Global Geoid Models Research Articles

Modelling geoid height errors for local areas based on data of global models

Abstract The development of global geoid models became feasible following the launch of specialised satellite missions. Today, the root mean square deviation of the heights in global models of high degree & order varies from centimetres to decimetres across different countries. In countries where the accuracy of such models is lower, there is potential to enhance their precision by applying specific corrections. This study presents a novel methodology for locally modelling the height errors of high degree & order global geoid models using levelling sub-benchmarks for GNSS stations. The methodology is based on a combination of optimal interpolation methods, filtering, and the concept of data weighting by gravity anomaly differences. The methodology is aimed at creating a hybrid model that aligns with the local characteristics of the geoid (or quasi-geoid) derived from the traditional levelling network. The advantage of this methodology lies in its ability to reduce the residual height errors of the EGM2008 and EIGEN6C4 models to less than 1 cm when using only four control points. Such results exceed the initial values of the systematic height errors of these models by 90–96 %. For the GECO model, the residual errors are around 2 cm, while for the XGM2019e_2159 model, they reach 3 cm. These results indicate that this methodology can be applied to all global models of high degree & order, although its effectiveness may vary depending on the specifics of a particular model.

Geoid Undulation Model as Vertical Reference in Indonesia

Indonesia released a new regional geoid model in 2020—the Indonesian Geoid 2020 (INAGEOID2020). It covers the Indonesian region with a spatial resolution of 0.01 × 0.01 degree with the unit in meters. The model was generated through a series of data and computations. Three components of gravity data, i.e., the observed free-air anomaly, the long-wave from the global geoid model, and the short-wave from the terrain model, were employed. The computation was performed using the Remove-Compute-Restore technique with the Fast Fourier Transformation approach. The output was then fitted to the geoid at tide stations by adding a fitting plane to the geoid model. The fitting plane was constructed based on the difference between the geoid model and each tide gauge benchmark. The final geoid model was evaluated by comparing the model with the reference data. Based on quality metrics, the accuracy of INAGEOID2020 varied between 6 cm to 29 cm. Any interested user can use this gridded geoid model to convert geodetic to orthometric heights and vice versa.

Improving mean water lake surface elevation estimates using dense lidar measurements from the GEDI satellite mission

Lakes are an essential component of the global water cycle and are considered as sentinels of climate change. An accurate estimate of lake's water levels is necessary for reliable continuous monitoring of their water balance. Due to their huge number worldwide, satellite altimetry has been identified as an efficient tool for measuring their temporal variations of water level. This technique can reach an accuracy of a few centimeters for water level estimates over large lakes. Due to the coarse across-track spatial resolution of the radar altimetry missions, their spatial sampling only covers a small part of the lakes surface. To obtain an accurate estimate of the lake water level, it is necessary to apply a correction to account for the small-scale orthometric height undulations occurring on the lake area and not present in the current global geoid models. In this study, the high-density lidar measurements from GEDI are used to estimate the mean lake surface. From the 1,366,211 GEDI data over 1239 tracks acquired over more than 6000 km2 of the surface of Lake Issy-Kul (Kyrgyzstan, Central Asia) between May 2019 and mid-November 2021, 654,592 shots over 843 tracks were selected after a multi-step quality-check and processed to generate a mean lake surface of Lake Issyk-Kul. Comparison between the GEDI-based mean lake surface and GNSS kinematic surveys corrected from the lake level variations exhibit an RMSE of 0.065 m. The principal objective of performing such mean lake surface is to further use it in the framework of the calibration/validation of the Surface Water and Ocean Topography (SWOT) mission.

