Upper-Atmosphere Mass Density Variations From CASSIOPE Precise Orbits

1. Introduction Low Earth Orbit (LEO) satellites are significantly affected by variable air drag forces, which are mainly altered by atmospheric expansion/contraction driven by solar and geomagnetic activity. Air drag reduces the orbital velocity of a satellite, its nominal altitude, and shortens its lifespan. The effect of air drag pressure on the position of a satellite orbiting at an altitude of around 450km may drag around 3m per revolution in the along-track axis, limiting the satellite’s lifespan to approximately 5–10years. In applications, such as remote sensing or satellite altimetry and gravity, the orbital trajectory and velocity (ephemeris) of satellites must be known to an accuracy of a few millimeters. Moreover, the exponential increase in presence of space debris (consider the recent destructive events of Fengyun-1C, Iridium, and Mission Shakti) has highlighted the importance of orbital tracking and prediction of potential collisions. The dynamic Precise Orbit Determination (POD) method tracks and predicts the orbital ephemeris by calculating an orbital trajectory through a double integration and linearization of Newton-Euler’s equation of motion (Montenbruck & Gill,2013). In the POD method, by combining force models with empirical observations, used for example in laser-ranging, Doppler, accelerometer, or Global Navigation Satellite System (GNSS) measurements, the position, and velocity of a satellite can be stochastically estimated with significant accuracy (Jin & Su,2020; Tapley etal.,2004). Due to variable air drag force being so important, in the last decade, thermospheric mass density (TMD) variations driven by solar and geomagnetic activity have been investigated using satellite technology to a great extent (e.g., Calabia & Jin,2016,2019; Chen etal.,2014; Cnossen & Förster,2016; Doornbos etal.,2010; Emmert & Picone,2010; Ercha etal.,2012; Guo etal.,2016; Lei etal.,2010,2012; H. Liu etal.,2009; R. Liu etal.,2010,2011; Müller etal.,2009; Panzetta etal.,2018; Sutton etal.,2009). But these studies have in turn exposed the limitations of the existing empirical models (e.g., JB2008 [Bowman etal.,2008], DTM [Bruinsma,2015], NRLMSISE-00 [Picone etal.,2002]) in accurately predicting TMD variations, especially during geomagnetic storm conditions. The resulting positioning errors, from these limitations, affect the POD accuracy so significantly, they fail to meet the operational requirements for precise orbital tracking (Anderson etal.,2009; Calabia etal.,2020). This is largely due to the limited quality and quantity of observations used Abstract Thermospheric mass density (TMD) measurements are invaluable to accurately estimate and predict the position and velocity of orbiting objects in Low Earth Orbit (LEO). Existing observational methods and predictive models have some problems (e.g., accuracy, resolution, coverage, cost, etc.) to describe and forecast the actual air drag variations as required for practical applications. With the increasing number of LEO satellites equipped with high-precision Global Navigation Satellite System (GNSS) receivers, the precise orbits can be used to obtain non-gravitational accelerations, and therefore estimate TMD variations. In this study, TMD is estimated from the precise orbits of CAScade SmallSat and IOnospheric Polar Explorer (CASSIOPE) at one-second time step, and the TMD variations following the February 2014 geomagnetic storm are investigated. Using this method, a more detailed description than previous methods and empirical models is given with short-term TMD variations during geomagnetic storm conditions. The empirical model NRLMSISE-00 shows less pronounced and more averaged variations, while CASSIOPE-derived TMD can reflect the abrupt disturbances triggered by the geomagnetic storm. CASSIOPE TMD shows a correlation of 72.4% to the merging electric field Em index, while the NRLMSISE-00 model shows a correlation of 42.1%. CALABIA AND JIN © 2021. The Authors. This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made. Upper-Atmosphere Mass Density Variations From CASSIOPE Precise Orbits Andrés Calabia1,2 and Shuanggen Jin1,3 1School of Remote Sensing and Geomatics Engineering, Nanjing University of Information Science and Technology, Nanjing, China, 2School