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In this work, we address the computational challenge of large‐scale physics‐based simulation models for the ring current. Reduced computational cost allows for significantly faster than real‐time forecasting, enhancing our ability to predict and respond to dynamic changes in the ring current, valuable for space weather monitoring and mitigation efforts. Additionally, it can also be used for a comprehensive investigation of the system. Thus, we aim to create an emulator for the Ring current‐Atmosphere interactions Model with Self‐Consistent magnetic field (RAM‐SCB) particle flux that not only improves efficiency but also facilitates forecasting with reliable estimates of prediction uncertainties. The probabilistic emulator is built upon the methodology developed by Licata and Mehta (2023), https://doi.org/10.1029/2022sw003345. A novel discrete sampling is used to identify 30 simulation periods over 20 years of solar and geomagnetic activity. Focusing on a subset of particle flux, we use Principal Component Analysis for dimensionality reduction and Long Short‐Term Memory (LSTM) neural networks to perform dynamic modeling. Hyperparameter space was explored extensively resulting in about 5% median symmetric accuracy across all data sets for one‐step dynamic prediction. Using a hierarchical ensemble of LSTMs, we have developed a reduced‐order probabilistic emulator (ROPE) tailored for time‐series forecasting of particle flux in the ring current. This ROPE offers accurate predictions of omnidirectional flux at a single energy with no pitch angle information, providing robust predictions on the test set with an error score below 11% and calibration scores under 8% with bias under 2% providing a significant speed up as compared to the full RAM‐SCB run. Plain Language Summary: Our study tackles the challenges of simulating the ring current in space and time, using a model called RAM‐SCB. By making our simulations faster, we can predict changes in the ring current faster than in real time. This is crucial for monitoring space weather and taking actions to protect satellites and other space assets. Our goal is to create a computer program (emulator) that is efficient, can forecast changes accurately, and gives reliable estimates of its predictions. We follow a method developed by Licata and Mehta (2023), https://doi.org/10.1029/2022sw003345 and extend it to the ring current. Discrete sampling is used to pick specific periods for our simulations. We focus on a part of the simulation data and use an advanced method, a hierarchical ensemble of Long Short‐Term Memory (LSTM) to build our emulator. This is called a ROPE, that can predict the ring current's behavior by providing forecasts with errors below 11% and calibration scores under 8% (how aligned the predictions are with the actual). Key Points: A probabilistic emulator for the ring current‐atmosphere interactions model with self‐consistent magnetic field (RAM‐SCB) particle flux is designed with a focus on reducing computational resources of time and spaceAn ensemble of long‐short term memory captures temporal variations and provides a probabilistic emulatorThe emulator makes a week‐long prediction for single energy flux in ∼20 s providing a significant speed‐up over the full RAM‐SCB run [ABSTRACT FROM AUTHOR]

Space 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. Plain Language Summary: Objects in low‐Earth orbit, are affected by atmospheric drag, which depends on density. A currently used thermosphere density model, JB2008, (https://doi.org/10.2514/6.2008‐6438), relies on a collection of space weather solar drivers as inputs. Currently, these drivers rely on a linear forecasting algorithm, which supplies single point forecasts for 6 days. No current methods exist for providing probabilistic forecasts and uncertainty estimates for three of the drivers. In this work, we introduce a machine learning approach which provides a probabilistic forecast of all solar drivers used by JB2008, (https://doi.org/10.2514/6.2008‐6438). The new approach uses a combination of individual predictions, which can be combined to produce less error than the current operational method. This new approach provides improvement over single point forecasting made by the operational method and provides a measure of confidence in the forecasted values. Key Points: A new striped sampling approach is developed to achieve improved performance on limited dataEnsemble methods show promise for short term forecasting of JB2008 solar drivers and provide robust and reliable uncertainty estimatesStacked neural network ensemble methods provide the best short‐term solar driver forecasts [ABSTRACT FROM AUTHOR]

Space 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. Plain Language Summary: F10.7 is a radio wave measurement that closely follows solar activity. Increased solar activity can cause heating and density changes in the Earth's upper atmosphere. These density changes directly affect the drag force felt by satellites and can alter their orbit. In order to better predict the upper atmosphere density and paths taken by these spacecraft, we need to increase our prediction skills of F10.7. In this work, we use machine learning techniques to make a set of forecasts of F10.7 that can be combined to provide less error than currently used forecasting methods. Forecasting through these ensemble methods outperform a commonly used operational method. In addition, this set of predictions can be used to determine a level of confidence in the forecasts. Key Points: Ensemble methods show promise for short term forecasting of F10.7 and are able to provide robust and reliable uncertainty estimatesNeural network (non‐linear) methods provide better short term forecasting than linear auto regressive methodsAddition of input data by backwards averaging or varying lookback window improves model performance [ABSTRACT FROM AUTHOR]

