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Learning from successful applications of methods originating in statistical mechanics or information theory in one scientific field (e.g. atmospheric physics or weather) can provide important insights or conceptual ideas for other areas (e.g. space sciences) or even stimulate new research questions and approaches. For instance, quantification and attribution of dynamical complexity in output time series of nonlinear dynamical systems is a key challenge across scientific disciplines. Especially in the field of space physics, an early and accurate detection of characteristic dissimilarity between normal and abnormal states (e.g. pre-storm activity vs. magnetic storms) has the potential to vastly improve space weather diagnosis and, consequently, the mitigation of space weather hazards. This presentation reports on the progress of a largely interdisciplinary International Team, combining expertise from both space physics and nonlinear physics communities, which was selected for funding by the International Space Science Institute (ISSI) in 2019. The Team attempts to combine advanced mathematical tools and identify key directions for future methodological progress relevant to space weather forecasting using Swarm, SuperMAG, and other space/ground datasets. By utilizing a variety of complementary modern complex systems based approaches, an entirely novel view on nonlinear magnetospheric variability is obtained. Taken together, the multiplicity of recently developed approaches in the field of nonlinear time series analysis offers great potential for uncovering relevant yet complex processes interlinking different geospace subsystems, variables and spatio-temporal scales. The Team provides a first-time systematic assessment of these techniques and their applicability in the context of geomagnetic variability.

The Earth masses reside in a near-hydrostatic equilibrium, while the deviations are, for example, manifested in the geoid, which is nowadays well determined by satellite gravimetry. Recent progress in estimating the density distribution of the Earth allows us to examine individual Earth layers and to directly see how the sum approaches the observed anomalous gravitational field. This study evaluates contributions from the crust and the upper mantle taken from the LITHO1.0 model and quantifies the gravitational spectra of the density structure to the depth of 435 km. This is done without isostatic adjustments to see what can be revealed with models like LITHO1.0 alone. At the resolution of 290 km (spherical harmonic degree 70), the crustal contribution starts to dominate over the upper mantle and at about 150 km (degree 130) the upper mantle contribution is nearly negligible. At the spatial resolution $$

8th Swarm Data Quality Workshop; Frascati, Italy, 8–12 October 2018

The European Space Agency (ESA) wind mission, Aeolus, hosts the first space-based Doppler Wind Lidar (DWL) world-wide. The primary mission objective is to demonstrate the DWL technique for measuring wind profiles from space, intended for assimilation in Numerical Weather Prediction (NWP) models. The wind observations will also be used to advance atmospheric dynamics research and for evaluation of climate models. Mission spin-off products are profiles of cloud and aerosol optical properties. Aeolus was launched on 22 August 2018, and the Atmospheric LAser Doppler INstrument (Aladin) instrument switch-on was completed with first high energy output in wind mode on 4 September 2018 [1], [2]. The on-ground data processing facility worked excellent, allowing L2 product output in near-real-time from the start of the mission. First results from the wind profile product (L2B) assessment show that the winds are of very high quality, with random errors in the free Troposphere within (cloud/aerosol backscatter winds: 2.1 m/s) and larger (molecular backscatter winds: 4.3 m/s) than the requirements (2.5 m/s), but still allowing significant positive impact in first preliminary NWP impact experiments. The higher than expected random errors at the time of writing are amongst others due to a lower instrument out-and input photon budget than designed. The instrument calibration is working well, and some of the data processing steps are currently being refined to allow to fully correct instrument alignment related drifts and elevated detector dark currents causing biases in the first data product version. The optical properties spin-off product (L2A) is being compared e.g. to NWP model clouds, air quality model forecasts, and collocated ground-based observations. Features including optically thick and thin particle and hydrometeor layers are clearly identified and are being validated.

Soon after its successful launch in August 2018, the spaceborne wind lidar ALADIN (Atmospheric LAser Doppler INstrument) on-board ESA's Earth Explorer satellite Aeolus has demonstrated to provide atmospheric wind profiles on a global scale. Being the first ever Doppler Wind Lidar (DWL) instrument in space, ALADIN contributes to the improvement in numerical weather prediction (NWP) by measuring one component of the horizontal wind vector. The performance of the ALADIN instrument was assessed by a team from ESA, DLR, industry, and NWP centers during the first months of operation. The current knowledge about the main contributors to the random and systematic errors from the instrument will be discussed. First validation results from an airborne campaign with two wind lidars on-board the DLR Falcon aircraft will be shown.