Прогнозування потенційних похибок аномалій висот глобальних моделей геоїда для різних систем припливів

The article presents the method of predicting the errors of height anomalies obtained from high-order global geoid models (EGM_2008, EIGEN_6C4, GECO, XGM2019e2159, SGG_UGM_2) and taking into account different tide systems (free/zero/mean-tide). A correct understanding of how much the choice of the global model height tide system affects the accuracy of calculating the normal heights of the Earth’s physical surface is an important component for obtaining reliable results. The purpose of the work is to predict the potential errors of height anomalies for three main concepts of tidal corrections (tidal systems) used in the creation of global geoid models. Method. The essence of the prediction method is to find a connection between the height anomalies of the global geoid models and the PL-quasi-geoid2021 regional quasi-geoid model. On the basis of the established connection, the prediction of potential errors of height anomalies was made, taking into account the choice of one or another system of tides. The prediction of the errors of height anomalies is implemented on the basis of 200 GNSS stations located on the territory of Ukraine and in the border sector. To find the connection between the heights of the global geoid models and the PL-quasi-geoid2021 regional model, a territory was allocated in the western border sector measuring 48°-52° in latitude and 21°-25° in longitude. For 36 GNSS stations located in the border area, a scale coefficient between global and regional height anomalies was found. Results. In the border sector, the factual errors of height anomalies are estimated at the level of 0.01-0.03 m based on the standard deviation and at the level of the mean square deviation of 0.17–0.18 m, 0.15-0.16 m, and 0.08–0.09 m for the free, zero and mean-tide systems, respectively. The standard deviations of the predicted potential errors for the border sector were 0.02-0.03 m, and the mean square values were 0.17–0.18 m, 0.13 m and 0.06 m for similar tidal systems. The residual errors of height anomalies for the border sector amounted to 0.03 m according to the standard and mean square deviation. Assessment of accuracy prediction of potential errors of height anomalies of models EGM_2008, EIGEN_6C4, GECO, XGM2019e2159, SGG_UGM_2 carried out on the basis of 200 GNSS stations was 0.03 m by standard deviation and 0.15 m (free-tide), 0.13 m (zero-tide) and 0.06 m (mean-tide) by mean square value. Scientific novelty. First implemented was the prediction of potential errors of height anomalies of global geoid models, which was performed by the scale factor for GNSS stations located on the territory of Ukraine and taking into account different tidal systems. Practical significance. The predicted errors of height anomalies make it possible to calculate the normal heights of GNSS stations and points on the Earth’s physical surface with an accuracy of about 3 cm. The obtained results allow the use of height anomalies of global geoid models of high order for more accurate geodetics work.

Assessment of latest global gravity field models by GNSS/Levelling Geoid

This paper focuses on making a comparing of GNSS/Levelling data and data obtained from global geopotential models. For comparison, geoid undulations obtained by GNSS/Levelling method and geoid undulations obtained from global geopotential models have been used. As global geopotential models, SGG-UGM-2, XGM2019e_2159, GO_CONS_GCF_2_TIM_R6e, ITSG-Grace2018s, EIGEN-GRGS.RL04.MEAN-FIELD, GOCO06s, GO_CONS_GCF_2_TIM_R6, GO_CONS_GCF_2_DIR_R6 GGMs are used. The data sets used in the improvements of the models are altimetry, satellite, location data and topography. The disparities between the geoid undulations obtained from the GNSS/Levelling method and geoid undulations obtained from global geoid models have been taken. Some statistical criteria for these differences have been calculated. These criteria, such as smallest, biggest, average, standard deviation, Root Mean Square RMS statistical values of deviations between GNSS/Levelling geoid and global geopotential models, are taken into consideration when comparing the models. According to the comparison, the global gravity field model that best fits the GNSS/Levelling is selected.

