Thermospheric global average density trends, 1967–2007, derived from orbits of 5000 near-Earth objects

Abstract

[1] We use orbit data on ∼5000 near-Earth space objects to investigate long-term trends in thermospheric total mass density, which has been predicted to decrease with time due to increasing CO₂ concentrations. We refine and extend to 2007 previous density trend estimates, and investigate solar cycle-dependent bias in empirical density models previously used to filter out solar irradiance effects. We find that the bias is caused in part by the solar cycle dependence of the long-term trends, and we develop a new representation of solar cycle, seasonal, and geomagnetic activity effects. At 400 km, we estimate an overall trend of –2.68 ± 0.49 % per decade and trends of ∼–5 and –2 % per decade at solar minimum and maximum, respectively, in fair quantitative agreement with theoretical predictions. The global average density trends also depend on the phase of the year, with the strongest trends around October and weak trends in January.

1. Introduction

[2] The Earth's thermosphere (∼90–800 km) is primarily heated by solar far and extreme ultraviolet (FUV and EUV) irradiance, and the primary cooling mechanism is downward conduction to the lower thermosphere and subsequent radiative cooling by CO₂ and other species [Roble, 1995]. Increasing CO₂ concentrations are therefore expected to result in enhanced cooling and consequent contraction of the thermosphere. Roble and Dickinson [1989] predicted that a doubling of CO₂ would result in a 40% reduction in density at a height of 400 km. An overview of theoretical and empirical studies of mesospheric and thermospheric climate change is given by Laštovička et al. [2006, 2008].

[3] The orbits of near-Earth satellites are affected by atmospheric drag, which increases the orbital mean motion (the inverse of the orbital period) in direct proportion to the total mass density along the orbital track. Because of this relationship, the historical orbital database of the thousands of objects routinely tracked by the U.S. Space Surveillance Network constitutes the most continuous and temporally extensive record of thermospheric density available, albeit at limited spatial and temporal resolution (usually >30° and ≥3 days). Previous analyses using a limited selection of long-lived objects indicated a long-term thermospheric density decline that is qualitatively consistent with model predictions of increasing CO₂ effects [Keating et al., 2000; Emmert et al., 2004; Marcos et al., 2005].

[4] In order to improve the quality of long-term trend estimates, we have built upon earlier studies in three ways. First, with an additional 6 years of data, we extended the time period for the trend analysis out to September 2007, thus incorporating recent solar minimum conditions. Second, we canvassed the entire U.S. orbit database, derived density from ∼5000 suitable objects, and combined the density values (thereby greatly reducing noise) to obtain a continuous time series of global average density as a function of height between 200 and 600 km. Third, we investigated previously identified solar EUV-dependent biases between orbit-derived density and empirical models. Accurate representation of the solar EUV dependence is critical to obtaining reliable estimates of long-term density trends, because thermospheric density above 400 km varies by more than an order of magnitude over a solar cycle.

[5] In the following sections we briefly describe our derivation of global average density. Then, we discuss issues associated with removal of solar EUV effects, and we describe a new empirical model that represents the solar cycle, seasonal, and geomagnetic activity dependence of global average density. Finally, we present updated density trend estimates and their dependence on solar cycle and season, and compare the estimates with other empirical and theoretical results. We concentrate on results at a height of 400 km, deferring similar results at other heights between 200 and 600 km to a more comprehensive paper.

2. Data and Methodology

[6] Expanding on the data set used by Emmert et al. [2004], which consisted of orbital data for 27 objects, we analyzed the entire 1967–2007 (through September 2007) database of unclassified two-line orbital element sets (TLEs) with perigee heights less than 600 km; this subset consists of orbits of ∼18,000 objects. We developed algorithms to eliminate objects unsuitable for inferring density from their orbital drag, based on the behavior of the orbital mean motion and on consistency of the derived density with the ensemble average temporal variation. After culling objects with weak orbital drag signals, maneuvering objects, objects with unstable ballistic coefficients, and objects producing outlying density time series, a set of ∼5000 objects remained for analysis. Most of the selected objects covered less than five years; in a given year there were typically 400–800 qualifying objects.