The geospace environment is volatile and highly driven. Space weather has effects on Earth's magnetosphere that cause a dynamic and enigmatic response in the thermosphere, particularly on the evolution of neutral mass density. Many models exist that use space weather drivers to produce a density response, but these models are typically computationally expensive or inaccurate for certain space weather conditions. In response, this work aims to employ a probabilistic machine learning (ML) method to create an efficient surrogate for the Thermosphere Ionosphere Electrodynamics General Circulation Model (TIE‐GCM), a physics‐based thermosphere model. Our method leverages principal component analysis to reduce the dimensionality of TIE‐GCM and recurrent neural networks to model the dynamic behavior of the thermosphere much quicker than the numerical model. The newly developed reduced order probabilistic emulator (ROPE) uses Long‐Short Term Memory neural networks to perform time‐series forecasting in the reduced state and provide distributions for future density. We show that across the available data, TIE‐GCM ROPE has similar error to previous linear approaches while improving storm‐time modeling. We also conduct a satellite propagation study for the significant November 2003 storm which shows that TIE‐GCM ROPE can capture the position resulting from TIE‐GCM density with <5 km bias. Simultaneously, linear approaches provide point estimates that can result in biases of 7–18 km. Plain Language Summary: Space weather has effects on the near‐Earth environment that cause a dynamic response in the upper atmosphere. Many models exist that use space weather inputs to produce a density response, but these models require many resources and compute time or are inaccurate for certain conditions. In response, this work aims to employ a probabilistic (or statistical) machine learning method to create an efficient alternative for the Thermosphere Ionosphere Electrodynamics General Circulation Model (TIE‐GCM), a physics‐based upper‐atmosphere model. Our method leverages dimensionality reduction techniques for TIE‐GCM and recurrent neural networks to model the dynamic behavior of the upper atmosphere much quicker than the numerical model. The newly developed reduced order probabilistic emulator (ROPE) uses Long‐Short Term Memory neural networks to perform time‐series forecasting in the reduced state and provide distributions (or probabilities) for future density. We show that across the available data, TIE‐GCM ROPE has similar error to previous linear approaches while improving storm‐time modeling. We also conduct a satellite motion study for a significant storm which shows that TIE‐GCM ROPE can capture the position resulting from TIE‐GCM density with <5 km bias. Simultaneously, linear approaches provide point estimates that can result in biases of 7–18 km. Key Points: A Long‐Short Term Memory neural network (LSTM) ensemble is developed on Thermosphere Ionosphere Electrodynamics General Circulation Model mass density data as part of a reduced order probabilistic emulatorA hierarchical approach is used to capture uncertainty resulting from different aspects of LSTM modelingThe resulting ensemble outperforms linear methods during storms and functions well as an emulator for long‐term prediction [ABSTRACT FROM AUTHOR]

We present results from a study of the time lags between changes in the energy flow into the polar regions and the response of the thermosphere to the heating. Measurements of the neutral density from the Challenging Mini‐satellite Payload (CHAMP) and Gravity Recovery and Climate Experiment (GRACE) missions are used, along with calculations of the total Poynting flux entering the poles. During two major geomagnetic storms in 2003, these data show increased densities are first seen on the dayside edge of the auroral ovals after a surge in the energy input. At lower latitudes, the densities reach their peak values on the dayside earlier than on the night side. A puzzling response seen in the CHAMP measurements during the November 2003 storm was that the density at a fixed location near the "Harang discontinuity" remained at unusually low levels during three sequential orbit passes, while elsewhere the density increased. The entire database of measurements from the CHAMP and GRACE missions were used to derive maps of the density time lags across the globe. The maps show a large gradient between short and long time delays between 60° and 30° geographic latitude. They confirm the findings from the two storm periods, that near the equator, the density on the dayside responds earlier than on the nightside. The time lags are longest near 18–20 hr local time. The time lag maps could be applied to improve the accuracy of empirical thermosphere models, and developers of numerical models may find these results useful for comparisons with their calculations. Plain Language Summary: The interaction of the solar wind with the Earth's magnetosphere causes varying levels of heating in the ionosphere. This heating is produced by auroral currents at high latitudes, which in turn causes the density of the upper atmosphere to change. A topic of importance is to determine how rapidly the density can increase at different locations around the globe following a surge in the heating, which can be calculated from measurements of the solar wind velocity and embedded magnetic fields. This study used measurements of the atmospheric density on two satellite missions known as Challenging Mini‐satellite Payload and Gravity Recovery and Climate Experiment. The results show that the density increases first near the poles, and much longer at lower latitudes, as expected. The time lags between changes in the energy input and the density response have been determined for the first time on a global scale. Maps of the time lags are derived. Near the equator the lags are shorter near local noon, and longer before local midnight. The time lag maps can used to improve empirical and numerical models of the thermosphere. More accurate models are needed for more precise predictions of the drag that satellites will encounter, and the subsequent changes in their orbits. Key Points: Results show the time lags between auroral energy input and neutral density response, and how these lags vary across the globeLag times are lowest in the polar regions, as expected, since this is where the heating occursNear the equator the dayside responds earlier than on the nightside, and time lags are the longest near 18–20 hr local time [ABSTRACT FROM AUTHOR]

