Gravitational forces are the major forces acting on near-Earth orbiting (e.g., altimetry) satellites. We perform a review of Earth’s mean time-variable gravity (TVG) field models developed in the past 23 years (2000–2023). This includes the models developed using CHAMP, GRACE, GRACE-FO, GOCE, SLR (Satellite Laser Ranging), and DORIS measurements. Some of these models contain just secular terms, while more recent models include also periodic (annual and semi-annual) variations of the Earth’s gravity. We show the impact of these models on precise orbit determination (POD) of selected altimetry satellites, namely TOPEX/Poseidon, Jason-1, Jason-2, and Jason-3 at the time interval from 1992 to 2023. The impact of these models is assessed for different orbit parameters as well as the root-mean-square (RMS) and mean values of SLR observation residuals and orbit differences. Furthermore, the impact of these models on altimetry (single- and multi-satellite) sea surface height crossover differences, radial errors, geographically correlated mean errors, and their trends is analyzed. We have found that the CNES RL05MF model derived using data of 1985–2022 performs best among the models tested in this study, particularly for the Jason-3 time span (2016–2023). Using this model reduces the RMS values of SLR observation residuals from 2.56 cm (for pre-CHAMP model GRIM5-C1) to 1.48 cm for this satellite. The RMS values of orbit differences in the radial direction fit within 0.7–0.8 cm for most recent TVG models, while using old GRIM5-C1 would result in 1.9 cm differences. It is important to reprocess regularly Earth’s TVG data covering the longest time span to minimize extrapolation errors of the models.

DTRF2020 is the latest realization of the International Terrestrial Reference System (ITRS) by DGFI-TUM and is based on the same input data as ITRF2020. It is generated using the DGFI-TUM two-step combination approach, combining cumulative normal equations from the individual techniques GNSS, SLR, VLBI and DORIS. DTRF2020 introduces three key innovations: (1) it is the first secular ITRS realization with scale determined jointly from VLBI and GNSS; (2) it applies non-tidal loading corrections from atmospheric, oceanic, and hydrological models; and (3) it models post-seismic deformation using logarithmic and exponential functions. In addition to SINEX and EOP files, DTRF2020 provides all information required to compute instantaneous station positions: non-tidal loading reductions, post-seismic deformation models, residual and translations time series. Non-tidal loading corrections reduce GNSS height RMS for 99

In 2022 and 2023, the new (2020) realizations of the International Terrestrial Reference System (ITRS), namely ITRF2020, JTRF2020, and DTRF2020, were published. One of the differences of these realizations as compared to the previous (2014) ones is the application of Satellite Laser Ranging (SLR) station- and satellite-specific long-term mean range biases (RBs) for the four geodetic satellites LAGEOS-1/-2 and Etalon-1/-2. These RBs were subtracted from the SLR observations used to compute the official ILRS (International Laser Ranging Service) contribution to the ITRS 2020 realizations. This strategy leads to the research question, whether these RBs should and can be applied in SLR-observation-based precise orbit determination (POD) for any satellite to obtain the highest orbit quality possible while using an ITRS 2020 realization as a priori reference frame. In this paper, based on the POD results for four altimetry satellites (TOPEX/Poseidon, Jason-1, Jason-2, and Jason-3) over the total time interval 1992-2021 and single- as well as multi-satellite altimetry crossover analyses for Jason-2 (2008-2019), we show that the application of LAGEOS-1 long-term mean RBs and the estimation of RBs for certain stations and time spans according to the ILRS Data Handling File (DHF) for SLRF2020 (DHF2020) reduces the root-mean-square fits of SLR observations, scatter of estimated empirical accelerations in along- and cross-track directions, as well as standard deviations of single-satellite crossover differences, and thus improves the orbit quality of all tested altimetry satellites. Consequently, we conclude that the DHF2020 can be used also for any other satellite than LAGEOS-1. However, since the RBs are not only station- but also satellite-dependent, optimal results might be achieved by determining SLR long-term mean RBs for all SLR-tracked satellites and by using the RBs in the POD of these satellites. The smallest residuals of SLR observations and the best orbit quality (smallest values of the standard deviations of single-satellite crossover differences) are obtained, when arc-wise RBs are estimated for each station. However, one should be careful with applying the latter approach, since frequently (i.e. with a high temporal resolution) estimated biases in the radial direction absorb, beside SLR measurement errors and system delays, also non-modeled or not-perfectly modeled geophysical signals (e.g., non-tidal station loading) which might be of particular importance for some analysis.