The Gravity field and steady-state Ocean Circulation Explorer (GOCE) satellite, launched on 17 March 2009, is designed to measure the Earth’s mean gravity field with unprecedented accuracy at spatial resolutions down to 100 km. The accurate calibration of the gravity gradiometer on-board GOCE is of utmost importance for achieving the mission goals. ESA’s baseline method for the calibration uses star sensor and accelerometer data of a dedicated calibration procedure, which is executed every 2 months. In this paper, we describe a method for monitoring the evolution of calibration parameter during that time. The method works with star sensor and accelerometer data and does not require gravity field models, which distinguishes it from other existing methods. We present time series of calibration parameters estimated from GOCE data from 1 November 2009 to 17 May 2010. The time series confirm drifts in the calibration parameters that are present in the results of other methods, including ESA’s baseline method. Although these drifts are very small, they degrade the gravity gradients, leading to the conclusion that the calibration parameters of the ESA’s baseline method need to be linearly interpolated. Further, we find a correction of −36 × 10−6 for one calibration parameter (in-line differential scale factor of the cross-track gradiometer arm), which improves the gravity gradient performance. The results are validated by investigating the trace of the calibrated gravity gradients and comparing calibrated gravity gradients with reference gradients computed along the GOCE orbit using the ITG-Grace-2010s gravity field model.

This paper describes the upgrade of the GOCE Level 1b gradiometer processing as part of ESA’s Payload Data Segment (PDS). Four processing steps have been identified which can be improved: 1. The optimal determination of the angular rates of the satellite, based on a combination of star sensor and gradiometer data. This is the so-called angular rate reconstruction. 2. The optimal determination of the spacecraft’s attitude, again based on a combination of star sensor and gradiometer data. 3. The combination of data of all simultaneously available star sensors. And, 4. the calibration of the measured accelerations is improved by taking the time dependence of selected calibration parameters into account. In this paper the complete upgrade of the gradiometer Level 1b processing is described, and the expected improvement of the gravity gradients as well as the gravity field solutions is quantified. The largest overall improvements are due to the new method for angular rate reconstruction, mainly at the low to medium frequencies and at the harmonics of the orbital revolution frequency. In addition, spurious artifacts in the gravity gradient V yy , which are caused by non-perfect common mode rejection, can be reduced significantly by the improved calibration approach. We show that the standard deviation of the gravity gradient tensor trace can be reduced by about 90 percent for the frequencies below the gradiometer measurement band (i.e. below 5 mHz) and by about 4 percent within the measurement band (from 5 to 100 mHz). The geoid error of satellite gravity gradiometry solutions based on 61 days of data is reduced from 3.0 to 2.2 cm between spherical harmonic degree 20 and 150. The corresponding gravity anomaly error, between the same degrees, is reduced from 0.7 to 0.5 mGal.

In this article, the processing steps applied to the raw GOCE science payload instrument data (level 0) in order to obtain input data for the gravity field determination (level 1b) are described. The raw gradiometer measurements, which are given at the level of control voltages, have to be transformed into accelerations and gradients. For the latter step, knowledge about the GOCE attitude is required, which is provided by the star trackers. In addition, the data of the satellite to satellite tracking instrument are used to date the measurements, after its clock error has been corrected. All intermediate steps of the processing flow are described. Together with the explanation of the processing flow, an overview of the main level 1b products is given. The final part of the article discusses the means of quality control of the L1b data currently used and gives an outlook on potential processor evolutions.

The European Space Agency’s Gravity field and steady-state ocean circulation explorer mission (GOCE) was launched on 17 March 2009. As the first of the Earth Explorer family of satellites within the Agency’s Living Planet Programme, it is aiming at a better understanding of the Earth system. The mission objective of GOCE is the determination of the Earth’s gravity field and geoid with high accuracy and maximum spatial resolution. The geoid, combined with the de facto mean ocean surface derived from twenty-odd years of satellite radar altimetry, yields the global dynamic ocean topography. It serves ocean circulation and ocean transport studies and sea level research. GOCE geoid heights allow the conversion of global positioning system (GPS) heights to high precision heights above sea level. Gravity anomalies and also gravity gradients from GOCE are used for gravity-to-density inversion and in particular for studies of the Earth’s lithosphere and upper mantle. GOCE is the first-ever satellite to carry a gravitational gradiometer, and in order to achieve its challenging mission objectives the satellite embarks a number of world-first technologies. In essence the spacecraft together with its sensors can be regarded as a spaceborne gravimeter. In this work, we describe the mission and the way it is operated and exploited in order to make available the best-possible measurements of the Earth gravity field. The main lessons learned from the first 19 months in orbit are also provided, in as far as they affect the quality of the science data products and therefore are of specific interest for GOCE data users.