The Mass Spectrometer and Incoherent Scatter radar (MSIS) model family has been developed and improved since the early 1970's. The most recent version of MSIS is the Naval Research Laboratory (NRL) MSIS 2.0 empirical atmospheric model. NRLMSIS 2.0 provides species density, mass density, and temperature estimates as function of location and space weather conditions. MSIS models have long been a popular choice of thermosphere model in the research and operations community alike, but—like many models—does not provide uncertainty estimates. In this work, we develop an exospheric temperature model based in machine learning that can be used with NRLMSIS 2.0 to calibrate it relative to high‐fidelity satellite density estimates directly through the exospheric temperature parameter. Instead of providing point estimates, our model (called MSIS‐UQ) outputs a distribution which is assessed using a metric called the calibration error score. We show that MSIS‐UQ debiases NRLMSIS 2.0 resulting in reduced differences between model and satellite density of 25% and is 11% closer to satellite density than the Space Force's High Accuracy Satellite Drag Model. We also show the model's uncertainty estimation capabilities by generating altitude profiles for species density, mass density, and temperature. This explicitly demonstrates how exospheric temperature probabilities affect density and temperature profiles within NRLMSIS 2.0. Another study displays improved post‐storm overcooling capabilities relative to NRLMSIS 2.0 alone, enhancing the phenomena that it can capture. Plain Language Summary: Uncertainty quantification (UQ) in modeling can be thought of as providing a range of values that can contain a solution as opposed to only providing a point estimate. UQ is currently not common‐place when it comes to atmospheric modeling even while we use imperfect models. One of the most commonly used atmospheric model families is the Mass Spectrometer and Incoherent Scatter radar (MSIS) series. The current iteration in the series is the Naval Research Laboratory (NRL) MSIS 2.0 empirical atmosphere model. NRLMSIS 2.0 provides estimates of multiple atmospheric constituents and temperature which have a wide array of applications. Using data derived from satellite sensors, we develop a model called MSIS‐UQ that predicts a parameter (exospheric temperature) which can be input to NRLMSIS 2.0 to provide calibrated estimates. Furthermore, MSIS‐UQ predicts a distribution of temperatures as opposed to a point estimate. We show how the MSIS‐UQ temperature predictions improve NRLMSIS 2.0 estimates of density by 25% and explore the usefulness of the uncertainty estimation capabilities of the model. We also perform a study where the magnetic model drivers are varied to investigate evidence of atmospheric overcooling after strong storms. Key Points: A global exospheric temperature model with uncertainty estimation capabilities is developed for NRLMSIS 2.0—called MSIS‐UQMSIS‐UQ provides an avenue to obtain calibrated uncertainty estimates from NRLMSIS 2.0 density predictionsMSIS‐UQ allows for NRLMSIS 2.0 to capture effects of post‐storm thermospheric overcooling [ABSTRACT FROM AUTHOR]

