An approach for improving the accuracy of global geopotential models over a local region: a case study in the Nile Delta, Egypt

The finite element method has been widely used to enable fatigue life predictions for electronic assemblies subjected to thermal cycling. The potential critical region of interest within a solder joint is relatively small relative to the entire package assembly. High-density meshes are typically used to build a package model when using traditional FE modeling approaches. Therefore, long computational times can be expected for an analysis involving several thermal cycles. In order to reduce the complexity of the model and the use of oversize elements, and improve the efficiency of calculation, the technique of global/local modeling (submodeling) has been developed. In this approach, interpolated displacements from coarse model (global model) are applied as boundary conditions to a refined model (local/submodel) of the critical area of interest. The accuracy and efficiency of submodeling finite element simulations for electronic packages have not been evaluated completely in the literature.In this work, submodeling approaches for BGA assemblies have been explored in detail. A typical BGA package assembly was modeled using several coarse meshes as global models; and the maximum aspect ratio within the global model was varied up to 25, which is near the warning limit of many commercial finite element codes. Once the critical solder joint was identified, then the local model was built using the technique of cut boundaries, and meshed with refined elements. The maximum aspect ratio was also reduced to 5. The simulation result shows the accuracy of solution was sensitive to the mesh quality of the local model, as well as the load step size for both global and local models. An improved simulation strategy using submodeling was developed to obtain the best compromise in the global and local models between the mesh quality and load step size.Although the submodeling is a powerful tool for a better solution in a local region of interest far away from the cut boundaries, it is still crucial to identify the critical region correctly from the global model or a misguided local solution might be performed. Initially, the global models were built using coarse meshes with nonlinear material properties as seen in literature, and then an improved geometric simplification of the solder joint incorporating energy based fatigue criteria was developed. In addition, minimization of the local model volume is still required for a detail analysis of a complex configuration in local region where a high-density mesh is needed. In the investigated approach, we determined the minimized height of the local boundary, and have shown the influence between the height and the solution of volume averaged inelastic strain energy dissipation in the local model. The proposed approach achieves a large reduction in computational time, better detailed modeling of local interest region, and improved simulation accuracy.

Earth gravitational model 2008

The performance of the new EGM2008 global geopotential model (GGM), over the northern Nile valley and delta in Egypt, has been evaluated. Over 305 global positioning system (GPS)/levelling stations, the standard deviation of the undulation differences has been estimated to be 0.23 m. Thus, it can be concluded that the EGM2008 is superior to earlier GGMs over the northern area of Egypt by a factor of 1.6. Moreover, four mathematical models have been investigated in order to incorporate local data sets with the EGM2008, leading to the conclusion that the first-order polynomial is the optimum one. An improvement of about 26% has been obtained after applying that regression model, and the standard deviation has been decreased to 0.17 m. As a result, the EGM2008 produces a crucial influence on integrated GPS surveys where the orthometric heights can be obtained without any additional costs. Such a practice presents a suitable alternative, from an economical point of view, to substitute the expensive traditional levelling technique particularly for topographic mapping.

In mountainous regions with scarce gravity data, gravimetric geoid determination is a difficult task that needs special attention to obtain reliable results satisfying the demands, e.g., of engineering applications. The present study investigates a procedure for combining a suitable global geopotential model and available terrestrial data in order to obtain a precise regional geoid model for Konya Closed Basin (KCB). The KCB is located in the central part of Turkey, where a very limited amount of terrestrial gravity data is available. Various data sources, such as the Turkish digital elevation model with 3 ″ × 3″ resolution, a recently published satellite-only global geopotential model from the Gravity Recovery and Climate Experiment satellite (GRACE) and the ground gravity observations, are combined in the least-squares sense by the modified Stokes’ formula. The new gravimetric geoid model is compared with Global Positioning System (GPS)/levelling at the control points, resulting in the Root Mean Square Error (RMS) differences of ±6.4 cm and 1.7 ppm in the absolute and relative senses, respectively. This regional geoid model appears to be more accurate than the Earth Gravitational Model 2008, which is the best global model over the target area, with the RMS differences of ±8.6 cm and 1.8 ppm in the absolute and relative senses, respectively. These results show that the accuracy of a regional gravimetric model can be augmented by the combination of a global geopotential model and local terrestrial data in mountainous areas even though the quality and resolution of the primary terrestrial data are not satisfactory to the geoid modelling procedure.