Swarm is a three-satellite constellation mission launched by the European Space Agency (ESA) on 22 November2013. It consists of three identical spacecraft, two of which (Swarm Alpha and Swarm Charlie) are flying almost side-by-side in polar orbits at lower altitude (about 470 km in September 2016) with an East-West separation of 1.4º in longitude corresponding to 155 km at the equator. The third satellite (Swarm Bravo) is in a slightly higher orbit (about 520 km altitude in September2016). Each of the three satellites carry a magnetometry package (consisting of absolute scalar magnetometer,fluxgate vector magnetometer, and star imager) for measuring the direction and strength of the magnetic field,and instruments to measure plasma and electric field parameters as well as gravitational acceleration. Time and position are provided by on-board GPS. The configuration of the various instruments on each of the three Swarm spacecraft is shown in Fig. 1. More information about the mission can be found at http://earth.esa.int/swarm.

With the launch of the Gravity field and Ocean Circulation Explorer (GOCE) in 2009 the science in gravity got another boost. After the time-lapse and long-wavelength studies from Gravity Recovery and Climate Experiment (GRACE) a new sensor was available for determination of the Earth's gravity field and geoid with high accuracy and spatial resolution. Equipped with a 6-component gradiometer and flying at an altitude of 260 km and less GOCE provides the most detailed measurements of Earth's gravity from space ever. On top, GOCE also provides gravity gradients, i.e., the three-dimensional second derivatives of the gravitational potential. This paper provides a review of the results presented at the ‘GOCE solid Earth workshop’ at the University of Twente, The Netherlands (2012), where an overview was given of the present status of the data models, and applications with GOCE which form the basis for this special issue and the review in this paper. An introduction will be given to the GOCE satellite followed by an overview of GOCE data and gravity models. The present state of GOCE related research in geodesy, oceanography and solid Earth sciences indicates the first steps taken to integrate GOCE in the different application fields. For all three fields an overview is given on the most recent scientific results and developments, and first results specifically focusing on these studies where GOCE data has made a unique contribution and provides insights that would not have been possible without GOCE

International audience; Data from the first year of ESA's Swarm constellation mission are used to derive the Swarm Initial Field Model (SIFM), a new model of the Earth's magnetic field and its time variation. In addition to the conventional magnetic field observations provided by each of the three Swarm satellites, explicit advantage is taken of the constellation aspect by including east-west magnetic intensity gradient information from the lower satellite pair. Along-track differences in magnetic intensity provide further information concerning the north-south gradient. The SIFM static field shows excellent agreement (up to at least degree 60) with recent field models derived from CHAMP data, providing an initial validation of the quality of the Swarm magnetic measurements. Use of gradient data improves the determination of both the static field and its secular variation, with the mean misfit for east-west intensity differences between the lower satellite pair being only 0.12 nT.

The European Space Agency (ESA) Swarm spacecraft mission is the first multisatellite ionospheric mission with two low-orbiting spacecraft that are flying in parallel at a distance of ~100–140 km, thus allowing derivation of spatial gradients of ionospheric parameters not only along the orbits but also in the direction perpendicular to them. A third satellite with a higher orbit regularly crosses the paths of the lower spacecraft. Using the Swarm magnetic and electric field instruments, we present a novel technique that allows derivation of two-dimensional (2-D) maps of ionospheric conductances, currents, and electric field in the area between the trajectories of the two lower spacecraft, and even to some extent outside of it. This technique is based on Spherical Elementary Current Systems. We present test cases of modeled situations from which we calculate virtual Swarm data and show that the technique is able to reconstruct the model electric field, horizontal currents, and conductances with a very good accuracy. Larger errors arise for the reconstruction of the 2-D field-aligned currents (FAC), especially in the area outside of the spacecraft orbits. However, even in this case the general pattern of FAC is recovered, and the magnitudes are valid in an integrated sense. Finally, using an MHD model run, we show how our technique allows estimation of the ionosphere-magnetosphere coupling parameter K, if conjugate observations of the magnetospheric magnetic and electric field are available. In the case of a magnetospheric multisatellite mission (e.g., the ESA Cluster mission) several K estimates at nearby points can be generated.

