Combining EGM2008 and SRTM/DTM2006.0 residual terrain model data to improve quasigeoid computations in mountainous areas devoid of gravity data

A global geopotential model, like EGM2008, is not capable of representing the high-frequency components of Earth?s gravity field. This is known as the omission error. In mountainous terrain, omission errors in EGM2008, even when expanded to degree 2,190, may reach amplitudes of10cm and more for height anomalies. The present paper proposes the utilisation of high-resolution residual terrain model (RTM) data for computing estimates of the omission error in rugged terrain. RTM elevations may be constructed as the difference between the SRTM (Shuttle Radar Topography Mission) elevation model and the DTM2006.0 spherical harmonic topographic expansion. Numerical tests, carried out in the German Alps with a precise gravimetric quasigeoid model (GCG05) and GPS/levelling data as references, demonstrate that RTM-based omission error estimatesimprove EGM2008 height anomaly differences by 10cm in many cases. The comparisons of EGM2008-only height anomalies and the GCG05 model showed 3.7 cm standard deviation after a bias-fit. Applying RTM omission error estimates to EGM2008 reduces the standard deviation to 1.9 cm which equates to a significant improvement rate of 47%. Using GPS/levelling data strongly corroborates thesefindings with an improvement rate of 49%. The proposed RTM approach may be of practical value to improve quasigeoid determination in mountainous areas without sufficient regional gravity data coverage, e.g., in parts of Asia, South America or Africa. As a further application, RTMomission error estimates will allow refined validation of global gravity field models like EGM2008 from GPS/levelling data

Expected accuracy of tilt measurements on a novel hexapod-based Digital zenith camera system: A Monte-Carlo simulation study

Digital zenith camera systems (DZCS) are dedicated astronomical-geodetic measurement systems for the observation of the direction of the plumb line. A DZCS key component is a pair of tilt meters for the determination of the instrumental tilt with respect to the plumb line. Highest accuracy (i.e., 0.1 arc-seconds or better) is achieved in practice through observation with precision tilt meters in opposite faces (180° instrumental rotation), and application of rigorous tilt reduction models. A novel concept proposes the development of a hexapod (Stewart platform)-based DZCS. However, hexapod-based total rotations are limited to about 30°–60° in azimuth (equivalent to ±15° to ±30° yaw rotation), which raises the question of the impact of the rotation angle between the two faces on the accuracy of the tilt measurement. The goal of the present study is the investigation of the expected accuracy of tilt measurements to be carried out on future hexapod-based DZCS, with special focus placed on the role of the limited rotation angle. A Monte-Carlo simulation study is carried out in order to derive accuracy estimates for the tilt determination as a function of several input parameters, and the results are validated against analytical error propagation.As the main result of the study, limitation of the instrumental rotation to 60° (30°) deteriorates the tilt accuracy by a factor of about 2 (4) compared to a 180° rotation between the faces. Nonetheless, a tilt accuracy at the 0.1 arc-second level is expected when the rotation is at least 45°, and 0.05 arc-second (about 0.25 microradian) accurate tilt meters are deployed. As such, a hexapod-based DZCS can be expected to allow sufficiently accurate determination of the instrumental tilt. This provides supporting evidence for the feasibility of such a novel instrumentation. The outcomes of our study are not only relevant to the field of DZCS, but also to all other types of instruments where the instrumental tilt must be corrected. Examples include electronic theodolites or total stations, gravity meters, and other hexapod-based telescopes

Improving EGM2008 by GPS and leveling data at local scale

The development of the Earth Gravitational Model 2008 (EGM2008) model is a significant contribution for modeling the Earth's gravity and geoid. Recently, it can be confidently used versus geometric models following a simple refinement procedure. Several studies show that, EGM2008 can reach the accuracy of regional or local geoid models after modeling the differences between the GPS-leveling geoid heights and EGM2008 derived geoid heights at identified control points. The study focuses on a corrector surface fitting (CSF) approach based on radial basis functions (RBF) as improvement procedure for EGM2008. A detailed mathematical model and solution algorithm of the proposed model is given, and it has been applied in different test areas covering the city borders of Bursa, Konya, Denizli and Gaziantep in Turkey. Accuracy of the improved model was evaluated in scattered check points within test regions. The geoid heights of all check points obtained by GPS-leveling measurements were compared with the geoid heights obtained from improved model. The discrepancies between the calculated and measured geoid heights were analyzed and discussed

