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. Given the ever more 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 article outlines four operations-ready thermospheric density models, describing their performance, computation time, required space weather inputs, and notes for implementation. 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. Models are evaluated against global HASDM density and local GRACE-FO satellite accelerometer densities and Swarm mission densities. Additionally, comparisons between HASDM and WAM-IPE nowcast and forecast density are revealed for the first time publicly.

The ESA GOCE satellite carried a gravity gradiometer consisting of three pairs of accelerometers on mutually orthogonal axes. For each accelerometer, bias and scale factors have been re-estimated by a dynamic precise orbit determination (POD) using improved gravity field modeling and standards. The kinematic orbit solution included in GPS-based Precise Science Orbit (PSO) product served as the baseline observables for 1210 daily arcs, covering the period from 1 November 2009 to 20 October 2013. Implementing improved force models almost completely resolved the deviations of the Y-axis scale factor obtained in earlier work (Visser and Ijssel 2016). A novel aspect is the verification by comparison with dynamic POD solutions based on SLR observations using 51 two-day orbital arcs. A high level of consistency was obtained between the kinematic PSO- and SLR-based accelerometer calibration parameters, e.g. within 0.01 nm/s2 for the X-axis pointing predominantly in the flight direction in terms of bias. One set of accelerometer scale factors was estimated for the entire mission. These were found to be consistent to within 0.005 for all accelerometer axes. The three-dimensional consistency between the dynamic orbits and the PSO reduced-dynamic orbit solutions has a mean Root-Mean-Square (RMS) of 4.5 and 10 cm, respectively, for the PSO reduced-dynamic and SLR-based dynamic orbit solutions. In addition, the one-dimensional RMS-of-fit of the PSO kinematic orbit solution improved significantly from 6.9 in Visser and Ijssel (2016) to 2.6 cm.

Valuable insights into the thermospheric mass density and horizontal winds can be obtained from satellites equipped with accelerometers. To derive these quantities, radiation pressure must be accurately modeled and removed from the calibrated accelerometer measurements. However, the documented surface reflection and absorption coefficients, as well as the satellite’s thermal properties, are often inaccurate or, in some cases, even absent. This study presents a method for optimizing these parameters jointly with the accelerometer scale factors. Focusing on GRACE data from 2009, a case where radiation pressure was dominant over aerodynamic force, enabled us to refine the radiation pressure model without detrimental effects from errors in aerodynamic force modeling. We evaluated three variants of estimating the scale factor: estimating no accelerometer scale factors, only the y-axis scale factor, or both the y- and z-axis scale factors. We use the difference between the measured and modeled accelerations (the residual) as our target functional. Estimating both scale factors yielded the lowest residual for both GRACE satellites, even though the radiation pressure model was tuned using GRACE-A data only. After the optimization, we observed a systematic feature in the cross-track residuals within the geographical domain, which strongly correlates with the magnetic field vector experienced by the spacecraft. While its cause remains unknown, we introduced an empirical correction that effectively removed the feature and significantly increased consistency between GRACE-A and GRACE-B. Overall, we were able to reduce the RMS of the residuals by more than 13% in the cross-track direction and 32% in the radial direction, indicating a significant increase in modeling accuracy. The presented method provides a generalizable approach that can also be applied to future satellite missions with accelerometers.

The Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) satellite, which operated at an altitude of ∼250km, provided neutral thermosphere mass density and crosswind observations in the dawn-dusk sectors throughout most of its operational lifetime (2009–2013). As a result of its Sun-synchronous orbit, GOCE’s large solar panels remained at a near-perpendicular angle to the incoming solar radiation, leading to a significant radiation pressure acceleration. In this research, we focused on revisiting and reprocessing GOCE thermosphere mass density and crosswind data. We selected the coefficients describing the thermo-optical surface properties and employed a high-fidelity satellite geometry in a ray-racing simulation. Additionally, we distinguished between the solar flux in the visible and infrared bands and introduced a model for the satellite’s thermal emission. The availability of the in situ thermistor measurements allowed for the validation of the thermal model. Moreover, we replaced the Level-1b ion thruster data with raw telemetry, filling multiple data gaps. We analysed how incremental improvements in the radiation pressure modelling affected the observed crosswind speed. By replacing the panel model with the high-fidelity satellite geometry, the crosswind speed decreased up to 5 ms⁻¹. The biggest difference reduction of 40ms⁻¹resulted from introducing the thermal model. Splitting the solar flux further decreases the observed crosswind speed by up to 8ms⁻¹. The reduction in crosswind speed was most prominent during the first years of the mission when the solar activity was low. We compared the newly processed GOCE zonal wind data with respect to the most recent previous release. We observed a median absolute deviation decrease of 10 ms⁻¹around the south magnetic pole in the dawn sector. The yearly consistency of low-latitude zonal winds did not change significantly. The main obstacle in quantifying the improvement compared to the previous crosswind dataset stemmed from the fact that the previous and new datasets were generated with different crosswind estimation algorithms. The difference in thermosphere density compared to previously published datasets is minor since the effect of radiation pressure is most prominent in the cross-track direction. Finally, we verified the assumption about the energy accommodation coefficient of 0.82 and concluded that it remains valid after implementing the radiation pressure modelling improvements.

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.

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.

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.

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.

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.

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.

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.

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.