The latest realizations of the ITRS, specifically the ITRF2020, the JTRF2020 and the DTRF2020, have been computed using input data series provided by the IAG technique services IVS, ILRS, IGS and IDS. They cover the entire observation period of the individual techniques until the end of 2020. Since 1996, recalculations of the ITRF have been performed approximately every 3 to 6 years. The main reason for recalculation is to ensure a high accuracy of the ITRF for current applications. In particular, seismic events that occure after an ITRF release as well as the general increase of the ITRF extrapolation error with time are key factors that cause the increase of the ITRF uncertainty. To enhance the frequency of ITRS realizations and consequently improve the accuracy of the ITRF, the ITRS Product Center plans to calculate annual updates of the ITRF2020 starting in 2024. The IAG technique services will provide three additional years of analyzed observations (2021-2023) collected after the end of the ITRF2020 observation period in February 2024. As an ITRS Combination Center, at DGFI-TUM, we will analyze the data series w.r.t. discontinuities, post-seismic deformations and their consistency with the input data series provided for the ITRS 2020 realizations. Model changes performed in between by the individual technique services, e.g. new PCO (phase center offsets) for GNSS satellites, updated mean long-term range biases for SLR satellites or gravitational deformation models for some more VLBI antennas, are expected to have an impact on the relevant ITRF parameters (station coordinates, EOP and datum parameters). Its order of magnitude and the effect of possible inconsistencies on the DTRF solution need to be investigated. We will present the first results of our analyses and draw preliminary conclusions regarding the accuracy of a possible DTRF2020 extension.

To update the ITRS 2020 realizations which are based on observations from the geodetic space techniques VLBI, SLR, GNSS and DORIS until the end of 2020, the ITRS Product Center asked the Technique Centers (TCs) for an extension of these series by as consistent as possible operational series. However, the GNSS input series which formerly realized an own GNSS scale, the full history of data was recomputed by the IGS TC by adopting the ITRF2020 scale based on the VLBI and SLR scale contributions.DTRF2020, calculated by DGFI-TUM, realizes the scale from VLBI and GNSS contributions and thus needs for its update IGS/GNSS series realizing the GNSS scale. Therefore, the IGS TC provided, in addition, an extension series consistent to the input series for the ITRS 2020 realization. Moreover, the GGFC provided extensions of the previous non-tidal loading (NTL) displacement time series as well as time series for new stations to be used in the DTRF2020 update to reduce non-linear station motions.We extended the DTRF2020 by using the provided extension series and the NTL input data until 2023. We analyzed the extended station position, datum parameter (origin and scale) and Earth Orientation Parameter time series, introduced additional discontinuities and accounted for post-seismic deformation of stations affected by earthquakes.We present the DTRF2020 update solution (i.e. DTRF2020-u2023) and discuss the consistency of the former and the extension series. In addition, we discuss the results of comparisons of the updates computed by the three ITRS Combination Centers, which reflect the internal accuracy achieved by today's ITRS realizations.

Since 2023, three different solutions for the latest (2020) realization of the International Terrestrial Reference System (ITRS) are publicly available, namely the ITRF2020, the JTRF2020 and the DTRF2020. All solutions are based on the same input data but were derived using different combination approaches and data correction strategies. Since the ITRS realizations are used as a priori reference frames for precise orbit determination (POD) of Earth orbiting satellites, it is important to investigate the impact of the different frames on the POD results. In this study, we briefly introduce the different features of the ITRS realizations and elaborate how the data correction models (e.g., periodic variations vs. non-tidal loading corrections) of the different xTRF2020 solutions can be optimally applied for the POD of selected satellites tracked by Satellite Laser Ranging (SLR) stations. We conclude the study with results obtained for various orbital parameters, such as the scaling factor of the non-gravitational (non-conservative) accelerations as well as the estimated empirical accelerations. Finally, we summarize the optimal settings of each ITRS realization for the satellite PODs discussed in this paper (i.e., LAGEOS-1, LARES-2, Jason-1/2/3).

