Thermospheric Mass Density Disturbances Due to Magnetospheric Forcing From 2014–2020 CASSIOPE Precise Orbits

1. Introduction The characterization of the Earth's thermosphere, especially during geomagnetic storms, is essential for applications such as Low Earth Orbit (LEO) satellite tracking and space weather research; thermosphere models are routinely used as input in precise orbit determination (POD) schemes so that the position and velocity of orbiting satellites can be accurately estimated (Montenbruck & Gill,2013). However, positioning errors caused by uncertainties in the existing models are still a major concern (Anderson etal.,2009; Jin etal.,2017; Calabia etal.,2020), largely due to the limited quality and quantity of data. Previously, thermospheric mass density variations have been monitored by a variety of instruments and methods (Jin etal.,2018), but only accelerometers on-board satellites have provided enough resolution to study high-cadence disturbances caused by, for example, geomagnetic storms. The first high-resolution studies based on accelerometers were by Marcos and Forbes(1985), and numerous scientific outcomes have followed since then (e.g., Bruinsma & Biancale,2003; Calabia & Jin,2016a; Doornbos etal.,2010; Mehta etal.,2017), in particular about disturbances caused by geomagnetic storms (e.g., Bruinsma etal., 2006, Calabia & Jin,2019; Lühr etal.,2004; Sutton etal.,2005). The upper-atmosphere is mainly composed of two parts, the thermosphere and the ionosphere. In the thermosphere, photoabsorption, photoionization, and photodissociation of molecules through extreme ultraviolet radiation (EUV) create the ions of the ionosphere, and thermal energy-transfer from ions to neutral particles drives the regular dynamics. However, this complex system is highly variable in space and time, and the physical processes and corresponding mechanisms are not well understood (Heelis & Maute,2020; Abstract Long-term thermospheric mass density disturbances due to magnetospheric forcing are not clear due to a lack of measurement data and imprecise models. In this study, the Global Navigation Satellite System (GNSS) precise orbits of CAScade SmallSat and IOnospheric Polar Explorer (CASSIOPE) are used to infer high-resolution thermospheric mass densities between the years 2014 and 2020. The CASSIOPE densities are comprehensively validated at altitudes from 325 to 425km at intervals of 25km with the High Accuracy Satellite Drag Model (HASDM) density database, and further compared with the Naval Research Laboratory Mass Spectrometer and Incoherent Scatter Radar Exosphere/2000 (NRLMSISE-00) and the Jacchia-Bowman/2008 (JB2008) empirical models. The CASSIOPE densities are very similar to the HASDM and JB2008 densities, while the NRLMSISE-00 largely overestimates (∼150%) during low solar-flux conditions. For density values above ∼10−12kg/m3, the correlation of CASSIOPE with HASDM is ∼5% better than the models, and the standard deviation is within 10% of the background density. For density values below ∼10−12kg/m3, systematic errors have shown to reduce the precision of the CASSIOPE densities. By setting geomagnetic contributions to zero in the models, the density disturbances due to magnetospheric forcing are isolated from the CASSIOPE time-series, allowing investigation into the correlations and time-delay responses to the models and to the merging electric field (Em). A new linear dependence of the time delay to the Em was found and then parameterized in this study. Time delays occurred at the 4–7h range during geomagnetic storms, and at 9–11h during quiet conditions; neither had significant dependence on altitude. The results represent the validation of the first high-resolution thermospheric mass density estimates inferred from commercial-off-the-shelf GNSS receivers. CALABIA AND JIN © 2021. American Geophysical Union. All Rights Reserved. Thermospheric Mass Density Disturbances Due to Magnetospheric Forcing From 2014–2020 CASSIOPE Precise Orbits Andrés Calabia1 and Shuanggen Jin1,2 1School of Remote Sensing and Geomatics Engineering, Nanjing University of Information Science and Technology, Nanjing, China, 2Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai, China Key Points: • Thermospheric mass densities from 2014 to 2020 are estimated from CAScade SmallSat and IOnospheric Polar Explorer Global Navigation Satellite System (GNSS) precise orbits • The high-resolution thermospheric mass densities inferred from commercial-off-the-shelf GNSS receivers are validated • The density disturbances due to magnetospheric forcing are investigated for correlations and time-delay responses to models and indices Correspondence to: S. Jin, [email protected]; [email protected] Citation: Calabia, A., & Jin, S. (2021). Thermospheric mass density disturbances due to magnetospheric forcing from 2014–2020 CASSIOPE precise orbits. Journal of Geophysical Research: Space Physics, 126, e2021JA029540. https://doi. org/10.1029/2021JA029540 Received 6 MAY 2021 Accepted 21 JUL 2021 Author Contributions: Conceptualization: Andrés Calabia, Shuanggen Jin Data curation: Andrés Calabia Formal analysis: Andrés Calabia Funding acquisition: Shuanggen Jin Investigation: Andrés Calabia Methodology: Andrés Calabia Project Administration: Shuanggen Jin Software: Andrés Calabia Supervision: Shuanggen Jin Validation: Shuanggen Jin Visualization: Andrés Calabia Writing – original draft: Andrés Calabia Writing – review & editing: Shuanggen Jin 10.1029/2021JA029540 RESEARCH ARTICLE 1 of 19 Journal of Geophysical Research: Space Physics Palmroth etal.,2021). These processes, generally called space weather, can influence on several segments of the economy negatively; satellites, communications, electric power distribution, airline industry, and Global Navigation Satellite Systems (GNSS) users. This shows how important it is for us to study the possible detrimental impacts scientifically, then to implement and maintain reliable and integrated geodetic space weather monitoring (Jin etal.,2011; Okoh etal.,2018; Blossfeld etal.,2019). While the regular dynamics of the thermosphere are mainly driven by the day-night and annual cycles of solar EUV (Calabia & Jin,2016a; Qian & Solomon,2012), the effects of geomagnetic storms can cause an increase in its density of up to 800% (Bruinsma etal.,2006; Calabia & Jin,2016b; Liu & Lühr,2005; Sutton etal.,2005). Usually, geomagnetic storms begin as a high latitude event located at the aurora region. Shortly after the beginning of the storm, the whole Earth's thermosphere responds with southward-traveling gravity waves, and a global density increase occurs. This can last anywhere between several hours to multiple days. Many studies have shown thermospheric variations during geomagnetic storms are difficult to investigate due to a lack of measurement data and large uncertainties in the models (e.g., Calabia etal.,2020; Chen etal.,2014; Jackson etal.,2020; Oliveira & Zesta,2019). On-board satellite accelerometers can measure non-gravitational accelerations and derive thermospheric mass density variation data with unprecedented details. However, the high instrumental costs and other technical issues (Bruinsma etal.,2004; Calabia & Jin,2017; Calabia etal.,2015; Siemes etal.,2016) have limited these technology payloads to be carried by only a small number of satellites. In the last 20years, the only missions carrying accelerometers were Challenging Minisatellite Payload (CHAMP), Gravity Recovery and Climate Experiment (GRACE), Gravity field and steady-state ocean circulation explorer (GOCE), and Swarm (Figure1). Currently, continuous high accuracy GNSS observation on-board LEO satellites has proven the capability to measure high-cadence, non-gravitational accelerations, and then estimate densities at a high resolution (Calabia & Jin,2017,2021a; Calabia etal.,2015; Li & Lei,2020; van den IJssel etal.,2020; Yuan etal.,2019). With the increasing number of LEO satellites being equipped with a high-precision GNSS receivers, and therefore more enhanced data processing and orbit determination strategies, GNSS-based thermospheric mass densities may become an essential data to effectively monitor global thermospheric fluctuations; GNSS Thermosphere Insitu Sensing (GNSS-TIS). Recently, for instance, commercial-off-the-shelf, geodetic grade, dual-frequency GNSS receivers on board small satellites have demonstrated their full capability for geodetic observations. These come at an affordable cost for low-budget space missions (Jin & Su,2020; Kim & Langley,2019), and can be used to retrieve high-resolution thermospheric mass densities (Calabia & Jin,2021a). It is very likely that in the near future, these upgraded GNSS receivers will become a common CALABIA AND JIN 10.1029/2021JA029540 2 of 19 Figure 1. Orbital altitudes (left axis) of the satellites capable to estimate high-resolution thermospheric mass densities. The CAScade SmallSat and IOnospheric Polar Explorer (CASSIOPE) satellite covers altitudes from ∼330 to ∼1,300km due to its elliptical orbit, while the others have circular orbits. The 81-days mean solar flux F10.7 index is show in red (right axis). 2000 2004 2008 2012 2016 2020 0 200 400 600 800 1000 1200 1400 1600 1800 km 60 80 100 120 140 160 180 200 220 240 s.f.u. GRACE Swarm B Swarm A/C GOCE CHAMP CASSIOPE 21699402, 2021, 8, Downloaded from https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2021JA029540 by Spanish Cochrane National Provision (Ministerio de Sanidad), Wiley Online Library on [28/11/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License Journal of Geophysical Research: Space Physics payload in most satellite missions, and their high-precision, high-accuracy GNSS ephemeris products will be used as standard to estimate thermospheric mass densities. In Calabia and Jin(2021a), the GNSS ephemeris of the CAScade SmallSat and IOnospheric Polar Explorer (CASSIOPE) satellite were used to investigate at high resolution the thermosphere's response to the geomagnetic storm of February 2014. The CASSIOPE satellite was launched on September 29, 2013. It is the first mission to cover both telecommunications and scientific research purposes (Yau etal.,2006). The main scientific objectives of the CASSIOPE mission are to better understand the complex processes that occur in the upper atmosphere, while performing high-speed communications at the same time. It