Thermosphere mass density and crosswind can be derived from accelerometer and GNSS tracking data. However, present datasets are often provided without comprehensive uncertainty specifications. We present a newly developed method that propagates measurement noise and errors in the satellite specification, thermosphere models, and radiation flux data to density observations to quantify their uncertainty. We focus specifically on density observations derived only from GNSS tracking data, which are limited in resolution along the orbit due to unavoidable smoothing. While the method can be applied to simulated and real data, making it useful for existing datasets and mission design, we demonstrated it using data from the GRACE B satellite. First, we compare the aerodynamic acceleration derived separately from the accelerometer and GNSS tracking data, highlighting the role of two significant noise sources: noise due to the differentiation of the positions and noise from the evaluation of the gravity vector at a noisy position. Averaging substantially reduces the noise in the aerodynamic acceleration as long as the differentiation noise dominates, which is the case at frequencies higher than the orbital frequency. Below, gravity vector evaluation noise becomes the dominating noise source, and consequently, averaging over longer periods leads to only marginal uncertainty reduction. Further, we investigate the uncertainty in the radiation pressure acceleration and demonstrate that averaging over one orbit substantially reduces the uncertainty in the along-track radiation pressure acceleration. We show that the uncertainty of density observations derived from the accelerometer data is about 4% of the density for data from 2003 when the GRACE B satellite was at 490km altitude during high solar activity. In 2008, solar activity was very low, and the altitude was still 476km, resulting in an uncertainty of 5%–20% because GNSS tracking noise and radiation pressure modeling errors play a much larger role as the aerodynamic acceleration becomes smaller. In the case of density observations derived only from GNSS tracking data, the uncertainty is about 5% in 2003 and 20%–50% in 2008 when averaging over one-third orbit. In 2008, GNSS tracking noise explains nearly all uncertainty in the density observation. Averaging over one orbit reduces the uncertainty to 4% and 5% in 2003 and 2008, respectively.@en

Uncertainties in radiation pressure modelling play a significant role in the thermospheric density and crosswind observations derived from the GRACE-FO accelerometer, especially during low solar activity. Under such conditions, the radiation pressure acceleration matches the magnitude of the aerodynamic acceleration along the track and exceeds it in the cross-track direction. The GRACE-FO mission has been operating for several years at such high altitudes during both low and rising solar activity, providing a perfect opportunity to study the effects of radiation pressure. This research uses ray tracing based on a high-fidelity satellite geometry model to calculate the radiation pressure acceleration. We numerically fine-tuned the coefficients describing the thermo-optical surface properties to obtain more accurate radiation pressure accelerations than those specified in the GRACE-FO mission manual. We also used in situ temperature measurements from thermistors on the solar arrays to model the satellite's thermal emission. These temperature measurements allowed a realistic setup of the thermal model, extended by the parameter describing the efficiency of the solar cells, and reproduced the acceleration of the thermal emission with an accuracy of RMS 0.148 nms⁻². The combination of the updated thermal model and the fine-tuning of the surface coefficients improved the accuracy of the crosswind acceleration to an RMS of 0.55 nms⁻², compared to an RMS of 4.22 nms⁻² when using panel models and instantaneous thermal radiation. We compared the observed crosswind with two models: HWM14 and TIE-GCM. While both models capture most of the salient features of the observed crosswind, HWM14 shows particularly good agreement at high latitudes. Compared to the previously employed radiation pressure model, the crosswind observations have been improved in low and mid-latitudes, especially during periods of higher solar activity. Since the effect of radiation pressure is most significant in the crosswind direction, the effect on density was small compared to previously published datasets.