Gravitational forces are the major forces acting on near-Earth orbiting (e.g., altimetry) satellites. Recently published Earth’s gravity field models used within the satellite precise orbit determination (POD) comprise observations of GRACE (Gravity Recovery And Climate Experiment) and GRACE-FO (GRACE-Follow-On), gravity field satellite missions between 2002 until 2017 and since 2018, respectively. In this presentation, we perform a review of selected Earth’s time-variable gravity field models developed in the past ten years (2014-2023). We analyze also the POD results obtained for selected altimetry satellites, namely, TOPEX/Poseidon, Jason-1, Jason-2, and Jason-3 at the time interval from 1992 to 2023 using various Earth’s gravity field models. A special focus is put on the CNES/GRGS mean gravity field models of releases 2 to 5, including the latest CNES_GRGS.RL05MF_COMBINED_GRACE_SLR_DORIS model. The impact of these models is assessed for different orbit parameters as well as the root-mean-square and mean values of Satellite Laser Ranging observation residuals and orbit differences. Furthermore, the impact of these models on altimetry (single- and multi-satellite) sea surface height crossover differences is investigated. From these crossover differences, radial errors and geographically-correlated mean errors are derived and analyzed. The results are used to conclude on the accuracy of current Earth’s time-variable gravity field models when used for the POD of altimetry satellites.

In this work, we analyse the performance of an Ensemble Kalman filter (EnKF) approach, the simultaneous multiplicative column normalized method SMART+ and the NeQuick model to estimate the topside ionosphere and plasmasphere. The slant total electron content (STEC) measurements of 11 Low Earth Orbit (LEO) satellites are used as input for the EnKF and SMART+ to update the NeQuick model which serves as background model.Our comparative case study is implemented globally for altitudes between 430 and 20 200 km for two periods of the year 2015 covering moderate to perturbed ionospheric conditions.The performance of the methods is investigated regarding their capability to reproduce electron densities. For that purpose, the independent electron density measurements of the Van Allen Probes (VAP) twin satellites, Swarm Langmuir Probes (LP) and FORMOSAT-3/COSMIC ionospheric radio occultation (IRO) profiles serve as reference.The results reveal that in median the NeQuick model underestimates the IRO electron densities in the moderate period and for high latitudes in the perturbed period. For the NeQuick model the median of the absolute relative residuals is about 33% in the moderate period and around 25% in the perturbed period. SMART+ reduces these residuals to about 24% and 23%, respectively, whereas EnKF doesn’t provide an improvement.The validation with VAP electron densities shows that in both periods and for all altitudes, the electron densities provided by the NeQuick model, the EnKF and SMART+ are in general significantly lower than the VAP measurements with a median of the relative residuals equal to about 80%. The lowest median and RMS values of the VAP residuals are produces by EnKF, reducing the NeQuick statistics by up to 9%.Further we observe that the electron densities provided by the NeQuick model are in median lower than the calibrated LP in-situ measurements for all three Swarm satellites in the moderate period and higher in the perturbed period. SMART+ shows the lowest median and standard deviation for the absolute relative residuals. These are up to 20% lower than for the NeQuick model. For the LP in-situ measurements, the EnKF has the worst performance.Overall, the results underpin that even though the data of 11 satellite missions has been assimilated to adjust the a priori information of the NeQuick model, only limited improvements can be achieved especially for the plasmasphere.

Abstract Global and regional sea level variations are important indicators of climate change and are derived from accurate sea surface height measurements and precisely determined orbits of altimetry satellites. To validate and improve the quality of these orbits, comparisons with external solutions are important. Since orbit solutions of different institutions are not necessarily provided at the same time instants, interpolation is required for comparison. In this study, we investigate the appropriate interpolation method and its degree to reduce interpolation errors to sub-millimetre levels. We also assess the magnitude of errors occurring at transformations when expressing orbit differences not only in the terrestrial reference frame (Cartesian coordinates), but also in local orbital and ellipsoidal coordinates. The analyses conducted in this study provide good results for Hermite interpolation of degrees 7–11 and Newton interpolation of at least degree 9 with a three-dimensional interpolation error of 0.6 mm and a scattering of 0.2 mm on average for satellite coordinates given with an accuracy of 1 mm in the SP3 format. These interpolation settings limit transformation errors between coordinate systems to ±0.01 mm and incorrect mapping of interpolation errors into certain components in the target system to ±0.02 mm. The spectral analysis of orbit differences is affected up to 0.1 mm in magnitude with appropriate interpolation settings. Extending the number of decimal digits of the satellite position and velocity in SP3 files by one digit benefits the orbit comparisons and reduces the interpolation error by 90% from 0.6 to 0.06 mm. The results are obtained using piece-wise interpolation and a validity interval inside the interpolation interval to minimise the effects of the Runge phenomenon. Graphical Abstract