is important to note that the initial purpose of the GNSS instruments on-board the CASSIOPE satellite were not intended to retrieve thermospheric mass densities; the GNSS-based densities could become an exceptional secondary data to assist in analysis and validation of the other payload measurement data. In this study, a new thermospheric mass density data set is estimated from CASSIOPE GNSS precise orbits during the period 2014 to 2020 and validated by the High Accuracy Satellite Drag Model (HASDM) density data set (Tobiska etal.,2021). The ratio (quotient) between the CASSIOPE and the HASDM densities is compared with that of the Naval Research Laboratory Mass Spectrometer and Incoherent Scatter Radar Exosphere/2000 (NRLMSISE-00) (Picone etal.,2002) and the Jacchia-Bowman/2008 (JB2008) (Bowman et al., 2008) empirical models, that is, NRLMSISE-00/HASDM and JB2008/HASDM, respectively. The trends and standard deviations of the ratios from 325 to 425km altitude at increments of 25km are analyzed. Then, by setting geomagnetic contributions to zero in the models, the “quiet” background is removed from the time-series to investigate the long-term correlations and time-lags of the disturbances due to magnetospheric forcing. In the following sections, the data and techniques used for thermospheric mass density retrieval are described. Then, the results as a function of time and altitude are analyzed, and the statistical comparisons for the validation and the assessment are performed. Finally, issues raised by the analyses, and some suggestions for future progression is discussed. 2. Data and Methods 2.1. Density Estimation From CASSIOPE GNSS Precise Orbits GNSS data from the CASSIOPE spacecraft are used to obtain the density estimates during the period 2014– 2020. The CASSIOPE satellite is equipped with 5 commercial-off-the-shelf dual-frequency GNSS receivers (L1 C/A and L2 P) tracking up to 12 Global Position System (GPS) satellites. The GNSS instrument is called GPS Attitude, Position, and profiling experiment (GAP), and is used for spacecraft position as well as for attitude determination and for ionospheric radio occultation. Positioning errors are within the range of a few decimeters and a few millimeters for individual pseudorange and carrier phase measurements, respectively. In this study, the precise orbit solutions computed from Montenbruck etal.(2019) are used. The authors computed the precise positions and velocities at a second interval in a reduced-dynamic approach with float-ambiguity estimation. The CASSIOPE mission has a slightly eccentric polar orbit of 81° inclination, with altitudes ranging from approximately 1,400km in the apogee to 325km in the perigee. Due to its precessing orbit, the in-situ measurements cover all longitudes and local solar time (LST) locations. Figure1 shows the orbital altitudes of the CASSIOPE satellite during the declining phase of the solar cycle 24. Based on the method of Calabia etal.(2015), GNSS-based total accelerations are retrieved through numerical interpolation of the precise velocity products. Subsequently, air-drag forces are obtained by removing gravitational and radiation-pressure force-models, which can be finally used for density estimation. More details of the methodology can be found in Appendix A and Appendix B. The most important sources of error in this method are caused by the accuracy of the velocity products, and the errors caused by the drag coefficient and the thermospheric winds models. The errors in the precise velocities are usually originated in the POD scheme (stochastic least squares adjustment between models and GNSS observables) and can cause noise and outliers in the resulting non-gravitational accelerations (Calabia etal.,2015). Here, in order to mitigate high-cadence variations, noises, and possible outliers, a 6min mean-average running filter is applied. We tested different filtering lengths for different periods along the time-series, and the optimal length was a 6min averaging window, as we can see in Figure2. Other lengths provide too average results or too large residual noises. In this way, the comparisons with the empirical models will be more suitable, CALABIA AND JIN 10.1029/2021JA029540 3 of 19 21699402, 2021, 8, Downloaded from https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2021JA029540 by Spanish Cochrane National Provision (Ministerio de Sanidad), Wiley Online Library on [28/11/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License Journal of Geophysical Research: Space Physics since these can only provide an averaged state of the actual variations. The errors due to zonal and meridional winds are estimated at 1% and 4% per 100m/s wind error, respectively (Bruinsma etal.,2004,2006), while drag coefficients under different gas-surface interaction assumptions are expected to differ by ∼15%, during solar minimum conditions, and by ∼2%–3%, during solar maximum (March etal.,2019a; Mehta etal.,2014,2017). Other minor systematic errors in the densities are directly connected to the aerodynamic modeling of the satellite (March etal.,2019b). In this study, a variable drag coefficient in terms of solar flux and altitude (Pardini etal.,2006) is used for satellites with hexagonal-prism shapes (Walker etal.,2014), and the density estimates are re-scaled to match with that of the HASDM data set, which is considered the most accurate up-to-date. According to this, under quiet magnetospheric conditions, a higher accuracy compared to using a constant drag coefficient and a flat plate model is expected; within 10% of the background density (Bruinsma etal.,2006). 