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The uncertainty on Thermospheric Mass Density (TMD), as derived from atmospheric models, can reach extremely high values. This effect is noteworthy in Low Earth Orbit (LEO), where atmospheric drag is the main perturbing force, as well as the most uncertain. LEO harbours almost 18,000 space objects at the end of 2021, around 60% of the total space debris population, and the rate of growth is increasing every year. Increasing the accuracy of TMD models, and thus the uncertainty characterisation, is important to ensure space environment sustainability in this congested and contested region. Accurate TMD modelling is a decisive factor in all space applications below the exopause, from LEO mission design to Space Situational Awareness (SSA) service provision: from conjunction assessment to re-entry and fragmentation analysis To enhance empirical TMD models, atmospheric density observations derived from satellite measurements are assimilated. This paper presents a novel approach for assimilating thermospheric density observations into atmospheric models to improve the accuracy of orbit predictions in short- to medium- term propagations. First, Global Navigation Satellite System (GNSS) derived density data from Swarm satellites are ingested from the publicly available Level 2 data products of the European Space Agency (ESA). In a second step, density data is assimilated into the empirical model NRMLSISE-00, using Principal Component Analysis (PCA) to decompose into the main temporal and spatial modes, providing useful physical insight into the main variables driving the model. Thirdly, the model is tested on several cases, whose data was not assimilated, such as LEO satellites that are well-tracked with GNSS-derived positions: Sentinel, and GRACE. The model is also tested with objects with less accurate reference trajectories, such as catalogued space debris in LEO. Finally, the orbits are propagated, using the improved drag model that includes the neutral density from the assimilation of the GNSS-derived observations into NLRMSISE-00. The accuracy of the method is assessed and compared to non-assimilated models. During the discussion of the results, other sources of uncertainty are analysed. To name a few, geomagnetic activity, solar radiation pressure coefficient, attitude knowledge, and spacecraft parameters such as mass, area, drag coefficient, and so on. The improvement on the state accuracy and uncertainty realism after a medium-term propagation is analysed and the application to catalogue maintenance discussed. @en

Daedalus MASE (Mission Assessment through Simulation Exercise) is an open-source package of scientific analysis tools aimed at research in the Lower Thermosphere-Ionosphere (LTI). It was created with the purpose to assess the performance and demonstrate closure of the mission objectives of Daedalus, a mission concept targeting to perform in-situ measurements in the LTI. However, through its successful usage as a mission-simulator toolset, Daedalus MASE has evolved to encompass numerous capabilities related to LTI science and modeling. Inputs are geophysical observables in the LTI, which can be obtained either through in-situ measurements from spacecraft and rockets, or through Global Circulation Models (GCM). These include ion, neutral and electron densities, ion and neutral composition, ion, electron and neutral temperatures, ion drifts, neutral winds, electric field, and magnetic field. In the examples presented, these geophysical observables are obtained through NCAR’s Thermosphere-Ionosphere-Electrodynamics General Circulation Model. Capabilities of Daedalus MASE include: 1) Calculations of products that are derived from the above geophysical observables, such as Joule heating, energy transfer rates between species, electrical currents, electrical conductivity, ion-neutral collision frequencies between all combinations of species, as well as height-integrations of derived products. 2) Calculation and cross-comparison of collision frequencies and estimates of the effect of using different models of collision frequencies into derived products. 3) Calculation of the uncertainties of derived products based on the uncertainties of the geophysical observables, due to instrument errors or to uncertainties in measurement techniques. 4) Routines for the along-orbit interpolation within gridded datasets of GCMs. 5) Routines for the calculation of the global coverage of an in situ mission in regions of interest and for various conditions of solar and geomagnetic activity. 6) Calculations of the statistical significance of obtaining the primary and derived products throughout an in situ mission’s lifetime. 7) Routines for the visualization of 3D datasets of GCMs and of measurements along orbit. Daedalus MASE code is accompanied by a set of Jupyter Notebooks, incorporating all required theory, references, codes and plotting in a user-friendly environment. Daedalus MASE is developed and maintained at the Department for Electrical and Computer Engineering of the Democritus University of Thrace, with key contributions from several partner institutions.

