Summary Improving Thermospheric Neutral Density (TND) estimates is important for computing drag forces acting on Low-Earth-Orbit (LEO) satellites and debris. Empirical thermospheric models are often used to compute TNDs for the precise orbit determination experiments. However, it is known that simulating TNDs are of limited accuracy due to simplification of model structure, coarse sampling of model inputs, and dependencies to the calibration period. Here, we apply TND estimates from accelerometer measurements of the Challenging Minisatellite Payload (CHAMP) and the Gravity Recovery and Climate Experiment (GRACE) missions as observations to improve the NRLMSISE-00 model, which belongs to the Mass Spectrometer and Incoherent Scatter (MSIS) family of models. For this, a novel simultaneous Calibration and Data Assimilation (C/DA) technique is implemented that uses the Ensemble Kalman Filter (EnKF) and the Ensemble Square-Root Kalman Filter (EnSRF) as merger. The application of C/DA is unique because it modifies both model-derived TNDs, as well as the selected model parameters. The calibrated parameters derived from C/DA are then used to predict TNDs in locations that are not covered by CHAMP and GRACE orbits, and forecasting TNDs of the next day. The C/DA is implemented using daily CHAMP- and/or GRACE-TNDs, for which compared to the original model, we find 27% and 62% reduction of misfit between model and observations in terms of Root Mean Square Error (RMSE) and Nash Coefficient, respectively. These validations are performed using the observations along the orbital track of the other satellite that is not used in the C/DA during 2003 with various solar activity. Comparisons with another empirical model, i.e., Jacchia-Bowman 2008, indicate that the C/DA results improve these quality measurements on an average range of 50% and 60%, respectively.

Global estimation of thermospheric neutral density (TND) on various altitudes is important for geodetic and space weather applications. This is typically provided by models, however, the quality of these models is limited due to their imperfect structure and the sensitivity of their parameters to the calibration period. Here, we present an ensemble Kalman filter (EnKF)-based calibration and data assimilation (C/DA) technique that updates the model’s states and simultaneously calibrates its key parameters. Its application is demonstrated using the TND estimates from on-board accelerometer measurements, e.g., those of the Gravity Recovery and Climate Experiment (GRACE) mission (at $$\sim 410$$ ∼ 410 km altitude), as observation, and the frequently used empirical model NRLMSISE-00. The C/DA is applied here to re-calibrate the model parameters including those controlling the influence of solar radiation and geomagnetic activity as well as those related to the calculation of exospheric temperature. The resulting model, called here ‘C/DA-NRLMSISE-00’, is then used to now-cast TNDs and individual neutral mass compositions for 3 h, where the model with calibrated parameters is run again during the assimilation period. C/DA-NRLMSISE-00 is also used to forecast the next 21 h, where no new observations are introduced. These forecasts are unique because they are available globally and on various altitudes (300–600 km). To introduce the impact of the thermosphere on estimating ionospheric parameters, the coupled physics-based model TIE-GCM is run by replacing the O2, O1, He and neutral temperature estimates of the C/DA-NRLMSISE-00. Then, the non-assimilated outputs of electron density (Ne) and total electron content (TEC) are validated against independent measurements. Assessing the forecasts of TNDs with those along the Swarm-A ($$\sim 467$$ ∼ 467 km), -B ($$\sim 521$$ ∼ 521 km), and -C ($$\sim 467$$ ∼ 467 km) orbits shows that the root-mean-square error (RMSE) is considerably reduced by 51, 57 and 54%, respectively. We find improvement of 30.92% for forecasting Ne and 26.48% for TEC compared to the radio occulation and global ionosphere maps (GIM), respectively. The presented C/DA approach is recommended for the short-term global multi-level thermosphere and enhanced ionosphere forecasting applications.