[7] In order to minimize bias among the densities derived from different objects, we followed the procedure of Emmert et al. [2006] for estimating ballistic coefficients for each object. There is an overall systematic uncertainty in the derived absolute densities due to imprecise knowledge of the drag coefficient of the spherical object to which the calibration is pegged [Emmert et al., 2006], but this does not affect the relative density variations described in this paper.

[8] The average density along an orbit is directly proportional to the change in the orbital mean motion from one TLE to the next. For each object, we computed the average density, relative to the NRLMSISE-00 empirical model [Picone et al., 2002], using equation (3) of Emmert et al. [2006] [see also Picone et al., 2005]. We then averaged the entire set of ∼5.2 million density ratios as a function of height and time. The time series of ratios are very coherent from one height bin to the next, indicating that the use of many objects successfully reduces the noise in the result. To obtain smoothed daily density ratios on a regular height-time grid, we fit the raw ratios to cubic B-splines in height (150 km node spacing) and time (3-day node spacing). This approach was very effective for interpolating across (relatively uncommon) areas with weak data coverage. We omitted from our analysis 36 days from the earlier years of the database, due to data gaps too large for interpolation.

[9] We found that the local time and latitude sampling provided by the collection of orbits is globally fairly even, and that our average density ratios can be approximately interpreted as the ratio of the measured global average density to the global average density predicted by NRLMSISE-00. Accordingly, we computed the absolute global average density at each height by calculating the NRLMSISE-00 global average density, smoothing it with 3-day cubic B-splines, and applying the smoothed density ratios.

3. Removal of Solar Irradiance Effects From the Density Time Series

[10] NRLMSISE-00 uses the 10.7 cm solar radio flux index (F_10.7) to represent the effect on the thermosphere of variations in solar FUV and EUV irradiance, the primary source of thermospheric heating. As noted by Emmert et al. [2004] and Marcos et al. [2005], orbit-derived densities have an F_10.7-dependent bias relative to empirical models NRLMSISE-00 and Jacchia-70 (J70) [Jacchia, 1970]. The bias is chiefly characterized by a steep drop-off of the measured densities toward solar minimum conditions. We have also observed this behavior in densities derived [Meier and Picone, 1994; Christensen et al., 2003; Emmert et al., 2006] from FUV limb scans by the Global Ultraviolet Imager (GUVI) on board the TIMED satellite. A comparison of orbit-derived and GUVI density residuals as a function of F_10.7 is shown in Figure 1a for the period January 2002 to March 2007. The GUVI ratios follow the TLE ratios closely at solar minimum, although they are smaller at solar maximum. Some of the differences may be due to sampling: The GUVI data only represent daytime mid and low latitude conditions and are not temporally continuous.

Figure 1

(a) Average log-density residuals at 400 km during 2002–2007, relative to NRLMSISE-00, as a function of the daily F_10.7 index. The TIMED/GUVI densities (red crosses) were measured only on the dayside at mid and low latitudes and contain temporal gaps, whereas the orbit-derived values (blue circles) continuously represent the global average density. (b) Global average log-density residuals relative to NRLMSISE-00 at 400 km as a function of the daily F_10.7 index, for three different solar cycles roughly centered on solar minimum as well as the most recent half-cycle. (c) Same as Figure 1b, but relative to the empirical model (GAMDM) described in the text. (d) Same as Figure 1c but for two periods: 1967–1985 and 1986–2007 (the reference period on which GAMDM is based). The error bars denote the estimated 1σ uncertainty of the mean.

