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PUBLICATIONS Space Weather RESEARCH ARTICLE 10.1002/2017SW001759 Special Section: Low Earth Orbit Satellite Drag: Science and Operational Impact Key Points: • An empirical exospheric temperature model (ETM) is developed • The thermospheric evolutions of temperature and mass density are well characterized by the ETM • The ETM can be embedded in the empirical model to provide better specification of the thermospheric variations

Correspondence to: J. Lei, [email protected]

Citation: Ruan, H., Lei, J., Dou, X., Liu, S., & Aa, E. (2018). An exospheric temperature model based on CHAMP observations and TIEGCM simulations. Space Weather, 16. https://doi.org/10.1002/ 2017SW001759 Received 6 NOV 2017 Accepted 30 JAN 2018 Accepted article online 7 FEB 2018

An Exospheric Temperature Model Based On CHAMP Observations and TIEGCM Simulations Haibing Ruan1,2

, Jiuhou Lei1,2,3

, Xiankang Dou1

, Siqing Liu4,5

, and Ercha Aa4

1

CAS Key Laboratory of Geospace Environment, University of Science and Technology of China, Hefei, China, 2Mengcheng National Geophysical Observatory, University of Science and Technology of China, Hefei, China, 3Collaborative Innovation Center of Astronautical Science and Technology, Harbin, China, 4National Space Science Center, Chinese Academy of Sciences, Beijing, China, 5College of Earth Sciences, University of Chinese Academy of Sciences, Beijing, China

Abstract

In this work, thermospheric densities from the accelerometer measurement on board the CHAMP satellite during 2002–2009 and the simulations from the National Center for Atmospheric Research Thermosphere Ionosphere Electrodynamics General Circulation Model (NCAR-TIEGCM) are employed to develop an empirical exospheric temperature model (ETM). The two-dimensional basis functions of the ETM are first provided from the principal component analysis of the TIEGCM simulations. Based on the exospheric temperatures derived from CHAMP thermospheric densities, a global distribution of the exospheric temperatures is reconstructed. A parameterization is conducted for each basis function amplitude as a function of solar-geophysical and seasonal conditions. Thus, the ETM can be utilized to model the thermospheric temperature and mass density under a specified condition. Our results showed that the averaged standard deviation of the ETM is generally less than 10% than approximately 30% in the MSIS model. Besides, the ETM reproduces the global thermospheric evolutions including the equatorial thermosphere anomaly.

1. Introduction Satellite drag associated with thermospheric density and winds plays an important role in the spacecraft operation, especially for the low Earth orbiting satellites. The thermosphere has complex spatial and temporal variations due to the fact that driving sources of the thermosphere, including solar and lower atmospheric forcing, vary greatly with both time and space. Consequently, the prediction of the thermospheric variability and the associated atmospheric drag is still a frontier research topic. The empirical thermospheric models, such as Jacchia-class model and Mass Spectrometer Incoherent Scatter (MSIS) model, are widely utilized and contribute greatly to the determination and prediction of thermospheric mass density (e.g., Emmert, 2015; Hedin, 1991; Hickey, 1988; Jacchia, 1970; Marcos, 2006). However, these empirical models suffer more or less from insufficient data coverage, and the thermospheric dynamics are missing or not well parameterized. The uncertainty or error in the density prediction of these empirical models is 15%–20% under geomagnetically quiescent condition (e.g., Pardini et al., 2012; Vallado & Finkleman, 2014), and it can go up an order of magnitude larger under the geomagnetically active conditions (e.g., Bruinsma et al., 2006; Lei, Thayer, Lu, et al., 2011). In the recent years, a great effort has been made to improve the specification and the accuracy of the thermospheric models (e.g., Bruinsma et al., 2017; Calabia & Jin, 2016; Lei, Matsuo, et al., 2012; Liu et al., 2013; Marcos et al., 1998; Matsuo et al., 2012; Mehta & Linares, 2017; Morozov et al., 2013; Storz et al., 2005; Sutton et al., 2012; Weimer et al., 2016; Weng et al., 2017; Yamazaki et al., 2015). With the assumptions of the hydrostatic and diffusion equilibrium, thermospheric mass density is generally determined by the exospheric temperature and the flection-height temperature in the traditional empirical models (e.g., Jacchia, 1970; Marcos et al., 1998; Storz et al., 2005; Sutton et al., 2012). Since the temperature at the flection height does not vary greatly, the correction of the exospheric temperature becomes a common way to improve the density specification (Choury et al., 2013; Marcos et al., 1998; Storz et al., 2005; Sutton et al., 2012; Weng et al., 2017).