Ionospheric models are applied for computing the Total Electron Content (TEC) in ionosphere to reduce its effects on the Global Navigation Satellite System (GNSS)-based Standard Point Positioning (SPP) applications. However, the accuracy of these models is limited due to the simplified model structures and their dependency on the calibration period. In this study, we present a sequential Calibration approach based on the Ensemble Kalman Filter (C-EnKF) to improve TEC estimations. Its advantage, over the frequently implemented state-of-the-art, is that a short period of GNSS network measurements is needed to calibrate model parameters. To demonstrate the results, the International Reference Ionosphere (IRI)-2016 model is used as reference and the Vertical TEC (VTEC) estimates from 53 IGS stations in Europe are applied as observation. The C-EnKF is applied to calibrate four selected model parameters (i.e., IG 12 , U RSI(771), U RSI(1327) and U RSI(1752) related to the ionospheric activity as well as height and density peak-modelling in the F2 layer), which are identified by performing a sensitivity analysis. The calibrated model, called 'C-EnKF-IRI', is localized within Europe and can be used for near-real time TEC estimations and forecasting of the next day (at least). Validation against the dual frequency GNSS measurements of three

<p>Increasing the quality of ionosphere modeling is crucial and remains a challenge for many geodetic applications such as GNSS Precise Point Positioning (PPP) and navigation. Ionosphere models are the main tool to provide an estimation of Total Electron Content (TEC) to be corrected from GNSS career phase and pseudorange measurements. Skills of these models are however limited due to the simplifications in model equations and the imperfect knowledge of model parameters. In this study, an ionosphere reconstruction approach is presented, where global estimations of geodetic-based TEC measurements are combined with an ionospheric background model. This is achieved here through a novel simultaneous Calibration and Data Assimilation (C/DA) technique that works based on the sequential Ensemble Kalman Filter (EnKF). The C/DA method ingests the actual ionospheric measurements (derived from global GNSS measurements) into the IRI (International Reference Ionosphere) model. It also calibrates those parameters that control the F2 layer’s characteristics such as selected important CCIR (Comité Consultatif International des Radiocommunicationsand) URSI (International Union of Radio Science) coefficients.  The calibrated parameters derived from the C/DA are then replaced in the IRI to simulate TEC values in locations, where less GNSS ground-station infrastructure exists, as well as to enhance the prediction of TEC when the observations are not available or their usage is cautious due to low quality. Our numerical assessments indicate the advantage of the C/DA to improve the IRI’s performance. Values of the TEC-Root Mean Square of Error (RMSE) are found to be decreased by up to 30% globally, compared to the original IRI simulations. The importance of the new TEC estimations is demonstrated for PPP applications, whose results show improvements in navigation applications.</p><p><strong>Keywords: </strong>Ionosphere, Calibration and Data Assimilation (C/DA), IRI, Total Electron Content (TEC), Precise Point Positioning (PPP), GNSS</p>

<p>The response of the Ionosphere - Thermosphere (IT) system to severe storm conditions is of great importance to fully understand its coupling mechanisms. The challenge to represent the governing processes of the upper atmosphere depends, to a large extent, on an accurate representation of the true state of the IT system, that we obtain by assimilating relevant measurements into physics-based models. Thermospheric Mass Density (TMD) is the summation of total neutral mass within the atmosphere that is derived from accelerometer measurements of satellite missions such as CHAMP, GOCE, GRACE(-FO) and Swarm. TMD estimates can be assimilated into physics-based models to modify the state of the processes within the IT system. Previous studies have shown that this modification can potentially improve the simulations and predictions of the ionospheric electron density. These differences could also be interpreted as an indicator of the ionosphere-thermosphere interaction. The research presented here, aims to quantify the impact of data satellite based TMD assimilation on numerical model results.</p><p>Subject of this study is the Coupled Thermosphere-Ionosphere-Plasmasphere electrodynamics (CTIPe) physics-based model in combination with the recently developed Thermosphere-Ionosphere Data Assimilation (TIDA) scheme. TMD estimates from the ESA’s Swarm mission are assimilated in CTIPe-TIDA during the 16 to the 20 of March 2015. This period was characterized by a strong geomagnetic storm that triggered significant changes in the IT system, the so-called St. Patrick day storm 2015. To assess the changes in the IT system during storm conditions due to data assimilation, the model results from assimilating SWARM mass density normalized to the altitude of 400 km are compared to independent thermospheric estimates like GRACE-TMDS. In order to evaluate the impact of the data assimilation on the ionosphere, the corresponding output of electron density is compared to high-quality electron density estimates derived from data-driven model of the DGFI-TUM.</p>