A new version of the US National Science Foundation National Center for Atmospheric Research (NSF NCAR) thermosphere-ionosphere-electrodynamics general circulation model (TIEGCM) has been developed and released. This paper describes the changes and improvements of the new version (3.0) since its last major release (2.0) in 2016. These include: (a) increasing the model resolution in both the horizontal and vertical dimensions, as well as in the ionospheric dynamo solver; (b) upward extension of the model upper boundary to enable more accurate simulations of the topside ionosphere and neutral density in the lower exosphere; (c) improved parameterization for thermal electron heating rate; (d) resolving transport of minor species N(D-2); (e) treating helium as a major species; (f) parameterization for additional physical processes, such as SAPS and electrojet turbulent heating; (g) including parallel ion drag in the neutral momentum equation; (h) nudging of prognostic fields near the lower boundary from external data; (i) modification to the NO reaction rate and auroral heating rate; (j) outputs of diagnostic analysis terms of the equations; (k) new functionalities enabling model simulations of certain recurrent phenomena, such as solar flares and eclipses. We present examples of the model validation during a moderate storm and compare simulation results by turning on/off new functionalities to demonstrate the related new model capabilities. Furthermore, the model was upgraded to comply with the new computer software environment at NSF NCAR for easy installation and run setup and with new visualization tools. Finally, the model limitations and future development plans are discussed.

A new data set of atomic oxygen (O) and molecular nitrogen (N-2) number density profiles, along with thermospheric temperature profiles between 180 and 500 km, has been developed. These profiles are derived from solar occultation measurements made by the Solar Ultraviolet Imager (SUVI) on the GOES-R satellites, using the 17.1, 19.5, and 30.4 nm channels. Discussed is the novel approach and methods for using EUV solar occultation images for measuring the thermospheric state. Measurement uncertainties are presented as a function of tangent altitude. At 250 km, number density random uncertainties are found to be 8% and 17% for O and N-2, respectively, and the random uncertainty for neutral temperature is 3%. The impact of effective cross section uncertainty on retrieval bias was assessed, revealing that the largest effects occur where O and N-2 are, respectively, the minor absorber. In contrast, total mass density and O/N-2 ratios show substantially lower sensitivity, with biases that remain small or nearly constant with altitude. Total mass density comparisons with the NRLMSIS 2.0 model show good agreement at the dusk terminator (average difference -2%), but larger discrepancies at dawn (-26%), particularly during low solar activity. Density comparisons with the IDEA-GRACE-FO and Dragster models show dawn/dusk differences of -24%/-2% and +2%/+13%, respectively. As this measurement relies only on real-time NOAA space weather SUVI images, these density and temperature profiles could be produced in real-time, supporting critical space weather monitoring and prediction, and helping fill a long-standing observational gap in thermospheric temperature and density.

This study examines storm-time variations in the drag coefficients of the GRACE and GRACE Follow-On (FO) satellites during selected extreme geomagnetic storms-the October 2003, November 2003, November 2004, and May 2024 storms. Orbit-averaged values derived using closed-form solutions show a 6%-12% decrease during the main phase of the storms. The storm-time variations in are primarily driven by (a) decreases in atomic oxygen (O) mole fraction with corresponding increases in nitrogen mole fraction, and (b) higher accommodation levels resulting from enhanced O density and neutral temperature. The drag coefficients are calculated using the neutral outputs from the NRLMSIS, GITM, and TIEGCM atmospheric models. The drag coefficients derived from GITM show the maximum storm-time variations (8%-12%), due to lower pre-storm O density and temperature, resulting in lower accommodation coefficients and greater sensitivity of gas-surface interaction (GSI) to storm-induced thermospheric changes. The drag coefficients are calculated using Diffuse Reflection with Incomplete Accommodation (DRIA) and Cercignani-Lampis-Lord (CLL) GSI models, which show similar storm-time variations with larger quiet-time differences that reduce after storm onset. A comparison of GRACE during the October 2003, November 2003, and November 2004 storms shows the lowest variation for October 2003 storm (5%-6%) and the highest variation for November 2004 storm (11%-12%). These differences occur because storms with higher F10.7 indices, such as the October 2003 storm (daily F10.7 = 275 sfu), correspond to more heated background thermosphere; hence the storm-induced changes produce smaller relative variations in .