©2018. American Geophysical Union. All Rights Reserved.

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Sutton et al. (2012) utilized the principal component analysis (PCA) to develop the basis functions to reconstruct the spatiotemporal variability of the temperature parameters, showing an improved representation over the standard spherical harmonic approach. Recently, Mehta and Linares (2017) derived the principal components in the variation of the upper thermosphere from the MSIS model with a small number of

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Figure 1. (a) Daily solar radio flux proxy F10.7, (b) geomagnetic activity index Ap, and (c) the effective exospheric temperature obtained from CHAMP observations (blue line), the Thermosphere Ionosphere Electrodynamics General Circulation Model (TIEGCM) model (red line) and the Mass Spectrometer Incoherent Scatter (MSIS) model (gray line) during 2002–2009.

modes and parameters. Then, a global variation of the upper thermosphere is regressed utilizing the sparse data from CHAMP satellite. In this study, we utilize thermospheric densities from CHAMP satellite during 2002–2009 and the simulations from Thermosphere Ionosphere Electrodynamics General Circulation Model (TIEGCM) to develop an empirical exospheric temperature model (ETM). The basis functions are first obtained from the TIEGCM simulations by the PCA, and the amplitudes of the basis functions are constrained by the CHAMP deriving exospheric temperatures. In this way, the global evolution can be reconstructed with the sparse observations. As a consequence of parameterizing the solar-geophysical dependence, the global thermospheric temperature and mass density can be predicted.

2. Observations and Model 2.1. CHAMP Observations The latest version of the thermospheric neutral mass densities derived from the accelerometer measurement on CHAMP satellite (Mehta et al., 2017) during 2002–2009, which is updated from the retrieved density of Sutton et al. (2005) but with the new drag coefficient, is utilized in this work. Figure 1 gives the daily average of the solar radio flux F10.7 and geomagnetic activity index Ap during this period. As illustrated in this figure, the solar radio flux F10.7 ranged from 70 solar flux unit (sfu) in 2008 to about 240 sfu in 2002 (1 sfu = 1022W m2 Hz1). The geomagnetic activity index Ap in Figure 1b varied a lot during 2002– 2009, and its variability is more profound during the high solar activity period. With the aid of the empirical model, the effective exospheric temperature can be derived from the mass density observations (Forbes et al., 2009; Weimer et al., 2016). The procedure of deriving exospheric temperatures from the CHAMP thermospheric densities can be found in Weng et al. (2017). The daily averaged exospheric temperatures from CHAMP data and the corresponding results from the TIEGCM and MSIS models are compared in Figure 1c. An obvious dependence on solar and geomagnetic activity is demonstrated in the evolution of the exospheric temperatures from CHAMP and the models. The derived CHAMP exospheric temperatures will be used in the data-driven process of the ETM development, as described later. 2.2. TIEGCM National Center for Atmospheric Research-TIEGCM (Richmond et al., 1992; Roble et al., 1988) is a timedependent, three-dimensional model solving fully coupled, nonlinear, hydrostatic, thermodynamic, and

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Figure 2. Variations of the basis functions (a–e) PC1–PC5 in unit of 10 (f) their relative contributions to the total variance.

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as a function of local time and latitudes and

continuity equations of neutral gas self-consistently with ion energy, ion momentum, and ion continuity equations from the upper mesosphere to the thermosphere (ranging from near 100 km to above 500 km). The TIEGCM version utilized in this work is 1.95. Neutral temperature stays constant with height above 300 km due to the molecular diffusion and so would be the horizontal distribution of the temperature. Neutral temperature at the altitude of ~500 km is referred to as the exospheric temperature in this work. The solar radio flux (F107) and geomagnetic index (Kp) are used as the model inputs. The horizontal resolution for the simulations is 5° × 5° in latitude and longitude. The ion convection patterns at high latitudes are specified by the empirical model of Weimer (2005), and lower atmospheric tides are the migrating diurnal and semidiurnal tides specified by the Global Scale Wave Model (Hagan & Forbes, 2002, 2003). Note that the field-aligned ion drag (Lei, Thayer, et al., 2012; Lei, Matsuo, et al., 2012) is also included to better represent the equatorial thermosphere anomaly (ETA). In this work, we conduct the TIEGCM simulations for the entire years from 2002 to 2009, covering the periods of CHAMP measurement.