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The thermospheric neutral density response to the 7–9 September 2017 storms is investigated based on the Swarm satellite observations and the thermosphere-ionosphere-electrodynamic general circulation model (TIEGCM) simulation. The Swarm data depicted a prominent interhemispheric asymmetry (IHA) in the afternoon sector during the second storm, a feature that was yet explained. Driven by realistic high-latitude electric potential and electron precipitation patterns, the TIEGCM is able to reproduce the observed storm-time neutral density response. The TIEGCM simulation reveals that the differences in the traveling atmospheric disturbances (TADs) is largely responsible for the observed IHA in the neutral mass density response at low and middle latitudes, whereas the difference in mean molecular mass between the two hemispheres may contribute to the IHA in neutral density at higher latitudes. The IHAs in TADs and mean molecular mass are attributed to the IHA in Joule heating dissipation on the night and dawn sides.

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In Low Earth Orbit (LEO), atmospheric drag is the largest contributor to trajectory prediction error. The current thermospheric density model used by the Combined Space Operations Center (CSpOC) in operations is the High Accuracy Satellite Drag Model (HASDM). Since HASDM is not available for use outside of the US Government, satellite operators are left to determine what publicly available, open-source density model they should integrate into their internal operational software. This decision is nontrivial due to the number of available density models, each having variable performance dependent on several factors including space weather conditions and orbit altitude. To compound matters, the rapid rise of this solar cycle suggests that the predicted solar maximum between 2024-2027 could be higher than the previous solar maximum, thus causing larger perturbations due to drag from atmospheric density on LEO satellites. Given the evermore challenging nature of operations in LEO, it is imperative for satellite operators to update legacy density models to a state-of-the-art density model to provide improved trajectory predictions for collision risk assessment and vital day-to-day operational decisions. This paper outlines several operations-ready thermospheric density models, describing their performance, computation time, required operational space weather input parameters, and notes for implementation. We define an operations-ready density model as a model that is well-documented, has verified and quantified model performance, and provides publicly available model code for implementation on a user’s own system. Operations-ready models include the Drag Temperature Model (DTM), the Jacchia-Bowman 2008 (JB2008) model, the US Naval Research Laboratory Mass Spectrometer and Incoherent Scatter radar 2.0 (NRLMSIS 2.0) model, and the Thermosphere– Ionosphere–Electrodynamics General Circulation Model (TIE-GCM). US Government operational density models, HASDM and the Whole Atmosphere Model and Ionosphere Plasmasphere Electrodynamics (WAM-IPE) model, are included for comparison in the Analysis section. Models are evaluated against global HASDM density and local Gravity Recovery And Climate Experiment Follow-On (GRACE-FO) satellite accelerometer density data. A propagation analysis is also included in which model performance is compared during quiet and storm conditions and resulting LEO object trajectory prediction errors are quantified at various orbit altitudes. The analysis shows that any of the named operations-ready density models (DTM2020, JB2008, NRLMSIS 2.0, TIE-GCM) are a viable option for satellite operations. In addition to LEO satellite operators, the results from this paper are also informative for the transition of civilian space traffic coordination efforts out of CSpOC and into the Department of Commerce. @en

We statistically investigate fluctuation amplitudes (normalized to the background values) of dayside low-/mid-latitude upper-thermospheric mass density as observed by the Gravity Recovery and Climate Experiment (GRACE) and GRACE-Follow-On (GRACE-FO) spacecraft at ∼500 km altitude between 2002 and 2022. There are three new findings in our results. First, the climatology closely replicates previous studies on stratospheric and upper-thermospheric gravity waves (GWs) below the GRACE(-FO) altitudes. For example, in low-latitude regions, the fluctuations are stronger above continents than in the oceanic area. Mid-latitude fluctuations prefer the local winter hemisphere to the summer, and the South American/Atlantic region in June solstice hosts stronger fluctuations than in any other low-/mid-latitude locations or seasons. Fluctuations are more intense under lower solar activity. The above-mentioned consistency of the GRACE(-FO) results with previous lower-altitude GW studies confirms that GWs can penetrate up to 500 km. Second, the anti-correlation of upper-thermospheric GW with solar activity, which has been earlier reported for multi-year time scales, can also be identified on the scale of the solar rotation period (∼27 days). Third, we demonstrate asymmetry between pre-noon and post-noon GWs. The former exhibits stronger GW activity, which may result from the colder thermosphere being more favorable for intense mass density fluctuations via secondary/tertiary GW generation.