ESA’s Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) was operated in an extremely low Earth orbit down to 229 km altitude to map the Earth’s gravity field. As anticipated, on 21 Oct 2013 drag-free control stopped owing to the depletion of fuel for GOCE’s ion propulsion system. To get the most out of what was still a fully functional spacecraft designed to fly in a drag environment, ESA kept operating the mission as long as possible in the ensuing orbital decay phase. Exceeding all expectations, the S/C remained functional and contact could be maintained down to extreme altitudes of little over 100 km, less than 1.5 hours before re-entry. This allowed collecting a set of most valuable data prior to GOCE’s demise on 11 Nov 2013 close to the Falkland Islands. The paper presents the preparation and execution of this unique operations campaign.

A force model for the lunar albedo effect on low lunar orbiters is developed on the basis of Clementine imagery and absolute albedo measurements. The model, named the Delft Lunar Albedo Model 1 (DLAM-1), is a 15 × 15 spherical harmonics expansion, and is intended for improved force modeling for low satellite orbits as well as to minimise aliasing of non-gravitational force model defects in future lunar gravity solutions. The development of the model from the available lunar albedo data sources is described, followed by a discussion on its calibration using absolute albedo measurements and its correlation with main selenological features. DLAM-1 is next applied in low lunar orbit determination, and results for orbits typical of lunar mapping missions are presented. Finally, the effect of lunar albedo on future gravity solutions is analysed with particular emphasis on gravity mapping from global data sets, i.e. satellite-to-satellite tracking, which is expected to be a core experiment of coming lunar missions. It is shown that albedo-induced orbit perturbations have a magnitude and frequency signature which are non-negligible for precise orbit and gravity modeling. Radial orbit errors for low orbits are in the order of 1–2 m for one week arcs.

Till the present day the recovery of the lunar gravity field from satellite tracking data depends in a crucial way on the level and method of regularisation. With Earth-based tracking only, the spatial data coverage is limited to only slightly more than 50% and the inverse problem remains severely ill-posed. The development of global gravity models suitable for precise orbit modeling as well as geophysical studies therefore requires a significant level of regularisation, limiting the solution power over the far-side where no gravity information is available. Unconstrained solutions, within the framework of global harmonic base functions, are only possible for very low degrees (

Lunar gravimetry mission in the Japanese lunar exploration project SELENE (Selenological and Engineering Explorer) is characterized by inter-satellite tracking by means of a relay satellite in a high eccentric orbit, combined with differential Very-Long-Baseline-Interferometry (ΔVLBI) and conventional 2-way Doppler tracking. ΔVLBI provides information on the satellite position and velocity complementary to conventional range and range rate measurement, and allows us to measure lunar gravitational accelerations in all the three components. In this article, ΔVLBI and 2-way Doppler numerical simulation results are compared to those obtained from 2-way Doppler observations only, so that we can evaluate the contribution of ΔVLBI to the SELENE lunar gravimetry mission.

ESA’s Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) has been operated from launch in 2009 up to mid-2012 in a very low Earth orbit at an altitude of 260 km. The spacecraft design features a unique aerodynamic shape and employs drag-free control with an ion propulsion system to counteract the atmospheric drag. While the routine mission of GOCE has been very successful, it is inevitably coming to an end once all consumables are exhausted. To maximize the scientific return of the mission prior to its end of life, ESA has implemented a campaign to lower the orbit of GOCE even further, culminating in May 2013 with reaching the new science altitude of 229 Km. This constituted a challenging endeavour, requiring major re-evaluations and changes on both space and ground segment. This paper presents the planning and execution of the low orbit operations campaign.

