Thermospheric Density Research Articles

A Global Thermospheric Density Prediction Framework Based on a Deep Evidential Method

AbstractThermospheric density influences the atmospheric drag and is crucial for space missions. This paper introduces a global thermospheric density prediction framework based on a deep evidential method. The proposed framework predicts thermospheric density at the required time and geographic position with given geomagnetic and solar indices. It is called global to differentiate it from existing research that only predicts density along a satellite orbit. Through the deep evidential method, we assimilate data from various sources including solar and geomagnetic conditions, accelerometer‐derived density data, and empirical models including the Jacchia‐Bowman model (JB‐2008) and the Naval Research Laboratory Mass Spectrometer and Incoherent Scatter Radar Extended (NRLMSISE‐00) model. The framework is investigated on five test cases along various satellites from 2003 to 2015 involving geomagnetic storms with Disturbance Storm Time (Dst) values smaller than −50 . Results show that the proposed framework can generate density with higher accuracy than the two empirical models. It can also obtain reliable uncertainty estimations. Global density estimations at altitudes from 200 to 550 km are also presented and compared with empirical models on both quiet and storm conditions.

Estimates of Spherical Satellite Drag Coefficients in the Upper Thermosphere During Different Geomagnetic Conditions

AbstractSatellite drag coefficients are crucial for determining the neutral mass densities that affect spacecraft operations in the thermosphere. Many studies typically utilize a constant drag coefficient of 2.2 to calculate the neutral density. However, due to the variability of space environment, uncertainties in the drag coefficient can lead to significant systematic discrepancies in neutral density measurements. Satellite drag coefficient may fluctuate in the thermosphere under various geomagnetic activities and altitudes. For the first time, we calculate the spherical satellite drag coefficient using data from the “Orbital Atmospheric Density Detection Experimental Satellite,” referred to as the QX satellite. Our findings reveal that the drag coefficient can be estimated by thermospheric temperature and density, which are dependent on geomagnetic activity and altitude. At an altitude of ∼510 km, drag coefficients are adjusted to around 2.425, instead of the constant value of 2.2. Furthermore, the drag coefficient may decrease due to the significant influence of increasing geomagnetic activity, such as geomagnetic storms, on thermospheric density and temperature. These estimates of the drag coefficient can also be used to reduce discrepancies when deducing the ballistic coefficient. Consequently, using the estimated drag coefficient can accurately determine the QX‐derived neutral density, which agrees well with the density from Swarm‐B satellite.

A review of global long-term changes in the mesosphere, thermosphere and ionosphere: A starting point for inclusion in (semi-) empirical models

The climate of the upper atmosphere, including the mesosphere, thermosphere and ionosphere, is changing. As data records are much more limited than in the lower atmosphere and solar variability becomes increasingly dominant at higher altitudes, accurate trend detection and attribution is not straightforward. Nonetheless, observations reliably indicate that, on average, the mesosphere has been cooling, the density in the thermosphere has been decreasing, and ionospheric layers have been shifting down. These global mean changes can be largely attributed to the increase in CO2 concentration, which causes cooling and thermal contraction in the middle and upper atmosphere. The decline in thermosphere density is particularly relevant from a practical viewpoint, as this reduces atmospheric drag and thereby increases orbital lifetimes and the build-up of space debris. Long-term changes in the ionosphere can have further practical implications and are not only driven by the increase in CO2 concentration, but also by changes in the Earth’s magnetic field. The empirical models that are mostly used to inform applications in industry on the state of the upper atmosphere, as well as being widely used in science, do not yet properly account for long-term trends in the mesosphere, thermosphere and ionosphere. This is problematic when long-term future projections are needed or models rely strongly on older data. This review provides an overview of the main evidence of long-term trends observed in the mesosphere, thermosphere and ionosphere, together with the latest insights on what causes these trends. It is hoped that this may serve as a starting point to include long-term trends in (semi-) empirical models to benefit all users of these models. We also offer some thoughts on how this could be approached.