In 2022-2023, new (2020) realizations of the International Terrestrial Reference System (ITRS) were published, namely ITRF2020, DTRF2020, and JTRF2020. One of the differences for these realizations with respect to the previous (2014) ones is the application of Satellite Laser Ranging (SLR) station-specific long-term mean range biases for the four geodetic satellites LAGEOS-1, -2 and Etalon-1 and -2. These range biases were subtracted at the observation level from the SLR observations used to derive the ITRS2020 realizations. In this context, a question arises if these range biases should be applied in SLR-observation-based precise orbit determination for any satellite to obtain the highest orbit quality possible, when using ITRS2020 realizations as the a priori reference frame. We present results of a study on the application of the SLR long-term mean range biases derived from LAGEOS-1, -2 and Etalon-1 and -2 for precise orbit determination of some altimetry and other spherical SLR satellites using ITRS2020 realizations as the a priori reference frame and make a conclusion on the necessity of application of these biases. Furthermore, we present results of precise orbit determination for altimetry satellites based on long-term mean range biases explicitly determined for the respective satellites.

The TOPEX/Poseidon (T/P) altimetry mission with its main objectives to monitor variations of the global and regional sea level as well as ocean circulation is a milestone in Earth observation. The spacecraft was launched in 1992 and it is the predecessor mission of the Jason series and Sentinel-6A. For laser ranging measurements from the Earth to the spacecraft, T/P was equipped with a non-ideally designed annular retroreflector array. Its large dimensions of over 160 cm in diameter caused huge optical phase centre variations which limit the orbit accuracy. In this study, we developed a continuous, analytical correction function that counteracts both, phase centre vari-ations at the spacecraft and station-related laser ranging measurement errors such as range biases. For most Satellite Laser Ranging (SLR) ground stations that tracked the T/P spacecraft, an individual set of six correction parameters is estimated. The parameters are valid for the entire mission or, in some cases, for a defined period. The developed function uses the observation's viewing angles to determine a correction value which is added to the range measurement. Applying the measurement correction reduces the overall T/P mission root mean square fit of SLR residuals from 33.78 cm to 1.97 cm (1.59 cm for SLR core stations). External orbits based on the joint analysis of two different space-geodetic techniques are used to validate the quality of our improved orbit solution. The com-parisons show good agreement. The mean values of the radial, transverse, and normal components differ by 0.0,-0.1, and-0.2 cm, respectively. To investigate the impact of the corrected orbit on sea level computations, a single-satellite crossover analysis is performed. When using the corrected measurements, the standard deviation of crossover differences reduces from 16 cm to 6 cm. The computed coef-ficients of the measurement correction function are provided publicly and can be used in any software package to obtain T/P orbits. (c) 2022 COSPAR. Published by Elsevier B.V. All rights reserved.

Precise orbits of altimetry satellites are a prerequisite for the investigation of global, regional, and coastal sea levels together with their changes, since accurate satellite positions in the radial direction are required for the reliable determination of the water surface height (distance between the altimeter position in space and the water surface). Significant progress in the improvement of altimetry satellite orbit quality has been achieved in the last 30 years increasing the orbit accuracy in the radial direction from decimeter to centimeter and even sub-centimeter level. That was possible due to the improvements in the modeling of Earth’s time variable gravity field, ocean tides, terrestrial and celestial reference frames, but also due to the accomplishments reached in the observation methods used for altimetry satellites, namely Satellite Laser Ranging (SLR), Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS), and Global Positioning System (GPS—used for some satellites). In this paper, we review the main improvements in the models used for the determination of orbits of altimetry satellites, namely, in so called Geophysical Data Records (GDR) orbit standards from GDR-C to Precise Orbit Ephemeris-F (POE-F), illustrate the impact of the improvements in precise orbit determination of these satellites on the orbit accuracy in the radial direction. Additionally we investigate orbit differences in the radial direction, single-satellite crossover differences, radial, and geographically correlated orbit errors of contemporary orbits of various altimetry satellites namely Cryosat-2, Envisat, ERS-1, ERS-2, Jason-1, Jason-2, Jason-3, SARAL, Sentinel-3A, Sentinel-3B, and TOPEX/Poseidon derived by different institutions.