2.2. Analysis Methods and Models To validate and assess the CASSIOPE densities, the recently released HASDM data set (Tobiska etal.,2021) is used as the control, and its quotient of densities (CASSIOPE/HASDM) is compared with that given by the NRLMSISE-00 and the JB2008 models, that is, NRLMSISE-00/HASDM and JB2008/HASDM, respectively. First to be analyzed is the distribution of the data in terms of LST and geographical coordinates with a spatial histogram analysis. Then, a Pearson's linear correlation analysis is performed between the HASDM densities and the densities from the CASSIOPE and the models. The paper also further compares the fluctuations and deviations of the ratio along the time-series of the data, applying both a 30-days mean-average and a 30-days standard-deviation running filters. The general form for the mean-average running-window filter is:        21 ia j i jia x Filt x a (1) CALABIA AND JIN 10.1029/2021JA029540 4 of 19 Figure 2. Thermospheric information with (a) density estimates from CAScade SmallSat and IOnospheric Polar Explorer (CASSIOPE) and models, (b) altitudes, (c) local solar time (LST), (d) longitude, and (e) latitude along the CASSIOPE orbit on February 20, 2014. In (a), at the inbound orbit, a set of four samples can be identified at steps of 25km in altitude. For the illustrated window, Dst=−90nT, and F10.7=153sfu. 350 450 Altitude (km) 0 1 2 3 Density (kg/m3) 10-11 CASSIOPE CASSIOPE smoothed NRLMSISE-00 JB2008 HASDM 11:00 UT 11:30 UT 20 February 2014 75°S 0° 75°N Latitude 130°E 0° 130°W Longitude 6h 18h LST d) e) c) b) a) 21699402, 2021, 8, Downloaded from https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2021JA029540 by Spanish Cochrane National Provision (Ministerio de Sanidad), Wiley Online Library on [28/11/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License Journal of Geophysical Research: Space Physics In this equation, xi is the time-series to filter at each sampling index i, a is half of the increment of time for each corresponding running-window. The standard deviation is calculated with similar form of Equation1. The resulting statistics provide means to assess the accuracy of the new CASSIOPE density estimates. Finally, the analysis to assess and investigate the disturbances due to magnetospheric forcing is introduced in the next section. The used models are presented as follows: 1. The HASDM values are derived from several dozens of calibration satellites, which are validated weekly by the U.S. Air Force Space Command and Space Environment Technologies (SET). This validation is able to recreate the densities of the global atmosphere, and the resulting data are provided every 3h at a grid size of 10°×15° (latitude, longitude), with 25km altitude steps between 175 and 825km. This data set is called the SET-HASDM density database. Due to the high accuracy of the HASDM data set (Tobiska etal.,2021), the differences to these, along with the comparisons to the existing models, will allow a reasonable validation and uncertainty assessment of the new CASSIOPE densities. 2. The NRLMSISE-00 model is the standard model of the Earth's atmosphere to aid predictions of satellite orbital decay due to atmospheric drag, and it has widely been used in numerous research studies and applications (e.g., Emmert & Picone,2010, Horvath & Lovell,2018; Pardini etal.,2006; Pilinski etal.,2011). This model is based on averaged data from several measurement techniques, including mass spectrometers, incoherent scatter radars, satellite drag data, and solar ultraviolet occultation. More details about the background database of the NRLMSISE-00 model can be found in Picone etal.(2002). 3. While NRLMSISE-00 uses the exponential Bates vertical profile (Bates,1959), the Jacchia-Bowman/2008 (JB2008) model represents the asymptotic behavior of the upper thermosphere with the arctangent function (Bowman etal.,2008). The measurement data sources employed in the JB2008 model include the Air Force daily density values (Bowman etal.,2004), the HASDM values (Bowman & Storz,2003; Storz etal.,2005), and the CHAMP and GRACE accelerometer-based densities. Recent studies have shown the very good performance of JB2008 against NRLMSISE-00 (e.g., Calabia & Jin,2019). 