Machine learning (ML) models are universal function approximators and—if used correctly—can summarize the information content of observational data sets in a functional form for scientific and engineering applications. A benefit to ML over parametric models is that there are no a priori assumptions about particular basis functions which can potentially limit the phenomena that can be modeled. In this work, we develop ML models on three data sets: the Space Environment Technologies High Accuracy Satellite Drag Model (HASDM) density database, a spatiotemporally matched data set of outputs from the Jacchia‐Bowman 2008 Empirical Thermospheric Density Model (JB2008), and an accelerometer‐derived density data set from CHAllenging Minisatellite Payload (CHAMP). These ML models are compared to the Naval Research Laboratory Mass Spectrometer and Incoherent Scatter radar (NRLMSIS 2.0) model to study the presence of post‐storm cooling in the middle‐thermosphere. We find that both NRLMSIS 2.0 and JB2008‐ML do not account for post‐storm cooling and consequently perform poorly in periods following strong geomagnetic storms (e.g., the 2003 Halloween storms). Conversely, HASDM‐ML and CHAMP‐ML do show evidence of post‐storm cooling indicating that this phenomenon is present in the original data sets. Results show that density reductions up to 40% can occur 1–3 days post‐storm depending on the location and strength of the storm. Plain Language Summary: Machine learning (ML) models are valuable universal function approximators and—if used correctly—can provide scientific information related to the data set used for fitting. A benefit to ML over other common models is that there are no background functions limiting what phenomena it can represent. In this work, we develop ML models on three data sets: the Space Environment Technologies High Accuracy Satellite Drag Model (HASDM) density database, a spatiotemporally matched data set of outputs from the Jacchia‐Bowman 2008 Empirical Thermospheric Density Model (JB2008), and an accelerometer‐derived density data set from CHAllenging Minisatellite Payload (CHAMP). These ML models are compared to the Naval Research Laboratory Mass Spectrometer and Incoherent Scatter radar (NRLMSIS 2.0) model to study the presence of post‐storm cooling in the upper atmosphere. We find that both NRLMSIS 2.0 and JB2008‐ML do not account for post‐storm cooling and perform poorly in periods following strong geomagnetic storms. Conversely, HASDM‐ML and CHAMP‐ML do show evidence of post‐storm cooling indicating that this phenomenon is present in the original data sets. Key Points: Machine learning is used to develop models from unique density data setsWe compared model predictions along the CHAllenging Minisatellite Payload (CHAMP) orbit during the 2003 Halloween stormsWe find that models developed on CHAMP and High Accuracy Satellite Drag Model density data can capture density depletion in the post‐storm period [ABSTRACT FROM AUTHOR]

A thermospheric neutral mass density model with robust and reliable uncertainty estimates is developed based on the Space Environment Technologies (SET) High Accuracy Satellite Drag Model (HASDM) density database. This database, created by SET, contains 20 years of outputs from the U.S. Space Force's HASDM, which currently represents the state of the art for density and drag modeling. We utilize principal component analysis for dimensionality reduction, which creates the coefficients upon which nonlinear machine‐learned (ML) regression models are trained. These models use three unique loss functions: Mean square error (MSE), negative logarithm of predictive density (NLPD), and continuous ranked probability score. Three input sets are also tested, showing improved performance when introducing time histories for geomagnetic indices. These models leverage Monte Carlo dropout to provide uncertainty estimates, and the use of the NLPD loss function results in well‐calibrated uncertainty estimates while only increasing error by 0.25% (<10% mean absolute error) relative to MSE. By comparing the best HASDM‐ML model to the HASDM database along satellite orbits, we found that the model provides robust and reliable density uncertainties over diverse space weather conditions. A storm‐time comparison shows that HASDM‐ML also supplies meaningful uncertainty estimates during extreme geomagnetic events. Plain Language Summary: An upper‐atmospheric density model with robust and reliable uncertainty estimates is developed based on the Space Environment Technologies High Accuracy Satellite Drag Model (HASDM) density database. This database contains 20 years of outputs from HASDM, which represents the state of the art for density and drag modeling. We use a decomposition tool called principal component analysis to reduce the dimensionality of the data set. Three loss functions, mean square error, negative logarithm of predictive density (NLPD), and continuous ranked probability score, are tested with three input sets to identify the best‐performing model. We optimize nine models (all three loss functions and input sets) and compare the prediction accuracy and the reliability of its uncertainty estimates. The models leverage Monte Carlo dropout to generate probabilistic outputs from which we extract model uncertainty. We find that using an input set containing a time series for the geomagnetic indices results in the most accurate models. In addition, the model using these inputs with the NLPD loss function has sufficient performance (approximately 10% absolute error) and the most calibrated/reliable uncertainty estimates on independent data. We test this model's uncertainty capabilities in the density space along satellite orbits from 2002 to 2010 showing the model's reliability across diverse space weather conditions. Key Points: Thermosphere model based on High Accuracy Satellite Drag Model (HASDM) outputs is developed with robust and reliable uncertainty estimatesHASDM‐ML provides predictions with approximately 10% error relative to HASDM database across 20 years of available historical dataGaussian loss function provides model with well‐calibrated uncertainty estimates across diverse space weather conditions [ABSTRACT FROM AUTHOR]

