GOCE precise orbit determination for the entire Mission – challenges in the final mission phase

The Gravity field and steady-state Ocean Circulation Explorer (GOCE), ESA’s first Earth Explorer core mission, was launched on March 17, 2009 into a sunsynchronous dusk-dawn orbit and eventually re-entered into the Earth’s atmosphere on November 11, 2013. A precise science orbit (PSO) product was provided by the GOCE High-level Processing Facility (HPF) from the GPS high-low Satellite-to-Satellite Tracking (hl-SST) data from the beginning until the very last days of the mission. We recapitulate the PSO procedure and refer to the results achieved until the official end of the GOCE mission on October 21, 2013, where independent validations with Satellite Laser ranging (SLR) measurements confirmed a high quality of the PSO product of about 2 cm 1-D RMS. We then focus on the period after the official end of the mission, where orbits could still be determined thanks to the continuously running GPS receivers delivering high quality data until a few hours before the re-entry into the Earth’s atmosphere. We address the challenges encountered for orbit determination during these last days and report on adaptions in the PSO procedure to also obtain good orbit results at the unprecedented low orbital altitudes below 224 km.

Doppler Orbit Determination of Deep Space Probes by the Bernese GNSS Software: First Results of the Combined Orbit Determination from DSN and Inter-Satellite Ka-Band Data from the Grail Mission

Navigation of deep space probes is most commonly operated using the spacecraft Doppler tracking technique. Orbital parameters are determined from a series of repeated measurements of the frequency shift of a microwave carrier over a given integration time. Currently, both ESA and NASA operate antennas at several sites around the world to ensure the tracking of deep space probes. Just a small number of software packages are nowadays used to process Doppler observations. The Astronomical Institute of the University of Bern (AIUB) has recently started the development of Doppler data processing capabilities within the Bernese GNSS Software. This software has been extensively used for Precise Orbit Determination of Earth orbiting satellites using GPS data collected by on-board receivers and for subsequent determination of the Earth gravity field. In this paper, we present the currently achieved status of the Doppler data modeling and orbit determination capabilities in the Bernese GNSS Software using GRAIL data. In particular we will focus on the implemented orbit determination procedure used for the combined analysis of Doppler and intersatellite Ka-band data. We show that even at this earlier stage of the development we can achieve an accuracy of few mHz on two-way S-band Doppler observation and of 2 µm/s on KBRR data from the GRAIL primary mission phase.

Mean dynamic topography and oceanographic parameters estimated from an inverse model and satellite geodesy, with link to model result in one single NetCDF file (392 MB), including the inverse data error covariance

Geostrophic surface velocities can be derived from the gradients of the mean dynamic topography-the difference between the mean sea surface and the geoid. Therefore, independently observed mean dynamic topography data are valuable input parameters and constraints for ocean circulation models. For a successful fit to observational dynamic topography data, not only the mean dynamic topography on the particular ocean model grid is required, but also information about its inverse covariance matrix. The calculation of the mean dynamic topography from satellite-based gravity field models and altimetric sea surface height measurements, however, is not straightforward. For this purpose, we previously developed an integrated approach to combining these two different observation groups in a consistent way without using the common filter approaches (Becker et al. in J Geodyn 59(60):99-110, 2012, doi:10.1016/j.jog.2011.07.0069; Becker in Konsistente Kombination von Schwerefeld, Altimetrie und hydrographischen Daten zur Modellierung der dynamischen Ozeantopographie, 2012, http://nbn-resolving.de/nbn:de:hbz:5n-29199). Within this combination method, the full spectral range of the observations is considered. Further, it allows the direct determination of the normal equations (i.e., the inverse of the error covariance matrix) of the mean dynamic topography on arbitrary grids, which is one of the requirements for ocean data assimilation. In this paper, we report progress through selection and improved processing of altimetric data sets. We focus on the preprocessing steps of along-track altimetry data from Jason-1 and Envisat to obtain a mean sea surface profile. During this procedure, a rigorous variance propagation is accomplished, so that, for the first time, the full covariance matrix of the mean sea surface is available. The combination of the mean profile and a combined GRACE/GOCE gravity field model yields a mean dynamic topography model for the North Atlantic Ocean that is characterized by a defined set of assumptions. We show that including the geodetically derived mean dynamic topography with the full error structure in a 3D stationary inverse ocean model improves modeled oceanographic features over previous estimates.

