Ionosphere-thermosphere Relation as Seen in Measured and Modeled Electron and Neutral Densities

The availability of in-situ neutral and electron densities along the orbit of the satellite missions GRACE 6 and CHAMP provide a good opportunity to study the ionosphere-thermosphere (IT) system. The aim 7 of this paper is (1) to use these data sets, to study the IT density relation empirically via correlation 8 properties for diﬀerent conditions depending on solar activity, geomagnetic latitude, and local time and 9 (2) to verify whether these relations are consistent with the output of the TIE-GCM model of the 10 thermosphere and ionosphere. 11 Our results show that the correlations of electron and neutral densities strongly depend on magnetic 12 local time (MLT) with a minimal correlation between 6-9h MLT, e.g., every 131 days for CHAMP 13 around 400 km altitude and every 160 days for GRACE around 500 km. During low solar activity, the 14 correlation of modeled and measured densities agrees well for both satellites. On the contrary, we note 15 that the correlations between the modelled values are higher, especially during high solar activity, 16 where the diﬀerence between correlations of modeled and measured densities is about 0.2. We suggest 17 that the reason for this misalignment might be related to the poor representation of the equatorial 18 density anomaly in the model especially during high solar activity. 19 We believe our results will be useful for studies that aim at assimilating electron densities into a 20 physical model to improve the prediction of neutral densities, since the skill of data assimilation 21 depends to a large extent on the representation of the correlation between both densities. 22 5 6 7 8 9 10 11 12 13 14 15 16 17

Introduction 26 Although the magnitude of the neutral density at the altitude of low-Earth orbiting satellites is only 27 10 −13 kg m −3 at 400 km, it causes a considerable drag on the satellite. Therefore, applications such 28 as satellite altitude and lifetime predictions, the propagation of space debris, collision prediction or 29 avoidance, and precise orbit determination require accurate information on the neutral density, which is  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57  58  59  60  61  62  63  64  65 usually taken from models. 31 The neutral mass density in the Earth's atmosphere is made up by many constituents, e.g., helium, 32 hydrogen and oxygen, and their altitude variations depend on solar radiation and magnetic forcing. The 33 resulting total neutral mass density varies at different temporal and spatial scales, e.g., it decreases nearly 34 exponentially with altitude due to aerostatic equilibrium. Additionally, sudden solar events, e.g., solar 35 flares, can cause short-term variations in the atmospheric temperature, density and ionization. 36 After integrating decades of data and extensive calibration efforts, empirical models, such as NRLMSIS2.  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57  58  59  60  61  62  63  64  65 the model data assimilation, i.e., in simulation ensembles. 61 In the observation space formulation (Evensen 2009), the corrections to model-simulated upper-air 62 constituent densities will follow directly from applying cross-correlations to the data increments, weighted 63 by assumptions on data and model errors. In the EnKF, the cross-correlations depend on implementation 64 (ensemble size and breeding) and on the couplings implemented within the model. Here we argue that, 65 by implementing the ergodicity hypothesis, comparing temporal cross-correlations from directly observed 66 data to model simulations will help us to assess the realism of model coupling, which will ultimately be 67 to test EnKF implementations in forthcoming work. 68 The ionosphere is immersed in the upper atmosphere and both are largely controlled by solar radiation, 69 especially at the extreme ultraviolet (EUV) wavelength. Enhanced EUV radiation produces more ions 70 and electrons in the ionosphere, but in the meanwhile it increases the temperature of neutral atmosphere 71 and results in larger density scale height, thus, density decreases less with increasing altitude. However, 72 the enlarged atmospheric density will increase the ion-neutral collision frequency, resulting in a decrease 73 of ionospheric plasma density. Therefore, the ionisation degree of the upper atmosphere depends on 74 the balance between enhanced EUV and atmospheric scale height. Additionally, the variability of the 75 ionosphere and upper atmosphere is associated with lower atmospheric processes, e.g., tidal and wave  Thus, due to the mentioned phenomena we can expect that there is sufficient correlation between the 79 thermosphere and ionosphere for the success of assimilating measured densities into physical models, but 80 this correlation will depend on dayside/nightside, solar/magnetic forcing, also on the timescale considered, 81 and it is unclear to what extent physical models consider all this correctly. So it is relevant to quantify 82 this correlation from data.