Solar radiative transfer simulations in Saharan dust plumes: particle shapes and 3-D effect

Radiative fields of three-dimensional inhomogeneous Saharan dust clouds have been calculated at solar wavelength (0.6 μm) by means of a Monte Carlo radiative transfer model. Scattering properties are taken from measurements in the SAMUM campaigns, from light scattering calculations for spheroids based on the MIESCHKA code, from Mie theory for spheres and from the geometric optics method assuming irregular shaped particles. Optical properties of different projected area equivalent shapes are compared. Large differences in optical properties are found especially in the phase functions. Results of radiative transfer calculations based on the Monte Carlo method are shown exemplarily for one dust cloud simulated by the cloud resolving atmospheric circulation model LM-MUSCAT-DES. Shape-induced differences in the radiation fluxes are pronounced, for example, the domain averaged normalized radiance is about 30% lower in the case of a dust plume consisting of spheroids or irregular particles compared to spheres. The effect of net horizontal photon transport (3-D effect) on the reflected radiance fields is only notable at the largest gradients in optical thickness. For example, the reflectance at low sun position differs locally about 15% when horizontal photon transport is accounted for. ‘Sharp edges' due to 1-D calculations are smoothed out in the 3-D case

Ellipsoidal area mean gravity anomalies - precise computation of gravity anomaly reference fields for remove-compute-restore geoid determination

Gravity anomaly reference fields, required e.g. in remove-compute-restore (RCR) geoid computation, are obtained from global geopotential models (GGM) through harmonic synthesis. Usually, the gravity anomalies are computed as point values or area mean values in spherical approximation, or point values in ellipsoidal approximation. The present study proposes a method for computation of area mean gravity anomalies in ellipsoidal approximation ('ellipsoidal area means') by applying a simple ellipsoidal correction to area means in spherical approximation. Ellipsoidal area means offer better consistency with GGM quasi/geoid heights. The method is numerically validated with ellipsoidal area mean gravity derived from very fine grids of gravity point values in ellipsoidal approximation. Signal strengths of (i) the ellipsoidal effect (i.e., difference ellipsoidal vs. spherical approximation), (ii) the area mean effect (i.e., difference area mean vs. point gravity) and (iii) the ellipsoidal area mean effect (i.e., differences between ellipsoidal area means and point gravity in spherical approximation) are investigated in test areas in New Zealand and the Himalaya mountains. The impact of both the area mean and the ellipsoidal effect on quasigeoid heights is in the order of several centimetres. The proposed new gravity data type not only allows more accurate RCR-based geoid computation, but may also be of some value for the GGM validation using terrestrial gravity anomalies that are available as area mean values

CORRECCIONES DIFERENCIALES VÍA NTRIP PARA DISPOSITIVO MÓVIL CON APLICACIÓN ANDROID

El posicionamiento en tiempo real usando GPS se hace mediante correcciones diferenciales enviadas desde una estación base hacia un receptor móvil. Generalmente, la corrección es enviada vía radio o por medio de satélites de comunicación. Con el desarrollo del internet inalámbrica y con el aumento de la cobertura de la señal mediante un Protocolo, conocido como IP, han hecho que se integren estas tecnologías para realizar mediciones para trabajos y estudios en tiempo real usando la tecnología GPS, y mediante el protocolo NTRIP. Esta técnica se ha estado desarrollando e implementando de forma constante en la región, siendo el presente y futuro de las mediciones para trabajos de precisión y en tiempo real. En este trabajo, se muestra la implementación de la técnica NTRIP para posicionamiento en tiempo real. El acceso a datos brutos del GPS en un móvil ANDROID y un navegador Mobile Mapper 10, la utilización de NTRIP para el envió de correcciones diferenciales por medio del protocolo IP, y el internet como red de información inmediata, fueron la base general para crear una aplicación que utiliza una corrección diferencial por posición. Los primeros resultados muestran una mejoría en la posición, pudiendo llegar a obtener un error medio de 2.3m en una Tablet con Android, y 1.6 m con el Mobile Mapper 10; en un tiempo de 5 minuto