[11] We investigated the strong biases observed at solar minimum, in order to ascertain how best to improve the filtering of solar cycle variations. Fundamentally, there are two possible sources of the bias: 1) The F_10.7 terms in the empirical models may not afford sufficient resolution to capture the statistical relationship between F_10.7 and thermospheric density; and/or 2) There is an F_10.7-dependent bias between the orbit-derived densities and the data used to generate the empirical models. A factor proposed by G. Keating (personal communication, 2004) that might contribute to source 2 is the solar cycle dependence of anthropogenic density trends combined with the different time periods covered by the empirical model databases and the comparison databases. The thermospheric cooling effect of increased atmospheric CO₂ is predicted to be largest at solar minimum due to a lesser contribution from NO cooling and smaller vertical scale heights under these conditions [Rishbeth and Roble, 1992; Qian et al., 2006]; observational evidence qualitatively supports this prediction [Emmert et al., 2004]. Conversely, the solar cycle dependence of thermospheric density should be changing as CO₂ increases. Because NRLMSISE-00 is largely based on pre-1983 measurements, one might expect to see a solar irradiance-dependent bias in recent measurements relative to this model. To test this hypothesis, Figure 1b shows F_10.7-dependent bias curves for four periods, each approximately covering a solar cycle centered on solar minimum. Figure 1b indicates that the depth of the low- F_10.7 dip is indeed increasing with time, suggesting that stronger trends at solar minimum are contributing to the overall F_10.7-dependent bias. However, some bias is observed even during the earliest period of 1967–1980 (the core period of the NRLMSISE-00 density and composition database), indicating that model resolution limitations (source 1) and/or other data-data biases (source 2) are also contributing to the residual F_10.7 dependence.

[12] In order to improve characterization of the solar cycle influence, we developed a new empirical model, the Global Average Mass Density Model (GAMDM), to describe the solar irradiance, geomagnetic activity, and seasonal dependence of global average density at fixed heights. The time-independent model includes the following terms:

where a_i, b_i, … g_i are the model coefficients, F_10.7 is the daily index 3 days prior to the observed density, _10.7 is the 81-day average index, ΔF_10.7 = F_10.7–_10.7, Δ_10.7 = _10.7– 150, ω = 2π/366 d^–1, d = day of year, and Kp is the daily average magnetic activity index. The superscripts ‘+' and ‘–' on the ΔF_10.7 and Δ_10.7 terms indicate that dependence on these arguments is piecewise linear, with different linear coefficients for positive and negative values of these arguments. The functions N_i are cubic B-splines with nodes at 60, 70, 80, 100, 150, 220, and 320; for robustness at the lower and upper boundaries, the fit is constrained to have zero curvature at F_10.7 = 60 and F_10.7 = 320. For each height level, we computed the model coefficients using a least-squares fit of data from January 1986 through September 2007. In developing the model formulation, we only retained terms that reduced both the variance of the 1986–2007 data used in the fit and that of the independent 1967–1985 data. This approach reduces the risk of over-fitting the data and contamination of the model terms by long-term trends. We chose 1986–2007 as the reference period because the data coverage is better than in earlier years.

[13] Figure 1c shows the F_10.7 dependence of the 400 km GAMDM residuals for four different solar cycles. The evolving F_10.7 dependence of the densities is clearly seen in this plot, with the solar minimum deflection changing from upward to downward. In addition, there is a fairly consistent progression of the residuals from higher to lower values, reflecting the overall downward trend in density. An exception to this consistency is the broad dip seen in the 1981–1990 data.

[14] Figure 1d shows the F_10.7 dependence of the residuals for two time periods: the reference period (1986–2007) on which the model is based, and the independent period (1967–1985). The average absolute density (not shown) for the reference period increases from 4.9 × 10⁻¹³ kg/m³ in the lowest F_10.7 bin (65 ≤ F_10.7 ≤ 67) to 6.0 × 10⁻¹³ kg/m³ in the next bin (67 ≤ F_10.7 ≤ 70), indicating that even at very low values, F_10.7 can be used to differentiate among different climatological density levels (at least to the resolution of our F_10.7 bins). The fact that the F_10.7 dependence of the reference period residuals is flat to within 1.5% all the way down to the lowest bin indicates that GAMDM is sufficiently flexible to capture the climatological variation of thermospheric density with F_10.7.

4. Long-Term Trends

[15] Figure 2 shows the 400 km density residuals relative to NRLMSISE-00 (2a) and GAMDM (2b) as a function of time, along with annual averages and inferred linear trends. The trend of the NRLMSISE-00 residuals is –3.55 ± 0.79 % per decade, and the trend of the GAMDM residuals is –2.68 ± 0.49 % per decade. The annual averages of the GAMDM residuals show a noticeably smaller scatter than those of NRLMSISE-00; the standard deviations are 5.0 and 7.7%, respectively. The estimated 1σ uncertainty in the trends is accordingly smaller in the trends computed from the GAMDM residuals (0.49 versus 0.79% per decade).