Abstract This study focuses on utilizing the increasing availability of satellite trajectory data from global navigation satellite system‐enabled low‐Earth orbiting satellites and their precision orbit determination (POD) solutions to expand and refine thermospheric model validation capabilities. The research introduces an updated interface for the GEODYN‐II POD software, leveraging high‐precision space geodetic POD to investigate satellite drag and assess density models. This work presents a case study to examine five models (NRLMSIS2.0, DTM2020, JB2008, TIEGCM, and CTIPe) using precise science orbit (PSO) solutions of the Ice, Cloud, and Land Elevation Satellite‐2 (ICESat‐2). The PSO is used as tracking measurements to construct orbit fits, enabling an evaluation according to each model's ability to redetermine the orbit. Relative in‐track deviations, quantified by in‐track residuals and root‐mean‐square errors (RMSe), are treated as proxies for model densities that differ from an unknown true density. The study investigates assumptions related to the treatment of the drag coefficient and leverages them to eliminate bias and effectively scale model density. Assessment results and interpretations are dictated by the timescale at which the scaling occurs. DTM2020 requires the least scaling (∼−7%) to achieve orbit fits closely matching the PSO within an in‐track RMSe of 7 m when scaled over 2 weeks and 2 m when scaled daily. The remaining models require substantial scaling of the mean density offset (∼30 − 75%) to construct orbit fits that meet the aforementioned RMSe criteria. All models exhibit slight over or under‐sensitivity to geomagnetic activity according to trends in their 24‐hr scaling factors.

Recent studies of TWINS Lyman-α observations have reported an increase in geocoronal column brightness during geomagnetic storms, indicating enhanced exospheric hydrogen atom density (NH). This suggests a complex role of exospheric neutrals in determining storm-time magnetosphere dynamics and their energy release through charge-exchange processes. We developed a Model for Analyzing Terrestrial Exosphere (MATE) to investigate storm-time exospheric behaviors and their physical drivers. MATE traces test hydrogen atoms backward in time from locations in the exosphere to a nominal exobase altitude of 500 km, employing Newtonian mechanics with gravitational force. The model then calculates the phase-space densities (PSDs) of test hydrogen atoms at the exobase using the Maxwellian distribution with physics-based exobase conditions from the TIMEGCM upper atmosphere model. MATE maps PSDs at the exobase to the exosphere using Liouville’s Theorem under collisionless assumptions and derives NH by integrating the PSDs across velocity space. We conducted MATE simulation before, during, and after a minor geomagnetic storm from 12 to 18 June 2008, and compared the model results with NH estimates from the TWINS geocorona data. MATE reproduces storm-time density enhancements soon after the minimum Dst is reached, matching well with a general trend of TWINS NH estimates. The results suggest that upper atmospheric heating during a geomagnetic storm increases the number of ballistic and escaping hydrogen atoms entering the exosphere from the exobase, thereby boosting NH. However, the magnitude of modeled NH mismatches the TWINS NH estimates. The potential mechanisms of this density discrepancy include the physics excluded in the MATE model — such as neutral-neutral collisions, neutral-plasma charge exchange, solar radiation pressure, and photoionization — as well as the higher exobase hydrogen density of TIMEGCM compared to typical empirical values, which will be addressed in future.