The ITRS CC at the Deutsches Geodätisches Forschungsinstitut of the Technical University of Munich (DGFI-TUM) has created the new DTRF website https://dtrf.dgfi.tum.de. On this site, DGFI-TUM provides background information and data access to the current and all previous DTRF solutions. In particular, the DTRF2020 processing strategy is presented and the results are described and explained. In addition to the actual solution, the DTRF2020 release contains further datasets that are necessary for a highly accurate application of the DTRF2020. The website clearly presents and makes available all datasets, partly map-based. Our poster gives an overview of the new DTRF website and provides examples of its use.

The DTRF2020 is the ITRS 2020 realization of the ITRS CC at DGFI-TUM.It was published earlier this year. The calculation of the DTRF2020 is based on a two-step approach: First, after a data pre-analysis, one TRF (normal equation system, NEQ) per technique, i.e. VLBI, SLR, GNSS and DORIS, is calculated. Second, the TRF NEQs are combined to the DTRF2020 solution. For the first time, all previously modeled non-tidal loading (NTL) components provided by IERS GGFC, i.e., the atmospheric, hydrological, and oceanic parts, are considered to reduce NTL signals in the station motions from the input NEQ. Post-seismic deformation (PSD) signals in station position time series are approximated by combinations of logarithmic and exponential functions and reduced from the NEQ in the same way as the NTL signals in the first step of our approach. The published dataset includes the DTRF2020 solution itself, i.e., station positions at the reference epoch 2010.0 and station velocities, as well as the consistently estimated EOP series. In addition, the model-based NTL time series used in the DTRF2020 calculation, the parameters of the PSD approximation functions, and the corresponding time series of the approximation signal considered in DTRF2020 (over the DTRF2020 time period) are provided for the users. Furthermore, residual time series of station positions and SLR translation time series are made available (the latter indicate the deviation of the instantaneous from the mean center of mass realized in DTRF2020). In this presentation, we discuss the final results of DTRF2020 and give an overview of the DTRF2020 dataset and the features it provides for its application. We also discuss the consistency of DTRF2020 with respect to its predecessor DTRF2014 and the limits of accuracy of reference frames. Further, we address the need for consistency with respect to datasets that will be used in DTRF2020 applications, such as the SLR Data Handling File and GNSS satellite PCV.

As one of the ITRS Combination Centres of the IERS, DGFI-TUM is in charge of computing an ITRS 2020 realisation. Since the ITRS 2014 realisation, many innovations have occurred. These include the six years longer observation period, but also new observation stations and satellites, and the use of refined background models in the analysis of the space-geodetic techniques. In addition, the combination strategy of the DTRF has also been improved. Namely, non-tidal loading (NTL) corrections over the full observation period and for all three components (atmospheric, hydrological and oceanic) are taken into account, as well as modelled post-seismic deformations (PSD). Both corrections are carried out - according to the combination strategy of DGFI-TUM - on the level of the normal equation (NEQ) by reducing each input NEQ. Due to all the improvements mentioned above, ranging from observation to analysis and combination, it can be assumed that all ITRS 2020 realisations are not only more up-to-date but also more accurate than their predecessors. In the presentation, we demonstrate the DTRF2020 solution as well as first comparisons and analyses. We will also present the DTRF2020 release which will include SINEX files and an EOP file, plus the time series of SLR translations, NTL and PSD corrections, and station position residuals.