(Table 2) Chemical composition of quenched glasses from the Mohns and Knipovich Ridges

The aim of this project was a petrogeochemical study of igneous rocks in the areas of the Mohns and Knipovich Ridges, both being the northern extensions of the Mid-Atlantic Ridge (MAR), using data available for quenching glass samples collected during Cruises 36 and 38 of R/V Akademic Mstislav Keldysh and during Cruise 15 of R/V Professor Logachev. Results of igneous rock studying from the Mohns and Knipovich Ridges at the background of evolution of the total North Atlantic Province, which had been identified earlier from tectonic and geophysical data, showed that igneous rocks of the Knipovich Ridge can be ranked as shallow tholeiites, primary melts of which were relatively rich in Na and Si and poor in Fe. This type of magma is characteristic of colder regions of the oceanic lithosphere. Its occurrence in the Knipovich Ridge and its potential propagation up to the Gakkel Ridge suggest that igneous rocks of this region originated under conditions of passive spreading in contrast to the MAR region in vicinity of Iceland and Azores, where substantial contribution of hotter material of a rising plume contributed to formation of the oceanic crust. The North Atlantic Ocean is the youngest province in terms of ocean-floor opening. Geologically and geophysically it is one of well studied regions of the World Ocean. Nevertheless some basic key items of its origin still remain to be clarified. In 1975 Scatler et al. proved specifics of this region manifested in growth of the gravity field, and also in relative height of the ocean floor in the region of 33-70°N, which was associated by them with rise of the hotter mantle, as compared with common regions of the Mid-Atlantic Ridge. Later this view was confirmed by character of magmatism, which differed in depth of generation and by melting degree of the resulting primary magma. Uniqueness of the North Atlantic region was also proved by the fact that this region was marked by extensive geochemical anomalies associated with Azores, Iceland, and Jan Mayen. All of these data allow to consider the northern part of the MAR (north of 33°N) as an united global geotectonic province. The Mohns and Knipovich Ridges located north of Iceland locate at the northern end of this province. This is the least known region. Therefore, new data for ridge areas of 73-77°N are needed for more complete geologic history of the Arctic Basin. The aim of this study was to carry out a complex comparison of magmatism at the Mohns and Knipovich Ridges with magmatism at large segments of the MAR northern province and to reconstruct mechanisms of primary magma formation, as well as conditions of their fractionation. This paper was based on results of studying quenched glasses, which reflect evolution of melt in the course of its formation.