In this paper, the equatorial thermosphere anomaly (ETA) is investigated using accelerometer measurements to determine whether the feature is density-dominated, wind-dominated, or some combination of the two. An ascending-descending accelerometry (ADA) technique is introduced to address the density-wind ambiguity that appears when interpreting the ETA in atmospheric drag acceleration analyses. This technique separates ascending and descending acceleration measurements to determine if a wind's directionality influences the interpretation of the observed ETA feature. The ADA technique is applied to accelerometer measurements taken from the Challenging Minisatellite Payload mission and has revealed that the ETA is primarily density-dominated from 9:00 to 16:00 local time (LT) near 400 km altitude, with the acceleration perturbations behaving similarly between 2003 and 2004 across all seasons. This finding suggests that the perturbations in the acceleration due to in-track wind perturbations are small compared to the perturbations due to mass density, while indicating that the formation mechanisms across these local times are similar and persistent. The results also revealed that in the terminator region at 18:00 LT the acceleration perturbations deviate appreciably between ascending and descending passes, indicating different or multiple processes occurring at this local time compared to the 9:00-16:00 LT ascribed to the ETA. These results help constrain ETA formation theories to specific local times and thermospheric property responses without the use of supplemental wind measurements, while also indicating regions where in-track winds cannot always be neglected. Earth's thermosphere, a layer in the upper atmosphere, is a highly variable region that contributes to satellite drag in low Earth orbit. The equatorial thermosphere anomaly (ETA) is a perturbation feature that produces increases and decreases in drag accelerations across the lower latitudes of the thermosphere. Direct measurements of the thermosphere are often limited, so satellite instruments, such as accelerometers, have been used to analyze the acceleration that a satellite experiences due to atmospheric drag to indirectly measure thermospheric properties. However, the measured drag acceleration is dependent on both mass density and wind, making it difficult to determine whether a change in drag across the ETA is due to either property. This has implications on what mechanisms are responsible for its formation. This work introduces an ascending-descending accelerometry technique to exploit the fact that while acceleration perturbations produced by mass density are independent of satellite direction, those arising from winds can either be positive or negative depending on the relative spacecraft motion. By separating satellite orbits into ascending (south-to-north) and descending (north-to-south) passes, it can be determined whether drag acceleration perturbations are due to mass density, wind, or a mixture of the two, helping constrain possible formation mechanisms. Accelerometer observations of the Equatorial Thermosphere Anomaly (ETA) cannot distinguish between in-track density and wind perturbations A new technique is applied to observations determining that the ETA, occurring between 9 and 16 LT, is a density-dominated feature The ETA demonstrates repeatable annual behavior for each season, suggesting a common and persistent formation mechanism

With the proliferation of low Earth orbit (LEO) satellites carrying GNSS receivers on-board commercial operators such as Spire, Starlink, OneWeb, and Amazon, an abundance of high-cadence tracking data could become available to the scientific community. While GNSS measurements from geodetic-grade receivers on satellites like SWARM, CHAMP, GRACE, and GOCE have been extensively used for atmospheric density retrieval, limited research has explored the potential of less accurate data from commercial operators. This study focuses on two methods to estimate atmospheric densities from precision orbit determination (POD) products-precise positions and velocities-utilizing synthetic data sets. The first method, termed "POD accelerometry" treats the POD products as measurements to a reduced-dynamic POD scheme with the goal of estimating densities using stochastic parameters. The second method known as the energy dissipation rate (EDR) approach derives densities from changes in orbital energy. The relative contributions of various error sources-dynamics model uncertainties, and POD noise-to the estimated densities are studied for a limited set of orbital regimes and space weather activity, and possible error mitigation strategies are suggested. The performance of the two methods and their sensitivities to these various error sources are compared for circular orbits in the altitude regime 300-800 km during solar minimum (F-10.7=72.5). EDR and POD accelerometry have comparable performances for high drag, low POD noise environments, whereas the latter performs considerably better in low drag (<10(-6) m/s(2)), high POD noise (>25 cm) environments, with densities retrieved at higher cadences for the orbital regimes considered in this work during solar minimum.

The boundary between the thermosphere and exosphere is often given the simplified description of being a separation between highly collisional continuum mechanics and a collisionless domain. The realistic smooth transition through this space has historically presented a challenge to model as the assumptions used to simplify the Boltzmann equation in fluid models are invalidated at higher altitudes. A lack of rigorous modeling of the region limits the ability to understand the dynamics of light atmospheric species. This manuscript describes the dynamics present in a two-way coupled fluid-particle atmospheric model extending from the mesosphere through the exosphere with a smooth transition between fluid and particle domains. This model is used to examine the coupled nature of the thermosphere and exosphere using the fluid simulation TIME-GCM and the direct simulation Monte Carlo simulation Monaco. The coupled model allows for examination of the thermosphere circulation and exosphere transport mechanisms, as well as their impacts on the distribution of hydrogen. In this analysis, upper transport regions in the exosphere are revealed and distinguished from lower transport regions during June solstice. Furthermore, coupling allows TIME-GCM to account for effects of lateral exospheric transport of hydrogen, altering its upper boundary condition and consequentially the spatial distribution of hydrogen throughout the thermosphere. Finally, it is asserted that a self-consistent hydrogen exobase distribution is necessary to constrain other analytical extrapolation techniques used to predict the vertical hydrogen profile in the exosphere. Plasma interactions are excluded from this study to isolate neutral dynamics.