Impact of Interplanetary Shock on Thermospheric Cooling Emission: A Case Study

AbstractInterplanetary (IP) shock is one of the most common phenomena that controls the shape and size of the magnetosphere. It affects the whole magnetosphere‐ionosphere‐thermosphere (MIT) system. We utilized the NO 5.3 m radiative emission, as observed by SABER (Sounding of the Atmosphere using Broadband Emission Radiometry) onboard NASA's TIMED (Thermosphere Ionosphere Mesosphere Energetics Dynamics) satellite, to investigate its response to fast forward shock during 26 January 2017. The high latitude NO emission exhibits a strong enhancement (three times with respect to pre‐event value) during IP shock within 5 hr of onset. We analyzed both the energy dissipation sources and subsequent chemical mechanisms. The Field‐Aligned‐Current observations from Active Magnetosphere and Planetary Response Experiment (AMPERE), EISCAT measurements of Pederson conductivity and the defense Meteorological Satellite Program (DMSP F18) calculated hemispheric power demonstrate a strong intensification. The low energy particle precipitation from DMSP F18 spacecraft shows an early enhancement for energy less than 1 keV. The particle flux of higher energy responds later which remained elevated for longer duration. The thermospheric density and temperature also experience significant variation during IP shock. The NO molecule and temperature displayed an early enhancement. NO density increased by an order of magnitude with respect to the pre‐event value. About 20 increase is noticed in the temperature variation. The atomic oxygen and atomic nitrogen illustrate an early depletion during IP event. The enhanced response of NO cooling to IP shock can be attributed to the combined effects of energy input and subsequent chemical mechanisms.

Tailored accelerometer calibration by POD for thermospheric density retrieval with GRACE and GRACE-FO

The density of the upper atmosphere can be determined by orbit and accelerometer data from low Earth orbit satellites as insitu measurements along the orbit. One main challenge therein is the estimation of physical accelerometer calibration parameters, meaning that these parameters should not absorb other effects and model deficiencies in the Precise Orbit Determination (POD) process. The accelerometers of all geodetic satellites like GRACE and GRACE-FO are affected by time dependent bias and scale factors. Therefore a calibration of the data is indispensable.A dynamic POD based physical accelerometer calibration is developed for the complete GRACE and GRACE-FO missions. We investigate different parametrization strategies and utilize different observation data, as the accurate inter-satellite ranging additionally to GPS orbit data. For the estimation parameters we distinguish between offset and scale, furthermore, cross-track and radial directions are significantly less sensitive than along-track and require a different evaluation. For the offset, constant and time dependent parameters are investigated. Furthermore, a continuous offset calibration over arc boundaries is implemented and tested. The sensitivity of the scale factor is lower, although, in contrast to the offset, it increases with higher total accelerations. This means that it needs to be estimated over longer time periods. We investigate periods between three hours and one month as well as results from Gravity Field Recovery (GFR). Monthly scale factors give valuable results, at least for x-axis and when the Solar activity is not very low. Nevertheless, we also estimate weighted constant scale factors from the monthly results and use these in a subsequent POD, giving more realistic offset results for most periods and cross-track and radial directions.From the used background models in the POD, Earth’s gravitational model has a noticeable influence on the estimated calibration parameters, especially the scale factors. We utilized several different models. Results with monthly ITSG solutions are distinctly better than the ones with the time dependent GOCO06s model.We show that the validation with usual metrics, like post-fit POD residuals, is not able to reflect the quality of the different estimated calibration parameters. For a quantitative validation we introduce an approach based on the modeled non-gravitational accelerations. Therefore, the uncertainty of the models is evaluated first. The influence of main error sources in the models is assessed and propagated to the results.We compare our scale parameters to available references and the complete calibration to TU Delft’s latest results. Finally we show the effect of different calibration options on the retrieved density.The estimated calibration parameters and non-gravitational accelerations for the whole GRACE and GRACE-FO missions are available on our data server www.zarm.uni-bremen.de/zarm_daten.