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On 3 February 2022, at 18:13 UTC, SpaceX launched and a short time later deployed 49 Starlink satellites at an orbit altitude between 210 and 320 km. The satellites were meant to be further raised to 550 km. However, the deployment took place during the main phase of a moderate geomagnetic storm, and another moderate storm occurred on the next day. The resulting increase in atmospheric drag led to 38 out of the 49 satellites reentering the atmosphere in the following days. In this work, we use both observations and simulations to perform a detailed investigation of the thermospheric conditions during this storm. Observations at higher altitudes, by Swarm-A (∼438 km, 09/21 Local Time [LT]) and the Gravity Recovery and Climate Experiment Follow-On (∼505 km, 06/18 LT) missions show that during the main phase of the storms the neutral mass density increased by 110% and 120%, respectively. The storm-time enhancement extended to middle and low latitudes and was stronger in the northern hemisphere. To further investigate the thermospheric variations, we used six empirical and first-principle numerical models. We found the models captured the upper and lower thermosphere changes, however, their simulated density enhancements differ by up to 70%. Further, the models showed that at the low orbital altitudes of the Starlink satellites (i.e., 200–300 km) the global averaged storm-time density enhancement reached up to ∼35%–60%. Although such storm effects are far from the largest, they seem to be responsible for the reentry of the 38 satellites.

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We present new neutral mass density and crosswind observations for the CHAMP, GRACE, and GRACE-FO missions, filling the last gaps in our database of accelerometer-derived thermosphere observations. For consistency, we processed the data over the entire lifetime of these missions, noting that the results for GRACE in 2011- 2017 and GRACE-FO are entirely new. All accelerometer data are newly calibrated. We modeled the temperature-induced bias variations for the GRACE accelerometer data to counter the detrimental effects of the accelerometer thermal control deactivation in April 2011. Further, we developed a new radiation pressure model, which uses ray tracing to account for shadowing and multiple reflections and calculates the satellitea's thermal emissions based on the illumination history. The advances in calibration and radiation pressure modeling are essential when the radiation pressure acceleration is significant compared to the aerodynamic one above 450 km altitude during low solar activity, where the GRACE and GRACE-FO satellites spent a considerable fraction of their mission lifetime. The mean of the new density observations changes only marginally, but their standard deviation shows a substantial reduction compared to thermosphere models, up to 15% for GRACE in 2009. The mean and standard deviation of the new GRACE-FO density observations are in good agreement with the GRACE observations. The GRACE and CHAMP crosswind observations agree well with the physics-based TIE-GCM winds, particularly the polar wind patterns. The mean observed crosswind is a few tens of m·s-1 larger than the model one, which we attribute primarily to the crosswind errors being positive by the definition of the retrieval algorithm. The correlation between observed and model crosswind is about 60%, except for GRACE in 2004- 2011 when the signal was too small to retrieve crosswinds reliably.

