Orthometric Heights Research Articles

Geoid Modelling of Kalimantan Island using Airborne Gravity Data and Global Geoid Model (EGM2008)

The availability of geoids, especially in survey and mapping activities, is useful for transforming the geometric heights obtained from observations of the Global Navigation Satellite System (GNSS) into orthometric heights that have real physical meanings such as those obtained from waterpass measurements. If a geoid is available, the orthometric heights of points on earth can be determined using the GNSS heighting method. The use of modern survey and mapping instruments based on satellite observations such as GNSS is more efficient in terms of time, effort, and cost compared to the accurate waterpass method. According to the Indonesian Geospatial Information Agency (BIG) it is stated that the application of geoid as a national Vertical Geospatial Reference System has an adequate and ideal category if the accuracy is higher than 15 cm. Recent studies have shown that it is possible to generate local geoid models with centimetre accuracy by utilizing airborne gravity data. We calculate free-air gravity anomaly data is calculated by processing airborne gravity and GNSS data using the Stokes Integral method on AGR software. Next a geoid model is created by calculating the contribution of three components, namely the long wave component represented by the EGM2008 global geoid data model, the shortwave component represented by the Shuttle Radar Topography Mission (SRTM) data and the medium wave component represented by the free-air gravity anomaly data. The geoid model validation was carried out using the geoid fitting method for geoid accuracy by calculating the difference between the gravimetric geoid and the geometric geoid and comparing it with the global geoid model EGM2008 degrees 2190. As a result, the total geoid model accuracy value was determined to be 49.4 cm on gravimetric geoid undulations with a standard deviation of 7.1 cm. Meanwhile, the results of the EGM2008 geoid undulation accuracy test at 2190 degrees resulted in an accuracy of 51.9 cm with a standard deviation of 9.9 cm. These results indicate that the local geoid model from airborne gravity measurement data produces a geoid model with a higher accuracy than the global geoid model EGM2008 degrees 2190. However, the accuracy of the resulting data is still below the BIG standard of 15 cm, so further research is needed to produce a geoid model which conforms to the standard.

Assessment of high-degree reference models and Recent Goce/Grace Global Geopotential Models over Sudan based on the GPS/Leveling data

Nowadays, Global Geopotential Models (GGMs) can be used as a reference to develop more detailed regional/local geoids, or they can be used to provide geoid heights on their own. Since 2000, several GGMs have been released, and they are mainly derived from satellite gravity measurements, satellite-only models, terrestrial gravimetry, altimeter-derived gravity data in marine areas, and airborne gravity data. With a precise geoid model, ellipsoidal heights obtained from GPS can be converted to orthometric heights, which is reasonably quite needed in Geodesy, Civil Engineering, etc. These heights reflect changes in topography as well as local variations in gravity. This paper evaluates some of the latest releases of high degree reference models and the satellite-only global gravity field model over Sudan using 19 GPS/Leveling stations. We have been selected 6 GGMs based on Gravity field Goce and Grace, and they released in 2020, 2019, 2014, 2008, and 1996 as shown in the International Centre for Global Earth Models website (ICGEM). The accuracy evaluation of the GGM models have been discussed, the accurate GGMs over Sudan are XGM2019e_2159 and GOCO05s, which have indicated -0.019 and 0.046 meters, respectively. The evaluation results produce valuable information to academia and geoid modeling research topics in Sudan, which shows the precise model from the selected GGMs in Sudan by using the available GPS/Leveling data.

Determination of Deflection of the Vertical Components: Implications on Terrestrial Geodetic Measurement