Ice loss in the Canadian Arctic Archipelago

Though much attention has been focused in recent years on the melting of ice from Greenland and Antarctica, nearly half of the ice volume currently being lost to the ocean is actually coming from other mountain glaciers and ice caps. Ice loss from a group of islands in northern Canada accounts for much of that volume. In a study published in April 2011 in the journal Nature, a team of researchers led by Alex Gardner of the University of Michigan found that land ice in both the northern and southern Canadian Arctic Archipelago has declined sharply. The maps above show ice loss from surface melting for the northern portion of the archipelago from 2004-2006 (left) and 2007-2009 (right). Blue indicates ice gain, and red indicates ice loss. In the six years studied, the Canadian Arctic Archipelago lost an average of approximately 61 gigatons of ice per year. (A gigaton is a billion tons of ice.) The research team also found the rate of ice loss was accelerating. From 2004 to 2006, the average mass loss was roughly 31 gigatons per year; from 2007 to 2009, the loss increased to 92 gigatons per year. Gardner and colleagues used three independent methods to assess ice mass, all of which showed the same trends. The team used a model to estimate the surface mass balance of ice and the amount of ice discharged. They also compiled and analyzed measurements from NASA's Ice, Cloud and Land Elevation Satellite (ICESat) to assess changes in the surface height of ice. Finally, they gathered observations from NASA's Gravity Recovery and Climate Experiment (GRACE) to determine changes in the gravity field in the region, an indicator of the amount of ice gained or lost. The Canadian Arctic Archipelago generally receives little precipitation, and the amount of snowfall changes little from year to year. But the rate of snow and ice melting varies considerably, so changes in ice mass come largely from changes in summertime melt. During the 2004 to 2009 study period, the Canadian Arctic Archipelago experienced four of its five warmest years since 1960, likely fueling the melting. Gardner notes that from 2001 to 2004, the sum of melting from all mountain glaciers and ice caps around the world (but not the Greenland and Antarctic ice sheets) contributed an estimated 1 millimeter per year to global sea level rise. Recent estimates suggest the Greenland and Antarctic ice sheets add another 1.3 millimeters per year to sea level. "This means 1 percent of the land ice volume-mountain glaciers and ice caps-account for about half of all ice loss to the world's oceans," Gardner said. "Most of the ice loss is coming from the Canadian Arctic Archipelago, Alaska, Patagonia, the Himalayas, and the smaller ice masses surrounding the main Greenland and Antarctic ice sheets."

Code and readme of a MATLAB-based graphical user interface program for computing functionals of the geopotential

We present a novel graphical user interface program GrafLab (GRAvity Field LABoratory) for spherical harmonic synthesis (SHS) created in MATLAB®. This program allows to comfortably compute 38 various functionals of the geopotential up to ultra-high degrees and orders of spherical harmonic expansion. For the most difficult part of the SHS, namely the evaluation of the fully normalized associated Legendre functions (fnALFs), we used three different approaches according to required maximum degree: (i) the standard forward column method (up to maximum degree 1800, in some cases up to degree 2190); (ii) the modified forward column method combined with Horner's scheme (up to maximum degree 2700); (iii) the extended-range arithmetic (up to an arbitrary maximum degree). For the maximum degree 2190, the SHS with fnALFs evaluated using the extended-range arithmetic approach takes only approximately 2-3 times longer than its standard arithmetic counterpart, i.e. the standard forward column method. In the GrafLab, the functionals of the geopotential can be evaluated on a regular grid or point-wise, while the input coordinates can either be read from a data file or entered manually. For the computation on a regular grid we decided to apply the lumped coefficients approach due to significant time-efficiency of this method. Furthermore, if a full variance-covariance matrix of spherical harmonic coefficients is available, it is possible to compute the commission errors of the functionals. When computing on a regular grid, the output functionals or their commission errors may be depicted on a map using automatically selected cartographic projection.

Geology, geochemistry, and mineralogy of sediments from the Trans Indian Ocean Geotraverse

The monograph is devoted to the main results of research on the Trans Indian Ocean Geotraverse from the Maskarene Basin to the north-western margin of Australia. These results were obtained by Russian specialists and together with Indian specialists during 15 years of cooperation in investigation of geological structure and mineral resources of the Indian Ocean. The monograph includes materials on information support of marine geological and geophysical studies, composition and structure of information resources on the Indian Ocean, bathymetry and geomorphology, structure and geological nature of the magnetic field, gravity field, plate tectonics, crustal structure and sedimentary cover, seismic stratigraphy, perspectives for detecting oil and gas, solid minerals, sediment composition, composition and properties of clay minerals, stratigraphy and sediment age, chemical composition of sediments, composition of and prospects for solid minerals.