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The quality and distribution in time and space of available atmospheric observations are crucial for the accuracy of semi-empirical thermosphere models. However, datasets can be inconsistent, and their qualities and resolutions are often unequal. The main thermospheric density datasets of this century are briefly described and then compared to each other when possible in order to quantify differences. Total mass densities used in the comparisons include all high-resolution CHAMP, GRACE and GOCE data, Swarm A, daily-mean Stella, global daily mean TLE densities, and the SET HASDM density database. The temperature data from TIMED-SABER are also reviewed. The recently updated daily-mean TLE densities (TLE2021) are 2–10 % smaller on average than the previous version (TLE2015). The differences are not constant offsets per altitude level, but fluctuations of up to 5 % are present. Compared to HASDM densities for 6 altitudes from 250 to 675 km, TLE2021 is 15–20 % smaller at 250 km, and then the difference diminishes with altitude to reach the same average value at 575 km. These mean differences also fluctuate by a few percent on time scales of months, to 10 % over half a solar cycle at 575 km. The TLE2021 and HASDM densities are larger than the accelerometer-inferred CHAMP, GRACE and GOCE densities and average offsets are 10–15 % and 10–20 %, respectively. The comparison to Swarm-A and Swarm-B showed mean offsets of 10 % and less, with significant positive trends seen in the comparison with HASDM. Finally, largest differences are found for Stella and HASDM at 800 km, up to 45 % with strong semiannual variations. This study clearly shows that the available density data cannot be simply assimilated or combined without first accurately calibrating the data. The HASDM database is a valuable asset due to its considerable coverage in space and time, but its uncertainty and true resolution are not well understood and are still being evaluated. Data compatibility requires employing physically accurate and harmonized aerodynamic force models in the density derivation procedure, which is presently not achieved. The accuracy of the procedure, independent of the quality of the instrument (GNSS receiver, ground-based orbit determination, or accelerometer), inevitably decreases with altitude due to weakening of the drag signal to noise ratio. The TIMED-SABER instrument provides measurements of pressure and temperature in the lower thermosphere. SABER temperature uncertainty is well-known. The SABER dataset now exceeds twenty years and has been continuously operating that entire time. It was ingested in NRLMSIS 2.0 and comparisons show the much-improved fit in comparison with NRLMSISE-00. The lower thermosphere temperatures significantly modify density at higher altitudes, and its measurement is essential for modeling and assessment.

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Swarm is the European Space Agency (ESA)'s first Earth observation constellation mission, which was launched in 2013 to study the geomagnetic field and its temporal evolution. Two Langmuir probes aboard each of the three Swarm satellites provide in situ measurements of plasma parameters, which contribute to the study of the ionospheric plasma dynamics. To maintain a high data quality for scientific and technical applications, the Swarm products are continuously monitored and validated via science-oriented diagnostics. This paper presents an overview of the data quality of the Swarm Langmuir probes' measurements. The data quality is assessed by analysing short and long data segments, where the latter are selected to be sufficiently long enough to consider the impact of the solar activity. Langmuir probe data have been validated through comparison with numerical models, other satellite missions, and ground observations. Based on the outcomes from quality control and validation activities conducted by ESA, as well as scientific analysis and feedback provided by the user community, the Swarm products are regularly upgraded. In this paper, we discuss the data quality improvements introduced with the latest baseline, and how the data quality is influenced by the solar cycle. In particular, plasma measurements are more accurate in day-side regions during high solar activity, while electron temperature measurements are more reliable during night side at middle and low latitudes during low solar activity. The main anomalies affecting the Langmuir probe measurements are described, as well as possible improvements in the derived plasma parameters to be implemented in future baselines.

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Satellite drag modeling remains the largest source of uncertainty affecting space operations in low Earth orbit. The uncertainty stems from inaccurate models for mass density and drag coefficient. Drag coefficient modeling also impacts scientific knowledge on the physics and dynamics of the upper atmosphere through the estimation of high-fidelity mass density from measurements of acceleration on-board satellites. Efforts over the last decade have pushed drag coefficient modeling in the right direction, however, have resulted in multiple methods and tools. We provide a comprehensive review of the drag coefficient modeling methods and tools. Current scale differences between thermospheric data sets mostly originate from errors in the aerodynamic modeling, specifically in the modeling of the satellite outer surface geometry and the gas-surface interactions. Enhancing these models’ accuracy is intrinsically connected to the satellite drag fidelity for science and operations. A team of invested scientists recently met under the community-driven International Space Weather Action Teams (ISWAT) initiative to discuss and consolidate the efforts towards a drag coefficient modeling baseline for consistency in science and operations. In this paper, we compare the available methods for drag coefficient modeling, their impact on the derived density estimates, and make recommendations for adoption of baseline methods for science and operations. Results show that the differences in derived densities estimates can reach tens of percent at altitudes above 4̃50 km during solar minimum conditions resulting mainly from differences in the modeling of gas-surface interactions. As a result, we conclude and recommend that robust uncertainty quantification be an integral part of any modeling efforts that employ the high-fidelity accelerometer derived density estimates. We also conclude and recommend that gas-surface interaction models that account for impact of altitude and solar variations be employed moving forward. Finally, we recommend future science missions to improve our understanding of gas-surface interactions and eventually the upper thermosphere variability.