Methodology for local correction of the heights of global geoid models to improve the accuracy of GNSS leveling

At present, one of the methods used to determine the height of points on the Earth's surface is Global Navigation Satellite System (GNSS) leveling. It is possible to determine the orthometric or normal height by this method only if there is a geoid or quasi-geoid height model available. This paper proposes the methodology for local correction of the heights of high-order global geoid models such as EGM08, EIGEN-6C4, GECO, and XGM2019e_2159. This methodology was tested in different areas of the research field, covering various relief forms. The dependence of the change in corrected height accuracy on the input data was analyzed, and the correction was also conducted for model heights in three tidal systems: “tide free”, “mean tide”, and “zero tide”. The results show that the heights of EIGEN-6C4 model can be corrected with an accuracy of up to 1 cm for flat and foothill terrains with the dimensionality of 1°×1°,2°×2°,and3°×3°. The EGM08 model presents an almost identical result. The EIGEN-6C4 model is best suited for mountainous relief and provides an accuracy of 1.5 cm on the 1°×1° area. The height correction accuracy of GECO and XGM2019e_2159 models is slightly poor, which has fuzziness in terms of numerical fluctuation.

Методика формирования цифровых моделей высот геоида для референцных систем координат

A technique was developed for generating digital models of geoid heights for reference coordinate systems using the Trimble Bussines Center software (TBC software). The source models can be the publicly available high-precision global geoid elevation models EGM2008, EIGEN6C4 and other models whose files with the *.ggf extension are compatible with the TBC software. The technique is based on the possibility of exporting orthometric heights from the TBC software in ASCII format to a user-specified area on the surface of the global WGS-84 ellipsoid for a uniform grid of nodes in lati-tude and longitude. The resulting data table is the starting point for calculating geoid heights for reference coordinate systems, which are determined by the parameters of the corresponding reference ellipsoids and Helmert parameters - spatial position, orientation and linear scale relative to the global coordinate system, according to Standard. The initial data are sufficient to calculate the digital model of the geoid heights for an arbitrary reference coordinate system. The expediency of the developed technique lies in the possibility of its use for a much more accurate calculation of the Helmert parameters for regional and other territories compared to the accepted standard values and, accordingly, a more accurate transformation of the three-dimensional positions of points between the general earth and reference coordinate systems (these issues will be discussed in a subsequent publication by the author). Approbation of the technique was carried out for several regional territories: Novosibirsk and Moscow regions, the territory of Western Siberia, the Republic of Belarus in the SK42 and SK95 coordinate systems, and the results are presented graphically in the form of geoid height maps.

ГЕОДЕЗІЯ, КАРТОГРАФІЯ І АЕРОФОТОЗНІМАННЯ

A number of factors can significantly affect the accuracy of height determination when applying the GNSS leveling method. In general, it is possible to distinguish those related to the process of GNSS observations and their post-processing, and those related to the selection of the geoid/quasi-geoid height model. This work focuses on aspects of GNSS leveling accuracy when choosing global geoid models. In particular, to better ensure accuracy, it is important to understand the significance of the heights tidal system selection of global geoid models. The purpose of the work is to analyze the influence of different tide systems of global geoid models on the accuracy of height determination by the GNSS leveling method. This paper considers the heights of global geoid models EGM08, EIGEN-6C4, GECO, and XGM2019e_2159 of high degree and order calculated in the tide systems of “tide-free”, “mean-tide”, “zero-tide”. The analysis of the actual accuracy of the geoid heights was carried out on the basis of the standard and root mean square deviations of the heights differences of global geoid models in the corresponding tidal systems in relation to the GNSS leveling data. GNSS leveling data were obtained at 14 high-precision geometric leveling points of accuracy class 1-2, covering the central part of the Lviv region. Similarly, the accuracy of the geoid models was analyzed taking into account the differences of gravity anomalies concerning the high-resolution anomalies of the WGM2012 model. Data presenting differences of height and gravitational anomalies allowed us to correct the height of the models according to the weighted average principle. In addition, corresponding statistics were calculated for them. The conducted analysis shows that for the EGM08 model, the system of “mean-tide” is optimal with an accuracy assessment at the level of σ=2-3 cm and m=4 cm. For the EIGEN-6C4 model, it is best to use the “zero-tide” system which will ensure accuracy up to 4-5 cm. The accuracy of the EGM08 and EIGEN-6C4 models is confirmed by the statistical characteristics analysis results of the gravity anomaly differences. The GECO and XGM2019e_2159 models give ambiguous results within 3-9 cm by both parameters and in all tidal systems. Only after correction of the heights, their accuracy is 2-5 cm. Considering the optimal tidal system, the heights of the EGM08 and EIGEN-6C4 models can provide an accuracy of 1-3 cm after the correction by weighting coefficients.

