample distance and terrain variations. In this study, 5 test sites distributed across India are considered to evaluate the performance of spatial interpolation techniques viz. IDW, Local Polynomial Interpolation, Kriging, Spline, and Global Polynomial Interpolation. Deduced the critical interpolation parameter values which can provide the best outcome. Also studied optimal sample spacing required in the field to derive precise geoid undulations. Accuracies of derived geoid undulations by interpolation techniques are evaluated by RMSE, MAE and Coefficient of Determination metrics. It is observed that kriging is the best interpolation method to derive geoid undulations with 10 cm accuracy for the Indian region with optimal model point spacing of 10kms. [ABSTRACT FROM AUTHOR]

Applications of optical clocks in physical geodesy for determining geopotential are of increasing interest to scientists as the accuracy of optical clocks improves and the clock size becomes more and more compact. In this study, we propose a data processing method using the ensemble empirical mode decomposition technique to determine the geopotential difference between two sites in Wuhan based on the frequency comparison of two optical clocks. We use the frequency comparison record data of two Ca+ optical clocks based on the optical fiber frequency transfer method, provided by the Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences (Wuhan, China). By optical clock comparisons we obtained a geopotential difference of 42.50 ± 1.03 m2∙s−2 (equivalent to height difference of 4.33 ± 0.11 m) between the two sites, which is excellent compared to the geopotential difference of 42.56 ± 0.29 m2∙s−2 (equivalent to height difference of 4.34 ± 0.03 m) measured by a spirit leveling. The results show that the optical fiber frequency transfer method is promising in determining the geopotential and potential for unifying the world height system. [ABSTRACT FROM AUTHOR]

The Hong Kong Principal Datum (HKPD) is the currently adopted official geodetic vertical datum at the Hong Kong territories. The HKPD is practically realized by heights of levelling benchmarks. The HKPD heights are, however, neither normal nor orthometric. The reason is that heights of levelling benchmarks were determined from precise levelling measurements, but without involving gravity observations along levelling lines. To reduce systematic errors due to disregarding the gravity information along levelling lines, we used terrestrial and marine gravity data to interpolate gravity values at levelling benchmarks in order to compute and apply the orthometric correction to measured levelling height differences. Our results demonstrate the importance of incorporating the gravity information even for a relatively small region but characterized by a rough topography with heights of levelling benchmarks exceeding several hundreds of meters. According to our estimates, the orthometric correction reaches (and even slightly exceeds) ±2 cm, with maxima along levelling lines crossing mountain chains. [ABSTRACT FROM AUTHOR]

This study has been carried out to estimate the differences between spheroidal orthometric, orthometric and normal heights at 141 GPS/levelling stations over South Africa. The comparison is mainly conducted for the purpose of establishing a height system which is more consistent with the South African spheroidal orthometric height system. This is a necessary step towards establishment of a geoid consistent vertical datum as spheroidal orthometric height system applied in South Africa does not correspond to the vertical datum reference surfaces (geoid or quasigeoid). The differences between the orthometric and normal heights are estimated as a function of Bouguer gravity anomalies and the topographic height. The differences between the normal and spheroidal orthometric heights and the orthometric and spheroidal heights are estimated from normal gravity and interpolated actual gravity at the 141 GPS/levelling stations. The magnitudes of the separation between orthometric and normal heights over South Africa are relatively small. However, the land levelling datum (South African spheroidal orthometric height system) is more consistent with the normal height system than orthometric height system. The mean and standard deviation of the differences between orthometric and normal heights at 141 GPS/levelling stations are 19.4 cm and ± 17.6 cm , respectively. The separation between the spheroidal orthometric and normal heights is 21.3 cm on average, with a standard deviation of ± 23.8 cm . The separation between spheroidal orthometric and orthometric heights is 40.7 cm on average, with a standard deviation of ± 25.3 cm . These results indicate that normal height system and the corresponding surface, the quasigeoid model, should be adopted when developing a geoid consistent vertical datum over South Africa. [ABSTRACT FROM AUTHOR]