of Land Surveying, Geodesy and Mapping Engineering, Universidad Politécnica de Madrid, Madrid, Spain, 3Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai, China Key Points: • Thermospheric mass densities are estimated from CAScade SmallSat and IOnospheric Polar Explorer precise orbits • The detailed thermospheric mass density responses are obtained during the February 2014 geomagnetic storm • CASSIOPE-derived thermospheric mass density is better than the NRLMSIS-00 model to reflect responses to the storm Correspondence to: S. Jin, [email protected]; [email protected] Citation: Calabia, A., & Jin, S. (2021). Upperatmosphere mass density variations from CASSIOPE precise orbits. Space Weather, 19, e2020SW002645. https:// doi.org/10.1029/2020SW002645 Received 6 OCT 2020 Accepted 29 MAR 2021 Author Contributions: Conceptualization: Andrés Calabia 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: Andrés Calabia Visualization: Andrés Calabia 10.1029/2020SW002645 Special Section: Small Satellites for Space Weather Research and Forecasting Workshops RESEARCH ARTICLE 1 of 10 Space Weather to better measure the TMD variability, and the lack of comprehensive approaches to calibrate the models (Emmert,2015; Jin etal.,2018). For example, accelerometer-based TMD estimates are very sensitive and globally distributed (usually at a second interval along orbits), but the measurement method is very expensive, has a low revisiting-time, calibration difficulties to estimate the actual TMD, and only a few missions have provided good data, viz. Challenging Minisatellite Payload (CHAMP) (Bruinsma etal.,2004; Sutton etal.,2007), Gravity Recovery and Climate Experiment (GRACE) (Calabia,2016; Doornbos,2012; Sutton,2008), Gravity field and steadystate ocean circulation explorer (GOCE) (Bruinsma etal.,2014), and Swarm (Siemes etal.,2016). Note that the original purpose of these missions was not the estimation of in situ TMD. Other methods also have their drawbacks varying in problems with accuracy, resolution, coverage, revisiting-time, calibration, complexity, and so on. A list of the existing measurement methods includes the semi-major axis variation method (Picone etal.,2005), the stochastic TMD estimation within the POD approaches (IJssel & Visser,2007; Kuang etal.,2014; McLaughlin etal.,2013; Visser etal.,2013), mass spectrometers (Tang etal.,2020), incoherent scatter radars (Nicolls etal.,2014), Broglio drag balance instruments (Santoni etal.,2010), miniaturized pressure gauge instruments (Clemmons etal.,2008), ultraviolet remote sensing (Meier & Picone,1994; Meier etal.,2015), and the techniques of atmospheric occultation (Aikin etal.,1993; Determan etal.,2007). Nowadays, with the increasing number of LEO satellites equipped with high-precision GNSS receivers, the precise orbits can be used to obtain non-gravitational accelerations at a high resolution, and therefore estimate TMD variations (Calabia & Jin,2017). Geomagnetic storms cause large and abrupt TMD increases lasting from several hours to several days (Calabia & Jin,2019), while the existing observational methods and empirical models fail to describe and predict these TMD variations with enough resolution and accuracy. Previous studies using the acceleration approach have attempted to stochastically estimate high-frequency TMD variations within the POD method (e.g., IJssel,2014; IJssel & Visser,2007; Kuang etal.,2014), but their results showed too low resolution with a unique solution in each estimation interval (∼20min) to study high-frequency disturbances caused by, for example, geomagnetic storms (Liangliang etal.,2019). For this work, TMD is calculated along CAScade SmallSat and IOnospheric Polar Explorer (CASSIOPE) precise orbits at one-second time step, and the density responses to the February 2014 geomagnetic storm are investigated and evaluated. A more detailed discussion in view of the achieved accuracy along the elliptic orbit is given in the following sections. 