Comparison of accelerometer data calibration methods used in thermospheric neutral density estimation

Ultra-sensitive space-borne accelerometers on board of low Earth orbit (LEO) satellites are used to measure non-gravitational forces acting on the surface of these satellites. These forces consist of the Earth radiation pressure, the solar radiation pressure and the atmospheric drag, where the first two are caused by the radiation emitted from the Earth and the Sun, respectively, and the latter is related to the thermospheric density. On-board accelerometer measurements contain systematic errors, which need to be mitigated by applying a calibration before their use in gravity recovery or thermospheric neutral density estimations. Therefore, we improve, apply and compare three calibration procedures: (1) a multi-step numerical estimation approach, which is based on the numerical differentiation of the kinematic orbits of LEO satellites; (2) a calibration of accelerometer observations within the dynamic precise orbit determination procedure and (3) a comparison of observed to modeled forces acting on the surface of LEO satellites. Here, accelerometer measurements obtained by the Gravity Recovery And Climate Experiment (GRACE) are used. Time series of bias and scale factor derived from the three calibration procedures are found to be different in timescales of a few days to months. Results are more similar (statistically significant) when considering longer timescales, from which the results of approach (1) and (2) show better agreement to those of approach (3) during medium and high solar activity. Calibrated accelerometer observations are then applied to estimate thermospheric neutral densities. Differences between accelerometer-based density estimations and those from empirical neutral density models, e.g., NRLMSISE-00, are observed to be significant during quiet periods, on average 22 % of the simulated densities (during low solar activity), and up to 28 % during high solar activity. Therefore, daily corrections are estimated for neutral densities derived from NRLMSISE-00. Our results indicate that these corrections improve model-based density simulations in order to provide density estimates at locations outside the vicinity of the GRACE satellites, in particular during the period of high solar/magnetic activity, e.g., during the St. Patrick's Day storm on 17 March 2015

Estimating and predicting corrections for empirical thermospheric models

Quantifying spatial and temporal changes in thermospheric neutral density is important for various applications such as precise orbit determination, estimating mission lifetime and re-entry prediction of Earth orbiting objects. It is also crucial for analysis of possible collisions between active satellite missions and space debris. Empirical models are frequently applied to estimate neutral densities at the position of satellites. But their accuracy is severely constrained by model simplifications and the sampling limitation of solar and geomagnetic indices used as inputs. In this study, we first estimate thermospheric neutral density by processing the high-accuracy accelerometer measurements on-board of the twin-satellite mission Gravity Recovery And Climate Experiment (GRACE). Daily density corrections (in terms of scales) are then computed for the commonly used NRLMSISE-00 empirical model. The importance of these daily scales is examined within an orbit determination practice. Finally, three data-driven prediction techniques based on Artificial Neural Network (ANN) are applied to forecast the daily density corrections for few days to months. Our numerical results indicate that GRACE derived scales are correlated with solar and geomagnetic indices and can improve the timing (from few hours to days) and magnitude of model simulations (up to 10–100 times) during high solar or geomagnetic activity when they usually perform poorly. We found that the Non-linear Autoregressive with Exogenous (External) Input (NARX) ANN technique performs well in predicting the corrections with an average fit of 0.8 or more in terms of squared correlation coefficients for time-scales of 7–90 days

Forecasting global and multi-level thermospheric neutral density and ionospheric electron content by tuning models against satellite-based accelerometer measurements

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 ∼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 (∼467 km), -B (∼521 km), and -C (∼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

Preliminary Validation of Thermosphere Observations from the TOLEOS Project

OBSERVATIONS of upper atmospheric neutral mass density (NMD) and wind are critical to understand the coupling mechanisms between Earth’s ionosphere, thermosphere, and magnetosphere. The ongoing Swarm DISC (data, innovation, and science cluster) project TOLEOS (thermosphere observations from low-Earth orbiting satellites) aims to provide better calibrated NMD and crosswind data from CHAMP, GRACE, and GRACE-FO (follow-on) satellite missions. The project uses state-of-the-art models, calibration techniques, and processing standards to improve the accuracy of these data products and ensure inter-mission consistency. Here, we present preliminary results of the quality of the data in comparison to the high accuracy drag temperature model DTM2020, and physics-based TIE-GCM (thermosphere ionosphere electrodynamics general circulation model) and CTIPe (coupled thermosphere ionosphere plasmasphere electrodynamics) models