In 2018 we celebrated 25 years of development of radar altimetry, and the progress achieved by this methodology in the fields of global and coastal oceanography, hydrology, geodesy and cryospheric sciences. Many symbolic major events have celebrated these developments, e.g., in Venice, Italy, the 15th (2006) and 20th (2012) years of progress and more recently, in 2018, in Ponta Delgada, Portugal, 25 Years of Progress in Radar Altimetry. On this latter occasion it was decided to collect contributions of scientists, engineers and managers involved in the worldwide altimetry community to depict the state of altimetry and propose recommendations for the altimetry of the future. This paper summarizes contributions and recommendations that were collected and provides guidance for future mission design, research activities, and sustainable operational radar altimetry data exploitation. Recommendations provided are fundamental for optimizing further scientific and operational advances of oceanographic observations by altimetry, including requirements for spatial and temporal resolution of altimetric measurements, their accuracy and continuity. There are also new challenges and new openings mentioned in the paper that are particularly crucial for observations at higher latitudes, for coastal oceanography, for cryospheric studies and for hydrology.Thepaperstarts with a general introduction followed by a section on Earth System Science including Ocean Dynamics, Sea Level, the Coastal Ocean, Hydrology, the Cryosphere and Polar Oceans and the ‘‘Green ” Ocean, extending the frontier from biogeochemistry to marine ecology. Applications are described in a subsequent section, which covers Operational Oceanography, Weather, Hurricane Wave and Wind Forecasting, Climate projection. Instruments’ development and satellite missions’ evolutions are described in a fourth section. A fifth section covers the key observations that altimeters provide and their potential complements, from other Earth observation measurements to in situ data. Section 6 identifies the data and methods and provides some accuracy and resolution requirements for the wet tropospheric correction, the orbit and other geodetic requirements, the Mean Sea Surface, Geoid and Mean Dynamic Topography, Calibration and Validation, data accuracy, data access and handling (including the DUACS system). Section 7 brings a transversal view on scales, integration, artificial intelligence, and capacity building (education and training). Section 8 reviews the programmatic issues followed by a conclusion. (cid:1) 2021 COSPAR. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/ by-nc-nd/4.0/).

Precise orbits of altimetry satellites are a prerequisite for the investigation of global, regional, and coastal sea levels together with their changes, since accurate orbit information is required for the reliable determination of the water surface height (distance between the altimeter position in space and the water surface). Orbits of altimetry satellites are nowadays usually computed using DORIS (Doppler Orbitography and Radiopositioning Integrated by Satellite), SLR (Satellite Laser Ranging), and, of some satellites, GPS (Global Positioning System) observations of a global network of tracking stations. Significant progress in the improvement of altimetry satellite orbit quality has been achieved in the last 30 years. However, the differences of the sea level and its trend computed using up-to-date orbit solutions derived at various institutions using different software packages, types of observations (DORIS+SLR as compared to GPS+DORIS) and different up-to-date models still exceed the requirements of the Global Climate Observing System for the uncertainties of the regional sea level (< 1 cm) and its trend (< 1 mm/year). In this study, we evaluate the current accuracy of orbits of altimetry satellites derived by various institutions in the state-of-the-art reference frames using up-to-date background models for precise orbit determination by using various observation types. We present some results of our analysis of geographically correlated errors and radial orbit differences for various orbit solutions. We also discuss possible reasons causing the orbit differences and potential ways to reduce them.

Launched in 1992, the TOPEX/Poseidon (T/P) mission is one of the first major altimetry missions. It is the predecessor of the Jason satellites which orbit the Earth on a very similar orbit. The geodetic space technique SLR (Satellite Laser Ranging) provides observations of this mission by targeting the Laser Retroreflector Array (LRA) mounted on the spacecraft. The T/P LRA is extremely large and not optimally designed. It thus causes big variations in the LRA phase center. These variations are a significant limiting factor of the orbit accuracy which makes it essential to apply a measurement correction for precise orbit determination. Up to now, only tabulated LRA corrections are available which require an interpolation. In this contribution, we present a new approach to determine station-dependent LRA corrections to improve the phase center variations. The approach is based on a continuous analytical correction function which only uses the observation azimuth and zenith angle in combination with four parameters. These parameters are computed within an estimation process for each observing SLR station. Therefore, uncorrected SLR residuals based on raw SLR normal point observations are used. The correction value is added to the SLR measurement and counteracts the LRA phase center variations. The advantages of this method are the continuous functional, which is easy to implement in existing software packages, as well as the avoidance of an interpolation between tabulated values. Furthermore, the differences between orbits determined with and without the LRA correction will be presented. Station coordinate time series and orbit comparisons with external T/P orbits are investigated in order to prove the high quality of the obtained LRA corrections.