2.3. Density Disturbances Due to Magnetospheric Forcing The disturbance storm time (Dst) index, in units of nT, is commonly used in upper atmosphere modeling during geomagnetic storms. Usually, Dst decreases as ring current energy increases, following a southward-turning of the interplanetary magnetic field (IMF). However, the Dst index lacks time delay for early warnings of hazardous variability of the thermospheric mass density. Another suitable parameter that closely correlates with mass density variations during geomagnetic storms, and that has a larger time delay, is the merging electric field Em (Calabia & Jin,2019,2021a; Liu etal.,2010), in units of mV/m. The Em index assumes that there is an equal magnitude of the electric field in the solar wind, the magnetosheath, and on the magnetospheric sides of the magnetopause (Kan & Lee,1979). The Em index is a physical quantity that can be easily obtained from solar wind and IMF data, and it correlates significantly with density changes during all storm phases. To compare high-cadence density disturbances due to magnetospheric forcing with the fluctuations of the Em index and models, we first remove the “quiet” background from the time-series. The “quiet” background refers to that of negligible geomagnetic conditions. The “quiet” background is estimated by computing the models at the same locations and times, but with the geomagnetic inputs set to zero. Then, a 30-days mean-average running filter is applied to both densities and Em time-series to remove the long-term variations. It is expected that the resulting short-term variations of both densities and Em time-series will contain the typical 27, 14, and 9-day periods caused by the magnetospheric forcing (Calabia & Jin,2020). Longterm variations of solar wind parameters and geomagnetic activity are usually delayed by two years in time with the activity of the solar-flux cycle (Echer etal.,2004), and its contribution to thermospheric density variability is difficult to detect due to large residuals in the models. Then, a correlation-delay study of the resulting short-term variations (<30days) at different altitudes is performed, to reveal the best possible fit at different lag times within a range of ±18h. In this step, the sequential calculation of the Pearson's linear correlation coefficient using a 30-days running window to obtain the time delays between the filtered densities and the Em index at maximum correlation is used. Finally, the fitting parameters are calculated for the magnitude   Em (kg/m3) and time delay  Em (h) of the density disturbances due to magnetospheric forcing CALABIA AND JIN 10.1029/2021JA029540 5 of 19 21699402, 2021, 8, Downloaded from https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2021JA029540 by Spanish Cochrane National Provision (Ministerio de Sanidad), Wiley Online Library on [28/11/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License Journal of Geophysical Research: Space Physics in terms of the Em index (mV/m) and the solar flux F10.7 index (s.f.u.) (sfu=10−22Wm−2/Hz) as follows:            10.7 15 E 10.7 m m E mm , E p1·E p2 10 100 Ft Ft (2a)       13 EE mm d1· 10 d 2 Em (2b) In these equations, p1, p2, d1, and d2 are the parameters, and t is the Coordinated Universal Time (UTC) in hours. 3. Results and Analysis The thermospheric mass densities from CASSIOPE GNSS precise orbits are estimated at a second interval for the period 2014–2020. Figure2a shows the resulting density estimates from CASSIOPE GNSS along with the HASDM database and the models for a case example on February 20, 2014. The altitudes of the satellite along the orbit are shown in Figure2b. During this period, CASSIOPE's orbital descending node (☋) was approximately located at 13h LST (Figure2c), and the latitudes and longitudes of the satellite along the orbit are shown in Figures2d and2e. In this figure, clear differences between estimates and models can be seen around the perigee location (i.e., location of highest density values along orbit). These differences are mostly caused by inaccuracies in the models during geomagnetic storms. A deeper analysis for this particular storm can be found in Calabia and Jin(2021a). In this study, the analysis of differences with the HASDM database have shown that scaling the CASSIOPE's drag coefficient of Calabia and Jin(2021a) by approximately 0.8 would provide a better match. Using this, the estimated altitude dependence on this scaling factor is given in Table1. The scale factors at each altitude were estimated as the median value of the rate between the time-series. In Figure3, the count of revisiting days is presented as spatial histograms in terms of altitude, latitude, longitude, and LST, for both low and high solar-flux conditions during the period 2014–2020. Here, both inbound and outbound orbits are included. The count has been binned at four altitude ranges (h1<350<h2<400<h3<450<h4<500km), and most of the bins have at least 30days or more. The resulting count is suitable for modeling schemes, statistical analyses, and data validation. The correlation coefficients for the CASSIOPE, JB2008, and NRLMSISE-00 densities with respect to the HASDM densities, at different altitudes, are shown in Table2. The best match is given by the CASSIOPE densities at the lowest altitude (325km), with a correlation of 99.4%. At this altitude, the JB2008 and NRLMSISE-00 densities correlate 1.4% and 3.5% lower, respectively. Then, at 350km altitude, the CASIOPE densities still provide better correlation, with 0.5% and 3% higher values than that given by the JB2008 and NRLMSISE-00 models, respectively. From 375km and above, the correlation given by the JB2008 model reaches a similar value to that of the CASSIOPE