2. Data and Methods 2.1. CASSIOPE Precise Orbit Data The CASSIOPE spacecraft was launched on September 29, 2013, into a slightly eccentric polar orbit of 81° inclination with a perigee of approximately 325km altitude and an apogee near 1,500km altitude. While previous commercial-off-the-shelf GNSS receivers have provided limited accuracy, the CASSIOPE satellite has demonstrated its full capability for geodetic observations at an affordable cost in low-budget space missions (Kim & Langley,2019). The CASSIOPE satellite uses five commercial-off-the-shelf, geodetic grade, dual-frequency GPS receivers L1 C/A and L2 P(Y) tracking up to 12 satellites, to be used for high precision navigation, attitude determination, time synchronization, and radio occultation measurements. The precise orbit solutions at a second interval were computed by Montenbruck etal.(2019) in a reduced-dynamic approach with float-ambiguity estimation using the ionosphere-free linear combination of dual-frequency code and carrier phase observations. Associated imperfections in the density and drag model were compensated through piecewise constant empirical accelerations with zero a priori values. This strategy allows counterbalancing both the disadvantages of the GNSS measurement noises and the uncertainties in the models. 2.2. Calculation of Air Drag Acceleration Non-gravitational accelerations acting on LEO satellites mainly include air drag and irradiative accelerations. The method proposed in (Calabia etal.,2015) computes instantaneous total accelerations through numerical differentiation of the precise velocities so that the “observed” air drag accelerations acting on the satellite are obtained by removing the gravitational and radiation pressure accelerations at each satellite’s CALABIA AND JIN 10.1029/2020SW002645 2 of 10 Writing – original draft: Andrés Calabia Writing – review & editing: Andrés Calabia, Shuanggen Jin 15427390, 2021, 4, Downloaded from https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2020SW002645 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 Space Weather position. As recommended by the authors, the 8-data point piece-wise Lagrange interpolation and a time-interval of 0.05s are suggested for the numerical differentiation. These settings limit the bias error in the numerical differentiation (arc-to-chord threshold approach) to approximately 10−9m/s2. Table1 summarizes the gravitational force models used in this study. The conventional gravity model is based on the EGM2008 with the underlying background for the secular variations (Petit & Luzum,2010). We employ the EOT11a ocean tides of Mayer-Gürr etal.(2012), the ocean pole tide of Desai(2002), and the third body tide caused by the Moon and Sun are calculated with the Jet Propulsion Laboratory (JPL) DE421 ephemeris following the indications of Montenbruck and Gill(2013). Time-varying Stokes’ coefficients up to a degree and order of 120 are computed (including sub-daily variations) with an increment of time small enough (∼3,600s) to desensitize from discontinuities in the resulting non-gravitational accelerations. We employ the first derivative of the gravitational potential in Cartesian coordinates (Frommknecht,2008) to compute the gravity at each epoch along the CASSIOPE orbits. The transformations between reference-systems follow the conventions of Petit and Luzum(2010). Irradiative accelerations mainly include the direct solar radiation, the radiation reflected at the Earth’s surface, and the Earth’s infrared radiation. While the Earth’s infrared radiation (long-wave radiation) is almost independent of illumination conditions, the other two solar radiations (short-wave radiation) must account for the planetary eclipse ratio (Montenbruck & Gill,2013). On the plates of the user’s satellite, one part of the incoming radiation is absorbed and the other is reflected diffusely and specularly. Luthcke etal.(1997) formulated the entire resultant force on the satellite due to the solar radiation, which accounts for each satellite’s plate areas and their orientation, its coefficients of diffusive (crd) and specular (crs) reflectivity, and the mass of the satellite (the CASSIOPE satellite has a mass of approximately 500kg). The Earth’s infrared radiation is computed following the indications of Knocke and Ries(1987), and the reflected radiant flux is calculated with the monthly averages of NASA’s Total Ozone Mapping Spectrometer (TOMS) reflectivity index following the indications of Bhanderi(2005). For these calculations, the geometry model of the CASSIOPE spacecraft is given in Figure1, and its surface properties are given in Table2. Additional details can be found in Montenbruck etal.