Global thermospheric mass density monitoring using LEO constellations: Simulation and analysis

Neutral thermospheric density is a crucial parameter for orbital tracking and upper atmosphere research. Here, we present a method to monitor global neutral thermospheric density testing simulations in various space environments with various satellite configurations and altitudes. The simulation results at 1° × 1° pixel resolution show that (1) within the range of 300–600 km orbital altitudes, the monitoring accuracy improves with the increase of the number of satellites, but this gain is significantly attenuated when the number of satellites increases to approximately 1,000; (2) the monitoring accuracy decreases with the increase of the altitude; and (3) the method presented in this study exhibits robustness under different space weather conditions. Furthermore, a differentiated satellite usage strategy (High Tightness and Low Looseness, HTLL) is developed to reduce the number of satellites used. Preliminary results indicate that the use of the HTLL method can reduce the number of satellites used from 2,592 to 1,044, whereas the maximum average relative deviation (ARD) does not exceed 1 %. The methods presented in this study have potential for future applications in the development of thermosphere research and satellite tracking.

An Index Description of the General Characteristics of Thermospheric Density Based on the Two‐Line‐Element Data Sets and the Spectral Whitening Method

AbstractThe thermospheric density and its variations are crucial to aerospace activities as well as space weather research and operation. However, due to the difficulties in observing the thermosphere, there has been a lack of effective descriptions for the general characteristics of thermospheric density. In this paper, the Two‐Line‐Element data sets (TLEs) from multi‐target low Earth orbit satellites are used to derive a proxy of the daily average atmospheric density in the thermospheric shell located in the vicinity of LEOs' orbital altitude. It captures the overall characteristics of the thermosphere and exhibits good correlations (∼0.9) with modeled and observed thermospheric density. By applying the spectral whitening method to this proxy, a new index is derived to describe non‐periodic perturbation of the density where the specific satellite passed by. The fact that the obtained from different satellites within the same thermospheric shell presents significant consistency to each other means that the new index is a good indicator for the overall feature of the variations of thermospheric density, and it is possible to define a unified regional index to describe density disturbances for the thermospheric shell where these satellites fly through. Moreover, the at different altitudes also present good consistency suggesting the possibility of defining a global index , capable of describing the density variation of the entire thermosphere.

Thermospheric Density Estimation Method Using a First-Order Gauss–Markov Process

Low-Earth-orbit (LEO) spacecraft are significantly influenced by atmospheric drag. Accurately estimating thermospheric density is pivotal for the precise calculation of drag acceleration. However, thermospheric density along a specific orbit, computed using existing thermospheric models, has certain inaccuracies. In this work, a first-order Gauss–Markov process is used to model the deviation of atmospheric drag acceleration. With the Markov parameter of the initial state iteratively computed through sequential estimation and the smoothing method, the thermospheric density is derived from high-precision GPS measurements. In simulation scenarios, the root-mean-square error and relative error of the estimated thermospheric density reduce by about 45 and 50% relative to the prior density, respectively. Using the estimated density for orbit propagation, satellite trajectories’ one-day position and velocity error are, respectively, within 100 m and 0.1 m/s, and an average improvement in orbit precision is over 80%. The proposed method has been applied to the real Tsinghua Science Satellite (Q-SAT) GPS measurements for effectiveness verification. It shows strong adaptability under extreme space weather and during the occurrence of geomagnetic storms. Due to the estimated Markov parameter of the initial state obeying the Langevin dynamics properties, the proposed method also offers short-term thermospheric density forecasting potential.