3. Methodology The PCA method is applied in this work. This technique is effective in capturing the most significant modes of the variability in a data set (Jolliffe, 1990; Preisendorfer, 1988). The exospheric temperatures from the 8 year TIEGCM simulations are reorganized into the grids as a function of latitude and local time (n grids = 36 latitudes × 72 local time) with hourly ensembles, U(X, t), in which X and t stand for the grids and universal time, respectively. The optimized decomposition of U(X, t), utilizing the time-independent basis functions (hereafter, called PC for short) and the time-dependent coefficients, α(t), is through the following equation: UðX; t Þ ¼

p X

αi ðtÞPCi ðX Þ;

(1)

i¼1

where the amplitude of αi is determined by the inner product between U and PCi, and the basis function, PCi, is orthogonal and normalized, and it is obtained by PCA. The series of PC satisfy the following equation: S  PCi ¼ βi PCi :

(2)

T

Here S is the covariance matrix computed as S = U U. βi and PCi are eigenvalues and eigenvector to the covariance matrix S, respectively, and they are derived from eigendecomposition. Note that the PCs are

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normalized to one, and their order is ranked according to the variance value of βi (from large to small). The front 5 orders of PCs are investigated in this work to capture the most important information of the data set. Figure 2 gives the variations of the first 5 orders of PCs as a function of latitude and local time, associated with their relative contribution to the total variance. As illustrated in Figure 2a, PC1 has a clear day-night difference. This suggests that PC1 could represent diurnal variation of the temperature. PC2 has different sign at Northern and Southern Hemispheres, implying that it might represent the seasonal variation of the temperature. For PC3, it is roughly symmetric about the equator with other small-scale distributions, indicating a secondary variation in the temperature as well. As shown in Figure 2f, PC1 takes up about 99.4% of the total variance, and the contribution of PC2 is about 0.51%. The contributions of PC3 and PC4 are similar and reach about 0.02%, while it is ~0.01% for PC5. 99.95% of the total variance is taken up by the first 5 orders of PCs. Thus, we utilized these 5 orders of PCs to develop the empirical model here.

As mentioned in equation (1), the PCs’ amplitudes αi can be determined from the TIEGCM simulations. Meanwhile, they are obtained from the (c) T from PC fitting data-driven method of the derived CHAMP effective exospheric tem1100 80 perature during 2002–2009. An example for one CHAMP orbit on day 60 80, 2004, is illustrated in Figure 3. As shown in Figure 3a, the effective 1000 40 temperature is low for about the first 45 min and high in the rest. This 20 900 0 is due to the day-night difference of CHAMP location as given in the -20 white lines in Figures 3b and 3c. The relative variation of TIEGCM exo-40 800 spheric temperature is generally consistent with the CHAMP effective -60 exospheric temperature, while the TIEGCM temperature is lower by -80 700 about 50 K. In addition, more small-scale structures are seen in the 0 4 8 12 16 20 24 Local time (hour) CHAMP temperatures. A least squares optimization is conducted using PCs 1–5, and the result given by the red line captures the dominating Figure 3. (a) Variation of the exospheric temperature from CHAMP, TIEGCM variation of the CHAMP temperatures. Figure 3b demonstrates the latiand the fitted result of one CHAMP orbit on day 80, 2004, and the maps of tudinal and local time variations of TIEGCM exospheric temperature the exospheric temperature from (b) TIEGCM and (c) the data-driven result. around the averaged universal time of the orbit, while Figure 3c is for The white lines stand for the corresponding orbit trajectory of CHAMP. the corresponding result from the CHAMP data-driven method by applying PCs 1–5 and their regressed amplitudes. Figures 3b and 3c gave similar diurnal and latitudinal variations, but the global temperatures after assimilating the CHAMP data are generally 50 K higher in Figure 3c than those in Figure 3b. This is consistent with the comparison in Figure 3a. It should be pointed out that future work should be pursued to investigate the possible overfitting issue in the above optimization, associated with the insufficient data coverage and the observational errors. 700

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4. Result Figure 4 shows the comparison of the PC amplitudes α from both the TIEGCM simulations and those derived from CHAMP data for 2004 and 2008. Different from derivation of PC amplitudes from CHAMP via least squares method, it is straightforward to get TIEGCM PC amplitudes from the convolution between the PCs and TIEGCM exospheric temperatures. The averaged amplitude of PC1 (α1) from CHAMP observations is about 5 × 104 during the year of 2004, while its maximum reaches over 7.5 × 104 associated with the 2004 November superstorm (Lei et al., 2010). In 2004, the evolution of TIEGCM PC1 amplitudes (red line) is generally consistent with CHAMP results. In 2008, TIEGCM PC1 amplitudes (red line in Figure 4b) are generally higher than the corresponding CHAMP amplitudes (blue line). This is because 10.7 cm solar radio flux (F10.7) is utilized as the input of the TIEGCM simulations in 2008, while it is higher than the extreme ultraviolet solar irradiation during the extreme solar minimum period of 2007–2009 (Solomon et al., 2011).