(2019). Detailed algorithms and accurate schemes to estimate irradiative accelerations can be found in numerous works, for example, Vielberg and Kusche(2020), Wöske etal.(2019), Jin etal.(2018), Calabia and Jin(2017), Doornbos(2012), Sutton etal.(2007). 2.3. Estimation of TMD TMD estimates are computed using the drag-force (FD) formula (Newton,1726):    2 DD D 1 . 2 r F am CAv (1) 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 TMD, 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 CALABIA AND JIN 10.1029/2020SW002645 3 of 10 Models Details Earth gravity EGM2008 with low degree rates. Degree 120. Petit and Luzum(2010). Third bodies Moon and Sun from JPL DE421. Montenbruck and Gill(2013). Earth tides Due to Moon and Sun, Wahr terms. Petit and Luzum(2010). Ocean tides EOT11a (256 tides). Degree 120. Mayer-Gürr etal.(2012). Solid Earth pole tide IERS 2010 using sub-daily wobble variables. Petit and Luzum(2010). Ocean pole tide From Desai(2002) using sub-daily wobble variables. Degree 120. Relativity Schwarzschild correction. Petit and Luzum(2010). Table 1 Gravitational Force Models Used in This Study 15427390, 2021, 4, Downloaded from https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2020SW002645 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 Space Weather 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. Unfortunately, Equation1 is incomplete, since both ρ and CD are usually unknown parameters. The accurate estimation of CD for LEO satellites is still a challenge (e.g., March etal.,2019; Mehta etal.,2014), and the lack of direct measurements complicates the estimation of the actual TMD. Estimating CD of LEO satellites depends on many factors, including energy accommodation, gas-surface interaction, molecular reflections distribution, atmospheric compositions and temperature, and satellite geometry, speed, attitude, temperature, composition, and so on. However, by using an approximation of the actual CD value, the results from Equation1 can provide estimates of the relative variations of TMD, which are very valuable to describe and localize in detail short-term disturbances caused by, for example, geomagnetic storms. Then, CALABIA AND JIN 10.1029/2020SW002645 4 of 10 Figure 1. Geometry model of the CASSIOPE spacecraft in the satellite’s body reference system (Xb, Yb, Zb). CASSIOPE, CAScade SmallSat and IOnospheric Polar Explorer. Panel Area(m2)XbYbZbMaterial crs VIS crd VIS crs IR crd IR Zenit 2.1 0 0 −1 Si glass-solar array 0.05 0.30 0.03 0.16 Nadir 1 1.2 0 0 +1 Teflon 0.68 0.20 0.19 0.06 Nadir 2 0.6 0 0 +1 SiOx/Kapton 0.40 0.26 0.23 0.15 Nadir 3 0.4 0 0 +1 Glass 0.05 0.30 0.03 0.16 Front 1.1 1 0 0 SiOx/Kapton 0.40 0.26 0.23 0.15 Rear 1.1 −1 0 0 SiOx/Kapton 0.40 0.26 0.23 0.15 Right/front 1 0.7 +0.86 +0.86 0 Si glass-solar array 0.05 0.30 0.03 0.16 Right/front 2 0.4 +0.86 +0.86 0 SiOx/Kapton 0.40 0.26 0.23 0.15 Right/rear 1.1 −0.86 0.86 0 Si glass-solar array 0.05 0.30 0.03 0.16 Left/front 1 0.7 −0.86 0.86 0 Si glass-solar array 0.05 0.30 0.03 0.16 Left/front 2 0.4 −0.86 0.86 0 SiOx/Kapton 0.40 0.26 0.23 0.15 Left/rear 1.1 −0.86 −0.86 0 Si glass-solar array 0.05 0.30 0.03 0.16 Note. For each surface, an estimate of the area, the components of its unit normal in the satellite reference system, the material, as well as its diffusive (crd) and specular (crs) reflectivity coefficients for the visible (VIS) and the infrared (IR) are provided. Table 2 Surface Properties for the CASSIOPE Spacecraft 15427390, 2021, 4, Downloaded from https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2020SW002645 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 Space Weather the NRLMSISE-00 semi-empirical model (Picone etal.,2002) can be used to assess for accuracy of the resulting estimates. Note that NRLMSISE-00 is based on averaged values from several measurement techniques, including mass spectrometers, incoherent scatter radars, satellite drag data, and solar ultraviolet occultation. In this study, we approximate a variable CD for CASSIOPE in terms of solar flux and altitude. The following assumptions are adopted. We first employ the CD values provided by Pardini etal.(2006) for a spherical satellite, which are dependent on altitude and solar activity. Then, we adjust these values to the hexagonal-prism shape of CASSIOPE (Figure1) with a scaling factor based on the work done by Walker etal.