Аналіз сучасних моделей відлікових поверхонь для визначення висот методом GNSS-нівелювання

This paper discusses various sources of information related to the issue of determining heights by GNSS-leveling. Implementation of the GNSS leveling method requires the presence of geoid or quasi-geoid heights, which today can be obtained from the corresponding models. In recent decades, scientists from around the world have developed many global, regional and local models of geoid and quasigeoid. This has contributed to the emergence of numerous publications on GNSS leveling. The purpose of the work is to perform the analysis of modern models of reference surfaces on the basis of materials of scientific publications according to the criteria that have a significant impact on research in the field of determining the height by GNSS-leveling. Method. The paper considers 44 publications published in the period 2001–2021. Among the research in this direction, there are three types of work: 1) 13 publications on methods of constructing the models themselves; 2) 12 works on their accuracy analysis and 3) 19 works on “adjustment” of model heights. At the first stage of the research the analysis was performed according to criteria related to geoid and quasi-geoid surface modeling, including Stokes and Molodensky theory, mathematical methods of data analysis and processing, tidal systems, zero-order geoid undulation and scale levels of geoid and quasi-geoid models. In the second stage, the frequency of publications by years was analyzed and the activity of publications of existing geoid and quasigeoid models on the sample of countries, which was made on the basis of all selected works in this study, was established. At the third stage, a quantitative analysis of official published models of geoid and quasi-geoid on the frequency of publications for the study period. The ratio of the accuracy of the heights of global geoid models in relation to the magnitude of the degree and order of their calculation is established. Results. In 58 % of the analyzed works, the authors use Stokes’ theory in their research, and in 42 % – Molodensky’s theory. Among the mathematical methods of data analysis and processing, 27 % use the method of mean square collocation, 20 % use the least squares method, the “delete-restore” method and the method of modifying Stokes’ formula with least squares (or KTH-method). The Fast Fourier transform method was used in 13 % of the works. Publications on the creation of global models of the Earth mostly use the parameters of the tide free tidal system in their calculations – a total of 40 % works. No less important criterion (33 % of works) should be taken into account the parameter of undulation of the geoid of zero order (“zero degree term”). In total, 41 % of research is aimed at creating and analyzing quasi-geoid models on a regional scale. During the study period, most works were published in 2012 and 2018. Leading countries in the development of quasi-geoid models are Canada, Poland, Sweden and the United States, and global geoid models are Germany, the United States and China. For the period 2001–2021, 99 global geoid models of various degree and order were officially presented, among which GOCO, EIGEN and EGM series models are most often used for research. Also during this period, 177 quasi-geoid models were presented, the most of which were published in 2019. Based on these data, the relationship with the frequency of publications in 2008–2021 can be traced. The accuracy of global geoid models in relation to the degree and order of their calculation is systematic in the range of 0.52–1.92 m, 0.38–0.50 m, 0.23–0.38 m and 0.12–0,14 m for models 60-220, 220-260, 260-720 and 720-2190 degree and order respectively. Scientific novelty. It is shown that the analysis of modern models of reference surfaces on the basis of materials of scientific publications in the field of GNSS-leveling method allows establishing the existing advantages and disadvantages of research in this field. Practical significance. The data of such analysis can be used to solve key problems in determining the height of the GNSS-leveling method, which require further research and to find modernized solutions.

An adaptive approach to optimise regional geoid undulation model for engineering applications

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 can be obtained by applying the proposed approach.