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Figure 4. The temporal variation of PC amplitudes (in unit of 10 ) from the TIEGCM simulations (red lines) and derived from CHAMP (blue lines) in 2004 (a, c, e) and 2008 (b, d, f).

The comparisons for PC2 amplitudes between the CHAMP data and TIEGCM simulations in 2004 and 2008 are shown in Figures 4c and 4d, respectively. The PC2 amplitudes derived from CHAMP data are in a good agreement with those from the TIEGCM simulations. Additionally, they are large in December–January and become low in June–July, that is, a clear annual variation. Figures 4e and 4f give the variations of PC3 amplitudes obtained from CHAMP data and TIEGCM simulations in 2004 and 2008, respectively. The temporal variation in CHAMP α3 is dramatic, while the averaged amplitude is close to 0 in both years of 2004 and 2008. The peak value of CHAMP α3 amplitudes reaches 1 × 104 in 2004 and 0.5 × 104 in 2008. For the TIEGCM α3, it is generally consistent with the corresponding CHAMP results in 2004. However, in 2008 there are larger discrepancies of PC3 amplitudes from the simulations and CHAMP data. Furthermore, the seasonal variations in the TIEGCM PC3 amplitudes tend to be larger than those in the CHAMP PC3 amplitudes. As shown in Figure 4, the PCs’ variations depend on the season and solar-geomagnetic activities. Figure 5 gives the evolution of CHAMP PCs 1–5 during 2002–2009. For the amplitudes in Figure 5, they all show the long-term variation; that is, they are larger at high solar activity in 2002–2004 and become lower at low solar activity in 2008–2009. This trend is consistent with the solar radio flux variation as given in Figure 1a. The quasi 27 day and multiday periodic oscillations, which are associated with solar activity change and recurrent geomagnetic activity (Lei et al., 2008; Lei, Thayer, Wang, & McPherron, 2011), are also seen in α1. This feature becomes clearer in Figures 4a and 4b. Except for the short periodic disturbances, the most significant variation in CHAMP PC2 is the annual variation. However, the amplitude of this annual variation deceases from 0.75 × 104 in 2002 to about 0.4 × 104 in 2009, which is due to the solar activity, as well. The CHAMP PC3 and PC5 amplitudes show a great variability, while it is more profound during the high solar and geomagnetic activity period, implying a significant solar-geophysical dependence. There are obvious deviations in

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Figure 5. Variations of PC amplitudes (in unit of 10 ) obtained from CHAMP fitting (blue dots) and the parameterization results (red lines) during 2002–2009.

PC4 with a period of ~130 days, which could be associated with satellite local time sampling or the overfitting issue in the least squares optimization. This aspect should be further investigated in the future. The amplitudes (αi) for each PC component from CHAMP data during the years of 2002–2009 are parameterized through the following formula: αi ¼ T SG T Time :

(3)

In equation (3), TSG denotes the solar and geomagnetic activity effect, and TTime is referred to UT/longitude and seasonal variations. The expressions of these two parameters are given as follows: ! 4 X gk Apk T SG ¼ ða1 þ s1 P1 Þða2 þ s2 P2 Þ a3 þ (4) k¼1

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Figure 6. Variations of the exospheric temperature calculated from the MSIS model and the ETM in March equinox under different solar activity levels at 12 UT.

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Relative Error (%) Figure 8. (a) Same as Figure 7a but for GRACE satellite and (b) the statistic distribution of relative errors of density between GRACE observations and ETM (red line) and MSIS (gray line) results. RMS = root-mean-square.

T Time

3  X

 2πkd 2πkd þ y2k cos þ: ¼bþ y1k sin 365:25 365:25 k¼1  3  X 2πkt 2πkt þ f 2k cos f 1k sin 24 24 k¼1

(5)