Atmospheric, oceanic and hydrological polar motion excitation mechanisms based on a combination of geometric and gravimetric space observations

The goal of our study is to determine accurate time series of geophysical Earth rotation excitations to learn more about global dynamic processes in the Earth system. For this purpose, we developed an adjustment model which allows to combine precise observations from space geodetic observation systems, such as Satellite Laser Ranging (SLR), Global Navigation Satellite Systems (GNSS), Very Long Baseline Interferometry (VLBI), Doppler Orbit determination and Radiopositioning Integrated on Satellite (DORIS), satellite altimetry and satellite gravimetry in order to separate geophysical excitation mechanisms of Earth rotation. Three polar motion time series are applied to derive the polar motion excitation functions (integral effect). Furthermore we use five time variable gravity field solutions from Gravity Recovery and Climate Experiment (GRACE) to determine not only the integral mass effect but also the oceanic and hydrological mass effects by applying suitable filter techniques and a land-ocean mask. For comparison the integral mass effect is also derived from degree 2 potential coefficients that are estimated from SLR observations. The oceanic mass effect is also determined from sea level anomalies observed by satellite altimetry by reducing the steric sea level anomalies derived from temperature and salinity fields of the oceans. Due to the combination of all geodetic estimated excitations the weaknesses of the individual processing strategies can be reduced and the technique-specific strengths can be accounted for. The formal errors of the adjusted geodetic solutions are smaller than the RMS differences of the geophysical model solutions. The improved excitation time series can be used to improve the geophysical modeling.

Improved geoid solution for the Weddell Sea region

We present a geoid solution for the Weddell Sea and adjacent continental Antarctic regions. There, a refined geoid is of interest, especially for oceanographic and glaciological applications. For example, to investigate the Weddell Gyre as a part of the Antarctic Circumpolar Current and, thus, of the global ocean circulation, the mean dynamic topography (MDT) is needed. These days, the marine gravity field can be inferred with high and homogeneous resolution from altimetric height profiles of the mean sea surface. However, in areas permanently covered by sea ice as well as in coastal regions, satellite altimetry features deficiencies. Focussing on the Weddell Sea, these aspects are investigated in detail. In these areas, ground-based data that have not been used for geoid computation so far provide additional information in comparison with the existing high-resolution global gravity field models such as EGM2008. The geoid computation is based on the remove-compute-restore approach making use of least-squares collocation. The residual geoid with respect to a release 4 GOCE model adds up to two meters and more in the near-coastal and continental areas of the Weddell Sea region, also in comparison with EGM2008. Consequently, the thus refined geoid serves to compute new estimates of the regional MDT and geostrophic currents.

Conservation laws for liquid bridges

Conservation laws for an inviscid liquid bridge set into motion by conservative forces are given in integral form. These laws provide useful information on the overall motion of the bridge in the presence of unexpected or uncontrolled disturbances and could, in addition, be monitored in a computational solution of the problem as an accuracy check. Many of the resulting conservation laws are familiar to fluiddynamicists. Nevertheless, a systematic approach providing an exhaustive list of these laws reveals the existence of new conserved properties hardly deducible in the classical way. Although the present analysis concerns the case of axial, and constant, gravity it can be applied, with minor refinements, when the gravity field varies with time in both direction and intensity.

Orbital debris mitigation through deorbiting with passive electrodynamic drag

The increase of orbital debris and the consequent proliferation of smaller objects through fragmentation are driving the need for mitigation strategies. The issue is how to deorbit the satellite with an efficient system that does not impair drastically the propellant budget of the satellite and, consequently, reduces its operating life. We have been investigating, in the framework of a European-Community-funded project, a passive system that makes use of an electrodynamics tether to deorbit a satellite through Lorentz forces. The deorbiting system will be carried by the satellite itself at launch and deployed from the satellite at the end of its life. From that moment onward the system operates passively without requiring any intervention from the satellite itself. The paper summarizes the results of the analysis carried out to show the deorbiting performance of the system starting from different orbital altitudes and inclinations for a reference satellite mass. Results can be easily scaled to other satellite masses. The results have been obtained by using a high-fidelity computer model that uses the latest environmental routines for magnetic field, ionospheric density, atmospheric density and a gravity field model. The tether dynamics is modelled by considering all the main aspects of a real system as the tether flexibility and its temperature-dependent electrical conductivity. Temperature variations are computed by including all the major external and internal input fluxes and the thermal flux emitted from the tether. The results shows that a relatively compact and light system can carry out the complete deorbit of a relatively large satellite in a time ranging from a month to less than a year starting from high LEO with the best performance occurring at low orbital inclinations.