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In this paper, we take advantage of simultaneous measurements of both neutral and electron densities 84 from the satellite missions Gravity Recovery and Climate Experiment (GRACE, Tapley 1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57  58  59  60  61  62  63  64  65 provides a good opportunity to investigate the interaction between the ionosphere and upper atmosphere 91 in terms of correlations. The aim of this paper is (1) to use these data sets, which have -to our knowledge 92 -not been compared yet, to extensively study the correlation properties for different conditions depending 93 on solar activity, geomagnetic latitude, and local time and (2) to see whether this is in line with model 94 physics as simulated by the physical density model TIE-GCM. Since we cannot directly assess coupling 95 strength in this way, we instead focus on the correlation of neutral and electron densities. It allows 96 us to empirically examine the strength of the relation between the ionosphere and thermosphere in the 97 model compared to measurements and thus assess the potential for predicting neutral density via the 98 assimilation of electron densities. In the next chapter, we summarize the density data sets and model 99 settings, which are the basis for our correlation studies presented in the result section.

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Our experiments are limited to the data of the GRACE and CHAMP missions, however, the analyses can 101 be applied to densities from other missions such as Swarm and GRACE Follow-On as well. The densities 102 in this study are not scaled to a specific altitude, instead we take the advantage of using collocated in-situ 103 measurements directly. Our focus is to study correlations in the view of data assimilation of measured 104 in-situ neutral and electron densities and, eventually, predicting neutral density and drag on objects in 105 space.

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Our correlation analyses might be limited by the sparse spatial resolution of the in-situ data, e.g., the 107 CHAMP satellite covers all local times within 131 days. The in-situ neutral densities are certainly affected 108 by calibration errors, but remaining biases and scales drop out in correlation studies. Another limitation 109 of our analyses is that the output of TIE-GCM requires extrapolation at the GRACE altitude especially 110 during nighttime, however, the gap between the upper model layer and the altitude of the satellite is only 111 a few kilometers.  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57  58  59  60  61  62  63  64  65 from changes in the satellite orbit. Orbit data are available from various tracking techniques such as 120 satellite laser ranging and are often provided as two-line element (TLE) data sets for objects back to the 121 1960s. The resulting densities represent average values for an orbital arc of several hours lengths, thus, 122 their temporal resolution is limited to at most once per orbit. For spherical satellites, the estimation of 123 the ballistic coefficient, which can be related to corrections for modeled densities, is also widely used but 124 the accuracy and spatial resolution is limited (Bowman 2002) and the ballistic coefficient is correlated 125 with other solved-for parameters. 126 Here, we derive in-situ neutral densities from non-gravitational accelerations acting on the satellite 127 measured by space-borne accelerometers, which are limited to very few missions (mostly designated 128 gravity field missions). In a first step, it requires a calibration of accelerometer data. We apply daily   (1) Finally, the thermospheric neutral densities can be obtained from rearranging the analytical equation    Here, we take advantage of in-situ electron densities with a high temporal resolution, which are limited  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57  58  59  60  61  62  63

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An equatorial anomaly is also slightly visible in the CHAMP densities with its peak around 18 • MLAT.

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In addition to the sensitivity of both densities to MLT and MLAT, neutral densities increase almost 248 linearly with the F 10.7 index -independent from geomagnetic activity and altitude (Fig. 4, bottom).

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In comparison, increasing electron densities also show linear dependencies on the F 10.7 index, however, 250 there is a shift in the amplitude of the electron density between the years of high and low solar activity.

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However, the resulting correlations differ only in that they are noisier, which is probably due to a larger 317 number of data gaps, and it does not help to further support our findings. We also looked at correlations 318 with respect to F 10.7 , however, no clear dependency of the correlations in the solar index has been found.   1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57  58  59  60  61  62  63  64  65 of the neutral density during low solar activity. We suspect that the reason for their success is related to 324 the fact that their model ensemble during these periods is more skillful in representing true correlations.

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At this point, we take a closer look at findings from other studies to better understand the discrepancy GRACE: 0.53), which is not the case for modeled data. We conclude that an altitude-dependency of the 343 correlations is not very likely because we would expect this to be visible in the results of measured and 344 modeled data. Instead, the performance of TIE-GCM might differ with altitude and solar activity.