The deflection of the vertical is an important parameter that combines both physical (astronomic) and geometric (geodetic) quantities. It is critical in such areas as datum transformation, reduction of astronomic observation to the geodetic reference surface, geoid modelling and geophysical prospecting. Although the deflection of the vertical is a physical property of the gravitational field of the earth; which almost all terrestrial survey measurements, with the exception of spatial distances, made on the earth surface are with respect to the Earth’s gravity vector, because a spirit bubble is usually used to align survey instruments. It has been ignored in most geodetic computation and adjustment. This research work is therefore aimed at computing the component of the deflection of the vertical component for part of Rivers State using a geometric method. This method involves the integration of Global Positioning System (GPS) to obtain the geodetic coordinate of points, precisely levelling to obtain the orthometric height of this point located within the study area. By least square using MATLAB program, the estimated deflections of vertical component parameters for the test station SVG/GPS-002 were; -0.0473” and 0.0393” arc seconds for the north-south and east-west components respectively. The associated standard errors of the North-south and East-west components were ±0.0093” and ±0.0060” arc seconds, respectively. The deflection of the vertical was also computed independently from gravimetric models of the earth as: ξ = 0.0204” ±0.0008814”, η = -0.0345” ±0.0014”; ξ =0.0157” ±0.000755”, η = -0.0246” ±0.0012”; ξ = -0.0546±0.0006014, η = -0.0208±0.0006014 for EGM 2008, EGM 1996 and EGM 1984 respectively. The two-tailed hypothesis test revealhat the estimated deflection component is statistically correct at 95% confidence interval. It was observed that the effect of the deflection of the vertical is directly proportional to the distance of the geodetic baseline. Therefore, including the derived component of deflection of the vertical to the ellipsoidal model will yield high observational accuracy since an ellipsoidal model is not tenable due to its far observational error in the determination of high-quality job. It is important to include the determined deflection of the vertical component for Rivers State, Nigeria.

Integration of satellite geodetic observations for regional geoid modeling using remove-compute-restore technique

Advanced satellite geodetic systems have contributed to improving knowledge on changes in global gravity fields in recent years. These systems offer profound opportunities in the determination of a high-precision, high-resolution gravimetric geoid models in data deficient regions. However, due to the absence of research competence in some regions, these conventional datasets have not been implemented to update the obsolete reference frames which have been in use in these regions. This study introduces the well-known Remove-Compute-Restore (RCR) technique in modeling a gravimetric geoid model for a large data deficient region in West Africa (Nigeria) using two sets of long and short wavelength data (a) EGM2008 (long) + Airborne gravimetric observation (AGO) dataset (short) (b) EGM2008 (long) + Terrestrial gravimetric undulation (TGU) dataset (short). This therefore resulted in obtaining two sets of resultant RCR-gravimetric details whose statistics comparative assessments are produced in the body of this work. The RCR-determined gravimetric geoid model showed a strong relationship with the observed terrestrial data. The goodness of fit for the orthometric height correlation between the computed gravimetric geoid and the terrestrial data is 97.87 %. Strong relationships between the computed model and the other height models determined from the primary data are also observed. The difference between the Flury and rummel geoid-based model and the Heiskanen and moritz model in the geoid-quasi geoid separation phase shows the importance of implementing the ‘rigorous modeling technique’ for geoid quasi-geoid separation instead of the approximation method. However, the discrepancy between both models can be overlooked in a case of low accuracy geoidal operations. The RCR-based Fast Fourier Transform (FFT), and the least squares modified stokes (LSMS) was used in the quasi-geoid determination of the study region. Using the 1-parameter fit, the modified Stokes integral (FFT(b)) outperformed the LSMS model with a root mean square (rms) difference of 0.6 cm, while the LSMS outperformed both the unmodified (FFT(a)) and the modified (FFT(b)) Stokes integral using the 4-parameter fit with a rms difference of 0.5 cm. The use of both models in this study created a better perception of the quasi-geoid differential analysis, and a more refined understanding of their interaction with the satellite based quasi geoid.

On the determination of a locally optimized Ellipsoidal model of the Geoid surface in sea areas