Probabilistic Short‐Term Solar Driver Forecasting With Neural Network Ensembles

AbstractSpace weather indices are used to drive forecasts of thermosphere density, which directly affects objects in low‐Earth orbit (LEO) through atmospheric drag force. A set of proxies and indices (drivers), F10.7, S10.7, M10.7, and Y10.7 are used as inputs by the JB2008, (https://doi.org/10.2514/6.2008‐6438) thermosphere density model. The United States Air Force (USAF) operational High Accuracy Satellite Drag Model (HASDM), relies on JB2008, (https://doi.org/10.2514/6.2008‐6438), and forecasts of solar drivers from a linear algorithm. We introduce methods using long short‐term memory (LSTM) model ensembles to improve over the current prediction method as well as a previous univariate approach. We investigate the usage of principal component analysis (PCA) to enhance multivariate forecasting. A novel method, referred to as striped sampling, is created to produce statistically consistent machine learning data sets. We also investigate forecasting performance and uncertainty estimation by varying the training loss function and by investigating novel weighting methods. Results show that stacked neural network model ensembles make multivariate driver forecasts which outperform the operational linear method. When using MV‐MLE (multivariate multi‐lookback ensemble), we see an improvement of RMSE for F10.7, S10.7, M10.7, and Y10.7 of 17.7%, 12.3%, 13.8%, 13.7% respectively, over the operational method. We provide the first probabilistic forecasting method for S10.7, M10.7, and Y10.7. Ensemble approaches are leveraged to provide a distribution of predicted values, allowing an investigation into robustness and reliability (R&R) of uncertainty estimates. Uncertainty was also investigated through the use of calibration error score (CES), with the MV‐MLE providing an average CES of 5.63%, across all drivers.

Improving Thermospheric Density Predictions in Low‐Earth Orbit With Machine Learning

AbstractThermospheric density is one of the main sources of uncertainty in the estimation of satellites' position and velocity in low‐Earth orbit. This has negative consequences in several space domains, including space traffic management, collision avoidance, re‐entry predictions, orbital lifetime analysis, and space object cataloging. In this paper, we investigate the prediction accuracy of empirical density models (e.g., NRLMSISE‐00 and JB‐08) against black‐box machine learning (ML) models trained on precise orbit determination‐derived thermospheric density data (from CHAMP, GOCE, GRACE, SWARM‐A/B satellites). We show that by using the same inputs, the ML models we designed are capable of consistently improving the predictions with respect to state‐of‐the‐art empirical models by reducing the mean absolute percentage error (MAPE) in the thermospheric density estimation from the range of 40%–60% to approximately 20%. As a result of this work, we introduce Karman: an open‐source Python software package developed during this study. Karman provides functionalities to ingest and preprocess thermospheric density, solar irradiance, and geomagnetic input data for ML readiness. Additionally, it facilitates developing and training ML models on the aforementioned data and benchmarking their performance at different altitudes, geographic locations, times, and solar activity conditions. Through this contribution, we offer the scientific community a comprehensive tool for comparing and enhancing thermospheric density models using ML techniques.

The 2022 Starlink Geomagnetic Storms: Global Thermospheric Response to a High‐Latitude Ionospheric Driver

AbstractIn this study, we present ionospheric observations of field‐aligned currents from AMPERE and the ESA Swarm A satellite, in conjunction with high‐resolution thermospheric density measurements from accelerometers on board Swarm C and GRACE‐FO, for the third and 4 February 2022 geomagnetic storms that led to the loss of 38 Starlink internet satellites. We study the global storm time response of the thermospheric density enhancements, including their decay and latitudinal distribution. We find that the thermospheric density enhances globally in response to high‐latitude energy input from the magnetosphere‐solar wind system and takes at least a full day to recover to pre‐storm density levels. We also find that the greatest density perturbations occur at polar latitudes consistent with the magnetosphere‐ionosphere dayside cusp, and that there appeared to be a saturation of the thermospheric density during the geomagnetic storm on the fourth. Our results highlight the critical importance of high‐latitude ionospheric observations when diagnosing potentially hazardous conditions for low‐Earth‐orbit satellites.