The community has leveraged satellite accelerometer data sets in previous years to estimate neutral mass density and exospheric temperatures. We utilize derived temperature data and optimize a nonlinear machine‐learned (ML) regression model to improve upon the performance of the linear EXospheric TEMPeratures on a PoLyhedrAl gRid (EXTEMPLAR) model. The newly developed EXTEMPLAR‐ML model allows for exospheric temperature predictions at any location with one model and provides performance improvements over its predecessor. We achieve reductions in mean absolute error of 2 K on an independent test set while providing similar error standard deviation values. Comparing the performance of both EXTEMPLAR models and the Naval Research Laboratory Mass Spectrometer and Incoherent Scatter radar Extended model (NRLMSISE‐00) across different solar and geomagnetic activity levels shows that EXTEMPLAR‐ML has the lowest mean absolute error across 80% of conditions tested. A study for spatial errors demonstrated that at all grid locations, EXTEMPLAR‐ML has the lowest mean absolute error for over 60% of the polyhedral grid cells on the test set. Like EXTEMPLAR, our model's outputs can be utilized by NRLMSISE‐00 (exclusively) to more closely match satellite accelerometer‐derived densities. We conducted 10 case studies where we compare the accelerometer‐derived temperature and density estimates from four satellites to NRLMSISE‐00, EXTEMPLAR, and EXTEMPALR‐ML during major storm periods. These comparisons show that EXTEMPLAR‐ML generally has the best performance of the three models during storms. We use principal component analysis on EXTEMPLAR‐ML outputs to verify the physical response of the model to its drivers. Plain Language Summary: Density in the upper atmosphere is highly variable and difficult to model. Empirical density models often rely on temperature profile predictions to determine species and mass densities. One of three key parameters in determining the temperature profiles is the asymptotic value at the top of the thermosphere called the exospheric temperature. By using temperatures derived from satellite acceleration measurements, we develop a machine‐learned global temperature model called EXospheric TEMPeratures on a PoLyhedrAl gRid Machine Learned (EXTEMPLAR‐ML). We achieve a 2 K reduction in mean absolute error on the independent test set relative to the model's predecessor. Additional analyses showed that EXTEMPLAR‐ML was more accurate than linear EXTEMPLAR across a majority of conditions and grid locations. We also look at temperatures and densities along satellite orbits during 10 major geomagnetic storms from the 21st century. In this study, we see major improvements over a significant empirical model called NRLMSISE‐00 and the linear predecessor to EXTEMPLAR‐ML. We leveraged a mathematical decomposition tool on the model outputs to assess its internal formulation. This shows that EXTEMPLAR‐ML is most heavily driven by solar activity and the seasons. Key Points: We develop a nonlinear global model for exospheric temperature prediction called EXospheric TEMPeratures on a PoLyhedrAl gRid Machine Learned (EXTEMPLAR‐ML)We leverage principal component analysis to improve our understanding of the EXTEMPLAR‐ML temperature formulationEXTEMPLAR‐ML shows increased accuracy relative to satellite observations across a majority of conditions, locations, and during geomagnetic storms [ABSTRACT FROM AUTHOR]

The EXospheric TEMperatures on a PoLyhedrAl gRid (EXTEMPLAR) method predicts the neutral densities in the thermosphere. The performance of this model has been evaluated through a comparison with the Air Force High Accuracy Satellite Drag Model (HASDM). The Space Environment Technologies (SET) HASDM database that was used for this test spans the 20 years 2000 through 2019, containing densities at 3 hr time intervals at 25 km altitude steps, and a spatial resolution of 10° latitude by 15° longitude. The upgraded EXTEMPLAR that was tested uses the newer Naval Research Laboratory MSIS 2.0 model to convert global exospheric temperature values to neutral density as a function of altitude. The revision also incorporated time delays that varied as a function of location, between the total Poynting flux in the polar regions and the exospheric temperature response. The density values from both models were integrated on spherical shells at altitudes ranging from 200 to 800 km. These sums were compared as a function of time. The results show an excellent agreement at temporal scales ranging from hours to years. The EXTEMPLAR model performs best at altitudes of 400 km and above, where geomagnetic storms produce the largest relative changes in neutral density. In addition to providing an effective method to compare models that have very different spatial resolutions, the use of density totals at various altitudes presents a useful illustration of how the thermosphere behaves at different altitudes, on time scales ranging from hours to complete solar cycles. Plain Language Summary: A recently developed computer model predicts the mass density of atoms and molecules in upper atmosphere, in the region known as the thermosphere. Changes in this "neutral density" following geomagnetic storms can perturb the orbits of the many satellites in this region, leading to imprecise knowledge of their paths and risk of collisions. This model uses measurements of the solar wind and the embedded magnetic field to predict the level of heating in the upper atmosphere, and the resulting expansion of the atmosphere to higher altitudes. In order to test the capabilities of the new model, its calculations were compared with density values derived by an Air Force data assimilation system based on radar tracking of multiple objects in Earth orbit over a 20‐year period. The results of this comparison show an excellent agreement, particularly at the higher altitudes where geomagnetic storms have the greatest influence. Key Points: Thermosphere neutral densities from the EXospheric TEMperatures on a PoLyhedrAl gRid (EXTEMPLAR) model are compared with the SET HASDM density database for a 20 year time periodThe use of mean densities on spherical shells at several altitudes is an effective way to compare the modelsThe EXTEMPLAR model performs well at altitudes of 400 km and above where geomagnetic storms produce the largest changes in neutral density [ABSTRACT FROM AUTHOR]