Deriving a local geoid model has drawn much research interest in the last decade, in an endeavour to minimize the errors in orthometric heights calculations, inherited by the use of global geoid reference models. In most parts of the earth, the local geoid surface may be tens of meters away from the Global Reference biaxial Ellipsoid (WGS84), which create numerus problems in topographic, environmental and navigational applications. Several methods have been developed for optimizing the precision of the calculation of the geoid heights undulations and the accuracy of the corresponding orthometric heights calculations. The optimization refers either to the method used for data acquisition, or to the geometrical method used for the determination of the best fit local geoid model. In the present work, we focus on the reference ellipsoid used for the geometric and geoid heights determination and develop a method to provide the one that fits best to the local geoid surface. Moreover, we consider relatively small sea regions and near to coast areas, where the usual methods for data acquisition fail more or less, and we pay attention in two directions: To obtain accurate measured data and to have the best possible reference ellipsoid for the area at hand. In this due, we use the “GNSS-on-boat” methodology to obtain direct sea level data, which we induce in a Moore Penrose pseudoinverse procedure to calculate the best fit triaxial ellipsoid. This locally optimized reference ellipsoid minimizes the geometric heights in the region at hand. The method is applied in two closed sea areas in Greece, namely Corinthian and Patra’s gulf and also in four regions in the Ionian Sea, which exhibit significant geoid alterations. Taking into account all factors of uncertainty, the precision of the mean sea level surface, produced by the “GNSS on boat” methodology, had been estimated at 5.43 cm for the gulf of Patras, at 3.76 cm for the Corinthian gulf and at 3.31 for the Ionian and Adriatic Sea areas. The average difference of this surface and the local triaxial reference ellipsoid, calculated in this work, is found to be less than 15 cm, whereas the corresponding difference with respect to WGS84 is of the order of 30m.

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

Abstract. 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).

Development of the Korean National Geoid Model (KNGeoid18) and Applications for the Height Determination of Coastal Land Points

Lee, J.; Kwon, J.H.; Lee, Y., and Lee, H., 2021. Development of the Korean National Geoid Model (KNGeoid18) and applications for the height determination of coastal land points. In: Lee, J.L.; Suh, K.-S.; Lee, B.; Shin, S., and Lee, J. (eds.), Crisis and Integrated Management for Coastal and Marine Safety. Journal of Coastal Research, Special Issue No. 114, pp. 405–409. Coconut Creek (Florida), ISSN 0749-0208. Since 2008, new land gravity data showing a homogeneous distribution and high precision have been obtained in Korea. In addition, a new version of the global geopotential models which were developed based on observations by the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) satellite are available. Thus, a gravimetric geoid was newly developed by the “Remove-Restore” technique using the experimental gravity field model 2016 (XGM2016) and more than 12,000 points of land gravity data. In addition, airborne, shipborne, and Danish Technical University 2010 (DTU10) altimeter gravity data, as well as a terrain model, were applied for geoid modeling. As a final product of the study, the hybrid geoid, Korean National Geoid model 2018 (KNGeoid18), was modeled by fitting the gravimetric geoid to a total of 2,791 points of global navigation satellite system (GNSS)/leveling data located over the entire Korean peninsula. The degree of fit of KNGeoid18 was calculated to be approximately 2.3 cm. One of the necessities of a local geoid model is to efficiently determine the orthometric height in terms of time and cost. Thus, GNSS surveying was conducted at 19 points and GNSS-derived orthometric heights were computed. Among the 19 points, the precision of the official orthometric heights at 12 points located in mountainous areas is known to be larger than 10 cm; hence, the GNSS-derived orthometric heights were calculated using Trimble business center (TBC), Leica geo-office (LGO), and Giodis, and compared with each other. As a result, it was found that the difference in heights at 12 points did not exceed 5 cm. The other 9 points, located in coastal areas, had a difference smaller than 3 cm compared to the official orthometric height. It is expected that orthometric heights with a target precision of 3–5 cm would be determined by GNSS surveying and the local geoid model, but an improvement of the geoid model in mountainous areas is still necessary.

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.

On determination of the geoid from measured gradients of the Earth's gravity field potential

The geoid is an equipotential surface of the static Earth's gravity field which plays a fundamental role in definition of physical heights related to the mean sea level (orthometric heights) in geodesy and which represents a reference surface in many geoscientific studies. Its determination with the cm-level accuracy or better, in particular over dry land, belongs to major tasks of modern geodesy. Traditional data and underlined theory have significantly been affected in recent years by rapid advances in observation techniques. This study reviews gradients of the disturbing gravity potential, both currently available and foreseen, and systematically discusses mathematical models for geoid determination based on gradient data. Fundamentals required for geoid definition and its estimation from measured potential gradients are shortly reviewed at the beginning of the text. Then particular mathematical models based on solutions to boundary-value problems of the potential theory, which include both integral transforms and integral equations, are formulated. Properties of respective integral kernel functions are demonstrated and discussed. With the new mathematical models introduced, new research topics are opened which must be resolved in order to allow for their full-fledged applicability in geoid modelling. Stochastic modelling is also discussed which estimates gradient spatial resolution and accuracy required for geoid modelling with the cm-level accuracy. Results of stochastic modelling suggest that the cm-geoid can be estimated using available gradient data if related problems, namely reduction of gradient data for gravitational effects of all masses outside the geoid and their downward continuation, are solved at the same level of accuracy.