Indirect evaluation of Mars Gravity Model 2011 using a replication experiment on Earth

Curtin University’s Mars Gravity Model 2011 (MGM2011) is a high-resolution composite set of gravity field functionals that uses topography-implied gravity effects at medium- and short-scales (~125 km to ~3 km) to augment the space-collected MRO110B2 gravity model. Ground-truth gravity observations that could be used for direct validation of MGM2011 are not available on Mars’s surface. To indirectly evaluate MGM2011 and its modelling principles, an as-close-as-possible replication of the MGM2011 modelling approach was performed on Earth as the planetary body with most detailed gravity field knowledge available. Comparisons among six ground-truth data sets (gravity disturbances, quasigeoid undulations and vertical deflections) and the MGM2011-replication over Europe and North America show unanimously that topography-implied gravity information improves upon space-collected gravity models over areas with rugged terrain. The improvements are ~55% and ~67% for gravity disturbances, ~12% and ~47% for quasigeoid undulations, and ~30% to ~50% for vertical deflections. Given that the correlation between space-collected gravity and topography is higher for Mars than Earth at spatial scales of a few 100 km, topography-implied gravity effects are more dominant on Mars. It is therefore reasonable to infer that the MGM2011 modelling approach is suitable, offering an improvement over space-collected Martian gravity field models

Determinação de função covariância local para a predição de anomalias da gravidade Bouguer e valores da gravidade visando à obtenção de números geopotenciais

Considerando as dimensões de um país como o Brasil, realizar observações gravimétricas sobre todas as linhas de nivelamento do país ainda constitui-se um problema pertinente quando o objetivo é a determinação de números geopotenciais e/ou quantidades relacionadas ao campo da gravidade (e.g. anomalias da gravidade). Funções de covariância locais foram construídas a partir de valores da gravidade disponibilizados pelo Instituto Brasileiro de Geografia e Estatística (IBGE). Estes valores foram digitalizados e anexados à base de dados do Laboratório de Referenciais Geodésicos e Altimetria por Satélites (LARAS) da UFPR, a qual já contém dados da rede gravimétrica argentina. Estas funções de covariância foram desenvolvidas para anomalias da gravidade Bouguer na região fronteiriça Brasil/Argentina. Estudos com funções polinomiais e de Fourier foram avaliadas utilizando dez por cento dos pontos originais para checagem. Os resultados obtidos em termos de Erro Médio Quadrático (RMS) para a função polinomial de quarta ordem e para a função de Fourier de terceira ordem foram do nível do mGal

An attempt to link the Brazilian Height System to a World Height System

This paper deals with the geopotential approach to investigate the present Brazilian Height System (BHS). Geopotential numbers are derived from Global Positioning System (GPS) satellite surveying and disturbing potential on selected benchmarks. A model for the disturbing potential can be obtained by an existing set of spherical harmonic coefficients such as the Earth Gravity Model 2008 (EGM08). The approach provides absolute evaluation of local normal geopotential numbers (aka spheropotential numbers) related to a so-called World Height System (WHS). To test the validity of the proposed methodology, a numerical experiment was carried out related to a test region in Southern Brazil. The accuracy of the derived geopotential numbers was tested versus local normal geopotential numbers based on 262 GPS/leveling points. The root mean square error (RMSE) value for metric offset of BHS derived from geopotential numbers and the disturbing potential modeling in the test area was estimated to be near 0.224 meters in the absolute view. Therefore, since these spheropotential numbers are referred to a local datum, these results of comparisons may be an indicator of the mean bias of local network due to the effect of local Sea Surface Topography (SSTop) and possible offset between the unknown reference for the BHS and the quasigeoid model in the region