International Height Reference System Research Articles

Residual least-squares collocation: use of covariance matrices from high-resolution global geopotential models

The paper presents a modified formulation of least-squares collocation. This residual least-squares collocation (RLSC) includes a remove--compute--restore procedure with a high-resolution global geopotential model (GGM) and a topographic gravitational potential model. In contrast to previous approaches, in RLSC, the remaining input residuals are modeled with error covariance matrices instead of signal covariance matrices. Therefore, we include the full variance--covariance information of a high-resolution GGM, namely the XGM2016, to the procedure. The included covariance matrices are anisotropic and location-dependent and enable a realistic error modeling of a target area. This fact represents an advantage over covariance matrices derived from signal degree variances or empirical covariance fitting. Additionally, due to the stochastic modeling of all involved components, RLSC provides realistic accuracy estimates. In a synthetic closed-loop test case with a realistic data distribution in the Andes we demonstrate the advantages of RLSC for regional geoid modeling and quantify the benefit which results mainly from a rigorously handled high-resolution GGM. In terms of root mean square deviations from the true reference solution, RLSC delivers an improvement of about 30% compared to a standard LSC approach, where the benefit is particularly pronounced in areas with a sparse data distribution. This improved performance, together with the fact that the resulting stochastic error estimates better reflect the true errors, might be an important aspect for the application of RLSC to derive gravity potential values and their uncertainties at reference stations of the international height reference system.

Análise da Evolução Temporal do Datum Vertical Brasileiro de Imbituba

Actualmente, los temas más centrales de Geodesia se vinculan a la provisión de un Sistema de Referencia Global único, al que puedan vincularse de forma unívoca y con exactitud los cambios globales de carácter geométrico y físico. El Global Geodetic Reference Frame tiene como objetivo la mejor estructuración de los Sistemas de Observación de la Tierra actualmente con perspectivas de la determinación de los cambios globales al nivel de una parte por mil millones, considerando varios parámetros geométricos y físicos. En este contexto, se pretende que el International Height Reference Frame, realizado por International Height Reference System, posea consistencia global de, por lo menos, un centímetro en su realización y control espacio/temporal en el orden del milímetro por año. Considerando estos aspectos, análisis y evolución temporal del Datum Vertical Brasileño de Imbituba utilizando datos mareográficos del nivel del mar de: Permanent Service for Mean Sea Level (1948 a 1968), University of Hawaii Sea Level Center (2001 a 2007) y Red Mareográfica Permanente para Geodésia (2006 a 2016), y datos de distintas misiones altimétricas del período 1991 a 2015 obtenidos del Banco de Datos del Deutsches Geodätisches Forschungsinstitut. Así como, datos de posicionamiento continuo GNSS del período de 2007 a 2016, de la Red Brasileña de Monitoreo Continuo, los cuales fueron utilizados para modelado de los movimientos locales de la corteza. Los resultados permitirán discriminar los movimientos de la corteza en relación al nivel del mar. Para esto, se utilizó la tendencia de variación del nivel del mar evidenciado por el mareógrafo, así como la variación del componente vertical obtenido con el procesamiento GNSS y de la Sea Surface Height obtenida de los datos de los satélites altimétricos.