Figure 2

(a) Global average log-density residuals at 400 km, relative to NRLMSISE-00, as a function of time. The blue curve shows the daily values, and the red circles show annual averages. The green line shows a linear trend fit to the annual averages; the value of the trend is given in the legend. (b) Same as Figure 2a, except that the residuals are relative to the empirical model (GAMDM) described in the text.

[16] As a procedural note, we mention that in earlier studies [Keating et al., 2000, Emmert et al., 2004, Marcos et al., 2005], the uncertainties of the overall trends were estimated based on the variance among trends derived from individual objects, because the object-to-object variance was viewed as the largest source of error. In this study, we have combined densities from a large number of different objects prior to computing trends, so the effect of object-to-object density variance on the computed trends is very small. We therefore estimated trend uncertainties based on the year-to-year variance of the residual annual density averages.

[17] Figure 3 shows trends computed from GAMDM residuals as a function of daily F_10.7. The residuals were sorted into eight partially overlapping F_10.7 bins (<75, 70–100, 80–110, 100–140, 110–160, 140–190, 170–220, >180) prior to computing trends. Figure 3a shows results at 550 km, along with corresponding results from Emmert et al. [2004], which were based on 25 objects with an average perigee height of ∼530 km. The new trends show a smoother dependence on F_10.7. As before, the trend magnitudes tend to decrease with increasing F_10.7; above F_10.7 ∼ 160, they increase slightly but not significantly.

Figure 3

(a) Density trends at 550 km as a function of daily F_10.7 (blue circles; eight overlapping bins). Error bars denote the estimated 1σ uncertainties of the trends. The red curve shows previous results, representative of 530 km, from Emmert et al. [2004]. (b) Density trends at 400 km as a function of daily F_10.7. Corresponding results from earlier studies are also shown; see text for details.

[18] Figure 3b shows results at 400 km, along with corresponding trends from theoretical simulations by Akmaev [2006] and Qian et al. [2006], and trends estimated from orbit data by Keating et al. [2000] and Marcos et al. [2005]. The latter reported overall trends with all F_10.7 conditions combined, so these results are represented by horizontal lines in the plot; the upper and lower lines are respectively the trends computed with and without normalizing for the F_10.7-dependent bias. There is fairly good quantitative agreement among the empirical results. The theoretical trends from Qian et al. [2006] at solar minimum and maximum are smaller than the corresponding empirical trends, but there is very good agreement in the interval 120 < F_10.7 < 160. The theoretical trend at 200 km computed by Akmaev et al. [2006], which includes the non-negligible effects of middle atmosphere ozone and water vapor trends, is much stronger than the observed trends under similar solar EUV conditions. A more rigorous comparison would restrict the analysis to the common time period covered by each study.

[19] Emmert et al. [2004] examined the effect of season on the trends by splitting the data into orbits with winter and summer perigees, and did not find a significant difference. Since the data used in this study are globally averaged, we cannot differentiate between local summer and winter, but we can sort the data into monthly bins; trends results for each month are shown in Figure 4. The January and February trends are much weaker than those at of other months, and are not significantly different from zero. The seasonal dependence of the trends appears to exhibit a mixed annual and semiannual variation, with the strongest trends occurring from September to November. We obtained similar trend results using NRLMSISE-00 residuals. Note that the amplitudes of the annual and semiannual density variations (coefficients c₁, d₁, c₂, d₂ in equation (1)) at 400 km are ∼9 and 13%, respectively. The strong dependence of global average density trends on the phase of the year is perhaps related to the processes that generate these variations, and requires further study.

Figure 4

Global average density trends at 400 km as a function of day of year (monthly bins). Error bars denote the estimated 1σ uncertainties of the trends.

Acknowledgments

[20] This work was supported by the Office of Naval Research and NASA's Living with a Star Program. Orbit data were obtained from www.space-track.org. Solar and geomagnetic activity indices were obtained from ftp://ftp.ngdc.noaa.gov/STP/GEOMAGNETIC_DATA/INDICES/KP_AP/.