El problema isostático inverso de Vening Meinesz. Teoría y desarrollo. Aplicación práctica para la determinación de la profundidad de la discontinuidad de Mohorovičić en la Península Ibérica

La discontinuidad de Mohorovičić, más conocida simplemente como “Moho” constituye la superficie de separación entre los materiales rocosos menos densos de la corteza y los materiales rocosos más densos del manto, suponiendo estas capas de densidad constante del orden de 2.67 y 3.27 g/cm3, y es un contorno básico para cualquier estudio geofísico de la corteza terrestre. Los estudios sísmicos y gravimétricos realizados demuestran que la profundidad del Moho es del orden de 30-40 km por debajo de la Península Ibérica y 5-15 km bajo las zonas marinas. Además las distintas técnicas existentes muestran gran correlación en los resultados. Haciendo la suposición de que el campo de gravedad de la Península Ibérica (como le ocurre al 90% de la Tierra) está isostáticamente compensado por la variable profundidad del Moho, suponiendo un contraste de densidad constante entre la corteza y el manto y siguiendo el modelo isostático de Vening Meinesz (1931), se formula el problema isostático inverso para obtener tal profundidad a partir de la anomalía Bouguer de la gravedad calculada gracias a la gravedad observada en la superficie terrestre. La particularidad de este modelo es la compensación isostática regional de la que parte la teoría, que se asemeja a la realidad en mayor medida que otros modelos existentes, como el de Airy-Heiskanen, que ha sido históricamente el más utilizado en trabajos semejantes. Además, su solución está relacionada con el campo de gravedad global para toda la Tierra, por lo que los actuales modelos gravitacionales, la mayoría derivados de observaciones satelitales, deberían ser importantes fuentes de información para nuestra solución. El objetivo de esta tesis es el estudio con detalle de este método, desarrollado por Helmut Moritz en 1990, que desde entonces ha tenido poca evolución y seguidores y que nunca se ha puesto en práctica en la Península Ibérica. Después de tratar su teoría, desarrollo y aspectos computacionales, se está en posición de obtener un modelo digital del Moho para esta zona a fin de poder utilizarse para el estudio de la distribución de masas bajo la superficie terrestre. A partir de los datos del Moho obtenidos por métodos alternativos se hará una comparación. La precisión de ninguno de estos métodos es extremadamente alta (+5 km aproximadamente). No obstante, en aquellas zonas donde exista una discrepancia de datos significaría un área descompensada, con posibles movimientos tectónicos o alto grado de riesgo sísmico, lo que le da a este estudio un valor añadido. ABSTRACT The Mohorovičić discontinuity, simply known as “Moho” constitutes the division between the rocky and less thick materials of the mantle and the heavier ones in the crust, assuming densities of the orders of 2.67 y 3.27 g/cm3 respectively. It is also a basic contour for every geophysical kind of studies about the terrestrial crust. The seismic and previous gravimetric observations done in the study area show that the Moho depth is of the order of 30-40 km beneath the ground and 5-15 km under the ocean basin. Besides, the different techniques show a good correlation in their results. Assuming that the Iberian Peninsula gravity field (as it happens for the 90% of the Earth) is isostatically compensated according to the variable Moho depth, supposing a constant density contrast between crust and mantle, and following the isostatic Vening Meinesz model (1931), the inverse isostatic problem can be formulated from Bouguer gravity anomaly data obtained thanks to the observed gravity at the surface of the Earth. The main difference between this model and other existing ones, such as Airy- Heiskanen’s (pure local compensation and mostly used in these kinds of works) is the approaching to a regional isostatic compensation, much more in accordance with reality. Besides, its solution is related to the global gravity field, and the current gravitational models -mostly satellite derived- should be important data sources in such solution. The aim of this thesis is to study with detail this method, developed by Helmut Moritz in 1990, which hardly ever has it put into practice. Moreover, it has never been used in Iberia. After studying its theory, development and computational aspects, we are able to get a Digital Moho Model of the Iberian Peninsula, in order to study the masses distribution beneath the Earth’s surface. With the depth Moho information obtained from alternative methods, a comparison will be done. Both methods give results with the same order of accuracy, which is not quite high (+ 5 km approximately). Nevertheless, the areas in which a higher difference is observed would mean a disturbance of the compensation, which could show an unbalanced area with possible tectonic movements or potential seismic risk. It will give us an important additive value, which could be used in, at first, non related fields, such as density discrepancies or natural disasters contingency plans.