A feasibility study is presented of high resolution and accuracy determination of the global grayity field of the Moon from a combination of low-low satellite-to-satellite range-rate observations and conventional tracking from stations on Earth. The European Moon ORbiting Observatory (MORO) mission, studied as a candidate for the third mediumsized science mission (M3) under the European Space Agency's Horizon 2000 scientific programme, is adopted for the simulation purposes. Global coverage and mapping of the fine details of the gravity field is achieved by satellite-to-satellite tracking (SST) of a small sub-satellite deployed by MORO in its 100 km polar orbit, whereas the long-wavelength features are obtained from Earth-based tracking. The combination of SST and Earth-based tracking therefore represents a powerful tool over a wide range of wavelengths. Moreover, tracking from Earth provides a clear reference for the satellite orbits, which are hard to determine from SST data only. The baseline mission proposal foresees a co-orbiting satellite pair in which the two satellites follow each other in essentially the same orbital plane with only a small spacing in time. The MORO gravimetry experiment requirements prescribe a surface level radial acceleration accuracy of a few mGal with a surface resolution of 50–100km. A number of satellite tracking configurations has been investigated and the influence of noise and systematic errors has been studied. Using perfect measurements and in the absence of systematic model errors the gravity field of the Moon, assumed to be pertectly represented by the 60 × 60 Lun60d model of Konopliv et al. (1993) with a surface resolution of 91 km, has been recovered with a radial acceleration accuracy better than 0.003 mGal using a 3° in-plane satellite spacing. Introducing uncorrelated random noise to the tracking links and a 10% model error in the direct solar radiation pressure model, still an accuracy better than 5 mGal can be achieved. Finally, it is shown that a small angular separation in right ascension of the ascending node of the orbital planes of MORO and its sub-satellite adds extra cross-track information to the SST range-rate signal and thus enables better determination of high sectorial and near-sectorial terms of the gravity field.

Sophisticated space weather monitoring aims at nowcasting and predicting solar-terrestrial interactions because their effects on the ionosphere and upper atmosphere may seriously impact advanced technology. Operating alert infrastructures rely heavily on ground-based measurements and satellite observations of the solar and interplanetary conditions. New opportunities lie in the implementation of in-situ observations of the ionosphere and upper atmosphere onboard low Earth orbiting (LEO) satellites. The multi-satellite mission Swarm is equipped with several instruments which will observe electromagnetic and atmospheric parameters of the near Earth space environment. Taking advantage of the multi-disciplinary measurements and the mission constellation different Swarm products have been defined or demonstrate great potential for further development of novel space weather products. Examples are satellite based magnetic indices monitoring effects of the magnetospheric ring current or the polar electrojet, polar maps of ionospheric conductance and plasma convection, indicators of energy deposition like Poynting flux, or the prediction of post sunset equatorial plasma irregularities. Providing these products in timely manner will add significant value in monitoring present space weather and helping to predict the evolution of several magnetic and ionospheric events. Swarm will be a demonstrator mission for the valuable application of LEO satellite observations for space weather monitoring tools.

Swarm a three satellite constellation to study the dynamics of the Earth's magnetic field and its interactions with the Earth system is expected to be launched in late 2013. The objective of the Swarm mission is to provide the best ever survey of the geomagnetic field and its temporal evolution in order to gain new insights into the Earth system by improving our understanding of the Earth's interior and environment. In order to derive advanced models of the geomagnetic field (and other higher level data products) it is necessary to take explicit advantage of the constellation aspect of Swarm. The Swarm SCARF (Satellite Constellation Application and Research Facility) has been established with the goal of deriving Level 2 products by combination of data from the three satellites and of the various instruments. The present paper describes the Swarm input data products (Level lb and auxiliary data) used by SCARF the various processing chains of SCARF and the Level 2 output data products determined by SCARF. Copyright © The Society of Geomagnelism and Earth Planetary and Space Sciences (SGEPSS).

ESA’s Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) is operated in an extremely low Earth orbit at 260 km altitude. The spacecraft has an aerodynamic shape and employs drag-free control with an ion propulsion system to counteract the atmospheric drag. GOCE’s extraordinary mission profile and spacecraft design led to many peculiarities for flight operations. The experience gained after launch has resulted in a significant evolution of the flight operations approach. Changes include a revised approach for orbit control manoeuvres, a new altitude selection owing to the low level of solar activity, and the decision to not interrupt science operations in eclipse season. Flight operations in 2010 were particularly challenging due to severe anomalies in the on-board data handling subsystem. Most notably, the spacecraft had to be operated “in the blind” with little to no status information for a period of about 1.5 months. This paper presents the experience gained when operating GOCE, describing the evolution of the flight operations approach and ground segment.