The High Accuracy Satellite Drag Model (HASDM) is the operational thermospheric density model used by the US Space Force Combined Space Operations Center. By using real‐time data assimilation, HASDM can provide density estimates with increased accuracy over other empirical models. With historical HASDM density data being released publicly for the first time, we can analyze the data to compare dominant modes of variability in the upper atmosphere as modeled by HASDM and the Jacchia‐Bowman 2008 Empirical Thermospheric Density Model (JB2008), a Jacchia family model upon which density corrections are made as a part of the HASDM framework. This model comparison is conducted through the use of principal component analysis (PCA) which shows the increased variability of the HASDM dataset. We highlight HASDM's ability to capture the movement of lighter species during solar minimum conditions, unlike many empirical models. We then compare density from both models to the CHAllenging Minisatellite Payload (CHAMP) and Gravity Recovery and Climate Experiment (GRACE) accelerometer‐derived density estimates. This comparison shows that HASDM more closely matches the accelerometer‐derived densities with mean absolute differences of 30.93% compared to CHAMP and GRACE‐A, respectively. The comparison also reveals improved representation of cooling mechanisms due to NO and CO2 by the HASDM database. Plain Language Summary: Many density models for the upper atmosphere have been developed using data from various sources to fit parametric equations. These are classified as empirical models which make up a large portion of those used in operations. While they are generally reliable, there are conditions where their accuracy falls short, such as during geomagnetic storms or during periods of low solar activity. The High Accuracy Satellite Drag Model (HASDM) uses observations from calibration satellites to make real‐time corrections (a process known as Dynamic Calibration of the Atmosphere) to density outputs from an empirical model, making it far more robust. In this paper, we analyze a 20 year dataset of HASDM outputs and compare it the baseline JB2008 model, upon which data is assimilated. By leveraging a mathematical tool called principal component analysis, we identify features in the HASDM dataset that are not modeled by JB2008, such as the movement of lighter species during solar minimum conditions. We also perform a case study where we compare both model outputs to high‐fidelity density observations from different satellites during two unique periods. Through this comparison, we find evidence that the HASDM dataset captures the effects of NO and CO2 cooling mechanisms. Key Points: We conduct principal component analysis of High Accuracy Satellite Drag Model (HASDM) and JB2008 database covering almost two solar cyclesHASDM models the movement of lighter species during solar minimum conditionsHASDM exhibits the ability to capture/model NO and CO2 cooling mechanisms [ABSTRACT FROM AUTHOR]

The SET HASDM density database is available for scientific studies through a SQL database with open community access. The information in the SET HASDM density database covers the period from January 1, 2000 through December 31, 2019. Data records exist every 3 h during solar cycles 23 and 24. The database has a grid size of 10° × 15° (latitude, longitude) with 25 km altitude steps between 175 and 825 km. A description of the source of the database, its validation, its information content, and its accessibility are provided. Plain Language Summary: The open community access SET HASDM density database is available for scientific studies. The database provides thermospheric densities covering the period from January 1, 2000 through December 31, 2019. Data records exist every 3 h during solar cycles 23 and 24. The database grid size is 10° latitude × 15° longitude with 25 km altitude steps between 175 and 825 km. Key Points: SET HASDM density database is available for scientific studiesData covers solar cycles 23 and 24 with 3 h time steps from 175 to 825 km in 25 km altitude steps and 10 × 15° latitude, longitude binsSET HASDM database densities are suitable for use as a new space weather benchmark against which space weather events are measured [ABSTRACT FROM AUTHOR]