Determination of the orthometric height difference based on optical fiber frequency transfer technique

The development of remote frequency transfer techniques, especially the appearance of optical clocks with unprecedented stability, has prompted geoscientists to study their applications in geodesy. Using remote frequency transfer technique, by frequency comparison of two optical clocks at two points P and Q connected by optical fibers, one can measure the signal's frequency shift between them, and the geopotential difference between them can be determined based on the gravity frequency shift equation. Given the orthometric height of P, the orthometric height of Q can be determined. Since the present stability of the optical clock has achieved 1 × 10−18 or better and comparing the frequency transfer via optical fiber provides stability at 10−19 level, the optical clock network enables determining the orthometric height at centimeter-level. This study provides a formulation to determine the height difference at one-centimeter level between two points on the ground based on the optical fiber frequency transfer technique.

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.

Global Estimation and Assessment of Monthly Lake/Reservoir Water Level Changes Using ICESat-2 ATL13 Products

Accurate and detailed information on lake/reservoir water levels and temporal changes around the globe is urgently required for water resource management and related studies. The traditional satellite radar altimeters normally monitor water level changes of large lakes and reservoirs (i.e., greater than 1 km2) around the world. Fortunately, the recent Ice, Cloud, and land Elevation Satellite-2 (ICESat-2) makes it possible to monitor water level changes for some small lakes and reservoirs (i.e., less than 1 km2). ICESat-2 ATL13 products provide observations of inland water surface heights, which are suitable for water level estimation at a global scale. In this study, ICESat-2 ATL13 products were used to conduct a global estimation and assessment of lake/reservoir water level changes. We produced monthly water levels for 13,843 lakes and reservoirs with areas greater than 0.1 km2 and all-season ATL13 products across the globe, in which 2257 targets are smaller than 1 km2. In total, the average valid number of months covered by ICESat-2 is 5.41 months and only 204 of 13,843 lakes and reservoirs have water levels in all the months in 2019. In situ water level data from 21 gauge stations across the United States and 12 gauge stations across Australia were collected to assess the monthly lake/reservoir water levels, which exhibited a high accuracy (RMSE = 0.08 m, r = 0.999). According to comparisons between the monthly water levels and changes from ATL08 products in another study and ATL13 products in this study, we found that both products can accurately estimate the monthly water level of lakes and reservoirs, but water levels derived from ATL13 products exhibited a higher accuracy compared with water levels derived from ATL08 products (RMSE = 0.28 m, r = 0.999). In general, the ATL13 product is more convenient because the HydroLAKES mask of inland water bodies, the orthometric height (with respect to the EGM2008 geoid) of water surfaces, and several data quality parameters specific to water surfaces were involved in the ATL13 product.

Determination of the height of Mount Everest using the shallow layer method

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.

Regional features of birth rate and mortality in the Lower Volga region in the famine of 1932-1933s

The paper is exploring the problem of the vital rate data in the Lower Volga region during the famine of 19321933. Despite the ample quantity of papers presenting this problem the estimations and indicators differ even in the papers of the same authors and valuation methods are not always reliable. The birth rate of the Lower Volga region was 76223 while the mortality was 184570 during the 1933 famine peak by our estimate. However, there are no vital rate data on the Kalmykia in the central statistical administration archives and the registration of 15,2 thousand deaths were not ascertained identically. The real losses from the famine of 19321933 in the Lower Volga region (excluding Kalmykia) are estimated at 175 thousand maximum and birth rate losses are 147 thousand in 19321934. The mortality of the Lower Volga region had clear geographical distribution and location. The high mortality regions were allocated on the Volga Upland and abutting the Oka-Don plain eastern frontier and on the Medium Syrt frontier in Saratov Krai. The allocation of high mortality regions to the Volga River is interpreted as associating with regions containing major cities and towns with high mortality neighborhoods to the Volga. Stalingrad Krai is defined as a region with lower mortality and gradual slow in its increase with a low peak displaced to July 1933. In 1933 the Lower Volga mortality dynamics was from north to south epidemic; whereas in the south there was time to assume the measures as opposed to northern regions. Some Lower Volga regions in 1933 were characterized by a catastrophic low birth rate and high mortality and at the same time by high birth rate and low mortality and positive vital rate data. The distribution of high mortality regions was determined by the character of local authorities activities and local conditions including geographical description (orthometric height), that requires background study.