Shallow layer method (SLM) based on the definition of the geoid can determine the gravity field inside the shallow layer. In this study, the orthometric height of Mount Everest (HME) is calculated based on SLM, in which the key is to construct the shallow layer model. The top and bottom boundaries of the shallow layer model are the natural surface of the Earth and the surface at a certain depth below the reference geoid, respectively. The model-combined strategies to determine the geoid undulation (N) based on SLM are applied to calculate the HME by two approaches: (1) direct calculation by combining N and geodetic height (h); (2) calculation by the segment summation approach (SSA) using the gravity field inside the shallow layer. On December 8, 2020, the Chinese and Nepalese governments announced an authoritative value of 8848.86 m, which is referred to a geoid determined by the International Height Reference System (IHRS) (i.e., the geopotential is 62636853.4 m2s-2). Here, our results (combined strategies (1) EGM2008 and CRUST1.0, (2) EGM2008 and CRUST2.0, (3) EIGEN-6C4 and CRUST1.0, and (4) EIGEN-6C4 and CRUST2.0) are referred to the geoid defined by WGS84 (i.e., the geopotential is 62636851.7 m2s-2). The differences between our results and the authoritative value (8848.86 m) are 0.448 m, −0.009 m, −0.295 m, and −0.741 m by the first approach, and 0.539 m, 0.083 m, −0.214 m, and −0.647 m by the second approach. When the reference surface WGS84 geoid is converted to the IHRS geoid, the differences are 0.620 m, 0.163 m, −0.123 m, and −0.569 m by the first approach, and 0.711 m, 0.225 m, −0.042 m, and −0.475 m by the second approach.

The height obtained through the GNSS method is the ellipsoidal height and to have an efficient application in surveying it has to be converted into orthometric height. This paper aims to determine a local geoid model for a part of Duhok region based on the known orthometric height using GPS/levelling and assessing the precision performance of the two Earth gravitational models (EGM1996 and EGM2008) in the study area. The EGMs were adjusted based on root mean square errors, calculated from the differences between two geoid heights, GPS/levelling and EGMs. The Kriging interpolation method was used for creating a local geoid model based on GPS/levelling. The result from the adjusted geoid models to the survey data at 54 points revealed that the mean accuracy of geoidal heights at 0.08 m level is attainable. The precision performance of EGM96 is more precise than EGM08 by 14 mm in the area of interest.

This paper describes a forensic investigation of groundwater in an urban context in Italy. The present case study was conducted to detect the hydraulic flow path between a sportfishing pond and a nearby industrial plant's contaminated groundwater site. The investigation was performed to evaluate the potential for diffusion of contaminants through groundwater flow into a fishing pond located downstream from a chemical factory. High-precision altitude measurements of monitoring stations combined with continuous water level monitoring were crucial to understand the groundwater flow dynamics and define the hydrogeological conceptual model. The study verified that the fishing pond, dug in low-permeability volcanic rock, was not hydraulically connected to the groundwater flow. The presence of contaminants in the pond may be related to the periodic topping-up activity performed using water from an existing well. The identified groundwater flow paths were consistent with the possible contaminant migration from the chemical factory to the water well near the fishing pond. [ABSTRACT FROM AUTHOR]

Known for unique ultrahigh spatial resolution and timing accuracy, the VLBI global observing system (VGOS) time transfer of ultralong baselines can achieve better long-term stability compared to other techniques. Because of the 1 mm positioning accuracy of the VGOS, comparing high-performance atomic clocks with VGOS time transfer can be used to accurately determine the geopotential difference between two remote stations and unify the world height system in the framework of the theory of general relativity. To investigate its performance in determining geopotential differences, we schedule continuous VGOS sessions with a 7-station network, simulate and estimate the corresponding VGOS observables and determine the geopotential differences of six baselines. Furthermore, the coefficients of the tropospheric turbulence model and clock stability are varied to analyze their influences. The results show that when using atomic clocks with 1.0 × 10 - 16 @1 d stability, the accuracy and precision of the weighted averaged geopotential difference remain at the level of 8 m2s−2 and are sensitive to variations in the troposphere. The improvement by upgrading clock performance is limited by other error sources. In addition, connecting twin telescopes with identical atomic clocks and combining clock parameters in estimation can improve the precision of the estimated geopotential difference by approximately 4%. [ABSTRACT FROM AUTHOR]