(2014), who estimated CD values for different satellite shapes as a function of atmospheric number density. Since the orbit of CASSIOPE ranges altitudes from approximately 300 to 1,400km, it is estimated that the maximum value of atmospheric number density for altitudes above 300km is approximately 1015. 3. Results and Analysis 3.1. Drag Coefficient for the CASSIOPE Spacecraft Figure2 shows NRLMSISE-00 estimates as a function of altitude for an arbitrary location. Walker etal.(2014) showed that for number density values below 1016 the drag coefficient for a spherical satellite is 2.2. Similarly, following the results of Walker etal.(2014), a value of approximately 2.3 is estimated for a satellite with a hexagonal-prism shape, analogous to that of CASSIOPE (slightly between a cube and a cylinder perpendicular to the flow). This corresponds to a drag coefficient ratio between a spherical satellite and a hexagonal-prism satellite of approximately 1.05. Following these hypotheses, all possible values of CD are calculated, and TMD can be estimated using Equation1. Figure3 shows the resulting drag coefficient CD for CASSIOPE as a function of altitude and solar activity, and the TMD results are shown in the next section. 3.2. TMD Estimation and Responses to the February 2014 Geomagnetic Storm In February 2014, four powerful Earth-directed coronal mass ejections (CMEs) triggered a highly complex, multiphase geomagnetic storm. The first two CMEs arrived on 19 and 20 February, the other two arrived on 23 and 27 February. The corresponding TMD responses as seen by CASSIOPE and NRLMSISE-00 are analyzed in Figures4 and5, focusing first on the storm of 20 February and then a complete 15-day period, respectively. In these figures, the merging electric field Em and the disturbance storm time Dst index are included to identify the progress of the events. It is well known that these two indices can represent with high resolution the TMD variations triggered by magnetospheric forcing (Calabia & Jin,2019). Note that a minor storm ranges −30nT>Dst>−50nT, a moderate storm −50nT>Dst>−100nT, an intense storm −100nT>Dst>−250nT, and a great storm Dst<−250nT (Gonzalez etal.,1999). The first storm started at 14:00 UT (universal time) on 18 February, showing a Dst drop down to −112nT at 09:00 UT on 19 February. The second storm began around 04:00 UT on 20 February (blue circles in Figure4c), showing a Dst drop from −40nT down to −86nT at 12:00 UT. The Dst index recovered rapidly up to −40nT at 19:00 UT, and then gradually increased to 4nT until the onset of the third storm at 08:00 UT on 23 February, followed to a minimum of −56nT at 00:00 UT on 24 February. The last storm began at 16:00 UT on 27 February, showing a minimum Dst of −99nT at 00:00 UT on 28 February. CALABIA AND JIN 10.1029/2020SW002645 5 of 10 Figure 2. Principal constituents of the upper atmosphere at a random location (φ=45°S, λ=180°E) estimated by NRLMSISE-00 on February 15, 2014 at 0h UT. 1051010 1015 Atmospheric number density (m-3) 280 400 520 640 760 880 1000 Altitude (km) He O N 2 O 2 Ar H N O + Total Figure 3. Drag coefficient for the CASSIOPE spacecraft as a function of altitude and solar activity. CASSIOPE, CAScade SmallSat and IOnospheric Polar Explorer. 200 400 600 800 1000 1200 1400 Altitude (km) 50 100 150 200 Flux 10.7 (sfu) 2.4 2.6 2.8 3 CD 15427390, 2021, 4, Downloaded from https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2020SW002645 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 Space Weather During this period, CASSIOPE’s orbital descending node (☋) was approximately located at 13:00 Local Solar Time (LST), reaching its lowest altitude at approximately 62°N latitude (location of the orbital perigee). Figure4d displays the latitude and altitude of the CASSIOPE’s orbital trajectory, and Figure4a shows the drag acceleration (aD) calculated from CASSIOPE precise orbits on February 20, 2014 (see the Methods section, Calculation of air drag acceleration aD). In this figure, enhanced air drag accelerations can be clearly seen a few hours after the storm, at 12:00 UT. The corresponding TMD estimates along with the estimates of the NRLMSISE-00 model are shown in Figure4b. In this study, the CASSIOPE TMD estimates have been smoothed with a 6min mean-average running filter to exclude signal-noises and outliers. Noises