densities, while the NRLMSISE-00 model reaches the similar correlation at 425km. 3.1. Ratio of Densities Relative to HASDM Figures4–8 show the CASSIOPE densities and those from the NRLMSISE-00 and JB2008 models, relative to the HASDM densities, for altitudes ranging from 325 to 425km at steps of 25km. Since the samples from the outbound orbits provide similar results, only the samples retrieved from the inbound orbits are shown. The three top panels picture the density ratios of CASSIOPE, NRLMSISE-00, and JB2008, and the solution of the 30-days mean-average running filter. Additions and subtractions of the 30-days standard-deviation running filter to the mean averages are also included, and their magnitudes in the logarithmic scale are shown in the fourth panels. The bottom panels show the background densities. In Figure4, data gaps are caused by the variable altitude of the satellite's perigee, which sometimes does not reach 325km altitude. For density values above ∼10−12kg/m3, the CASSIOPE densities have smaller ratios and smaller standard deviations than that of NRLMSISE-00 and JB2008. For densities above ∼10−11kg/m3, CALABIA AND JIN 10.1029/2021JA029540 6 of 19 Altitude (km) CD scale factor w.r.t. Calabia and Jin(2020) 325 0.86 350 0.82 375 0.81 400 0.78 425 0.77 Table 1 Scale Factor Applied to CD w.r.t. That of Estimated by Calabia and Jin(2021a) 21699402, 2021, 8, Downloaded from https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2021JA029540 by Spanish Cochrane National Provision (Ministerio de Sanidad), Wiley Online Library on [28/11/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License Journal of Geophysical Research: Space Physics it is remarkable that the standard deviations of CASSIOPE can reach 2% of the background density. However, for density values below ∼10−12kg/m3, systematic errors seem to reduce the precision of the CASSIOPE densities. It can be seen that, during low solar flux conditions, the variation of the ratio fluctuates largely (e.g., ±25% in January 2018, 50% in January 2019), but the standard deviation has a moderate increase (below 10%). In Figures5c–8c, the fluctuation of CASSIOPE densities show a clear periodic trend of around 2months, which increases in amplitude with a low-density background. A similar variation, but very less pronounced, is found in the models, with similar variations on May 2017, January 2019, etc. The exact period of 62.5days was estimated by fast Fourier transform (FFT) spectral density analysis. This period was identified with that of the latitudinal variation (periodograms not included). The increases of the density ratio are correlated with higher latitudes, while the ratios decrease with lower latitudes. The existence of systematic errors suggests potential to improve results further. The similarities between the JB2008 and the HASDM densities are significant, in comparison to the NRLMSISE-00 model. This is expected, since the HASDM values are included as empirical basis of the JB2008 model. The discrepancies to the NRLMSISE-00 model show different trends of the ratio, and a variable amplitude of the standard deviation. In general, larger ratios and larger standard deviations at all altitudes are seen from the NRLMSISE-00 densities, in comparison to the JB2008 (full time-series) and the CASSIOPE (density values above ∼10−12kg/m3) densities. For the CASSIOPE and the JB2008 models, the ratio is centered to unit, while the NRLMSISE-00 appears to provide larger ratios during low solar CALABIA AND JIN 10.1029/2021JA029540 7 of 19 Figure 3. Spatial histograms of revisiting days as seen from CAScade SmallSat and IOnospheric Polar Explorer (CASSIOPE)'s orbits for the period 2014–2020. From top to bottom, 4 altitude ranges by rows: (a, e, i, and m) h1<350km, (b, f, j, and n) 350<h2<400km, (c, g, k, and o) 400<h3<450km, and (d, h, l, and p) 450<h4<500km. Low solar flux conditions (F10.7<75s.f.u.) are on the left panels (a–h), and high solar flux conditions (F10.7>75s.f.u.) are on the right panels (i–p). First and third columns (a–d, and i–l) are the geographical coordinates (6°×6° bin), second and fourth columns (e–h, and m–p) are the local solar time (LST) distributions (6°×1-h bin). 45°S 0° 45°N 45°S 0° 45°N 45°S 0° 45°N 90°W 0° 90°E 45°S 0° 45°N 6h 12h18h 90°W 0° 90°E 050100 150200 6h 12h18h m) j) n) a) i) b) f) e) o) k) g) c) d) h) l) p) days Altitude (km) Casssiope NRLMSISE-00 JB2008 325 0.994 0.959 0.980 350 0.992 0.962 0.987 375 0.987 0.961 0.986 400 0.977 0.961 0.985 425 0.956 0.960 0.985 CASSIOPE, CAScade SmallSat and IOnospheric Polar Explorer; HASDM, High Accuracy Satellite Drag Model; JB2008, Jacchia-Bowman/2008; NRLMSISE-00, Naval Research Laboratory Mass Spectrometer and Incoherent Scatter Radar Exosphere/2000. Table 2 Correlation of CASSIOPE, NRLMSISE-00, and JB2008 Densities to the HASDM Densities for the Period 2014–2020 21699402, 2021, 8, Downloaded from https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2021JA029540 by Spanish Cochrane National Provision (Ministerio de Sanidad), Wiley Online Library on [28/11/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License Journal of Geophysical Research: Space Physics CALABIA AND JIN 10.1029/2021JA029540 8 of 19 Figure 4. The (a) Naval Research Laboratory Mass Spectrometer and Incoherent Scatter Radar Exosphere/2000 (NRLMSISE-00), (b) Jacchia-Bowman/2008 (JB2008), and (c) CAScade SmallSat and IOnospheric Polar Explorer (CASSIOPE) densities relative to the High Accuracy Satellite Drag Model (HASDM) densities at 325km altitude. Samples from inbound orbits. Values of (a–d) are dimensionless. Panels (a and b) include the 30-days running window median averages (μ) and standard deviations (μ±σ) of the ratios. Panel (d) shows the standard deviations (i=M, J, C) for comparison, and the background density is shown in (e). 