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Cold Atom technology has undergone rapid development in recent years and has been demonstrated in space in the form of cold atom scientific experiments and technology demonstrators, but has so far not been used as the fundamental sensor technology in a science mission. The European Space Agency therefore funded a 7-month project to define the CASPA-ADM mission concept, which serves to demonstrate cold-atom interferometer (CAI) accelerometer technology in space. To make the mission concept useful beyond the technology demonstration, it aims at providing observations of thermosphere mass density in the altitude region of 300–400 km, which is presently not well covered with observations by other missions. The goal for the accuracy of the thermosphere density observations is 1% of the signal, which will enable the study of gas–surface interactions as well as the observation of atmospheric waves. To reach this accuracy, the CAI accelerometer is complemented with a neutral mass spectrometer, ram wind sensor, and a star sensor. The neutral mass spectrometer data is considered valuable on its own since the last measurements of atmospheric composition and temperature in the targeted altitude range date back to 1980s. A multi-frequency GNSS receiver provides not only precise positions, but also thermosphere density observations with a lower resolution along the orbit, which can be used to validate the CAI accelerometer measurements. In this paper, we provide an overview of the mission concept and its objectives, the orbit selection, and derive first requirements for the scientific payload.

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Interplanetary missions have typically relied on Radio Science (RS) to recover gravity fields by detecting their signatures on the spacecraft trajectory. The weak gravitational fields of small bodies, coupled with the prominent influence of confounding accelerations, hinder the efficacy of this method. Meanwhile, quantum sensors based on Cold Atom Interferometry (CAI) have demonstrated absolute measurements with inherent stability and repeatability, reaching the utmost accuracy in microgravity. This work addresses the potential of CAI-based Gradiometry (CG) as a means to strengthen the RS gravity experiment for small-body missions. Phobos represents an ideal science case as astronomic observations and recent flybys have conferred enough information to define a robust orbiting strategy, whilst promoting studies linking its geodetic observables to its origin. A covariance analysis was adopted to evaluate the contribution of RS and CG in the gravity field solution, for a coupled Phobos-spacecraft state estimation incorporating one week of data. The favourable observational geometry and the small characteristic period of the gravity signal add to the competitiveness of Doppler observables. Provided that empirical accelerations can be modelled below the nm/s ² level, RS is able to infer the 6 × 6 spherical harmonic spectrum to an accuracy of 0.1–1% with respect to the homogeneous interior values. If this correlates to a density anomaly beneath the Stickney crater, RS would suffice to constrain Phobos’ origin. Yet, in event of a rubble pile or icy moon interior (or a combination thereof) CG remains imperative, enabling an accuracy below 0.1% for most of the 10 × 10 spectrum. Nevertheless, technological advancements will be needed to alleviate the current logistical challenges associated with CG operation. This work also reflects on the sensitivity of the candidate orbits with regard to dynamical model uncertainties, which are common in small-body environments. This brings confidence in the applicability of the identified geodetic estimation strategy for missions targeting other moons, particularly those of the giant planets, which are targets for robotic exploration in the coming decades.

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The re-estimates of thermospheric winds from the Gravity field and steady-state Ocean Circulation Explorer (GOCE) accelerometer measurements were released in April 2019. In this study, we compared the new-released GOCE crosswind (cross-track wind) data with the horizontal winds measured by four Fabry-Perot interferometers (FPIs) located at low and middle latitudes. Our results show that during magnetically quiet periods the GOCE crosswind on the dusk side has typical seasonal variations with largest speed around December and the lowest speed around June, which is consistent with the ground-FPI measurements. The correlation coefficients between the four stations and GOCE crosswind data all reach around 0.6. However, the magnitude of the GOCE crosswind is somehow larger than the FPIs wind, with average ratios between 1.37 and 1.69. During geomagnetically active periods, the GOCE and FPI derived winds have a lower agreement, with average ratios of 0.85 for the Asian station (XL) and about 2.15 for the other three American stations (PAR, Arecibo and CAR). The discrepancies of absolute wind values from the GOCE accelerometer and ground-based FPIs should be mainly due to the different measurement principles of the two techniques. Our results also suggested that the wind measurements from the XL FPI located at the Asian sector has the same quality with the FPIs at the American sector, although with lower time resolution.