The representation of the Earth’ topography in a 3D digital format is a vital constituent in a wide range of geographic, geomatics, environmental, and engineering activities. However, the accuracy of such representations could define its applicability and validity for a specific utilization. This chapter presents an analysis of four open-source Global Digital Elevation Models (GDEMs) and compares them on two topographic profiles (nearly flat, and hills regions) for mapping and geomatics applications in two countries. The main goal is to determine whether GDEMs-based heights, contour intervals, slopes, and topographic profiles are accurate for all topographic map scales, which is a significant problem in mapping operations. For the purpose of illustrating flat and moderate-topography patterns, two case studies—the Nile delta in Egypt and Makkah city in Saudi Arabia—have been used. The investigated GDEMs include the most-recent released models: ASTER v.3, ACE 2, SRTMGL1 v. 3, and NASADEM_HGT v.1 released in 2019 and 2020 with spatial resolutions of 1 and 3 arc seconds. There are 540 accurate Ground Control Points (GCP) available in the Nile delta and 175 in Makkah. It has been determined based on the available datasets in two study locations that  the accuracy of investigated GDEMs over known checkpoints range from ±2.5 and ±5.1 meters in the Nile delta region, while it varies between ±5.1 and ±8.0 meters in the Makkah area. This suggests that the use of GDEMs in topographic mapping varies greatly between spatial areas that are flat and those that are hilly. Therefore, it is advised against utilizing GDEMs to create topographic maps at scales of 1: 25,000 or greater in flat areas and 1: 50,000 or greater in hilly areas. Additionally, the achieved results demonstrated that throughout cross sections up to 30 kilometers in length, no GDEM-based slope matches the real slopes from known GCP. This leads to the conclusion that GDEMs are not the appropriate heights' source for topographic mapping at medium and large map scales, and could not be utilized for topographic profiling in precise engineering and geomatics applications. Such findings should be vitally taken into account in mapping and engineering applications not just in Egypt and Saudi Arabia but worldwide as well.

We present results of analyses of the evaluation of the method for local quasigeoid modelling based on the geophysical inversion of gravity data (the GGI method). Relying on precise (with an accuracy level of ± 1 cm) GNSS/levelling height anomalies and surface gravity data, we analysed the method accuracy by a) assessing the accuracy of the model which is based on selected available global geopotential model; b) evaluating the influence of the accuracy of the input data (GNSS/levelling and gravity) on the output model accuracy; and c) analysing the influence of the global model resolution on the quasigeoid model accuracy. Analyses were performed for the area of Poland. As the basic accuracy parameter the standard deviation (σΔζ) of the differences between measured (GNSS/levelling) height anomalies and those established from the model were selected. The results indicate that the accuracy of the quasigeoid output model (in terms of σΔζ) was evaluated at cca ± 1.2 cm irrespective of the global geopotential model used. Such accuracy was also achieved using the global model coefficients only up to the degree Nmax = 90. To achieve the above-mentioned accuracy of the output model, the accuracy of input data should not be lower than cca ± 2.0 cm for GNSS/levelling height anomalies and ± 1.3 mGal for gravity data.

Local gravimetric geoid determination requires data comprising three components namely long-wavelength, medium-wavelength, and short-wavelength components. The long-wavelength component is derived from the Global Geopotential Model (GGM). The medium-wavelength is obtained from terrestrial gravity data, and the short-wavelength component is derived from Digital Terrain Model (DTM) data. Among these three components, the GGM data contributes the most significant value and error. This study has evaluated the influence of the GGM resolution on local geoid model for the area with a good and dense terrestrial gravity data distribution, case study in Yogyakarta Special Region (DIY). This evaluation was carried out to determine the optimal degree value of the GGM for local geoid modelling. The gravimetric geoid computation was done using 2D FFT (Fast Fourier Transform). The utilized variation of the degree values were 360, 540, 720, 1080, 1440, 1800, 2160 and 2190 of the EGM2008 data. The evaluation of the variation of the GGM degree values contribution to the local geoid modelling was done using the geometric geoid derived from collocated GPS-levelling data. The results showed that using the lowest degree value (360 degree) produces the optimal (best) local geoid accuracy for the case study of DIY province.