Applications of optical clocks in physical geodesy for determining geopotential are of increasing interest to scientists as the accuracy of optical clocks improves and the clock size becomes more and more compact. In this study, we propose a data processing method using the ensemble empirical mode decomposition technique to determine the geopotential difference between two sites in Wuhan based on the frequency comparison of two optical clocks. We use the frequency comparison record data of two Ca+ optical clocks based on the optical fiber frequency transfer method, provided by the Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences (Wuhan, China). By optical clock comparisons we obtained a geopotential difference of 42.50 ± 1.03 m2∙s−2 (equivalent to height difference of 4.33 ± 0.11 m) between the two sites, which is excellent compared to the geopotential difference of 42.56 ± 0.29 m2∙s−2 (equivalent to height difference of 4.34 ± 0.03 m) measured by a spirit leveling. The results show that the optical fiber frequency transfer method is promising in determining the geopotential and potential for unifying the world height system.

The height obtained through the GNSS method is the ellipsoidal height and to have an efficient application in surveying it has to be converted into orthometric height. This paper aims to determine a local geoid model for a part of Duhok region based on the known orthometric height using GPS/levelling and assessing the precision performance of the two Earth gravitational models (EGM1996 and EGM2008) in the study area. The EGMs were adjusted based on root mean square errors, calculated from the differences between two geoid heights, GPS/levelling and EGMs. The Kriging interpolation method was used for creating a local geoid model based on GPS/levelling. The result from the adjusted geoid models to the survey data at 54 points revealed that the mean accuracy of geoidal heights at 0.08 m level is attainable. The precision performance of EGM96 is more precise than EGM08 by 14 mm in the area of interest. [ABSTRACT FROM AUTHOR]

It is well known that the success in precise determinations of the gravimetric geoid height (N) and the orthometric height (H) rely on the knowledge of the topographic mass distribution. We show that the residual topographic bias due to an imprecise information on the topographic density is practically the same for N and H, but with opposite signs. This result is demonstrated both for the Helmert orthometric height and for a more precise orthometric height derived by analytical continuation of the external geopotential to the geoid. This result leads to the conclusion that precise gravimetric geoid heights cannot be validated by GNSS-levelling geoid heights in mountainous regions for the errors caused by the incorrect modelling of the topographic mass distribution, because this uncertainty is hidden in the difference between the two geoid estimators.

Louisiana State University Center for GeoInformatics, as part of Regional Geospatial Modeling research funded by the National Geodetic Sun·ey (NGS) and Louisiana Board of Regents, is developing relationships among, aric, us gec, detic vertical data. Louisiana's geology is drnamic, making research here particularly interesting. This report is about an effort to prove the effectiveness of the first, foundational step toward an objective of relating terrestrial gravimetric potentials to the geodetic heightsl using the global nm'igation satellite system (GNSS) continuously operating reference station (CORS) antenna reference points (ARPs). It is being accomplished via trigonometric leveling techniques (tacheometry) with precision approaching il nini which determine the relative heights of a conventional benchmark to the ARP. Dependent steps to be followed include gravimetry and deflection of the vertical observation and are a subject for another time. A CORS antenna was temporarily· erected on the Engineering Research and Development building on the LSU campus iii Baton Rouge. Monuments wei-e installed at ground level nearb, to facilitate proof of the technique. A state-of-the-art I.eica TDRA6000 theodolite/total station was acquired for making the observations. One nioitument set nearly vertically below the antenna acts as a model CORS reference mark (RM). Several sets of observations were made. The difference was verified using a steel tape and a level offset from the ARP, and a handheld laser range finder. The result is the excellent consistency of relative heights within nearly 1 mm among the obsen'ation points. This result supports efforts to provide (1) precise elevations relative to the CORS and therefore the National Spatial Reference System (NSRS), and (2) a ft)undation from which one can develop several related surfaces, particularly a more precise geoid model. [ABSTRACT FROM AUTHOR]