Space weather indices are commonly used to drive operational forecasts of various geospace systems, including the thermosphere for mass density and satellite drag. The drivers serve as proxies for various processes that cause energy flow and deposition in the geospace system. Forecasts of neutral mass density are a major uncertainty in operational orbit prediction and collision avoidance for objects in low Earth orbit (LEO). For the strongly driven system, accuracy of space weather driver forecasts is crucial for operations. The High Accuracy Satellite Drag Model (HASDM) currently employed by the U.S. Air Force in an operational environment is driven by four solar and two geomagnetic proxies. Space Environment Technologies (SET) is contracted by the space command to provide forecasts for the drivers. This work performs a comprehensive assessment for the performance of the driver forecast models. The goal is to provide a benchmark for future improvements of the forecast models. Using an archived data set spanning 6 years and 15,000 forecasts across Solar Cycle 24, we quantify the temporal statistics of the model performance. Key Points: Four solar (F10.7, S10.7, M10.7, and Y10.7) and two geomagnetic (ap and Dst) driver indices are used as inputs by the operational HASDM systemTemporal statistics using 6 years of historical data for driver forecasts are developedBaseline for future developments within the community are provided [ABSTRACT FROM AUTHOR]

Mass density variations can deviate from the expected behavior caused by temperature due to changes in the composition. Such deviations can be especially significant during solar minimum conditions. Model‐data differences are typically resolved through temperature corrections while overlooking the role of errors in lower boundary composition. In this work, we use a data‐driven methodology to simultaneously estimate thermosphere composition and temperature contributions to model‐data differences. The methodology uses modal decomposition to extract high‐dimensional, reduced order basis functions for the covariance of the neutral thermospheric species and temperature. The extracted basis functions are combined with CHAllenging Minisatellite Payload and Gravity Recovery And Climate Experiment mass density measurements using a nonlinear least squares solver. We demonstrate the methodology using the Naval Research Laboratory's empirical Mass Spectrometer and Incoherent Scatter (MSIS) model to derive the high‐dimensional basis functions. We characterize and quantify the contribution of temperature and lower boundary effects with oxygen and helium since the two species have a direct impact on drag and orbit prediction through gas‐surface interactions and mass density. We analyze the month of December in 2008, based on the work of Thayer et al. (2012), and estimate that lower boundary composition errors contribute approximately 50% of the model‐data differences. Key Points: Developed methodology for simultaneously inferring thermosphere composition and temperature corrections based on high‐dimensional modal analysisEstimated high‐dimensional state for self‐consistent calibration via ingestion of CHAMP/GRACE mass density measurementsQuantified the contribution of lower boundary composition (50%) and temperature (50%) to model‐data differences during December 2008 [ABSTRACT FROM AUTHOR]

Abstract: Accurate specification and prediction of the ionosphere‐thermosphere environment, driven by external forcing, is crucial to the space community. In this work, we present a new transformative framework for data assimilation and calibration of the physical ionosphere‐thermosphere models. The framework has two main components: (i) the development of a quasi‐physical dynamic reduced‐order model (ROM) that uses a linear approximation of the underlying dynamics and effect of the drivers, and (ii) data assimilation and calibration of the ROM through estimation of the ROM coefficients that represent the model parameters. A reduced‐order surrogate for thermospheric mass density from the Thermosphere‐Ionosphere‐Electrodynamics General Circulation Model (TIE‐GCM) was developed in previous work. This work concentrates on the second component of the framework—data assimilation and calibration of the TIE‐GCM ROM. The new framework has two major advantages: (i) a dynamic ROM that combines the speed of empirical models for real‐time capabilities with the predictive capabilities of physical models, which has the potential to facilitate improved uncertainty quantification using large ensembles, and (ii) estimation of model parameters rather than the driver(s)/input(s), which allows calibration of the model, thus avoiding degradation of model performance in the absence of continuous data. We demonstrate and validate the framework using simulated and real measurement scenarios. The simulated case uses Mass Spectrometer and Incoherent Scatter model output as measurements, while the real data case uses accelerometer‐derived density estimates from CHAllenging Minisatellite Payload and Gravity Field and Steady‐State Ocean Circulation Explorer. The framework is a first of its kind, simple yet robust and accurate method with high potential for providing real‐time operational updates to the state of the upper atmosphere in the context of drag modeling for space situational awareness and space traffic management. [ABSTRACT FROM AUTHOR]