After a descent phase of about half a year, the Gravity field and steady-state Ocean Circulation Explorer (GOCE) reached the final orbital altitude of the first measurement and operational phase (MOP-1) in September 2009. Due to this very low orbital altitude and the inactive drag compensation during descent, the generation of reliable predictions of the GOCE trajectory turned out to be a major challenge even for short prediction intervals. As predictions of good quality are a prerequisite for frequent ranging from the tracking network of the International Laser Ranging Service (ILRS), Satellite Laser Ranging (SLR) data of GOCE was very sparse at mission start and made it difficult to independently calibrate and optimize the orbit determination based on data of the Global Positioning System (GPS). In addition to the GOCE orbit predictions provided by the European Space Agency (ESA), the Astronomical Institute of the University of Bern (AIUB) started providing predictions on July 22, 2009, as part of the Level 1b to Level 2 data processing performed at AIUB. The predictions based on the 12-h ultra-rapid products of the International GNSS Service (IGS) were originally intended to primarily serve the daylight passes in the early evening hours over Europe. The corresponding along-track prediction errors were often kept below 50 m during the descent phase and allowed for the first successful SLR tracking of GOCE over Europe on July 29, 2009, by the Zimmerwald observatory. Additional predictions based on the IGS 18-h ultra-rapid products are provided by AIUB since September 20, 2009, to further optimize the GOCE SLR tracking. In this article, the development of the GOCE prediction service at AIUB is presented, and the quality of the orbit predictions is assessed for periods with and without active drag compensation. The prediction quality is discussed as a function of the prediction interval, the quality of the input products for the GPS satellite orbits and clocks, and the availability of the GOCE GPS data. From the methodological point of view, different approaches for the treatment of the non-gravitational accelerations acting on the GOCE satellite are discussed and their impact on the prediction quality is assessed, in particular during the descent phase. Eventually, an outlook is given on the significance of GOCE SLR tracking to identify systematic errors in the GPS-based orbit determination, e.g., cross-track errors induced by mismodeled GOCE GPS phase center variations (PCVs).

GOCE, ESA’s first Earth gravity mission, is currently to be launched early in 2009 into a sun-synchronous orbit. Using the full-scale numerical propagator, we investigated the satellite’s free fall from the initial injection altitude of 280 km down to the first measurement phase altitude (at 264 km). During this decay phase the satellite will pass below the 16:1 resonance (268.4 km). The effect of this resonance, together with the uncertainty in the solar activity prediction, has a distinct impact on the evolution of the orbital elements. Then, to maintain a near-constant and extremely low altitude for the measurement operational phases, the satellite will use an ion thruster to compensate for the atmospheric drag. In order to obtain the groundtrack grid dense enough for a proper sampling of the gravitational field, ESA set constraints for a minimum groundtrack repeat period. We studied suitable repeat cycles (resonant orbits) in the vicinity of 16:1 resonance; we found that they differ greatly in stability towards small perturbations of the satellite’s mean altitude and in temporal evolution of the groundtrack coverage. The results obtained from the usual analytical treatment of orbital resonances were refined by more realistic numerical simulations. Finally, we formulated suggestions that might be useful in GOCE orbit planning.

In this paper a new approach is presented for enhancing image super-resolution via a filtered scale integral reconstruction. Based on the concept that any sensed quantity (from an instrumental point of view) must be necessarily considered as an averaged value in a suitable time and space continuum, the local reconstruction approach expects to map a space of average values onto another one (filtered scales) with a reduced extension and possibly, in an asymptotic limit, onto the space of points. The only assumption is that measurements are given in the integral average sense i.e., for some reason, they have to be considered as integral average values for given computational domains or cells. The proposed algorithm can be used to correlate averaged values to point values; yet the most reliable results, in a probabilistic sense, can be obtained if the ratio between input and output scales is not too high. The essential concept of this working methodology is the possibility to correlate average measurements to point-wise measurements upon suitably weighting the contribution of the molecules surrounding the inspected one

“What's up?” is a question that is answered by the gravity field. Gravity not only determines what is up and down but also reflects the Earth's mass distribution and its changes with time.