The problem of datum transformation؛ determination of parameters for transferring curvilinear coordinate from one ellipsoid to another, is one of the main problems in geometrical geodesy. The problem draws the attentions of many researchers due to its role in the integration of all types of data in the geospatial database framework. Although the problem is one of the oldest geometrical problems by its nattire, it is still challenging because of the newly introduced Earth gravitational models and precise global coordinate measurements using the global positioning systems. Different methods have been introduced by many famous geodesists like Molodensky (1962), Vanicek (1986) and others. In this paper, we developed a full mathematical model for determination of datum tansformation parameters based on ellipsoidal approximation. It is theoretically and numerically compared with the previously developed model with spherical approximation. For small area, both models lead to the same accuracy while we expect to achieve higher with the ellipsoidal approximation in wider area. Moreover, lack of ellipsoidal height in the old data sets is one of the main obstacles for the hnplementation of the classical transformation schemes. TIerein, we introduced two methods for solving this problem. The Earth Gravitational Models (EGMs) which were wieldy available in the new century, thanks to the Earth gravity field's dedicated missions, were employed to get an estimate of the geoidal heights of the data point with enough accuracy. Alternatively, the idea of the widely used polynomial approxhnating correcting surface was considered to model the geoid height at the area of computation. The numerical results showed that the second alternative was most helpful. Higher accuracy and better fitness in terms of statistical goodness of fit criteria were the outcomes of the implementation of the polynomial approximating correcting surface. In order to show the performance of the ellipsoidal approximation as well as the idea of polynomial correcthig surface, 150 points were selected in the Nigeria. The curvilinear coordinates of the data points were given both in the CLARCK-1880 (local old coordinates) and the World Geodetic System 1984 (WGS84) as the global new coordinates. The old coordinates of the data points were geodetic latitudes, geodetic longitudes and orthometric heights where the new coordinate set is fully geodetic components. A quadratic polynomial mathematical model was employed to approximate the geoid surface in the county. The achieved results showed its reasonable accuracy. [ABSTRACT FROM AUTHOR]

This study covers the restoration of 124,910 parcels between 2013 and 2016 within the scope of the digital cadastre renovation work of northern Cyprus. The renovation work was commissioned by the Republic of Turkey Land Registry and Cadastre General Directorate via the tender process and turned over to the Turkish Republic of Northern Cyprus (TRNC). The geodetic infrastructure of the project consisted of 37 C2 and 68 C3 geodetic control points. 3D location calculations of the C2 and C3 networks were obtained based on the Continuously Operating Reference Stations Turkey (CORSTR) System (in reference epoch 2005.00 and datum ITRF96) and interpolation was determined via annual velocity vectors. In order to include the C2 and C3 networks in the TRNC Vertical Control Network, nine compatible vertical control points were included in the calculations. In this study, an orthometric elevation model specific to northern Cyprus was formed by using the 3D position information obtained via the Global Navigation Satellite System and the Cyprus geoid data. [ABSTRACT FROM AUTHOR]

The vertical positioning has two indispensable constituents: the height and the relevant reference surface. The definition of the height differs according to the appointed reference surface. Global Navigation Satellite Systems (GNSS) ensure ellipsoidal heights relative to a geodetic reference ellipsoid surface. However, many field applications require heights that are related to a physically meaningful surface (e.g. the geoid). Such physically meaningful heights often provided in terms of orthometric heights. The geoid undulation is the relation between the ellipsoidal and orthometric heights. The ellipsoidal heights can be transformed to orthometric heights via two principal approaches: a gravimetric geoid model, and geometrical interpolation between geoid undulations where GNSS observations have been collocated with benchmarks. The purpose of this study is investigating the applicability of a back propagation artificial neural network as a height transformation tool.