and outliers may be originated from errors induced in the stochastic POD solution, or even actual accelerations along the orbits (further study is required). Assuming that the TMD estimates above ∼800km altitude should be zero, that is, TMD estimate reflects only noise there, the standard deviation of the CASSIOPE estimates during this period, and for altitudes above 800km, has shown to be 1.3×10−12Kg/m3. However, the actual error at lower altitudes would likely be larger due to the existence of other error sources, which are proportional to the TMD signal, for example, the drag coefficient. Future investigations will address the accuracy of a larger TMD data set, and the possible dependence of the errors to other factors, including altitude, latitude, LST, and annual and solar cycles. The upper bounds of TMD (lowest altitude) are plotted in dashed lines for clarity (Figure4), showing obvious differences between CASSIOPE and NRLMSISE-00 TMD estimates. NRLMSISE-00 shows less pronounced and more averaged variations, while CASSIOPE TMD can reflect the abrupt disturbances triggered by the geomagnetic storm, following the variations of the merging electric field Em. The corresponding delay-time of approximately 7h with the maximum of the merging electric field Em (arrowheads) agrees well with the reported values in Calabia and Jin(2019). Figures5a and5b show the CASSIOPE and NRLMSISE-00 TMD CALABIA AND JIN 10.1029/2020SW002645 6 of 10 Figure 4. In (a), we show the drag acceleration (aD) from CASSIOPE’s precise orbits on February 20, 2014 (☋≈13:00 LST). The corresponding TMD estimates (original and smoothed at 6min mean-average running filter) along with the NRLMSISE-00 estimates are shown in (b). The upper bounds of TMD are plotted in dashed lines, the circles indicate the relative minimum and maximum values, and the arrowheads show the delay-time of approximately 6h with respect to the maximum of the merging electric field Em. In (c), we show the merging electric field Em and the disturbance storm time Dst index. In (d), we include the orbit latitude and altitude of CASSIOPE. CASSIOPE, CAScade SmallSat and IOnospheric Polar Explorer; TMD, thermospheric mass density. 0 1 2 3 TMD (kg/m3) 10-11 CASSIOPE NRLMSISE-00 CASSIOPE smoothed 06:00 UT 12:00 UT 18:00 UT 20 February 2014 -75 0 75 Latitude (degrees) 375 900 1425 Altitude (km) -100 -50 0 Dst (nT) 800 5000 9200 Em (V/m) -8 -4 0 aD (m/s2) 10-6 d) c) b) a) 15427390, 2021, 4, Downloaded from https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2020SW002645 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 Space Weather estimates below 400km altitude for the second half of February 2014. The differences between these figures are displayed in Figure5c. This figure shows the limited performance of NRLMSISE-00 to localize and represent, with high resolution, the short-term variations, and small features during the different phases of the storm. Similar to Figure4b, Figure5d shows the upper bounds of TMD (lowest altitude) as described by CASSIOPE and NRLMSISE-00. In this figure, both CASSIOPE and NRLMSISE-00 upper-bounds display similar values previous to the storm (15–18 February), but afterward a clear bias develops as the storm gets more complex. This feature suggests that NRLMSISE-00 underestimates the recovery phase of highly complex, multiphase geomagnetic storms. Finally, Figure6 shows the lag-time Pearson linear correlation coefficients for both CASSIOPE and NRLMSISE-00 upper bounds of TMD (lowest altitude) with respect to the Em index. In this analysis, we employ the second half of February 2014, and apply a lag-time range of ±18h. The maxima correlation corresponds to CASSIOPE with 72.4% at a time delay of 7.5h. These results agree very well with the reported values of Calabia and Jin(2019) for the northern hemisphere. On the other hand, NRLMSISE-00 shows a maxima correlation of 42.1%, with a time delay of 9.3h. Besides the poor correlation to the Em index, these results also suggest that NRLMSISE-00 retards the actual TMD responses in about 1.8h. CALABIA AND JIN 10.1029/2020SW002645 7 of 10 Figure 5. TMD estimates below 400km altitude from (a) CASSIOPE’s precise orbits and from (b) NRLMSISE-00 during the second half of February 2014. The differences are shown in (c). Similar to Figure4, the upper bounds of TMD are plotted in (d). In (e), we show the merging electric field Em and the disturbance storm time Dst index. CASSIOPE, CAScade SmallSat and IOnospheric Polar Explorer; TMD, thermospheric mass density. 