Ultra‐Fast Kelvin Wave Packets in Mars' Atmosphere and Their Interactions With Tides as Viewed by MAVEN/NGIMS and MRO/MCS

AbstractA key element of successful aerobraking operations at Mars is accurate thermospheric density predictions. Evidence suggests that much of the longitude variability in Mars' aerobraking region is associated with atmospheric tides, and the day‐to‐day variability is connected with tidal modulation by longer‐period global‐scale waves. Specifically, ultra‐fast Kelvin waves (UFKWs) and their modulation of the tidal spectrum play a key role in coupling Mars' lower (<∼80 km) and middle (∼80–100 km) atmosphere with the aerobraking region above. In this study, over 5 years of Mars Atmosphere and Volatile Evolution Neutral Gas and Ion Mass Spectrometer CO2 density observations are employed to reveal prominent, frequent, and persistent 2.5‐ to 4.5‐day UFKW packets in the whole Martian middle and upper thermosphere (ca. 150–200 km), and large secondary waves arising from their nonlinear interactions with the tidal spectrum. Detailed analyses focusing on a prominent ∼2.5‐day UFKW event in late 2015 demonstrate primary and secondary wave amplitudes growing twofold with altitude from ∼7%–14% near 150 km to ∼12%–25% near 200 km and their combined effects to account for ∼60%–80% of the altitude‐longitudinal variability of Mars' thermospheric density. Concurrent temperature measurements from Mars Reconnaissance Orbiter Mars Climate Sounder reveal consistent wave signatures near 80 km altitude suggesting propagation of both primary and secondary waves from the lower atmosphere. This study demonstrates that UFKWs and secondary waves from UFKW‐tide interactions are sources of significant altitude‐longitude variability in the Mars' aerobraking region that should be accounted for when analyzing satellite observations and nonlinear models.

GRACE-FO radiation pressure modelling for accurate density and crosswind retrieval

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.

Quiet Time Thermospheric Gravity Waves Observed by GOCE and CHAMP

AbstractThe Gravity Field and Steady‐State Ocean Circulation Explorer (GOCE) and CHAllenging Minisatellite Payload (CHAMP) satellites measure in‐situ thermospheric density and cross‐track wind. When propagating obliquely to the satellite track in a horizontal plane (i.e., not purely along‐track or cross‐track), gravity waves (GWs) can be observed both in the density and cross‐track wind perturbations. We employ the Wavelet Analysis, red noise model, dissipative dispersion and polarization relations for thermospheric GWs, and specific criteria to determine whether a quiet‐time (Kp < 3) thermospheric traveling atmospheric disturbances (TADs) event is a GW or not. The first global morphology of thermospheric GWs instead of TADs is reported. The fast intrinsic horizontal phase speed (cIH > 600 m/s) of most GWs suggests that they are not generated in the lower/middle atmosphere (where cIH < 300 m/s). A second population of GWs with slower speeds (cIH = 50–250 m/s) in GOCE are likely from the lower/middle atmosphere, but they occur much less frequently in CHAMP. GW hotspots occur during the high‐latitude and the winter midlatitude regions. GW amplitudes exhibit semi‐annual and annual variations. These findings suggest that most GOCE and CHAMP GWs are higher‐order GWs from primary GW sources in the lower/middle atmosphere. Finally, the average propagation direction of the CHAMP GWs exhibits a clear diurnal cycle, with clockwise (counterclockwise) occurring in the northern (southern) hemisphere and equatorward propagation occurring at ∼13 LST. This suggests that the predominant GW propagation direction is opposite to the background wind direction.