Debris objects such as rocket bodies can pose a threat to active space assets in orbit and to assets and humans on the ground through reentry. Orbit and reentry predictions for low-perigee resident space objects are strongly influenced by atmospheric drag. Such predictions are typically performed using fixed or fitted drag/ballistic coefficients that can result in large prediction errors. Accurate drag coefficients require, among other things, knowledge of the attitude. This paper develops an approach to compute accurate drag coefficients for debris objects toward accurate orbit and reentry predictions. The method uses a nonlinear least-squares estimator to estimate the attitude and angular velocities using light curves for debris objects with known shape models. This paper focuses on rocket bodies in particular. The estimated attitude and angular velocities are then used to compute the drag coefficients using a flat-plate panel method. The technique is validated using simulated data scenarios with a number of representative rocket body models. Good performance is observed for the developed approach. Results show that neglecting attitude variations for resident space objects in highly elliptic orbits can result in orbit errors of more than 100 km after just ten brief passes through the atmosphere. [ABSTRACT FROM AUTHOR]

Abstract: Thermospheric mass density is a major driver of satellite drag, the largest source of uncertainty in accurately predicting the orbit of satellites in low Earth orbit (LEO) pertinent to space situational awareness. Most existing models for thermosphere are either physics based or empirical. Physics‐based models offer the potential for good predictive/forecast capabilities but require dedicated parallel resources for real‐time evaluation and data assimilative capabilities that are still under development. Empirical models are fast to evaluate but offer very limited forecasting abilities. This paper presents methodology for developing a reduced order dynamic model from high‐dimensional physics‐based models by capturing the underlying dynamical behavior. The quasi‐physical reduced order model for thermospheric mass density is developed using a large dataset of Thermosphere‐Ionosphere‐Electrodynamics General Circulation Model (TIE‐GCM) simulations spanning 12 years and covering a complete solar cycle. Toward this end, a new reduced order modeling approach, based on dynamic mode decomposition with control that uses the Hermitian space of the problem to derive the dynamic and input matrices in a tractable manner is developed. Results show that the reduced order model performs well in serving as a reduced order surrogate for TIE‐GCM while almost always maintaining the forecast error to within 5% of the simulated densities after 24 hrs. [ABSTRACT FROM AUTHOR]

Atmospheric drag is the largest source of uncertainty in accurately predicting the orbit of satellites in low Earth orbit (LEO). Accurately predicting drag for objects that traverse LEO is critical to space situational awareness. Atmospheric models used for orbital drag calculations can be characterized either as empirical or physics-based (first principles based). Empirical models are fast to evaluate but offer limited real-time predictive/forecasting ability, while physics based models offer greater predictive/forecasting ability but require dedicated parallel computational resources. Also, calibration with accurate data is required for either type of models. This paper presents a new methodology based on proper orthogonal decomposition toward development of a quasi-physical, predictive, reduced order model that combines the speed of empirical and the predictive/forecasting capabilities of physics-based models. The methodology is developed to reduce the high dimensionality of physics-based models while maintaining its capabilities. We develop the methodology using the Naval Research Lab's Mass Spectrometer Incoherent Scatter model and show that the diurnal and seasonal variations can be captured using a small number of modes and parameters. We also present calibration of the reduced order model using the CHAMP and GRACE accelerometer-derived densities. Results show that the method performs well for modeling and calibration of the upper atmosphere. [ABSTRACT FROM AUTHOR]

Drag coefficient is a major source of uncertainty in calculating the aerodynamic forces on satellites in low Earth orbit. Closed-form solutions are available for simple geometries under the assumption of free molecular flow; however, most satellites have complex geometries, and a more sophisticated method of calculating the drag coefficient is needed. This work builds toward modeling physical drag coefficients using the direct simulation Monte Carlo method capable of accurately modeling flow shadowing and concave geometries. The direct simulation three-dimensional visual program and the direct simulation Monte Carlo analysis code are used to compare the effects of two separate gas-surface interaction models: diffuse reflection with incomplete accommodation and quasi-specular Cercignani-Lampis-Lord models. Results show that the two gas-surface interaction models compare well at altitudes below ~500 km during solar maximum conditions and below ~400 km during solar minimum conditions. The difference in drag coefficient of a sphere at ~800 km calculated using the two gas-surface interaction models is ~6% during solar maximum and increases to ~10% during solar minimum. The difference in drag coefficient of the GRACE satellite computed using the two gas-surface interaction models at ~500 km differs by ~15% during solar minimum conditions and by ~2-3 % during solar maximum conditions. [ABSTRACT FROM AUTHOR]