In different ways, the previous chapters present critical views on the present-day understanding and modelling of the lunar gravity field. Starting from the satellite selenodetic standpoint of orbit quality using linear perturbation theories, passing via a thorough assessment of the true selenopotential information provided by the available tracking data, and ending in an in-depth discussion on the role of regularisation for the lunar gravimetric problem, it has been demonstrated that the data alone do not warrant the recovery of an extended global model, even if the near-side data contain valuable high-frequency orbit perturbation information. It has, however, also been shown that the effects of under-sampling remain largely restricted to the same unsampled areas. In other words, based on present models, care should be taken not to draw premature conclusions for unsampled regions of the Moon. In addition, it has been pointed out that the choice of constraint relations, and in particular the choice of one or more regularisation parameters, may influence the solution by “tuning” it toward a particular type of application. Obviously, in such a situation, unambiguous recovery of the selenopotential is impossible, since the constraints cannot be verified; and, even if they could, they would be incapable of adequately decorrelating the estimated parameters. Spectral leakage is therefore a significant problem. A third and related conclusion of the previous chapters was that there might be a “datum shift” between the gravity field model best-suited for orbit modelling (excellent fit of orbit data) and a model that is well-suited for local, regional or global selenophysical studies. Such problems have previously been long debated in the satellite geodetic community for the terrestrial gravity field determination problem, where it was found that optimal orbit performance in many cases also implied reduction of parameters not related to the gravity field, but still affected the satellite orbit. In other words, it may well be the case that models starting from a selenophysical perspective, rather than that of orbit-derived measurements, e.g. when in situ gravimetric surface measurements become available, will behave differently from a model derived with optimal orbit determination performance in mind.

All present-day lunar gravity field models are — with the exception of a minor contribution from lunar laser ranging data to the second-degree harmonics — satellite-only models. Orbit analysis is therefore a fundamental tool for quality assessment, alongside arguments of compatibility imposed by selenophysics. A general problem in selenodesy and selenophysics is the lack of independent data to serve purposes of calibration and validation of basically any result. Model assessment techniques may therefore be quasi-circular and far from independent. Regarding the use of prior information from lunar physics, primarily the assumptions on coefficient amplitudes and the distribution of the selenopotential signal power over the degrees, the indicia of their correctness are for the larger part provided by the induced improvement in measurement fit of the satellite orbits. One prob-lem of satellite orbit and orbit error measures, on the other hand, is that they are “global” measures of the selenopotential quality, as opposed to a direct function of location on the lunar sphere, and that RMS-of-fit values over several-day satellite arcs actually contain very little spatial information on the intrinsic selenopotential model quality. Nevertheless, gravity field models capable of predicting reasonable mass anomaly structures and estimates of crustal thickness tend to be considered reliable. It should therefore be clear that it is only through continued iteration over the available data sets, along with improved modelling in several branches of selenoscience, that solid quality assessment and statistically significant quality improvement of lunar gravity field models may be achieved.

Throughout the previous chapters, the role of prior information in the determination of the selenopotential has been stressed. It has been shown that such information, frequently in the form of a priori upper bounds on the coefficient amplitudes, may be used to tune the gravity field solution, and, hence, arrive at models for different types of applications. Although there obviously is a unique gravity field, a major conclusion of the previous chapters is that, at present, no such thing as a general-purpose lunar gravity field model exists, satisfying the needs of all users with sufficient accuracy.

There are four principal scientific reasons for a return to the Moon, popularly described as the science of the Moon, science from the Moon, science on the Moon and, fourth, the exploration and possible future utilisation of lunar resources. All of these contribute in their own way to the understanding of the solar system and in particular to the knowledge of the origin and development of the Earth-Moon system. In this book, focus is on the role of gravity analysis as an independent discipline as well as the scientific return through interaction with other selenophysical and selenochemical data sets; in other words gravity-related science of the Moon. Such analysis is, however, inherently tangled with satellite orbit analysis, and, hence, both precise orbit requirements for mapping purposes and more general mission design considerations (long-term orbit behaviour, frozen or periodic orbits) are also discussed.