Roman Aqueduct Flow Estimation Using Geomatic Measurement

The aqueducts built by the ancient Romans are among the most impressive evidence of their engineering skills. The water inside the aqueducts was transported for kilometers, exploiting only the slight but constant differences in altitude throughout the route. To keep the differences in height constant, the aqueducts could proceed underground or aboveground on well-known arched structures that supported lead, ceramic or stone pipes. In order to reconstruct the characteristics of these structures, it is necessary to carry out an accurate survey of the orthometric heights, and therefore the most suitable technology is geometric levelling. In this case, however, it is not applicable, and therefore here we propose an alternative methodology. The final goal of this work was to estimate the flow of some sectors of these aqueducts preserved in the area south of the city of Rome. This has two main purposes: The first is to reconstruct the flow rate of these aqueducts for historical studies; the second is to check how much the orthometric heights have changed over the centuries, in order to reconstruct the movements from a geophysical and geodynamic point of view. The latter analysis will be developed in a following phase of this research. For this purpose, a high-precision geomatic survey was carried out in the area under study, partly retracing a survey already carried out in 1917 whose purpose and methodologies are not known. The area has been affected by a gradual subsidence over centuries, including since 1917. The observed sections of the aqueducts showed average inclinations, slightly lower than the 2 per thousand that is reported in the literature for similar aqueducts. The measurements carried out allowed the flow rate of the two specific aqueducts to be estimated more accurately, both as they were originally and in the presence of deposits that have accumulated during the years of use of the aqueducts. The reconstruction of the initial geometry will later be used as a reference to estimate how much the geodynamic deformations of the area have deformed the aqueducts themselves.

A Comparison of Orthometric Heights Calculated from (GPS/Leveling) and (EGM08) Methods Based–GIS

Interest in the study of global gravitational models has increased recently all over the world because it is necessary for height datum transformations. Today the International Center for Global Earth Models (ICGEM) provides the largest collection in the world produced through gravitational data from the gravitational satellite’s missions CHAMP, GRACE, and GOCE … Etc. To allow easy access through the internet with its more intelligent technologies, it is one of the International Gravity Organization’s services. While the Global Positioning System (GPS) has become one of the most preferred technologies in engineering surveying, a major dilemma in GPS survey lies in oval-based elevations. At the same time, orthometric heights are commonly used in the engineering field. Therefore, it is necessary to convert the measured heights by satellites assigned to the elliptical surface into orthometric heights and supported to the geoid surface (mean sea level) through an accurate geodetic model. The differences between orthometric measurement heights from DGPS/leveling data (obtained from 57 points in the study area) are increasingly used by professionals geographical information systems(GIS). However, the local determination of Geoid is necessary for better accuracy of the orthometric height from DGPS. This paper aims to introduce a modern technique for determining elevation, avoiding cumbersome and time-consuming spirit leveling operations. Fast vertical positioning can be obtained using DGPS with geoid models. The Root Mean Square Error (RMSE) is ± 0.19 m with high precision of DGPS derived with EGM08; thus, the more it describes the Earth’s gravitational field in more detail.

Estimation the components of deflection of the vertical for a point in Baghdad City - Iraq

In the age of the satellite geodesy, the GNSS is widely used in development of geodetic networks and that give much application, for that reason the study is to estimate deflection of the vertical of a point in Baghdad City in Iraq, the estimated depends on the orthometric height, which computed through the levelling and the ellipsoidal height, which computed from the GPS observations. Due to the lack of survey data and the difficulty of taking terrestrial measurements as a result of the security situation the authors used only 5 points for the national network in Baghdad. The deflection of the vertical component component ξ in the north-south direction calculated as ξ=2.5”±0.001” and the prime vertical component η in the east-west direction calculated as η=5.23” ±1.5”. The results were obtained showing that it can calculate the deflection of the vertical at sufficient accuracy.