РЕАЛІЗАЦІЯ МІЖНАРОДНОЇ РЕФЕРЕНЦНОЇ СИСТЕМИ ВИСОТ – СУЧАСНИЙ СТАН

РЕАЛІЗАЦІЯ МІЖНАРОДНОЇ РЕФЕРЕНЦНОЇ СИСТЕМИ ВИСОТ – СУЧАСНИЙ СТАН

OFFSET EVALUATION OF THE ECUADORIAN VERTICAL DATUM RELATED TO THE IHRS

Abstract Considering the definition of the International Height Reference System (IHRS) in the geopotential space (Resolution 1/2015, International Association of Geodesy - IAG), among the present main objectives of the international geodetic community is the materialization of IHRS around the world. One fundamental task for this is the offset determination of each national vertical datum related to the IHRS. In this manuscript we establish the relationship between the Ecuadorian Vertical Datum (EVD) and the IHRS in the geopotential space following the foundations of the Resolution 1/2015 IAG. Gravity data, heights from the Ecuadorian Fundamental Vertical Network, Global Geopotential Models and Digital Elevation Models were used in the computations. Based on the Least Squares Collocation method, empirical covariance functions and spectral decomposition techniques, we realized the modelling of the geopotential in the study region (4° x 4° centered in the La Libertad tide gauge, Ecuador). Based on the referred approaches, we solved the free Geodetic Boundary Value Problem for determining the discrepancy of the EVD related to the IHRS. An offset of approximately 29 cm ± 3 cm was estimated for the W 0 - W 0 i relation when the GO_CONS_GCF_2_DIR_R5 model was used in the modeling of the medium and long wavelengths of the terrestrial gravity field, and approximately 43 cm ± 3 cm when the EIGEN6C4 model was used.

Definition and Proposed Realization of the International Height Reference System (IHRS)

Studying, understanding and modelling global change require geodetic reference frames with an order of accuracy higher than the magnitude of the effects to be actually studied and with high consistency and reliability worldwide. The International Association of Geodesy, taking care of providing a precise geodetic infrastructure for monitoring the Earth system, promotes the implementation of an integrated global geodetic reference frame that provides a reliable frame for consistent analysis and modelling of global phenomena and processes affecting the Earth’s gravity field, the Earth’s surface geometry and the Earth’s rotation. The definition, realization, maintenance and wide utilization of the International Terrestrial Reference System guarantee a globally unified geometric reference frame with an accuracy at the millimetre level. An equivalent high-precision global physical reference frame that supports the reliable description of changes in the Earth’s gravity field (such as sea level variations, mass displacements, processes associated with geophysical fluids) is missing. This paper addresses the theoretical foundations supporting the implementation of such a physical reference surface in terms of an International Height Reference System and provides guidance for the coming activities required for the practical and sustainable realization of this system. Based on conceptual approaches of physical geodesy, the requirements for a unified global height reference system are derived. In accordance with the practice, its realization as the International Height Reference Frame is designed. Further steps for the implementation are also proposed.

Vertical datum unification for the International Height Reference System (IHRS)

The International Association of Geodesy released in July 2015 a resolution for the definition and realisation of an International Height Reference System (IHRS). According to this resolution, the IHRS coordinates are potential differences referring to the equipotential surface of the Earth's gravity field realised by the conventional value W0 = 62 636 853.4 m2s−2. A main component of the IHRS realisation is the integration of the existing height systems into the global one; i.e. existing vertical coordinates should be referred to one and the same reference level realised by the conventional W0. This procedure is known as vertical datum unification and its main result are the vertical datum parameters, i.e., the potential differences between the local and the global reference levels. In this paper, we rigorously derive the observation equations for the vertical datum unification in terms of potential quantities based on the geodetic boundary value problem (GBVP) approach. Those observation equations are then empirically evaluated for the vertical datum unification of the North American and South American height systems. In the first case, simulations performed in North America provide numerical estimates about the impact of omission errors and direct and indirect effects on the vertical datum parameters. In the second case, a combination of local geopotential numbers, ITRF coordinates, satellite altimetry observations, tide gauge registrations and high-resolution gravity field models is performed to estimate the level differences between the South American height systems and the global level W0. Results show that indirect effects vanish when a satellite-only gravity field model with a degree higher than n ≥ 180 is used for the solution of the GBVP. However, the component derived from satellite-only global gravity models has to be refined with terrestrial gravity data to minimise the omission error and its effect on the vertical datum parameter estimation. The empirical evaluations demonstrate that the vertical datum unification should be based on geodetic stations of highest quality and standardised geodetic data; for example, geometric coordinates should refer to the same ITRF and be given in the same tide system and reference epoch as the geopotential numbers and gravity field model. After a standardisation of the input data used in the unification of the South American height systems and a rigorous error propagation analysis, we demonstrate that the vertical datum parameters can be estimated with accuracy better than ± 5 cm in well-surveyed regions and some decimetres (± 40 cm) in sparsely surveyed regions. This paper concludes with detailed guidelines for the appropriate data treatment when the integration of a local vertical datum into the IHRS is desired. These guidelines may be applicable in any region of the world.