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The lower-Thermosphere-ionosphere (LTI) system consists of the upper atmosphere and the lower part of the ionosphere and as such comprises a complex system coupled to both the atmosphere below and space above. The atmospheric part of the LTI is dominated by laws of continuum fluid dynamics and chemistry, while the ionosphere is a plasma system controlled by electromagnetic forces driven by the magnetosphere, the solar wind, as well as the wind dynamo. The LTI is hence a domain controlled by many different physical processes. However, systematic in situ measurements within this region are severely lacking, although the LTI is located only 80 to 200 km above the surface of our planet. This paper reviews the current state of the art in measuring the LTI, either in situ or by several different remote-sensing methods. We begin by outlining the open questions within the LTI requiring high-quality in situ measurements, before reviewing directly observable parameters and their most important derivatives. The motivation for this review has arisen from the recent retention of the Daedalus mission as one among three competing mission candidates within the European Space Agency (ESA) Earth Explorer 10 Programme. However, this paper intends to cover the LTI parameters such that it can be used as a background scientific reference for any mission targeting in situ observations of the LTI.

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ESA’s Next Generation Gravity Mission (NGGM) is a candidate Mission of Opportunity for ESA–NASA cooperation in the frame of the Mass Change and Geosciences International Constellation (MAGIC). The mission aims at enabling long-term monitoring of the temporal variations of Earth’s gravity field at relatively high temporal (down to 3 days) and increased spatial resolutions (up to 100 km) at longer time intervals. This implies also that time series of GRACE and GRACE-FO can be extended towards a climate series. Such variations carry information about mass change induced by the water cycle and the related mass exchange among atmosphere, oceans, cryosphere, land and solid Earth and will complete our picture of global and climate change. The main observable is the variation of the distance between two satellites measured by a ranging instrument. This is complemented by accelerometers that measure the nongravitational accelerations, which need to be reduced from ranging measurements to obtain the gravity signal. The preferred satellite constellation comprises one satellite pair in a near-polar and another in an inclined circular orbit. The paper focuses on the orbit selection methods for optimizing the spatial sampling for multiple temporal resolutions and then on the methodology for deriving the engineering requirements for the space segment, together with a discussion on the main mission parameters. @en

Gravity fields derived from GPS tracking of the three Swarm satellites have shown artifacts near the geomagnetic equator, where the carrier phase tracking on the L2 frequency is unable to follow rapid ionospheric path delay changes due to a limited tracking loop bandwidth of only 0.25 Hz in the early years of the mission. Based on the knowledge of the loop filter design, an analytical approach is developed to recover the original L2 signal from the observed carrier phase through inversion of the loop transfer function. Precise orbit determination and gravity field solutions are used to assess the quality of the correction. We show that the a posteriori RMS of the ionosphere-free GPS phase observations for a reduced-dynamic orbit determination can be reduced from 3 to 2 mm while keeping up to 7% more data in the outlier screening compared to uncorrected observations. We also show that artifacts in the kinematic orbit and gravity field solution near the geomagnetic equator can be substantially reduced. The analytical correction is able to mitigate the equatorial artifacts. However, the analytical correction is not as successful compared to the down-weighting of problematic GPS data used in earlier studies. In contrast to the weighting approaches, up to 9–10% more kinematic positions can be retained for the heavily disturbed month March 2015 and also stronger signals for gravity field estimation in the equatorial regions are obtained, as can be seen in the reduced error degree variances of the gravity field estimation. The presented approach may also be applied to other low earth orbit missions, provided that the GPS receivers offer a sufficiently high data rate compared to the tracking loop bandwidth, and provided that the basic loop-filter parameters are known.

