Volume 15, Issue 1

Ionospheric electron density (IED) and vertical total electron content (VTEC) are two of the most important characteristics that interpret the ionosphere. Today, satellite geodesy plays an important role in providing these data. Apart from monitoring the ionosphere by means of Global Navigation Satellite System observations, predictions of these ionospheric characteristics have also been taken into consideration. The majority of prediction methods in the ionosphere are focused on VTEC prediction. The continuity equation in the ionosphere is a spatiotemporal partial differential equation that can be used to predict both IED and VTEC. In this study, we address this issue during May 8, 2016, which was a day of high geomagnetic activity. For this purpose, first, high-accuracy IED grids with a spatial resolution of 0.5° × 0.5° in longitude and latitude, 50 km in altitude, and a temporal resolution of 10 min are prepared. These IED grids are called analysis grids and are derived by assimilation of GPS-derived VTECs into the background IED grids provided by international reference ionosphere. Second, the analysis grids can be utilized as the initial and boundary values in the continuity equation to predict IED for the next 3 h with a step of 10 min. The analysis grids are constructed over the Iran region, and the performance of the continuity equation in the ionosphere prediction is investigated during the strongest geomagnetic storm of 2016. Finally, the accuracy of the predictions has been evaluated in two ways. First, analysis grids with high accuracy are available for each epoch in which the prediction is presented. On average, the root mean square (RMS) of the differences between the predicted IEDs and the analysis IEDs is 1.66 × 10 10 el/m 3 for 1-h predictions and 5.33 × 10 10 el/m 3 for 3-h predictions. Second, by numerical integration of the predicted grids in the vertical direction, VTECs are estimated and compared with VTEC values of test data that were already known. On average, the RMS of their difference was 1.29 total electron content unit (TECU) for 1-h predictions and 2.57 TECU for 3-h predictions. An acceptable accuracy for both IED and VTEC prediction by a continuity equation has been obtained up to 3 h on the most active ionospheric day. Graphical abstract

This article investigates the strain and stress tensors of the Afar region using the integration of global navigation satellite system (GNSS) and persistent scatterer interferometric synthetic aperture radar (PSInSAR) data. We first estimated the three-dimensional displacement field of the Afar area using combined GPS and PSInSAR data for the period 2006–2009. Secondly, the variance component estimation is applied to the heterogeneous GNSS and PSInSAR data and the displacement field is computed. Then, the behaviour of crustal movement within the study area is investigated by dividing the region into several small triangles or tetrahedrons using the Delaunay triangulation and applying the finite element method (FEM) to estimate the strain and stress tensors for each tetrahedron. The average stress tensor elements τ x x , τ y y {\tau }_{xx},\hspace{.25em}{\tau }_{yy} , and τ z z {\tau }_{zz} of the study area are 0.067, 0.121, and 0.126 MPa in the North, East, and Up coordinates, respectively. The result also shows that the nearby post-diking deformation has been followed by the Afar Tectono-Magmatic Event that happened in September 2005. Graphical abstract

The Nordic and Baltic Sea region is topographically varied, making gravity potential field modelling in the region a challenge. With new gravity data in and around the Baltic Sea, this study investigates improvements in the accuracy of quasigeoid determination in the region. The quasigeoid determination method is the remove–compute–restore using a spherical fast Fourier transform to solve Molodensky’s integral, using a Wong–Gore kernel modification. Different kernel modification ranges of the Stokes’ kernel are tested. The gravimetric quasigeoids are compared to global navigation satellite systems (GNSS)-levelling datasets in the region to assess the accuracy of the models. The best fitting model has a normalised root mean square error (RMSE) of the residuals to GNSS-levelling height anomalies for a subregion of below 2 cm, while the normalised RMSE to GNSS-levelling height anomalies in the whole region is 2.8 cm, matching the official regional gravimetric Nordic geodetic commission quasigeoid from 2015. A simple planar tilt correction of the residuals improves the fit in Denmark and Latvia. The correction indicates systematic tilts in the national GNSS-levelling networks of said countries. The investigation of different kernel modification ranges shows that the long transition intervals are less sensitive to the choice of bounding degrees, compared to short intervals, and more robustly give a better fit to the GNSS-levelling data in the region. Graphical abstract