A Local Geoid for Egypt's Mediterranean Coast: A Model Based on Artificial Neural Networks

The principal goals of this study are to assess five global geoid models, namely EGM2008, EIGEN-6C4, GECO, SGG-UGM-1, and XGM2019e_2159, as well as to create a centimeter-accurate local geoid model for Egypt's Mediterranean coast. To generate the geoid model for the Mediterranean coast, GNSS/leveling points were integrated with the best global geoid model in the region. This process is a cost-effective replacement for the more expensive conventional leveling technique. The Artificial Neural Network (ANN) was created and is now being utilized to do interpolation and statistical geoid height prediction. The findings show that XGM2019e_2159 is the best global model for modeling the geoid surface on the Mediterranean coast, with a Standard Deviation of 14 cm. The findings showed that using this model constructed with the aid of the ANN, it is feasible to determine the geoid height with a Standard Deviation of 3 cm in the Mediterranean coastal areas.

Establishment of a corrective geoid surface by spline approximation of Iranian GNSS/levelling network

The performance of the gravimetric geoid models is usually evaluated by comparison of geoid heights with the GNSS/levelling derived geoid. But the GNSS/levelling network can be infected by significant systematic biases and random errors, especially in large and uneven areas. This contribution addresses the challenging problem of the corrector surface development along with the elimination of biases. To this end, fitting an appropriate geometric surface to the GNSS/levelling geoid heights is required, which is accomplished by applying the least squares B-spline approximation theory to the GNSS/levelling data. In addition, the 3D affine transformation is used to detect systematic effects of the GNSS/levelling network compared to a global geoid model. This strategy is applied to the adjustment of the Iranian GNSS/levelling network. A significant tilt is observed across the country ranging from −0.35 m to 0.04 m. The entire study area is divided into four zones and the corrector surfaces are obtained in each zone. The accuracy of three global geoid models, EGM2008, EIGEN-6C4 and SGG-UGM-1, along with that of the Iranian regional geoid model IRG2016, are then investigated based on the raw GNSS/levelling heights and the corrector surfaces. The evaluations show the reliable results regarding the corrector surfaces against the raw data set. All geoid models show their maximum RMSE values of discrepancies in the mountainous zones and their minimum RMSEs in the zones having lower variety in topography. This indicates that the irregular topographies are not well detected by the global models over the study area.

The Potential Application of the GNSS Leveling Method in Local Areas by Means of Sector Analysis

The purpose of this work is to perform the comparison of heights of global geoid models EGM08, EIGEN-6C4, GECO, and XGM2019e based on sector analysis that are obtained relative to the ellipsoid WGS84 and GRS80 in order to implement the method of GNSS leveling in local areas. The heights of the global geoid models determined from the ellipsoid WGS84 should be reduced by −41 cm (“zero-degree term”) in order to scale them to the calculated geoid by GNSS leveling. Heights determined from the ellipsoid GRS80 should be increased by +52 cm. Spatial analysis of the heights of geoid models in the relative system for the northern territory shows that the standard deviation of the heights of geoid models is 13.6 cm, and for the southern territory it is 36.5 cm. The elevation errors of the geoid models in the relative system were estimated to be standard deviations of 2.9 cm within the northern area and 2.3 cm within the southern one. The root mean square values of initial errors of the models EGM08, EIGEN-6C4, GECO, and XGM2019e are 8.6 cm, 4.6 cm, 4.4 cm, and 3.8 cm, respectively, and standard deviation values are 2.0 cm, 2.2 cm, 3.2 cm, and 2.4 cm. The paper also performs a sector analysis of the geoid model errors in order to correct them for the application of the GNSS leveling method within the research area. The standard deviations of the residual error of the corrected model heights are 1.8 cm, 1.9 cm, 2.5 cm, and 2.0 cm for EGM08, EIGEN-6C4, GECO, and XGM2019e. The root mean square values of these residual errors for the geoid models are 1.9 cm, 2.0 cm, 2.5 cm, and 2.0 cm, respectively.