This study presents a data-driven approach to quantify uncertainties in the quantities of interest (QoIs), i.e., electron density, plasma drifts, and neutral winds, in the ionosphere-thermosphere (IT) system due to varying solar wind parameters (drivers) during quiet conditions (Kp$<$4) and fixed solar radiation and lower atmospheric conditions representative of March 16th, 2013. Ensemble simulations of the coupled Whole Atmosphere Model with Ionosphere Plasmasphere Electrodynamics (WAM-IPE) driven by synthetic solar wind drivers generated through a multi-channel variational autoencoder (MCVAE) model are obtained. The means and variances of the QoIs, as well as the sensitivities of the QoIs with respect to the drivers, are estimated by applying the polynomial chaos expansion (PCE) technique. Our results highlight unique features of the IT system’s uncertainty: 1) the uncertainty of the IT system is larger during nighttime; 2) the spatial distributions of the uncertainty for electron density and zonal drift at fixed local times present 4 peaks in the evening sector which is associated with the low density regions of longitude structure of electron density; 3) the uncertainty of the equatorial electron density is highly correlated with the uncertainty of the zonal drift, especially in the evening sector, while it is weakly correlated with the vertical drift. A variance-based global sensitivity analysis is further conducted. Results suggest that the IMF Bz plays a dominant role in the uncertainty of the electron density when IMF Bz is 0 or southward, while the solar wind speed plays a dominant role when IMF Bz is northward.

The recovery of the thermosphere after a strong geomagnetic storm on 12 May 2021 is investigated using lower and middle thermospheric temperature (Tdisk), ratio of atomic oxygen and molecular nitrogen column densities (O/N2), cooling due to Nitric Oxide (NO), and model simulations. The peak influence of the geomagnetic storm lasted about five hours and generated latitudinal gradients in Tdisk and O/N2. Following the storm, the latitudinal gradient in temperature recovered faster compared to that of O/N2. Measured NO-cooling rate and simulated NO-densities are enhanced on the storm day compared to a quiet-day, consistent with a rapid recovery in temperatures. Based on this, we conclude that the faster recovery of the Tdisk latitudinal gradient is driven by the combined effect of NO cooling and strong thermal conductivity. Furthermore, the slower recovery of the O/N2 latitudinal gradients can be attributed to the lack of poleward advection after the storm.

AbstractThe Iterative Driver Estimation and Assimilation (IDEA) data assimilation technique was used with the Whole Atmosphere Model (WAM) to improve neutral density specification in the upper thermosphere. Two different neutral density data sources were examined to enhance the capability of simulating the global thermospheric state. The first were accelerometer estimates of neutral density from the Challenging Mini‐Satellite Payload (CHAMP) satellite. The second were neutral density estimates from the Global Ultraviolet Imager (GUVI) limb‐scan airglow observations aboard the Thermosphere Ionosphere Mesosphere Energetics and Dynamics satellite. Due to the intensity of the November 2003 storm, two changes were necessary in WAM. The first was allowing the Kp geomagnetic index to exceed 9 and the second was changing the relationship between Kp and the solar wind parameters used to drive the model. With these changes, results show that IDEA effectively captures the thermospheric neutral density at the CHAMP satellite altitude and follows the time‐dependence through the November 2003 storm period. Furthermore, a cross‐comparison was conducted with the GUVI dayside limb scan measurements. GUVI neutral densities within 270–320 km show the closest agreement with WAM when CHAMP data was assimilated by IDEA. We speculate on the potential for observations from GUVI at 300 km to be used as a data source in the IDEA‐WAM simulations. These simulations demonstrate the utility of the IDEA data assimilation technique with physical models and that using either accelerometer observations or ultraviolet airglow limb measurement during extreme storm periods could be used.