Modern height surveying obtains orthometric heights through geoid undulations and ellipsoidal heights derived from global navigation satellite system (GNSS), a process referred to as 'GNSS levelling'. In this study, an efficient survey technology, the e-global navigation satellite system (e-GNSS), was used instead of static satellite surveying to execute GNSS levelling. The e-GNSS in Taiwan is based on Virtual Reference Station-Real-Time Kinematic technology and networks. The orthometric heights were calculated by subtracting the geoid undulations, derived from three geoid models (gravimetric, hybrid, and geometric models), from the ellipsoidal heights, derived from the e-GNSS. Additionally, two corrector methods, namely the difference and the corrector surface method, were adopted to improve the accuracies and the systematic errors. The experiment showed that the two corrector methods improved the accuracies of the orthometric heights in the gravimetric model by approximately 66.3 and 80.0% and mitigated the systematic errors in the gravity model by approximately 96.2 and 99.9%. [ABSTRACT FROM AUTHOR]

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In this communication, we present the results of the first experimental verification of a quantum level based on the use of the effect of a gravitational time shift and the method of relativistic synchronization. The difference in orthometric heights was measured between a point in Moscow oblast and Nizhny Novgorod at a distance of about 480 km. We used a highly stable mobile quantum clock with a relative instability of 1 × 10–15, which provided a measurement error of about 9.1 m. [ABSTRACT FROM AUTHOR]

The purpose of this study is to precisely determine the orthometric height considering tropospheric delay at the top of the mountain where the height difference with reference ground surface is large. So, GNSS surveying was carried out at Cheonwangbong on Mount Jiri to determine the orthometric height, and GNSS data were processed by both DGNSS and PPP methods to determine ellipsoidal height using Bernese version 5.0 software. In this process, KNGeoid14 Korean geoid model was used and the effects of troposphere delay on the coordinates and orthometric height were analyzed. The study results showed that the tropospheric delay was reduced by 3.04 cm with every 100 m increase of the ellipsoidal height. The orthometric height and RMSE determined by the DGNSS method were found to be 1915.4596 m and 0.0520 m, respectively, and the orthometric height and RMSE determined by the PPP method were found to be 1915.4059 m and 0.0527 m, respectively. So, the difference between the DGNSS method and the PPP method when tropospheric corrections were applied showed a difference of 5.37 cm in orthometric height. And, the results also showed that the difference in whether or not the tropospheric delay model was applied in the calculation of the orthometric height was 1.53 cm in the same DGNSS method. [ABSTRACT FROM AUTHOR]

Leveling is a traditional geodetic surveying technique that has been used to realize a vertical datum. However, this technique is time consuming and prone to accumulate errors, where it relies on starting from one station with a known orthometric height. Establishing orthometric heights using Global Navigation Satellite Systems (GNSS) and a geoid model has been suggested [14], but this approach may involve less precisions than the direct measurements from leveling. In this study, an experimental study is presented to adjust the highly accurate leveling observations along with orthometric heights derived from GNSS observations and a geoid model. For the geoid model, the National Geodetic Survey's gravimetric geoid model (TxGEOID16B) and hybrid geoid model (GEOID12B) were applied. Uncertainties in the leveled height differences, GNSS derived heights, and the geoid models were modeled, and a combined adjustment was implemented to construct the optimal combination of orthometric, ellipsoidal, and geoid height at each mark. As a result, the discrepancy from the published orthometric heights and the CSM (Corrector Surface Model) based adjusted orthometric heights with GEOID12B showed a mean and RMS of -8.5 mm and 16.6 mm, respectively, while TxGEOID16B had a mean and RMS of 28.9 mm and 34.6 mm, respectively. It should be emphasized that this approach was not influenced by the geodetic distribution of the stations where the correlation coefficients between the distance from the center of the surveying network and the discrepancy from the published heights using TxGEOID16B and GEOID12B are 0.03 and 0.36, respectively. [ABSTRACT FROM AUTHOR]