The objective of the present work consists in gathering and examining the maximum amount of data concerning the geochemistry of the Nile solid load. To this end, the distributions of 28 major and trace elements in 176 soil and sediment samples collected from the Egyptian section of the Nile River and Nile Delta were determined via epithermal neutron activation analysis. Compared with the Upper Continental Crust corresponding data, the reached results appear to indicate the presence of detrital material of igneous origin, most probably resulting from weathering on Ethiopian highlands as transported by the Blue Nile, the Nile main tributary. The Ni, Zn and As concentrations perceived in the investigated areas appear to be in line with UCC corresponding data. The Na geographical distributions along with the principal component analysis achieved results prove to suggest a possible atmospheric supply from the neighboring Mediterranean and Red Seas.

This paper presents an analysis of four open-source Global Digital Elevation Models (GDEMs) and compares them on two topographic profiles (nearly flat, and hills regions) for mapping and geomatics applications. The chief intention is to investigate if GDEMs-based heights, contour intervals, slopes, and topographic profiles are valid for all map scales of topographic mapping, which constitutes a major issue in mapping activities. Two case studies, the Nile delta in Egypt and Makkah city in Saudi Arabia, have been utilized to represent flat and moderate-topography patterns. The investigated GDEMs include the most-recent released models: ASTER v.3, ACE 2, SRTMGL1 v.3, and NASADEM_HGT v.1 released in 2019 and 2020 with spatial resolutions of 1 and 3 arc seconds. Available accurate Ground Control Points (GCP) consist of 540 stations in the Nile delta and 175 stations in Makkah. Based on the available datasets in two study areas, it has been found that the accuracy of investigated GDEMs over known checkpoints ranges from ±2.5 and ±5.1 meters in the Nile delta region, while it varies between ±5.1 and ±8.0 meters in the Makkah area. That indicates that the utilization of GDEMs in topographic mapping differs significantly between flat and hilly spatial regions. Therefore, it is recommended to avoid using GDEMs for developing topographic maps of scale 1:25,000 or larger in flat regions and map scale 1:50,000 or larger in hilly regions. Additionally, the accomplished results showed that all GDEM-based slopes do not match with the actual slopes from known GCP over cross section’s length up to 30 kilometers. Thus, it is concluded that GDEMs are not the appropriate heights’ source for topographic mapping at medium and large map scales, and could not be utilized for topographic profiling in precise engineering and geomatics applications.

In GNSS, 3D geometric position is calculated with high accuracy. This position is the ellipsoidal latitude, longitude and ellipsoidal height $$\left( {\lambda ,\phi ,h} \right) $$ with respect to WGS84 coordinates system. These coordinates are integrated with local horizontal/projected coordinates (X, Y) by mathematical coordinate’s transformations and map projections. The geometric ellipsoidal height (h) obtained by means of GNSS has to be integrated with the physical/orthometric heights (H) obtained by means of precise leveling. The physical surface defining the difference between both height systems is the geoid represented by the geoid undulation (N) at a given position. Different methods are used to build geoid models. Global models using terrestrial and satellite data are available to calculate the geoid heights as function of the earth potential (W). The most recent high degree and order models are EGM2008, Eigen05c, Eigen06c4, etc. (GFZ-Potsdam, ‘List of available global models. http://icgem.gfz-potsdam.de/ICGEM/modelstab.html , 2017). Some regional geoid models are available like the European Gravimetric Geoid (EGG97). These models mostly do not fit the local datum due to datum definition problems. Here, a group of precise height reference benchmarks measured with GNSS is used to fit the global models with the local vertical datum to define the local height reference system of Palestine. The accuracy of the different global geopotential models is evaluated before and after the application of the geoid fitting.