Statistical models of the variability of plasma in the topside ionosphere: 1. Development and optimisation

This work presents statistical models of the variability of plasma in the topside ionosphere based on observations made by the European Space Agency’s (ESA) Swarm satellites. The models were developed in the “Swarm Variability of Ionospheric Plasma” (Swarm-VIP) project within the European Space Agency’s Swarm+4D-Ionosphere framework. The configuration of the Swarm satellites, their near-polar orbits and the data products developed, enable studies of the spatial variability of the ionosphere at multiple scale sizes. The statistical modelling technique of Generalised Linear Modelling (GLM) was used to create models of both the electron density and measures of the variability of the plasma structures at horizontal spatial scales between 20 km and 100 km. Despite being developed using the Swarm data, the models provide predictions that are independent of these data. Separate models were created for low, middle, auroral and polar latitudes. The models make predictions based on heliogeophysical variables, which act as proxies for the solar and geomagnetic processes. The first and most significant term in the majority of the models was a proxy for solar activity. The most common second term varied with the latitudinal region. This was the Solar Zenith Angle (SZA) in the polar region, a measure of latitude in the auroral region, solar time in the mid-latitude region and a measure of latitude in the equatorial region. Other, less significant terms in the models covered a range of proxies for the solar wind, geomagnetic activity and location. In this paper, the formulation, optimisation and evaluation of these models are discussed. The models show very little bias, with a mean error of zero to two decimal places in 14 out of 20 cases. The models capture some, but not all, of the trends present in the data, with Pearson correlation coefficients of up to 0.75 between the observations and the model predictions. The models also capture some, but not all, of the variability of the ionospheric plasma, as indicated by the precision, which ranged between 0.20 and 0.83. The addition of the thermospheric density as an explanatory variable in the models improved the precision in the polar and auroral regions. It is suggested that, if the thermosphere could be observed at a higher spatial resolution, then even more of the variability of the plasma structures could be captured by statistical models. The formulation and optimisation of the models are presented in this paper. The capability of the model in reproducing the expected climatological features of the topside ionosphere, in supporting GNSS-based ionospheric observations and the performance of the model against the Thermosphere-Ionosphere-Electrodynamics General Circulation Model (TIE-GCM), are provided in a companion paper (Spogli L et al. 2024. J Space Weather Space Clim https://doi.org/10.1051/swsc/2024003).

Evaluation of the Exospheric Temperature Modeling From Different Empirical Orthogonal Functions

AbstractIn this paper, we constructed the Exospheric Temperature Models (ETM) on the basis of CHAMP and GRACE data using different empirical orthogonal functions (EOFs). The EOFs of the exospheric temperature can be derived either from satellite data directly or from the outputs of the Thermosphere Ionosphere Electrodynamics General Circulation Model (TIEGCM) and MSIS models by applying the Principal Component Analysis method. Then, the thermospheric mass densities calculated from ETM are used to compare with the observed data in order to evaluate the performance of different ETM models. It was found that all these three models can provide good specification of thermospheric density including day‐night, seasonal, and latitudinal variations. However, the ETM based on CHAMP and GRACE data gives a better performance in modeling the Equatorial Thermospheric Anomaly and the Midnight Density Maximum features than the MSIS‐ETM and TIEGCM‐ETM. Specifically, independent SWARM‐C data comparison showed that the Relative Deviations and corresponding Root‐Mean‐Square‐Errors of our Texo models are less than 8.9% and 22.8%, much better than the MSIS‐00 model.

Variations in thermospheric density during two consecutive geomagnetic storms of different solar wind conditions in November 2022

Geomagnetic storms can cause severe space weather impacts on space technology, such as anomaly and loss of satellites and spacecraft. We investigate solar wind conditions in responsible for two consecutive geomagnetic storms driven by different sources: a high-speed solar wind stream (HSS) on November 3-4, 2022, and a coronal mass ejection (CME) associated with an M5.2 solar flare on November 7, 2022. Spatial and temporal variations in thermospheric density and auroral activity are studied for the two geomagnetic storms. Measurements from the Swarm satellite show that the HSS-driven geomagnetic storm enhanced the thermospheric density by ~69.4% at 462 km and by ~92.8% at 511 km, and the CME-driven geomagnetic storm enhanced it by ~99.4% at 462 km and by ~145% at 511 km. Images taken by the F17 DMSP/SSUSI indicate the auroral emission produced by CME-driven geomagnetic storm is significantly stronger than that produced by HSS-driven storm, while the HSS-driven auroras last longer than the CME-driven ones. The correlation between the hourly moving averaged SymH data and the thermospheric density is stronger for Swarm-A than for Swarm-B. The response times of the thermospheric density for the HSS-driven geomagnetic storm are zero at 462 km and ~47 minutes at 511 km, while for the CME-driven geomagnetic storm are ~28 minutes and ~35 minutes, respectively. This study sheds light on the mechanisms underlying the change in the thermospheric density in relation to different geomagnetic activities.