VERIFICATION OF THE CONSISTENCY OF THE PROPOSED TRANSFORMATION OF GLOBAL GEOID METHOD ACCURACY FOR LOCAL GEOID MODEL OF NIGERIA DETERMINATION

The proposed transformation of the global geoid model method for the determination of the local geoid model of Nigeria has only been applied in part of the Federal Capital Territory, Abuja. To determine the consistency of the accuracy of the method for the intended purpose, there is a need to apply it in some other parts of the country. As a result, this study presents the verification of the consistency of the proposed transformation of global geoid method accuracy for local geoid model of Nigeria determination. DGNSS observations were carried out to obtain the coordinates of the used points. The processed global geographic coordinates were used with online software (GeoidEval) to obtain the EGM 08 geoid heights of the points. The global geographic coordinates, the global geoid heights of the points and the transformation parameters from WGS 84 to Minna datum were applied to obtain the transformed (local) geoid heights of the points using a Microsoft Excel program. The transformed geoid heights were compared with their corresponding geoid heights from the gravimetric-geometric local geoid model of the study area to obtain the model RMSE (accuracy). The obtained accuracy (2.0172 m) was compared with those of the gravimetric-geometric geoid model of the study area (0.675 m) and the transformation of global geoid heights when the method was applied in part of Abuja (0.0014 m). The comparison results showed the inconsistency of the accuracy of the proposed method. It is recommended that the method should not be applied for the intended purpose.

Accuracy Assessment of Different Polynomial Geoid Models in Orthometric Height Determination for Akure, Nigeria

Height is an important component in three dimensional coordinates and determination of the position of points for any meaningful development. Ellipsoidal heights from GNSS require geoid model which could be global, regional and local for transformation to orthometric height. The absence of a national geoid model in Nigeria remains a great drawback to develop local geoid for local application in place of global geoid models. The study aims to assess the accuracy of polynomial geoid models in orthometric height determination. Differential Global Positioning System (DGPS) observations were carried out to determine ellipsoidal heights of the point while nine and eleven coefficients were used for the geoid and orthometric height modelling. Model A and Model C used 2-D (x, y) positions with nine and eleven parameters while model B used 3-D (x, y, ∆h) positions with nine parameters. The least-squares method was adopted in computing the parameters of the models. Root Mean Square Error (RMSE) was used to assess the accuracy of the models with the RMSE of model A is 14.3 cm, model B is 15.7 cm and model C is 14.5 cm, respectively. The inclusion of height term (∆h) in model B does not improve the accuracy over model A and model C. Model A with the lowest RMSE is hence the better of the three models. One-way ANOVA test conducted at 95% confidence level, however, revealed that the three models did not differ significantly. Model A having lower RMSE is recommended with GPS determined ellipsoidal heights as an alternative to conventional spirit levelling for orthometric height determination within Akure for engineering and environmental applications.

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.

Combination of regional and global geoid models at continental scale: application to Iranian geoid

High precision geoid determination is a challenging task at the national scale. Many efforts have been conducted to determine precise geoid, locally or globally. Geoid models have different precision depending on the type of information and the strategy employed when calculating the models. This contribution addresses the challenging problem of combining different regional and global geoid models, possibly combined with the geometric geoid derived from GNSS/leveling observations. The ultimate goal of this combination is to improve the precision of the combined model. We employ fitting an appropriate geometric surface to the geoid heights and estimating its (co)variance components. The proposed functional model uses the least squares 2D bi-cubic spline approximation (LS-BICSA) theory, which approximates the geoid model using a 2D spline surface fitted to an arbitrary set of data points in the region. The spline surface consists of third- order polynomial pieces that are smoothly connected together, imposing some continuity conditions at their boundaries. In addition, the least-squares variance component estimation (LS- VCE) is used to estimate precise weights and correlation among different models. We apply this strategy to the combined adjustment of the high-degree global gravitational model EIGEN-6C4, the regional geoid model IRG2016, and the Iranian geometric geoid derived from GNSS/leveling data. The accuracy of the constructed surface is investigated with five randomly selected subsamples of check points. The optimal combination of the two geoid models along with the GNSS/leveling data shows a reduction of 21 mm (~20%) in the RMSE values of discrepancies at the check points.