Note that the 10.7 cm solar radio flux (F10.7) might not represent well the solar extreme ultraviolet radiation during the extreme solar minimum period (Chen et al., 2011, 2012; Solomon et al., 2011); the composite MgII proxy (Weber, 1999) (http://www.iup.uni-bremen.de/gome/gomemgii.html) is used to investigate the solar activity dependence of each PC amplitude. To be comparable, MgII proxy is first scaled to F10.7 in the same unit of sfu by the formula of M10.7 = 8083(MgII)-1154, which is due to the linear relationship between MgII proxy and F10.7 during the years of 1978–2006. Thus, in equation (4), Pk(k = 1, 2) represents daily M10.7 for previous day and 81 day averaged M10.7 with centering at current day. Ap1 is the daily averaged Ap, and Apk(k = 2, 3, 4) is for the 3 h averaged Ap of every 3 h since 6 h earlier to the current universal time. d and t in equation (5) stand for the day number of the year since 1 January and the current universal time, respectively. The parameterization above is conducted for each PC in this work, and the results given by the red lines in Figure 5 are in good agreement with the CHAMP PCs. The correlations of the optimized regression are 0.985, 0.98, 0.81, 0.56, and 0.68 for the PCs, respectively. Since the other higher orders of PCs could have small contribution to the temperature variation, 5 orders of PCs and their parameterized amplitudes are utilized to develop this empirical model of the exospheric temperature. The comparison of the exospheric temperatures between the ETM and MSIS models in March equinox (day of year = 80) in Figure 6 provides a kind of validation. As shown in Figures 6a and 6b, during low solar

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activity condition (F107 = 70), the exospheric temperatures from the ETM are similar to those from the MSIS; however, the daytime temperatures from the MSIS are higher than those from the ETM. Figures 6c and 6d show the comparison of the exospheric temperatures between the ETM and MSIS models under high solar activity (F107 = 200). The spatial-temporal evolution of the exospheric temperature from the MSIS in Figure 6d is quite similar to the one in Figure 6b except that the temperature is much greater at high solar activity. However, a salient equatorial thermospheric anomaly is seen in Figure 6c. That is, the ETM predicts the ETA in daytime under high solar activity. The local time and latitudinal structure of the ETA is consistent with previous studies (Liu et al., 2007; Lei, Thayer, et al., 2012; Lei, Matsuo, et al., 2012). A further comparison is presented between the ETM and the MSIS in Figure 7. Note that the exospheric temperatures from the ETM, along with the corresponding solar-geomagnetic conditions, are used as input of the MSIS to calculate thermospheric density at CHAMP satellite position. As illustrated in Figure 7a, thermospheric densities from the ETM are in good agreement with CHAMP data for the whole period of 2002– 2009, as expected. The MSIS densities in Figure 7a are general consistent with the CHAMP data during 2002–2005. However, there is obvious discrepancy seen between the MSIS densities and CHAMP observations during 2006–2009. This feature becomes clear in Figure 7b, in which the seasonal-averaged ratios between the mass densities from the models and observations are shown. The ratios between the ETM and the data are generally in the range of 0.9–1.1, implying the error of less than 10% in the ETM prediction. However, the ratios between MSIS and observations are greater and they are about 1.66 in 2008. Therefore, the ETM has a better performance for the density prediction than the MSIS model. The validation of the ETM, utilizing an independent satellite data set of Gravity Recovery and Climate Experiment (GRACE) is performed and also illustrated in Figure 8. Figure 8a shows the daily averaged mass densities derived from GRACE and the corresponding results from the models of the ETM and MSIS. The prediction of the ETM is generally consistent with the GRACE observation, while MSIS does not well capture the thermospheric mass densities especially during the solar minimum period of 2008–2009. Figure 8b further exhibits the statistical distribution of relative errors of daily mean for thermospheric densities between the models and GRACE data. The averaged deviation and root-mean-square of these daily means are 0.19% and 18%, respectively, for the ETM, while they are 67.4% and 44% for MSIS. Again, the ETM has a better performance in predicting thermospheric density.

5. Conclusion In this work, we develop an empirical ETM by combining the TIEGCM simulations with the CHAMP thermospheric density data during 2002–2009. The basis functions of ETM are first derived from the PCA of the TIEGCM simulations, and their amplitudes are data driven by the observations from CHAMP. Utilizing the ETM exospheric temperature as the MSIS input, the vertical profile of thermospheric density could be modeled as well. The validations for the ETM with the MSIS model and the independent data set of GRACE measurements are also carried out. The ETM reproduced ETA well, and the error in the ETM is much lower than that in the MSIS, especially during the low solar activity period. However, as it took about 130 days for CHAMP satellite to sample a full 24 local time, the 8 year CHAMP data set used in this work is still sparse. More observations are desired to be included to further improve the ETM in the future. Acknowledgments Thermospheric densities obtained by CHAMP and GRACE are obtained from http://tinyurl.com/densitysets, and the developed ETMs are available from http://staff.ustc.edu.cn/~leijh/publication/2017SW001759/. This work was supported by the National Natural Science Foundation of China (41325017, 41274157, and 41421063), the project of Chinese Academy of Science (KGFZD135-16-013), the Thousand Young Talents Program of China and 61st Chinese Postdoctoral Science Foundation (2017M612082). The authors wish to thank E. Sutton for his suggestion to improve the manuscript.

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