Cyclo-Stationarity in Sea Level Variability from Satellite Altimetry Data and Correlation with Climate Indices in the Mediterranean Sea

The exploitation of altimetric datasets from past and current satellite missions is crucial to both oceanographic and geodetic applications. For oceanographic studies, they allow the determination of sea level anomalies as deviations from a static mean sea level. This chapter deals with numerical experiments for the statistical analysis of Sea Level Anomaly (SLA) variations in the Mediterranean. SLA empirical covariance functions were calculated to represent the statistical characteristics of the sea variation for the period between 2002 and 2016. The variation of monthly SLA time series was investigated, and a correlation analysis was performed in terms of epoch-based pattern re-occurrence. To identify possible correlations with global and regional climatic phenomena that influence the ocean state, three indexes have been investigated, namely the Southern Oscillation Index (SOI), the Mediterranean Oscillation Index (NOI), and the North Atlantic Oscillation (NAO). Finally, Empirical Orthogonal Functions (EOF) and Principal Component Analysis (PCA) were applied to all SLA time series and for each satellite mission to extract the individual dominant modes of the data variability. After the analysis, the SLA field is separated into spatial structures (EOF modes) and their corresponding amplitudes in time, the Principle Components (PCs)

Sea surface topography, bathymetry and marine gravity field modelling

Bibliography: p. 289-302

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

A Quasigeoid-Derived Transformation Model Accounting for Land Subsidence in the Mekong Delta towards Height System Unification in Vietnam

A vertical offset model for Vietnam and its surrounding areas was determined based on the differences between height anomalies derived from 779 Global Navigation Satellite System (GNSS)/levelling points and those derived from a dedicated high-resolution gravimetric-only quasigeoid model called GEOID_LSC. First, the deterministic transformation model to effectively fit the differences between the quasigeoid and GNSS/levelling heights was based on a third-order polynomial model. Second, the residual height anomalies have been interpolated to a grid employing Least-Squares Collocation. Finally, the distortions were restored to the residual grid. This model can be used for combination with a gravimetric quasigeoid model in GNSS levelling. The quality of GNSS/levelling data in Vietnam was analyzed and evaluated in this study. The annual subsidence rate from ALOS-1 was also used to analyze the effects of subsidence on the quality of GNSS/levelling data in the Mekong Delta. From this we made corrections to improve the accuracy of GNSS/levelling data in this region. The offset model was evaluated using cross-validation technique by comparing with GNSS/levelling data. Results indicate that the offset model has a standard deviation of 5.9 cm in the absolute sense. Based on this offset model, GNSS levelling can be carried out in most of Vietnam’s territory complying third-order levelling requirements, while the accuracy requirements for fourth-order levelling networks is met for the entire country. This model in combination with the developed gravimetric quasigeoid model should also contribute to the modernization of Vietnam’s height system. We also used high-quality GNSS/levelling data and the determined quasigeoid model to determine the geopotential value W0 for the Vietnam Local Vertical Datum. The gravity potential of the Vietnam Local Vertical Datum is estimated equal to W 0 LVD = 62,636,846.81 ± 0.70 m2s−2 with the global equipotential surface realized by the conventional value W0 = 62,636,853.4 m2s−2

GOCE Downward Continuation to the Earth’s Surface and Improvements to Local Geoid Modeling by FFT and LSC

One of the main applications of the gravity field and steady-state Ocean Circulation Explorer (GOCE) satellite data is their combination with local gravity anomalies for geoid and gravity field modeling purposes. The aim of the present paper was the determination of an improved geoid model for the wider Hellenic area, using original GOCE SGG data filtered to retain only useful signals inside the measurement bandwidth (MBW) of the satellite. The filtered SGGs, originally at the satellite altitude, were projected to a mean orbit (MO) and then downward continued to the Earth’s surface (ES) in order to be combined with local gravity anomalies. For the projection to an MO, grids of disturbing gravity gradients from a global geopotential model (GGM) were used, computed per 1 km from the maximum satellite altitude to that of the MO. The downward continuation process was then undertaken using an iterative Monte Carlo (MC) simulated annealing method with GGM gravity anomalies on the ES used as ground truth data. The final geoid model over the wider Hellenic area was estimated, employing the remove–compute–restore method and both Fast Fourier Transform (FFT) and Least Squares Collocation (LSC). Gravity-only, GOCE-only and combined models using local gravity and GOCE data were determined and evaluation of the results was carried out against available GNSS/levelling data in the study area. From the results achieved, it was concluded that even when FFT is used, so that a combined grid of local gravity and GOCE data is used, improvements to the differences regarding GNSS/levelling data by 14.53% to 27.78% can be achieved. The geoid determination with LSC was focused on three different areas over Greece, with different characteristics in the topography and gravity variability. From these results, improvements from 14.73%, for the well-surveyed local data of Thessaly, to 32.88%, over the mountainous area of Pindos, and 57.10% for the island of Crete for 57.10% were found