Various techniques and procedures for refining ERS-1 orbits

The satellite ERS-1 was launched in July 1991 in a period of high solar activity. Sparse laser tracking and the failure of the experimental microwave system (PRARE) compounded the orbital errors which resulted from mismodelling of atmospheric density and hence surface forces. Three attempts are presented here to try and refine the coarse laser orbits of ERS-1, made prior to the availability of the full altimetric dataset. The results of the first attempt indicate that by geometrically modelling the satellite shape some improvement in orbital precision may be made for any satellite; especially one where no area tables already exist. The second and third refinement attempts are based on the introduction of data from some second satellite; in these examples SPOT-2 and TOPEX/Poseidon are employed. With SPOT-2 the method makes use of the orbital similarities to produce along-track corrections for the more fully tracked SPOT-2. Transferring these corrections to ERS-1 produces improvements in the precise orbits thus determined. With TOPEX/Poseidon the greater altitude results in a more precise orbit (gravity field and atmospheric errors are of less importance). Thus, by computing height differences at crossover points of the TOPEX/Poseidon and ERS-1 ground tracks the poorer orbit of ERS-1 may be improved by the addition of derived radial corrections. In the positive light of all three results several potential modification are suggested and some further avenues of investigation indicated.

Resonance studies of artificial earth satellites

Orbit determination from artificial satellite observations is a key process in obtaining information about the Earth and its environment. A study of the perturbations experienced by these satellites enables knowledge to be gained of the upper atmosphere, the gravity field, ocean tides, solid-Earth tides and solar radiation. The gravity field is expressed as a double infinite series of associated Legendre functions (tesseral harmonics). In contemporary global gravity field models the overall geoid is well determined. An independent check on these gravity field harmonics of a particular order may be made by analysis of satellites that pass through resonance of that order. For such satellites the perturbations of the orbital elements close to resonance are analysed to derive lumped harmonic coefficients. The orbital parameters of 1984-106A have been determined at 43 epochs, during which time the satellite was close to 14th order resonance. Analysis of the inclination and eccentricity yielded 6 lumped harmonic coefficients of order 14 whilst analysis of the mean motion yielded additional pairs of lumped harmonics of orders 14, 28 and 42, with the 14th order harmonics superseding those obtained from analysis of the inclination. This thesis concentrates in detail on the theoretical changes of a near-circular satellite orbit perturbed by the Earth's gravity field under the influence of minimal air-drag whilst in resonance with the Earth. The satellite 1984-106A experienced the interesting property of being temporarily trapped with respect to a secondary resonance parameter due to the low air-drag in 1987. This prompted the theoretical investigation of such a phenomenon. Expressions obtained for the resonance parameter led to the determination of 8 lumped harmonic coefficients, coincidental to those already obtained. All the derived lumped harmonic values arc used to test the accuracy of contemporary gravity field models and the underlying theory in this thesis.