TOLEOS: Thermosphere Observations from Low-Earth Orbiting Satellites

The objective of the TOLEOS project is to process the CHAMP, GRACE, and GRACE-FO accelerometer measurements with improved processing standards to obtain thermosphere density and crosswind data products. These new data products will cover the entirety of the accelerometer missions and complement the existing ESA databases for Swarm and GOCE. The improvements in the processing focus on the radiation pressure modelling, which is expected to have a significant effect on the density and crosswind data, in particular at altitudes above 450 km during solar minimum conditions. Substantial validation activities are performed since the project’s start in June 2021 and will continue until the end of the project in July 2022

Ciceros Staatsschrift und die philosophische Tradition der Verfassungsdebatte bei Cassius Dio und Philostrat. Wiener Studien|Wiener Studien 129 129|

In the tradition of the political theory established by Plato and Aristotle Cicero asks for the best constitution and gives the answer in his work On the state. In a fictional dialogue, dated to the political crisis of the Gracchi in 129, Roman politicians led by Scipio Africanus come to the result that either the mixed constitution of the Roman republic or the monarchy is the best constitution for the Roman state. It is shown that with the form and contents of this fictional dialogue Cicero, in all probability, becomes the literary model for similar constitutional debates in the works of Cassius Dio and Philostrat

Alte Freunde im Gespräch: Anspruch und Wirklichkeit der amicitia bei Cicero - Old Friends in Conversation: Aspiration and Reality of Friendship in Cicero

What is the relationship between the idealised pair of amici Scipio and Laelius, as portrayed in Cicero’s Laelius, and the real-life pair of amici, Cicero and Atticus, which appear in the Letters? Was Cicero’s intention to use the character of Laelius in the treatise to voice his own views on friendship – a character whose name Cicero regularly borrows in his letters as a pseudonym? Can we see in the guidelines set down by Laelius in the dialogue a reflection of Cicero’s friendship with Atticus and with other political figures, influenced as these were by the social upheaval of the Late Republic? The article seeks to answer these questions through a parallel reading of the Laelius and a selection of Cicero’s Letters to Atticus. In so doing, I argue that key theoretical principles of the dialogue are based on Cicero’s and Atticus’ shared lived experiences, as Atticus himself was able to appreciate (Lael. 5, cuius tota disputatio est de amicitia, quam legens te ipse cognosces).   In welchem Verhältnis steht das ideale Freundespaar Scipio und Laelius in dem gleichnamigen Dialog Ciceros zu dem realen Freundespaar Cicero und Atticus, das uns aus den Briefen entgegentritt? Mochte Cicero seine Dialogfigur Laelius, deren Namen er in den Atticusbriefen für sich als Pseudonym wählte, als Sprachrohr nutzen, um eigene Gedanken über das Wesen der Freundschaft auszudrücken? Spiegeln sich in den von Laelius formulierten Gesetzen der Freundschaft Erfahrungen, die Cicero mit seinem Freund Atticus, aber wegen veränderter gesellschaftlicher Rahmenbedingungen in der späten Republik auch mit politischen Freunden gemacht hatte? Der Vergleich paralleler Stellen des Laelius und der Briefe an Atticus ergibt, dass zentrale Theoreme des Dialogs auch auf persönlich gefärbten Erfahrungen beruhen, die Cicero in seiner Freundschaft mit Atticus gemacht hatte, und Atticus sich daher, wie Cicero es ausdrückt (Lael.5, cuius tota disputatio est de amicitia, quam legens te ipse cognosces), bei der Lektüre des Dialogs über die Freundschaft auch selbst wiedererkennen konnte.   Qual’è il rapporto tra la coppia ideale di amici Scipione-Lelio, rappresentata nell’omonimo dialogo di Cicerone, e la coppia reale di amici Cicerone-Attico, che ci appare nelle Epistole? Era intenzione di Cicerone usare il personaggio di Lelio, il cui nome egli sceglie nelle lettere ad Attico come proprio pseudonimo, in qualità di portavoce dei propri pensieri all’intorno all’essenza dell’amicizia? Nelle leggi dell’amicizia formulate da Lelio si riflettono le esperienze che Cicerone aveva fatto sia con Attico, sia – a causa dei cambiamenti sociali verificatisi nell’età della tarda repubblica – con altri amici nella cerchia dei politici? Dal confronto tra passi paralleli del Laelius e delle lettere ad Attico risulta che teoremi centrali del dialogo si fondano anche su esperienze attinte dalle vicende personali che Cicerone aveva vissuto con Attico e nelle quali, come testimonia Cicerone (Lael. 5, cuius tota disputatio est de amicitia, quam legens te ipse cognosces), lo stesso Attico, leggendo il dialogo sull’amicizia, aveva potuto riconoscersi