1 2 M/H 1 2 J/H 1 2 C/H 2014 2015 2016 2017 2018 2019 0 1 2 (kg/m3) 10-11 0.01 0.1 1 ( i/H ) a) b) c) d) e) Figure 5. The (a) Naval Research Laboratory Mass Spectrometer and Incoherent Scatter Radar Exosphere/2000 (NRLMSISE-00), (b) Jacchia-Bowman/2008 (JB2008), and (c) CAScade SmallSat and IOnospheric Polar Explorer (CASSIOPE) densities relative to the High Accuracy Satellite Drag Model (HASDM) densities at 350km altitude. Samples from inbound orbits. Values of (a–d) are dimensionless. Panels (a and b) include the 30-days running window median averages (μ) and standard deviations (μ±σ) of the ratios. Panel (d) shows the standard deviations (i=M, J, C) for comparison, and the background density is shown in (e). 1 2 M / H 1 2 J / H 1 2 C / H 2014 2015 2016 2017 2018 2019 0 1 2 (kg/m 3 ) 10-11 0.01 0.1 1 ( i / H ) a) b) c) d) e) 21699402, 2021, 8, Downloaded from https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2021JA029540 by Spanish Cochrane National Provision (Ministerio de Sanidad), Wiley Online Library on [28/11/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License Journal of Geophysical Research: Space Physics CALABIA AND JIN 10.1029/2021JA029540 9 of 19 Figure 6. The (a) Naval Research Laboratory Mass Spectrometer and Incoherent Scatter Radar Exosphere/2000 (NRLMSISE-00), (b) Jacchia-Bowman/2008 (JB2008), and (c) CAScade SmallSat and IOnospheric Polar Explorer (CASSIOPE) densities relative to the High Accuracy Satellite Drag Model (HASDM) densities at 375km altitude. Samples from inbound orbits. Values of (a–d) are dimensionless. Panels (a and b) include the 30-days running window median averages (μ) and standard deviations (μ±σ) of the ratios. Panel (d) shows the standard deviations (i=M, J, C) for comparison, and the background density is shown in (e). 1 2 M / H 1 2 J / H 2014 2015 2016 2017 2018 2019 0 1 2 (kg/m 3 ) 10-11 0.01 0.1 1 ( i / H ) 1 2 C / H a) b) c) d) e) Figure 7. The (a) Naval Research Laboratory Mass Spectrometer and Incoherent Scatter Radar Exosphere/2000 (NRLMSISE-00), (b) Jacchia-Bowman/2008 (JB2008), and (c) CAScade SmallSat and IOnospheric Polar Explorer (CASSIOPE) densities relative to the High Accuracy Satellite Drag Model (HASDM) densities at 400km altitude. Samples from inbound orbits. Values of (a–d) are dimensionless. Panels (a and b) include the 30-days running window median averages (μ) and standard deviations (μ±σ) of the ratios. Panel (d) shows the standard deviations (i=M, J, C) for comparison, and the background density is shown in (e). 1 2 M / H 1 2 J / H 1 2 C / H 2014 2015 2016 2017 2018 2019 0 1 2 (kg/m 3 ) 10-11 0.01 0.1 1 ( i / H ) a) b) c) d) e) 21699402, 2021, 8, Downloaded from https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2021JA029540 by Spanish Cochrane National Provision (Ministerio de Sanidad), Wiley Online Library on [28/11/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License Journal of Geophysical Research: Space Physics A2. Radiation Pressure Acceleration (aR) Radiation pressure accelerations include the direct solar radiation and the Earth's albedo (aR=asr+aea). The direct solar radiation (asr) was formulated by Luthcke etal.(1997):                 , ,, 1 21 c ˆˆ ˆˆ ˆ ˆ 3 npsr i rd i rsi rsi i E An s c a cns n c s m sat i sun sat sat sr i sun i sun (A2) In this equation, np is the number of plates, Ai is the plate area, c is the speed of light, crd,i is the coefficient of diffusive reflectivity, crs,i is the coefficient of specular reflectivity, m is the satellite mass, ˆi n is the unit plate normal, ˆ ssat sun is the unit sun-satellite vector, and    2 1366 1AU / sat sr sun E sh s is the flux on the Earth's atmosphere (1366W/m2), corrected from the yearly period of the Earth's orbit eccentricity and from the planetary eclipse ratio (sh) (Montenbruck & Gill,2013). Similarly, the Earth albedo acceleration (aea) can be computed as follows:                   ,, ,, 11 21 ˆ cˆ 3 ˆˆ ˆˆ np grid ea j i rd i rs i rs i ij E An s c a cns n c s m sat ij sat sat ea i j i j (A3) In this equation, the parameter   IR , R ea j ea ea E EE is the combination of the radiation reflected at the Earth's surface R ea E and the Earth's infrared radiation IR ea E . The Earth's reflected solar radiation R ea E at each satellite position is estimated using the monthly averages of the NASA's Total Ozone Mapping Spectrometer (TOMS) reflectivity index (σ) (Bhanderi,2005):        R ea, j 2 ˆˆ ˆˆ ˆ jj j j sr Ans ns E fvE s sun sat jj jj sat j (A4) In this equation, fj is field of view of the satellite, vj is the sunlight function, and Aj is the area of each