The aerodynamic drag depending on the neutral density of the thermosphere is the largest non-gravitational force that decelerates Low Earth Orbiting (LEO) satellites with altitudes lower than 1000 km. Consequently, the knowledge of the thermospheric neutral density is of crucial importance for many applications in geo-scientific investigations, such as precise orbit determination (POD), re-entry prediction, manoeuvre planning or satellite lifetime predictions. The accuracy of existing thermosphere models depends on observation data of the thermosphere, which are quite sparse. Evaluations of different thermosphere models indicate considerable differences, especially for time epochs of severe space weather events. Hence, an improvement of thermosphere models is absolutely necessary.In this study, discrepancies between the empirical thermosphere model NRLMSISE-00 and the results of two geodetic observation techniques are discussed. For this purpose, two approaches are applied to calculate scale factors between the modelled density from the NRLMSISE-00 model and those from geodetic techniques. The first approach applies the POD of LEO satellites to estimate scale factors with a time resolution of 12 hours derived from Satellite Laser Ranging (SLR) tracking measurements. The SLR missions used here include the spherical satellites Starlette, Westpac, Blits, Stella and Larets. As our second approach, scale factors are computed by evaluating the aerodynamic acceleration using the on-board accelerometer data of the Challenging Mini-satellite Payload (CHAMP) mission and the Gravity Recovery and Climate Experiment (GRACE) mission. Here, the time resolution of scale factors is fixed to be 12 hours to be comparable with the first approach. Finally, we investigate the resulting scale factors from the above mentioned satellites at various altitudes, e.g. 960 km for Starlette and 400 km for GRACE. Especially, the temporal variation as well as the altitude dependency of the scale factors will be discussed.

A major problem in the precise orbit determination of Low-Earth-Orbiting (LEO) satellites at altitudes below 1000 km is the modeling of the aerodynamic drag which mainly depends on the thermospheric density and causes the largest non-gravitational acceleration. Typically, empirical thermosphere models such as NRLMSISE-00, JB2008 or DTM2013 are used to calculate density values at satellite positions. However, since the current thermosphere models cannot provide the required accuracy, unaccounted variations in the thermospheric density may lead to significantly incorrect satellite positions. At EGU 2021, we presented a study comparing thermospheric density corrections for the NRLMSISE-00 model in terms of scale factors calculated from satellite laser ranging (SLR) measurements to various spherical LEO satellites (Starlette, Stella, Larets, etc.) with the corresponding values from accelerometer measurements on-board CHAMP and GRACE. In the meantime we significantly extended our study and published the results (Zeitler et al. 2021). Our results demonstrate that both measurement techniques can be used to derive comparable (with correlations of up to 80% and more depending on altitude) scale factors of the thermospheric density with a temporal resolution of 12 hours, which vary around the value 1. This indicates to which extent the NRLMSISE-00 model differs from the observed thermospheric density. On average, during high solar activity, the model underestimates the thermospheric density and should be scaled up using the estimated scale factors. We find our estimated scale factors close to the results from Emmert et al. (2021); except for the most recent period where a different trend is observed. We also find a linear decrease of the estimated thermospheric density scale factors above 680 km of about −5% per decade due to climate change. This fits well to the results from Solomon et al. (2015). Furthermore, we validate the approach of deriving scale factors from SLR measurements by using two independent software packages. Emmert, J. T., Dhadly, M. S., & Segerman, A. M. (2021). A Globally Averaged Thermospheric Density Data Set Derived From Two-Line Orbital Element Sets and Special Perturbations State Vectors. Journal of Geophysical Research: Space Physics, 126 (8), e2021JA029455. doi: 10.1029/2021JA029455 Solomon, S. C., Qian, L., & Roble, R. G. (2015). New 3-D simulations of climate change in the thermosphere. Journal of Geophysical Research: Space Physics, 120 (3), 2183–2193. doi: 10.1002/2014JA020886 Zeitler L., Corbin A., Vielberg K., Rudenko S., Löcher A., Bloßfeld M., Schmidt M., & Kusche J. (2021). Scale factors of the thermospheric density ‐ a comparison of SLR and accelerometer solutions. Journal of Geophysical Research: Space Physics, 126, e2021JA029708. doi: 10.1029/2021JA029708