Neutral-Plasma charge exchange is a fundamental physical process that occurs ubiquitously across the universe.In geospace, charge exchange occurs in the Earth's topside ionosphere, polar wind, plasmasphere, inner magnetosphere, and magnetosheath.Past and current space missions have profiled plasma and electromagnetic characteristics in various parts of the Earth's magnetospheric system.However, observations of the exosphere, i.e., neutrals above 500 km altitude, are still sparse and, in some regions, non-existent, which limits our understanding of the neutral contribution to the overall dynamics of the geospace environment.Cold exospheric neutrals (< 10 eV) play an important role in the Sun-Earth interaction.Variability of exospheric density provides key information of the Earth's atmospheric loss under dynamic space environment conditions.Various neutral species and their density variations in the polar wind can alter ion outflow patterns, modifying global magnetospheric dynamics.Exospheric neutrals also provide an energy sink for the inner magnetosphere by creating Energetic Neutral Atoms (ENAs) through charge exchange with high-energy ring current ions, which subsequently leave our geospace system unimpeded by magnetic fields.Exospheric neutrals also provide a means to observe the global interaction of the solar wind -magnetosphere, through global imaging of the system via ENAs (e.g., the TWINS and IMAGE missions) and soft X-rays (e.g., the upcoming LEXI and SMILE missions), the byproducts of neutral-plasma charge exchange.In the coming decade, we advocate that our community needs to increase our exploration of the neutral populations in the outermost reaches of the Earth's atmosphere.It is imperative that we improve both in-situ and remote-sensing technologies for measuring key neutral species in our exosphere.We also encourage dedicated exosphere missions and to stimulate model developments of our exosphere and its interaction with the co-located magnetospheric system and neighboring Ionosphere -Thermosphere -Mesosphere system.

The past decade saw the development of several data assimilation systems for the ionosphere, thermosphere, and mesosphere (ITM).To fully realize the capabilities of ITM data assimilation systems for both scientific investigations and operations, several critical advances are needed.This white paper outlines some of the outstanding challenges facing ITM data assimilation that need to be addressed in the coming decade in order to achieve robust, highquality, ITM data assimilation systems.Benefits to both the scientific and operational communities of advancing ITM data assimilation capabilities are also provided.These include, but are not limited to, providing the framework for investigating ITM predictability, scientific investigations into day-to-day ITM variability driven by the lower atmosphere and geomagnetic storms, as well as advancing space weather forecasting capabilities.

Upper thermosphere mass density over the declining phase of solar cycle 23 is investigated using a day‐to‐night ratio (DNR) of thermosphere properties to evaluate how much relative change occurs climatologically between day and night. Challenging Minisatellite Payload (CHAMP) observations from 2002 to 2009, MSIS 2.0 output, and TIEGCM V2.0 simulations are analyzed to assess their relative response in DNR. The CHAMP observations demonstrate nightside densities decrease more significantly than dayside densities as solar flux decreases. This causes a steadily increasing CHAMP mass density DNR from around two to greater than four with decreasing solar flux. The MSIS 2.0 nightside densities decrease, with decreasing solar flux, more significantly than the dayside, resulting in the same trend as CHAMP. TIEGCM V2.0 displays an opposite trend in density DNR with decreasing solar flux due to dayside densities decreasing more significantly than nightside densities. A sensitivity analysis of the two models reveals the TIEGCM V2.0 to have greater sensitivity in temperature to levels of solar flux, while MSIS 2.0 displayed a greater sensitivity in mean molecular weight. The pressure DNR from both models contributed the most to the density DNR value at 400 km. As solar flux decreases, the two models' estimate of pressure DNR deviate appreciably and trend in opposite directions. The TIEGCM V2.0 dayside temperatures during middle‐to‐low solar flux are too cold relative to MSIS 2.0. Increasing the dayside temperature values by about 50–100 K and decreasing the nightside temperature slightly would bring the TIEGCM V2.0 into better agreement with MSIS 2.0 and CHAMP observations.

Abstract In Low Earth Orbit (LEO), atmospheric drag is the largest contributor to trajectory prediction error. The current thermospheric density model used in operations, the High Accuracy Satellite Drag Model (HASDM), applies corrections to an empirical density model every 3 hr using observations of 75+ calibration satellites. This work aims to improve global thermospheric density estimation by utilizing a physics‐based space environment model and precise GPS‐based orbit estimates of LEO CubeSats. The data assimilation approach presented here estimates drivers of the Thermosphere‐Ionosphere‐Electrodynamics General Circulation Model (TIE‐GCM) every 1.5 hr using CubeSat GPS information. In this work, Spire Global CubeSat data are used to demonstrate the method using only 10 satellites; the true strength of the method is its potential to exploit data already collected on large LEO constellations (hundreds of CubeSats). Precise Orbit Determination (POD) information from 10 CubeSats over 12 days is used to sense a global density field when Kp historical data show a minor and moderate geomagnetic storm in succession. This paper provides a direct comparison of estimated density, derived by our new method, to HASDM and Swarm mission derived density. A propagation analysis is also executed by comparing the CubeSat POD data to orbits propagated using our estimated density versus HASDM density. The analyses show that the estimated density is within 35% of HASDM during storm‐time conditions, and that the propagation using the estimated density yields an improvement of 26% over NRLMSISE‐00 compared to HASDM, while outperforming HASDM during the second storm peak.