15427390, 2021, 4, Downloaded from https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2020SW002645 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 Space Weather 4. Conclusions We have examined the efficacy of TMD estimation using CASSIOPE’s precise orbit position and velocity derived from GNSS measurements, and the results can confirm the high resolution of the new TMD estimates. In this approach, “observed” air drag accelerations are computed through numerical differentiation of the precise velocities, so that gravitational and radiation pressure accelerations can be subsequently removed. Afterward, the resulting air drag accelerations allow the computation of high-cadence TMD estimates. Due to the lack of direct CD or TMD measurements for validation, we have approximated a variable CD for the CASSIOPE satellite, and compared the resulting TMD estimates with that modeled by the NRLMSISE-00 model. In this study, the new TMD estimates from CASSIOPE GNSS receivers have shown a great potential to describe in detail the short-term variations caused by the February 2014 geomagnetic storm. TMD estimates from both CASSIOPE and NRLMSISE-00 have displayed similar values previous to the storm, but these started to disagree as the geomagnetic-storm disturbances evolved. Moreover, NRLMSISE-00 has exhibited to underestimate the recovery phase of this highly complex, multiphase geomagnetic storm. Finally, the correlation to the Em index has confirmed the poor performance of NRLMSISE-00 to represent the TMD disturbances during this storm, and a time-lag of about 1.8h. Estimating high-resolution TMD is a very relevant topic, since the performance of existing models used in POD is limited, especially during geomagnetic-storm times. In this manuscript, we have demonstrated that the GNSS-derived TMD estimates of the CASSIOPE satellite are valuable observations to be used and investigated in numerous studies. TMD is essential for space technologies and research, but the existing measurement techniques fail in quantity and quality to develop accurate empirical models. Using this technique, TMD can be sensed at high-resolution from GNSS receivers, and this will provide numerous TMD data sets from other missions to improve the existing state-of-the-art. Future works are addressed, but not restricted, to improve the force models, to mitigate the signal noises, and to investigate the accuracy of a larger TMD data set. Finally, we highlight the need to increase the research efforts to accurately estimate or directly measure the actual TMD and/or drag coefficient CD of satellites. Data Availability Statement The CASSIOPE precise orbit data are publicly available from https://epop-data.phys.ucalgary.ca and ftp:// 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 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 R. Liu etal.(2010). The geomagnetic data are available from the International Service of Geomagnetic Indices (ISGI), http://isgi.unistra.fr/data_download.php. All data supporting the findings of this study will be available upon request. References Aikin, A. C., Hedin, A. 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Acknowledgments This work was supported by the National Natural Science Foundation of China-German Science Foundation (NSFC-DFG) Project (Grant No. 41761134092), the Startup Foundation for Introducing Talent of NUIST (Grant No. 2243141801036), and the Talent Start-Up Funding project of NUIST (Grant No. 1411041901010). Great appreciation is extended to ESA’s Swarm mission and to CASSIOPE/e-POP team at the University of Calgary for providing the precise orbit data, and to NASA and ISGI for the space weather and geomagnetic indices. The authors are very thankful to the anonymous reviewers, Dr. Liu Jiandong, Ms. Catherine M Jones, and Ms. Yijie Ning for their revisions and suggestions to improve a previous version of the manuscript. 15427390, 2021, 4, Downloaded from https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2020SW002645 by Spanish Cochrane National Provision (Ministerio de Sanidad), Wiley Online Library on [28/11/2025]. 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