FIR, IIR and Wavelet Algorithms for the Rigorous Filtering of GOCE SGG Data to the GOCE MBW

Gravity field and steady-state Ocean Circulation Explorer (GOCE) data are strongly affected by noise and long-wavelength errors outside the satellite measurement bandwidth (MBW). One of the main goals in utilizing GOCE data for gravity field modeling is the application of filtering techniques that can remove gross errors and reduce low-frequency errors and high-frequency noise while preserving the original signal. This paper aims to present and analyze three filtering strategies used to de-noise the GOCE Level 2 data from long-wavelength correlated errors and noise. These strategies are Finite Impulse Response (FIR), Infinite Impulse Response (IIR), and Wavelet Multi-resolution Analysis (WL), which have been applied to GOCE residual second order derivatives of the gravity potential. Several experiments were performed for each filtering scheme in order to identify the ideal filtering parameters. The outcomes indicate that all the suggested filtering strategies proved to be effective in removing low-frequency errors while preserving the signals in the GOCE MBW, with FIR filtering providing the overall best results

Strategy for the realisation of the International Height Reference System (IHRS)

In 2015, the International Association of Geodesy defined the International Height Reference System (IHRS) as the conventional gravity field-related global height system. The IHRS is a geopotential reference system co-rotating with the Earth. Coordinates of points or objects close to or on the Earth’s surface are given by geopotential numbers C(P) referring to an equipotential surface defined by the conventional value W0 = 62,636,853.4 m2 s−2, and geocentric Cartesian coordinates X referring to the International Terrestrial Reference System (ITRS). Current efforts concentrate on an accurate, consistent, and well-defined realisation of the IHRS to provide an international standard for the precise determination of physical coordinates worldwide. Accordingly, this study focuses on the strategy for the realisation of the IHRS; i.e. the establishment of the International Height Reference Frame (IHRF). Four main aspects are considered: (1) methods for the determination of IHRF physical coordinates; (2) standards and conventions needed to ensure consistency between the definition and the realisation of the reference system; (3) criteria for the IHRF reference network design and station selection; and (4) operational infrastructure to guarantee a reliable and long-term sustainability of the IHRF. A highlight of this work is the evaluation of different approaches for the determination and accuracy assessment of IHRF coordinates based on the existing resources, namely (1) global gravity models of high resolution, (2) precise regional gravity field modelling, and (3) vertical datum unification of the local height systems into the IHRF. After a detailed discussion of the advantages, current limitations, and possibilities of improvement in the coordinate determination using these options, we define a strategy for the establishment of the IHRF including data requirements, a set of minimum standards/conventions for the determination of potential coordinates, a first IHRF reference network configuration, and a proposal to create a component of the International Gravity Field Service (IGFS) dedicated to the maintenance and servicing of the IHRS/IHRF.https://www.ngs.noaa.gov/GRAV-D/data_ms05.shtm

Strategy for the realisation of the International Height Reference System (IHRS)

In 2015, the International Association of Geodesy defned the International Height Reference System (IHRS) as the conventional gravity feld-related global height system. The IHRS is a geopotential reference system co-rotating with the Earth.Coordinates of points or objects close to or on the Earth’s surface are given by geopotential numbers C(P) referring to anequipotential surface defned by the conventional value W0=62,636,853.4 m2 s−2, and geocentric Cartesian coordinates Xreferring to the International Terrestrial Reference System (ITRS). Current eforts concentrate on an accurate, consistent,and well-defned realisation of the IHRS to provide an international standard for the precise determination of physical coordinates worldwide. Accordingly, this study focuses on the strategy for the realisation of the IHRS; i.e. the establishment ofthe International Height Reference Frame (IHRF). Four main aspects are considered: (1) methods for the determination ofIHRF physical coordinates; (2) standards and conventions needed to ensure consistency between the defnition and the realisation of the reference system; (3) criteria for the IHRF reference network design and station selection; and (4) operationalinfrastructure to guarantee a reliable and long-term sustainability of the IHRF. A highlight of this work is the evaluation ofdiferent approaches for the determination and accuracy assessment of IHRF coordinates based on the existing resources,namely (1) global gravity models of high resolution, (2) precise regional gravity feld modelling, and (3) vertical datumunifcation of the local height systems into the IHRF. After a detailed discussion of the advantages, current limitations, andpossibilities of improvement in the coordinate determination using these options, we defne a strategy for the establishmentof the IHRF including data requirements, a set of minimum standards/conventions for the determination of potential coordinates, a frst IHRF reference network confguration, and a proposal to create a component of the International Gravity FieldService (IGFS) dedicated to the maintenance and servicing of the IHRS/IHR

Analysis of sea level trends with altimetry around the coastal zone of gavdos permanent cal/Val facility

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