When starting any GNSS measurements, there is a need to establish a survey plan with the required optimal baselines. The optimal GNSS baselines can be chosen by solving the geodetic second-order design (SOD). The particle swarm optimization PSO is used widely to solve geodetic design issues. This work employed the particle swarm optimization (PSO) algorithm, a stochastic global optimization method, to select the optimal GNSS baselines. The optimal baselines satisfy the set criterion matrix at a reasonable cost. The fundamentals of the algorithm are presented. The effectiveness and usefulness of the technique are then demonstrated using a Nile Delta GNSS network as an example. In some cases, we have to observe many GNSS benchmarks with limited instrumentations. PSO represents a powerful tool for optimizing baseline to get the required accuracy with limited capabilities (like limited receivers). The PSO algorithm, a stochastic global optimization approach, was used in this paper to find the best observation weights to measure in the field that will match the predetermined criterion matrix with a fair degree of precision. The method’s fundamentals are presented with an actual geodetic network over the Nile delta in Egypt. In the current work, two survey strategies were applied. One represents a case with 9 GNSS receivers (high capability), and another one represents the tested survey plan with limited GNSS receivers (3 receivers, low capability) after applying PSO. By comparing two survey strategies, applying the PSO algorithm to a real Nile delta geodetic network shows its effectiveness on the obtained coordinate accuracy. This obtained accuracy ranged from 2 mm to 3 mm in X, Y, Z, and 3 mm in height. Also, the linear closure error between known and estimated coordinates improved to be 1.4 cm after applying PSO.

An integrated framework for urban resilience to climate change – Case study: Sea level rise impacts on the Nile Delta coastal urban areas

The launch of dedicated satellite missions at the beginning of the 2000s led to significant improvement in the determination of Earth gravity field models. As a consequence of this progress, both the accuracies and the spatial resolutions of the global geopotential models increased. However, the spectral behaviors and the accuracies of the released models vary mainly depending on their computation strategies. These strategies are briefly explained in this article. Comprehensive quality assessment of the gravity field models by means of spectral and statistical analyses provides a comparison of the gravity field mapping accuracies of these models, as well as providing an understanding of their progress. The practical benefit of these assessments by means of choosing an optimal model with the highest accuracy and best resolution for a specific application is obvious for a broad range of geoscience applications, including geodesy and geophysics, that employ Earth gravity field parameters in their studies. From this perspective, this study aims to evaluate the GOCE High-Level Processing Facility geopotential models including recently published sixth releases using different validation methods recommended in the literature, and investigate their performances comparatively and in addition to some other models, such as GOCO05S, GOGRA04S and EGM2008. In addition to the validation statistics from various countries, the study specifically emphasizes the numerical test results in Turkey. It is concluded that the performance improves from the first generation RL01 models toward the final RL05 models, which were based on the entire mission data. This outcome was confirmed when the releases of different computation approaches were considered. The accuracies of the RL05 models were found to be similar to GOCO05S, GOGRA04S and even to RL06 versions but better than EGM2008, in their maximum expansion degrees. Regarding the results obtained from these tests using the GPS/leveling observations in Turkey, the contribution of the GOCE data to the models was significant, especially between the expansion degrees of 100 and 250. In the study, the tested geopotential models were also considered for detailed geoid modeling using the remove-compute-restore method. It was found that the best-fitting geopotential model with its optimal expansion degree (please see the definition of optimal degree in the article) improved the high-frequency regional geoid model accuracy by almost 15%.

Research on privacy protection of multi source data based on improved gbdt federated ensemble method with different metrics

Although there are several factors could affect the accuracy performance of Global Geopotential Models (GGMs), the current research investigates if the order of a model represents the key aspect influencing its accuracy. Fourteen GGMs, with variable orders, have been selected to be tested over 1,100 Global Navigation Satellite Systems (GNSS)/Levelling stations in Egypt. The performance of global models has been analyzed against that of a national geoid model. Additionally, the performance of GGMs over variable topography in Egypt has been investigated too. Based on the available data and the attained findings, it has been found that the low-order GGMs produced mean geoid undulations very far from that of the national model. Over the available checkpoints, it has been recognized that the accuracy of high-order GGMs is less than ± 0.276 m. However, a particular medium-order model produced a better performance with a standard deviation equals ± 0.193 m. Other medium-order models resulted in accuracy varies between ± 0.238 m and ± 0.371 m. In addition, the models produced slightly better performance over high-elevation topography in Egypt. Furthermore, statistical analysis demonstrates that the correlation between model’s order and accuracy equals −0.38 which indicates that such an association is weak. The regression coefficient of determination has been estimated as 0.14 which concludes that the regression is feeble since only 14 % of the accuracy variations are affected by the model’s order. Such remarks highlight that there is no significant association between the order and accuracy of GGMs over GNSS/Levelling stations in Egypt.