Accurate estimates of neutral mass densities obtained from measurements of satellite drag acceleration are vital to NASA science objectives, including the construction of atmospheric models, the understanding of thermospheric physics and its influence on other regions of geospace, the investigation of long-term behavior in the thermosphere, and the monitoring of space weather impacts on operational assets.The interpretation of drag measurements depends strongly on the assumptions made about molecular interactions with a satellite's surfaces, which vary with altitude and local time, with changes in the thermosphere resulting from space-weather, as well as with long-term (multi-decadal) variations in the atmosphere.Through the modification of the aerodynamic drag coefficient (CD), such assumptions introduce errors into atmospheric models and limit our ability to assimilate diverse datasets into operational models.Though recent progress has been made in the area of gas-surface interactions (GSI), there is still much that is unknown about this topic, especially above the Oxygen/Helium transition where most low Earth orbiting satellites reside.In order to take full advantage of data derived from measurements of satellite drag, it is necessary to quantify GSI parameters throughout the thermospheric column.A successful approach to addressing questions in GSI and drag coefficient modeling will include a combination of techniques.These multiple approaches will require satellite constellations flying now and in the near future, state-of-the-art laboratory experiments, and comprehensive multi-instrument analyses from single satellites that are made possible by upcoming missions such as GDC.

The conceptual design, scientific rationale and relevance, and technology and programmatic needs of a neutral atmosphere density monitoring system are explored.This system could monitor atmospheric density in low Earth orbit (LEO) which varies in response to changes in solar activity and Earth's geomagnetic conditions.The overarching science goal of this monitoring system is to improve physics-based, data assimilative, upper atmospheric models and to ultimately reduce uncertainties in neutral density forecasts for orbital operations.

Solar and stellar ultraviolet occultations provide a capability essential for advancing our understanding of the thermosphere and its coupling with the ionosphere and lower atmosphere.Advances over the past decade have demonstrated the power of occultations for measuring gravity waves and tides over large altitude ranges and across atmospheric domains.Additionally, occultation instruments measure neutral density in the thermosphere directly using technology that is readily miniaturized, making them ideal candidates for space weather monitoring sensors.Future missions for studying the thermosphere should include instruments specifically designed for occultations to maximize the quality of science measurements.Future technology development efforts should focus on EUV stellar occultations and active remote sensing at FUV and EUV wavelengths.

Themospheric conditions during a minor geomagnetic event of 3 and 4 February 2022 has been investigated using disk temperature (T-disk) observations from Global-scale Observations of the Limb and Disk (GOLD) mission and model simulations. GOLD observed that the T-disk increases by more than 60 K during the storm event when compared with pre-storm quiet days. A comparison of the T-disk with effective temperatures (T-eff, i.e., a weighted average based on airglow emission layer) from Mass Spectrometer Incoherent Scatter radar version 2 (MSIS2) and Multiscale Atmosphere-Geospace Environment (MAGE) models shows that MAGE outperforms MSIS2 during this particular event. MAGE underestimates the T-eff by about 2%, whereas MSIS2 underestimates it by 7%. As temperature enhancements lead to an expansion of the thermosphere and resulting density changes, the value of the temperature enhancement observed by GOLD can be utilized to find a GOLD equivalent MSIS2 (GOLD-MSIS) simulation-from a set of MSIS2 runs obtained by varying geomagnetic ap index values. From the MSIS-GOLD run we found that the thermospheric density enhancement varies with altitude from 15% (at 150) to 80% (at 500 km). Independent simulations from the MAGE model also show a comparable enhancement in neutral density. These results suggest that even a modest storm could impact the thermospheric densities significantly and GOLD data can be used to improve the empirical and assimilative models of the thermosphere.