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 thermosphere density model. The United States Air Force (USAF) operational High Accuracy Satellite Drag Model (HASDM), relies on JB2008, 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 approach providing an average CES of 5.63%, across all drivers.

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 CHAMP and 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 $60^{\circ}$ and $30^{\circ}$ 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 h 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.

We present a proof of concept for the probabilistic emulation of the Ring current-Atmosphere interactions Model with Self-Consistent magnetic field (RAM-SCB) particle flux. We extend the workflow developed by Licata and Mehta (2023) by applying it to the ring current and further developing its uncertainty quantification methodology. We introduce a novel approach for sampling over 20 years of solar and geomagnetic activity to identify 30 simulation periods, each one week long, to generate the training, validation, and test datasets. Large-scale physics-based simulation models for the ring current can be computationally expensive. This work aims at creating an emulator that is more efficient, capable of forecasting, and provides an estimate on the uncertainty of its predictions, all without requiring large computational resources. We demonstrate the emulation process on a subset of particle flux: a single energy channel of omnidirectional flux. A principal component analysis (PCA) is used for the dimensionality reduction into the reduced-space, and the dynamic modeling is performed with a recurrent neural network. A hierarchical ensemble of Long-Short Term Memory (LSTM) neural networks provides the statistics needed to produce a probabilistic output, resulting in a reduced-order probabilistic emulator (ROPE) that performs time-series forecasting of the ring current’s particle flux with an estimate on its uncertainty distribution. The resulting ROPE from this smaller subset of RAM-SCB particle flux provides dynamic predictions with errors less than 11% and calibration scores under 10%, demonstrating that this workflow can provide a probabilistic emulator with a robust and reliable uncertainty estimate when applied to the ring current.

The High Accuracy Satellite Drag Model (HASDM) is the operational thermospheric density model used by the US Space Force (USSF) Combined Space Operations Center (CSpOC). By using real-time data assimilation, HASDM can provide density estimates with increased accuracy over empirical models. With historical HASDM density data being released publicly for the first time, we can analyze the data to identify dominant modes of variations in the upper atmosphere. As HASDM is a close relative to the Jacchia-Bowman 2008 Empirical Thermospheric Density Model (JB2008), we look at time-matched density data to better understand the models’ characteristics. This model comparison is conducted through the use of Principal Component Analysis (PCA). We then compare both datasets to the CHAllenging Minisatellie Payload (CHAMP) and Gravity Recovery and Climate Experiment (GRACE) accelerometer-derived density estimates. By looking at the principal components and PCA scores from the two models, we confirm the increased complexity of the HASDM dataset while the CHAMP and GRACE comparisons show that HASDM more closely matches the accelerometer-derived densities with mean absolute differences of 23.81% and 30.84% compared to CHAMP and GRACE-A, respectively.

The EXospheric TEMeratures 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 hour time intervals at 25 km altitude steps, and a spatial resolution of 10 degrees latitude by 15 degrees 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.

Space traffic management is difficult. Monitoring and predicting the accurate, real-time position of satellites for collision avoidance in low earth orbit is an engineering challenge. The dominant source of error in satellite prediction tracking models is in the determination of space weather driven atmospheric drag. The High Accuracy Satellite Drag Model (HASDM) (Storz et al., 2005) was developed by the U.S. Air Force Space Command (AFSPC) between 2000–2005 to help solve this problem. It is a data assimilative modeling system using the JB2008 thermospheric density model (Bowman et al., 2008) plus continuously derived densities from several dozens of calibration satellites to achieve <5% density uncertainty at most epochs. The HASDM data is being made available to the community of scientists and operators for the first time. Under authority from the AFSPC, Space Environment Technologies (SET) has extracted two solar cycles of operational High Accuracy Satellite Drag Model (HASDM) data for scientific use and this is called the SET HASDM database. Navigating and extracting information from this database quickly and efficiently to manage satellite space traffic is currently complex and tedious. We present the development of a data-driven model for the HASDM mass density using Machine Learning and an attempt to quantify the associated uncertainties.

The community has leveraged satellite accelerometer datasets in previous years to estimate neutral mass density and subsequently exospheric temperatures. We utilize derived temperature data and optimize a nonlinear machine-learned (ML) regression model to improve upon the performance of the linear EXTEMPLAR (EXospheric TEMPeratures on a PoLyherdrAl gRid) model. The newly developed EXTEMPLAR-ML model allows for exospheric temperature predictions at any location with a single model and provides performance improvements over its predecessor. We achieve a 4.2 K reduction in mean absolute error and a 3.42 K reduction in the standard deviation of the error. Like EXTEMPLAR, our model’s outputs can be utilized by the Naval Research Laboratory Mass Spectrometer and Incoherent Scatter radar Extended (NRLMSISE-00) model to more closely match satellite accelerometer-derived densities. We conducted two case studies where we compare the CHAllenging Minisatellite Payload (CHAMP) and Gravity Recovery and Climate Experiment (GRACE) accelerometer-derived temperature and density estimates to NRLMSISE-00, EXTEMPLAR, and EXTEMPALR-ML during two major storm periods. The storm-time temperature comparison showed error reductions of 7-10% and 2-5% relative to NRLMSISE-00 and EXTEMPLAR, respectively, and the density comparison showed error reductions of 20-55% and 8-12%. We use Principal Component Analysis to identify the dominant modes of variability in the model over one solar cycle. This shows the model is dominantly driven by solar activity, and there is a strong latitudinal variation related to the Summer and Winter hemispheres.

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 hours during solar cycles 23 and 24. The database has a grid size of 10{degree sign} × 15{degree sign} (latitude, longitude) with 25 km altitude steps between 175-825 km. A description of the source of the database, its validation, its information content, and its accessibility are provided.

A high-resolution model of exospheric temperatures has been developed, with the objective of predicting the global values of exospheric temperatures with greater accuracy. From these temperatures, the neutral densities in the thermosphere can be calculated. This model is derived from measurements of the neutral densities on the CHAMP, GRACE, and Swarm satellites. These data were sorted into 1620, triangular cells on a spherical, polyhedral grid, using coordinates of geographic latitude and local solar time (longitude). A least-error fit of the data is used to obtain a separate set of regression coefficients for each grid cell. Several versions of model functions have been tested, using parameters such as the day-of-year, Universal Time, solar indices, and emissions from nitric oxide in the thermosphere, as measured with the SABER instrument on the TIMED satellite. Accuracy is improved with the addition of parameters that use the total Poynting flux flowing into the Northern and Southern hemispheres. This energy flux is obtained from the solar wind velocity and interplanetary magnetic, using an empirical model. Given a specific date, time, and other inputs, a global map of the exospheric temperature is obtained. These maps show significant variability in the polar regions, that are strongly modulated by the time-of-day, due to the rotation of the magnetic poles around the geographic pole. Values at specific locations are obtained using a triangular interpolation of these results. Comparisons of the exospheric temperatures from the model with neutral density measurements are shown to produce very good results.