cell j of TOMS. The reflection angle on each cell is defined by the directions of the satellite ˆsat j s , the Sun ˆsun j s , and the cell normal-vector ˆj n . The Earth's infrared radiation IR ea E can be modeled as a black body with a surface temperature of 288K, whose spectrum is mainly IR with an exitance of about 239W/m2 (Taylor,2005). In a similar way, the IR irradiance IR ,ea j E from each visible cell j of the Earth's surface has been computed as follows:       2 IR , IR, 2 1AU 2 ˆˆ ˆ 39 sat jj j ea j j j jsat sun j An s Ef e ss (A5) In this equation, the Earth IR radiation IR, j e for each cell j was parameterized in terms of latitude and season by Knocke and Ries(1987):   0 11 2 2 e e P sin e P sin IR e (A6)       1 01 0 2 0 k k cos t k sin te JD JD (A7) Here, t0 is the epoch of December 22, 1981, ω is the Earth orbit rotation rate around the Sun (2π/365.5), φ is the equatorial geocentric latitude, JD is the Julian Date, Pn is the Legendre polynomial of degree n, and e0=0.68; e2=−0.18; k0=0; k1=−0.07, and k2=0. Detailed algorithms and accurate schemes to estimate irradiative accelerations can be found in numerous works, for example, Calabia and Jin(2017), Doornbos(2011), Jin etal.(2018), Sutton(2008), Vielberg and Kusche(2020), Wöske etal.(2019), and the approximated values of CASSIOPE's panel properties are given in Calabia and Jin(2021a), where the visible (VIS) and the infrared (IR) part of the electromagnetic spectrum can be weighted by the amount of solar flux given for each spectral window (43% for VIS, and 53% for IR). CALABIA AND JIN 10.1029/2021JA029540 16 of 19 21699402, 2021, 8, Downloaded from https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2021JA029540 by Spanish Cochrane National Provision (Ministerio de Sanidad), Wiley Online Library on [28/11/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License Journal of Geophysical Research: Space Physics Appendix B: Thermospheric Mass Density (ρ) Retrieval GNSS-based thermospheric mass densities are computed using the drag-force (FD) formula:    2 DD Dr 1A 2 F am C v (B1) In this equation, aD is the acceleration due to air-drag, m is the mass of the satellite, CD is the drag coefficient, ρ is the thermospheric mass density, and A is the cross-sectional area perpendicular to the relative velocity of the atmosphere with respect to the spacecraft vr, which includes the co-rotating atmosphere and the horizontal winds. Horizontal wind velocities are calculated from the horizontal wind model HWM14 (Drob etal.,2015), and the velocity of the co-rotating atmosphere is computed as the vector product between the Earth's angular rotation and the satellite's position vector. In this study, a variable drag coefficient CD is approximated for the CASSIOPE satellite in terms of solar flux and altitude. Modification of the values is provided by Pardini etal.(2006) and for the hexagonal-prism shape of the CASSIOPE satellite using the results of Walker etal.(2014). Conflict of Interest The authors declare no conflicts of interest relevant to this study. Data Availability Statement The CASSIOPE precise orbit data are publicly available from https://epop-data.phys.ucalgary.ca and https://swarm-diss.eo.esa.int. The reflectivity data are available from the Total Ozone Mapping Spectrometer (TOMS) project, http://disc.sci.gsfc.nasa.gov/acdisc/TOMS. The HASDM density data are provided for scientific use courtesy of SET. The space weather data are available from the website of the Low Resolution OMNI (LRO) data set of NASA, http://omniweb.gsfc.nasa.gov/form/dx1.html. The merging electric field Em is computed with the NASA's space weather data following the indications of Liu etal.(2010). The geomagnetic data are available from the International Service of Geomagnetic Indices (ISGI), http://isgi.unistra.fr/ data_download.php. Density data supporting the findings of this study (Calabia & Jin,2021b) are available at http://doi.org/10.5281/zenodo.5079186. References Anderson, R. L., George, H. B., & Forbes, J. M. (2009). Sensitivity of orbit predictions to density variability. Journal of Spacecraft and Rockets, 46(6), 1214–1230. https://doi.org/10.2514/1.42138 Bates, D. R. (1959). Some problems concerning the terrestrial atmosphere above 100km level. 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Thermospheric mass density variations during the March 2015 geomagnetic storm from GRACE accelerometers (pp. 4976–4980). Proceeding of Progress In Electromagnetics Research Symposium (PIERS2016). https://doi.org/10.1109/ PIERS.2016.7735812 Calabia, A., & Jin, S. G. (2017). Thermospheric density estimation and responses to the March 2013 geomagnetic storm from GRACE GPS-determined precise orbits. Journal of Atmospheric and Solar-Terrestrial Physics, 154, 167–179. https://doi.org/10.1016/j.jastp.2016.12.011 CALABIA AND JIN 10.1029/2021JA029540 17 of 19 Acknowledgments This work was supported by the National Natural Science Foundation of China (NSFC) Project (Grant No. 12073012), the Startup Foundation for Introducing Talent of NUIST (Grant No. 2243141801036), and the Talent StartUp Funding project of NUIST (Grant No. 1411041901010). 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