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The satellite acceleration data from the CHAMP, GRACE, GOCE, and Swarm missions provide detailed information on the thermosphere density over the last two decades. Recent work on reducing errors in modelling the spacecraft geometry has greatly reduced scale differences between the thermosphere data sets from these missions. However, residual inconsistencies between the data sets and between data and models are still present. To a large extent, these differences originate in the modelling of the gas-surface interactions (GSI), which is part of the satellite aerodynamic modelling used in the acceleration to density data processing. Physics-based GSI models require in-situ atmospheric composition and temperature data that are not measured by any of the above-mentioned satellites and, as a consequence, rely on thermosphere models for these inputs. To reduce the dependence on existing thermosphere models, we choose a GSI model with a constant energy accommodation coefficient per mission, which we optimize exploiting particular attitude manoeuvres and wind analyses to increase the self-consistency of the multi-mission thermosphere mass density data sets. We compare our results with those based on variable energy accommodation obtained by different studies and semi-empirical models to show the principal differences. The presented comparisons provide novel opportunity to quantify the discrepancies between current GSI models. Among the presented data, density variations with variable accommodation are within ±10%, and peaks can reach up to 15% at the poles. The largest differences occur during low solar activity periods. In addition, we utilize a series of attitude manoeuvres performed in May 2014 by the Swarm A and C satellites, which are flying in close proximity, to evaluate the residual inconsistency of the density observations as a function of the energy accommodation coefficient. Our analysis demonstrates that an energy accommodation coefficient of 0.85 maximizes the consistency of the Swarm density observations during the attitude manoeuvres. Using such coefficient, for Swarm A and Swarm C, the new density would be lower in magnitude with a 4-5% difference. In recent studies, similar energy accommodation coefficients were retrieved for the CHAMP and GOCE missions by investigating thermospheric winds. These new values for the energy accommodation coefficient provide a higher consistency among different missions and models. A comparison of neutral densities between current thermosphere models and observations indicates that semi-empirical models such as NRLMSISE-00 and DTM-2013 significantly overestimate the density, and that an overall higher consistency between the observations from the different missions can be achieved with the presented assumptions. The new densities from this work provide consistencies of 4.13% and 3.65% between the minimum and maximum mean ratios among the selected missions with NRLMSISE-00 and DTM-2013, respectively. A comparison with the WACCM-X general circulation model is also performed. Similar to the other models, WACCM-X seems to provide higher estimates of mass density especially under high and moderate solar activities. This work has the objective to guide density data users over the multiple data sets and highlight the remaining uncertainties associated with different GSI models.

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After the detection of many anomalies in the Swarm accelerometer data, an alternative method has been developed to determine thermospheric densities for the three-satellite mission. Using a precise orbit determination approach, non-gravitational and aerodynamic-only accelerations are estimated from the high-quality Swarm GPS data. The GPS-derived non-gravitational accelerations serve as a baseline for the correction of the Swarm-C along-track accelerometer data. The aerodynamic accelerations are converted directly into thermospheric densities for all Swarm satellites, albeit at a much lower temporal resolution than the accelerometers would have been able to deliver. The resulting density and acceleration data sets are part of the European Space Agency Level 2 Swarm products. To improve the Swarm densities, two modifications have recently been added to our original processing scheme. They consist of a more refined handling of radiation pressure accelerations and the use of a high-fidelity satellite geometry and improved aerodynamic model. These modifications lead to a better agreement between estimated Swarm densities and NRLMSISE-00 model densities. The GPS-derived Swarm densities show variations due to solar and geomagnetic activity, as well as seasonal, latitudinal and diurnal variations. For low solar activity, however, the aerodynamic signal experienced by the Swarm satellites is very small, and therefore it is more difficult to accurately resolve latitudinal density variability using GPS data, especially for the higher-flying Swarm-B satellite. Therefore, mean orbit densities are also included in the Swarm density product.

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