Retrieval and analysis of thermospheric mass densities below 200 km altitude based on precise orbit data of the re-entry objects SZ-10 MODULE and TIANGONG 1

Atmospheric mass densities in the lower thermosphere below 200 km have not been adequately determined, but they are crucial for re-entry prediction of space objects. In this paper, based on precise orbit data of the re-entry objects SZ-10 MODULE and TIANGONG 1 (COSPAR identifiers 2013-029H and 2011-053A, respectively; NORAD catalog numbers 39193 and 37820, respectively), the semi-major axis decay numerical method and the improved energy balance method are adopted to retrieve thermospheric mass densities below 200 km altitude, and a total of 7044 and 4698 points of valid densities data with one-minute temporal resolution are obtained, respectively. Then the retrieved densities after preprocessing are compared with the NRLMSISE-00 empirical model of the atmosphere. It shows that there is an excellent consistency between these two methods with the Pearson correlation coefficients around 1.00, the retrieved densities of which are also in good agreement with the model with the Pearson correlation coefficients above 0.97 (their systematic biases are about 1.1% and 4.5% with standard deviations of about 14% and 20% for these two objects respectively), but the retrieved densities of the semi-major axis decay numerical method have a smaller systematic bias from the model than the results of the improved energy balance method which is computationally more efficient. In addition, the corresponding retrieved densities and their ratios to the model are further analyzed in terms of latitude and local solar time, and the retrieved densities of these two methods are also in good consistency within about 97%. The maximum mean deviations from the model in both dimensions reach about 12%. It reveals the variations of the thermospheric mass densities below 200 km altitude with latitude and local solar time due to solar activity. Additionally, it also indicates that the NRLMSISE-00 model underestimates the thermospheric densities at high solar activity and overestimates the densities at low solar activity, as compared to the retrieved densities that are regarded as true values.

Probabilistic Solar Proxy Forecasting With Neural Network Ensembles

AbstractSpace weather indices are used commonly to drive forecasts of thermosphere density, which affects objects in low‐Earth orbit (LEO) through atmospheric drag. One commonly used space weather proxy, F10.7cm, correlates well with solar extreme ultra‐violet (EUV) energy deposition into the thermosphere. Currently, the USAF contracts Space Environment Technologies (SET), which uses a linear algorithm to forecast F10.7cm. In this work, we introduce methods using neural network ensembles with multi‐layer perceptrons (MLPs) and long‐short term memory (LSTMs) to improve on the SET predictions. We make predictions only from historical F10.7cm values. We investigate data manipulation methods (backwards averaging and lookback) as well as multi step and dynamic forecasting. This work shows an improvement over the popular persistence and the operational SET model when using ensemble methods. The best models found in this work are ensemble approaches using multi step or a combination of multi step and dynamic predictions. Nearly all approaches offer an improvement, with the best models improving between 48% and 59% on relative MSE with respect to persistence. Other relative error metrics were shown to improve greatly when ensembles methods were used. We were also able to leverage the ensemble approach to provide a distribution of predicted values; allowing an investigation into forecast uncertainty. Our work found models that produced less biased predictions at elevated and high solar activity levels. Uncertainty was also investigated through the use of a calibration error score metric (CES), our best ensemble reached similar CES as other work.

Comparison of Empirical and Theoretical Models of the Thermospheric Density Enhancement During the 3–4 February 2022 Geomagnetic Storm

AbstractOn 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.