Having elaborated extensively on the nature and practical consequences of the ill-conditioning of the lunar gravimetric problem, it is only natural to devote the final chapter to the suitable remedies. Indeed, the main line of the previous chapters has been to zoom in on the practical consequences of the under-sampling of the selenopotential field, and to show that the currently available data sets do not lead to a unique and unambiguous gravity field solution. Rather, regularisation methods and the related problem of the determination of (a set of) regularisation parameters, as well as “design philosophies”, e.g. in terms of data weighting schemes and intent of the regularisation schemes, are found to greatly influence the gravity modelling process. Likewise, the data scarcity implies that very few means are at hand to verify the solution, which only adds to the myriad of problems facing the gravity field analyst.

Swarm mission constellation, launched into orbit on November 22, 2013, consists of three satellites that precisely measure magnetic signal of the Earth. Each of the three satellites is equipped with three μASC Camera Head Units (CHU) mounted on a common optical bench (OB), which has a purpose of transference of the precisely determined attitude from the star trackers to the vector magnetometer (VFM) measurements.Although pre-launch analyses were made to minimize thermal and mechanical instabilities of the OB, significant signal with thermal signature is discovered when comparing relative attitude between the three CHU's. These misalignments between CHU's, and consequently geomagnetic reference frame, are found to be correlated with the optical bench temperature variation.In this paper, we investigate the propagation of thermal effects into the μASC attitude observations and demonstrate how thermally induced attitude variation can be predicted and corrected in the Swarm data processing. The results after applying thermal model significantly improves attitude determination which, after correction, meets the requirements of Swarm satellite mission. This study demonstrates the importance of the OB pre-launch analysis to ensure minimum thermal gradient on satellite optical system and therefore maximum attitude accuracy.

As a fully autonomous star tracker, the micro Advanced Stellar Compass has been operating successfully on numerous satellite missions ranging from Low Earth Orbiters (e.g. ESA’s Swarm) to Deep Space missions (e.g. NASA’s Juno), accurately providing absolute attitude observations.Besides its primary function of attitude determination, the µASC is also capable of detecting particles with energies high enough to penetrate its camera shielding, where particles passing the focal plane CCD detector leave detectable ionization tracks. For electrons, and the typical shielding employed, the minimum energy required to penetrate is >10MeV whereas protons will require an energy in excess of 80MeV. The signature of passing particle will only persist in one frame time, but the signature differs between electrons and protons. To ensure full attitude performance operations even during the most intense CMEs, the signatures are removed before star tracking. By counting the signatures, and using a model for the flux transport through the shielding, an accurate measure of the instantaneous high energy particle flux is achieved at each update cycle (250ms). With this feature installed on both LEO (Swarm) and HEO (MMS) spacecraft, an hitherto unprecedented accurate mapping of the high energy particle population is achieved.In this work, we present the global flux distribution of particles, the radial variation in their associated drift shells. We further present the highly variable flux, with detailed profiling of the direction, associated with injection processes and their relaxation time scales.

Swarm mission constellation, launched into orbit on November 22, 2013, consists of three satellites that precisely measure magnetic signal of the Earth using the ASM and VFM, integrated with three Advanced Stellar Compass star trackers cameras. By using a minimum of magnetic material close to the magnetometer sensors (optimal for the magnetic measurements), the resulting shielding is insufficient to stop the more energetic part of the particle flux encountered in the Swarm constellation orbit, where protons above 60MeV and electrons above 10MeV may penetrate to the focal plane detectors. To eliminate the ASC cameras sensitivity to passing energetic particles, the ASC employ a suite of morphological filters removing the effects from such particles before the stars observed are matched to the onboard catalogue. The efficacy of these filters is high enough to ensure full performance even during the most intense CMEs, moreover, the measured rate of these penetrating particles, effectively monitors the high energy particle flux. Since May 2018, the spacecraft thus have sent the measured fluxes to ground, enabling very precise map of this part of the energetic flux. World map of the AP-8 MAX integral proton flux >10 MeV at 500 km altitude (Heynderickx, 1996) Particles flux for Swarm spacecrafts Ionizing particles in the Swarm orbits DTU Space μASC We present world maps of the energetic particle flux, its variation with altitude, local time, direction and seasonal variations. We further present a view of the dynamic part of the flux, from injection sources such as CMEs, which gives a detailed profiling of the direction, injection time scales and relaxation times.