Derivation of MSL Riverbank Line from UAV DSM Data based on Tidal Slope Analysis

Deriving a riverbank line at a tidal river is complicated, since dynamic factors such as tide and slope topography influence its location. Hence, this study utilises the Unmanned Aerial Vehicle (UAV), geodetic, and tidal data to identify the exact riverbank line based on Mean Sea Level (MSL) value from UAV products. We carried out two epochs of UAV data collection during low and high tide conditions. Orthometric height (H) has been applied in UAV data processing to produce a high accuracy of orthophoto and Digital Surface Model (DSM). UAV-MSL derived riverbank lines have been identified from the UAV orthophoto image using supervised classification and feature extraction techniques. DSM model provides the topographical height in three-dimensional (3D) view and enables identifying low and high tide, MSL, and lowest astronomical tides (LAT) at the riverbank. The study found that UAV-MSL derived riverbank line was identified in between the MSL value (at 2.302 m) and chart datum (at 1.043 m). This study also identified the correlation model, R2 value at 0.9288 between UAV-MSL derived riverbank line with MSL-tide gauge data. This study provides an alternative for researchers to determine riverbank lines based on UAV derived MSL instead of using only tide gauge data.

Evaluating two numerical methods for developing a local geoid model and a local digital elevation model for the Red Sea Coast, Egypt

Global Navigation Satellite System (GNSS) provides ellipsoidal heights, whereas engineering projects need orthometric heights of points. Thus, to take advantage of GNSS in engineering work, the relation between orthometric and ellipsoid height must be determined as a function of position by geoid modeling. The Red Sea coastal cities have various natural potentials that render them economically promising cities that are attractive to numerous investors and visitors alike. Over the past years, there has been an increased governmental awareness of setting up large projects in these cities. With the increasing utilization of GNSS in a number of these projects, there is an imperative need to develop a local geoid model in this region. This study is an attempt to use a geometric method for the study area in order to develop a local geoid model and a local digital elevation model. In addition, the performance of EGM2008, SRTM, and ASTER is evaluated. In order to develop the local geoid model, the polynomial regression method and Artificial Neural network (ANN) technique are employed. Performance evaluation of the studied methods is based on a compilation of various statistical parameters and goodness-of-fit measures, followed by a comparison of methods outputs. The study indicates significant improvements in the local geoid model when using both methods. Additionally, the model resulting from the ANN appears more reliable compared to the calculated model using polynomial regression. In this study, the accuracy of EGM2008 is about ±0.466 m. Moreover, regarding the global digital elevation model, ASTER outperforms SRTM by about ±0.905 m.

Collocation and FFT-based geoid estimation within the Colorado 1 cm geoid experiment

In the frame of the International Association of Geodesy Joint Working Group 2.2.2 “The 1 cm geoid experiment”, terrestrial and airborne gravity datasets along with GPS/leveling data were made available for the comparison of different geoid modeling methods and techniques in the wider area of Colorado, USA. We discuss the methods and procedures we followed for computing gravimetric quasi-geoid and geoid models and geopotential values from the available datasets. The procedures followed were based on the remove-compute-restore approach using XGM2016 as a reference geopotential model. The higher frequencies of the gravity field were computed via the residual terrain correction, using (a) the CGIAR-CSI SRTM digital elevation model with the classical technique and (b) a spectral one. Least-Squares Collocation was used for the downward continuation of the airborne data and for gridding. Finally, the geoid models were obtained by applying Least-Squares Collocation and spherical FFT-based methods, while the influence of the orthometric height correction on geoid heights was taken into account by employing simple and complete Bouguer reductions. All results were evaluated with available GPS/leveling benchmarks. Moreover, potential values were determined in support of the International Height Reference System/Frame. From the results acquired, a final accuracy of 5–7 cm for the determined geoid models was achieved depending on the adopted method and data combination, without considering the accuracy of the GPS/leveling data used for their evaluation. The contribution of the airborne gravity data was deemed as limited in combination solutions although the airborne only solution provided equal level of accuracy to the terrestrial and the combined ones. Better consistency was obtained on the points of the GSVS17 line, when compared to the GPS/leveling data, where an accuracy of 2.4 cm and 2.8 cm was reached for the FFT and LSC based methods, respectively.