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).

Sensitivity of Enhanced SRTM for Sea-Level Rise Variation on Egyptian Coasts

The accuracy of digital elevation models (DEMs) is very critical to planning adaptation strategies for coastal areas under changing scenarios of global climate and sea-level rise. This research assesses the accuracy of the interferometric DEM from the SRTM mission as it is one of the free available DEMs that have been widely used in many applications. The SRTM model is enhanced using the best fit global geoid model for Egypt instead of EGM96 and by applying a mathematical scale factor formula. This research aims to obtain a higher vertical accuracy of the SRTM model that achieves the requirements for coastal inundation studies with minimum field measurement data. The methodology approach consists of three phases. In the first phase, the enhancement scale factor formulas were derived using uniformly distributed ground control points (GCPs) at two different terrains data in Egypt. The second phase contains the evaluation and validation process. It was observed that the enhanced accuracy achieved ranged from 45% to 60 % based on the type of terrains. In the last phase, the sensitivity of these DEMs to sea-level projections using the recent available local tide gauge data was analyzed. It is recommended to investigate this method approach to determine the optimal size and distribution of reference ground control points needed to adjust various free open DEMs of low vertical accuracy for further studies and other applications.

Mapping mean lake surface from satellite altimetry and GPS kinematic surveys

Lake water height is a key variable in water cycle and climate change studies, which is achievable using satellite altimetry constellation. A method based on data processing of altimetry from several satellites has been developed to interpolate mean lake surface (MLS) over a set of 22 big lakes distributed on the Earth. It has been applied on nadir radar altimeters in Low Resolution Mode (LRM: Jason-3, Saral/AltiKa, CryoSat-2) in Synthetic Aperture Radar (SAR) mode (Sentinel-3A), and in SAR interferometric (SARin) mode (CryoSat-2), and on laser altimetry (ICESat). Validation of the method has been performed using a set of kinematic GPS height profiles from 18 field campaigns over the lake Issykkul, by comparison of altimetry’s height at crossover points for the other lakes and using the laser altimetry on ICESat-2 mission. The precision reached ranges from 3 to 7 cm RMS (Root Mean Square) depending on the lakes. Currently, lake water level inferred from satellite altimetry is provided with respect to an ellipsoid. Ellipsoidal heights are converted into orthométric heights using geoid models interpolated along the satellite tracks. These global geoid models were inferred from geodetic satellite missions coupled with absolute and regional anomaly gravity data sets spread over the Earth. However, the spatial resolution of the current geoid models does not allow capturing short wavelength undulations that may reach decimeters in mountaineering regions or for rift lakes (Baikal, Issykkul, Malawi, Tanganika). We interpolate in this work the geoid height anomalies with three recent geoid models, the EGM2008, XGM2016 and EIGEN-6C4d, and compare them with the Mean Surface of 22 lakes calculated using satellite altimetry. Assuming that MLS mimics the local undulations of the geoid, our study shows that over a large set of lakes (in East Africa, Andean mountain and Central Asia), short wavelength undulations of the geoid in poorly sampled areas can be derived using satellite altimetry. The models used in this study present very similar geographical patterns when compared to MLS. The precision of the models largely depends on the location of the lakes and is about 18 cm, in average over the Earth. MLS can serve as a validation dataset for any future geoid model. It will also be useful for validation of the future mission SWOT (Surface Water and Ocean Topography) which will measure and map water heights over the lakes with a high horizontal resolution of 250 by 250 m.