In America, height systems were established during the twentieth century by connecting the leveling network to a tide gauge. In 1997, the Geodetic Reference System for the Americas (former Geocentric Reference System for South America) created Working Group III, called Vertical Datum, to assist in establishing a unified vertical reference system for the Americas. In this context, this article aims to trace the evolution of height systems in America, especially South America, and present the current situation in the region to contribute to the International Height Reference Frame. A brief chronological description of the systems of South American countries and the efforts developed by Working Group III over the past 25 years is presented. A bibliometric study assesses the scientific community’s involvement in this field. The results revealed that some countries have been standing out in engagement in recent years. Finally, an evaluation is performed between recent global geopotential models and a regional gravity field model at the 17 stations that comprise the International Height Reference Frame in Latin America. The results indicate that the Andes region requires efforts in gravity densification and improvement of global models. Graphical abstract

We have, using altimetry observations, investigated the nature and magnitude of variations in the local mean dynamic topography (MDT) along the Norwegian coast. Following our findings, we argue that the MDT is well approximated by the nearest observation and demonstrate how the results can be improved using variogram based kriging. Cross validation at tide gauges along the coast confirms the applicability of the approach and, therefore, gives us some confidence in its ability to weigh altimetry and tide gauge observations appropriately. Accordingly, altimetry is a potentially very important source of information on mean sea level outside the Norwegian baseline.

This article presents a large-scale surface gravity network in Colombia, developed during a 3-year collaboration between Ohio State University (OSU) and Colombia’s national mapping agency, the Instituto Geográfico Agustín Codazzi . The network spans approximately one-third of the country’s surface area and consists of 498 stations, including 22 absolute gravity (AG) constraints. We applied the OSU field protocol and adjustment technique, extending it to address the challenge of traffic-induced noise at benchmarks located near major roads. Our methodology employed measurements with an unusually high degree of redundancy, with 87% of the gravity lines surveyed using a minimum of four relative gravimeters. Additionally, we utilized both automatic (Scintrex CG-6) and manual (LaCoste and Romberg Model G) instruments to leverage their complementary strengths in different environments. The resulting gravity values were determined with a typical uncertainty (1 sigma) of ± 0.03 mGal. The leave-one-out cross-validation tests using the AG stations demonstrated the robustness of our solution, with all residuals statistically indistinguishable from zero. Our findings show that the combination of enhanced observational redundancy and the use of multiple gravimeter types effectively mitigates measurement challenges under suboptimal conditions, with only a modest increase in field time.

Surface displacement caused by natural and anthropogenic activities poses a significant risk to subsurface pipelines, particularly in areas experiencing subsidence. Stress and strain induced by deformation can lead to pipeline buckling and potential vulnerability. This study applies a multidisciplinary approach integrating interferometric synthetic aperture radar (InSAR) deformation analysis, well data, and geological context to assess the risk to oil and gas pipelines in Iran’s Qazvin plain. The focus is on evaluating the impact of an unconfined aquifer, which has a lower risk of subsidence compared to a confined aquifer, on pipeline infrastructure. We analyzed multitemporal Sentinel-1 data collected between 2014 and 2021. Our findings reveal that 2,400 km 2 of the study area is experiencing subsidence with vertical rates reaching up to 14 cm/year with an average S k {S}_{{\rm{k}}} , or skeletal storage value of 0.04. We explore the reasons for this unexpectedly high subsidence, finding that compressible unconfined aquifers with historically low water levels are also at risk for significant inelastic, or permanent, subsidence. We also evaluate pipeline profiles, which show spatial subsidence, much higher than typically seen in unconfined aquifers, with variations of up to 1 m, indicating long-term risks to the infrastructure. This study demonstrates the potential of InSAR techniques in assessing the risk to critical infrastructure, such as oil and gas pipelines, in regions with land deformation due to groundwater withdrawal. Our approach underscores the importance of continuous monitoring and offers valuable insights for addressing the challenges posed by subsidence on pipeline infrastructure. Graphical abstract